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Standardization in Spectrophotometry

and Luminescence Measurements

Proceedings of a Workshop Seminar

Held at the National Bureau of Standards

Gaithersburg, Maryland, November

November 19-20, 1975

Edited by:

K.D. Mielenz, R.A. Velapoldi,

and R. Mavrodineanu

Analytical Chemistry Division

Institute for Materials Research

National Bureau of Standards

Washington, D.C. 20234

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued May 1977
Library of Congress Cataloging in Publication Data

Workshop Seminar on Standardization in Spectrophotometry and

Luminescence Measurements,

National Bureau of Standards, 1975. Standardization in spectrophotometry and luminescence measurements. (NBS special publication ; 466)

"Organized by the Analytical Chemistry Division, Institute for Materials Research, at the National Bureau of Standards."

"Reprinted from the National Bureau of Standards Journal of Research, Section A. Physics and Chemistry, vol. 80A, nos. 3 and 4, MayJune, and July-Aug. 1976." Supt. of Docs. no. C13. 10:466

1. Spectrophotometry-Cnngresses. 2. Fluorimetry-Congresses.

3. Phosphorimetry—Congresses. I. Mielenz, K. D. II. Velapoldi, R. A.

III. Mavrodineanu, Radu, 1910- IV. United States. National Bureau

of Standards. Analytical Chemistry Division. V. Title. VI. Series: United States. National Bureau of Standards. Special publication ; 466. QC100.U57 no. 466 [QD79.P46] 602'. Is [543'.085] 77-4739

Library of Congress Catalog Card Number:

National Bureau of Standards Special Publication 466

Nat. Bur. Stand. (U.S.), Spec. Publ. 147, 155 pages (May 1977)

CODEN: XNBSAV

Reprinted from the National Bureau of Standards

Journal of Research, Section A. Physics and Chemistry

Vol. 80A, Nos. 3 and 4, May-June, and July-Aug. 1976.

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1977

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

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Abstract

This volume contains 15 papers presented at the Workshop Seminar on Standardization in Spectrophotometry and Luminescence Measurements organized by the Analytical Chemistry

Division, Institute for Materials Research, at the National Bureau of Standards, and held from

November 19 to 20, 1975. These papers discuss the problems encountered where accurate measurements are required

in the fields of luminescence quantum yields, diffuse reflectance spectroscopy, and ultraviolet absorption spectrometry. They also define the needs for standardization of measurements in these fields and suggest materials that could be used as Standard Reference Materials. Considerations on some applications of such standards in the field of environmental pollution and

health are included.

Key words: Accuracy; critical parameters; diffuse reflectance; fluorescence; instrumentation;

luminescence; quantum yield; spectrophotometry; Standard Reference Materials; standardization.

Ill
Foreword

A major function of the Institute for Materials Research of the National Bureau of Standards

is the development of Standard Reference Materials (SRM's). These are: well characterized materials

that can be used to calibrate a measurement system or to produce scientific data which can be re- ferred to a common base. In order to assure that these SRM's meet real needs and are certified

to a realistic degree of accuracy, the Institute for Materials Research has sponsored a series of

'Workshop Seminars' in which leading domestic and foreign experts meet with NBS staff members to define the state of the art and to establish priorities for future efforts. The Workshop Seminar on 'Standardization in Spectrophotometry and Luminescence Measurements' was organized by the Analytical Chemistry Division, and was held at the National Bureau

of Standards in Gaithersburg, Md., on November 19 and 20, 1975. Approximately forty participants,

coming from seven different countries and representing industries, universities, as well as standardizing laboratories, gathered to exchange ideas on improved standards and measurement techniques.

Three specific topics were discussed: luminescence quantum yields, diffuse reflectance spectroscopy,

and ultraviolet absorption spectrometry. The fifteen papers given represented the points of view of

chemists and physicists using these techniques for widely different applications: analytical and clinical chemistry, photochemistry, photometry and colorimetry, laser physics, and space research.

Previous work in our Division has resulted in the development of several SRM's for spectrophotometry and luminescence spectrometry: neutral density filters for verifying the transmittance

accuracy of spectrophotometers, liquid absorbance standards for the uv and visible, calibrated quartz

cuvettes as pathlength standards for absorption spectrometry, and fluorescence emission standards to calibrate the spectral responsivity of luminescence spectrometers. These Proceedings will provide the

basis for further progress.

Philip D. LaFleur, Chief

Analytical Chemistry Division

January 1977

IV
Preface

Due to advances in optical instrumentation, electronics, and computer technology, spectrophotometry and luminescence measurements can now be performed with a precision that frequently ex- ceeds the accuracy of the results by a wide margin. The achievement of comparable accuracies

requires improved standards as well as a better understanding of the measurement process. Thus, in

organizing this Workshop Seminar on 'Standardization in Spectrophotometry and Luminescence Measurements' at NBS, we have endeavored to provide an interdisciplinary forum for chemists and

physicists to present their views on how to achieve this goal. In this manner, we could learn from

one another and, perhaps, also close the communications gap that sometimes appears to exist in

these fields. The first part of these proceedings contains five invited papers on the measurement of lumines- cence yields. The introductory paper by J.B. Birks reviews the basic principles of fluorescence spectrometry and defines the parameters to be measured. A. Bril and A.W. de Jager-Veenis discuss

radiometric methods of luminescence efficiency measurements, J.N. Demas and B.H. Blumenthal

describe the actinometric determination of luminescence quantum yields, and J.B. Callis illustrates

the use of calorimetric techniques. In the final paper of this section, K.H. Drexhage discusses the

chemistry of fluorescent dyes and proposes new fluorescence standards.

In the section on diffuse reflectance spectroscopy, R.W. Frei reviews the numerous applications

of this technique and H.G. Hecht summarizes the theories that are used for interpreting the results

obtained. W. Budde discusses the calibration of diffuse reflectance standards, and J.B. Schutt and

G.J. Buffone present practical examples of this technique in space technology and clinical chemistry.

Errors in spectrophotometry and standards used to avoid them are discussed by A.G. Reule

and A.R. Robertson. The suitability of potassium dichromate solutions as ultraviolet absorbance

standards is demonstrated by R.W. Burke and R. Mavrodineanu. Considerations on semi-reflecting

metallic films as transmittance standards are presented by R. Mavrodineanu, and the physical

parameters that affect the properties of these metallic films are discussed by H.E. Bennett and J.L. Stanford.

The important contributions of these authors are acknowledged with appreciation.

The Workshop Seminar was planned and organized by K.D. Mielenz, R.A. Velapoldi and R. Mavrodineanu (conference chairpersons), under the guidance of P.D. LaFleur (Chief, Analytical

Chemistry Division) and J.R. DeVoe (Chief, Special Analytical Instrumentations Section), and

with considerable help from R.B. Johnson, R.S. Maddox (Institute for Materials Research), S.R.

Torrence (Office of Information Activities). E.S. Kershow, E.L. Zimmerman, and C.I. Wingo (Analytical Chemistry Division).

J.N. Demas (University of Virginia), G. Weber (University of Illinois). F. Grum and R.N.

Rand (Eastman Kodak Co.) and R.W. Burke (NBS I served as conference co-chairpersons and

discussion leaders.

V
The seminar had the encouragement of R.S. Melville ( Executive Secretary, National Institute

of General Medical Sciences). NIGMS has also supported the development of advanced instrumentation for absorption and fluorescence spectrometry at NBS, and its use to develop and certify

Standard Reference Materials for these fields. The fifteen papers reprinted in this volume were originally published in the Journal of Research

of the National Bureau of Standards, 80A, 389-428 and 551-658 (1976). Special thanks are due

to D.D. Wagman (Associate Editor, J. Res. NBS), W.R. Tilley, M.S. Reid, and M.V. Betizel (Office

of Technical Publications) for their considerable efforts in publishing these papers.

We hope that the collection of these papers in a single volume will be a worthy sequel to the

Proceedings of the 1972 Conference on Accuracy in Spectrophotometry and Luminescence Measurements (NBS Special Publication 378, U.S. Govt. Print. Office, 1973).

K. D. Mielenz

R. A. Velapoldi

R. Mavrodineanu

January 1977

VI
Contents

Page

Foreword iv

Preface v

Part 1. Luminescence Quantum Yields

Fluorescence quantum yield measurements. J. B. Birks 1

Some methods of luminescence efficiency measurements. Alfred Bril and A. Willy de Jager-Veenis. 13 On the actinometric measurement of absolute luminescence quantum yields. J. N. Demas and B. H. Blu- menthal 21

The calorimetric detection of excited states. James B. Callis 25

Fluorescence efficiency of laser dyes. K. H. Drexhage 33

Part 2. Diffuse Reflectance Spectroscopy

Diffuse reflectance spectroscopy; applications, standards, and calibration (with special reference to chromatography). R. W. Frei 41

The interpretation of diffuse reflectance spectra. Harry G. Hecht 57

Calibration of reflectance spectra. W. Budde 75

Understanding bidirectional reflectance and transmission for space applications. John B. Schutt 87

Standardization of light scattering measurement in conjunction with immunochemical analysis. Gregory J. Buffone 95

Part 3. Ultraviolet Absorption Spectrometry

Errors in spectrophotometry and calibration procedures to avoid them. A. G. Reule 99

Standardization in transmission spectrophotometry in the visible and ultraviolet spectral regions. A. R. Robertson H5

Acidic potassium dichromate solutions as ultraviolet absorbance standards. R. W. Burke and R. Mavrodineanu 121

Considerations for the use of semi-transparent metallic thin films as potential transmittance standards in spec- trophotometry. R. Mavrodineanu 127

Structure-related optical characteristics of thin metallic films in the visible and ultraviolet. H. E. Bennett and

J. L. Stanford 133

Index of Key Words 149

VII

Part 1. Luminescence Quantum Yields

NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 466, Standardization in Spectrophotometry and Luminescence

Measurements, Proceedings of a Workshop Seminar Held at NBS, Gaithersburg, Md., November 19-20, 1975 (issued May 1977).

Fluorescence Quantum Yield Measurements

Four molecular fluorescence parameters describe the behaviour of a fluorescent molecule in very

dilute (~ 10-6 M) solution:

(i) the fluorescence spectrum Fu{v) ;

(ii) the fluorescence polarization PM :

(iii) the radiative transition probability kFu\ and

(iv) the radiationless transition probability kmThese parameters and their temperature and solvent dependence are those of primary interest to the photophysicist and photochemist. Fm (v) and Pm can be determined directly, but km and k/M can only

be found indirectly from measurements of the secondary parameters,

(v) the fluorescence lifetime tm, and

(vi) the fluorescence quantum efficiency qFM,

where kFM = qFiu/TM and kSM = (l — qFin) tm •

The real fluorescence parameters F(v), t and 4> F of more concentrated (c > 10~5 M) solutions usually differ from the molecular parameters Fm(v), Tm and qFM due to concentration (self) quenching,

so that t >tm and <\> F < qF\i. The concentration quenching is due to excimer formation and dissociation (rates koine and kitD, respectively) and it is often accompanied by the appearance of an excimer

fluorescence spectrum Fd(v) in addition to Fm(v), so that F{v) has two components. The excimer

fluorescence parameters Fi>{v), Pd, kFo and km, together with koM and k.\w, and their solvent and temperature dependence, are also of primary scientific interest. The observed (technical) fluorescence parameters F T (P). t

t and <pj. in more concentrated_spludons

usually differ from the real parameters F(v), t and (/>/ ,' due to the effects of self-absorption and sec- ondary fluorescence. The technical parameters also depend on the optical geometry and the excitation wavelength. The problems of determining the real parameters from the observed, and the molecular

parameters from the real, will be discussed.

Methods are available for the accurate determination of F T (v) and r

T

. The usual method of deter- mining ^involves comparison with a reference solution R, although a few calorimetric and other

absolute determinations have been made. For two solutions excited under identical conditions and

observed at normal incidence

where n is the solvent refractive index. Two reference solution standards have been proposed, quinine sulphate in iV H2SO4 which has no self-absorption, and 9,10-diphenylanthracene in cyclohexane which has no self-quenching. The

relative merits of these solutions will be discussed, and possible candidates for an "ideal" fluorescence

standard with no self-absorption and no self-quenching will be considered.

Key words: Fluorescence lifetime; fluorescence quantum efficiency; fluorescence quantum yields;

fluorescence spectrum; fluorescence standards; molecular fluorescence parameters: observed (technical) fluorescence parameters; polarization; radiative and non-radiative transition probabilities;

real fluorescence parameters.

J. B. Birks

University of Manchester, Manchester, U.K.

(April 9, 1976)

*Paper presented at the Workshop Seminar 'Standardization in Spectrophotometry and Luminescence Measurements' held ai the National Bureau of Standards, Gaithersburg, Md., Nov. 19-20, 1975.

1
1 . Introduction

Most atoms, molecules, polymers and crystals emit

ultraviolet, visible or infrared photons following excitation of their electronic energy levels. This emission

or luminescence is classified according to the mode of

excitation:

photoluminescence due to optical (non-ionizing)

radiation;

cathodoluminescence due to cathode rays (electron beams);

radioluminescence {scintillations) due to ionizing

radiation;

electroluminescence due to electric fields;

thermoluminescence produced thermally after

prior irradiation by other means;

triboluminescence due to frictional and electrostatic forces;

sonoluminescence due to ultrasonic radiation;

chemiluminescence due to a chemical process,

commonly oxidation;

electrochemiluminescence due to a chemical

process, initiated by an electric field; and

bio luminescence due to a biological process,

usually enzymatic in origin.

Luminescent materials can be divided into several

broad groups.

(i) Aromatic molecules constitute the largest group.

They emit luminescence in the vapour, liquid, polymer

and crystal phases and in fluid and rigid solutions

[I] 1

. They are used extensively in organic liquid,

plastic and crystal scintillators [2], luminescent dyes

and paints, detergent and paper whiteners, luminescent screens, dye lasers, etc.

(ii) Many inorganic crystals, including diamond,

ruby, alkali halides, zinc sulphide and calcium tungstate, luminesce efficiently. The emission is usually

from impurity centres (activators) or, in the absence

of such impurities, from crystal defects [2]. Luminescent inorganic crystals are used as scintillators [2],

luminescent screens, solid-state lasers, jewels, etc.

(hi) Noble gases (He, Ne, Ar, Kr, Xe) luminesce in

the vapour, liquid, and solid phases and in liquid and

solid solutions [2, 3]. They are used in discharge

lamps, gas lasers and scintillators.

(iv) Many simple inorganic molecules luminesce in

the vapour phase [4]. Some, like H2 , D2 , N2 , and Hg

are used in discharge lamps; others, like N2 , I 2 , and

CO) are used in gas lasers.

(v) Some inorganic ions, notably those of the rare earth elements, are luminescent. They are used as

activators in inorganic crystals (see (ii) above), glasses

and chelates. Applications include inorganic crystal

and glass scintillators and Nd glass lasers.

(vi) Many biological molecules are luminescent.

These include

(a) aromatic amino-acids (tryptophan, tyrosine,

phenylalanine) in proteins;

(b) nucleotides (adenine, guanine, uracil, cytosine, thymine) in DNA and RNA;

(c) retinyl polyenes in the visual pigments;

(d) chlorophylls and carotenoids in the photosynthetic chloroplast; and

(e) several vitamins and hormones.

The study of biomolecular luminescence is an important

area of biophysical research [5]. (vii) Aliphatic molecules, such as the paraffins and

cyclohexane, once considered to be nonluminescent,

are now known to emit in the far ultraviolet (~ 200 nm)

with low quantum yield [6]. This list, which is not ex- haustive, illustrates the wide range of luminescent

materials and their applications.

2. Luminescence of Aromatic Molecules

2. 1 . Radiative transitions

The initial discussion is limited to aromatic molecules

(i) , but it will be later extended to other luminescent

materials (ii)-(vii). Most aromatic molecules have an even number of 7r-electrons, giving a ground singlet

electronic state So in which the electron spins are

paired. The excited it electronic states of the molecule

are either

singlet states: Si,S2 . . . Sp; or

triplet states : TU T2 . . . Tq

. A spin-allowed radiative transition (luminescence) between two states of the same multiplicity (e.g. Si —* So,

Sp So, Tq —> Ti) is called fluorescence (F). A spinforbidden radiative transition between two states of

different multiplicity (e.g. 7\ —»So) is called phosphorescence (P). The energy difference between the initial

and final electronic state is emitted as a fluorescence

photon (hvF ) or phosphorescence photon (hvp ). The fluorescence occurring immediately after the

initial excitation of Si (or Sp) is known as prompt

fluorescence. In some molecules or molecular systems

there are mechanisms by which Si (or Sp) may become

excited subsequent to the initial excitation, resulting

in delayed fluorescence. The two principal mechanisms

are as follows [1].

(i) Thermal activation of molecules in the lowest

triplet state Tu which is long-lived because the 7\ —> So

transition is spin-forbidden, repopulates the fluorescent

singlet state Si, resulting in E-type (eosin-type)

delayed fluorescence, so called because it occurs in

eosin and other dye molecules.

(ii) Diffusional interaction between pairs of 7Yexcited molecules in solution or T\ excitons in a crystal

creates singlet-excited molecules by the process

' Figures in brackets indicate the literature references at the end of this paper. ri+ri-»Si(orSP )+So (i)
resulting in P-type (pyrene-type) delayed fluorescence,

so called because it occurs in pyrene and other aro- matic hydrocarbons.

2.2. Radiationless Transitions

Radiative transitions are between electronic states

of different energy. In a complex molecule or crystal

there are also radiationless transitions between different

electronic states of the same energy. These isoenergetic radiationless transitions are induced by molecular

or crystal vibrations.

A spin-allowed radiationless transition between two

states of the same multiplicity is called internal conver- sion {IC). A spin-forbidden radiationless transition

between two states of different multiplicity is called

intersystem crossing (ISC).

2.3. Vibrational Relaxation

After the initial excitation or after an isoenergetic

radiationless transition, the molecule is usually in a vibronic state S* (or Tq) corresponding to a vibrationally-excited level of a particular electronic state

Sp

(or Tq). In a condensed medium (solution, liquid,

polymer, crystal) or a high-pressure vapour the excess

vibrational energy S*—S° (or T* — T°

q

) is rapidly

dissipated collisionally to the environment leading to vibrational relaxation (VR).

The dissipative VR process, which is distinct from

the nondissipative IC and ISC processes, plays an

essential role in the thermal equilibration of the

excited molecules. At normal temperatures VR is rapid (~ 10~ 12 — 10~ 13 s, depending on the excess

vibrational energy to be dissipated) and much faster

than IC, ISC, F or P.

Isolated excited molecules in a low-pressure vapour,

where VR is inhibited by the low collision rate, behave

in a different manner than those in the condensed

phase [6]. In an isolated molecule the fluorescence occurs from the vibronic state Sp initially excited or from isoenergetic vibronic states Sf, S* • • • • of

lower electronic states populated by IC. This phenomena is called resonance fluorescence. In the condensed

phase VR brings the excited molecules rapidly into

thermal equilibrium and all the processes (F, P, IC

and ISC) occur from an equilibrated system of

molecules.

2.4. Photophysical Processes and Parameters

Figure 1 shows schematically the photophysical

processes that can occur in an aromatic molecular

system in very dilute solution (~ 10 ~6 M) following

excitation into S2.

S2 decays by

(a) IC to Si*, followed by VR to S,

(b) IC to So***, followed by VR to S0 ; or

(c) S2 ~* So fluorescence FiFigure 1. Schematic diagram of radiative (solid vertical lines), radiationless (wavy horizontal lines), and vibrational relaxation

(broken vertical lines) transitions between electronic states (solid

horizontal lines) S>, Si, Ti and So of an aromatic molecule in a condensed medium.

F = fluorescence, P = phosphorescence, IC = internal conversion, ISC = intersystem

crossing, VR = vibrational relaxation.

is forbidden since S2 and Si have the same parity

(ungerade) [1].

Si, from (a), decays by

(d) Si-^So fluorescence Fi;

(e) ISC to 77, followed by VR to 7\; or

(f) IC to So**, followed by VR to So.

T\, from (e), decays by

(g) 7\—»So phosphorescence P; or

(h) ISC to So*, foUowed by VR to So

F, P, IC, and ISC are the rate-determining processes,

since VR is much faster. Icab is defined as the rate

parameter of the B^A process, where B is the initial

state and A is the product radiation (F or P) or final

state (for IC or ISC) [1]. Subscripts G — So, T=T\,

M — Si, and H = S2 indicate the different states.

S,(H)

GH

S, (M)

GM FM FH

TM

T, (T)

S0

(G)

Figure 2. Rate parameters of radiative transitions (solid vertical

lines) and radiationless plus vibrational relaxation transitions (broken vertical lines) between electronic states (solid horizontal

lines) S2, Si, T[, and So of an aromatic molecule in a condensed

medium.

S2~^Si fluorescence, which COuld potentially OCCUr, The notation of the states, radiations and rate parameters is indicated.

3
Figure 2 shows the rate parameters corresponding to the processes of figure 1. In the rate parameter

description the VR subsequent to each IC or ISC is omitted, but the distinction between the isoenergetic

radiationless transitions and the vibrational relaxation

should not be overlooked.

The 52, Si and T\ decay parameters are given by

£tf = kyH + k.UH + kcH = 1/t//

k\i = kt\i + krM + kcM = 1/t,w

kr—kpT+ kcT— 1/tt

(2)

(3)

(4)

where rH , tm and tt are the S2, Si and 7\ lifetimes,

respectively.

The quantum efficiency q,\B of any photophysical

process, rate k.iB, from an excited state B is defined

as the fraction of the excited molecules in B that

decay by that process, so that

qAB = k Milks (5)

The S 2 ~* So and Si —> So fluorescence quantum efficiencies are, respectively.

qtH — kpfilkH

QFM = kFAflkli

(6)

(7)

the T\ —> So phosphorescence quantum efficiency is

qi>T=ki>T\k T (8)

the S2 —* S * internal conversion quantum efficiency is

<7a/« _ ksinlkn (9)

and the S\-^T* and 7\ —» S0* intersystem crossing

quantum efficiencies are, respectively,

9TM — kTMlk\l

qar — karlkr

(10)

(11)

The rate parameters (fig. 2), the decay parameters

and lifetimes (2)-(4), and the quantum efficiencies

(5)— { 11) are molecular parameters. They refer to very

dilute (~ 10~6M) solutions, containing no dissolved

oxygen or other impurity quenchers.

An increase in the solution molar concentration c does not change the unimolecular rate parameters,

but it introduces bimolecular processes due to interactions between excited molecules in S2, Si or 71 and

unexcited molecules in So, producing concentration

quenching. To a first approximation the S->, Si and T\

concentration quenching rates may be expressed as kcHC, kaac and kcrc, and the S2, Si and Tt decay

parameters become

k'H = kH + kcHC— 1/t'h (2a)

k'\i— k\f + kcxtc — 1/t'u

k'r = kr + kcrc = l/rf

(3a)

(4a)

respectively, where t'h, t'm and tt are the S2, Si and

7j lifetimes in a solution of molar concentration c. An

exact treatment also considers the rate parameters of

the excimers produced by the concentration quenching and their dissociation [1], but the Stern-Volmer

approximation of (2a)-(4a) is adequate for the present

discussion.

The quantum yield 4> of any photophysical process

in a solution of concentration c is defined in the same

manner as the quantum efficiency, except that the

limitation to very dilute solutions is removed. The

S-2~* So and Si—* So fluorescence quantum yields are, respectively

<f>FH —

kFH q/H

kn + kcHC 1 + KchC

(12)

krM qFM

FM~

and the 7i

kin + kcMC 1 + KcmC

So phosphorescence quantum yield is

kpT qpT

(13)

4> kr + kcrc 1 + KctC

(14)

The parameters KCh(= kC HlkH ) , KCm(= kC MlkM ) and Kcrikcrl kr) are the Stern-Volmer coefficients of

concentration quenching of S2, Si and 7\, respectively.

The &2~*S* internal conversion quantum yield is

q\iH

kH + k CH c 1 + KchC

(15)

and the S\-^T* and T\ —* So intersystem crossing

quantum yields are, respectively,

qTM

TM'

4>(;T —

kM + kcufC 1 4- KcmC

kcr qc.r kr+ kcrc 1 + KctC

(16)

(17)

The above expressions for quantum efficiencies and

yields all refer to direct excitation of the state from

which the process occurs, and they require revision

when the state is not excited directly. Thus for excitation into S2, the Si^So fluorescence quantum yield

is

4>fm— 4>mh4>fm (18)

For excitation into Si, the T\ —* So phosphorescence

quantum yield is

4>p T — 4>tm4>pt (19)
2.5. Vavilov's Law and Kasha's Rules

It is commonly assumed that <^a/h = 1-0 for S2 —*S*

IC and that <£= 1 for IC between higher excited states

within the singlet (Sp ) manifold, so that ($>fm is independent of the excitation wavelength \ex up to the ionization potential. This assumption, known as Vavilov's

law, has been confirmed for many compounds in solution. Major deviations from Vavilov's law have, however, been observed for solutions of benzene, toluene,

p-xylene, mesitylene, fluorobenzene, naphthalene,

2-methylnaphthalene, 1,6-dimethylnaphthalene [1],

tryptophan, tyrosine and phenylalanine [7]. In each

case it is observed that 4>"M/(j)FM — $mh < 1- In benzene

and its derivatives and possibly in the other compounds, the effect is due to efficient S2~* S$** IC

(Icgh) competing with S2 S* IC (Icmh) [8]. In fluores- cence quantum yield measurements it is essential

either to verify that Vavilov's law applies, or to limit

the excitation to the region of the So -*Si absorption

spectrum.

Kasha's rules [9], another well-known generalization,

state that in a complex molecule luminescence occurs

only from the lowest excited state of a given multiplicity, i.e., Si~»So fluorescence and T\—* So phosphorescence. For many years azulene and its derivatives, which emit S2 ~~> So fluorescence and negligible

Si ->So fluorescence, were the main exceptions to Kasha's rules. Recently the picture has changed

dramatically.

In addition to the normal Si —

So fluorescence, weak

S2 ~* So fluorescence has been observed in benzene,

toluene, p-xylene, mesitylene, naphthalene, pyrene,

1 : 2-benzanthracene, 3:4-benzopyrene, l:12-benzoperylene and ovalene, weak S3—^So fluorescence has

been observed in p-xylene, mesitylene, naphthalene,

pyrene and l:2-benzanthracene, and weak S-t^So

fluorescence has been observed in pyrene and fluoranthene [6, 10].

Such fluorescence from higher excited states was

predicted by the author in 1954 [11]. Its detection is difficult, since it occurs in the region of the So -> SP absorption spectrum, and its quantum yield is only ~ 10~5 4>FM [6]. Subsequent attention will be focused

on the main Si —> So fluorescence.

2.6. The Fluorescence Spectrum

The Si—»So fluorescence spectrum occurs from a system of Si excited molecules in thermal equilibrium

in solution. The fraction of these molecules with vibrational energy Ev is proportional to exp (—Ev/kT),

where k is Boltzmann's constant and T is the absolute

temperature. A large majority are in the zero point

level S°, and to a first approximation the fluorescence of

the "hot" molecules can be disregarded.

The SJ—»So fluorescence occurs into S}}, the zero- point level of So, and into the many vibrational levels

of So. The SJ —* Sq transition, or 0-0 fluorescence transition, of wavenumber (^oo)f is the highest energy transition in the SJ—*So fluorescence spectrum. In the

vapour (^oo)f coincides with (voo)a , the corresponding

So~^Sy 0-0 absorption transition. In solution, due to solvent polarization effects

(v0o)a— (v0o)f = A v0o (20)

where AFoo varies from 0 to a few hundred cm-1 depending on the solvent [1]. In benzene the 0-0 fluores- cence and absorption transitions are symmetry-forbidden and they are absent from the vapour spectra. They

appear as weak solvent-induced bands (the Ham bands)

in solution spectra, the intensity depending on the

solvent [1]. At low temperatures the S\—> So (=S?—* So)

fluorescence spectrum Fu(i>) consists of a complex

series of a few hundred narrow lines of different

intensities, which may be analysed into progressions

and combinations of the different vibrational modes

of the unexcited molecule. When the temperature is increased, thermal broadening and solvent-solute

interactions obscure most of the vibrational structure.

At room temperature Fm(v) commonly consists of a few prominent broad bands with little other structure.

Thus Fm(v) for anthracene in cyclohexane solution

consists of a progression of 5 broad bands, spaced

about 1400 cm-1 apart, corresponding to CC vibrational modes. Similar vibrational progressions occur

in Fm(v) for other condensed hydrocarbons [1]. For

large molecules, e.g., dyes, with many degrees of

vibrational and/or rotational freedom, F,u ( v) at room

temperature often consists of a single broad band with no vibrational structure. Berlman [12] has recorded

the fluorescence spectra of many aromatic molecules.

The solvent has a strong influence on Fm(v) at room temperature. In a polar solvent like ethanol the

vibrational bands are broad and poorly resolved, and

the separation A^oo between the absorption and

fluorescence 0-0 bands is relatively large. In a nonpolar aliphatic hydrocarbon solvent, like cyclohexane

or n-hexane, the spectral resolution is improved and

Ai^oo is reduced. In a fluorocarbon solvent, like perfluoro-n-hexane (PFH), each of the vibrational bands

has a well-resolved fine structure, similar to that in

the vapour phase, and Ai>0o = 0 [13]. PFH is an ideal

spectroscopic solvent, apart from cost and the low

solubility of aromatic molecules in PFH.

At temperatures above about — 100 °C the "hot"

vibrationally-excited Si molecules with a Boltzmann

distribution of energies S* (=S° + EV ) also contribute

to Fm{v). Each component S* —* So spectrum is similar

to the S?—»So spectrum, except that it is shifted by

an amount Ev towards higher energies, and its intensity is proportional to exp (—Ev/kT). Most of the

Sf—* So spectral distribution lies below the SJ—> So

spectrum and is obscured thereby. However, each

component S*—> So spectrum extends beyond Voo to

i>oo + Ev , giving rise to hot fluorescence bands, the

intensity and extent of which increase with tempera5
ture. These hot fluorescence bands, which are an

integral part of the Si —* So fluorescence spectrum

Fm(v) at room temperature, occur in all aromatic

molecules, although they are not often recorded. The

emission bands are in the same region as the So -* Si

absorption, and special care is needed to observe

them [6].

2.7. The rate parameters

Observations of qFM and Tm for a very dilute solution

enable

Icfm = Qf.mItm (21)

km — kFM + kGM = ( 1 — qFM ) tm (22)

to be determined. Birks and Munro [14] have reviewed

methods of measuring tm- Observations of qm

(= kmI km) , by one of the several methods described

by Wilkinson [15], enable k Tu and kc.si to be evaluated.

The measurement of qpT and tt permits kpr and kcr

to be determined [1]. Thus measurements of five

quantities qFM, Tm, qm, qpr and tt are required to determine the five Si and Ti unimolecular rate parameters kFM , kTM, kGM, kpr and kcr. Observations of t'm and t't (or <$>fm and 4>pt) as a

function of the molar concentration c enable the

bimolecular rate parameters kcM and kcr to be determined. The observations and analysis may be ex- tended further to obtain the fluorescence {kF D) , ISC

(kro), IC(kcD) and dissociation (A;,wd) rate parameters

of the singlet excimer [1]. This involves observations

of the molecular (0fa/) and excimer {<}>fd) fluores- cence quantum yields of concentrated solutions.

It is the rate parameters and their dependence on

temperature, solvent, substitution etc. that are the

quantities of interest to the photophysicist and photochemist, and not the properties from which they are

derived. The latter may be of technical interest for

particular applications. Of the three quantities qFM,

tm and qrM required to determine the Si rate parameters kFM, kTM and kGM, the published values of

q FM (or 4>fm, which is often implicitly equated to

<7em) show the largest scatter. When the solution

concentration c is increased, self-absorption effects

introduce difficulties in the determination of 4>fm- It

is hoped that this paper will help to improve the

situation.

2.8. The Fluorescence Rate Parameter

A theoretical expression for kFM has been derived

from the Einstein radiation relation using the zero-order

Born-Oppenheimer approximation [16, 17]

^= 2.88x10-^(^-3)^ (23)

riA J v

where nF and n.\ are the mean refractive indices of the

solvent over the Si—»So fluorescence and So -*Si

absorption spectra, respectively, {v~f)~\w

IS tne

reciprocal of the average value of v~3 over the fluores- cence spectrum, e(^) is the decadic molar extinction

coefficient, and the integral is taken over the So -

Si

absorption spectrum. Relation (23) has been tested for a number of molecules, and excellent agreement between kFM and kFM has been obtained for several

molecules in different laboratories [1, 12, 16, 17, 18].

Such molecules may be useful as fluorescence

standards.

If the solvent optical dispersion is small nF — ua =

n, and (23) can be simplified to

k'FM = ri 2 (k'FM ) 0 (24)

where (kFM )o is a molecular constant, independent of

the solvent and the temperature. Relation (24) has been

verified for several solutes in different solvents over

a wide temperature range [19].

In some molecules there are large discrepancies

between kFM and kFM. A detailed study of these anomalies has revealed the presence of electronic states not

observed spectroscopically [20, 21]. The nature and

origin of such radiative lifetime anomalies are discussed elsewhere [22]. The factors determining the

other Si and 7i rate parameters km, kcM, kpr and kcr

have been considered previously [1, 6, 8].

2.9. Molecular Fluorescence Parameters

The Si —» So fluorescence of an aromatic compound

in very dilute solution is characterized by the following molecular parameters.

(a) The fluorescence spectrum Fm(v) depends

on the solvent and temperature (see 2.6).

(b) The fluorescence polarization pm depends

on the direction of the transition dipole

moment relative to the molecular axes. For

a tt* '—» tt electronic transition this lies in the

molecular plane along one of two orthogonal axes depending on the symmetry of Si. For

naphthalene the fluorescence is long-axis

polarized; for anthracene it is short-axis

polarized [1]. (c) The fluorescence rate parameter kFM is proportional to the square of the transition dipole

moment [1]. In the absence of any anomalies

kFMlri2 is independent of the solvent and

temperature (24).

(d) The Si radiationless rate parameter km (== krM

+ kGM) describes the processes competing

with the fluorescence, km usually depends

markedly on the solvent and on the temperature [1].

Fm{v) and pm can be observed directly. The

evaluation of kFM and km involves measurements of

two secondary parameters:

(e) The fluorescence lifetime tm; and

(f ) the fluorescence quantum efficiency qFM6
Several accurate methods are available for measuring

ta/[14]. Reliable methods are available for measuring

qfmi but they are often used incorrectly [23].

The molecular fluorescence parameters Fm(v),

Pm, Ufm and km are independent of the molar concentration c. The secondary fluorescence parameters

tm and 4>fm decrease with increase in c due to

(g) the concentration quenching rate parameter

kcMkciu, which depends markedly on the solvent viscosity

and the temperature,, is a further molecular parameter

of photophysical interest.

3. Other Luminescent Materials

The preceding discussion of the luminescence of

aromatic molecules is applicable to the other luminescent materials considered in the Introduction. It applies directly to biological molecules (vi) and aliphatic

organic molecules (vii). Noble gases (iii) also have

singlet ground states, and there are close analogies

between them and the aromatic hydrocarbons, particularly in excimer formation [3]. There are no radiationless transitions in the noble gases (qFM = Qfh = 1.0)

because of the absence of internal vibrations. They

form excimers in the vapour, liquid, and solid phases,

and the vibrational modes of these may generate radiationless transitions and vibrational relaxation in the

condensed phase [3]. Simple inorganic molecules (iv) are similar. They

normally have singlet ground states and excited singlet

and triplet states. Although they have internal vibrations, the vibronic state density is low, and there are normally no radiationless transitions except at high

excitation energies, where predissociation may occur

[4].The luminescence of inorganic crystals (ii) and in- organic ions (v) in a solid matrix is closely related to that of aromatic molecular crystals. Unfortunately

there are major terminological differences between

inorganic crystal photophysics and organic molecular

crystal photophysics. Table 1 is based on a brief

survey of the inorganic luminescence literature, and

may require revision in the light of any recent changes.

Table 1. Terminology of photophysical processes

Process Organic Inorganic

1. Luminescence,

(a) spin-allowed Fluorescence (F) Fluorescence

(b) spin-forbidden Phosphorescence (P) Fluorescence

(c) thermally-activated E-type delayed Phosphoresdelayed fluorescence cence

2. Radiationless transition

(a) spin-allowed Internal conversion

(/C)

(b) spin-forbidden Intersystem crossing

(ISC)

3. Vibrational relaxation Vibrational relaxation (VR)

4. Radiationless transi- IC (or ISC) and VR Multiphonon

tion plus vibrational process

relaxation

The inorganic luminescence terminology predates

the discovery of electron spin, and it has not been

adjusted to take account of this. Because of spin,

processes 1(a) and Kb) differ in lifetime by a factor of

up to 108

, and it would seem appropriate to distinguish

them. In 1933 Jablonski [24], the originator of figure

1, showed that the two slow emissions 1(b) and 1(c)

observed in organic dyes originated from a common

metastable state X, and he proposed that they be

called ^-phosphorescence and a-phosphorescence,

respectively. Since 1944 when Lewis and Kasha [25]

demonstrated that X==T\, the lowest excited triplet

state, 1(b) has been called simply phosphorescence,

while 1(c) which has the same emission spectrum as

1(a) is called E-type delayed fluorescence.

Standardization of luminescence terminology is long overdue. Those responsible for organizing international luminescence conferences and publishing

luminescence journals have unfortunately neglected

to formulate a scientific language common to workers

in organic and inorganic luminescence. Perhaps the

National Bureau of Standards can assist in the matter.

4. Fluorescence Measurements

4.1. Fluorescence Spectra

A true (corrected) fluorescence spectrum is plotted

as the relative quantum intensity Fm(V) (relative number of quanta per unit wave-number interval) against

wavenumber v. A few spectrometers have been developed which record directly the true fluorescence

spectrum. The majority provide spectra which require

correction for the dispersion of the analyzing monochromator, the spectral response of the photomultiplier or detector, and any light losses. This involves the

preparation of an instrumental calibration curve, by

measurements

(a) with a calibrated lamp through a neutral

filter; (b) with a thermopile or bolometer;

(c) of reference solution fluorescence spectra

[26]; or

(d) with a fluorescent quantum counter.

A quantum counter is a system which has a constant

fluorescence quantum yield over a broad spectral

range. To achieve this it should have a high and

relatively constant absorption over the spectral range

of interest, it should have negligible self-absorption (no

overlap of fluorescence and absorption spectrum),

it should obey Vavilov's law, and it should be stable

photochemically. Systems commonly used as quantum

counters include:

(i) 3 gl _1 Rhodamine B in ethylene glycol

(210-530 nm),

(ii) 4 gl"1 quinine sulphate in N H2S04 (220-340

nm), and

(iii) ilO _2M 1-dimethylaminonaphthalene 5-(or 7-)

sodium sulphonate in 0.1 /V Na2 C03 (210 —

400 nm).

7
An extension of this list would be advantageous.

Three common optical geometries are used in fluor- escence measurements;

(a) front-surface or reflection geometry, in which

the fluorescence from the irradiated sur- face of the specimen is observed;

(b) 90° geometry, in which the fluorescence is observed in a direction normal to the incident

beam; and

(c) transmission geometry, in which the fluores- cence is observed from the opposite side of

the speciment to the excitation.

For very dilute solutions (~ 10~6M) the three geometries give the same fluorescence spectrum, quantum

efficiency and lifetime. The 90° geometry, used by Birks

and Dyson [17] and others, has the advantage of

minimizing background incident light and of allowing

the fraction of incident light absorbed in the specimen

to be monitored directly.

An increase in the solution concentration c reduces

qp\t and t.w to <$>fm and t.'u, respectively, due to concentration quenching. It also attenuates the highenergy region of Fu{v) due to self-absorption arising

from the overlap of the absorption and fluorescence

spectra. As c is increased the intensity of the 0-0

fluorescence band decreases towards zero due to its overlap with the 0-0 absorption band. At room temperature and high c the self-absorption may extend to the 0-1 and 0-2 fluorescence bands, which overlap

the 1-0 and 2-0 hot absorption bands, due to thermally

activated molecules in the first and second vibrational

levels of So- These self-absorption effects are a maximum in the transmission geometry (c), somewhat

reduced in the 90° geometry (b), and they are least in

the reflection geometry (a), which is normally used

for fluorescence studies of more concentrated solutions.

The effect of self-absorption on Fu(v) observed in

reflection can be minimized by Berlman's technique

[12] of excitation at an intense absorption maximum,

thereby minimizing the penetration depth dex of the

exciting light. This technique does not, however,

compensate for the secondary fluorescence produced

by the self-absorption and which modifies <\>m and

tm, as discussed below.

4.2. Fluorescence Quantum Yields

Absolute determinations of fluorescence quantum

yields have been made using integrating spheres to collect the fluorescence emission over a full 4tt solid

angle, by calorimetry to distinguish radiative processes

from radiationless processes and vibrational relaxation, by actinometry to integrate light intensities

photochemically, and by polarization and scattering

measurements. These methods have been reviewed

by Lipsett [27] and Demas and Crosby [28].

The superscript T is introduced to refer to the

observed (technical) fluorescence parameters Fli(v),

cf)J. M and rjtf, which may differ from the true fluores- cence parameters F\i(v), and t!m, due to self- absorption and secondary fluorescence. Absolute

determinations of ^>fm are difficult and uncommon,

and it is normal practice to measure (f>JM by comparison

with a standard of known fluorescence quantum yield

(f)Jn. If Fl,{v) and Fj-(v) are the corrected fluores- cence spectra of the specimen and standard, respectively, excited under identical conditions (same excitation wavelength, optical density and geometry) and

observed at normal incidence in reflection, then

4>fm n~

I FTM (v)dv

<t> TFR n% FTR { v )dv

Jo

where n and nR are the refractive indices of the specimen solution and the standard solution, respectively.

The integrations are often made using a quantum

counter [28].

The refractive index term is a correction for the

solution optical geometry. The angular dependence of

the fluorescence flux F(4>) from a small isotropically

emitting source behind an infinite plane surface in a medium of refractive index n is

F(0) = F0 (cos (^)n- 1 (n2 - sin2 ^)-1 ' 2 (26)

where F0 is a constant (^^fm) and F(cf)) is the flux

(in quanta cm2 s _1

) falling on a small aperture at an

angle </) from the normal to the face. For 4> = 0° (26)

reduces to

F(0)=Foln2 ' (27)

leading to (25). Relation (26) has been verified by

Melhuish [29] who recommended the use of cuvettes

with blackened back and sides for fluorescence yield

measurements to minimize internal reflection errors. Shinitzky [30] has pointed out a further potential source of error in fluorescence quantum yield and

lifetime measurements. When a fluorescent system is excited by unpolarized light and its emission is detected without a polarizer, the emission intensity has

a typical anisotropic distribution which is directly

related to its degree of polarization. This effect can

introduce an error of up to 20 percent in all fluores- cence quantum yield and lifetime measurements, but

it is eliminated when the fluorescence is detected at an angle of 55° or 125° to the direction of excitation,

provided that the emission detection system is un- biased with respect to polarization. Procedures for

the elimination of polarization errors for partially

polarized excitation and biased detection systems

were developed by Cehelnik, Mielenz, and Velapoldi

[31] and Mielenz, Cehelnik. and McKenzie [32].

If n and tir differ, it is recommended that the specimen and reference solutions be excited at 55° incidence angle and observed at normal incidence, to eliminate the polarization effect and simplify the refractive index correction. The latter correction disappears

if n = nR, and the excitation and front-face observation

8
directions need only differ by 55°. The angles of incidence and "reflection" should differ to minimize

scattered light.

The self-absorption attenuates the high-energy end

of Fm(v), but it does not affect the low-energy end.

If F.u(i/), observed in very dilute solution, and F[, , observed at molar concentration c, are normalized in

the low-energy region, then the parameter

where

represents the self-absorption probability. This normalization procedure, introduced for anthracene crystal

fluorescence [33], has been applied by Birks and Christophorou [34] to concentrated solutions of aromatic

hydrocarbons. Substitution of Am in place of A M in

(25) gives 4>fm in place of 4> TFM. For materials of low

<t>FM (< 0.3), the linear Stern-Volmer plots of qFiul<l>FM

against c of gradient Kcm (13) confirm the validity of

the procedure, which corresponds to assuming

<t>FM= (1- a) 4>fm (31)

This relation neglects the secondary fluorescence

resulting from the self-absorption. Allowing for this,

the author [11, 35] has shown that

<P?.v/--j 77 (32)

1 — aq>FM

which approximates to (31) when a (f) F, y < 1, and that

Relation (33) is considered to be generally valid.

Relation (32) is considered to be valid for the transmission and 90° geometries. It is also valid for the

reflection geometry, except for specimens of high 4>fmUnder the latter conditions the secondary fluorescence

contributes markedly to the observed fluorescence

intensity, so that 4>J U> 4>fm in reflection, although

(j>FM< <f>FM in transmission as predicted by (32). Figure

3 plots Melhuish's observations [36] of (/>£,V/ as a function of c for 9,10-diphenylanthracene (DPA) in benzene

solution, excited at 366 nm with front-face observation. Due to secondary fluorescence <f)FM increases

from qFM = 0-83 in very dilute solution to <£>£A/=1.0 at c 2* 1.5 X 10~3M. Correction for self-absorption and

secondary fluorescence, using a much more complex

relation than (32), showed that 4>fm — 0.83 ±0.02 over

(M)

FIGURE 3. 9,10-diphenylanthracene in benzene.

Front-surface observation at \ex = 365 nm. Technical fluorescence quantum yield <f>^ (/ (+ ) and true fluorescence quantum yield $fm (o) against molar concentration c. Data

from Melhuish [36].

the whole range of c, thus demonstrating that DPA is immune to concentration quenching [36].

The secondary fluorescence contribution to increases with decrease in the excitation penetration

depth dex . Berlman's [12] choice of an intense absorption band for excitation (Aex = 265 nm for DPA) minimizes dex . This minimizes the effect of self-absorption on F^i{v), but it also maximizes the effect of secondary

fluorescence on 4>tfm- To reduce the latter, a weak

absorption region should be chosen for excitation, and

c should be kept as low as possible.

To summarize, there are no particular problems in

determining (f> FM for (a) very dilute solutions (b) more

concentrated solutions observed in the transmission

or 90° geometries, and (c) more concentrated solutions

of 4> Fm < ~ 0.3 observed in the reflection geometry.

The effects of self-absorption and secondary fluores- cence are, however, difficult to compensate in concentrated solutions of high (f> FM observed in the reflection

geometry. One simple solution is to abandon the re- flection geometry and to observe such systems in the

more tractable transmission geometry. The alternative

is to utilize one of the numerous mathematical relations, some simple [11, 35], some complex [27, 36],

which have been developed to describe self-absorption

and secondary fluorescence.

4.3. Fluorescence Standards

Melhuish [36] proposed the use of a 5 X 10 _3M solution of quinine bisulphate (QS) in IN sulphuric acid

as a fluorescence standard. From careful measure- ments he obtained $FM = 0.510 for c = 5XlO~W in- creasing to qFM = 0.546 at infinite dilution at 25 °C.

The value of di FM at any other concentration can be

evaluated using the Stern-Volmer relation (13). The

QS solution is stable under prolonged irradiation, its fluorescence is not quenched by dissolved air (unlike

most aromatic molecules), and it has a very small over9
lap of the absorption and fluorescence spectra,

suffers from three minor disadvantages:

It

(a)

(b)

(c)

concentration quenching;

the temperature coefficient of d) FM is about — 0.25 percent per degree over the range 10°

to 40° C; and

sulphuric acid is not a conventional solvent

for aromatic molecules and this necessitates

using the refractive index correction in (25).

Nevertheless the QS standard, and various secondary

standards derived therefrom, have been adopted in

this and many other laboratories [28, 37]. Quinine is the fluorescent entity, and the use of quinine sulphate

in place of the bisulphate does not appear to affect

the values of qFM and <f) FM [28]. Unfortunately many

authors have chosen to use 0.1 N sulphuric acid as the

solvent, rather than 1 /V as recommended by Melhuish

[36], while assuming his fluorescence quantum yield

values to be unchanged. There is evidence that (f> F M

increases by 6-8 percent on increasing the solvent

normality from 0.1 N to 1 TV [28].

Table 2 lists comparative data on tm and qFM for

very dilute solutions of several aromatic compounds

obtained using the QS standard [16-18]. The consistency of the data from three different laboratories is gratifying. The close agreement between the experiment values of /cfa/(= QfmItm) and the theoretical

values of k'FM from (23) for several compounds shows

the error in qFM for the QS standard to be small. Gelernt

et al. [36] have recently calorimetrically determined

qFM for QS in 1 ./V sulphuric acid at 25 °C. The calorimetric value of qFM — 0.561 (±0.039) agrees satisfactorily with the fluorimetric value of qFM — 0.546 [34].

Other fluorescence standards have been discussed by

Demas and Crosby [28].

Table 2. Fluorescence lifetimes (tm ) and quantum efficiencies (^fm) of very dilute solutions

Compound Solvent tm (ns) 9fu /cfmIH-m Ref.

Quinine Bisulphate LV H,S04 20.1 0.54 0.73 [17] IN H,S04 19.4 .54 .75 [18]

Perylene benzene 4.9 .89 .93 [17] benzene 4.79 .89 .90 [16] benzene 5.02 .89 .90 [18]

Aeridone ethanol 11.8 .83 1.02 [16] ethanol 12.5 .825 1.05 [18]

9-Aminoacridine ethanol 13.87 .99 1.15 [16] ethanol 15.15 .99 1.02 [18]

9,10-Diphenyl benzene 7.3 .85 0.99 [17] anthracene benzene 7.37 .84 .98 [18]

Berlman [12] used a 10~3M solution of 9,10-diphenylanthracene (DPA) in cyclohexane, excited at 265 nm

(an absorption maximum) and observed in reflection, as a fluorescence standard. Under these conditions

the DPA solution has a technical fluorescence quantum

yield of cf>J, u = 1.0, due to self-absorption and secondary

fluorescence, although the true fluorescence quantum

yield is 0^= ^= 0.83 (±0.02) (fig. 3). Relation (25)

requires that the specimen and standard be compared

under identical conditions of excitation and optical

density, so that the 10~3M DPA solution standard is only suitable for observations of 0JM

on concentrated

solutions in reflection geometry. The QS standard is more versatile since it does not limit the specimen

concentration or optical geometry.

Berlman [12] observed tIi with heterochromatic

excitation and Fli{v) with monochromatic excitation

(these parameters need to be observed under identical

conditions for (32) and (33) to be applicable [35]). He

evaluated d> TFM by comparison with FTH {1>) for the DPA

standard observed under similar conditions, although

the optical densities and excitation wavelengths of

the specimen and standard appear to have differed.

Apart from the usual hot band elimination and some

0-0 band attenuation, Ffo(v) approximates to the

molecular spectrum FM (v). <$.*M and tm do not cor- respond to qFM and tm, as implicitly assumed by

Berlman [12], who used them to "evaluate" kFM . They require correction for self-absorption and

secondary fluorescence to obtain <j) FAt and tm, and

these parameters need correction for concentration

quenching to obtain qFM and tm- Birks [1] tried to correct Berlman's <f>fM data [12] by renormalizing them

to <?//< = 0.83 for DPA, but this procedure has since

been shown to be invalid [23].

It is of interest to note the effect of substituting dif- ferent fluorescence parameters in the relations used

to evaluate kFM and km. From (3a), (13), (21), (22),

(32) and (33)

qF M 4> F m _

tm t'm kF M

FM

TM

(l—a)kF M

(1 —qFM) _

TM

(1-0TM) (1-Vfu)

tIM

Tm TM

ClM' kcMC.

(34)

(35)

(36)

(37)

An ideal fluorescence standard for aromatic solutions should

(i) have no self-absorption,

(ii) have no concentration quenching,

(hi) be in a common solvent suitable for other

aromatic molecules (to eliminate the refractive index correction),

(iv) be readily available as a high-purity material

(or be insensitive to impurities), and

(v) be photochemically stable.

10
QS satisfies (iv) and (v) and it approximates closely

to (i), but it does not satisfy (ii) and (iii). DPA meets

criteria (ii)-(v), but it exhibits strong self-absorption.

To minimize self-absorption in an aromatic hydrocarbon solution it is necessary that Si is a

x Lb state, so

that the So~*Si absorption is weak, and not a

1 L a state, giving strong So~>Si absorption, as in DPA [1]. There are two hydrocarbons which exhibit no concentration quenching (ii), have S— so that self-absorption (i) is reduced, and satisfy (iii) and (v). These

compounds, phenanthrene and chrysene, merit consideration as fluorescence standards. They can be

obtained, but are not yet readily available, as highpurity materials (iv). Aromatic excimers satisfy all the criteria for a fluores- cence standard, since they have no self-absorption

(i) or concentration quenching (ii) [1]. In concentrated

solutions the excimer spectrum Fd{v) can be readily

distinguished from the attenuated monomer spectrum

FJf(v) [34], although the presence of the latter may

be undesirable. It can be eliminated by the use of a pure liquid or crystal. A pyrene crystal has ($>fd = Qfd = 1.0 at low temperatures and pd — q fd = 0.65 at room temperature, a broad structureless fluorescence

spectrum between 400 and 550 nm with a maximum

at 470 nm, and no self-absorption in any optical geometry [1]. It would appear to be an ideal crystal fluores- cence standard.

5. References

[1] Birks, J. B., Photophysics of Aromatic Molecules, (Wiley-Interscience, London, and New York, 1970).

[2] Birks, J. B., The Theory and Practice of Scintillation Counting

(Pergamon Press, Oxford 1964).

[3] Birks. J. B.. Excimers. Rpts. Prog. Phys. 38, 903 (1975).

[4] Herzberg, G., Molecular Spectra and Molecular Structure.

I. Spectra of Diatomic Molecules (Van Nostrand, Princeton

1950).

[5] Birks, J. B., (Ed.) Excited States of Biological Molecules. Proc.

Intern. Conf. Lisbon 1974 (Wiley-Interscience, London, and

New York, 1976).

[6] Birks, J. B., Organic Molecular Photophysics, Vol. II, Ed. Birks,

J. B. (Wiley-Interscience, London, and New York, p. 409,

1975).

[7] Tatischeff, I., and Klein, R., ref. [5], p. 375 (1976).

[8] Birks, .1. B., Organic Molecular Photophysics, Vol. I, Ed. Birks,

.1. B. (Wiley-Interscience, London, and New York, p. 1, 1973).

[9] Kasha, M., Disc. Faraday Soc. 9, 14 (1950).

[10] Nickel, B., Chem. Phys. Letters 27,84 (1974).

[11] Birks, J. B., Phys. Rev. 94, 1567 (1954).

[12] Berlman, I. B., Handbook of Fluorescence Spectra of Aromatic

Molecules (Academic Press, New York. 1st edition, 1965: 2nd edition, 1971).

[13] Lawson, C. W., Hirayama, F., and Lipsky, S., J. Chem. Phys.

51, 1590(1969).

[14] Birks, J. B., and Munro, I. H., Progress in Reaction Kinetics, 4,

239(1967).

[15] Wilkinson, F., Organic Molecular Photophysics, Vol. II, Ed.

Birks, .1. B. (Wiley-Interscience, London, - and New York,

p. 95, 1975).

[16] Strickler, S. J., and Berg. R. A., J. Chem. Phys. 37, 814 (1962).

[17] Birks, J. B., and Dyson, D. J., Proc. Roy. Soc. A275, 135 (1963).

[18] Ware, W. R., and Baldwin, B. A., J. Chem. Phys. 40, 1703

(1964).

[19] Cundall R. B., and Pereira, L. C, J. Chem. Soc. Faraday Trans. 11,68, 1152(1972).

[20] Birks, J. B., and Birch, D. J. S., Chem. Phys. Letters, 31,

608(1975).

[21] Birch, D. .1. S., and Birks, J. B., Chem. Phys. Letters, in press.

[22] Birks, J. B., Z. Phys. Chem. (N.F.) submitted for publication.

[23] Birks, J. B., J. Luminescence 9, 311 (1974).

[24] Jablonski, A., Nature 131, 839 (1933); Z. Phys. Lpz. 94, 38

(1935).

[25] Lewis, G. N., and Kasha, M., J. Amer. Chem. Soc. 66, 2100

(1944).

[26] Melhuish, W. H., J. Phys. Chem. 64, 792 (1960).

[27] Lipsett, F. R., Progress in dielectrics 7, 217 (1967).

[28] Demas, J. N., and Crosby, G. A., J. Phys. Chem. 75, 991 (1971).

[29] Melhuish, W. H.. J. Opt. Soc. Amer. 51, 278 (1961).

[30] Shinitzky.M.J. Chem. Phys. 56,5979(1972).

[31] Cehelnik, E. D., Mielenz, K. D., and Velapoldi, R. A., J. Res.

Nat. Bur. Stand. (U.S.), 79A (Phys. and Chem.), No. 1, 1-15 (Jan.-Feb. 1975).

[32] Mielenz, K. D., Cehelnik, E. D.. and McKenzie, R. L.J. Chem.

Phys. 64, 370 (1976).

[33] Birks, J. B., and Little, W. A., Proc. Phys. Soc. A 66, 921

(1953).

[34] Birks, J. B., and Christophorou, L. G., Proc. Roy. Soc. A 274,

552 (1963).

[35] Birks, J. B.. Molec. Cryst. Liq. Cryst. 28, 117 (1975).

[36] Melhuish, W. H., J. Phys. Chem. 65, 229 (1961).

[37] Parker, C. A., Photoluminescence of Solutions. (Elsevier,

Amsterdam 1968).

[38] Gelernt, B., Findeisen, A., Stein, A., and Poole, J. A., VIII

Intern. Conf. Photochemistry, Edmonton, August 1975,

Abstract 810.

(Paper 80A3-890)

11

NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 466, Standardization in Spectrophotometry and Luminescence

Measurements, Proceedings of a Workshop Seminar Held at NBS, Gaithersburg, Md., November 19-20, 1975 (issued May 1977).

Some Methods of Luminescence Efficiency Measurements *

Alfred Bril and A. Willy de Jager-Veenis

Philips Research Laboratories, Eindhoven, The Netherlands

(April 9, 1976)

Methods of absolute and relative radiant and quantum efficiency measurements are described

for ultraviolet, visible, cathode-ray, and x-ray excitations. Data on some standard luminescent materials

are given.

Key words: Cathode-ray excitation; luminescence; luminescence standards; phosphors; quantum

efficiencies; radiant efficiencies; UV excitation; x-ray excitation.

1 . Introduction

Methods of absolute radiant and quantum efficiency

measurements are given together with methods of

relative efficiency measurements. The methods are especially suitable for powder materials for which the

angular distribution of the emitted luminescent radiation is Lambertian.

The relative measurements are performed with the

aid of standard phosphors, whose efficiencies have

previously been determined by absolute measurements.

Methods are given for excitation of the phosphors by

ultraviolet and visible radiation, cathode rays and

x rays.

For samples with non-Lambertian emission distributions, a method is described in which an Ulbricht's

sphere or an elliptical mirror is used.

2. Ultraviolet Excitation

All powder phosphors are measured using a thick

layer (thickness about 2 mm) at the irradiated side.

The detection takes place perpendicular to the plane

of the phosphor, the excitation is at an angle of 50°

with that plane (see fig. 1). The excitation wavelength

(\ exc ) or regions are isolated from a high pressure

mercury lamp by interference filters, the arc being

focused on the phosphor with a quartz lens. In this

way a high excitation density is reached, but generally

well below the excitation region where saturation

effects start. This is especially advantageous when a

relatively insensitive thermoelement is used as a

detector.

* Paper presented at the Workshop Seminar 'Standardization in Spectrophotometry and Luminescence Measurements' held at the National Bureau of Standards, Gaithersburg. Md., November 19-20, 1975.

Mirror M

Thermopile

— Chopper

Filters

Sample

Figure 1. Schematic diagram of the apparatus for the efficiency measurements.

The radiant efficiencies, from which the quantum

efficiencies are calculated, are determined directly

(when the spectral power distribution is known).

2.1 . Relative Measurements, Giving Absolute Efficiency

Values

Phosphors can be measured with respect to the

following standard samples whose efficiency is generally agreed upon.

(a) The standards issued by the National Bureau

of Standards, Washington, D.C. (See ref. [1-4]).

(b) Sodium salicylate (See ref. [5]).

This phosphor is also suitable for excitation

13
in the far ultraviolet (vacuum ultraviolet)

because of its constant efficiency as a function

of A exc up to 350 nm.

(c) The standard "Ekta S10" 1 proposed by Grum

[6].

(d) "Lumogen T red GG," which can be used in

the excitation region between 190 and 550

nm [7].

2.2. Absolute Measurements

The absolute radiant efficiency can in fact be

determined with the aid of a relative measurement,

being the ratio of the amount of emitted power and

that of the absorbed exciting power [l].2 For one or two

wavelengths the absolute efficiencies can be determined. For other \exc the relative excitation spectrum

can be determined from which the absolute efficiency

at any A exc can be derived.

For this determination three quantities are measured:

(a) The diffuse reflection of the exciting radiation

against BaSGVj for which the reflection is known.

(b) The luminescence + reflection of the exciting

radiation (without using a filter).

(c) The luminescence of the phosphor, using a

filter between phosphor and detector that

passes only the luminescence.

From these three measured quantities the

reflection and radiant efficiency of the phosphor

can be determined.

The expressions found for the radiant efficiency t) p and the reflection rp are given here for the case of

using as a detector a thermopile or thermoelement with

flat radiant response. Three erafs are measured, viz,

VR due to the reflection standard (e.g., BaS04 [8],

reflection R), VP due to the phosphor (luminescence

intensity L + reflected exciting radiation of intensity

I) and Vp, p due to the phosphor when a filter F absorbing the exciting radiation is placed in front of the

detector. We assume that the filter has a transmission

t in the emission region of the phosphor. This leads to the following equations:

CVR = IR

CVp = Irp + L

CVp, f = tL

where C is a constant.

After solving for rp and L we find

L =

R Vp,f ^

7(1 -rp ) r(l-rp ) VR

p Vp - VP , f]t

r,, - R

~~v«

1 In order to describe materials and experimental procedures adequately, it is occasionally necessary to identify commercial products by manufacturer's name or label. In no instance does such identification imply endorsement by the National Bureau of Standards, nor does

it imply that the particular product or equipment is necessarily the best available for that purpose.

2 Figures in brackets indicate the literature references at the end of this paper.

As a cross-check the reflection found in this way can j be compared with that measured directly with a spectrophotometer.

The method described can be used in the same way

for the case of a varying spectral response of the detector and/or a varying spectral transmission of the

filter, even when the filter transmits partly in the region

of the exciting radiation. Of course the equations

become somewhat more complicated in this case. The quantum efficiency qp

is found from the radiant

efficiency by

j

Xp (k)d\

Qp = 7 KxJ pMdk

where p(A) is the emitted luminescent power and

\exc is the exciting wavelength.

The NBS standards mentioned in 2.1 are not excited

in the visible (only No. 1030 would be suitable in the

blue-violet) region. Therefore, other standards are necessary in the visible region. These can be found

among the "lumogen" phosphors. A yellow luminescent

lumogen was described by Kristianpoller and Dutton

[9], yellow and red ones by Vavilov[10]. Morgenshtern,

Neustruev and Epshtein [11] and Kiittner, Selzle and

Schlag [12]. The latter used 5-(p-dimethylaminobenzyliden)-barbituric acid as a red lumogen; they found

a quantum efficiency of 45 percent at \exc = 405 nm. We chose the red luminescent "Lumogen T red GG"

which was already mentioned in section 2.1. It is commercially available from the Badische Anilin

und Soda Fabrik (Ludwigshafen, Germany). The

properties of the phosphor are described in reference

[7]. It has a red luminescence and shows a quantum efficiency which is not quite constant but varies

in a limited range between 40 percent and 60 percent

in the spectral region between 220 nm and 550 nm

(see fig. 2).

Figure 2. "Lumogen T red GG"

q = quantum efficiency, R ~ diffuse reflection and E = spectral power distribution.

The spectral power distributions at room temperature

and liquid nitrogen temperature are given in figures 3

and 4. The temperature dependence curve is given in

figure 5 for X exc = 365 nm. The quantum efficiency

14
together with the diffuse spectral reflection are given

in figure 2. An important advantage of this phosphor

over liquid standards like rhodamine B is that the

absorption is high in the whole region, the lowest

value being 78 percent near k = 380 nm (diffuse re- flection — 22 percent).

50

i 1 1 1 l/A

Rel. Soectr. piwer di'str. /

I 1

Lun.wen T Red GG 1 Room temp- /

i I i is i 1 3501 400 450 500 " 550 600 650 700

' A(nm)

Figure 3. Spectral power distribution of "Lumogen T red GG" at room temperature.

I denotes the spectral radiant power in arbitrary units.

1 1 1 1

Rel. Soectr. power distr. A

1 1

Lumoaen T Red GG

Temp. 77 K

i i i —\~y 1 1 1 350 400 450 500 550 600 650 700 _ *~A(nm)

Figure 4. Spectral power distribution of "Lumogen T red GG" at liquid nitrogen temperature.

See further subscript fig. 3.

temp. (°C)

FIGURE 5. Temperature dependence of the luminescence of "Lumogen T red GG" for k erc = 365 nm.

The absorption of rhodamine B is given in figure 6,

showing the enormous variation through the spectrum

leading to a similar large variation in light output.

Another drawback of liquid samples is the different

geometry of the set-up needed for the measurement.

2.5

250 300 400 500 600

»~ A(nm)

FIGURE 6. Spectral absorbance of rhodamine B.

Various authors have reported measurements using

254 nm mercury vapour discharge excitation. Here

we give additional measurements on some standards

for longer wavelength excitation at A. exc = 365 nm.

The phosphors measured were sodium salicylate, the

"Ekta S10" sample, introduced by Grum [6] and

"Lumogen T red GG" [7] (see tables 1 and 2). The results for diffuse reflection at the exciting and

emission wavelength, the practical and intrinsic radiant

efficiencies, and the practical and intrinsic quantum

efficiencies are given.

Table 1. Efficiencies at k exc = 36S nm

Diffuse Radiant Quantum

Phosphor reflection at efficiency efficiency

A = 365 nm ^ em t] i Qp Qi % % % % % %

Na-salicylate 30 80 33 37 37 41 "EktaSlO" , 15 67 37 45 41 50

"Lumogen T red GG" 13 25 41

Table 2. Efficiencies at \ »xc = 260 nm

Diffuse Radiant Quantum

Phosphor reflection at efficiency efficiency

A = 260 nm Vp V i Qp % % % % % %

Na-salicylate 7 80 34 37 55 60

"Lumogen T red GG" 6 22 53

Because of the thick layer used, a correction has to be made for the loss of the light absorbed in the layer.

The intrinsic radiant efficiency -n, can then be approximated by [2]

15
where r x is the reflection coefficient of the phosphor

for an infinitely thick layer.

The diffuse reflection of "Ekta S10" is given in

figure 7, the spectral power distribution in figure 8.

300 350 WO 450 500

A(nm)

Figure 7. Diffuse reflection of "Ekta S10."

200-

150

700-

50-

Rel. Soectr. power distr. Ekta S-10

as the dependence on excitation density. During one

month the efficiency of the lumogen was measured

every two days. The stability in time proved to be very

good; no changes were observed within the error of

measurement, which was of the order of ±10 percent.

The efficiency values were not affected even when

the intensity of the UV-radiation was attenuated a thousand times.

3. Excitation in Selected Narrow Absorption

Peaks

A method to determine the efficiencies of phosphors

that have a small absorption of a few percent in narrow,

well defined excitation levels (for the normal case of

Xexc =£ \em ) was described earlier by us [13, 14].

Examples of these powders are rare-earth activated

phosphors, such as YV04 — Eu3+ and NaYF4 — Er^,

where the (visible) excitation peaks are those of the

rare-earth ion. The host lattice absorbs in the UV

region.

A diagram of the set-up is shown in figure 9. The

phosphor is irradiated via a scanning monochromator.

Two measurements have to be carried out, differing

only in the filter used in front of the photomultiplier.

0\ 1 l i I l_ I 3 375 WO 425 450 475 500 525 *-A(nm)

Figure 8. Spectral power distribution of "Ekta S10."

See further subscript fig. 3.

The efficiency data for Na-salicylate at A. exc = 260

nm can be compared with the data given in Samson's

book (ref. [3] ) which are discussed by us in reference

[7], together with some additional data.

Polarization effects in our measurements proved to be negligible, as may be expected for powder materials.

Measurements were carried out with incident polarized

UV radiation, in two directions perpendicular to each

other.

The stability of the lumogen was also tested as well

Figure 9. Schematic diagram of the experimental set-up: ph =

phosphor sample, f= filters, pm = photomultiplier.

One filter transmits only the fight reflected from the

sample, giving the absorption spectrum. In the second

measurement the other filter selects the emission

wavelength region, thus obtaining the excitation

spectrum of that emission. The curves are of the type

shown in figure 10 for YVO4 — Eu3+

. The efficiency is calculated as follows.

The radiant efficiency is the ratio of the emitted

power E to the absorbed exciting power A. The latter

is determined by the area under the absorption curve

of a certain peak with correction for the transmission

Ta of the filter used and for the photomultiplier re- sponse G(\a) in the absorption region. The emitted

16
d) Excitation

spectrum

b) Reflection

spectrum

/

>

YVOA -Eu

/n

§

ov.

-QO

3

Q.O

cb

o

v.

O

co

o

0>103

466 469 466

A (nm)

469

Figure 10. Relative light output of Eu:s - -emission (curve a) and

diffuse reflection (curve b) as a function of wavelength

forYVOrEu.

For curve b ihe zero line is suppressed (the absorption peak has a depth of about 13 percent).

power E is determined by the corresponding area under the excitation curve with correction for the

transmission te of the filter used in this case and the

response G(KE ) in the emission region. For single narrow peaks we can take the ratio of the ordinate

maxima in the absorption and excitation spectra

Ua and UB , respectively, instead of the area. We then

find for the emitted power

E=UE

(kE )dkE

j

p(kE )G(kE ) TE (kE )dkE

where p(kE )dkE is the relative emitted power in a region dkE (integration extended over the total spectral

region of the emission). The absorbed power is given

by

A =

Ua

G(kA )TA Then the radiant efficiency rj is

E

UE TA G(kA ) j

p(kE )dkE

UA jp(kE )G(kE ) TE (kE )dkE

7? =I

=

The quantum efficiency q is derived from the radiant

efficiency by

<7 = 7) f

kEp(kE )dkE

kA j

p(kE )dkE

The error in this type of measurement may be of the

order of 10-25 percent, depending on the value of

the absorption. This large error is caused by the low

value of the absorption in the rare-earth ion.

4. Cathode-Ray Excitation

The radiant efficiency r)p for cathode-ray excitation [2-4, 15, 16] is generally defined as the ratio of

the amount of emitted luminescent power in the

spectral region under consideration to the power of

the incident cathode-ray beam (and not to the power

absorbed by the phosphor layer). Thus no correction

is made for the loss due to reflection of primary

electrons [2, 15, 16].

In this case two really absolute measurements are necessary, viz., that of the emitted power and that of

the power of the cathode-ray beam (fig. 11).

FIGURE 11. Experimental set-up for efficiency measurements with

C. R. excitation.

A. metal chamber, h. anode, f. filament, g. cap, F. focusing coil, D. deflection coils, B. glass tube, C. metal cylinder, P. target plate, a, b, c, and d quartz windows, M. micro- ammeter.

17
The measurements are carried out on thick layers

at the irradiated side. Precautions should be taken to ensure that charging up of the layer is negligible.

The radiant output of the phosphor was compared

with the radiation of a standard lamp which was

diffusely reflected by a MgO layer. A thermopile was

used [2]las a detector .

i i

5. X-Ray Excitation

To measure radiant efficiencies with x-ray excitation

[17-19] thin phosphor layers are used (~ 100/u-m).

This is necessary to minimize the loss in light output

due to scattering and absorption of the emitted

luminescence. The total back-screen emission is collected by a 2 7r-geometry elliptical mirror and

focused onto the photomultiplier detector (see fig. 12),

Calibra ted

detector

Diaphragm

Calibrated source

Figure 12. Diagram for efficiency measurement of light emitting

diodes.

lead shield

elliptic mirror

detector

Figure 13. Experimental set-up for x-ray efficiency measurements.

calibrated detector (A/W • cm2

), e.g., a 150 CV

or 150 UV photocell (calibration National

Physical Laboratory, Teddington, England).

(2) the luminescent output is compared with the

output of a calibrated standard lamp, e.g., a 200 W or 1000 W tungsten - halogen lamp;

calibrated by the National Bureau of Standards

in Washington, D.C. (W/nm • cm2

). In this case

the diode to be measured is replaced by a BaS04-coated screen S.

The use of a 27r-geometry elliptical mirror [21]

instead of an Ulbricht's sphere gave nearly the same

results.

7. References

which is calibrated in absolute units (A/W). The x-ray

absorption coefficients are measured i with a scintillation crystal as well as calculated from the tables of

Storm and Israel [20].

6. Measurements of Light-Emitting Diodes,

Crystals, etc

In cases where the angular distribution of the

emitted radiation does not obey Lambert's law it is not sufficient to measure the emitted radiation in one

direction but the total radiation should be determined.

This can be carried out with the aid of an Ulbricht's

sphere or with an elliptical mirror.

The absolute output can be calibrated in two ways

(see fig. 13):

(1) the luminescent output is measured with a

[1] Nat. Bur. Stand. (U.S.), Tech. News Bull. 42, 145 (1958)

Bril, A., and Hoekstra, W., Philips Res. Repts. 16, 356,

(1961) and Philips Res. Repts. 19,296(1964).

[2] Bril, A., in Kallman-Spruch, Luminescence of Organic and

Inorganic Materials, p. 479 (John Wiley and Sons. Inc. New

York 1962).

[3] Ludwig, G. W., and Kingsley, J. D., J. Electrochem. Soc. 117,348(1970).

[4] Kingsley, J. D., and Ludwig, G. W., J. Electrochem. Soc. 117,353(1970).

[5] See e.g. Samson, J. A. R., Techniques of Vacuum Ultraviolet Spectroscopy, p. 216 (John Wiley and Sons. Inc.. New York.

1967).

[6] Grum, F., CLE.-Report of Subcommittee on Luminescence,

18th Session, London, 1975.

[7] Bril, A., and de Jager-Veenis, A. W., The Electrochemical

Society, Spring Meeting at Toronto, May 1975; J. Electro- chem. Soc. 123, 396 (1976).

[8] Grum, F., and Luckey, G. W., App. Optics 7, 2289 (1968).

[9] Kristianpoller, N., and Dutton, D., Appl. Opt. 3, 287 (1964).

[10] Vavilov, V. S., J. Chem. Phys. Solids 8, 223 (1959).

[11] Morgenshtern, Z. L., Neustruev, V. B., and Epshtein, M. I., J. Appl. Spectros. 3, 35 (1965).

18
[12] Kiittner. H. G.. Selzle. A. L., and Schlag, E. W., Z. Naturf. 29a, 224 (1974).

[13] Bril, A., Blasse, G., and Bertens, J. A. A., J. Electrochem.

Soc, 115, 395 (1968).

[14] Bril, A., Sommerdijk, J. L., and de Jager, A. W., J. Electro- chem. Soc. 122, 5 (1975).

[15] Lehmann, W., J. Electrochem. Soc. 118, 1164 (1971).

[16] Meyer, V. D., J. Electrochem. Soc. 119, 920 (1972).

[17J de Poorter, J. A., and Bril, A., J. Electrochem. Soc. 122,

1086(1975).

[18] Ludwig, G. W., J. Electrochem. Soc. 118,1152(1971).

[19] Grum, F., Costa, L. F., Donovan, J. L., J. Opt. Soc. Am. 59,

848(1969).

[20] Storm, E., and Israel, H. I., Report LA 3753. Los Alamos Scientific Laboratory of the University of California, 1967.

[21] van der Does de Bye, J. A. W., Rev. Sci. Instrum. 40 , 320

(1969)

(Paper 80A3-891)

19

NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 466, Standardization in Spectrophotometry and Luminescence

Measurements, Proceedings of a Workshop Seminar Held at NBS, Gaithersburg, Md., November 19-20, 1975 (issued May 1977).

On the Actinometric Measurement of

Absolute Luminescence Quantum Yields

J. N. Demos and B. H. Blumenthal

Chemistry Department, University of Virginia, Charlottesville, Virginia 22901

(April 9, 1976)

The theory of the measurement of luminescent quantum yields using chemical actinometry is described. The sample's emission intensity is measured by nearly completely surrounding the sample

with an actinometer solution, and the excitation intensity is directly measured with the same type of actinometer. The ratio of the measured sample emission intensity corrected for the fraction escaping

through the excitation ports to the measured excitation intensity is the absolute luminescence yield.

Equations, a suitable cell design, and computer calculated correction factors for different cell dimensions and optical densities are given. The absolute yield of the actinometer is not needed, only

its relative response with wavelength. New quantum-flat actinometers which should greatly simplify the measurements are described.

Key words: Absolute yield; chemical actinometry; correction factors; luminescence; quantum-flat

actinometer; quantum yield.

1 . Introduction

The measurement of absolute luminescence quantum

yields is an important but experimentally difficult area [1, 2, 3]. 1 Most yield measurements are made

relative to a luminescence standard rather than by an

"absolute" method. It is thus imperative for good

accuracy that the luminescent standards be accurately

calibrated. To date, these standards have been derived

almost exclusively from calorimetry or by reference to a standard scatterer, usually with a luminescent

quantum counter detector.

The history of quantum yield measurements has

demonstrated quite painfully that it is exceedingly

difficult to detect and eliminate all systematic errors. Thus, materials selected for standards should be tested

by as many independent and presumably reliable

"absolute" methods as possible and rechecked as new

techniques become available.

We describe here the theory of a conceptually new

"absolute" method for measuring luminescence quantum yields based on chemical actinometers. The

technique avoids many of the intrinsic error sources of

* Paper presented at the Workshop Seminar *Standardization in Spectrophotometry and Luminescence Measurements' held at the National Bureau of Standards, Gaithersburg, Md., November 19-20, 1975.

1 Figures in brackets indicate the literature references at the end of this paper.

the other methods and thus promises to be a useful

check on existing and new standards. The current

availability of numerous lasers with both high intensites and a wide range of wavelengths ranging from

< 250 nm to > 800 nm coupled with new broadband,

quantum-flat actinometers make the actinometric

method most attractive. In addition to the theory we

present a suitable cell design, tabular correction

factors, and describe suitable actinometers.

2. Theory

The actinometric approach for determining yields

measures the excitation intensity and the sample

emission intensity by chemical actinometry; the ratio

of the emission to excitation intensity, both corrected

for the fraction of the excitation beam absorbed, is the absolute quantum yield. The total emitted intensity

is measured by nearly completely surrounding the

sample with the actinometer solution except for a small excitation port and correcting for the small port

losses. The same type of actinometer is then used to measure the excitation beam intensity.

For the actinometer monitoring the emission intensity of the luminescent unknown, the amount of

reaction in the actinometer, Dx (mol of product), is given by

21
Dx = lu

t xFxWE &*

Fx =T(l-10~A x) (1)

where 70 (einstein/s) is the incident excitation intensity,

Ms) is the irradiation time, F., is the fraction of

incident excitation light absorbed by the unknown, T

is the effective transmittance of the entrance window,

A x is the absorbance of the solution to the excitation

beam, 0 is the sample's absolute luminescence effi- ciency, F'E

is the fraction of emitted light captured by

the actinometer, and 0j(mol/einstein) is the actinometer's effective photochemical quantum yield for

the emission band. It is assumed that the excitation

beam is monochromatic, all of the emission passing

into the actinometer is absorbed, and reabsorptionreemission corrections are negligible. O^-is given by

r F{v)Qx {v)dv

j>5

(2)

)dv

where i7 is energy in cm-1

, F(J7) (relative quanta/cm -1

of bandwidth) is the corrected relative emission spectrum and 6x (v) (mol/einstein) is the variation of the

actinometer yield with excitation energy.

In the measurement of the excitation beam intensity,

the amount of reaction in the actinometer, Z)s(mol), is givei, by

Ds = Iot sFsQs

(3)

FS =T(1-10-A

s)

where t s{s) is the irradiation time, Fs is the fraction of

the excitation beam absorbed by the actinometer, T is the same as eq 1, A s is the absorbance of the actinometer solution to the laser, and 0S (mol/einstein) is the actinometer's yield at the excitation wavelength.

The absolute luminescence quantum yield is then

given by

i - io-M / a

1-10-v \e (4)

The D's, A's and t's are directly measurable and Fk

can be evaluated from geometric considerations (see

below). At first it might appear that this method can be no more accurate than the absolute accuracy of the

evaluation of the actionometer's yield, 0(F), a process

which is rarely good to better than_10 percent. In reality

since eq 4 uses the ratio of 0S to 0X, only the variation

of 0(F) with v need be known accurately. As long as data from the same workers are used, this error is likely to be substantially smaller than 10 percent and

quite possibly less than 5 percent. Also, as we shall

show, actinometers with intrinsically quantum-flat

responses are becoming available which will make

0s/0x = 1.000 within ~ 1-2 percent, regardless of how

accurately the absolute yield is known.

0SiB —P0 m c

i i LASER BEAM

\\ A

-:i->~

IB

T2R_L

Figure 1. Cell design for luminescence quantum yield measure- ments by actinometry.

a. Luminescent sample, b. Filling stem for sample, c. Actinometer solution compartment, d. Filling stems for actinometer which are also suitable for a flow actinometer system,

e. Silvering on actinometer jacket ends to reflect emission transmitted down glass walls back into solution. To extend the maximum wavelength of the actinometer, the entire actinometer jacket could be silvered to double the absorption path for emission.

The Model

Figure 1 shows an easily fabricated cell suitable for

measuring absolute yields by actinometry. The cell,

built much like a reflux condenser, has a long, central

irradiation volume with a small diameter filling stem.

The outer jacket contains the actinometer solution

which intercepts and absorbs a large fraction of the

emitted light. The two filling ports on the actinometer

jacket facilitate filling and permit the use of flow

actinometers.

This cell design has numerous advantages. The

system is only suitable for use with laser excitation;

therefore, the monochromatic laser fight eliminates,

in virtually all solution cases, the need for effective

absorbance corrections arising from variation of

absorbance over the excitation band [4]. Questionable

refractive index corrections are also eliminated. The

high symmetry and entering and exiting excitation

ports simplify evaluation of Fx and F'g, further, the

exit port removes unabsorbed excitation fight from the

system so that it cannot affect the actinometer. By

silvering the ends of the actinometer jacket, radiation

light piped down the glass walls can be directed back

into the actinometer. By making LjR large, F'E can be

made to approach unity as closely as desired. By choosing a large L/R, one can easily absorb a large fraction

of the exciting light and still keep the reabsorptionreemission correction small. Thus, the system combines some of the best features of the optically dense

and dilute approaches.

Evaluation of ft To evaluate F'E we make several assumptions, all of

which will be quite accurate or will introduce negligible errors in a well-designed cell. These assumptions are:

(1) the laser beam is centered and its diameter is small

compared to R, (2) all emission not directly striking

the windows is absorbed by the actinometer, (3) all of

the emission transmitted by the cell windows is lost,

(4) reabsorption-reemission corrections are negligible,

and (5) the windows and cell walls are nonabsorbing.

F'e is divided into two terms, a geometric factor for

direct capture of the emitted light and a correction for

22
the emitted light reflected by the windows back into

the cell which is subsequently absorbed by the

actinometer. F'E is given by

F'e — Fe-^ (1 —FE)reffF[tA (5)

where Fe is the fraction of primary emission that would

be absorbed if the windows were perfectly transparent

with no reflection losses, re/f is the fraction of primary

emitted radiation reflected back into the cell by the

windows, and Fra is that fraction of this reflected

radiation which is eventually absorbed by the actinometer, the remainder eventually escaping. Fe can be

evaluated by

2b) /„ { cos arctan

+ cos arctan

R Ad/ (6)

A =

eCexp [-In (10) eC/]

{1-exp [-In (10) eC/]}

5=l-exp [-In (10) eCL]

where e is the sample's molar extinction coefficient at the excitation wavelength and C is the sample concentration. The first and second cosine terms account

for the fraction of radiation striking the entrance and

exit windows respectively as a function of position in

the cell. The A term accounts for the decrease in

emission intensity along the tube caused by absorption. The B term corrects for the total fraction of excitation light absorbed in the cell. For a very large LjR and not too high an optical

density, Fe will approach unity. For extremely high

optical densities, however, the emission front sur- faces at the entrance window where half the radiation

could escape, and Fe approaches 0.5. Equation 6 has no obvious analytical solution and

was evaluated numerically using Simpson's rule. Be- cause of the discontinuities in the integrand at / = 0

and f = L, the evaluation limits were just set very near

both windows. Initially calculations were done on a Hewlett Packard 2000 2 system in time sharing BASIC,

but its —6 — 7 significant figures proved inadequate.

All calculations presented here were done on a Hewlett

Packard 9100 B programmable desk calculator which

has 10-12 significant figures; there were no problems

with convergence. Integration was performed over the

range //L=10"5 to 0.99999 with 200 subdivisions.

Increasing the number of divisions to 1000 caused no changes in the fifth significant figure. Our calculated

F^'s are thus accurate to better than 0.1 percent.

Calculated results for F£'s as a function of LjR and

Ax are given in table 1.

2 In order to describe materials and experimental procedures adequately, it is occasionally necessary to identify commercial products by manufacturer's name or label. In no

instance does such identification imply endorsement by the National Bureau of Standards,

nor does it imply that the particular product or equipment is necessarily the best available

for that purpose.

3. Discussion

Table 1 reveals that, as expected, Fe approaches

unity for large values of LIR with low to intermediate

values of Ax. Also, for very large values of Ax, Fe

seems to approach 0.5. Fe decreases as Ax increases

because of the movement of the emission towards one end where the escape factor is greater.

Table 1. Emission absorption fraction, FE \ L/R

5 10 20 50 100 200

0.5 0.8141 0.9001 0.9479 0.9786 0.9892 0.9946

1.0 .7986 .8866 .9385 .9738 .9865 .9932

1.5 .7776 .8681 .9255 .9670 .9828 .9912

2.0 .7551 .8478 .9109 .9593 .9785 .9889

2.5 .7333 .8277 .8960 .9513 .9739 .9864

3.0 .7136 .8089 .8818 .9434 .9693 .9839

3.5 .6962 .7916 .8683 .9357 .9648 .9814

4.0 .6808 .7760 .8556 .9282 .9604 .9790

5.0 .6555 .7488 .8327 .9141 .9585 .9741

6.0 .6357 .7263 .8125 .9010 .9437 .9694

7.0 .6199 .7072 .7947 .8887 .9359 .9649

8.0 .6071 .6910 .7786 .8773 .9284 .9604

9.0 .5964 .6770 .7642 .8665 .9212 .9561 10.0 .5875 .6647 .7512 .8564 .9143 .9518

As a practical consideration Fe should be as close

as possible to unity. Fortunately this is not difficult.

Even for a cell which is only 2.5 times longer than its diameter (L/R = 5) , Fe is > 75 percent for Ax =S 2, an

acceptable value. More realistic values of L/R for

actinometer cells would be 20-50 which yield Fe > 90

percent for Ax

s£ 2.0. Even values of L/R of 100-200

are feasible; a 50 cm cell would be 0.5-1 cm in diameter; in these cases Fe would exceed 90 percent for

Ax =£ 3. It is thus clear that excellent collection effi- ciency of the emission can be readily obtained.

In the evaluation of 0, F'E rather than Fe is actually

required. We have not done a quantitative analysis

for F'E because re// and Fra are quite difficult to evaluate, but in a well-designed cell the error associated

with replacing F'E by Fe is quite small. For example,

in a cell with a large LjR, most of the emission incident on the cell windows will be at near normal incidence;

thus, we can use re//~0.04 for a glass-air interface.

For Fe = 90 percent, F'E will be < 0.5 percent greater

than Fe-, and the error falls for larger F^'s.

Until recently the potential choices of actinometers were limited to ferrioxalate and Reinecke's salt. The

ferrioxalate actinometer will yield total absorption

of the emitted radiation up to ~ 480 nm using a 5 cm

thick actinometer solution (0.15 F). The yield is not

strongly wavelength dependent from 254 nm to 480

nm, and calibration is_sufficiently detailed to permit

accurate evaluation of Qx . Reinecke's salt offers much deeper red penetration, ~ 610 nm for 2 X 10 2M solution and a 5 cm minimum

cell length. The yield is more nearly constant than

ferrioxalate over the 390-620 nm range. Unfortunately

23
Reinecke's salt has serious disadvantages. The yield

changes sharply below 390 nm, and detailed data in

this region are lacking. The complex is difficult to dissolve at high concentrations and undergoes a

relatively rapid thermal reaction (~ 0.6%/h). Although

it is about an order of magnitude less sensitive than

ferrioxalate, this is not likely to be a problem with a high intensity laser excitation source. New photosensitized actinometers promise to eliminate the previous difficulties. For example, the tris- (2,2-bipyridine)ruthenium(ll) photooxidation of tetra- methylethylene has been developed as an actinometer

for high power lasers [5]. The system should be in- trinsically quantum flat, because the lowest excited

state is responsible for the sensitization; luminescence

experiments have verified that the efficiency of population of the emitting state is constant to ~ ±2 percent over this region [6]. A solution 10 -3A/in the ruthenium

complex will absorb all radiation below ~ 520 nm in a 2 cm pathlength. By using similar osmium(ll) complexes as the sensitizer [6, 7, 8], total absorption of the

emission and a quantum flat response below ~ 700

nm should be realized. These systems use volumetric

monitoring of the consumed 02 and are thus not very

sensitive, but laser excitation supplies adequate

intensity. Finally, because the consumed O2 must be

replaced and inhomogeneity of the reactants can be a problem in a static system, these actinometers must be

operated in a flow system.

An analogous system which also shows promise is the methylene blue sensitized photooxidation of tetra- methylethylene. Solutions can easily be made totally

absorbing to beyond 700 nm in a 1 cm pathlength, and

the yield is comparable to the Ru(ll) and Os(ll) systems.

The quantum yields may, however, not be perfectly

flat, and minor corrections may be required.

In summary, we feel that the actinometric method,

although too complex for routine measurements, will

prove especially useful in developing primary lumines- cence quantum yield standards. This method eliminates most of the error sources inherent in other

absolute techniques, and thus supplies a valuable

check. The technique is currently feasible for compounds emitting below 520 nm, and with the natural

evolution of actinometry, operation to 700 nm and

beyond should soon be feasible.

Acknowledgment is made to the National Science

Foundation, the donors of the Petroleum Research

Fund, administered by the American Chemical Society,

and to the Research Corporation for support of this

work.

4. References

[1] Lipsett, F. R., Progr. Dielectrics, 7 , 217 (1967).

[2] Demas, J. N., and Crosby, G. A., J. Phys. Chem. 75, 991 (1971).

[3] Crosby, G. A., Demas, J. N., and Callis, J. B., J. Res. Nat. Bur. Stand. (U.S.), 76A (Phys. and Chem.), No. 6, 561-577 (NovDec. 1972).

[4] Demas, J. N., Anal. Chem. 45, 992 (1973).

[5] (a) Demas, J. N., Harris, E. W., and McBride, R. P., Lasers in Physical Chemistry and Biophysics (Elsevier, New York,

N.Y., 1975), p. 477.

(b) Demas. J. N., McBride. R. P., and Harris. E. W., J. Phys.

Chem.. accepted.

[6] Demas, J. N., and Crosby, G. A., J. Am. Chem. Soc. 93 , 2841

(1971).

[7] Demas, J. N., Harris, E. W., Flynn, Jr., C. M., and Diemente, D.,

J. Am. Chem. Soc. 97. 3838 (1975).

[8] Demas. J. N.. Harris. E. W.. and McBride. R. P.. submitted.

(Paper 80A3-892)

24
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 466, Standardization in Spectrophotometry and Luminescence

Measurements, Proceedings of a Workshop Seminar Held at NBS, Gaithersburg, Md., November 19-20, 1975 (issued May 1977).

The Calorimetric Detection of Excited States

James B. Callis

Department of Pathology, University of Washington Medical School, Seattle, Washington 98195

(April 9, 1976)

Calorimetric techniques offer the photophysicist and photochemist the opportunity to measure

a number of parameters of excited states which may be difficult to obtain by other techniques. The

calorimetric strategy seeks to measure the heating of a sample resulting from radiationless decays or chemical reactions of excited states. Heating is best measured through volume and pressure trans- ducers, and four calorimeters based on these are described. With calorimetric instrumentation one

can perform measurements on samples in the gas, liquid and solid phases over a wide temperature

range. Moreover time dependent processes with time constants ranging from microseconds to seconds

are amenable to study. Examples of the application of calorimetric techniques to the determination

of quantum yields of fluorescence, triplet formation and photochemistry are given.

Key words: Absolute quantum efficiency; absolute quantum yield; calorimetry: luminescence; photoacoustic spectrometer; piezocalorimeter; transducers; triplet formation

1 . Introduction

In understanding the nature of excited electronic

states it is well appreciated that a wide variety of

parameters are accessible to photometric measurement. Among them are the absorption spectrum of

the excited state, the excitation spectrum, and the

lifetime. If the excited state decays by emission of

photons, one can also measure the spectral distribution of emission, the polarization, and the quantum

yield of emitted photons. Unfortunately, it is not so generally appreciated that a number of parameters of an excited state are also accessible to calorimetric

measurement. The calorimetric strategy seeks to measure how much of the light absorbed by a sample

is converted to heat energy by radiationless processes

and/or photochemistry. Parameters which can be

measured include: the lifetime of an excited state,

the excitation spectrum for a particular process, the

energy yield of a radiationless process, and the en- thalpy of a photochemical process.

A simple example illustrates how calorimetric meas- urements can complement photometric measurements.

Most air saturated liquid solutions of luminescent

organic molecules exhibit only fluorescence at room

temperature. By measuring the ratio of the heating of

the fluorescent substance in response to photoexcitation to that of a non-fluorescent but equally absorbing

substance, one obtains the energy yield of radiation-

*Paper presented at the Workshop Seminar 'Standardization in Spectrophotometry and Luminescence Measurements' held at the National Bureau of Standards. Gaithersburg, Md., November 19-20, 1975.

less processes Yh [1, 2].

1 In the absence of photochemistry, the fluorescence energy yield is the complement of Yh, and the quantum yield of fluorescence

<!>/ is related to it by the formula

4>/= (valvf)(l-Yh ) (1)

where i> a and i>f are the average frequencies of absorbed and emitted photons respectively. Calorimetric quantum yields determined in this manner

[1, 2, 3] are among the most precise and accurate

reported in the literature, and in addition provide a valuable independent technique for verifying the many

assumptions that go into the derivation of quantum

yields from photometric measurements [4, 5]. Despite

these advantages, very few quantum yields have been

measured calorimetrically. This unfortunate situation

exists because most workers in the field are unfamiliar with calorimetric techniques, and moreover,

the measurements are time consuming and tedious

to perform. It is the purpose of this paper to point out

some recent work which shows that using capacitor

microphones and piezoelectric crystals as heat flow

transducers, calorimetry can be a rapid, simple and

sensitive technique for use in measuring a wide

variety of parameters of excited states. Also, samples

in the gas, liquid and solid phases, including thin

films and monolayers are amenable to study.

1 Figures in brackets indicate the literature references at the end of this paper.

25
2. Types of Calorimeters Suitable for Measuring Photochemical and Photophysical

Processes

The most obvious approach for detection of heat

production is to use a conventional calorimeter based

upon the usual temperature sensors: thermistors and

thermopiles. We will not discuss these instruments

here because they have already been reviewed [3, 4,

5] and because they have inherent disadvantages in

sensitivity, risetime and speed at which measurements

can be made. Instead, we will concentrate on alternative strategies for measuring heat flow based on volume and pressure changes produced in the sample.

In general, addition of an amount of heat dQ to the

sample gives rise to both a pressure change dP and a volume change dV according to the thermodynamic

relationship [6]

dQ=^jr+cAdP (2)

ay a

where Cp and Cv are the heat capacities at constant

pressure and constant volume, V the volume of the

solution, a = V~ 1 (dV/dT)p is the coefficient of thermal

expansion, and /3 =— V'^dV/dP) T is the compressibility of the sample. Three of the calorimeters we will

describe use the capacitor microphone to detect

volume changes in the sample. In all of these devices

the sample is enclosed in a cell with rigid walls. One

of these walls, generally normal to the direction of

propagation of exiting light is replaced by the compliant

diaphragm of a capacitor microphone. Because of the

diaphragm, a second relationship between dP and

dV must be simultaneously obeyed:

dP= K dVIV. (3)

We have assumed that the changes are small so that

a linear relationship exists, and k, the linear constant,

is approximately given for a cubic cell by k\€ where k

is the force constant for displacing the diaphragm,

and /' is the linear dimension of the cell. Combining

eq (2) and (3) we have

dV=aVdQI(CP + CvK(3). (4)

Equation (4) shows that: (a) the volume change is in- dependent of any gradients in the distribution of energy

in the cells; (b) the largest volume changes are obtained

for samples which have the highest values of a and

the lowest heat capacities (gases give the largest signals; water gives low signals); (c) the compliance of

the diaphragm must be kept low enough so that the

product k/3 is as small as possible.

The capacitor microphone for measuring the volume

changes consists of the diaphragm and a stationary

electrode spaced a small distance apart; together they

form a capacitor whose capacitance C is given by

C = eAjx (5)

where e is the dielectric constant, A is the area of the

electrodes, and x is the spacing between them, and

edge effects were neglected. If the change in spacing

of the electrodes is small enough, the capacitance will

be related to it linearly. Several methods have been

used successfully for the detection of the capacitance

change. In the most common method [7], the microphone is polarized either with an externally supplied

dc voltage or by placing an electret [8] in the gap

between the electrodes; when the capacitance changes,

charge flows to maintain a constant voltage. The charge

flow is then converted to a voltage change by a charge

sensitive pre-amp [9]. Capacitance changes can also

be detected with an ac bridge circuit [10]. Even with

simple detection systems, a displacement of the diaphragm of the order of one angstrom is easily measured

with a bandwidth of 10 kHz [6]. The frequency re- sponse of the microphone is linear over a very wide

range; the upper limit is set by the lowest mechanical

resonance of the diaphragm (10-20kHz), and the lower

limit is determined by the low frequency cut-off of the

electronics or the thermal instabilities of the system.

With these fundamental considerations in mind, we

may now discuss three types of calorimeters based

upon the use of capacitor microphone pressure

transducers: the "acoustic spectrophone" for study

of gas phase systems, the "optoacoustic cell" for study

of thin films and thin sections of solid materials, and

the "flash calorimeter" for studies of liquid samples.

The acoustic spectrophone has been widely used as a technique for infrared gas analysis [12] and for

measuring vibrational relaxation rates [13]. A typical

acoustic spectrophone [11] consists of a cylindrical

cell with transparent windows at each end to allow

radiation to enter and leave; the microphone is generally mounted on the cylindrical wall with the diaphragm normal to the direction of propagation of the

excitation beam. Often, a regulated leak is provided

so that long term pressure drifts can be relieved.

The design of acoustic spectrophones is discussed

in detail by Rosengren [14], Parker and Ritke [11] and

Kerr and Atwood [15]. The ultimate limit of signal to noise arises from the Brownian motion of the gas

molecules. Present designs can come within two

orders of magnitude of this limit at reasonable gas

pressures. The present limitations arise from noise

in the detection electronics, temperature instabilities

(especially at low frequencies) and spurious contributions to the signal arising from gas adsorbed on the

windows [14]. Even with these limitations, energy in- puts as small as one microwatt may be easily detected.

Parker has shown [11] that the rise time for the volume

change is set by the lowest acoustical resonance

frequency in the cavity whose frequency is given by

c/2/, where c is the speed of sound in the gas, and / is the length of the cavity.

A device similar to the acoustic spectrophone has

been developed by Rosencwaig [17] for the study of

radiationless processes and photochemistry in thin

films of solids, and semisolid materials such as crystals, evaporated films, powders, gels, thin layer

26
chromatography plates, and even thin layers of tissue.

The photoacoustic cell is quite similar to the acoustic

spectrophone of Parker, except it is much shorter in

cavity length. The thin sample is simply mounted

flush with the exit window, and the cell is filled with a suitable gas which is transparent to the exciting

radiation.

The origin of the photoacoustic effect is believed to be as follows [11, 18]: irradiation of the sample with

pulsed or chopped steady state fight results in a localized heating due to non-radiative decay processes

by the excited states. Some of the heating is transferred via diffusion from the solid to a thin boundary

layer of gas adjacent to the solid. Adiabatic expansion

of the gas then gives rise to a pressure wave in the

gas which is detected by a capacitor microphone. A

quantitative version of this process has been proposed

[11, 18]. Like the acoustic spectrophone this device can easily detect microwatts of absorbed radiation,

and the risetime is set by the transit time for sound in

the cavity.

The third device based on the use of the capacitor

microphone is the flash calorimeter of Callis, Gouterman and Danielson [6]. A schematic of the device is given in Figure 1. The sample cell is constructed

from 25X25 mm square Pyrex 2 tubing. Joined to the

sides are two 4-mm Pyrex-Teflon vacuum stopcocks.

One of these provides connection to a vacuum fine,

allowing for introduction of degassed samples. The

other stopcock opens into a small relief reservoir. It

provides a controlled leak so that liquid can slowly

enter or leave the cell, thus preventing slow pressure

changes that would occur in a completely closed cell

subject to temperature drifts. To allow use of a circular

diaphragm a short piece of 25-mm Pyrex tubing is fused

to the top of the cell. The diaphragm is made from 1 mm aluminum, which is sufficiently thick so that it does not deform permanently under vacuum, yet not so thick that the product k/3 exceeds unity. The microphone consists of the diaphragm, an epoxy glass

circuit board spacer, and a stationary electrode-guard

ring assembly fabricated from brass and epoxy glass

circuit board material. The spacer ring is ground down

until the gap between diaphragm and stationary electrode is approximately 0.25 mm and the entire assembly is potted with epoxy cement. The cell is mounted

in a brass block which is temperature stabilized by

means of a thermoelectric heat pump. The entire

assembly is mounted in an acoustically shielded

aluminum box which rests on a vibration isolation

table.

As with other devices based on the use of microphones, the rise time of the flash calorimeter is determined by the transit time for sound in the cavity. This

limits the use of the instrument in kinetic studies to phenomena with time constants longer than 100/u.s. The

sensitivity of the flash calorimeter is quite remarkable:

a displacement of the diaphragm of 10~8 cm is easily

detected with a bandwidth of 10 kHz. For ethanol

this corresponds to a temperature rise of ~ 10-6 °C or

Stationary electrode guard ring

FIGURE 1. Flash calorimeter schematic.

2 In order to adequately describe materials and experimental procedures, it is occasionally necessary to identify commercial products by manufacturer's name or label. In no instance does such identification imply endorsement by the National Bureau of Standards, nor does

it imply that the particular product or equipment is necessarily the best available for that purpose.

an energy input of ~ 64/i.J. The limits of detection at high frequencies are largely due to the noise in the

preamplifier stage; we are presently many orders of

magnitude above the limit imposed by the thermal

noise of the sample.

27
We now describe an instrument which is particularly

well suited for measurement of radiationless processes

in bulk solids. This device, the piezoelectric calorimeter, uses a piezoelectric crystal to measure pressure

changes in the sample. In certain crystals and polycrystalline materials with assymetric charge distribution, an applied pressure results in displacement of

the positive and negative charges relative to each

other. The displacement of the charges can be measured by applying electrodes to the surfaces and measuring the potential difference between them caused

by charge migration. Piezoelectric crystals are available which are rugged, inexpensive, and linear and

which will perform at temperatures from 4 K to 700 K.

A simple piezoelectric calorimeter is shown in

figure 2. It consists of a cylindrical sample (we have

used polymethyl methacrylate samples in which the

organic compound of interest is dissolved), and a

cylindrical piezoelectric transducer of the same radius

as the sample. The transducer and sample are clamped

rigidly together by an aluminum frame.

- -Frame

Piezoelectric effect

transducer

-•-[--Aluminum foil

electrode

Plastic sample

FIGURE 2. Piezocalorimeter schematic.

The piezoelectric crystal may be conveniently

thought of as measuring the pressure generated by

heating at constant volume. Equation (4) then becomes

dP=dQalpCv (6)

The open circuit voltage response to a pressure change

is given by:

E = gtdP (7)

9 where g is the open circuit voltage constant in units

of m2/C, t is the thickness of the crystal in m, and E

is the voltage produced [7]. The simplest method for

operating these devices is to use a charge sensitive preamplifier, as with the capacitor microphone. The upper

end of the frequency response will then be limited by

the lowest acoustic resonance, while the lower end will

be limited by the low frequency response of the

preamplifier.

The response of the piezoelectric calorimeter to an infrared heating flash shows characteristics similar

to that of the flash calorimeter. The ring period is shorter due to the higher speed of sound in the cavity,

but is not damped as effectively. With the present

apparatus we can easily detect a step rise of E =S 10_3 V

which corresponds to a pressure change of 0.073

dyn/cm2 for a lucite rod of 1 cm thickness, which in

turn corresponds to a temperature change of 6.7 X 10"7 °C. For our samples we find that dQ ~ 4.7 ptcal is easily

detected.

In addition to the calorimeter, the measurement of

calorimetric parameters also requires a light source,

a means for selecting a bandwidth of the radiation,

and suitable signal processing electronics. The ideal

light source for calorimetry must be of high intensity,

stable with time, and of high spectral purity. Clearly

the laser approaches most closely this ideal, and a number of authors have employed both cw and pulsed

lasers. For excitation spectrum studies a Xenon arc lamp-monochromator combination possesses the one

advantage of infinite wavelength tunability and the

capability of ultraviolet irradiation. Since the calorimeters are ac coupled, the light source must be intensity

modulated. For a cw light source, a simple and common

method to achieve intensity modulation is with a mechanical chopper. In this case, the most attractive

form of signal processing is to use a phase sensitive

amplifier, operated in synchrony with the chopper. If

all of the heating from the sample appears with a rate

constant greater than the chopping rate, then all of

the signal will be in phase with the chopper. However,

if some of the heating arises from processes which

have rate constants comparable to or less than the

chopping rate, then some of the heating will be out of

phase. Quantitation of these effects leads to methods

for measuring rates of relaxation of excited states and

the yield of heating of a particular process. The disadvantages of modulation of a cw source and phase

sensitive detection is that the signal decreases linearly

with the frequency, and that a series of measurements

must be made at a number of different frequencies if the order of the kinetics is to be specified.

For the measurement of the time dependence of

the heating, the use of a pulsed fight source is advantageous. Large amounts of energy can be output in

very short times, thus providing a good signal to noise

ratio for fast time dependent processes, as well as giving the heating curve directly. This technique re28
quires some method for transient recording and signal

averaging is often desirable. A potential problem with

pulsed excitation is that it strongly excites the lowest

cavity resonance of the chamber. The resultant oscillation is superimposed on the signal and often ob- scures the heating curve at short times.

3. Applications of Calorimetric Techniques

3.1. Fluorescence Quantum Yields

In the introduction, we noted the advantages of the

calorimetric strategy for determination of quantum

yields. Thus far, all of these measurements have been

done on dilute liquid solutions which are easily done

photometrically. In contrast determination of quantum

yields from thin layers of powdered samples is a very

difficult procedure to perform photometrically [19, 20].

Some pioneering work by Rosencwaig [17, 21] illus- trates how the optoacoustic spectrometer can be used

to advantage on these systems. A number of trivalent rare earth ions show narrow absorption bands in the

visible and ultraviolet which arise from inner shell

f-f* transitions. Some of these levels exhibit fluorescence, and the fluorescence quantum yield of a

particular level exhibits a marked dependence upon

which level is excited [22]. Rosencwaig studied the

photoacoustic excitation spectrum of samples of

powdered holmium oxide. The first sample contained

cobalt and fluorine impurities in sufficient quantity to quench all of the luminescence. He found that the

photoacoustic spectrum, when corrected for the wavelength dependence of the relative output of the

excitation beam, corresponded well with the observed

absorption spectrum. In contrast, the photoacoustic

spectrum of pure H02O3 exhibited a spectrum in which

some of the fines were greatly diminished in intensity;

the latter of course involve excited states which decay

by radiative processes. The information contained in

these two scans, together with lifetimes and lumines- cence spectra taken by exciting at each major

absorbance would provide, for the first time, a complete

picture of the dynamic interrelationships of these

excited states.

3.2. Quantum Yields of Triplet Formation

A knowledge of quantum yields of triplet formation is important in understanding the intersystem crossing

process, and also in understanding the many photochemical reactions and energy transfer process which

take place through the intermediacy of a triplet state. A number of ingenious methods exist for determination

of triplet yields [23] but all are based on the use of

various assumptions which are difficult to verify

experimentally. The calorimetric strategy offers an

attractive alternative to the other techniques, and also

provides an independent check on the assumptions

used in the other methods.

The calorimetric method is based on the fact that

the lifetime of the lowest triplet state of an organic

molecule is long compared to that of its excited singlet

states. Thus, we expect that a delta function excitation

pulse will produce fast heating due to relaxation of the

singlet states, and slow heating due to relaxation of the

triplet states. The heating may then be partitioned into

(?tot = C?fast (?slow (8)

It has been shown (6) that <& t can be obtained from the

relation:

(&t = Qsl0V,[hpin -<Z>fhvf]IQmE! (9)

where 4>/ and 4>r are the quantum yields for fluores- cence and triplet yields, vj and Vin are the average

fluorescence and absorbed frequencies, and Et is the

energy of the triplet state. As an example of the use of the flash calorimeter

we show the heating response of 10-4 M acridine

orange to flash excitation in figure 3. The results are

the average of 100 flashes. Clearly, there are two kinds

of heating, as expected. Furthermore, the observed

heating obeys the expected [6] time dependent form,

<?(*)= [<?fast + £>s.ow ( 1 -e-# ) ] e-tlRC ( 10)

where k* is the triplet decay time, and RC is the decay

time of the ac coupled electronics. For comparison,

in figure 4 we show the heating response of 10~ 4 M

anthracene in polymethyl methacrylate as studied

with the piezoelectric calorimeter. It also shows the

10" M Acridine Orange in Glycerol

lOOn

Time , m sec

Figure 3. Calorimetric response of degassed acridine orange in glycerol at room temperature.

29
90-,

Time, msec

FIGURE 4. Calorimetric response of anthracene in polymethyl

methacrylate at room temperature.

same type of heating response as predicted by eq (10).

The value <J>, = 0.72 for anthracene in plastic compares

well with that determined in mineral oil by other

methods [23].

3.3. Applications to Photochemistry and Photobiology

In addition to heating from radiationless transitions,

one may also detect heating from photochemical

processes. Suppose that the sample is excited by Nex photons of energy jF,,,, and either decays radiationlessly

to the ground state, or by photochemistry with a probability Op to a stable product state of energy Ep

above the ground state. The total heating dQ will then

be given by

dQ = NeAEin -<i>pEp). (11)

Equation (11) shows that energy levels of photochemical products can be obtained if the yields are known, or the yields can be determined if the energy

levels are known. Also, the rates of formation of the

photochemical products can be measured or deduced

and finally, as Rosencwaig has pointed out [17], the

excitation spectrum of the photochemical process can

be obtained, and compared with the conventional

absorption spectrum.

The work of deGroot et al. [24] illustrates the use

of the acoustic spectrophone to study photochemical

processes of acetaldehyde. These authors find that

at pressures below a few torr the optoacoustic spectrum

in the region 230-360 nm resembles the normal

absorption spectrum of the compound. When the

pressure is increased, however, a minimum appears in

the spectrum at 290 nm which indicates that at least

some of the absorbed light energy is no longer con- verted to heat on the time scale of chopping. The

authors ascribe this phenomenon to the efficient

formation of a high energy unstable intermediate, a dioxetene. Studies with a pulsed light source shows

that the intermediate decays to stable low energy

products with a time constant of 2 ms. At wavelengths shorter than 290 nm the heating is again rapid;

this is ascribed to the rapid decomposition of

vibrationally hot dioxetene to low energy products.

Another interesting study using the acoustic

spectrophone has been reported by Kaya, Harshbarger

and Robin [251. These investigators observed the gas

phase optoacoustic excitation spectrum of biacetyl

under a wide variety of conditions. They were able to demonstrate that the lowest excited triplet could be

populated only by excitation at wavelengths longer

than 443 nm; irradiation at shorter wavelengths re- sulted in intersystem crossing to the second excited

triplet which then decayed rapidly and directly to the

ground state. In mixtures of benzene and biacetyl,

the authors were able to show that energy transfer

from benzene to the biacetyl triplet manifold takes

place only when exciting into the lowest vibronic bands

of the lowest excited singlet of the donor. In pyridinebiacetyl mixtures, the lowest ra — 77* state of pyridine

was found to transfer to the triplet manifold of biacetyl,

but the lowest 77 — 77* state does not. A final study by Callis, Parson and Gouterman [26]

illustrates the potential application of calorimetric

techniques to the study of photobiological systems. A

very useful model system for the study of the bioenergetics of photosynthesis is the chromatophore of

photosynthetic bacteria. The chromatophores are vesicular fragments of the bacterial membrane, which

contain the photosensitive pigments and most of the

enzymes necessary for light induced electron transport

and coupled phosphorylation. In the chromatophore

light induces a cyclic electron flow which is coupled

in some unknown manner to the formation of high

energy phosphate bonds, in which the free energy

available from the photons are stored.

In the study of photochemical reactions in the liquid

and solid phases using a volume transducer we must

include the possibility of a volume difference AVr between reactants and products, as well as a contribution from heating. For a system which either returns

radiationlessly to the ground state or converts to a product state Ep with efficiency <J> P , the total volume

change A.V will be

AV=Nex (Ein - 3>pEp ) {a/pCp ) + Nex <t> p AVr . ( 12

If Ep and &Vr are temperature independent, the

measurement of bV at two different temperatures

allows one to obtain Ep and AVr . Figure 5 shows the volume response of Chromatium

chromatophores to weak flashes at temperatures of

23 °C and 4°C. The traces labeled "light" were

obtained in the presence of a strong cw light which

saturated all photochemical processes, and resulted

in the conversion of all of the input energy to heat.

The light response at 4°C is much smaller due to the

30
LIGHT

FIGURE 5. Volume changes ofChromatium chromatophores in response to flash excitation.

reduced magnitude of a/pCp

at this temperature. In

the dark at 23 °C, a weak flash causes an instantaneous

volume decrease which is then followed by a fast

recovery almost to the base line. In the dark at 4°C

we observe an instantaneous volume decrease which

recovers about half way with a time constant of 250 /jls. From a quantitative evaluation of these data, we have

concluded that: (a) the initial high energy state of the

photosynthetic apparatus does not possess a significant

enthalpy change from the ground state, and thus the

free energy change available from the photon is stored

in an excited state characterized by negative entropy;

(b) the high energy state also has a decreased volume

from the ground state. Further studies have shown

that the volume changes are altered by the presence

of ion transporting antibiotics, and uncouplers of

phosphorylation. The flash calorimeter thus appears

to be a valuable tool for the study of energy conservation in photosynthetic systems.

4. Conclusions

Calorimetric techniques can be used to measure a number of parameters of excited states such as

lifetimes, excitation spectra, energy yields of radiationless and photochemical processes, and enthalpies of

photochemical reactions. Simple calorimeters capable

of measuring these parameters have been developed

for the study of molecules in the gas, solid and liquid

phases. A wide variety of measurements now exist

which show the usefulness of calorimetric techniques

for studies of absolute fluorescence quantum effi- ciencies, quantum yields of triplet formation, photochemical processes in the gas phase, and for studies

of energy storage in photosynthesis. As more in- vestigators realize how simple and convenient these

measurements are, we can expect an increase in the use of calorimetric techniques in photophysical and

photochemical studies.

5. References

[1] Alenstev, M. A., National Research Council of Canada Technical Translation TT-433, Zh. Eksp. Fiz. 21, 133 (1951).

[2] Seybold, P. G., Gouterman, M., and Callis, J. B., Photochem.

Photobiol. 9,229(1969).

[3] Gelernt. B., Findeisen, A., and Poole, J., J. Chem. Soc. Faraday

Trans. II, 70, 939 (1974).

[4] Demas, J. N., and Crosby, G. A., J. Phys. Chem. 75, 991

(1971).

[5] Crosby, G. A.. Demas, J. N., and Callis, J. B., J. Res. Nat. Bur. Stand. (U.S.), 76A (Phys. and Chem.), No. 6, 561-577

(Nov.-Dec. 1972).

[6] Callis, J. B., Gouterman, M., and Danielson, J. D. S., Rev. Sci.

Inst., 40, 1599(1969).

[7] Lion, K. S., Instrumentation in Scientific Research (McGrawHill, New York, 1959).

[8] Sessler, G. M., and West, J. E., J. Acoust. Soc. Am., 40, 1433

(1966).

[9] McCray, J. A., and Cahill, T. A.. Electronic Circuit Analysis

for Scientists (Wiley and Sons, New York, 1973).

[10] Koidan, W.J. Acoust. Soc. Am. 29, 813 (1957).

[11] Parker, J. G., and Ritke, D. N., J. Chem. Phys., 59, 3713

(1973).

[12] Hill, D. W., and Powell, T., Non Dispersive Infra-Red Gas

Analysis in Science, Medicine, and Industry (Plenum, New

York, 1968).

[13] Cottrell, T. L., and McCoubrey, J. C, Molecular Energy Transfer in Gases (Butterworths, London, 1961), pp. 64-73.

[14] Rosengren, L., Appl. Opt. 14, 1960 (1975).

[15] Kerr, E. L., and Atwood, J. G.. Appl. Opt. 7, 915 (1968).

[16] Patel, C. K., Burkhardt, E. G., and Lambert, C. A., Science,

184,1173(1974).

[17] Rosencwaig, A., Anal. Chem. 47, 592A (1975).

[18] Rosencwaig, A., and Gersho, A.. Science, 190 , 557 (1975).

[19] Wrighton, M. S.J. Phys. Chem. 78, 2229 (1974).

[20] Bril, A., Somerdijk, J. A., and de Jager-Veenis, A. W. J., Elec- trochem. Soc. 122, 660 (1975).

[21] Rosencwaig, A., Physics Today, 28, 23 (1975).

[22] Wybourne, G. G., Ed., Spectroscopic Properties of the Rare

Earths (Inter-science Publ., New York, 1965).

[23] Callis, J. B., Ph.D. Thesis, University of Washington, Seattle, 1970.

[24] deGroot. M. S., Emeis, C. A., Hesselman. I. A. M., Drent. E., and Farenhorst, E., Chem. Phys. Lett. 17, 332 (1975).

[25] Kaya, K„ Harshbarger, W.. and Robin, M., J. Chem. Phys.,

60,4231 (1974).

[26] Callis, J. B., Parson, W. W., and Gouterman, M., Biochem.

Biophys. Acta, 267, 348 (1972).

(Paper 80A3-893)

31

NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 466, Standardization in Spectrophotometry and Luminescence

Measurements, Proceedings of a Workshop Seminar Held at NBS, Gaithersburg, Md., November 19-20, 1975 (issued May 1977).

Fluorescence Efficiency of Laser Dyes *

K. H. Drexhage

Research Laboratories, Eastman Kodak Company, Rochester, New York 1 4650

(April 9, 1976)

The fluorescence efficiency of xanthene dyes, oxazine dyes, and 7-aminocoumarins is discussed.

Relations with the molecular structure are pointed out and dependence on solvent and temperature is explained. Several new fluorescence standards are suggested.

Key words: Aminocoumarins; carbazine dyes; deuterium effect: fluorescence quantum yield: laser dyes; molecular structure; oxazine dyes; quenching; xanthene dyes.

1 . Introduction

The recent development of the dye laser [1]

1 has

opened up an important new field of applications for

organic dyes. This has led to a renewed interest in the

theory of nonradiative transitions in dyes and also to the synthesis of new highly fluorescent dyes. In this

article we review briefly the relations between fluor- escence and molecular structure in the most important

classes of laser dyes: xanthenes, oxazines, and 7-aminocoumarins. Following this discussion specific suggestions for improved fluorescence standards are made. 2

2. Xanthene Dyes

The chromophore of xanthene dyes has typically

the following structures

R'

* Paper presented at the Workshop Seminar 'Standardization in Spectrophotometry and Luminescence Measurements' held at the National Bureau of Standards, Gaithersburg, Md., November 19-20, 1975.

1 Figures in brackets indicate the literature references at the end of this paper.

2 In order to describe materials and experimental procedures adequately, it is occasionally necessary to identify commercial products by manufacturer's name or label. In no instance does such identification imply endorsement by the National Bureau of Standards, nor does

it imply that the particular product or equipment is necessarily the best available for that purpose.

R'

Depending on the end groups, in particular number

and type of the substituents R, the maximum of the

main absorption band falls somewhere in the range

480-580 nm. The transition moment is parallel to the

long axis of the molecule [2]. With R' = H and amino

end groups the dyes are called pyronins. Due to a con- venient syntheses with phthalic anhydride many

xanthene dyes have R ' — carboxyphenyl and are called

fluorescein or rhodamines (fig. 1). The methyl substituents of Rhodamine 6G have practically no influence on the optical properties of the dye except for the

dimerization in aqueous solution which we are not

concerned with here. The absorption maximum of the

main band occurs almost at the same wavelength in

pyronins and rhodamines, if the end groups are

identical. The absorption band near 350 nm is stronger

in rhodamines than in pyronins, and rhodamines show

a slightly larger Stokes shift than pyronins. The

chemical stability of rhodamines is generally su- perior, as pyronins in alkaline solution are readily

oxidized by dissolved oxygen to form a colorless,

blue fluorescing xanthone.

33
Rhodamme 110

510 nm

Rhodamine 6G

530 nm

C?H2n 5 Rhodamine B 554 nm

Figure 1. Molecular structure of rhodamine dyes; absorption maximum in ethanol.

C ?H2n5

Rhodamines like Rhodamine B react to pH variations

in an interesting manner. The carboxyl group is completely protonated in acidic solution, but dissociates in

alkaline solution. The negative charge has an inductive

effect on the central carbon atom of the chromophore.

The maxima of the main absorption band and of the

fluorescence are shifted to shorter wavelengths,

and the extinction coefficient at the absorption maximum is slightly reduced. While these effects are rather

weak in aqueous solution [3], the wavelength shift

amounts to about 10 nm in polar organic solvents

(methanol, ethanol, etc.) [4, 5, 6, 7]. When Rhodamine

B, which is usually obtained as the hydrochloride,

concentration (except for aqueous solutions, where aggregation takes place, and for strongly acidic conditions, where protonation of the amino groups occurs).

Because of the symmetry of the rhodamine chromophore, there is no dipole moment parallel to its long

axis. As a consequence, the Stokes shift is small, and

the fluorescence band overlaps strongly the absorption

band (fig. 2) [10]. Also, there is only little variation of absorption and fluorescence maxima with solvent polarity

[4, 5]. Provided there are no heavy-atom substituents,

the rate of intersystem crossing from Si is very low

in xanthene dyes, which is in accordance with our loop

rule [11]. Phosphorescence is weak even in low temperH 5 C^©

H5C2

C? HS

+ H

is dissolved in ethanol, the relative amounts of the two

forms of the dye are determined by this acid-base

equilibrium. The dissociation increases on dilution

causing a shift of absorption and fluorescence to shorter wavelengths. This concentration dependence

of the spectra is therefore not due to a monomerdimer equilibrium, as was claimed in recent papers

[8, 9]. In less polar organic solvents (e.g., acetone)

the unprotonated (zwitterionic) dye undergoes a reversible conversion to a lactone:

Because the conjugation of the chromophore is interrupted, this is a colorless compound. On addition of

acid or complex-forming metal ions the chromophore

is regenerated. If the carboxyl group is esterified as in

Rhodamine 6G, all these reactions do not take place,

and the absorption maximum is independent of pH and

ature glasses and has a lifetime in the order of 0.1 s, which is short compared with, for instance, acriflavine

and some aromatic compounds.

The fluorescence of rhodamines is quenched ex- ternally by I" and SCN", less efficiently by Br"

and CI". No quenching was observed by C104 " and

BF4 "

[4, 5]. The quenching process apparently involves a charge transfer from the anion to the excited

dye molecule. It is not a heavy-atom effect. In polar

solvents like ethanol, Rhodamine 6G-iodide is completely dissociated at a concentration of 10"4 mol/1

and no quenching takes place, because the lifetime

of the excited state is of the order of a few nano- seconds, much shorter than the diffusion time the

quencher would need to reach an excited dye molecule.

In less polar solvents like chloroform the dye salt

does not dissociate and its fluorescence is totally

quenched. The perchlorate of Rhodamine 6G behaves strikingly differently: its fluorescence efficiency

is independent [12] of solvent polarity (0.95 based on

the value 0.90 for fluorescein). It is, however, reduced

by heavy-atom solvents (0.40 in iodomethane), and the

fluorescence of this dye is completely quenched by

nitrobenzene, presumably due to the high electron

affinity of this solvent.

There are two structural features that influence the

rate of internal conversion in xanthene dyes: mobility of the amino groups and hydrogen vibrations.

34
/

200 300 400 500 600 700

Wavelength (nm)

FIGURE 2. Rhodamine 6G in ethanol.

Absorption spectrum molar decadic extinction coefficient); quantum spectrum of fluorescence (arbitrary

units).

We found that the fluorescence efficiency of rhodamines that carry two alkyl substituents at each nitrogen, e.g., Rhodamine B, varies strongly with solvent

and temperature [4, 5, 11]. We ascribe this to mobility

of the amino groups. If the amino groups are rigidized as in the new dye Rhodamine 101 (A abs = 577 nm in

ethanol) the quantum efficiency is practically unity,

dyes, it is noticeable for instance in Rhodamine 6G.

On solution in O-deuterated ethanol, H is exchanged

for D in the amino groups of the dye. With the greater

mass of deuterium the nonradiative decay is less likely

and the fluorescence efficiency increases from 0.95

to 0.99.

Rhodamine 101

independent of solvent and temperature. It is interesting that the amino groups are not mobile when they

are less than fully alkylated (Rhodamine 6G, Rhodamine 110). However, in such dyes there is a proba3. Oxazine Dyes

When the central carbon atom in the xanthene

chromophore is replaced by nitrogen, the chromophore

of an oxazine dye is obtained. The central /V-atom acts as a sink for the 7r-electrons, causing a wavelength

shift of about 80 nm to the red. As within the xanthene

class the absorption of oxazines also shifts to the red

with increasing alkylation of the amino groups (fig. 3). Apart from the pronounced red shift of the So — Si

transition there is little difference between the electronic transitions of oxazines and rhodamines [2]. The electron-withdrawing effect of the central Natom causes the amino groups to be more acidic. Thus

addition of a little base to a solution of Oxazine

4 in ethanol changes the color from blue to red due to deprotonation of one of the amino groups:

H,C

H 5Cf ©

+ OH

e

2 n5

bility that the electronic excitation energy is funneled

into N-H vibrations, causing nonradiative decay to

So- Although this effect is rather weak in xanthene

H,C

5^2"

CH,

2 n 5

Oxazines with fully alkylated amino groups do not

undergo any change on addition of base. On the other

hand, all oxazines are protonated in strong acids.

35
Oxozme 118 588 nm

H5cr H

5C2 Oxazine 4

611 nm

Oxazine I 645 nm

^C2H 5 "C2 H 5

Cresyl Violet

601 nm

H 5 Cr

Oxazine 170 627 nm

Nile Blue 635 nm

FIGURE 3. Molecular structure of oxazine dyes; absorption maximum in ethanol.

Some oxazine dyes have a structure modified by an added benzo group (fig. 3). This causes a slight red

shift of absorption and fluorescence. Furthermore,

the shape of the absorption spectrum is different

than in other oxazine dyes and depends on the temperature [13]. These effects are probably caused by steric

interference of the amino group with a hydrogen of the

added benzo group [11].

The triplet yield of oxazines is generally very low in

accordance with the loop rule. No phosphorescence has

been observed in these dyes. The fluorescence quenching processes, discussed for xanthene dyes, are also

found with oxazines. Owing to the smaller energy

difference between Si and So, internal conversion plays

a greater role in oxazines than in rhodamines. Thus the

fluorescence efficiency of Oxazine 1-perchlorate is less

than 0.1 in ethanol, but much higher in dichloromethane

and in 1,2-dichlorobenzene. Likewise, the effect of

hydrogen vibrations is much more pronounced. The

fluorescence efficiency of Oxazine 4 is a factor of 2

higher in O-deuterated ethanol than in normal ethanol.

4. 7-Aminocoumarins

As a consequence these compounds show a large

Stokes shift, in particular in polar solvents (fig. 4).

Absorption and fluorescence maxima depend much

more on solvent polarity than is the case with xan- thenes and oxazines [4, 5]. A large number of highly

fluorescent derivatives have been synthesized in re- cent years [4, 5, 14-18]. Here we can give only a few

examples (fig. 5). Absorption and fluorescence of

7-aminocoumarins are not influenced by a small

amount of base present in the solution. However,

they react with strong acids in a variety of ways

[4, 5, 11]. The amino group of Coumarin 1, for in- stance, is easily protonated and thus decoupled from

the chromophore. As a consequence the absorption

band at 373 nm disappears. This reaction is inhibited,

if the amino group is rigidized as in Coumarin 102.

In the excited state Si, the keto group is more basic

than the amino group and thus is protonated if sufficient acid is present so that the diffusion is faster

than the decay of Si. Frequently a new fluorescence

band appears due to the protonated form. Most

coumarins are very soluble in organic solvents, but

insoluble in water. However, derivatives have been

reported recently that are highly soluble in water

(fig. 6) [18].

The most important laser dyes in the blue and green

region of the spectrum are coumarin derivatives that

have an amino group in 7-position:

A B

The chromophore is not symmetric as in the xanthenes

and oxazines discussed above. The ground state can be described by structure A, the excited state

Si by B. While there is some dipole moment in the

ground state, it is much greater in the excited state.

5. Fluorescence Standards

The optical properties of an ideal fluorescence standard should be independent of the environment (solvent

composition, temperature, etc.). This means, among

other things, that the compound should not be involved in chemical equilibria. Alkaline solutions are to be avoided, because their alkalinity changes

gradually due to absorption of carbon dioxide. Furthermore the fluorescence should not be quenched by

oxygen and the fluorescence efficiency should be in- dependent of temperature variations. The commonly

used fluorescence standards fail badly on one or more

of these requirements. A number of better standards can be suggested on the basis of the foregoing

discussions.

36
Coum. 153 Coum. 314 Coum. 6 423 nm 436 nm 458 nm

FIGURE 5. Molecular structure of 7-aminocoumarin derivatives; absorption maximum

in ethanol.

37
Coum. 175 Coum 386

353 nm 388 nm

Figure 6. Molecular structure of water-soluble 7-aminocoumarins;

absorption maximum in water.

Coumarin 1. This compound (7-diethylamino-4-

methyleoumarin) is the most readily available 7-aminocoumarin. It is easily purified by recrystallization

from ethanol. It is highly soluble in most organic

solvents, but not in water. The fluorescence quantum

efficiency is about 0.5 in ethanol, generally higher in

less polar solvents, and is almost independent of

temperature. There is little or no quenching by oxygen.

A disadvantage is the possible protonation in acidic

solvents. If this is a problem, Coumarin 102 or Coumarin 153 may be used. The latter compound is particularly interesting because of its large Stokesshift and the very broad fluorescence spectrum. The

fluorescence efficiency of Coumarin 102 was measured

as 0.6 and that of Coumarin 153 as 0.4 (both in ethanol).

Another compound, possibly useful as a standard,

is Coumarin 6 (quantum efficiency 0.8 in ethanol),

which absorbs at longer wavelengths than most

other coumarin derivatives. The latter compounds

are commercially available, but the price is still high.

However, this should not be a deterrent, as the price

will certainly come down and generally only a few

milligrams are required. We feel that Coumarin 1

is superior to quinine bisulfate in every respect. It can be used in almost any solvent except water.

Rhodamine 6G-C104. As was pointed out previously

in this article, the frequently used standard Rhodamine

B undergoes acid-base reactions that affect its optical

properties. Its fluorescence efficiency depends

strongly on type of solvent and temperature. Therefore it is not surprising that the quantum yield values

reported in the literature vary considerably. As discussed above, Rhodamine 6G-perchlorate is superior

to Rhodamine B, because its quantum efficiency

has the value 0.95 almost independent of solvent and

temperature. The dye chloride is readily available in

rather pure form. It can be further purified by column

chromatography on basic alumina with ethanol or methanol as the solvent. The perchlorate is insoluble

in water and is easily prepared by adding HCIO4

to an aqueous solution of the dye chloride. It can be

recrystallized from alcohol-water mixtures. The ethyl

ester perchlorate of Rhodamine 101 has the same

useful properties as Rhodamine 6G-perchlorate, while

absorption and fluorescence are shifted about 50

nm to the red. However, this dye is not yet commercially available.

Oxazine 170-ClO4. Of all available oxazines this

derivative has the highest fluorescence efficiency

(—0.5 in ethanol). Its fluorescence properties are

closely related to those of Rhodamine 6G-CIO4.

Absorption and fluorescence are shifted by about

100 nm to the red (fig. 7). As in the case of Oxazine

4, the fluorescence efficiency increases nearly a factor

of 2 on deuteration of the amino groups. Apart from

this effect, it is almost independent of solvent and

temperature. However, variations of temperature have

some effect on the absorption spectrum due to the

annellated benzo group. In this respect Oxazine

200 300 400 500 600 700 800

Wavelength (nm)

FIGURE 7. Oxazine 170 in ethanol.

Absorption spectrum (e molar decadic extinction coefficient); quantum spectrum of fluorescence (arbitrary

units).

38
4-ClOj would be preferable. As pointed out earlier,

these dyes cannot be used in basic solution. Being

perchlorates, they are practically insoluble in water.

Hexamethylindodicarbocyanine (HIDC) and Hexamethylindotricarbocyanine (HITC). Very few dyes

are known that are relatively stable and fluoresce well

in the infrared region of the spectrum. Of the commercially available materials, the cyanine dyes

1,1 ',3,3,3' ,3'-hexamethylindodicarbocyanine (HIDC)

iodide and 1,1 ',3,3,3',3'-hexamethylindotricarbocyanine (HITC) iodide stand out on both counts. Contrary to the other compounds

HIDC (n = 2)

HITC (n = 3:

H,C

: CH) —CH

suggested here, the fluorescence efficiency of these

dyes depends markedly on type of solvent and temperature. It appears to be highest in sulfoxides (dimethyl

sulfoxide, tetramethylene sulfoxide). As shown in

figure 8, the fluorescence of HITC extends to 900 nm.

The photochemical stability is much higher than in

related thiacarbocyanines. A concentrated solution

of HIDC-iodide in dimethyl sulfoxide is currently

in use in our laboratory as a photon counter that

operates up to 700 nm. It is much more sensitive than

equally concentrated solutions of methylene blue

as this has a lower fluorescence efficiency.

The fluorescence spectra and efficiencies of the

suggested dyes need to be determined accurately. To

us this seems to be of greater benefit than perpetuating bad standards whose only justification today is their common usage.

6. References and Notes

[1] Dye Lasers (F. P. Schafer, Ed.) Topics in Applied Physics,

Vol. 1 (Springer, Berlin, 1973).

[2] Jakobi, H., and Kuhn, H., Z. Elektrochem. Ber. Bunsenges.

Phys. Chem. 66,46(1962).

[3] Ramette, R. W., and Sandell, E. B., J. Am. Chem. Soc. 78,

4872(1956).

[4] Drexhage, K. H., VII Intern. Quant. Electron. Conf., Montreal,

Canada, paper B.5 (1972).

[5] Drexhage, K. H., Laser Focus 9(3), 35 (1973).

[6] Ferguson, J., and Mau, A. W. H., Chem. Phys. Lett. 17, 543

(1972).

[7] Ferguson, J., and Mau, A. W. H., Austral. J. Chem. 26, 1617

(1973).

[8] Selwyn. J. E., and Steinfeld, J. I., J. Phys. Chem. 76 , 762

(1972).

[9] Wong, M. M., and Schelly, Z. A., J. Phys. Chem. 78, 1891

(1974).

[10] The absorption of Rhodamine 6G (2g/l in ethanol), whose

maximum is at 530 nm, is still noticeable at 633 nm, far beyond the fluorescence maximum of 555 nm: a 5mW He-Ne

laser excites yellow anti-Stokes fluorescence that can be

observed visually.

400 500 600

Wavelength (nm)

800

30

£o

'<oo

E

O

20

1 1 1 1

HITC

i i AA

-

—.

i

t -—-~i

/ M

/ ' \ J I I

I \ / 1 \ / l \ / I \

l \

/ \

i "

l

1

\

\ \\

\

\\

\

200 300 400 500 600

Wavelength (nm)

7' o 800 900

Figure 8a, and b. HIDC and HITC in ethanol.

Absorption spectrum (c molar decadic extinction coefficient); quantum spectrum of fluorescence (arbitrary units).

39
[11] Drexhage, K. H., Structure and properties of laser dyes, in: Dye Lasers (F. P. Schafer, Ed.), Topics in Applied Physics,

Vol. l,p. 144 (Springer, Berlin, 1973).

[12] This statement has to be taken with a grain of salt. We found

indeed variations up to 10 percent with solvent. But the accuracy of our quantum efficiency measurements was probably less than this, when solvents with widely varying re- fractive index were involved. We feel, however, that the accuracy of the measurements was sufficient to justify the

interpretations given here and elsewhere in this article. [13] Gacoin, P., and Flamant, P., Opt. Commun. 5,351 (1972).

[14] Tuccio, S. A., Drexhage, K. H., and Reynolds, G. A., Opt.

Commun. 7, 248 (1973).

[15] Drexhage, K. H., and Reynolds, G. A., VIII Intern. Quant.

Electron. Conf., San Francisco, Calif., paper F.l (1974).

[16] Schimitschek, E. J., Trias, J. A., Hammond, P. R., and Atkins,

R. L. Opt. Commun. 11, 352 (1974).

[17] Reynolds, G. A., and Drexhage, K. H., Opt. Commun. 13,

222(1975).

[18] Drexhage, K. H., Erikson, G. R., Hawks, G. H., and Reynolds,

G. A., Opt. Commun. 15 , 399 (1975).

(Paper 80A3-894)

40
Part 2. Diffuse Reflectance Spectroscopy

NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 466, Standardization in Spectrophotometry and Luminescence

Measurements, Proceedings of a Workshop Seminar Held at NBS, Gaithersburg, Md., November 19-20, 1975 (issued May 1977).

Diffuse Reflectance Spectroscopy; Applications, Standards, and

Calibration (With Special Reference to Chromatography)

R. W. Frei

Analytical Research and Development, Pharmaceutical Department

Sandoz Ltd., 4002 Basel, Switzerland

(May 26, 1976)

The multitude of areas in which diffuse reflectance spectroscopy can be applied has been

described in several books and reviews and ranges from color measurements of textiles,

pharmaceuticals, building materials, paper and pulp materials etc., to adsorption studies

and other basic investigations in physical, inorganic and organic chemistry.

The major area of application is still the measurement of color which has become indispensible in the quality control of colored products, dyes and pigments. Color matching practices and techniques with sophisticated instrumentation which can be fully computerized

as well as the use of simpler filter instruments for quality control are mentioned.

Transferability of reflectance data i.e., color coordinates, depends on the quality of standards particularly when absolute measurements are desired. The difficulty of finding

suitable "white standards" with good reflection properties at low UV and with a good long

term stability is discussed. Similar arguments hold for sphere coating materials. For the

measurement of fluorescing surfaces suitable standards are lacking which renders transfer

of such data almost impossible.

The usefulness of diffuse reflectance techniques to study adsorption phenomena on small

particle adsorbents is demonstrated with a malachite green-o-carboxylic acid lactone system

studied by Kortiim. This or similar systems could be adopted to the measurement of rela- tive surface areas on certain chromatographic adsorbents yielding more realistic values than

theBET-method.

The most recent area of application has been in the field of chromatography for the in situ evaluation of chromatographic zones in flat-bed chromatography, electrophoresis and

isoelectric focusing. In chromatograpt^r, standardization is less problematic since usually relative measure- ments are sufficient. On the other hand one has to find suitable calibration procedures. The

use of the Kubelka-Munk function is often questionable since we are usually not dealing

with layers of infinite thickness and below 300 nm the conventional adsorbents such as

silica gel, alumina or cellulose are strongly absorbing. Experiences with a new function

combining the laws of Kubelka-Munk and Lambert-Beer are therefore presented.

The problem is also to find calibration techniques which account for chromatographic

parameters. Until recently it was believed that a quantitative evaluation of chromatograms

required a number of reference zones to be developed on the same chromatogram. In our

experience this is no longer true. A novel calibration technique which utilizes the concept of transferable calibration factors is discussed. With this approach a quantitative evaluation

of a chromatogram with only one reference spot is possible. Here again scanning and data

acquisition can be fully automated. The application of proper calibration procedures to

differential reflectance techniques and the measurement of multi-component systems is briefly mentioned.

Finally it is demonstrated that it is possible to carry out in situ quantitative measure- ments on low UV absorbing compounds (down to 190 nm) separated on silica gel surfaces,

provided suitable techniques and instrumentation are used.

Key words: Chromatography; color matching; color measurement; diffuse reflectance;

Kubelka-Munk function; reflectance; reflectance standards; thin layer chromatography

I. Introduction became available [l]

1 and a little later a spectrophotometer type reflectometer [2] was manufactured.

Diffuse reflectance spectroscopy has found its A first comprehensive treatise of color measureapplication in a number of areas. The first and still ment became available in 1936 [3], Since that time

most prominent is in the field of color measurement the literature on color measurement has increased

and color matching. The paper, paint, dye, textile, exponentially peaking out somewhat in the 1960's

EE? ?£hn!lf ^

industries hav

? m.ade,use ?

i with not less than seven books appearing on this

tnis technique for the measurement of color m , . r A_ini routine quality-control functions as early as 1920. subject [4 iuj.

At that time the first Useful filter refl ectometers i Figures in brackets indicate the literature references at the end of this paper.

41
Later the principles of color measurements were

extended to other areas including studies of biological

systems, geological specimens, food stuff, building

materials, and pharmaceuticals. With the expansion

and improvement of the quality of available re- flectometers on the instrumental scene it also became

possible to carry out physical-chemical measurements, requiring extremely reproducible experimental and instrumental conditions. Comprehensive

discussions and surve}^ have been given on these

applications and on the instrumental developments

in several books [11-15] and reviews [16-17].

Essentially no new aspects have been added to

this to my knowledge. I see therefore not much point

in repeating information which can be read in these

cited references.

For pharmaceutical applications the technique

is being used extensively for production control,

formulation studies and for investigations of aging

and illumination effects. This has been developed

to the stage of automatic tablet inlet systems to the

Hunter Color Meter 2 D25 DA.

The data aquisition is fully automated with a Hewlett-Packard 9100 desk calculator. This system

will be discussed and published at an international

pharmaceutical congress in Berlin in spring 1976 [18].

The field of instrumental color matching and color

formulation has also strongly developed in the direction of automation and data evaluation by on-line

and off-line computer systems, and I shall briefly

mention this area. The newest area of application of diffuse reflectance techniques has been in the field of chromatography [14-16, 19] for the in situ evaluation of chromatographic zones in flat-bed chromatography (PC,

TLC), electrophoresis and isoelectric focusing. It is therefore not surprising that the most rapid changes

and developments have taken place in this field,

and I shall attempt to present some of the recent

work in this area which has partially not yet been

published.

Closely related to all these applications have been

the problems of standardization and calibration.

These, as we shall see, are still far from being solved

satisfactorily and an assessment of the present status

shall be attempted in this paper.

II. Instrumental Color Measurement

The technique of color matching and formulation

by modern instrument-computer combinations is in a worldwide rapid development stage. This development is catalyzed by the growing need of color con- suming industries to optimize the coloration

processes. Color and dye manufacturers, instrument

makers, and their customers alike are therefore

responsible for this recent surge in color measurement

technology.

2 In order to adequately describe materials and experimental procedures, it was occasionally necessary to identify commercial products by manufacturer's name or label. In no instances does such identification imply endorsement by

the National Bureau of Standards, nor does it imply that the particular product

or equipment is necessarily the best available for the purpose.

Unfortunately, very little information is available

on this relatively young science and much of it is already out of date. This is not astonishing, considering that the major developments come from

color manufacturing industries and competition has

prevented much of the know-how to become

accessible.

One of the better accounts of the present state of

the art was given by Gall [20]. Other workers, such

as Brockes [21] and Kuehni [22], have also reported

on this subject, the former specifically on textiles.

A brief but very illustrative introduction into the

concept of color in general and color measurement in

particular has been given by Berger and Brockes [23]

which can be highly recommended to new-comers in

the field.

On the instrument side one can observe a trend to

integration of on-line computers into more sophisticated reflectometers which results in a reduction

of software requirements for the user. The disadvantage is the complete dependence of each operation

step on the computer which can make trouble shooting difficult for the non specialist. Another trend on

the market of such systems is an increased emphasis

and demand for stand-alone formulation systems

(available also to smaller colorists) rather than for

time-sharing systems.

A. Types of Measuring Systems

Three different types of automatic color matching

and formulation systems are now frequently used in

larger companies in North America, Europe, Japan,

and Australia.

(1) The first system consists of a high-quality

spectrophotometer for automatic measurement of

reflectance spectra, an electronic interface for datastorage, a connection to the teletype and a large

centralized computer facility.

The spectrophotometer measures the reflectance of

standard color samples (at least 6 different concentrations per dye) and of the samples to be matched.

The reflectance data are transferred via the interface

to the teletype and presented in a suitable form

(cards or tapes)

One then feeds these data to the computer centre

along with a characterization of the samples, dyes

and substrates to be used for a computation of the

formulation, price and metamerism. This can be

done via a cable connection or completely off line.

(2) Following the trend of decentralization, instrument manufacturers are now marketing complete

systems for automatic computation of formulations.

They consist again of a high-quality monochromator

instrument or a reflectometer equipped with filters

producing spectral bands of 10 nm or 20 nm width.

They then have an interface to a teletype and an

on-line minicomputer. The spectral data are fed to

the minicomputer and the same data as above are produced. The same system also can be utilized for

corrections of formulations.

The teletype in this case has two functions. It serves as the means to feed-in manually or auto42
matically the additional data needed for formulation

such as color codes and names of dyes and substrates, maximum number of dyes to be used per

formulation (usually 3-4) etc. In addition it prints

the final formulations, price, metamerism and other

data. The software is often provided by the instrument manufacturer.

(3) Since systems of tj^pe 2 are still too expensive

to be used by a smaller coloring outfit or the individual colorist in a laboratory, a third system has

been developed (by CIC) . It makes use of system 1 as a centralized facility in a large company or a

centralized service facility for colorists and a low-cost

filter colorimeter which is placed directly in the

colorist's laboratory or production unit.

With this filter instrument the day-light color

coordinates X, Y, Z of the sample are measured.

In case of metamerism the color coordinates for an

artificial illumination source have to be determined.

These data are then transferred to the central

facility. The spectrophotometer is then solely used

to measure the dyes to be used in the formulation

and the blank measurement on the substrate.

The disadvantages of this systems are time delays

for the availability of the formulation and an increased risk for deviations from the true sample.

This can be due to larger sj^stematic errors on the

low-cost unit and poor correlation of the measuring

geometries on the two instruments.

B. Criteria for the Evaluation of Measuring Systems

The most important factors for the efficiency of a

formulation computing system are the quality of

the calibration samples of the dyes available for

the formulation and the quality of the software.

One would expect the following information to be

provided by an useful system

(1) Computation of all the possible alternatives

'or a formulation (combinations of 2-4 dyes) or ndications for adjustments with one additional dye

f none of the possible combinations leads to the

lesired result.

(2) For each possible formulation the degree of

netamerism with respect to one or more standard

lluminants and compared to day-light condition

should be given.

(3) The color difference between sample to be

natched and each of the possible formulations should

De computed automatically for day-light condition.

The advantages of a color measuring system for

;omputation of formulation as described above in

jomparison to the conventional use of sample colections are obvious

(1) The computation and fine-adjustment can be

lone faster since the chances of hitting the correct

solution are enhanced.

(2) An efficient system usually provides several

solutions of which the optimal with regard to quality

)f the color, metamerism and price can be chosen

(such a choice of course requires the services of a

specialist).

(3) The system is usually of sufficient flexibility

to be used for trouble shooting in coloring processes

(i.e., identification and quantitation of sources of

error)

The systematic use of such formulation-computation systems will therefore result in a gradual upgrading of coloring techniques at lower prices.

III. Standardization

In the majority of cases for work carried out within

one laboratory measurements relative to a reflection

standard tailored to a particular experiment are

sufficient. For adsorbate-adsorbent interaction

studies for example, one would choose the same

adsorbent as a reference material. The same holds

for chromatographic work. Instruments are then

utilized either in the substitution mode or the

comparison mode (double beam operation). The

level of instrument technology is now sufficiently

good to assure a satisfactory reproducibility of

measurements on the same instrument [14]. The

problem arises when data have to be reproduced by

several different laboratories. Instrument and measurement geometries are far from being uniform,

which causes considerable variations in measured

values. The trend for adaptation of a uniform

integration sphere design which would permit at

least the reproduction of reflectometer values with

instruments of different manufacturers can now be

observed. The inherent limitation of construction

possibilities with such a standard sphere, however,

still keeps many instrument designers reluctant to

follow this trend.

But even this would not guarantee the availability

of absolute reflectance values, independent of the

instrumentation, since such a condition depends

strongly on the quality of available standards.

W. Erb [24] has recently discussed the current status

of reflection standards and it is apparent that little

progress has been made during the past years to

obtain better standard materials.

The properties that one would expect from a useful

standard are as follows

—They should be rugged enough for transportation

or at least easily reproducible in each laboratory —-Along with this goes the demand for easy

handling and a minimum of contamination

danger. —They should be relatively inert and stable

toward radiation and temperature fluctuations

and have good aging properties. —Other requirements include an ideally diffuse

reflecting, homogenous and smooth surface

which is nontransparent, nonfluorescent and

spectrally nonselective.

43
Obviously a reference material having all these

properties does not exist.

A number of possible materials of fine powder

texture have been investigated by Korttim et al.

[25], (see fig. 1). From this we can see that the

condition of spectral nonselectivity is not ideally

observed, particularly not in the lower UV-region.

Of these MgO seems to have the best spectral

properties and it has for a long time served as the

most widely used standard. Its extreme sensitivity

toward atmospheric conditions, UV-irradiation [27]

and aging [14, 26] is well known. MgO-standards

are also difficult to reproduce.

For this reason MgO has gradually been replaced

by BaS04 whose spectral properties are not as good

(see fig. 1) but whose stability is superior.

The limited transportability of powder standards

1.00 0.90

0.80

1.00 090

0.80 100

LijC03

. 300* C, 7.5m

NaF. 300* C. 25m

Aerosil. 20* C. 0.05-0.2m

Si0 2'*1 300" C, 25m

Glucose""'. 100* C J L

4000 6000 8000 10.000 X 1000

20.000 50030,000 33040,000 46, 250

,000 cm

220 nm

Figure 1. Absolute diffuse reflectance of several white standards

as a function of wavelength.

Measurements with reference to freshly prepared MgO. (Temperatures given

are drying temperatures; n=maximum grain size) [25].

has prompted the development of glassy or ceramic

standard materials such as Carrara, Didymium,

Vitrolite etc., the latter being a white structural

glass provided by NBS.

Since these materials have to have a matte surface

(ideal diffusers), they are porous and therefore subject to contamination. Many of them have undesirable fluorescence and their spectral properties

are inferior to the powders discussed particularly in

the lower UV region < 250 nm.

The use of binders such as BaS04 , to render powder

surfaces more stable, is another approach frequently

used. Organic binders mostly have been used (polyvinyl alcohols) which seriously decreases the re- flectance in the 200-300 nm region.

Schutt et al. [28] have suggested a number of

inorganic binders which guarantee a similar mechanical stability but with significantly increased

reflectivity in the 200-300 nm region (see fig. 2.)

The same workers also claim improved aging and

irradiation characteristics which should render this

material suitable for transportable standards or as a

highly reflecting coating in integration spheres.

From the foregoing discussion it is obvious that

the development of better reference standards is still of prime necessity particularly for the UV

region and much imagination and ingenuity will

have to go into this research area. As of 1969 the International Commission on

Illumination (CIE) has replaced all previous primary

standards by the "perfect reflecting diffuser,"

possessing a reflectance of 100 percent. Since

this can not be reached materially one can, beside

the general improvement of standards, approach

this problem from the instrumental .side by basing

the universally accepted reflectance scales on standardized instrumental designs. By relating such

measurements on available standards to the "perfect

reflecting diffuser" one obtains absolute reflectance

values.

Instrument designs for the measurement of

spectral radiance factors /3(A) have been discussed

by several groups. A recent account and the description of an apparatus at the "Physikalisch-Technische

Bundesanstalt," Braunschweig, GFR, has been

given by Erb [27]

200 240 260 WAVELENGTH (nm)

Figure 2. Reflectance spectra of barium sulphate coatings with different binders.

KiSOt binder; 0(NH4 ) 2 SOr K2 SOi binder; (NH^SOi binder Polyvinyl alcohol binder [28].

360

44
This technique uses an integrating sphere with

d/0 geometry and is based on the fact that the

spectral radiance of the hemisphere irradiating the

specimen could also be obtained if the "perfect

reflecting diffuser" would be in place of the original

standard.

Additional problems are encountered with the

measurement and standardization of fluorescent

surfaces, since for these the spectral distribution of

the light source becomes another critical parameter.

According to Berger and Strocka [29] artificial light sources coming as close as possible to the standard

illuminant D 65 (xenon lamp) with regard to their

irradiance distribution should be used.

The same group recommended the use of three

standard samples for the assessment of fluorescent

surfaces.

IV. Investigation of Solid Surfaces

Diffuse reflectance spectroscopy can be a powerful

tool for the physico-chemical study of surfaces. It can yield valuable complementary data to other sur- face techniques such as ESCA, regular microscopy,

scanning electron microscopy etc. Kortum has given

an excellent survey of these possibilities in his book

on reflectance spectroscopy [13]. Most of the work

has been done on systems in the adsorbed state and

much light has been shed on processes such as Lewis

acid-base reactions, electron donor-acceptor complexation, redox reactions, photo-chemical reactions

and others on solid surfaces. Adsorption phenomena

have also been studied by Zeitlin et al., using this

approach [14]. Use of reflectance techniques at elevated temperatures has been done by Wendlandt

et al. [11, 12]. This group utilized either isothermal

or dynamic (continuous measurement over a temperature range) high-temperature reflectance techniques

to investigate the degradation, deaquation etc., of

salts and metal complexes. These data were often

used complementary to other thermoanalytical techniques, such as TGA and DTA.

Since chromatographic techniques often involve

adsorption processes, the reflectance techniques can

be adopted advantageously to preliminary investigations of actual chromatographic systems as one can

see in the following example:

The reversible ring cleavage of compounds such as malachite green-o-carboxylic acid lactone (MGL) on

active surfaces has been studied by Kortum and

Vogel [30] and Kortum and Oelkriig [31]. A blue

color develops upon adsorption of the colorless

lactone on an activated adsorbent surface due to

cleavage of the lactone ring. Since only chemisorption

occuring in the first monomolecular layer can bring

about this cleavage, the development of blue color

will eventually reach a plateau at which point all adsorption sites have been covered. This phenomenon

is demonstrated in figures 3 and 4. By extrapolation

of the adsorption isotherm obtained for chemisorption, one can get a relative measure of the surface area of the adsorbent. The same phenomenon can

600 500 £.00 300

Wavelength ( nm

Figure 3. The dependence of the Kubelka-Munk functions of

several bands of MGL on concentrations of MGL adsorbed on dry NaCl [30].

Concentration (moleratio)

Figure 4. Adsorption isotherms of MGL adsorbed on dry

NaCl [30].

also be observed on activated silica gels or alumina

and offers an alternative to the BET-method for the

determination of relative surface areas. In modern high-pressure liquid chromatography

adsorbents with pore sizes ranging from 60 A to

1000 A and more and accordingly decreasing sur- face areas are now available. It would therefore

be valuable to determine relative surface areas with

molecules larger than N2 since, particularly in an

adsorbent with small pore size, the nitrogen may

reach active sites which are not necessarily available

to the chromatographed organic compounds. The

availability of such data facilitates the choice of the

45
proper adsorbents with regard to loading capacity

and retention properties.

V. Calibration

A. Calibration Functions

The Kubelka-Munk function [32, 33] for lightscattering, infinitely thick media, is most widely used

for investigations of a quantitative analytical nature

by diffuse reflectance spectroscopy. Many different

types of calibration functions have been proposed

for the in situ evaluation of thin-layer or other open,

flat-bed chromatograms by UV or visible reflectance

spectroscopy [14, 19]. Most of the functions were

modifications of the Beer-Lambert or the KubelkaMunk laws; others were purely empirical. All of them

claim reproducible linearity over various concentration regions even though the limitations are quite

serious. The Beer-Lambert function gives reasonable

linearity at very low concentrations; the KubelkaMunk function works at medium concentration

ranges but fails at lower and higher concentrations.

The limitations of the Kubelka-Munk theory are quite obvious for chromatographic systems, since

except for monochromaticity of the irradiated light,

other conditions such as infinite layer thickness,

homogenous distribution of absorbing material and

nonabsorbing support are in most cases not fulfilled.

The inhomogeneity caused by tailing or other

deformation of chromatographic zones has been

countered by some workers by scanning chromatographic zones with a small spot of monochromatic

light in a zig-zag fashion (flying spot principle [34]).

Equal success, but with a technically simpler

approach, has been reported by Treiber et al. [35],

with a two-dimensional scanning approach (fig. 5).

10 20

X(mm)

Figure 5. Schematic representation of the scanning pattern

em-ployed for the two-dimensional integration principle [35].

Such a scanning device is now commercially available. The same group [36] has proposed a combination of the two spectroscopic laws (Lambert-Beer

and Kubelka-Munk; as shown below) in order to

extend the linearity of the calibration range.

Kx

- C=Kt

• In y Lambert-Beer (1)

KX -C=KT HD' a4

2-Ro.

Kubelka-Munk

by combining 1 and 2 one obtains:

(2)

KX -C=KT -

2 T0

(3)

A simple transformation : leads to

KI .C=Kfl -(j-°+^-2)+Zr .ln^

Kx

(4)

=constant depending on the substance chromatographed

KR (Kr ), KT (Kt ) =constants depending on the properties of the adsorbent layer

(determined empirically)

k constant depending on

adsorbent layer

the

e =molar absorbance of the substance chromatographed

C =concentration of the substance

chromatographed in weight per

surface unit

Ix =intensity of the light leaving the

sample

I0 =constant, maximal light intensity

on the adsorbent layer free from

any substance chromatographed.

A comparison of the i^-M-function with the

combined function eq (4) for sulforidazine scanned

automatically by the two-dimensional technique at

275 nm is shown in table I with some statistically

computed values.

A significant improvement can be noted particularly for the lower concentration region (0-2 jug).

Our own work [45] confirms that significant

improvements can be obtained using the Treiberfunction in comparison to plotting peak area or peak area square (Fmax or F

2m^ in fig. 6) . The study

46
was carried out with thioridazine as a test substance

on Merck Si02 commercial plates. The measurements

were carried out with a Zeiss-Chromatogram Spectrophotometer PMQ II, with automatic scanning unit.

For the data aquisition a combination with Info tronics Integrator CRS 208, W+W-recorder,

Teletype ARS 33 and Hewlett-Packard HP-Calculator 9830 with plotter was used.

The following figures are direct plotter read-outs.

Measurements were made at the two possible

absorption maxima for thioridazine at 262 nm and

at 315 nm.

Table I. A statistical comparison of calibration curves for

sulforidazine

Range Slope Correlang tion

Relative st. dev.

K-Mfunction:

Combined

function

0-10

0- 2

2-10

0-10

0- 2

2-10

1079

733

1154

2088

2088

2069

0. 99778

. 97005

. 99941

0. 99991

. 99876

. 99988

25. 5

91. 7

22. 9

(± 2.4 %)

(±12.5 %)

( ± 2. 0 %)

9. 6 (± 0.46%)

52. 1 (± 2. 5 %)

18.3 (± 0.88%)

Figure 6 shows the relatively poor correlations obtained with the commonly used function A (Fmax) and

A2 (i^majt) over a concentration range of 1-10 ng/

spot. For calibration plots using the Treiber-function,

KR in eq (4) has been kept constant at 1 and KT has been varied as can be seen in figure 7. The best

calibration plot going through the point of origin

has been obtained for KT =Q, which means that the

Beer-Lambert-term dropped out and that the system

behaves essentially according to the Kubelka-Munk

function. By studying the same system at a different

concentration range (0.2-2 jug/spot) we can see

in figure 8 that the Treiber-function is quite concentration dependent, now the optimum value for KT

is 0.9 to 1.1 This means that the influence of the

transmission effect (Beer-Lambert-function) is about

equal to the reflectance effect (K-M-iunction) , which

is somewhat astonishing since at 262 nm one would

not expect any energy to be transmitted through

the plate.

*DEN5 I TQMETR I 5CHE REGRESSION*

THIWIDRZIN I-IB 252W1 BC2

Figure 6. Calibration curves peak area (F) and peak area square (F2 ) for thioridazine in the concentration range 1—10

fig/spot at \ =262 nm.

Figure 7. Treiber-f'unctions (Tr.-f) with varying KT-values.

Conditions as in figure 6.

47
Figure 8. Treiber-f'unctions (Tr.-f) with varying Kr-values at 262 nmfor a concentration range

0.2-2 ng/spot.

Figure 9. Treiber-functions (Tr-.f) with varying KT-values at 816 nmfor a concentration range

1-10 uglspot.

The Treiber-function is also wavelength dependent. This can be observed by comparing figure 9 to

figure 7 where measurements have been made at

315 and 262 nm respectively at the same concentration range (1-10 jug/spot). The optimum .K^-value in

figure 9 would be around 0.3 which means that a

portion of the light is being transmitted. This is to be

expected at 315 nm. The reason for the X-dependence

of the Treiber-function is easily explained, but at the

moment we are unable to give a satisfactory reason

for the concentration dependence. Treiber has not

observed or at least not reported on these very important effects.

The above experiments demonstrate also that it is now possible to automate completely the entire

densitometric measurement and data evaluation

steps. This should enhance the usefulness of densitometric methods for routine analysis.

B. Control of Linearity

No matter which functions are utilized, one of

the major requirements for a good quantitative

procedure is a proper linear working range. This

should be controlled by consistently _ checking the

correlation coefficients of the calibration curves. A

48
simple approach to thi9 end which is frequently used

in our control laboratories is described below.

For the purpose of saving space for the application

of unknowns, the system was restricted to 3 standard

concentrations, hence only three fixed points determine the calibration curve and therefore even

highly significant correlation coefficients do not

yield much information.

In order to permit meaningful control of the

linearity of our working concentration range and

to have an absolute value of slope deviations

from linearity a more realistic approximation has

been proposed (see fig. 10).

A2 =mc+n

A\=ac-{-ni

A2

2 =bc+n2

42 42

ClOO CS0

6=

. A 2

C120 c100

(5)

(5a)

(5b)

(6)

(7)

The total regression of the 3 calibration points can be separated into two segments. As can be

seen in figure 10, a deviation from ideal correlation

has its most serious effect when the concentration

of the unknown is closest to the ideal 100 percent

standard concentration; in other words, the largest error could be expected for the best samples.

The magnitude of this poor correlation can be

seen by comparing the slopes a and b respectively

of the two segments (fig. 10) : According to this,

the slope difference 6— a is a measure of the calibration quality. With this quality factor, it is also

possible to screen for the best linearity range. If

b— a is consistently positive or negative, we are

definitely in a nonlinear range and another concentration region has to be chosen.

This systematic error cannot be seen by calculating the correlation coefficient.

After determination of the slope of each segment,

one can compute the error of the analytical result,

caused by the calibration error (see fig. 11).

cv =concentration of unknown

Cj/exp. =expected concentration of unknown

(true concentration)

I 1 1 1 ^ c °80 C 100 C 120

Figure 10. A schematic calibration curve depicting the deviation from ideal

correlation.

cso, Cioo» C120: concentration of the standard solutions with 80 percent,

100 percent, 120 percent of the expected concentration of unknown.

A2m A2m, A2m: squared values of the measured peak areas of the spots with

c80j c100j Ci20-

49
-u'

Figure 11. A schematic presentation of the errors that can be expected due to calibration errors.

-4Z- . 10Q=U[%] (8)

°t/ exp.

-^2_ . 100=Z7' [%] (9)

exp.

f^- • 100=£7" [%] (10)

From eqs 8-9 one derives the definitions for

analytical errors AU

AU=U' -U[%] (11)

AU=U"-U [%] (12)

consequently we have

for condition b —a>0 : AC>0

for condition 6—a<0 : AU<CO.

The term A £7 according to eqs 11 and 12 should

always be considered for the computation of analytical results.

Chromato-plates which yield a AU higher than 2a

of the method should be rejected since for a 95

percent probability the analytical results have to be

within U±2a.

C. Transferability of Calibration Functions

The difficulties of external or transferable calibration for the reflectance spectroscopic evaluation

of thin-layer chromatograms are well known [14].

Usually each plate has to carry its proper set of

standards. A quantitative method with transferable

calibration curves by means of an internal standard

has been described by Klaus [37, 38], but its general

applicability is somewhat questionable. Our efforts

were also directed towards achieving a maximum of

external transferable information to enhance the

analytical capacity of the method [39].

The usual picture for a set of calibration curves from different plates (see fig. 12) is a large variation

of slopes for a given concentration range and the curves do not usually pass through the origin. As a

result it is impossible to have a complete external

calibration. At least two measured points are re- quired to determine the coefficients for slope b and

the ordinate intercept a (A=a+6c).

If one attempts to clear the tangle of calibration curves in figure 12 by sorting them out according to

experimental series, one can see that they differ more

from series to series than within the same series

(figs 12a-12d). It is also apparent that they vary

less in slopes b than in intercept a. On the basis of these observations, we have tried

to use the slope b for external calibration.

This was done by two different approaches

1. Direct Transfer of the Mean Slope- Value

b is computed from the slope values of several plates

A=ai +bi'C A=an +bn -c (13)
6=^—' (bt individual slope value)

n

and is selected as the direct transfer factor. The

individual ordinate intercept at for each plate is then

computed from a single calibration value as shown below.

(Ax , Ciipeak area and concentration of the standard)

measured transferred known

computed

2. Transfer of a Relative Slope- Value

This approach was selected in order to compensate

for the fluctuation of mean slope values F between the

different series (fig. 12).

Value b for each plate is divided by a reference

value Au which is ideally the mean value of the

range of calibration.

Am—

n

(14)

^lsrt =individual peak area of standard.

With three standards used as is usually the case

for our routine methods this would be

(15)

The mean relative slope value brel is then computed

for several plates

b -A. 6rel_ = (16)

>6re i= —~— (bre i t

: individual rel. slope Value).

n

e) series 1-4

21 plates

concentration region

used for calibration

cU'g]

Figure 12. Calibration plots A=a+bc for four different series of compound

x [39].
Slope b t of the individual calibration curve on each

plate is calculated by back-multiplication of the

measured value Ax of a single calibration spot with

b~^i (see scheme below). The individual ordinate intercept di is then computed.

transferred

computed

(17)

A comparison of these two techniques of transferred

calibration was carried out with a drug substance

for which multiple analyses were carried out (see

also fig. 12).

The results are shown in table II. As is to be

expected no significant improvement is observed

between direct and relative transfer when the four

separate series are considered. For the total series,

however, the mean error for the direct transfer

approach is twice as high.

Table II. Mean values of the relative errors of analyses of

compound x corresponding to figure 12

lAL^reil-Values after

transferee! calibration

Transferred 4 Separated Total series value groups

b_ 0.9% 1.2%

6rel 0.6% 0.6%

The mean error A C7re i is defined as

| j£ tranaf. callbr. U Individual callbr, _ -j^qq (18)

^Individual callbr.

Thus, table II also shows, that transferred calibration

techniques are practically equivalent to individual

calibration on each plate. Five analysis can be

carried out per plate which represents an increase

in capacity of 60 percent. The method is applicable

to UV, visible and fluorescence measurements by

reflectance techniques and also after utilizing dipping

or spraying procedures.

The only limitation is that the test series is from

the same concentration region and of course that

they fall into a linear calibration range.

D. Multicomponent Systems

If this condition of linearity is adhered to (no

matter which function is used) then it is also possible,

analogous to regular spectrophotometric principles,

to carry out differential reflectance measurements

with highly or weakly absorbing compounds [40] or to evaluate multicomponent systems [41].

The latter has been demonstrated with dye

mixtures on a silica gel substrate, and the KubelkaMunk-function was used eq (2) as a linear relationship in the concentration range studied.

For a powder mixture containing n light-absorbing

components whose reflectance functions are additive,

the Kubelka-Munk function F (R^) can be adapted

for simultaneous analysis. The function of the total

reflectance RmT of the mixture at some wavelength

i may be represented as the sum of all individual

reflectance functions.

P.f)t=S)T^ (19)

j=i

where j refers to components and r is the slope of

the Kubelka-Munk plot of F(RJ) versus C.

Equation (19) can be written in a more explicit

manner by writing as many equations as there are components in the mixture.

F(R„ t) 1 = t u C1 + t 12 C2 +. . . r ln Cn (20)

F(Ra, T) 2 =r21 C1 + T 22 C2 +. . . T2n Cn . (21)

The additivity of the F (Ra ) -values is shown

in figure 13 for a mixture of Fuchsin and Brilliant

green. From the corresponding calibration curves

(fig. 14) the slopes are determined and utilized in

eqs. (19-21) for a computation of the individual

concentrations.

The precision, computed as relative standard

deviation for four sets of four samples, was ±2.4

percent and the deviation from the true value

(accuracy) was 2.1 percent for Fuchsin and 3.1

percent for Brilliant green.

The same principle is also applicable in the

UV-region. Mixtures of rutile and anatase [42]

have been studied. Similar applications in the color

industry and pharmaceutical industry have also

been discussed [14].

|AC7

52
2

430 470 510 550 590 630 670 7l6 WAVELENGTH imp)

Figure 13. Reflectance spectra of Q, Fuchsin; #, Brilliant green; x, a mixture

of the two [41].

VI. Applications in Chromatography

Applications have been discussed in recent books

[14, 15, 19] and the latest instrument developments

have greatly enhanced the use of diffuse reflectance

spectroscopy in this area. I do not feel that there

is a need in this paper to go into further detail. I would just like to mention one recent application area mainly UV-reflectance spectroscopic measurements of chromatographic zones on silica gel in the

wavelength range of 180-210 nm. U. Hexel [43] has

shown that with the necessary precautions such

as nitrogen purge below 195 nm (ultrapure N2 below 190 nm), the use of good optics (to eliminate

stray-light effects), and a special deuterium lamp

and window (all items commercially available),

it is possible to obtain quantitative results in this

spectral region. This is somewhat surprising since

it is well known that silica gel starts absorbing

strongly below 280 nm (see also fig. 1). However,

the determination of the absolute reflectance of

silica gel in this spectral region is difficult since

good LTV-reflectance standards are lacking.

The absorption spectrum and calibration curves

of a trioleine compound [43] (triglyceride) are shown in

figures 15 and 16. Measurements were done with the

Zeiss Chromatogram spectrophotometer equipped

with a suprasil window and a deuterium lamp H

30 DS. No nitrogen purge was necessary at the

working wavelength XI 96 nm. A precision of ± 2

percent rel. S.D. is possible.

This approach has much merit for the investigation of compounds with G = C, C = O or C = N

bonding and otherwise poor chromophores.

53
0.100 0.200 CONCENTRATION ( mg/ml

0.300

Figure 14. Kubelka-Munk plots for , Brilliant green at 6%6

nm A, Fuchsin at 626 nm; # Brilliant green at 545 nm and

|, Fuchsin at 545 nm [41].

a,u

o

w5

190 194 198 202 206 210 X[nm]

80 ctpgl

Figure 16. Calibration curves for the trioleine standard measured at 196 nm [43].

Actual groups of compounds tested to this date

are caprolactams (\=194 nm) [43], atropine sulfate

(\=195 nm) [43], Lipids (\=196-210 nm) [44] and

some peptides (X=200 — 220 nm) [45].

VII. Conclusion

In conclusion one can say that diffuse reflectance

spectroscopy is by no means a forgotten or obsolete

technique. It is adopted heavily in highly specialized areas such as color measurement and chromatographic techniques. Automation and computer usage

play an important role in both areas and the instrument technology is at a good level.

Some helpful innovations have been made on

calibration techniques which can make quantitative

diffuse reflectance spectroscopy competitive in some

cases with transmission techniques.

The problem of standardization is very much with

us with regard to finding better reference materials

and better standardization of instruments. A great

deal of effort and imagination will have to go into

this areas for genuine progress.

Figure 15. Absorption spectrum of trioleine standard measured

by diffuse reflection [43].

H. Bethke, P. Buchner, U. Hezel, and H. Loof

are to be thanked for providing tome of the data and

informations and for helpful discussions.

54
VIII. References

[1] Taylor, A.H., J. Opt. Soc. Am. 4, 9 (1919); Benford, F., Gen. Elec. Rev. 23, 72 (1920).

[2] Hardy, A.C., J. Opt. Soc. Am. 18, 96 (1929).

[3] Hardy, A.C., Handbook of Colorimetry (M.I.T. Press Cambridge, Mass. 1936).

[4] Evans, R.M., An Introduction to Color (John Wiley and

Sons, London, 1948).

[5] Le Grand, Y., Light, Colour and Vision (Chapman and

Hall, London, 1957).

[6] Judd, D.B., and Wyszecki, G., Color in Business, Science

and Industry (John Wiley and Sons, London, 1963),

2d. edition.

[7] Billmeyer, F.W., and Saltzmann, M., Principles of Color

Technology (Interscience, New York, 1966).

[8] Wyszecki, G., and Stiles, W.S., Color Science, Concepts

and Methods, Quantitative Data and Formulas

(John Wiley and Sons, New York, 1967), 2d. edition.

[9] Optical Society of America, The Science of Color;

(Vail-Ballou Press, Binghampton, N.Y., 1968), 2d.

edition.

[10] Wright, W.D., The Measurement of Colour (Adam Hil- ger Ltd., London, 1969), 4th edition.

[11] Wendlandt, W.W., and Hecht, H.G., Reflectance

Spectroscopy (John Willey and Sons, N.Y., 1966).

[12] Wendlandt, W.W., Modern Aspects of Reflectance

Spectroscopy (Plenum Press, N.Y., 1967).

[13] Kortiim, G., Reflexionsspektroskopie (Springer Verlag

Berlin, 1969).

[14] Frei, R.W., and MacNeil, J.D., Diffuse Reflectance

Spectroscopy in Environmental Problem Solving

(CRC-Press, Cleveland, 1973).

[15] Frei, R.W., Frodyma, M.M., and Lieu, V.T., Diffuse

Reflectance Spectroscopy; Wilson & Wilson Comprehensive Analytical Chemistry, Vol. IV (Elsevier,

Amsterdam, 1975).

[16] Frei, R.W., Critical Reviews in Analytical Chemistry

CRC-Press, Vol. 2, 1972), p. 179.

[17] Surles, T., Erickson, J., and Priesner, D., Internat. Lab.

May-June issue, 29 (1975).

[18] Schonleber, D., and Koci, P., Sandoz internal communication.

[19] Frei, R. W., In Progress in Thin-Layer Chromatography

and Related Methods, Vol. II (Niederwieser, Pataki

Eds.) ; (Ann Arbor Science Publishers, Ann Arbor,

Mich., 1971).

[20] Gall, L., Computer Colour Matching; Colour 73, (Adam

Hilger Ltd., London, 1973), pp 153-178.

[21] Brockes, A., J. Am. Assoc. Text. Chem. and Colorists 6 No 5 (1974).

[22] Kiihni, R., J. Am. Assoc. Text. Chem. and Colorists 6

No 8 (1974).

[23] Berger, A., and Brockes, A., Bayer Farbenrevue, Sonderheft No 3/1 (1971).

[24] Erb, W., A summary of properties and reflection values

of materials which are used as reflection standards;

Physikalisch-Technische Bundesanstalt, PTB-Report,

June 1975, Braunschweig.

[25] Kortiim, G., Braun, W., and Herzog, G., Angew. Chem.

Intern. Ed. 2 333 (1963).

[26] Terstiege, H., Lichttechnik 26 277 (1974).

[27] Erb, W., Appl. Opt. 14 493 (1975).

[28] Schutt, J. B., Arends, J. F., Shai, C. M., and Stromberg, E., Appl. Opt. 13 2218 (1974).

29] Berger, A., and Strocka, D., Appl. Opt. 14 726 (1975).

[30] Kortiim, G., and Vogel, J., Chem. Ber. 93 706 (1960)

[31] KortjTM. G-> and Oelkrug, D., Z. Phys. Chem. 34 58

[32] Kubelka, P., and Munk, F., Z. Tech. Phys. 12 593 (1931).

[33] Kubelka, P., J. Opt. Soc. Am. 38 448 (i948).

[34] Goldman, J., and Goodall, R. R., J. Chromatog. 40 345

(1969).

[35] Treiber, L. R., Oertegren, B., Lindsten, R., and Oertegren, I., J. Chromatog. 73 151 (1972).

[36] Treiber, L. R., J. Chromatog. 100 123 (1974).

[37] Klaus, R., J. Chromatog. 40 235 (1969).

[38] Klaus, R., J. Chromatog. 62 99 (1971).

[39] Bethke, H., and Frei, R. W., Anal. Chem. 48 50 (1976).

[40] Lieu, V. T., Zaye, D. F., and Frodyma, M. M., Talanta

16 1289 (1969).

[41] Frei, R. W., Ryan, D. E., and Lieu, V. T., Can. J. Chem.

44 1945 (1966).

[42] Kortiim, G., and Herzog, G., Z. Anal. Chem. 190 239

(1962).

[43] Hezel, U., Zeiss Ltd., Oberkochen, Germany; private

communication.

[44] Murawski, U., Egge, H., and Zilliken, F., Z. Klin, Chem.

Klin. Biochem. 12 644 (1974).

[45] Frei, R. W., Sandoz internal communication.

(Paper 80A4-901)

55

NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 466, Standardization in Spectrophotometry and Luminescence

Measurements, Proceedings of a Workshop Seminar Held at NBS, Gaithersburg, Md., November 19-20, 1975 (issued May 1977).

The Interpretation of Diffuse Reflectance Spectra

Harry G. Hecht

Department of Chemistry, South Dakota State University,

Brookings, South Dakota 57006

(May 26, 1976)

Numerous treatments of the diffuse reflecting properties of scattering media have been

described. Many theories give an adequate account of the reflectance for a specific set of conditions for which the model was constructed and the solution tested experimentally.

Only those models which are considered to be fairly general are considered here.

It is convenient to divide the theories into those based upon continuum models and

those based upon statistical models. The continuum models typically describe the scattering

and absorbing properties of a given medium in terms of two phenomenological constants. These models may all be regarded as varying levels of approximate solution to the general

equation of radiative transfer. This provides a convenient basis for comparison of the various

theories.

The statistical models are based upon a summation of transmittances and reflectances

from individual layers or particles. Thus, some assumptions must be made about the nature

of the fundamental units, and the validity of the ultimate result will depend upon how closely

these assumptions correspond with reality. Only the statistical models lead to expressions

from which absolute absorptivities and scattering coefficients can be calculated and related

to the actual particle characteristics.

The relationship between the various models will be discussed and the features which

typify the absorptivity and scattering coefficient according to each will be compared and re- lated to the available experimental data. This leads to a consideration of the characteristics

of appropriate model systems and standards.

Key words: Absolute absorptivities; continuum models; diffuse reflectance; radiative trans'

fer; reflectance spectra; scattering coefficients; statistical models.

List of Principal Symbols Used

(Note: Where a given letter is used in both capital

and lower case form (e.g., r,R and t,T), the capital

letter refers to the macroscopic observable and the

lower case letter to the corresponding variable for an

individual particle or layer of the material. A bar

over a given symbol means the average value for

that variable)

a total absorption of a single particle

(layer) ; also —^— (equation (18))

a,

b

ft

. s . Gaussian weighting function (equation

(33))

J Rozenberg constants (equation (23)ff.)

(a2 -!) 1 '2 (equation (21))

IJl\ polarization of radiant beam (equation (24))

fraction of radiation reflected (equation

(75»

fraction of radiation transmitted (equation (76))

Rozenberg constant (equation (29))

I

V

3

J

k

K

KU K2

I

L

m

M

V

P„(m)

2

Q

H-integral of Chandrasekhar (equation

(35))

radiant intensity

component of source function for selfradiation (equation (5))

scattering function (equation (2)) source function (equation (4))

absorptivity

Kubelka-Munk absorption constant

(equations (16) and (17))

Attenuation constants in GureviS layer

model (equations (10) and (11))

particle diameter or layer thickness

^free" path length of Antonov-Romanovsky (equation (58))

Gurevifi constant =yjK2

* —K*

mean number of reflections

transmittance of a particle for a single

pass

radiant flux density

phase function (equation (2))

Legendre polynomial

Rozenberg constant (equation (29))

Rozenberg multiple reflection constant

(equation (26))

57
r total reflectance of a single particle

(layer)

?'0 simple reflectance of a single particle

(layer) surface

r* mean external reflection coefficient for

side scatter

re reflectance of a particle (layer) for

externally incident radiation

r t reflectance of a particle (layer) for

internally incident radiation

R reflectance of a (macroscopic) layer

R„, reflectance of an infinitely thick layer

s effective path length (equation (58))

S Kubelka-Munk scattering constant

(equations (16) and (17))

S(n,n0) Rozenberg weak scatter constant (equation (29))

t total transmittance of a single particle

(layer)

_ T transmittance of a (macroscopic) layer

u radiation emerging from a particle per

unit solid angle u0 shading factor (equation (70))

ud fraction of radiation emerging from a

particle in a downward direction

us fraction of radiation emerging from a

particle in a sideways direction

uu fraction of radiation emerging from a

particle in an upward direction

x length

y Johnson multiple reflection factor (equation (51)) a absorption coefficient

|8 a/a (equation (23))

7 Fassler-Stodolski constant (equation (82))

5 Fassler-Stodolski constant (equation (82))

6 polar angle

k attenuation coefficient=a-|-<r (equation

(D)

X wavelength

m cos 6

Hi one of the roots of the Legendre polynominal P»(ju)

£ effective hole cross section (equation

(100))

p density

o- scattering coefficient (equation (2))

t optical thickness (equation (3))

<t> azimuthal angle

$e radiant flux w0 albedo of single scatter (equation (30))

I. Introduction

It is now recognized that diffuse reflectance spectroscopy is a very useful companion technique to

transmission, spectroscopy. Not only can it provide

absorption data in some cases where transmission

measurements fail, but for many industrial and re- search applications, it may in fact be the preferred

technique.

Our discussion will be concerned with the behavior

of radiation within a scattering medium. For simplicity we assume the scattering centers, which may

also absorb radiation, are imbedded in a medium

which neither scatters nor absorbs. The medium

may usually be taken as air, although there are many other cases of interest in which the refractive

index of the medium is much greater than unity.

We will not deal specifically with these cases in the

present review, nor with those processes which alter

the frequency of the radiation, such as luminescence

and fluorescence.

Scattering takes place under a wide variety of

conditions. One may be concerned with the glowing

photosphere of the sun, which is surrounded by a

cloud of electrons that reradiate the direct sunlight

incident on them. Surdight is also reradiated by cos- mic dust, which accounts for the outer part of the corona. In a more down-to-earth situation one may be

dealing in the laboratory with the spectroscopy of a powder, paper, opal glass, photographic emulsion,

etc. As so often happens, concepts developed in one

area of science are slow to find their way into another.

We will attempt to show that there is a close relationship between the astrophysical solutions, which

are based largely on radiative transfer theory, and the

various models which are more familiar to the

spectroscopist.

Since we will not be following a historical development, it may be useful to point out some relationships between the early studies. The first attempt to

account for transmission and reflection of a layered

material was carried out by Stokes in about 1860

[l],

1 and led to some very useful relationships which

have also been derived by other workers (vide infra).

Lord Rayleigh [2] and Mie [3] developed the theory

of single scatter to a high degree, but Schuster [4] was the first to consider multiple scatter. He was

concerned with the cloudy atmospheres of stars, and

developed a plane-parallel plate model in which the

radiation field was divided into forward and backward components. This same model was used much

later by Kubelka and Munk [5], whose names are usually attached to it by spectroscopists. Schwarzschild [6] showed that the radiation field should be

characterized by a complete -angular distribution,

and if one integrates over the forward and backward

hemispheres, the Schuster model is obtained as a

first approximation. A further generalization of the

Schwarzschild formulation leads to an integrodifferential equation known as the equation of radiative transfer, which is very general in concept, but

can be solved exactly in only a few cases. The radiative transfer theory and various models

stemming from it are referred to as Continuum

Models. They have in common the characterization

of the scattering and absorbing properties of the

medium through phenomenological constants, usually

two in number. These theories will be considered in section II. A completely satisfactory theory

must of course relate the measurable quantities to

1 Figures in brackets indicate the literature references at the end of this paper.

58
fundamental properties of the scattering material,

such as particle size, refractive index, and absorptivity. This is the goal of the statistical theories.

Many have been proposed; those which show the

most promise are discussed in section III. In section

IV we discuss some of the strengths and weaknesses

of the various models and some relationships between them. Section V considers the meaning of the

absorption and scattering coefficients often used to

interpret reflectance data, as well as the characteristics required of appropriate model systems.

We will limit our discussion to ideal, homogeneous

dispersions. There have been interesting developments in the theory of nonhomogeneous media, mixtures, luminescing materials, diffusing media in

which photochemical reactions are taking place, and

reflectance for materials dispersed in a highly re- fracting matrix, but these topics are considered to

be outside the scope of the present review. Many

of these topics are covered in the books which have

been written on the subject [7,8,9]. Further information has been presented at various sj'mposia which

have been held, and the proceedings of at least two

of them are available [10,11]. These sources, together

with various reviews devoted to applications in

particular fields, have made workers aware of the

power of the technique. Thus we will confine ourselves to certain theoretical aspects.

The present paper may be regarded as an update

to a former review of the subject by the author [12].

Most of the theoretical work of the intervening years

has been in the development of more refined statistical models, and in showing the relationship between the various theories. At present there is some

reason to feel optimistic that out of a morass of

apparently divergent and unrelated theory, some

order is beginning to emerge.

II. Continuum Theory

y

As is often the case with applications of physical

theory, the real media with which diffuse reflectance

spectroscopy is concerned are intermediate between

two extreme cases, each of which is well understood.

The one limiting case involves the propagation of

radiation through quasi-homogeneous matter, where

the radiation field is characterized by smoothly and

slowly varying functions of the coordinates. The

other extreme involves the emission, absorption, and

scattering of radiation by single particles in a homogeneous medium. The local transformation of

the radiation field at the boundaries of quasihomogeneous media is a special case which has

likewise been characterized for a long time, and leads

to such well-known phenomena as reflection, refraction, etc. In dense scattering media, it is important to

consider the manner in which the radiation fields

from the various scattering centers interact with one

another. Rozenberg [13, 14, 15] has pointed out that

the interaction can be treated as a sum of two parts,

one of which is coherent and the other incoherent.

The coherent part is largely due to nearest neighbor

interactions and gives rise to dispersion effects; i.e., is involved with changes of refractive index. The

incoherent part is that with which we are primarily

concerned in the present discussion. It involves

multiple scattering as a sum of interactions throughout the entire medium. In most treatments the

multiple scattering, because of its complexity, is separated rather arbitrarily from dispersive effects.

Such a separation reduces the problem to one involving geometrical optics, and allows one to write a

radiative transfer equation in which the absorbing

and scattering properties of the medium are treated

as phenomenological constants (spoken of as "external parameters" by Stepanov[16]).

The concept that each volume element is irradiated

by scattering from every other volume element of

the medium (The Principle of Self-Illumination) , is a

basic concept of radiative transfer theory which

clearly pervades the writings of such early workers

as Schuster [4, 17], King [18], and Schwarzschild [6]. The equation of radiative transfer can in fact be

regarded as a simple statement of the law of conservation of energy. The change in intensity of a beam along its direction of propagation, dl, is equal

to the radiation which is lost through absorption and

scattering —upldx, plus that which is scattered in

this direction from all other directions, jpdx:

dI=—KpIdx-\-jpdx (1)

Here p is the density, k is the attenuation coefficient,

j is the scattering function, and dx is the element of

path length. The scattering function can be written

as

(2)

where cr is the scattering coefficient and p(0,0;

6' ,0') is the phase function which defines the

probability that radiation which travels initially in

the direction (0',0') is scattered into the direction

(0,0). Equation (1) is usually solved in terms of

the optical thickness

r= Kpdx (3)

Defining 0 as the angle with respect to the inward

surface normal gives

^/(r, m, 0) =/(t> M> <^)_t7( T) „t j) (4)

where p, = cos 0 and J=j/<r is the source function.

The equation of radiative transfer can be generalized to include dispersion effects as well as scattering

[14, 15]. In terms of the components of the Stokes

vector, I,

59
(5)

The term 1/ (6,<f>) accounts for possible self radiation

of the volume element, which is of importance in

the infrared spectral region or in luminescing media.

As mentioned above, this term will be suppressed in

the present discussion.

A. The Layer Model

A model in which the scattering medium is approximated by plane-parallel layers has been used

by numerous workers as a basis for reflectance

theory [7, 8]. We consider a pair of adjacent layers,

with R{ ,Rj and Tu T, as the reflectances and transmittances for radiation incident in one direction,

and Ri,Rj and TT, Tj as the reflectances and transmittances for radiation incident in the other

direction.

If the incident beam is of unit intensity, then the

portion Rt is reflected and the portion Tt transmitted

by the first layer. At the second layer the portion

TfRj is reflected and TiTj is transmitted. The beam

T{Rj strikes the underside of layer i where TtRjTj

is transmitted, while TtRjRj is reflected. Continuing

this process indefinitely (see fig. 1) we find that the

transmittance and reflectance of the combined

layers are given by

Ti+j =Ti Tj {l+RIR] +RI

2Rj2 + . . . ) Rt+j =Ri +Ti TIRJ (l+RIRj +RI

2Rj2 + . . . ) Summing the geometric series gives

i+r

1 —RjRj

Ri+j =Ri

1 —RjRj

(6)

(7)

Figure 1. Reflectance and transmittance of a pair of inhomogeneous layers (Kubelka [19]).

We generally deal with the case where 7

,

i =Ti and Ri =RI ; i.e., where the reflectance and transmittance of a layer do not depend on the direction

of incidence. This is quite a general condition

which applies even to the case of nonhomogeneous

sheets [19]. With these substitutions eqs (6) and (7)

reduce to

T T

(8): -Rt Rj

Ri+j =Ri J

r T?R>

1

Rt Rj (9)

We now make the assumption that the layers are homogeneous and thick compared with individual

particle dimensions so that no intrinsic inhomogeneities are evident. We can then write that the reflectance of a given layer is proportional to its thick- ness [20],

R(dx)=Kl dx. (10)

Similarly we write

T(dx)=l-K2 dx. (11)

Here Ki and K2 are phenomenological constants

which characterize the medium. We assume that

K2 >KU where the inequality applies to absorbing

media and the equality to nonabsorbing media.

We substitute R(x) and T(x) for Rt and T{ in eqs (8)

and (9), with R(dx) and T(dx) from eqs (10) and (11)

being substituted for R} and T} . Writing Ri+j and

Tt+j as R{x-\-dx) and T(x+dx) allows eqs (8) and (9)

to be expanded in series to give

and

dR=Kl T2dx

dT=-T(K2 -K1 R)dz.

Integrating this set of coupled differential equations subject to the boundary conditions R(0)=0,

7/(0) =1 gives

R=R.

2Lx

l-Rte-2Lx

„-Lx T={l-RD —R

2„-2Lx

(12)

(13)

Rm is the reflectance of an infinitely thick layer, and

it is related to Ki and K2 through

R =K2 -L K2 -JK2

2 -KS

while L is given by

L=^K2

2 -KX

2

(14)

(15)

Equations (12) and (13) were derived long ago by

Stokes [1] for plane-parallel plates, with similar subsequent derivations by Schuster [4, 17] and Gurevic

60
[20] for light-scattering layers. These are now known

to be a special case of the more general KubelkaMunk theory [21], which we will now consider.

B. The Kubelka-Munk Theory

The Kubelka-Munk theory [5] is based upon a model in which the radiation field is approximated by

two fluxes, the one, I+, traveling from the illuminated

sample surface, and the other, 7_, traveling toward

the illuminated surface (see fig. 2). As radiation

travels from the surface, its intensity is decreased by

scattering and absorption processes, both assumed

to be proportional to the thickness of the medium

traversed. This is partially offset by scattering from

the other beam, so we have

dI+=-(S+K)I+dx+SI-dx. (16)

The component travelling toward the illuminated

surface is similarly described:

dI-=(S+K)I.dx-SI+dx. (17)

^(R-RJ/R^-RJR-l/RJexp [SXjl/R.-RJ]

Rg -R„-{Rg -llRJ exp [SX(l/Ra -RJ]

(20)

Rg is the reflectance of the background (see fig. 2)

and Rn is once again the reflectance of a layer which

is so thick that further increase in thickness does

not alter the reflectance. If eq (19) is integrated over

the limits x=0 to z=co , a simple formula results [5]

Ra> =limR=a-(a2 -l) l/2 =a-b (21)

X—>oo

Using eq (18) this can be rearranged to give the

well-known Kubelka-Munk function F(Ra )

We note in passing that this result follows directly

from eq (12) in the limit x^»*> [23], which once again

shows the close relationship of the Gurevifi and

Kubelka-Munk models.

The constants which we have introduced here are once again phenomenological constants which

describe scattering (S) and absorption (K) within

the medium. If we make the following definition,

S+K

' S

(18)

we can write

-dl.

Sdx

dlSdx

which can be combined into a single differential

equation,

1 mrR2-2aR+l (19)

where R = IJI+ . Equation (19) can be easily integrated over the entire thickness x of the scattering

medium to obtain [5]

!-". . .

///^Backing of Reflectance R g //^/^ // / /////////// / ////

T

dx

Figure 2. Model for the Kubelka-Munk analysis of reflectance and transmittance of a scattering medium [6].

C. Rozenberg Solutions

For a homogeneous semi-infinite medium, a good

approximate treatment of the reflectance for strong

absorbers has been given by Rozenberg [13-15]. The

solution involves summing various successive contr butions to the reflecting power by scattering of

different degrees of multiplicity, and is based upon

concepts developed by Kuznetsov for problems of

visibility [23]. To the nth degree of approximation,

the reflected intensity in an isotropic medium is given

by

(23)

t=l (1+0)'

In this case 6 and <f> define the direction of observation, 1° is the incident beam intensity, 0=- is the

a

ratio of the absorption and scattering coefficients,

and the index i runs over the four components of

the radiation field (see eq (5)). The a u coefficients in

eq (23) are given by

o>u=^2 am(d, 4>)C°(Qo> 0o)

j=i

where the C?(0O) 0o) = J?//? define the polarization

of the incident beam, and the aijt (0, <t>) are coefficients which depend only on the angles of incidence

(0o ,0o) and observation (6,<t>), and on the form of the

scattering indicatrix.

The reflectance of the medium is given by

CiR=J± (Lit n (i+/3)'

(24)

61
where Cl =Ti II1 is the polarization of the reflected

radiation. It will be observed that as /3 increases,

scattering of higher multiplicities becomes less important. Ambartsumian [24] has shown that the

mean multiplicity of scatter in the case of reflection

from a semi-infinite turbid medium is Vl + l//3- Thus

when j8 > 1/3, a fairly accurate solution is obtained by

inclusion of terms up to second or third degree. It is further assumed that the scatter is independent of /3, which should be a good approximation for mixtures

of polydispersive media with different a and a; i.e., as with the addition of dye to a suspension. The re- sulting equation is

R_0 _0AW

R

1 +

(25)

where R0 is the reflectance of the medium itself

(when (8=/30), and

0=1 ai- <+1 (26)

Thus Q is a quantity which defines the relative

contribution of higher multiplicities of scattering

when /3=/30. Both it and R0 are constants which are independent of the nature and concentration of the

colorant.

Equation (25) may be regarded a- a generalization

of Lambert's law to the case of colored media. It

has been derived in a somewhat different form by

Chekalinskaia [25] from scattering theory. In terms

of the reflection (r), forward scatter (t), and absorption (a) constants of a single scattering layer( a-\-r

+£=1) used by Chekalinskaia, the Rozenberg constants can be written

0= a

r+t'

t r+t (27)

D. Exact Solutions

In problems of spectroscopy we often assume

isotropic scatter. We know that in no case is single

scatter actually isotropic [3], although the random

distribution of anisotropic particles and scatter

apparently tends toward an isotropic result [15].

Problems in highly anisotropic scattering media

have been considered by some workers [29-34]. A

detailed discussion of these solutions, often obtained

by numerical computer methods, will not be discussed

here.

For the simple case of isotropic scatter, the

phase function (see eq (2)) can be written

<r-\-a

(30)

Here w0 is known as the albedo of single scatter.

It represents the fraction of the radiation lost by

scattering in a medium where both absorption (a)

and scattering (<r) take place. With this assumption,

the equation of radiative transfer for a planeparallel semi-infinite medium becomes independent

of the azimuthal angle 0 and we have

dl(r, m)

dr

' m) ~^ c°o J_1 /(t.mW- (31)

The integral occurring in eq (31) may be approximated by a Gaussian quadrature, in which case a

set of coupled linear differential equations is obtained,

dli 1 +n

Cut 6 }=—n

(32)

The constants as are Gaussian weighting functions

given by

d)=-p }/ \ f

dp (33)

Pn (ftj) J-i M V-i

Il'ina and Rozenberg [26] have demonstrated the

validity of eq (25) in several instances. Obviously

in a highly absorbing medium where /3>>1, eq (25)

further simplifies to

§=$3. (28)

In the other limit; i.e., where /3<<1, Rozenberg

[15, 27] has shown that the reflectance can be written

as an exponential of the form,

fl.Gi, Mo)=— mo) exp [-4V?0£(m, Mo)] (29)

7T

where h(n, n0), S (n, n0), and q are quantities which

depend on the form of the scattering indicatrix. Romanova [28] has determined these quantities by exact

solution of the radiative transfer equation.

and H) is one of the zeros of the Legendre polynomial,

p.oo. ,

. Passing to the limit n—»<» gives an exact solution

which Chandrasekhar [35] has shown to be of the

form,

/r(M)=x *<(mo) -r- BWBfa). (34)

4 MT"Mo

Here Ir (y) is the reflected intensity in the direction

in from a collimated incident beam in the direction

ju 0 , whose flux per unit area normal to the beam is 7r*e (Mo)- The if—integrals are defined by

HW_HjSd£S£4, (35)

and tables of them have been given by Chandrasekhar [35].

62
Giovanelli [36] has given explicit expressions for

several cases of interest. The total reflectance for

light incident in the direction n0 is

£(M0) =l-#U)(l-co0) 1/2

while that for diffused incident radiation is

ik=l-2(l-«0) 1/2 nH(n)dn.

(36)

(37)

Tables of the first moment of the H — integral,

which occurs in eq (37), have also been given by

Chandrasekhar [35].

Exact solutions to the equation of radiative

transfer can be derived for other phase functions

as well. In general, the phase function may be

expanded as a series of Legendre polynomials

CO p(cos 0)=S o>iPi(cos 9)

1=0

where axial symmetry is assumed. Terms higher

than first degree contribute very little [36, 37],

and thus the approximate phase function.

p(cos e)=w0 (l+a; cos 6)(0'^x^l)

is sometimes used. Exact solutions are available

for scatter according to this phase function also

[36].

Equations (36) and (37) for isotropic scatter can

be readily applied using tables given by Giovanelli

[36], and they of course are of considerable theoretical

interest since they represent exact solutions to

which the various approximate theories can be

compared. We do not expect all media to scatter

isotropically, but we might expect the range of

applicability of the equations to be extended if an

appropriate average scattering coefficient were used.

If we consider a diffuser in which each scatteringcenter scatters light symmetrically about the direction of incidence, we may write [38]

where

or e«=(l—m)<t

r+i

| I(jt)fdn

r+i

I I(n)dn

(38)

(39)

In this approach it is assumed that the same isotropic

solutions (eqs (36) and (37)) may be used for

arbitrary angular^distributions of scatter, so long as the scattering is averaged according to eqs (38) and

(39). Blevin and Brown [38] have shown that the

reflectance curves are essentially the same for

isotropic scatter or for scatter according to the

phase functions 1+P^n), 1+P2 (m), and 1+P,fr*).

This suggests that the reflectance is not a sensitive

function of the scattering indicatrix, and the isotropic

solutions are in fact a goo'd approximation for real

scattering media.

III. Statistical Theory

Continuum models, as we have seen, are somewhat

limited. They involve the use of phenomenological

constants with no obvious relationship in general to

the fundamental constants with which we are familiar

(molar absorptivity, refractive index, particle size

and shape, etc.). Statistical theories, on the other

hand, involve the construction of an appropriate

model and the success of the theory depends on just

how closely the model approximates real sample

conditions.

It appears certain that one of the most severe

limitations of continuum models is the assumption

that they remain valid even when infinitesimal thick- nesses are considered. This is in fact contrary to the

assumption of homogeneous layers previously invoked (see section II-A) , and it is this contradiction

which is largely responsible for limiting the range of

applicability of continuum models, as our subsequent discussion will show.

Let us return to eqs (8) and (9) and assume that

we are now dealing with thin layers whose thickness

is that of the individual particles. If we take layer i to be the first layer and layer j to be the combination

of all the other layers of an 7i-layer sample, we have

*1, 2, 3, . . . n~

t\t 2i 3,4, ... n

1 ^'1^2,3,4, . . . n and

n,2,8. . . . n=ry

ti

2r2 , ,4,...n

1 ^1^2,3,4, . . . n

(40)

(41)

Passing to the limit n—> °° , we write

^1,2,3, . . . n =h,3, i, . . . n =Tco —0

rl, 2,3,... n—r2, 3, i, . . . n =Ro>

Equation (41) then becomes

t

2Rm R„=r- l-rRc (42)

where we have assumed that all layers are the same

so the subscripts on r and t can be dropped. Equation

(42) can be solved for Ra to give an expression for

the reflectance of an infinitely thick sample in terms

of the reflectance and transmittance of a single layer.

The result is

R~= l+r2 -t2

2r

(43)

This equation is fundamental to essentially all statistical theories, the only difference being in the

method used to calculate r and t.

63
We have seen that the Kubelka-Munk theor}^

leads to a solution of the form,

(l-RJ2 =K

2Ra S

When this is solved for R^, we get

R =K+S-^(K+S)2 -S2 s

(44)

plot of F(Rm ) versus K deviates from linearity for

high values of K [7-9], and it appears that eq (48) can be used to explain the deviations in part. It

should be recognized that the deviations at high

values of K are probably a result of anomalous dispersion effects also, but eq (48) does represent an improvement in the range of validity and shows the

need to consider the particulate nature of scattering

media in developing a more precise theory by which

absolute absorptivites can be determined.

which is not of the same form as eq (43).

We assume with Simmons [39] that the planeparallel layers of the Kubelka-Munk model cannot

be made infinitesimally small, but are restricted to

layers of finite thickness I, where I may be interpreted as the mean particle diameter of the sample.

Then the fundamental differential equations of the

Kubelka-Munk theory (eqs (16) and (17)) are re- placed by the finite difference equations:

<Z/WJ+) 1+1 -(J+),

dx I (K+S) (/+),+W_) <+ , (45)

dx

J-±=(K+S) (J_),+x-S(/+), (46)

I

where the subscripts i and (i+1) refer to the ith. and (i+l)st sample layers, respectively. Now for an

infinitely thick sample.

R,

(/-)« (/-)

and Eqs (45) and (46) can be solved to give

2(S+K-KlS-KH/2)

-^(S+K-KlS-K2 l/2) 2 -±S2 2S

(47)

Equations (43) and (47) are identical if we make the

following identifications

S=r/l

K=(l-r-t)/l=a/l

where a is the fraction of the incident radiation which

is absorbed by the layer.

The difference between the traditional and modified Kubelka-Munk solutions may be seen by writing

eq (47) in the form,

K K21 \r J 2r

(48)

It will be recognized that the difference lies in the

addition of the last two terms. It is well known that a

A. The Bodo Model

Bodo [40] used a procedure similar to that used to

derive eq (43) for the derivation of r and t. We will

denote the simple reflectance of the layer surface

by r0 , the absorptivity (defined through I=I0 exp

(—kx)) by k, and the layer thickness (equivalent to

the mean particle diameter) by I. Then according to

figure 3, the reflectance and transmittance of a single

layer are given by

-ikl r=r0 + (1 -r0)

2d-2kl +(l-r0)We

+ (l-r„)Ve-6l! + •

t = ( 1 -r0)

2e ~ kl + ( 1 -r0) We~ 3k l + ( 1 -r0) We-TM1

+ (l-r0)

2r0V7*'+ • •

Summing these series gives

r0[l+(l-2r0) exp (-2H)]

r=- l-r0

2 exp (—2kl)

(l-r0 )

2 exp {-kl)

l-r0

2 exp (—2kl)

'

(49)

(50)

Equations (49) and (50) together with eq (43)

constitute the Bodo formulation, which is in fact

equivalent to that of Stokes [1] and Girin and

Stepanov [41]. Bodo [40] obtained good results with

these formulae for powdered glass samples using the

arbitrary assumption that r0 =0.10. Karvaly [42] has

shown that this was at least in part due to a particularly favorable position for the absorption band

i, ,*2 r -2kl

,, _ *2 r 3 -4kl

(l-r0 ) 2

r 0 V6kl

(,-r0 )V"

,2 2 -3kl

(1- r 0 ) r 0 e

I ,2 4 -Ski

(1 - ro) r0 e

. ,2 6 -7kl

(1 - "<>) r0 e

Figure 3. Reflectance and transmittance of a single layer of thickness I according to Bodd [40].

64
chosen for study, but in the general case, R^ is a very

sensitive function of r0

. Bauer [43] showed that in some cases the layers

should be considered to have rough surfaces where

total internal reflection can take place, and he has

derived expressions analogous to eqs (49) and (50)

for this case.

B. The Johnson Model

Johnson [44] has carried out the summation somewhat differently than Bodo, but with quite similar

results (see fig 4). It is assumed that there are p

layers and that the mean number of attenuating

reflections which the rays undergo in the 2p traversal is yp, so that the reflectance is given by

R,=r0 +2r0 J}(l-r0y* exp (-2kpl). (51)

V

Thus y can be regarded as an adjustable parameter

which gives a semi-empirical account of multiple

reflections as well as scattering losses. The sum for an infinite number of layers is

Ra,=r0 +2r0 exp [y In (1—r0)—2kl]

1—exp [y In (1—

0) —2kl]

which is equivalent to eq (43) with

r=r0[l+(l-r0y exp (-2M)]

t=(l-rQ) v/2 exp (—kl).

(52)

(53)

(54)

The denominator of equation (52) can be expanded

to eive

This result could also be obtained directly by integration of eq (51), which suggests that it may in fact

be a more realistic representation of a real sample

whose particles actually have a range of diameters.

,, .2 -2kl

r0 (l- r o) «

)2r0 (,-r0 ) 3 "e- 6kl

I T

It will be observed from figure 4 that y should be

set equal to 4 for the case of no multiple reflections.

In such a case only one half of the incident light is reflected, however. Johnson has suggested that y can

be estimated from eq (55) by setting Rco = l for

k=0. This gives

(l-ro)*- 1 1 , 1 1 1 y

-2+

4

r° , '6 ?

'0+8

ro+ - (56)

from which y=2 is seen to be a satisfactory approximation for refractive indices smaller than 1.5. A

smaller value of y is required for larger refractive

indices. Companion and Winslow [43] have used a model similar to Johnson's, but which includes all multiple reflections. The summation was carried out

by computer and no explicit expression for the re- flectance was given by these workers.

Johnson [44] also suggested that r0 be equated to

1.5 times the normal Fresnel reflectance. This is meant to account for the random distribution of

particle surfaces and corresponds with an average

incidence angle of approximately 30°. It was shown

[44] that eq (55) yields absorption coefficients for

KC1:T1, KBr:Tl, and didymium glass which agree

satisfactorily with those obtained by transmission

measurements of the same materials.

C. The Antonov-Romanovsky Model

Antonov-Romanovsky [22] has developed expressions which can be used to calculate the true absorption coefficient from reflectance measurements by

connecting the Kubelka-Munk and Bodo theories.

Antonov-Romanovsky treats two limiting cases of

regularly-shaped sample particles, spheres and parallelepipeds (see fig. 5).

For spherical particles the radiation impinges on

the surface from within at the same angle that it entered the particle, since the angles which the cord

of a circle makes with respect to the surface normal

must be the same. Therefore, total internal reflection

is impossible, and I will approximate the particle

diameter, I, actually being somewhat smaller.

In the case of the parallelepiped, some total

internal reflection is possible, but most radiation

probably exits through an opposite face without

further reflection. In this case also it is obvious that I

Figure 4. Model for Johnson analysis of reflectance from a

scattering medium [44]- Figure 5. The Antonov-Romanovsky model for regular spheres

and parallelepipeds [22].

65
is approximately of the same magnitude as I, but

somewhat larger.

Thus for regularly shaped particles it is assumed

that ~l~ I and

l 1n (l-ro) 2 -2ro(l-2r0)F(ig„)

2l

m

(l-r0 )

2 -2r0^(i?co ) (57)

This is an approximate form of the Bod6 model which

is valid for media in which r0

2 «l.

For irregularly shaped particles it is assumed that

the emerging radiation meets the surface of the

particle with an equal probability for all angles. This

will be the case if the mean number of reflections in

the layer m, is large

m>l (n>1.5)-

This condition requires that

klf<^l

where lf is defined as the "free" path length. The

effective path length is then

s=mlf (58)

and it is assumed by Antonov-Romanovsky that

lf =l/2. (59)

The assumption that the emerging radiation is independent of angle allows us to divide it equally

between the two sides of the layer whose thickness is

I, the mean particle diameter. We write

r—

0 =t

and from the law of conservation of energy,

(l-r0)(l—exp(—sk))=l—r—t.

Equations (60) and (61) can be solved to give

_2r0 +(l—r0) exp ( — mkl/2)

t _(1—

c ) exp (—mkl/2)

(60)

(61)

(62)

(63)

Using these in eq (43) gives

, A It, (l-ro) 2 -(l-r0 )F(R„)

ml m

(l-r0 )*-2r0F(RJ

D. The Melamed Model

(64)

_ In contrast with the statistical theories previously

discussed, Melamed carried out a summation over

the reflectance and transmittance of individual

particles rather than layers [46]. Some features of

this model are better understood using an alternative derivation of Karvaly [47], which we follow

here (see fig. 6). A single particle of the surface layer

is shown in the figure; it is shifted laterally with each

reflection to illustrate the path of the radiation.

Of the diffuse radiation which is incident on a given surface particle, the fraction 2ure is reflected,

where the subscript e is used to indicate reflection

of externally incident radiation. Here u is defined as the radiation emerging per unit solid angle from a

particle. 4wu is the solid angle which would be

observed from the second layer if a particle were

removed (see fig. 7).

Of the radiant flux (l-2we) which enters the

particle, the part (l-2ur e )ut contributes to the re- flectance from the first internal reflection, and the

part40 = (l-2ur e ) (l-u)t strikes the underlying layers,

which are considered to form an infinitely thick

powder mass of reflectance R„. The transmission

of an individual particle is represented by the

symbol t. The part AQR„ is reflected back into the

layer,_ where A0 Rw (l-r e ) enters the particle and

AQ Rm r e is reflected back into the underlying layers.

Of that part which entered the particle, A0Rm (lr_ e)ut contributes to the reflectance and A0Ra \lr e)(\-u)t is reflected downward again. This combines

with that externally reflected to give A0Rm r e +

A0RM-rt )(l-^)t=A0Ra> \r e +(l-^t)t]=A0Ra,Q as the

flux reflected downward of which AQRJQ returns

to the layer, etc.

\ t / / /

1 2ui. (l-2ur.)ul A0 R.[l-r.)ul A„R. Q (1 • r. }ut

A„ i (1 - 2ur.|(l-u)l O = i. (1 -u)t

Figure 6. The Melamed Model for powder reflectance as viewed by Karvaly [47].

Figure 7. Illustration of the meaning of the radiant intensity

factor u [47].

66
Proceeding in this manner we can write the following expressions for the reflectance and transmittance

of a layer for radiation from outside (r 1( t x ) and

inside \rIt tT) the sample:

r1 =2ure +(l —2u7e)u-t (65)

rT =r e +(l-re )(l-u)t (66)

*i=(l-2w7e )(l—u)* (67)

tT = (l —r e )u-t (68)

Putting these expressions into (cf. equation (7))

t\t rRa 1-rjR,

for an infinite number of layers gives

(l-2ure )(l-Rto r e )u-t R=2ur,

'(l-Rm ? e )-(l-u)(l-7e )Rj (69)

The application of eq (69) requires some assumptions. Melamed assumes the sample to be composed

of randomly-shaped particles which can be approximated as spheres. Then if we assume the absorbance

is small (kl<l) and that the radiation leaves the

sphere iso tropically,

u== u0

l — (l—2u0 )t (70)

where the shading factor u0 for close-packed spherical

particles is 0.284. The transmittance of a single

spherical particle including multiple internal reflections is written in terms of the internal reflectivity r*:

t=

(l-r{ )M

l-?M

where

M=^[1-(H+1) exp (-kl)]

(71)

(72)

E. The Fassler-Stodolski Model

Fassler and Stodolski [50-52] have pointed out

that the Melamed theory is not only cumbersome to

apply, but contains an inconsistency as well. It is assumed in the Melamed treatment that the radiation is distributed isotropically. However, we have

seen in the previous section that when the Melamed

equation is expressed in terms of the general layer

model, we require different reflectances and transmittances for external and internal radiation (see

eqs (65-68)).

A model which preserves some of the features of

the Melamed theory, but which removes the inconsistency, has been constructed by Fassler and Stodolski as follows: we assume radiation to be externally

incident on a particle layer. The part r e is reflected

at the surface, and the part (1—r e) penetrates the

layer. If we use the symbol a to represent the part

which is absorbed in the layer, including the effect

of multiple reflections, then the part (1—a)(l — r e) leaves the particle either above or below the layer.

We use jr and jt to represent the fractions of the

radiation directed upward and downward, where

Then the reflectance and transmittance of the layer

are given by

r=re +jT (\-a) (l-re)

«.=/, <! -o) (i-y.)

(75)

(76)

For weakly absorbing systems it is assumed that

jr —jt, corresponding with the Antonov-Romanovsky

treatment of irregular particles. In the general case,

fr <Cff Equations (75) and (76) with /,.=/,=% can be

put into eq (42) to get

F(Rj=(i-?e y

a

l +re —(1— re )a

(77)

FiR)^ is once again the Kubelka-Munk function.

Solving eq (77) for a gives

O+Te) F(RJ

(l-re ) [(l-re )+F(Rw )) (78)

is the transmittance of the particle for a single

pass_ [48]_. The mean external and internal reflectivities, re and ?<, were calculated by Melamed as the averages over the Fresnel reflectivity r(0),

- ' f

x/2 r e =2 r(9) sin 6 cos Odd ' (73)

re' r<=(l-sin2 0c) +2 I r(6) sin 6 cos 0dB (74)

for an ideal diffusing surface obeying the Lambert

cosine law [49]. Here 6C is the critical angle.

If we assume the radiation within the powder

layer to be isotropic, we can write (1 —t) as the

fraction absorbed, where t represents the transmittance of a given particle taking multiple reflections into account. Letting us represent the fraction

of the radiation from a given particle which remains

within the layer, we have us t as the part which

enters a neighboring particle where (1— t)us

t is absorbed. Continuing in this way we once again

generate a geometric series which can be summed to

give the absorbance of the layer:

*=i^r (79)

67
Following Melamed [46] the radiation is distributed

among the fractions going up {u u ), going down (ud), and going sideways (us)

uu +ud +us =l.

Since we assume an isotropic distribution of the

radiation, we can write ud =uu =uQ , and so

us =l—2u0

where once again u0 —0.284 for spherical particles.

Using this in eq (79) gives

a=

(i-l+W)

Introducing eq (71) we can express this result in

terms of the transmittance for a single pass,

a= M

-1

^-l+2wo(l-rf )

(80)

The Duyckaerts equation for M (eq (72)) leads to a very complex expression, but with the Felder

approximation [53],

M=exp |j—| hJ> (81)

equations (78) and (80) can be combined to give

where

and

3 l +(y-8)F(RJ

(82)

y2^(1-70(1+7,)

(l-^e) 2

27, 5=

(l-7e )

2

The parameters y and <5 may be treated as constants which depend only on the refractive index,

n. When kl is small, (y-8)F(Rm )^l and dF(Rm )<£l,

and eq (82) simplifies to

(83)

Thus there is a simple linear relationship between the

true bulk absorption coefficient and the KubelkaMunk function for weakly absorbing materials.

F. The Si mmons Model

Simmons [54] has used a simplified particle model

to relate diffuse reflectance to fundamental optical

constants without the use of the cumbersome equations which result from the more refined Melamed

theory [46].

The law of conservation of energy requires that

the total radiant flux impinging on a particle ($e ) must equal that returning from it ($/) except for the

part which is absorbed

*,=*,'+$,<&,

If the spherical particles are assumed to scatter

iso tropically then e =irl2Me , where Me is the

radiant flux density, and

3>

e =irPMe/a-a). (84)

Since the reflectance of an infinitely thick sample is independent of depth, we can write the two alternative expressions for the reflectance,

R= (t12MJ2)

R=

>Z2/2) f

J T

Me (6) sin ede

Me(6) sin Odd

(tt1

2MJ2)

(85)

(86)

<£

e is the total flux integrated over the whole sphere,

so eq (85) and (86) combine to give

,= (wl2/2) £

e (6) sin edd=Trl2Me {R+R-l )j2.

Equating this to eq (84) gives

R=[l-(2a-a2

) l/2]/(l-a). (87)

We let M equal the absorption from a single pass

through the spherical particle. Of the incident

radiation the fraction (1—re) penetrates the particle

where the fraction (1— re ) (1

M) is transmitted, and

of this, the fraction r { is internally reflected. The

total fraction absorbed following an infinite number

of such inter-reflections is

a={\-re){{\-M)+rlM{l-M)

+7/M2 (l-M)+ . . .]. _

(l-7e)(l-M)

1—rM

Again using the Felder approximation [53] (equation

(81)) for spherical particles gives

a= (l-7e)[l-exp (-2H/3)]

1—7 4 exp (-2kl/3)

(88)

A simple expression which is valid for small values

of a can be derived by noting that eq (87) represents

the leading terms of a series expansion of the form,

R=l-(2ay/2 +a- . . . =exp [-(2a) 1 /2

]. (89)

68
expanded we find

a- (l—re)2kl/S l-Te 2kl

(90) l—r i +2ktr il3 l—?t 3

It can be shown that [54]

1-7,

With this result eq (90) can be combined with eq

(89) to give

R=exp [-2n(kl/3y /2

]. (91)

This gives a simple relationship between reflectance

and the fundamental optical parameters which

has been shown to be valid for weakly absorbing

samples [54].

It was found that the above simple particle theory

disagrees with the Melamed theory for large refractive indices [55]. The discrepancy has been attributed

to a breakdown of the assumption that the externally

incident radiation reflected at the particle surface

is scattered equally in the upward and downward

directions, an assumption which obviously becomes

more questionable as n increases. By correcting

the simplified particle model for this non-isotropic

reflection of incident radiation, the relationship

3

r=g re + (l —r {) (l —fe ) GO

Rre/2+l-a (92)

was derived, which gives reflectances which agree

well with those of .the Melamed theory for large

refractive indices [55].

Johnson [56] has pointed out that the Melamed

theory [46] predicts that the diffuse reflectance

decreases with increasing values of the relative

refractive index, n. The same applies to the simplified

particle model described above. Such behavior

is reasonable for large values of n, but for values near unity it has been shown [56] experimentally

that 2? —>0 as n—*l, as would be expected.

The failure of the Melamed theory and the

simplified particle model theory of Simmons for

n values near unity is thought to be due to the

invalid assumption that radiation is returned

equally in all directions from a given particle [57].

It is found that for a rough-surfaced particle; i.e.,

one whose surface obeys the Lambert cosine law,

three-fourths of the incident radiation reverses

its direction while one-fourth does not [55]. It is assumed that the radiation which is incident at a particle surface may be divided into that which

is randomly scattered and that which is transmitted.

If that part which is scattered becomes isotropically

distributed and the direction of the transmitted

radiation is essentially unchanged, then the following

expressions can be derived

1 H-)H?-)'

l—r t t

1

(93)

I —Tit

(94)

These equations for r and t are used with eq (43) to

calculate the reflectance. It is found that the agreement with Johnson's data [56] is only qualitative,

although the solution does have the feature that

R —> 0 as n —> 1.

IV. Discussion of the Various Theories

If we assume isotropic radiation and the simplest

Gaussian quadrature n=l in eq (32), we obtain the

Kubelka-Munk equations (16) and (17), with

S= a and K= ^"

• <r-\-a a-j-a

Thus the Kubelka-Munk function may be regarded

as a first approximation to the complete solution for

the equation of radiative transfer. Detailed comparisons show that the two solutions differ by no more

than a few percent, and even this difference is of

little consequence in a comparative-type measurement [12].

The KubeLka-Munk theory is in fact quite general,

and encompasses many other two-constant theories

which have been derived to suit certain select ex- perimental conditions [7,23]. With the KubelkaMunk solution expressed in terms of hyperbolic functions, it is possible to write formulas for many specific

applications, and to show the connection with several

other theories. It was shown explicitly by Kubelka

[21] that the various equations of Gurevic [20] and

Judd [58] could be derived from the Kubelka-Munk

equations. The Gurevic and Judd theories are less

general, however, and do not encompass completely

the Kubelka-Munk results.

The Gurevic layer model is sufficiently general to

allow us to use it in making some general observations concerning the continuum models and their

range of applicability. Since Kubelka [21] has de69
rived eq (12) of GureviS in terms of the hyperbolic

solution, we have a connection between the parameters used in the two cases. In particular,

L=(a2 -iy<2S=bS

where a is defined by eq (18), and Rw has the same

meaning in the two theories. L and Rm are related

in turn to the Gurevic constants Kx and K2 through

eqs (14) and (15).

It will be recalled that Kx and K2 are positive

definite constants which are characteristic of the

light scattering medium (see eqs (10) and (11)).

That is, we assumed thin homogeneous layers where

T and R depend linearly on x. We find, in fact, that eqs (10) and (11), and cor- respondingly all continuum model results, are applicable only within a limited range. From eq (11) we

have the obvious restriction that K2dx<C_l. It is equally obvious that the equations do not apply

when dx is made arbitrarily small, since the assumption of homogeneous layers requires it to be large

compared with the dimension I of the scattering

particles [14, 39]. Thus we have [16]

l<£dx<C K2

which can alternatively be written

We see that the attenuation due to absorption

within a layer of thickness I must be very small

compared with unity, and we are restricted to

weakly absorbing and weakly scattering materials.

It can in fact be shown by expanding eqs (12) and

(13) in series as a function of x that eqs (10) and

(11) follow only if one assumes that the medium

scatters and absorbs weakly [59].

Several authors have investigated the relationship

between continuum and statistical theories, ter

Vrugt [60] compared the Kubelka-Munk and Bodo

theories and found that the absorption constants

determined by the two methods agree quite well. It

was shown that for weak absorbers the parameters

are related by

Kx=kl (95)

and

Sx=^- (96) 1—r

If the crystals are not too irregular, the mean path

length of radiation in the particle will be approximately equal to the particle diameter and the

absorption constants described by the two methods

will be nearly equal. A more general relationship is

exp (2fcZ)=

2(1—r)

F(RJ/F(r)-1 (97)

Poole [61] has shown that the Kubelka-Munk and

Melamed theories lead to the same results for small

values of the refractive index, n. In general, the

absorption constants determined by the two methods

are not the same and a curve is given by Poole

which relates them as a function of n. It was subsequently shown by Karvaly [47] that the proportionality factor can be expressed analytically as

2 , 1—re S

U

l + re (98)

which is valid for materials of medium absorption

as well.

and that this relationship can in fact be used to

estimate n for a powdered material.

Several of the theories were compared by Companion [62] in an attempt to interpret reflectance

spectra of metal oxides such as NiO and V205. It was

found that the Kubelka-Munk theory gives unexplained distortions and peak shifts, the Melamed

theory requires a shading factor it 0 ~0.1 rather than

0.284 which is appropriate for spherical particles, and

the Johnson estimate of the factor y is not a good

approximation. These disci epancies are all thought

to be a result of the failure of the theories to explicitly include anomalous dispersion effects.

Karvaly [47] has shown that the Johnson model is a limiting case of the Bod6 theory which should be

valid in the limit of large particles or materials of

large optical thickness. Antonov-Romanovsky's formulae for regularly shaped particles are likewise

derivable from the Bodo theory [47]. Careful measurements of the reflectance of two didymium glass

powder samples (Z=7.3 and 12.2 nm) by Karvaly and

Pinter [63] have shown that the Bod6 and AntonovRomanovsky theories give absorption constants

which are accurate to about ±35 percent, whereas

the Johnson and Melamed theories did not lead to

satisfactory results in this case. As mentioned above, the Melamed theory fails to

predict that i?—>0 as n—>1, as must be the case since

there are then no scattering centers in the medium

[56]. In the Johnson and Bodo models the path of

the radiation is altered by internal and external

reflections and refractions at particle surfaces, whereas in the Melamed model it is diverted by "scattering" according to the Lambert cosine law. In all three cases it is assumed that £»A. This allows

scattering to be neglected in the Johnson and Bodo

models. The dependence of R on n in the Melamed

theory is apparently due to the scattering of radiation

internally incident on the particle surface which is

taken to be independent of n. It is interesting to

note that the three theories give about the same

reflectance for refractive indices 1.7<n<2.0.

It is of course not necessary to assume that the

particles are rough-surfaced, i.e., that they scatter

according to the Lambert cosine law. In the other

limit they may be approximated as smooth-surfaced

spheres whose reflection and refraction is governed

by Fresnel's laws. This case has been treated by

Simmons [64] and represents the opposite extreme

between which most real systems lie.

70
The recently published modified particle model

.. theory of Simmons [57] (Equations (93) and (94))

removes the discrepancy in the Melamed treatment.

This modified particle model theory is thought by

Simmons to be the most nearly correct of all diffuse

reflectance theories [39]. It may very well be true,

but its general acceptance must of course await a thorough testing under a variety of conditions by

various workers.

The Fassler and Stodolski theory also shows considerable promise, but has not yet been thoroughly

tested. It does lend itself to the investigation of

important effects such as the influence of particle

size distribution on reflectance properties [52, 65],

and will probably receive considerable attention in

the future.

V. Interpretation of Reflectance Parameters

One of the difficulties with weighing the relative

merits of the various reflectance theories is the necessity of comparing them over a wide range of experimental conditions. In general, the data are rather

incomplete and we must content ourselves with

pointing out the physical significance of the parameters used. We will do this in the present section,

together with making some remarks concerning the

characteristics of appropriate model systems.

The internal transmittance of a powder layer in

terms of hyperbolic functions has been given by

Kubelka, [21]

Tr-

(a sinh bSX+b cosh bSX)

where a and b are previously defined (eqs (18) and

(21)). If we assume that S is small compared with K,

a~b~ K

S

and

T{ ~ exp (-KX).

Under these conditions the transmittance follows a Lambert-type law and K can be regarded as ah

absorptivity characteristic of the substance.

The Kubelka-Munk constant K for a scattering

medium is not equivalent to that which would be

determined by transmission measurements on an

identical material without scatter, however. For a beam traveling through the infinitesimal layer dx at an angle 6, the path length in the layer is dx/cosd,

and thus the mean path length of radiation traveling

downward is

• r9-^—

(99)

Jo 7+60 cos 0

dx lWj

where dl+ /dd is the angular distribution of the intensity in the positive x direction. We of course have

an analogous expression for the 7_ component. If

we assume that the medium is an ideal diffuser the

intensity is the same in all directions, and the angular

distribution of intensity through a given plane

becomes

so that eq (99) becomes equal to 2dx. Thus the effective path length in the scattering laj^er is twice the

normal layer width because of the random angular

distribution, and the apparent absorptivit3r should be

larger by a factor of two.

The above result has been tested using colored

filter glass by Kortum and Oelkrug [66]. By measuring both the reflectance and scattered transmission

of thin layers, both the scattering and absorption

coefficients can be determined. Even though the

powder cannot be packed to the same density as the

original glass, the ratio of reflectance to transmittance values exceeded the theoretical limit, being

in the range K/k~2.6-2.9. This difference was

attributed to effects of total internal reflection which

should increase the path length even further [8]. There are numerous factors which can cause deviations from the factor of two in non-ideal samples, and

these factors have been discussed by Van den

Akker [67]. We will continue to restrict our discussion to ideal systems, however.

The statistical theories predict this ratio between

absorptivity determined by reflectance and transmittance with varying degrees of success. As already

mentioned, ter Vrugt [60] found them to be equal

for weak absorbers (cf. eq (95)). The AntonovRomanovsky theory [22] gives

K=

l-r0 k l+r0

'

For the BG 24 filter glass used by Kortum and

Oelkrug [66] the ratio is 0.92, which does not agree

well with the experimental values.

For low refractive indices Poole [61] showed that

the Kubelka-Munk and Melamed theories agree with

a proportionality factor of 2.7, but much higher

values are required for higher n values (cf. eq (98)).

Fassler and Stodolski [68] have also derived a relationship between K and k which involves the re- fractive index of the medium:

1 k 3u0 (l —r e )

The ratio is calculated to be in the range 2.9-3.1 for

the filter glass used by Kortum and Oelkrug [66],

which is in excellent agreement with the experimental

values. The ^-dependence of K/k has also been calculated by Simmons [71] from his particle model

theory. The result is

k~ 3

which also agrees fairly well with the Kortum

and Oelkrug data [68].

71
Multiple scattering in dense media is a phenomenon

which is not completely understood. Mie [3] has

given an exhaustive treatment of single scatter and

has shown that the scattering varies from the X

-4- dependence of Rayleigh scatter for very small particles to a X-independence for particles which are large compared with the wavelength of the radiation.

There is no a priori reason to expect that these re- sults would apply quantitatively in the case of multiple scatter, but it has in fact been found that

there is a rather close correlation. Kortiim and

Oelkrug [66] found that the scattering varies as ~A~3 - 5 for Z<X, as for and as ~X° for

X, where I is the mean particle diameter. It is safe

to assume that the scattering coefficient S is independent of wavelength in most studies, but deviations are sometimes observed in the short wavelength

end of the spectrum which are probably due to a breakdown of this assumption [69].

The scattering coefficient has been found in several

studies to be inversely proportional to the mean

particle diameter I, [70-72] the proportionality factor

depending apparently on the nature of the material

being studied. Using the simplified particle model,

Simmons was able to derive the result [69].

s=r\

This should not be taken as much more than an order

of magnitude estimate, since a proportionality factor

somewhat larger than unity is apparently more appropriate in many cases [66]. The modified particle

model gives [39]

s=i-* +~ (1-r.) (1-

(l-r,/2) (l-7«/2)

l+Tit/2 ]}

Although this result appears to not yet be thoroughly

tested, the term in braces is said to be relatively

insensitive to changes in absorptivity [41], and

probably varies significantly only with changes in

refractive index, n. The same is true of the AntonovRomanovsky result [22],

S-- vi Wv

and that derived b}^ ter Vrugt [60] (see eq (96)).

Quantitative calculations with the Antonov-Romanovsky expression give scattering constants that are too small by about a factor of three [47].

By taking the particle size distribution into ac- count, Fassler and Stodolski [65] were able to calculate scattering coefficients which agree very well

with those determined experimentally. Their ex- pression is

SI': \—f*—k -a-(2/-l)(l-a)

l+F*+£

-(2/,-l)(l-a)

(100)

where a and/; have their previously defined meanings, it being recognized that the factor (2ft-l)

defines the anisotropy of radiation in the particle

\&yer. £ is the effective cross section for holes in the

particle la}^er, r* is the mean external reflection

coefficient for side scatter taking account of holes

and back scatter, and T is a parameter which is related to the mean particle diameter. For a particle

size distribution function of the form

I' is given by

f(l)=AlBeB1/1

7,_£+3 7 ~~ B

Fassler and Stodolski [65] emphasize the fact that

the scattering is particle size-dependent, so that for

quantitative reflectance spectroscopy it is essential

to have a set of standards with known, small particle

size distribution and of various mean particle diameters. Then it is possible to mix the sample with a standard of similar particle size so that the scattering

characteristics are not greatly changed. This is important for comparative measurements.

The effect of particle shape is also important. It appears at the present time that there is no better

way to test the various reflectance theories than

to make transmission and reflectance measurements

on a given glass sample before and after grinding,

respectively. The characteristics of glass samples

subjected to various grinding conditions have been

studied by Karvaly and Pinter [73]. These factors

will not be discussed here, but it should be emphasized that the proper definition of reflectance

standards must certainly quantify not only size and

shape, but the precise nature of any adsorbent

materials and the surface conditions as well.

VI. References

[1] Stokes, G. G., Proc. Roy. Soc. (London), 11, 545 (1860-

62).

[2] Rayleigh, Lord, Phil. Mag. 41, 107 (1871).

[3] Mie, G., Ann. Physik, 25, 377 (1908).

[4] Schuster, A., Astrophys. J. 21, 1 (1905).

[51 Kubelka P., and Munk, F., Z. tech. Phys. 12, 593 (1931).

[6] Schwarzschild, K., Sitz. ber. Preuss. Akad. Wiss. Berlin

1914, 1183.

[7] Wendlandt, W. W., and Hecht, H. G., Reflectance

Spectroscopy (Interscience, 1966).

[8] Kortum, G., Reflexionsspektroskopie, (Springer-Verlag,

1969; published also in an English edition).

[9] Frei, R. W., and MacNeil, J. D., Diffuse Reflectance

Spectroscopy in Environmental Problem-Solving (The

Chemical Rubber Co. Press, 1973).

[10] Transactions of the First Conference on the Spectroscopy of Light-Scattering Media, Moscow, 29-30

March 1956, Izvest. Akad. Nauk. SSSR, Ser. Fiz.,

21(11), 1957; (Columbia Technical Translation, Bull. Acad. Sciences SSSR, Physical Series, 21(11) (1958)).

72
[11] Wendlandt, W. W., Modern Aspects of Reflectance

Spectroscopy, Proceedings of the American Chemical

Society Symposium on Reflectance Spectroscopy,

Chicago, 11-12 September 1967 (Plenum Press, 1968).

[12] Hecht, H. G., The Present Status of Diffuse Reflectance

Theory, in ref. [11], pp. 1-26.

[13] Rozenberg, G. V., Usp. fiz. Nauk 56, No. 2 (1955).

[14] Rozenberg, G. V., Izvest. Akad. Nauk SSSR, Ser. Fiz.

21, 1473 (1957).

[15] Rozenberg. G. V., Usp. fiz. Nauk 69, 57 (1959).

[16] Stepanov, B. I., Izvest. Akad. Nauk SSSR, Ser. Fiz. 21,

1485 (1957).

[17] Schuster, A., Phil. Mag. 5, 243 (1903).

[18] King, L. V., Phil. Trans. Roy. Soc. (London), A212, 375

(1913).

[19] Kubelka, P., J. Opt. Soc. Am. 44, 330 (1954).

[20] Gurevic, M., Phys. Zeits. 31, 753 (1930).

[21] Kubelka, P., J. Opt. Sec. Am. 38, 448 (1948).

[22] Antonov-Romanovsky, V. V., Zhur. ekspr. i teor. fiz. 26, 459 (1954).

[23] Kuznetsov, E. S., Izvest. Akad. Nauk SSSR, Ser. geog.

i geofizika. 5 247 (1943).

[24] Ambartsumian, V. A., Dokl. Akad. Nauk Armenian

SSR, 8, 101 (1948); J. Phys. USSR 8, 65 (1944).

[25] Chekalinskaia, I. I., Izvest. Akad. Nauk SSSR, Ser.

Fiz. 21, 1494 (1957).

[26] Il'ina, A. A., and Rozenberg, G. V., Dokl. Akad. Nauk

SSSR 98, 3 (1954).

[27] Rozenberg, G. V., Dokl. Akad. Nauk SSSR 145, 775

(1962).

[28] Romanova, L. M., Opt. i Spektroskopia 17, 250 (1964).

[29] Romanova, L. M., Opt. i Spektroskopia 13, 429, 819

(1962); 14, 262 (1962).

[30] Sagan, C, and Pollack, J. B., J. Geophys. Research

72, 469 (1967).

[31] Orchard, S. E., J. Opt. Soc. Am. 59, 1584 (1969).

[32] Reichman, J., Appl. Optics 12, 1811 (1973) ; Egan, W. G.,

Hilgeman, T., and Reichman, J., ibid., 12, 1816

(1973).

[33] Chu, C. M., and Churchill, S. W., J. Phys. Chem. 59,

855 (1955); Evans, L. B., Chu, C. M., and Churchill,

S. W., J. Heat Transfer, 87C, 381 (1965); Chu, C. M.,

Churchill, S. W., and Pang, S. C, in Electromagnetic

Scattering, M. Kerker, Ed. (MacMillan Company,

New York, 1963).

[34] Irvine, W. M., Astrophys. J. 152, 823 (1968).

[35] Chandrasekhar, S., Radiative Transfer, (Clarendon

Press, 1950) (Reprinted by Dover Publications,

Inc., 1960).

[36] Giovanelli, R. G., Optica Acta 2, 153 (1955).

[37] Pitts, E., Proc. Phys. Soc. B67, 105 (1954).

[38] Blevin, W. R., and Brown, W. J., J. Opt. Soc. Am. 51,

975 (1961).

[39] Simmons, E. L., Appl. Optics 14, 1380 (1975).

[40] Bod6, Z., Acta Phys. Hung. 1, 135 (1951).

[41] Girin, O. P., and Stepanov, B. I., Zhur. ekspr. i teor.

fiz. 27, 467 (1954).

[42] Karvaly, B., Acta Phys. Chem. 16, 107 (1970).

[43] Bauer, G. T., Acta Phys. Hung. 14, 311 (1962).

[44] Johnson, P. D., J. Opt. Soc. Am. 42, 978 (1952).

[45] Companion, A., and Winslow, G. H., J. Opt. Soc. Am.

50, 1043 (1960).

[46] Melamed, N. T., J. Appl. Phys. 34, 560 (1963).

[47] Karvaly, B., Acta Phys. Hung. 28, 381 (1970).

[48] Duvckaerts, G., Spectrochim. Acta 7, 25 (1955).

[49] Judd, D.B., J. Res. Nat. Bur. Stand. (U.S.), 29, 329-332

(Nov. 1942) RP1504.

[50] Fassler, D., and Stodolski, R., Z. Chem. 11, 276 (1971).

[51] Fassler, D., and Stodolski, R., Z. Chem. 11, 434 (1971).

[52] Fassler, D., and Stodolski, R., Z. Phys. Chem. (Leipzig),

251, 183 (1972).

[53] Felder, B., Helv. chim. Acta, 47, 488 (1964).

[54] Simmons, E. L., Opt. Acta 18, 59 (1971).

[55] Simmons, E. L., Opt. Acta 22, 71 (1975).

[56] Johnson, P. D., J. Appl. Phys. 35, 334 (1964).

[57] Simmons, E. L., J. Appl. Phys. 46, 344 (1975).

[58] Judd, D. B., J. Res. Nat. Bur. Stand. (U.S.), 12, 345-351

(Mar. 1934) RP660; ibid., 13, 281-291 (Sept. 1934)

RP709.

[59] Stepanov, B. I., Chekalinskaia, I. I., and Girin, O. P., Trudy (Transactions Inst. Phys. Math. No. 1, 152

(1956)).

[60] ter Vrugt, J. W., Philips Res. Repts. 20, 23 (1965).

[61] Poole, C. P., Jr., Z. Naturforschung 19a, 394 (1964).

[62] Companion, A. L., in 'Developments in Applied Spectroscopy,' Vol. 4, E. N. Davis, Ed. (Plenum Press, 1965).

[63] Karvaly, B., and Pinter, F., Acta Phys. Hung. 29, 203

(1970).

[64] Simmons, E. L., South African J. Sci. 70, 219 (1974).

[65] Fassler, D., and Stodolski, R., Z. Phys. Chem. (Leipzig),

252, 133 (1973).

[66] Kortum, G., and Oelkrug, D., Z. Naturforschung 19a,

28 (1964).

[67] Van den Akker, J. A., Theory of Some of the Discrepancies Observed in Application of the Kubelka-Munk

Equations to Particulate Systems, in ref. [11], pp.

27-46.

[68] Fassler, D., and Stodolski, R., Z. Chem. 11, 395 (1971).

[69] Simmons, E. L., Opt. Acta 19, 845 (1972).

[70] Kortum, G., Braun, W., and Herzog, G., Angew. Chem.

Intern. Ed. 2, 333 (1963).

[71] Kortum, G., and Haug, P., Z. Naturforschung 8a, 372

(1953).

[72] Kortum, G., and Vogel, J., Z. Phys. Chem. N.F. 18, 110

(1958).

[73] Karvaly, B., and Pinter, F., Silikattechnik 21, 7 (1970).

(Paper 80A4-902)

73

NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 466, Standardization in Spectrophotometry and Luminescence

Measurements, Proceedings of a Workshop Seminar Held at NBS, Gaithersburg, Md., November 19-20, 1975 (issued May 1977).

Calibration of Reflectance Standards

W. Budde

National Research Council of Canada, Ottawa, Canada K1A OR6

(May 26, 1976)

Measurements of the diffuse spectral reflectance are usually not made as direct measure- ment of the incident and the reflected radiant flux but rather as measurements relative to a

standard of known reflectance value.

For the calibration of such standards, different methods have been described in the

literature

1. Goniophotometric methods, also called Indicatrix methods or point-by-point

methods.

2. Methods based on the Kubelka-Munk theory.

3. Integrating sphere methods according to Taylor, Benford, Sharp-Little, van den

Akker, Korte.

Various materials such as magnesium oxide, barium sulfate or opal glass are being used

as standards. Their suitability as transfer or as working standards will be discussed.

The results of comparative measurements between some of these methods will be given.

Key words: Barium sulfate; diffuse reflectance spectra; magnesium oxide; opal glass;

radiant flux; reflectance standards; standards calibration.

I. Introduction

Measurements of the diffuse spectral reflectance

have been used for many years as a tool in the

measurement of color [l].

1 However the extensive use of such measurements in analytical chemistry

has been developed only recently [2]. In general

the measurement of a reflectance requires the

measurement of the flux reflected from a surface

and that incident on this surface. Such measurements

are difficult and therefore in most practical applications only reflectance measurements relative to a standard of known value are being made. The

"calibration" of such standards is then done either

by a definition or convention (e.g., to agree [5] that

the reflectance of smoked MgO=1.0), or by suitable

measurements.

It is the purpose of this paper to outline some of

the most important methods for such calibrations,

to discuss briefly the physical properties of various

materials which are used as standards, and to

present a few intercomparative data. In presenting

the various methods only the main features will

be given and those characteristics which are important for distinguishing the methods and the

quantities which are measured. Giving the full theory for each method and all experimental details

is beyond the frame of this paper and it must be

left to the reader to study the details in the original

references.

'National Research Council Paper No. 15041.

1 Figures in brackets indicate the literature references at the end of this paper.

There are essentially three groups of methods for

absolute reflectance measurements:

(1) Goniophotometric measurements of the re- flectance indicatrix with numerical integration.

(2) Methods based on the Kubelka-Munk theory.

(3) Methods using integrating spheres.

Although examples for all three groups will be given

the emphasis will be on methods in the last group

which has many interesting varieties and is most

widely used.

II. Terminology

The terminology in this paper will generally be in

accordance with CIE terminology [3] with the following exceptions and additions:

(1) The terms radiance and luminance are being

used interchangeably. Luminance is used mainly

where photometric measurements are involved, while

radiance is used in the context of spectral measurements. Geometrically these terms are identical, however luminance refers to values measured with a

detector whose spectral sensitivity distribution agrees

with the CIE photometric standard observer function.

(2) Standards for diffuse reflectance measurements

may be calibrated in three different geometries

(a) diffuse/diffuse (d/d)

(b) normal/diffuse (0/d)

(c) diffuse/normal (d/0).

75
The first term always describes the geometry of

illumination whereas the second term describes the

geometry of the measurement. Diffuse illumination

is achieved by means of an integrating sphere. For

the measurement of diffusely reflected radiation

either a goniophotometer, a hemispherical mirror or an integrating sphere is used.

For colorimetric measurements the CIE recommends four geometries: 0/d; d/0; 0/45 and 45/0. For

the purposes of this paper the d/d geometry is added

whereas the 0/45 and 45/0 geometries are not discussed. The reason for this selection is that many

techniques in diffuse reflectance spectroscopy are based on the Kubelka-Munk theory which requires

the use of an integrating sphere.

(3) The term "reflectance" applies only for the

d/d and the 0/d geometry. For the d/0 geometry the

term "reflectance factor" (3 d/0 applies which is defined [3] as: ratio of radiant (luminous) flux re- flected in the directions limited by the cone to that of

the perfect reflecting diffuser identically irradiated

(illuminated). If a sample is highly opaque and very

matte so that its reflection indicatrix approximates

that of a perfect diffuser, then the reflectance factor

j3 d/0 will have the same value as the reflectance

Po/d and the reflectance pd/d. For simplicity the term

reflectance will occasionally also be used here for the

d/0 geometry.

(4) In this paper the word "calibration" is used for

two different procedures

(a) Calibration of a physical standard means to

establish its reflectance value by a suitable procedure.

According to the old CIE convention [5] this procedure consisted of preparing a smoked MgO surface

and giving this surface the reflectance value 1.0.

Now [4, 6] this procedure consists in an absolute

reflectance measurement which establishes the re- flectance of a physical standard with respect to the

perfect reflecting diffuser.

(b) Calibration of an instrument for relative

measurements refers to the adjustment of this

instrument so that correct reflectance values of

arbitrary specimens can' be determined. For this

adjustment a suitable standard with a known

reflectance value is used.

This method is usually time consuming and

difficult. Since the reflected flux must be measured

at many angles and the measurement of the incident

flux requires a considerable change in the experimental set-up, great care must be taken that source and detector are stable over extended periods of

time. The greatest difficulty arises from the fact that

the incident flux and the flux reflected into the

narrow cone defined by the photometer differ by

about 3 to 4 orders of magnitude. This difficulty is usually overcome by using an auxiliary source which

provides an intermediate level of signal so that two

ratios of about 100 to 1 are to be measured.

This method was used for the earliest diffuse

reflectance measurements, strangely enough for

determining the reflectance of black materials such as soot [9-11]. However, after integrating sphere

methods were developed the goniophotometric method was practically only used for comparison: e.g., McNicholas [12], Taylor [13], Korte [7] and Egan

[14] report such comparison of values obtained by

goniophotometry or with the integrating sphere

method. In recent years Kartachevskaia [15] and

Morren [8] used the goniophotometric method by

itself to determine reflectances of various materials.

All measurements of the reflected flux at various

angles and the integration may be combined into one

single step if a hemispherical mirror is used. In

figure 1 sample S and detector T are mounted in two

closely spaced conjugate points of a hemispherical

mirror M. The incident beam is first directed to the

detector for the measurement of the incident flux.

Then the beam is switched to irradiate the sample.

The total flux reflected from the sample is collected

by the hemispherical mirror and directed to the

detector.

In this technique the reflectance of the hemispherical mirror must be known. It may be determined if a

flat sample of the mirror material is mounted at the

sample port and a normal measurement is made. The

resulting ratio of the two responses is the square of

the mirror reflectance.

This technique was used for the earliest reflectance

measurements by Roj'ds, 1910 [10] and Coblentz,

1913 [11] and more recently by Derksen et al in

1957 [16].

III. Goniophotometric Measurements

This method is also called the "indicatrix-method"

or "point-by-point method." The sample is irradiated

with a narrow beam usually in the direction of or near the normal (angle of incidence e! = 0°) and the

reflected radiation is measured at various angles

(angle of observation 0°<e2 <90°) and various

azimuths. The incident flux </> 0 is determined by

measuring either the intensity of the source [7] or the irradiance at the plane of the sample surface [8]. The reflected flux <j> r is determined by numerically

integrating the measured goniometric values of the

radiance [8] or the intensity [7] of the sample.

Figure 1. Hemispherical mirror method: M—hemispherical

mirror; S =sample; T= detector = thermocouple.

76
The hemispherical mirror technique is not considered to be an integrating sphere technique because

it consists in the actual measurement of the ratio

of the reflected to the incident flux whereas in

integrating sphere techniques the effect of the

sample on the radiance of the sphere wall is utilized.

This effect is considerably more complex than the

simple reflection from the hemispherical mirror.

IV. Methods Based on the KubelkaMunk Theory

The Kubelka-Munk theory [17, 18] provides

various relations between reflectance values of

translucent materials such as powders, sheets of

paper, layers of paint over various backgrounds

and other physical parameters such as thickness

of the layer, "dilution" of a powder with other

powders, transmittance, absorption coefficient, etc. These equations suggest certain methods for absolute

reflectance measurements which have been tried

and reported in the literature.

Stenius [19] measured the reflectance of a sheet

of paper over backgrounds of different reflectances

relative to a standard and was able to show how

the absolute reflectance of the standard used for the

relative measurements could be determined from

these values (eqs. 12 and 14 of his paper). However

it appears that his values are of poor accuracy and

he concluded that the Kubelka-Munk equations

are not immediately applicable to hand-made

sheets of paper. In 1968 A. E. Aneliunas presented

a paper at the annual meeting of the Canadian

Pulp and Paper Association in which he investigated

various aspects of Stenius' method and proposed

a modification which consisted in the measurement

of different numbers of sheets of paper thus varying

the thickness of the layer by known amounts. From

the thicknesses and the associated relative reflectances he determined the scattering coefficient and

the absolute reflectance. Although the reflectance

values for pressed MgO determined by this method

agreed closely with those determined by other

methods, indicating the suitability of this method,

it was not published in print [63].

A different approach was taken by Butler [20]

who was determining absorption coefficients, re- flectances and scattering coefficients of various

scattering materials from transmittance measurements of layers of various thicknesses. The theory

shows that under certain conditions the optical

density (= log(l/J') where Tis the measured transmittance) is a linear function of the thickness X.

The ordinate intercept of this line is related to the

reflectance of an infinite layer of the material.

Law and Norris [21] used measurements on small

glass spheres as a model particulate system to test

the suitability of the method. However in these two

papers reflectance values were only a by-product

while other parameters such as refractive index,

particle size, scattering and absorption coefficients were of major interest. No measurements of the

reflectance of commonly used reflectance standards

are reported.

The third method was proposed by Lindberg [22]

who "diluted" BaS04 powder with Fe2 03 powder

in known concentrations and showed that from

these concentrations and the relative reflectances

measured for each concentration the absolute

reflectance of the standard used for the relative

reflectance measurements could be determined. For

a pure BaS04 he found values very close to those

published elsewhere. However, the method is timeconsuming and it was estimated that the determination of the reflectance "should be good to 0.5

percent" which is a poorer level of accuracy than

can be achieved by other methods.

It appears that only the last of these three

methods was developed specifically for the calibration

of reflectance standards. It was attempted to

achieve this with instrumentation which is standard

equipment in an analytical laboratory: a spectrophotometer with a reflectance attachment and a weight scale.

Interesting as these methods are their complexity

and lack of accuracy and the fact that they are not

immediately applicable to all types of reflectance

standards seem to have precluded these methods

from being adopted by major standardizing laboratories for the calibration of reflectance standards.

V. Integrating Sphere Methods

In 1912 Nutting [23] published a method for absolute reflectance measurements based on the theory

of two parallel infinite planes (which he realized by

means of a ring mirror). His method is not of interest

and has rarely been used afterwards. His values were

discussed and rejected in 1920 when three papers

were published on reflectance measurements by

means of integrating spheres.

A. The Taylor Methods

Based on certain considerations developed during

the construction of an 88 inch integrating sphere for

luminous flux measurements [24], A. H. Taylor in

1920 published a paper [13] in which "five absolute

methods of measuring reflection factors are described,

at least three of which are apparently new." One of

these methods is for the measurement of specular

reflectance and one is a goniophotometric method as described in section III. This latter method was used

to verify the values obtained by the sphere methods.

The three integrating sphere methods are the "new

methods" and are described as follows.

First Taylor Method

The integrating sphere, see figure 2a, has two en- trance ports A and C and one sample port S which

comprises about 10 percent of the total sphere area. Through a viewing port V a photometer views an

area on the opposite wall for measurements of the

luminance ("brightness" in Taylor's terminology)

77
I

Figure 2. First and second Taylor method: A and C apertures

for entering beam; V=window for photometer; S = sample

aperture; L= light source.

of the wall. For this method the light source L re- mains at port A.

For the determination of the reflectance of the

sphere wall two measurements are made

(1) The sample port remains open or is covered

with a nonreflecting sample. A luminance B0 is measured.

(2) The sample port is covered with a sample

having the same paint as the sphere wall. A

luminance B is measured.

From the measured ratio k=B/BQ and the known

geometrical constants of the sphere (diameter of

sphere and sample port) the diffuse-diffuse reflectance pw ("ra" in Taylor's eq 9) is calculated. For

the determination of the reflectance px of an arbitrary sample the sample port is covered with this

sample and a lum' nance Bx of the sphere wall is measured. From the ratio kx =Bx/BQ (where B0 is the luminance of the wall with S uncovered as before) the geometrical sphere constants, and pW)

the reflectance px is calculated.

This method obviously yields the diffuse/diffuse

reflectance of sphere paint and sample. It is necessary

to determine the reflectance of the sphere paint,

before that of a sample can be determined. In

Taylor's theory the apertures for photometer and

entering beam are considered negligibly small.

Preston [25] and Middleton and Sanders [26] ex- panded the theory to make corrections for these

apertures and proposed some modifications to the

experimental technique. While Taylor and Preston

used white light for their experiments, Middleton

and Sanders incorporated a monochromator in the

apparatus and reported spectral values. Budde [27]

used this method with a small sample aperture so that the difference between the flat sample area and

the spherical cap over the sample area was negligibly

small. Thus the theoretical considerations and the

final equations were simplified and a close resemblance to the "fractional sphere method", see section 5.2, was obtained without the limitation of

the fractional sphere method which is applicable to

sphere paints only.

Second Taylor Method

In this method the reflectance pm of the sphere

paint is determined as in the first Taylor method.

Then the source L is mounted at the entrance

port C, see figure 2b. The sample port is again

covered with the flat sample of the sphere paint and a luminance B' is measured on the sphere wall. Then

the unknown samp e s mounted at the sample port

and the luminance Bx is measured. From the ratio

R=BX/B', the geometrical sphere constants, and

pw , the reflectance px is calculated (Taylor's Eq 16).

In this method the did reflectance of the sphere

paint is determined in the first step but in the

second step the 0/d reflectance of the flat sphere

paint sample is compared with that of the unknown

sample. The assumption is that Pd/d=Po/d for the

sphere paint which is only true if the paint is very

matte and opaque.

Third Taylor Method

Taylor describes this method as follows: "the

sample was placed in a sphere and a very narrow

beam of light was projected through a small hole

in the sphere wall onto the sphere surface at a point

unscreened from the observation window, then

onto the sample so placed that none of the first

reflected light from it could reach the observation

window. The ratio of the brightness of the window

in the second case to that in the first case is the

reflection factor of the test surface."

Taylor gives no drawings for this method but

figures 3a and 3b may be used to explain the salient

facts. The sphere has a screen B which blocks any

direct radiation from the sample S to the observation

window W which is probably a ground glass. It also

may be the area viewed by a photometer through an

aperture in the opposite wall. First the incident flux

<t>0 irradiates the sphere wall and the observation

window receives radiation directly from the irradiated area as well as by multiple reflection from the

sphere. Then the source is moved around to irradiate

the sample S. The observation window receives only

radiation by multiple reflection. The ratio of the two

irradiances at the window is the 0/d reflectance of

the sample.

4> 0 \

s s

(a) (b)

Figure 3. Third Taylor method: <t>o=ftux entering the sphere;

S = sample; B=baffle; W= observation window.

The sphere is shown in two different views to illustrate the location of the baffle.

78
The essential feature of this method is the introduction of the screen B which blocks the observation

window from receiving radiation from the irradiated

spot on the sample. It is important to note that in

this method it is not necessary to determine first the

reflectance of the sphere paint. The measured ratio

is not that of sample reflectance to sphere wall

reflectance but rather the absolute reflectance of the

sample itself. For this method, Taylor constructed a simple

instrument which is described in reference 28. The

influence of the apertures and the goniophotometric

properties of the sphere paint were investigated by

Reule [28a].

It must be mentioned that in the literature the

terms "Taylor Method" or "Taylor Sphere" are often used without a clear indication which of the

three methods is meant.

B. The Fractional-Sphere Method

Also in 1920 F. A. Benford published a paper [29]

on an integrating sphere method in which the sphere

has one or more removable sections. The method is based on the fact that the luminance of the sphere

wall depends, among other factors, on the reflectance

of the sphere paint and on the actual amount of the

wall area if the sphere is incomplete. If the sphere has

removable areas so that two fractional spheres with

remaining relative wall areas ai—Ai/4:irr2 and a2 =

A2 /4:irr2 are obtained and if the two luminances or irradiances of the wall measured in the two fractional

spheres are Rx and R2 , the amount of radiation entering the spheres being identical, then it can be shown

that the reflectance of the sphere wall is given by the

simple relation

R\ —R2 w U\Ri —a2R2

This method is directly applicable only for materials

which can be applied to the inner surface of the sphere

and yields the d/d reflectance of the material. It has

a strong resemblance to the first part of the first

Taylor method for the determination of the re- flectance of the sphere paint. However in Taylor's

method the removable portion of the sphere is flat

and this makes Taylor's theoretical considerations

and the final equation rather complicated. In Benford's method all removable sections are spherical

and the theory and final equation are simple.

In two subsequent papers [30, 31] extensions and

applications are described. In 1955 Tellex and Waldron [32] used this method for the determination of

the reflectance of electrostatically deposited, smoked

C. The Sharp-Little Method

The third paper on integrating sphere methods

published in 1920 was that by Sharp and Little

[33]. This method is in fact a geometrical inversion

of the third Taylor method and may be explained

using figure 4. Flux <f> 0 enters the sphere and forms an

irradiated spot at the wall from which flux <p' 0 is reflected. The sample S receives only indirect ir- radiation from the sphere wall due to multiple

reflections because of the screen B while all other

areas of the wall receive direct illumination from

<t>' 0 as well as the indirect radiation. The photometer

P measures first the luminance Bs of the sample and

then the luminance Bw of the unscreened sphere

wall; the d/0 reflectance px of the sample is given by

Pz=Bs/Bw . Here again the essential part is the baffle B which

prevents the direct illumination of the sample from

the irradiated area (which may be considered a secondary source within the sphere).

The authors assumed that the apertures for the

entering flux and for the photometer were negligibly

small. Budde [34] expanded the theory to allow

corrections for the apertures and also indicated that

the same type of corrections are applicable to the

third Taylor method.

The schematic diagram of an instrument [35] which

may be easily converted from the Sharp-Little

geometry to that of the third Taylor method is shown in figure 5. The lamp is imaged by lens Jji

into lens L2 which in turn images the aperture

Fi onto the sphere wall. The baffle near the center

of the sphere blocks any direct radiation from the

image (the secondary source within the sphere)

to the sample. The "Filter" is one of a set of interference filters in a filter wheel to allow spectral

measurements. A photometer system, consisting

of lens L3 , aperture F2 , an opal glass and a photomultiplier, measures the radiance of the sample

Bs and then swings around to measure the radiance

Bw of the sphere wall. It can be shown that

_BS A0 px BW A,+A2

where -Ao=47rr2 =total sphere area, ^4i =area of

sample port and ^42 =area of remaining sphere wall.

The factor AQ/(Ai+A2) represents a correction

factor for the entrance aperture and the two observation apertures which are supposed to be black.

In this set-up the instrument yields the diffuse/

Figure 4. Sharp-Little method: <j> 0 flux entering the sphere;

<t> 0

' = diffuse source within the sphere; B=baffle; S = sample;

P = photometer viewing either the sample or the sphere wall.

79
Multiplier

Opal glass \.

"A.Vn Position

Filter

Lamp

Baffle

Nr'7\ Position

Figure 5. Detailed schematic diagram of an instrument for measurements of p d/ 0 (according to Sharp-Little) or p 0n (according to the third Taylor method)

Explanations in the text.

normal reflectance factor according to the SharpLittle method. It may be easily converted to the

inverse geometry by exchanging the source (with

lens LO and the detector (with the opal glass).

Then it yields the normal/diffuse reflectance according to the third Taylor method.

This instrument has been constructed at the

National Research Council of Canada and is being

used for the calibration of reflectance standards

[35].

D. The Double-Sphere Method

In 1966 van den Akker et al. [36] published a paper on absolute spectral reflectance measurements

in which an auxiliary sphere is mounted at the

sample port of the integrating sphere of a diffusereflectance, double-beam spectrophotometer, see

figure 6. At the reference port of the spectrophotometer a flat sample is mounted which has the

same paint as the auxiliary sphere. If the ratio of

the port area of the auxiliary sphere to the total

inner area of this sphere is p and the ratio of the

reflectance of the auxiliary sphere to that of the

flat sample (the ratio measured by the spectrophotometer) is r then it is shown that the diffuse/diffuse

reflectance of the sphere paint, and the flat sample,

is given by:

Pm=(r-p)f[r(l-p)]

An application of this method and some error analysis

was published shortly afterwards in a paper by

Goebel et al. [37], and this method was also adopted

in ASTM and TAPPI Standards.

SAMPLE WITH

AUX . SPHERE

PAINT

SPECTROPHOTOMETER

SPHERE

AUXILIARY

SPHERE

Figure 6. Double sphere method.

This method is presently used at the NBS for the

calibration of reflectance standards.

E. The Korte (PTB) Method

While in all previous methods the samples were

mounted at a port of the integrating sphere Korte [7] described a method where the sample is mounted

in the center of an integrating sphere. Six lamps are mounted in one hemisphere so that they do not

irradiate the sample surface directly. The sample is irradiated only indirectly from the other hemisphere,

see figure 7. The ratio of the radiance Ls of the sample

observed through window Vi to the radiance L of

the illuminating hemisphere observed through window V2 gives the reflectance factor (3d/0 =Ls /L of the

sample which in this case for a matte sample is equal

to the reflectance, p0 /d80
Figure 7. Korte-method: B=baffles; S= sample with front

surface facing observation window V\; V\ and V 2 = observation windows.

For the measurement of the sphere radiance the photometric system is looking

past the sample at the sphere wall in the vicinity of window Vi.

The most important property of the instrumental

arrangement is the uniformity of the radiance of the

irradiating hemisphere. Korte reports that a test was

made on this uniformity and that it was better than

0.1 percent. The irradiating hemisphere has an

aperture for the photometer. A correction for this

aperture, which is a nonirradiating area, must be

made.

Erb [38] modified this method by placing just one

lamp near the center of the sphere at the back of the

sample.

This method was already described in principle by

de la Perelle [39]. However Korte refined this method

considerabty to make it suitable for the calibration

of standards at the ETB, Germany. Morren [53] also

used this method in addition to his goniophotometric

measurements for the extension of the wavelength

range to the near infrared.

VI. Properties of Reflectance Standards

The "primary" standard of reflectance is the

perfect reflecting diffuser which reflects all incident

radiation (p=1.0) in a perfectly diffuse or Lambertian manner so that its radiance (luminance) is constant for all angles of viewing or that its radiant

(luminous) intensity varies with the cosine of the

angle between the normal and the angle of viewing.

This theoretical concept will probably never be

realized materially but the techniques for the

measurement of absolute reflectances provide the

calibration of material standards relative to this

primary standard.

The selection of a material for calibration as a secondary reflectance standard must take into ac- count not only the physical properties but also the

application. The most important physical properties

to be considered are

(1) Reflectance value: in most cases a very high

reflectance is desirable so that in relative measurements ratios larger than 1.0 do not occur; however

other specific values may be desired, e.g. for the

measurement of one type of paper opacity a standard

having a reflectance of 0.890 is required.

(2) Goniophotometric indicatrix: for certain applications a very matte standard is required while in

other cases a glossy surface is preferable.

(3) Opacity: a very high opacity is usually desirable

in order to avoid edge losses [59].

(4) Uniformity: across the surface.

(5) Flatness oj the surface: some instruments are very sensitive to small distances between the sample

surface and the plane of the sample port.

(6) Stability: either short term (days or weeks) or long term (months or years)

(7) Cleanability : the cleaning of a standard may

be necessary, particularly in industrial use, and

should not change its reflectance.

(8) Transportability: a standard may be required

to be mechanically stable and rugged enough to be

sent by mail.

(9) Absence of: fluorescence, hygroscopic effects,

thermochromic and photochromic effects.

(10) Spectral nonselectivity: it may be necessary to

have a spectrally nonselective standard.

Considering the application or use of reflectance

standards two major categories must be distinguished :

(a) "Transfer Standards" which are used to

transfer a calibration (or as it is sometimes expressed,

a "scale") from one instrument to another, for

example, from an absolute reflectometer to a commercial instrument for relative measurements.

(b) "Instrument Standards" which are used as day-to-day "working standards" in a particular

instrument or as "master standards" for the periodical checking of a working standard. Ideally

instrument standards are calibrated against a transfer standard in the instrument in which they are to

be used.

The requirements with respect to most of the

above listed physical properties are rather obvious

for both categories of standards. However there

are some significant differences which must be

clearly understood.

Transfer standards which are exchanged between

a laboratory with instrumentation for absolute

reflectance measurements and a laboratory with an

instrument for relative measurements, must be

insensitive to differences in the geometric conditions,

that -is they should maintain their reflectance value.

Obviously a standard for an instrument with a

d/0 geometry should be calibrated in an absolute

reflectometer with the same geometry. However,

differences may exist in the diameter of the sphere,

the existence or location of a gloss trap, the locations

of detector aperture, screens, etc., and the transfer

standard should be insensitive to them. This insensitivity to geometric differences requires that the

standard be very matte, highly opaque and uniform.

These are the most important characteristics of a

transfer standard and the accuracy of a calibration

will depend mostly on the conformity with these

requirements.

81
Materials which approximate the ideal matte

surface together with high opacity and uniformity

are: pressed BaS04 plates [40], which according to

Billmeyer [41] are Lambertian diffusers for angles of

incidence up to 50°, pressed MgO and the Russian

opal glass MS-20 [60] with a matte surface. Also

carefully prepared BaS04 paint [42, 49] and matte

ceramic tiles [35] may be used. Pressed BaS04 tablets are so indifferent against changes in geometry

that Pdio-=Poid=Pdis=Pzid [34, 43].

For instrument standards the major requirements

are: long term stability and cleanability. The latter

property is often achieved by giving the material a

glossy surface which is much less liable to collect

dirt and easier to clean than a matte surface. Examples of such instrument standards are Vitrolite, 2 opal glass, enamel tiles, or ceramic tiles. A glossy

surface of the Russian opal glass MS-20 has also

been used [44].

The differences in the requirements for both categories of standards cannot be emphasized enough.

Trans1 ucent or glossy standards (such as Vitrolite)

should never be used as transfer standards and even

a change in the geometry within one instrument

such as the introduction of a gloss trap necessitates

the recalibration of the instrument standard if it is not matte and opaque.

Various properties of materials, particularly the

stability, have been discussed in a paper by Erb [45].

Effects of polarization on the reflectance of materials for standardization purposes have recently

been investigated [46-48], and it becomes quite

obvious that matte powders do not depolarize incident polarized radiation and that radiation reflected

from such surfaces is partially polarized even if the

incident radiation is unpolarized. However this is not important for integrating sphere measurements

because the geometry is usually symmetrical and

polarization effects cancel out.

The stability of BaS04 and other reflectance

standard materials or sphere paints was also discussed in a paper by Grum and Luckey [49].

The effect of pressure in the preparation of pressed

tablets was investigated by Schatz [50] who concludes that "in general for oxide powders (BaS04 , MgO, etc.) the reflectance of the compacts decreased

with increasing pressure."

Some remarks are necessary on the Russian opal

glass MS-20 which has been proposed for calibration

purposes:

(1) A polished surface of this material seems to be

adequate as a working standard. A depolished,

matte surface may be used as transfer standard only

for short periods. Cleaning such a matte surface is very difficult and requires a carefully established

cleaning procedure in order to yield repeatable

values.

5 In order to adequately describe materials and experimental procedures, it was occasionally necessary to identify commercial products by manufacturer's name or trademark. In no instances does such identification imply endorsement by the National Bureau of Standards.

(2) The material is fluorescent if irradiated by

radiation below 370 nm. This fluorescence appears

as a faint orange general emission with occasional

limited areas of considerably stronger orange

emission. This clearly indicates some non-uniformity

in the material which may be seen under grazing

angles on a polished surface as a very faint difference

in the surface texture. Consequently the material

should be inspected for these inhomogeneities under

fluorescent light and it should not be used in the UV.

A new material "Halon," which is a fluorocarbon,

has been recently proposed by Grum [61]. However

more experiences in practical applications are neces- sary before its suitability may be established.

VII. Reflectances of Transfer-Standard

Materials

A survey and discussion of reflectance values of

smoked MgO and of BaS04 and their properties was

given by Budde in 1960 [51]. A ver}^ comprehensive

literature survey of the properties and reflectances

of smoked MgO, pressed MgO, pressed BaS04 and

several integrating sphere paints was recently prepared by Erb [52]. A report on an international

intercomparison of reflectance measurements organized by CIE Technical Committee 1.2, Photometry

and Radiometry was prepared by Kartachevskaia

et al [55].

For the purposes of this paper it. is interesting to

collect in a condensed form values measured according to those methods which are employed by various

standardizing laboratories

(1) Goniophotometric methods used at

(a) LCE, Belgium [8] (b) PTB, Germany [7] (c) ETL, Japan [56]

(d) VNIIM, USSR [15]

(e) IEN, Italy [56]

(2) Sharp-Little method [34] used at NRC,

Canada.

(3) Double sphere method [36, 37] used at NBS,

USA and by Grum [49].

(4) Korte-method [7, 54] used at PTB, Germany

and also by Morren [53] at LCE, Belgium.

Data which allow a comparison between goniophotometric and integrating sphere methods are

difficult to find. Only in reference 55 _ are direct

comparisons of measurements made in various

laboratories on one material (BaS04) reported.

Otherwise Taylor [13] finds satisfactory agreement

between the goniophotometric method and his

second integrating sphere method whereas Korte [7] states that his goniophotometric values are 0.3

to 0.4 percent higher than his sphere values. However he concludes that the difficulties of the goniophotometric method make it less accurate than his

sphere method.

82
In collecting data from the literature either

spectral reflectances or the luminous reflectance are found. For reflectance standards having approximately nonselective spectral reflectance distributions

the luminous reflectance is very close or equal to the

spectral reflectance at 550 nm. Consequently, if in the following tables only a value in the 550 nm

column appears, the original value is a luminous

reflectance.

Reflectance data for pressed BaS04 other than the

Eastman White Reflectance Standard are given in

table 1. In this table all values refer to BaS04 produced by Merck, Product No. 1748, distributed

by C. Zeiss [43, 57] except for group 3 which refers

to an average for powders of four different suppliers

and for group 4b which refers to BaS04 produced

by Merck, Product No. 1750 which has a slightly

lower reflectance than Merck Product No. 1748

(see ref. 34 where data for both products are given)

Reflectance data for pressed BaS04 sold as Eastman White Reflectance Standard are collected in

table 2. No reflectance data determined by the goniophotometric method were found.

These tables show two features:

(1) that the largest variation of values occurs at

the blue part of the spectrum where the reflectance

values start to decrease. This is also the spectral

region where the reflectance changes slightly [62] for

the first few days after pressing and where UV

radiation produces the strongest changes in

reflectance [38, 45].

(2) The double- sphere method always yields the

highest values. There is, of course, a difference

between the geometries: the double sphere method

yields d/d-reflectance whereas the two other sphere

methods yield d/0 reflectances and the goniophotometric methods yield 0/d reflectances. Whether the

discrepancies are inherent in the methods or are due

to effects in the material such as retroreflectance is not known and will be the subject of future

investigations.

The measurements given in table 1 and 2 refer to

samples which were made by different persons in

various institutes and possibly also from different

charges. Consequently some variations in the reflectance values must be attributed to sample differences.

A direct comparison without such sample differ- ences between the Korte-method and the SharpLittle-method as modified by Budde [34] was ar- ranged as follows: four BaS04 samples were pressed

at NRC and their reflectances at 457 and 550 nm

compared in an Elrepho. It was found that the

reflectances of these 4 samples agreed to better than

±.02 percent (about ±.0002 in reflectance). Two of

these 4 samples were hand-carried to PTB- Germany

for measurements according to the Korte method

and two were measured at NRC, Canada, according

to the Sharp-Little method. The results are given in

table 3. The agreement is rather satisfactory, particularly in view of the fact that different arrangements

and theoretical treatments are used in the two

methods.

VIII. Concluding Remarks

(1) At several stages in the preceding sections the

simplifying assumption was made that the reflectance

factor j8d /o is equal to a reflectance pd/0 which has the

same value as the inverse reflectance p Q/d . It must be

emphasized that this simplification is not generally

permissible and that its applicability must be

investigated. Only for very matte and opaque

Table 1. Reflectance of pressed BaSOt other than Eastman White Reflectance Standard

Wavelength (nm)

400 500 550 600 700

1. Gonio-methods 0/d

LCE, Morren [53] 0. 983

ETL [55] . 986

2. Sharp-Little method NRC, Budde [34] d/0 0. 976 0. 986 . 985 0. 986 0. 987

3. Double-Sphere method NBS, Goebel [37] d/d . 983 . 989 . 991 . 990 . 991

4. Korte-method d/0

(a) PTB, Korte [7] . 984

(b) Morren [53] d/0 . 965 . 980 . 982 . 983 . 984

(c) Erb [54] d/0 . 975 . 983 . 984 . 986 . 987

Table 2. Reflectance of pressed Eastman White Reflectance Standard BaSOt

Wavelength (nm)

400 500 550 600 700

1. Sharp-Little method NRC, Budde [34] d/0 0. 986 0. 991 0. 991 0. 991 0. 991

2. Double Sphere method Grum [49] d/d . 995 . 998 . 998 . 998 . 997

3. Korte-method Morren [53] d/0 . 980 . 987 . 987 . 990 . 990

83
Table 3. Absolute Spectral Reflectance Factors (d/0) of BaSOt—Comparison of NRC and PTB

X /VoOO X 0 d/o(X)

(nm) NRC PTB (nm) NRC PTB

370 0. 959 0. 962 480 0. 986 0. 985

380 . 968 . 970 500 . 987 . 986

390 . 974 . 975 550 . 988 . 988

400 . 978 . 979 600 . 988 . 988

420 . 982 . 983 650 . 987 . 988

440 . 985 . 984 700 . 988 . 989

460 . 986 . 985 750 . 988 . 988

samples is such simplification permissible. Pressed

BaS04 seems to be such a substance [34] and also the

Russian opal MS-20, if ground matte.

(2) With respect to precision and accuracy of

reflectance calibrations it is found that a precision of

±0.002 is possible whereas accuracies in the order

of ±0.003 are claimed. However the discrepancies

between values obtained in the double sphere method

on one side or in the Sharp, Little and Korte-method

on the other side are larger than these claimed

accuracies and therefore only after these discrepancies have been explained can a more general statement on accuracy be made.

(3) The question may be asked why absolute

measurements have been made mainly in national

standardizing institutes and why instrument makers

have generally refrained from making instruments

which yield absolute values. The answer to this

question is that absolute reflectance measurements,

in spite of the apparent simplicity of the integrating

sphere methods, are complex and accident prone.

The design of an absolute reflectometer requires a complete understanding of the parameters which

may affect the measurements. And to maintain an

absolute reflectometer in perfect working order is often beyond the capabilities of an industrial testing

laboratory. The International Organization for

Standardization (ISO) has recognized this situation

with its efforts to establish international agreement

in reflectance measurements by delegating the

calibration of transfer standards to a few recognized

laboratories and recommending only relative measurements throughout the international paper industr}^ [58]. Preliminary results justify this procedure.

Basically this procedure is used with many measured quantities such as resistance voltage, weight,

etc., where standardizing laboratories provide the

absolute calibration of standards while in industry

only measurements relative to those standards are made. There are many good reasons for applying

this procedure also to the complicated field of

reflectance measurements.

IX. References and Notes

[1] Formally spectrophotometry was introduced for colorimetric purposes with the adoption of ihe CIE 1931

Standard Colorimetric Observer. See Judd-Wyszecki:

Color in Business, Science and Industry, 3rd edition

(Wiley & Sons, 1975).

[2] See, for example, Kortum G., Reflectance Spectroscopy

Springer, Berlin, Heidelberg, New York, 1969). or:

Frei, R. W., and MacNeil, J. D. Diffuse Reflectance

Spectroscopy in Environmental Problem Solving (The

Chemical Rubber Co., 1973).

[3] Commission Internationale de l'Eclairage (CIE) Publication No. 17 (1970) International Lighting Vocabulary.

Available in the United States from: Mr. L. E. Barbrow, Room B-152 Technology, National Bureau

of Standards, Washington, D.C. 20234

[4] CIE Publication No. 15 (1971) Colorimetry, available

as per ref. [3]. [5] CIE Proceedings 8th Session, Cambridge, 1931, p. 23.

[6] CIE Proceedings 14th Session, Brussels, 1959, and Meeting of Committee E-l.3.1 Colorimetry, Washington,

1967.

[7] Korte, H., and Schmidt: Uber Messungen des Leuchtdichtefaktors an beliebig reflektiercnden Proben,

Lichttechnik 19„ Nr. 11, p. 135 A (1967).

[8] Morren, L., Mesure Absolue des Facteurs de Luminance

et de Reflexion, Lux, No. 45, 448 (1967).

[9] Royds, T., Das Reflexionsvermoegen schwarzer Flaechen, Physik. Z. 11, 316 (1910).

[10] Royds, T., The reflective power of Lamp- and Platinum

black, Philos Mag. 21, 167 (1911).

[11] Coblentz, W. W., The diffuse reflecting power of various

substances, Bull. Bur. Stand. 9, 283 (1913).

[12] McNicholas, H. J., Absolute methods in reflectometry,

J. Res. Nat. Bur. Stand. (U.S.), 1, 29-73 (Oct. 1927)

RP-3.

[13] Taylor, A. H., The measurement of diffuse reflection

factors and a new absolute reflectometer, J. Opt. Soc. Am. 4, 9 (1920).

[14] Egan, W. G., and Hilgeman, T., Integrating spheres

between 0.185 and 12 jam, Appl. Opt. 14, 1137 (1975).

[15] Kartachevskaia, V. E., and Skachkova, S. P., New

method of determining the luminance factors and

total 'reflectances of VNIIM sample plates, Svetoteknika 1, 16 (1966). Also available as translation NRC,

TT-1265 from National Research Council of Canada,

Ottawa, Canada.

[16] Derksen, W. L., Monohan, T. I., and Lawes, A. J., Automatic recording reflectometer for measuring dif- fuse reflectance in the visible and infrared regions, J. Opt. Soc. Am. 47, 995 (1957).

[17] Kubelka, P., and Munk, F., Ein Beitrag zur Optik der

Farbanstriche, Z. tech. Phys. 12, 593 (1931).

[18] Kubelka, P., New contributions to the optics of the

intensely light-scattering materials, Part 1, J. Opt.

Soc. Am. 38, 448 (1948); Part II, J. Opt. Soc. Am.

44, 330 (1954).

[19] Stenius, A. S., The application of the Kubelka-Munk

theory to the diffuse reflection of light from paper,

Sven. Papperstidn. 54, 663 (1951).

[20] Butler, W. L., Absorption of light by turbid materials,

J. Opt. Soc. Am. 52, 292 (1962).

[21] Law, S. E., and Norris, K. H., Kubelka-Munk lightscattering coefficients of model particulate systems,

Trans. ASAE p. 914, 1973.

[22] Lindberg, J. D., A Simple Method for Measuring

Absolute Diffuse Reflectance with a Laboratory

Spectrophotometer, National Technical Information

Service, U.S. Dept. Comm. AD-771 216, Nov. (1973).

[23] Nutting, P. G., A new method and an instrument for

determining the reflectance power of opaque bodies,

Trans. Ilium. Eng. Soc. (1912), p. 412.

[24] Rosa, E. B., and Taylor, A. H., The integrating photometric sphere, its construction and use, Trans. Ilium.

Eng. Soc. (1916) p. 453.

[25] Preston, J. S., The reflection factor of magnesium oxide,

Trans. Opt. Soc. (London) 31, 15 (1929-30).

84
[26] Middleton, W. E. K., and Sanders, C. L., The absolute

spectral diffuse reflectance of magnesium oxide, J. Opt. Soc. Am. 41, 419 (1951).

[27] Budde W , Die Messung des spektralen Reflexionsgrades von ' Weiss-Standards, I. Die Farbe 7, 17 (1958);

II. Die Farbe 7, 295 (1958).

[28] Taylor, A. H., A Simple Portable Instrument for the

Absolute Measurement of Reflection and Transmission

Factors, Sci. Pap. Bur. Stand. 17, 1 (1920) No. 405.

[28a] Reule, A., Zur Theorie der Taylor-Kugel Zeiss Mitt. 2, 371 (1962).

[29] Benford, F. A., An absolute method for determining

coefficients of diffuse reflection, Gen. Elec. Rev. 23,

No. 1, 72 (1920).

[30] Benford, F., A reflectometer for all types of surfaces,

J. Opt. Soc. Am. 24, 165 (1934).

[31] Benford, F. A., Lloyd, G. P., and Schwarz, S., Coefficients

of reflection of magnesium oxide and magnesium

carbonate, J. Opt. Soc. Am. 38, 445 (1948).

[32] Tellex, P. A., and Waldron, J. R., Reflectance of magnesium oxide, J. Opt. Soc. Am. 45, 19 (1955).

[33] Sharp, C. H., and Little, W. F., Measurements of reflection factors, Trans. Ilium. Eng. Soc. 15, No. 9, 802 (1920).

[34] Budde, W., and Dodd, C. X., Absolute reflectance

measurements in the D/O0 geometry, Die Farbe 19,

94 (1970).

[35] Budde, W., and Chapman, S. M., The calibration of standards for absolute brightness measurements with

the Elrepho, Pulp and Pap. Mag. Can. 69, No. 7, T206 (1968).

[36] Van den Akker, J. A., Dearth, L. R., and Shillcox, W. M.,

Evaluation of absolute reflectance for standardization

purposes, J. Opt. Soc. Am. 56, 250 (1966).

[37] Goebel, D. G., Caldwell, B. P., and Hammond, H. K.,

Use of an auxiliary sphere with a spectroreflectometer

to obtain absolute reflectance, J. Opt. Soc. Am. 56,

783 (1966).

Note: There are misprints in eqs (1) and (2) in this

paper and also in the equation in TAPPI Standard

T679.

[38] Erb, W., Aenderungen der strahlungsphysikalischen

Eigenschaften von Reflexionsnormalen nach UVBestrahlung, Lichttechnik 7, 345 (1973).

[39] De la Perelle, E. T., Moss, T. S., and Herbert, H., The

measurements of absorptivity and reflectivity, Infrared

Phys 3, 35 (1963).

[40] Richter, M., and Terstiege, H., Bariumsulfat-Tabletten

als Standard fuer Farbmessungen von Aufsichtsfarben,

Lichttechnik 22, 446 (1970).

[41] Billmeyer, F. W., Lewis, D. L., and Davidson, J. G.

Goniophotometry of pressed barium sulphate, Color

Eng. (May/June' 1971), p. 31.

[42] Middleton, W. E. K., and Sanders, C. L., An improved

sphere paint Ilium. Eng. 48, 254 (1953).

[43] German Standard DIN 5033, Blatt 9 (1970) in which

the preparation of pressed BaS04 tablets is described.

It is stated that if the tablets are prepared according

to the procedure described, the spectral reflectance

factors Pd/8: Pd/o and the reflectance ps /d are identical.

[44] Clarke, F. J. J., High Accuracy Spectrophotometry at the National Physical Laboratory, Nat. Bur. Stand.

(U.S.), Spec. Publ. 378, 1-29 (May 1973); J. Res.

Nat. Bur. Stand. (U.S.) 76A (Phys. and Chem.),

No. 5, 375-403 (Sept.-Oct. 1972).

[45] Erb, W., Requirements for reflection standards and the

measurement of their reflection values, Appl. Opt

14, 493 (1975).

[46] Robertson, A. R., Effect of polarization on reflectance

factor measurements, Appl. Opt. 11, 1936 (1972).

[47] Kaase, H., Depolarisation der an BaS04 diffus reflek- tierten Strahlung, Optik 38, 433 (1973).

[48] Clarke, F. J. J., Garforth, F. A., and Parry, D., Goniophotometric and polarization properties of the common

white reflection standards, NPL Report Mom 13,

Sept. 1975.

[49] Grum, F., and Luckey, G. W., Optical sphere paint and

a working standard of reflectance, Appl. Opt. 7, 2289

(1968).

[50] Schatz, E. A., Effects of pressure on the reflectance of compacted powders, J. Opt. Soc. Am. 56, 389 (1966).

[51] Budde, W., Standards of reflectance, J. Opt. Soc. Am.

50, 217 (1960).

[52] Erb, W., A summary of properties and reflection values

of materials which are used as reflection standards,

Report PTB-Opt-3, June 1975, Physikalisch Technische Bundesanstalt, Braunschweig, Germany.

[53] Morren, L., Vandermeersch, G., and Antoine, P., A study

of the reflection factor of usual photometric standards

in the near infra-red, Lighting Research and Technology 4, No. 4, 243 (1972).

[54] Erb, W., Bestimmung des spektralen Leuchtdichtekoeffizienten fuer die Messgeometrie 45°/normal, Die

Farbe 20, 179 (1971).

[55] Kartachevskaia, V. E., Korte, H., and Robertson, A. R.,

International comparison of measurements of lumi- nance factor and reflectance of white diffusing samples,

Appl. Opt. 14, 2696 (1975).

[56] Report of CIE TC-1.2 which is published in condensed

form in Ref. [55]. [57] Pamphlet No. 50-665/ 1-e, C. Zeiss, Oberkochen, Germany.

[58] Budde, W., and Chapman, S. M., Measurement of brightness and opacity according to ISO standards,

Trans. CPPA 1, No. 2, 61 (19'75). International

Standards ISO 2469: Paper, board and pulps—meas- urement of diffuse reflectance factor; and ISO 2470:

Measurement of diffuse blue reflectance factor (ISO

brightness).

[59] Atkins, J. T., and Billmeyer, F. W., Edge-loss errors in

reflectance and transmittance measurement of trans- lucent materials, Materials Research and Standards 6,

564 (1966).

[60] An earlier version of this, the MS-14 is described in: Voyshvillo, N. A., and Pavlova, L. I., The applications

of opal glass standard instead of magnesium oxide in colorimetry, Svetotekhnika 7, 16 (1965).

[61] Grum, F., and Saltzmann, M., New white standard of

reflectance, Paper No. 77 presented at the 18th CIE

Session, London, September 1975. To be published in

the Proceedings of this session.

[62] Terstiege, H., Spektralphotometrische, Untersuchungen

an Weiss-Standards, Lichttechnik 6, 277 (1974).

[63] Correction in proof: it was published as follows:

Aneliunas, A. E., and Chapman, S. M., A practical

method for measuring absolute reflectances, Pulp &

Paper Mag. Can. 69, No. 16, 53 (19 July 1968).

(Paper 80A4-903)

85

NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 466, Standardization in Spectrophotometry and Luminescence

Measurements, Proceedings of a Workshop Seminar Held at NBS, Gaithersburg, Md., November 19-20, 1975 (issued May 1977).

Understanding Bidirectional Reflectance and Transmission

for Space Applications

John B. Schutt

Goddard Space Flight Center, Greenbelt, Maryland 20771

I (May 26, 1976)

Applications for optical diffusers in space projects are presented which include the

functions of reflection, transmittance, and collection. These modes encompass such diverse uses as temperature regulation and ozone concentration monitors. Discussed is the co- operative aspect of diffuse reflectance and environmental stability. Magnesium oxide,

sodium chloride and barium sulphate are evaluated in some detail. The importance of scene

scattering behavior to modeling the earth's radiation budget and in determining thermal

inertias of the earth's surface are discussed, because solar albedo serves as the weighting

function in the solar input irradiance. Finally, work in the area of canopy reflectance modeling

is reviewed with verification data included whenever available. Some knowledge of the

bidirectional reflectance properties of vegetation is necessary for identification, acreage

computations, and scene transferrance.

Key words: Bidirectional radiometry; canopies; diffuse reflectance; diffuse transmission;

reflectance standards; scattering surfaces.

I. Introduction

Uses of diffusely reflecting and transmitting materials in spacecraft design are numerous, so numerous

in fact that they are taken for granted. They are taken for granted in the sense that the extent of their

diffuseness often is judged by eyeballing. Perhaps

this turns out to be the situation because the experimental procedure for determining diffuseness re- quires great care, and becomes tedious if the hemisphere is to be covered for wavelengths comprising

the solar spectrum, 250 to 2500 nm. On the other

hand, it is customary to carry out bidirectional re- flectance measurements on diffusers applied to the

surfaces of integrating spheres, but normally in the

principal plane only.

The nature of the application of diffusers usually

puts them in a pivotal role. For example, in the

control of satellite temperatures, mirror effects are eliminated whereby solar inputs exceeding one solar

constant can occur for coupled surfaces. In the

development of spacecraft paints, it turned out that

certain pigments, particularly zinc oxide, can be

processed to have greater environmental stability

than any type of binder. Inorganic and silicone binders

have intermediate stabilities, but can be well masked

because they can accept high pigment concentrations, so high in fact that the resultant coating becomes a diffuser. Under these circumstances there

results classes of paints which are surprisingly space

stable [l]. 1 Another pivotal role is that of a collector.

1 Figures in brackets indicate the literature references at the end of this paper.

Reflectors are utilized in this manner to monitor

ozone concentrations in the earth's atmosphere. The

collector utilized in the Backscatter Ultraviolet

Experiment (BUV) [2, 3] flown on Nimbus 3 and 4

is a ground aluminum plate overcoated with an

evaporated layer of aluminum. This configuration was

selected after much screening because its long term

environmental stability is excellent [4]. Although it has an easily detected specular quality, the instrumentation is sufficiently sensitive to enable detection

of components from 250 to 300 nm which comprise the

earth's albedo and are representative of the ozone

profile. To provide calibration of BUV, sounding

rockets are launched from selected sites during over- head passage of the satellite. The pivotal element in

this ozone monitoring experiment is a collector comprising a silica sphere coated internally with a

transmission diffuser. Originally, smoked magnesium

oxide was employed, but ease of application prompted

a switch to barium sulphate bound with polyvinyl

alcohol. In optimum configuration, however, Krueger

[5] found that a black spot placed exterior_ to the

sphere opposite to the exit neck could eliminate

illumination fluctuations, thereby providing a more

uniform flux to the detector.

Most recently, interest has developed in the

reflective patterns of the earth and earth scenes. Nimbus F (currently in orbit) [6] has an experiment

designed to monitor the earth's energy balance.

Formally known as the Earth Radiation Budget

Experiment (ERB), this experiment has_ been

designed to hopefully permit the calculation of

energy balances to an accuracy approaching one

87
percent. Broadly, the experiment views the sun as the

satellite ascends from the South Pole. As it proceeds

northward energies are measured from 0.3 to 50 /urn. At the same time the entire disk is viewed and

synopsized. The goniometric dependence is taken in

the principal plane of the sun and assumed to

characterize the reflectance hemisphere. These data

provide all the necessary input for calculating

terrestrial energy balances. Planned for launch in the

spring of 1978 is a scanner designed to measure

reflected energy from 500 to 1100 and characterize emitted energy in the 10.5 to 12.5 /xm band.

The purpose of the Heat Capacity Mapping Mission

(HCMM) [7] is to characterize the earth's surface

with respect to the mission spectroscopy. Because

the spacecraft will pass over the same area at about

1 :30 pm and 2 :30 am, the most sophisticated application for its data will be for computations of thermal

inertia. For a representative value of this quantity

an energy balance must be established at the earth's

surface. Simplifying assumptions which enter

modeling of the energy balance are:

(1) that the scene is Lambertian,2

(2) that the 500 to 1100 /mi band adequately

estimates the solar albedo normally defined

for energy balance purposes from 250 to 4000

Mm,

(3) that the Planck function will peak in the 10.5

to 12.5 jLtm interval permitting a reliable

brightness temperature to be calculated,

(4) meteorlogical approximations which involve

the connective and advective heat transfer

between the earth and atmosphere,

(5) radiation contributions which result from

exchanges between earth and atmosphere,

earth and sensor and earth reflected sky

radiation,

(6) an atmospheric transfer function in order to

correct sensed radiations to the earth's surface.

If we are content with relative thermal inertias

rather than representative values, certain of these

approximations may be useful provided sufficient

sensitivity is offered by such a modeling scheme to

provide useful images. The simplest images offered

by the HCMM are those obtained from mapping

(1) albedo

(2) differential temperatures

(3) a ratio of 1 to 2.

Of the three, the ratio of one to two offers the closest

approximation to thermal inertia.

Finally, there are remote sensing requirements for

ciop signatures; these again may be representative

or relative. But establishing a library of these data

goes beyond spectral characterization alone and

2 Although not explicitly included, the importance of albedo in weighting solar irradiance is self-evident because the sun is virtually always the dominant heat

source by orders of mangnitude.

would entail knowledge of the diffuse versus specular

quality of the reflectance as a function of sun and

sensor positions. For example, viewing mature barley

and wheat from the nadir position does not provide

a basis for differentiation, however, as the view angle

is increased, distinctions become increasingly apparent [8]. Otherwise, exclusive use must be made of

differing spectral signatures occurring from phenological changes recorded in conjunction with individual crop calendars. These data provide bases for

crop identification and acreage estimations.

In the following sections a summary of white

diffusers is given. Subsequently, radiation transfer

models employed in calculating the reflectances of

crops are presented and verification data included

whenever available.

II. Summary of Information on Selected

DifFusers

Of all the diffusers, magnesium oxide [9] generated

and applied by burning magnesium under controlled

conditions was probably the one most utilized until

the development of the barium sulphate-polyvinyl

alcohol system [10]. Disadvantages of magnesium

oxide include:

(1) its slow rate of deposition by virtue of the

smoking process,

(2) a thickness of 3 to 4 mm to provide capacity

in the 0.7 to 2.4 /xm region,

(3) a coating with poor adhesion and weak

cohesion,

(4) a required investment in time of three days to

two weeks of continuous effort to coat an

eight inch diameter integrating sphere,

(5) a coating not accessible to repairing,

(6) a system of electrostatically charged particles

reactive with atmosphere moisture to form

Brucite, Mg(OH) 2 , with an accompanying

decrease in infrared and ultraviolet

reflectances.

Under ideal conditions the usefulness of this coating

may extend to one year.

A more rugged integrating sphere coating possessing optical properties comparable to magnesium

oxide can be provided by sodium chloride. Initially

developed by Kneisel [12] at the National Bureau of

Standards, the system was modified by Stuart [13]

to increase its ease of application and mechanical

strength. Initially sodium chloride was_ dispersed in

alcohol, but improvements were obtained by employing an admixture of toluene and 1, 3 butanedial

or propj-lene glycol with the alcohol. The resultant

coating is free of the usual water bands occurring in

the vicinity of 1200, 1400, and 1900 nm. Further88
more, the system is easily repaired and dries under

sufficient compressive stress to provide a coating

able to support a substantial shock. The life of the

coating is known to be in excess of two years. Its

major disadvantage resides in its moisture sensitivity.

Relative humidities close to 90 percent cause sagging.

Optically, the coating commences to lose reflectance

around 360 nm, but remains the best all around

integrating sphere coating for determining the solar

albedo of materials.

Ease of application, repair, and optical stability

make the barium sulphate-polyvinyl alcohol coating

the most useful system. It does have infrared absorptions due to the presence of water, but sources of

energy in this spectral region have sufficient intensity

to eliminate fhis as a potential disadvantage.

Furthermore the system does not suffer from the near

ultraviolet fall off characteristic of sodium chloride.

Over the spectral region employed in solar albedo

calculations, this system has been found to have a

lifetime in excess of two years. However, Krueger

[15] has shown that a substantial loss in reflectance can occur from about 250 to 200 nm within a period

of three months. In an attempt to better utilize

the high reflectance of virtually pure barium sulphate

in the region of 200 to 250 nm for the express purpose of detecting Cerenkov radiation [16], it was

found that polyvinyl alcohol could be replaced by

potassium sulphate while maintaining the reflectance

of the system to within 2 percent of that of the

powder. The coating was monitored for optical

degradation in this region over a period of six

months. All observed changes were found to be

within the accuracy of the spectroreflectometer,

which is nominally one to two percent. Table 1 qualitatively summarizes some properties of these

coatings.

III. Models of Canopy Reflectance

Investigations into the attenuation of light in a

plant canopy were initiated utilizing a one parameter

relation customarily referred to as the BouguerLambert law [17]. This approximation accounts

satisfactorily for transmittance, while ignoring the

reflectance of the medium. Stokes [18] extended the

method to account for reflectance by including an

additional parameter. He verified his approach in

experiments with glass plates. Some years later

Schuster [19] reassessed the problem of radiation

diffusion and wrote down a system of two equations

for radiation transfer in a medium with sources. He

assumed that light passing through an infinitesmal

layer (dx) is increased by the backscattered component and decreased by the forward component.

For simplicity he assumed further that the forward

(t) and back (s) scattered components here equal,

viz:

ds 1 p , 1 p.

where y. and S are the absorption coefficients. The

source terms have been omitted. Rayleigh [20]

showed later that equal scattering resulted only for

the case where particles are much smaller than the

wavelength of light. Silberstein [21] reformulated the

Schuster equations eliminating the equality in forward and backscattered components. He also pointed

out that the residue of unscattered radiation (Ix) passing through a medium is properly written

*= _ (M+B+nr„

where B and F represent back and forward scattered

components. These results closely resemble those of

the Kubelka-Munk [22] representation for canopy

scattering,

dn = -{>x+S)Ix +Ss,

ds _ dn (jx+S)s-SIx ,

TABLE 1. Summary of important properties of coatings

Systems employed as diffuse standards

Average reflectance values

Material Binder 0.2-0.25 0.25-0.3

Mm yum

0.3-0.8 0.8-2.4

Mm

Atmospheric

stability

Directional

reflectance

Freshly

smoked

MgO

Electrostatic,

water

0. 9 0.98 0. 98 0. 95 Poor Lambertian to 45 degrees

NaCl NaCl Poor Less than

0.7

. 96 . 96 Poor if RH is greater than

0.85

Unknown

BaS04 PVA . 85 .93 . 95 . 92 Excellent Ref. [11]

BaS04 K2 S04 . 94 .97 . 97 . 92 Excellent Unknown

89
where IT is now interpreted as the forward scattered radiation.

In this case t has been replaced by Iz and n represents the cumulative leaf area index. 3 Figure 1, taken

from Allen and Richardson [23] shows some results

obtained for stacked cotton leaves. The K-M

parameters n and S were obtained esperimentally.

Duntley [24] combined the equations of Schuster

with observation of Silberstein concerning passage

of the unscattered beam through a medium. Namely

he chose to distinguish the forward diffusing scattered radiation from the unscattered radiation. Under

these circumstances three equations result containing

six parameters,

^=_(/+jB'+2P')/s>

j-=F'Is -pt-Bt+Fs,

-~B'Ix -ns-Fs+Bt.

Primed quantities differentiate the behavior of the

unscattered beam (Ix) from that of the diffused

100 |

,

0.5 1.0 1.5 2.0 2.5 WAVELENGTH IN MICRONS

Figure 1. Reflectance (solid lines) and transmittance (dashed

lines) of 2, 4, 6, 8, stacked mature cotton leaves. The lines are theoretical; the circles are experimental. Standard deviation between

observed and calculated points is about 1 percent [ref. 23).

3 Cumulative leaf area index is defined as the one sided leaf area per unit ground

area, and represents the sum over all leaves encountered between top and base of the plant.

portion. First set up to model diffusion in pigmented

materials from experiments carried out to give values

of the phenomenological constants, it has been

subsequently utilized by Suits et. al. [25], to calculate

the bidirectional reflectance of corn. The approach

necessitates a prior knowledge of the transmittance

and reflectance of canopy components, usually only

leaves. In addition these parameters are weighted by

the projected area on the appropriate component

plane. To compute the representation Suits et. al. refer to dividing the canopy into layers, and then

rewrite Duntley's equation for the passage of the

unscattered component as

ax

with k=.(n'+B' +F') in Duntley's notation. 7, t, and S are now functions of the layer being considered and the position within that layer, z. In

establishing equations for k, fi, B, B' , and F' plant

geometry and optical constants were assessed, and

diffusers assumed Lambertian.

Based on the successful application of K-M theory

to predict the reflectance and transmittance of

stacked cotton leaves, Allen and Richardson [23]

indicated that their procedure was sufficiently general for application to plant canopy. Unfortunately

this application has not been made by them. Although

they do suggest that assuming uniform distributions

of leaves would be a reasonable approximation, it

was previously shown by Nichiporovich [26] and

de Wit [27] not to be valid. Physically, the assumption amounts to suggesting that plant canopy

reflectance would not vary during the day. That the

effect is present is shown by many authors, in

particular by Fritschen [28] for alfalfa, barley,

wheat, oats, cotton and sorghum. It is precisely this

behavior of crop canopies which led de Wit [27],

and Idso and de Wit [29] to develop leaf distribution

functions for six leaf inclinations: planophile canopies where horizontal leaves are most frequent;

erectophile canopies where vertical leaves are most

frequent; plagiophile canopies where leaves assume

an oblique inclination; extremophile canopies, where

leaves are least frequently at oblique inclinations;

spherical canopies where the relative frequencies of

inclinations is the same as the relative frequency

of the surface elements of a sphere; and a measured

leaf distribution for corn. For light incident at 0, averaged over the crop a& a whole 0P(ir/2—d),

corrected for the projection of the soil in the direction (ir/2 —d) and weighted for the area per leafy

layer, S, Idso and de Wit derive for the reflectance

P, Y^op^pm

[_ cos e j

for a leaf area index, LAI, Figure 2 [29] shows

a comparison of calculated and measured results

for a stand of corn. Agreement appears to be best

for the uppermost clusters of leaves. The model

90
10

ccUJ>

< 15 -

>

CLO 20 <

25

30

CALCULATED

•MEASURED

50 100 REFLECTANCE (%) TRANSMISSION (%) R/T (%)

Figure 2. Calculated and measured profiles of reflection R

and transmission T in a corn crop. R is computed as upward moving radiation divided by incident radiation and T

as downward moving radiation divided by incident radiation [ref. 29].

of Smith and Oliver [30, 31, 32] treats the interaction of radiant flux with the vegetation canopy

utilizing a probability for the distribution of gaps

and foliage elements within the canopy. Their

starting point is then the Idso-de Wit equation

given above for gap probability with

LAI

n

replaced by the difference between the number of

canopy layers n and the number of contacts, k such

that the probability distribution for k foliage contacts

in the direction 07 is [31]

n—k

Foliage elements are assumed to act as Lambertianresponse surfaces. The problem is the determination

of OP(6T ). Idso and de Wit have expressed this

quantity in terms of four angles: sun zenith angle,

leaf inclination, and two boundary angles differentiating upperside and underside illumination of the

leaves. Methods for obtaining an average plant

and canopy scattering function have been reviewed

by Oliver [31]. Techniques fall into two categories.

The first is by a direct mensuration process and the

second carried out photographically. One such

approach involves the determination of plant

geometry from photographs taken for orthogonal

planes which are subsequently processed onto

a grid. A second approach utilizes infrared photography. A diffuse image of the subject is obtained

for bidirectional views. Utilizing these data, Oliver

presents numerical methods by which gap and

contact probabilities can be obtained. Emplo3r ing

the above equation for dT , and applying sequentially

through the canopy for all k and n, there results

an expression for the reflectivity p(6' T) [31]:

. pm

sin2 (0 r +A0r )-sin2 (0' r -A0r )

for incidence in zone (0r + A0r ). Figures 3, 4, and

5 show verification results for this model. Each

series of curves shows maximum disagreement at

about 650 nm. The authors attribute this behavior

to possible specular reflection at the long wavelength

chlorophyll absorption band. Overall agreement

is quite good. In figure 6 relative reflectance is

plotted as a function of zenith angle from data

obtained by Watlington et. al, LANDSAT band

4 (500-600 nm). These reflectance data, plotted

on a linear scale, show considerably less variation.

Because the sensor viewed about one square foot

of projected plant area, it is tentatively assumed

that the dip at 64° results from polarization of

the light. The sharp rise in reflectance beyond this

point is as a result attributed to depolarization

as the sensor viewing angle increases away from

the Brewster Angle.

1.00

0.50

o

z

<o 0.10

111 cc 0.05

0.01

35° ZENITH SUN ANGLE

28° ZENITH VIEW ANGLE

+ MEASURED — PREDICTED

J I 0.4 0.5 0.6 0.7 WAVELENGTH ||im)

0.8

Figure 3. Comparison between model predictions and field observations for a dense canopy of blue grama.

1.0

LU§ 0.8 <

m 0.6

<

zO

H

U

LU

cc5

cc<

Q.Q-<

0.4

0.2

0.1

WESTERN WHEATGRASS

SOLAR ZENITH ANGLE 30

c WAVELENGTH 8000A

MEASURED

PREDICTED

_l_ 15 25 35 45 55 ZENITH VIEW ANGLE (DEGREES)

65

Figure 4. Comparison between model predictions and field observations for a sparse canopxj of western wheatgrass.

The measurement was made at an azimuth of 45° from the sun and is believed to account for the apparent differences [ref. 31].

91
1.00 0.80 -

0.60

0.40

0.20

<

£ 0.10 3 0.08

iu 0.06

0.04

0.02

0.01

TIME 1100 HOURS

"° O- <y <x

•••.(>. •••

A.

—O— o.85 MICRONS

—X— 0.70 MICRONS — 0.45 MICRONS

_L

65 55 45 35 25 15 ZENITH VIEW ANGLE

Figure 5. Angular variation in spectral response for three

selected wavelengths.

The non-Lambertian spatial response for the apparent directional reflectance for the canopy is clearly evident. The solar disk was contained in the 25 degree

sensor view angle band [ref. 30].

IV. Discussion

Based upon the coatings systems mentioned

previously, it is apparent they share several formulating concepts to varying degrees. First of all,

each pigment was chosen from combinations of

elements in the Periodic Table whose electronegativity differences are closely maximized. This being

the case, it is hardly possible to extend the ultraviolet

absorption cutoff. Creating diffusers from such

materials as sapphire, lithuim flouride, magnesium

fluoride and fused silica provides little help because

roughening a surface or grinding a single high purity

crystal simply serves to retract the ultraviolet

absorption cutoff. Second, the pigments used are

all of the highest purity. Third, the pigment to

binder ratio is made as great as possible; for sodium

chloride it is infinite.

In connection with the transmission diffuser

previously mentioned, the ability of the barium

sulphate polyvinyl alcohol system to diffuse a

specular beam during a single pass through the

coating was unsatisfactory. For this application a

thickness of about six mils is normally applied.

In a closed system such as an integrating sphere,

this problem is not so serious. The black dot artifice

of Krueger to block light having passed through

the diffuser but once suggests that the diffuser

could be more efficient or else its ability to diffuse

is intensity dependent. It was pointed out to be

by Heath, [34] that the accuracy of the BUV is currently limited solely by fact that the specular

component from the diffuser can be measured to no

better than 2 percent. Common to crop reflectance

models is the assumption that single reflections

result in the total diffusion of specular inputs. So

unless a canopy can approximate the action of an

integrating sphere, the canopies will provide an

observer with specular reflections. Then as the

spatial resolution is decreased by observing larger

and larger canopies, Lambertian behavior will

provide an exact description.

It is interesting to note that accurate descriptions

of diffusers are difficult to come by because particle

shapes, sizes, and their dispersions within binders

are not readily amenable to modeling. On the other

hand, modeling a canopy for the spacecraft view is a tractable problem, if only for the fact that the components can be directly measured, photographed,

and therefore represented geometrically.

6

| i i i i i

i i

i i 50 42 34 26 18 10 ZENITH ANGLES DEGREES

Figure 6. Reflectance of unstressed mature soybean plants taken for LANDSAT

band 4 {600-600 nm bandwidth) [ref. S3].

92
Finally, it is interesting to note that the Idso-de

Wit canopy model does work for the uppermost

vegetation layers by considering geometrical factors

only. Absent from the model are provisions for

including optical properties. This leads to the conclusion that in setting up leaf distribution functions,

probably all specimens were in the nearly turgid

state. Subsequently for verification of their model,

they chose a crop stand in very nearly the same

state. This observation suggests that the evolution

of crop canopy geometry with respect to moisture

content may serve as a new basis for canopy reflectance modeling.

In conclusion it should be pointed out that in the

development image processing algorithms, goniometric data may serve only a tutorial function, unless

simpler schemes are developed for its acquisition.

In conjunction with the profusion spacecraft imagery

now available, however, it could serve the important

function of allowing like subjects imaged at different

times and in widely spaced locales to be accurately

referenced with respect to one another.

V. References

[1] Schutt, J. B., Shai, C. M., Formulation Procedures,

Rationale, and Preliminary IMP-H Flight Data for Silicone Paints With Improved Stability, GSFC,

X-764-73-373 (December 1973).

[2] Nimbus III User's Guide, National Space Science Data

Center, Goddard Space Flight Center, Greenbelt,

Maryland, March 1969.

[3] Nimbus IV User's Guide, National Space Science Data

Center, Goddard Space Flight Center, Greenbelt

Maryland, March 1970.

[4] Unpublished data.

[5] Private communication.

[6] Nimbus VI User's Guide, National Space Science Data

Center, Goddard Space Flight Center, Greenbelt,

Maryland, February 1975.

[7] Applications Explorer Missions (AEM), Mission Planners Handbook, Goddard Space Flight Center,

Greenbelt, Maryland, May 1974.

[8] Committee on Remote Sensing for Agricultural Purposes, Remote Sensing, National Academy of Sciences,

Plate 9 (1970).

[9] Tellex, P. A., Waldron, J. R., Reflectance of magnesium

oxide, J. Opt. Soc. Am. 45, 19 (1955).

[10] Grum, F., Lucky, G. W., Waugh, G. P., Spectro Reflectometric Reference Standard and Method, U.S.

Patent 3512895 (May 1970).

[11] Brandenberg, W. M., Neu, J. T., J. Opt. Soc. Am. 56,

97 (1966).

[12] Unpublished notes.

[13] Stuart, J., Diffuse Reflective Coating, 3, 702, 775 Issued

to NASA (November 14, 1972).

[14] Private communication.

[15] Private communication.

[16] Schutt, J. B., Arens, J. F., Shai, V. M., Stromberg, E., Highly reflective stable white paint for the detection

of ultraviolet and visible radiations, J. Appl. Optics

13, 2218 (1974).

[17] Hardy, A. C, Perrin, F. H., The Principles of Optics

(McGraw-Hill Book Co., New York, 1932, 1st ed.,

Chil.), p. 24.

[18] Stokes, G. G., Proj. Roy. Soc. (London) 11, 545 (1862).

[19] Schuster, A., Astrophys. J. 21, 1 (1905).

[20] Lord Rayleigh, Proc. Roy. Soc. A 90, 219 (1914).

[21] Silberstein, L., Phil. Mag, 4, 129 (1927).

[22] Kubelka, P., Munk, F., Z. Tech. Physic. 11, 593 (1931).

[23] Allen, W. H., Richardson, A. J., Interaction of light

with a plant canopy, J. Opt. Soc. Am. 58, 1023 (1968).

[24] Duntley, S. H., The optical properties of diffusing

materials, J. Opt. Soc. Am. 32, 61 (1942).

[25] Suits, G. H., Vincent R. K., Horowitz, H. M., Erickson,

J. D., Optical Modeling of Agricultural Fields and

Rough-textured Rock and Mineral Surfaces, NASA

CR-134243, ERIM 31650 (1973).

[26] Nichiporovich, A. A., Soviet Plant Physiology, 8, 428

(1961).

[27] de Wit, C. T., Photosynthesis of Leaf Canopies, Agr.

Res. Rept. 663 (Wagenengen, 1965), chap. 4, p. 11.

[28] Fritschen, L. J., Agr. Meteorol. 4, 55 (1967).

[29] Idso, S. B., de Wit, C. T., Light relations in plant

canopies, J. Appl. Optics 9, 177 (1970).

[30] Smith, J. A., Flevei, R. E., Plant Canopy Models for Simulating Composite Scene Spectroradiance in the

0.4 to 1.05 Micrometer Region, Proc. Eighth Inter. Symp. on Remote Sensing of the Environment, p. 1333 (Oct. 1972).

[31] Oliver, R. E., A Stochastic Canopy Model of Diurnal

Reflectance, Dissertation, Colorado State Univ., 1974.

[32] Oliver, R. E., Smith, J. A., Vegetation canopy Reflectance Models, Colorado State Univ., Final Report.

U.S. Army Research Office, Durham, N.C., 1973

(DA-ARO-0-31-126-71-G165).

[33] Watlington, R., Wood, F., Schutt, J., de Gasparis, H.,

Shima, L., Unpublished Data Taken at the Plant

Industry Station; USDA, Beltsville, Md.

[34] Private communication.

(Paper 80A4-904)

93

NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 466, Standardization in Spectrophotometry and Luminescence

Measurements, Proceedings of a Workshop Seminar Held at NBS, Gaithersburg, Md., November 19-20, 1975 (issued May 1977).

Standardization of Light Scattering Measurement in Conjunction

With Immunochemical Analysis

Gregory J. Buffone

Department of Clinical Laboratories

Children's Hospital National Medical Center

and George Washington University

Washington, D.C. 20009

(May 26, 1976)

Light scattering methods for the physical analysis of synthetic and biological polymers

necessitates the use of scattering standards and absolute light scattering measurements.

Standardization has not been employed when light scattering has been used to monitor

immunochemical reactions using a kinetic or thermodynamic mode.

The concentration of a specific protein present in a complex matrix such as urine, serum

or cerebrospinal fluid, is measured by reacting the protein of interest with its specific antibody and then measuring the excess light scattering of the solution produced by the formation

of antigen antibody complexes. The lack of established light scattering standards in the area

of immunochemical measurements makes instrumental quality control difficult and has

hindered direct comparison of data among investigators. Both solid and liquid light scattering

standards would be necessary to encompass the wide range of instrumentation currently in

use. Several solid standards which have been used in the past include reflecting diffusers

such as vitrolite, magnesium carbonate crystals with a ground surface, magnesium oxide

coatings on magnesium carbonate crystal, casein paint on vitrolite, and solid opal glass

transmitting diffusers such as flashed opal glass and solid opal glass. These standards, while

applicable to manual light scattering photometers, are not suitable for recently developed

automated instrumentation. Liquid standards in the form of Ludox®, solutions of polystyrene, suspensions of small diameter latex spheres and even pure organic solvents could

be used more easily with the continuous flow and discrete automated analyzers. The introduction of instrumental standards at this level of analysis would result in improved overall

quality control and facilitate data and method comparison between laboratories.

Key words: Antibodies; antigens; biological polymers; immunochemical analysis; light

scattering; polymers; proteins; solid standards.

I. Introduction

Nephelometry, as applied to immunochemistry,

measures the excess scatter caused by antigen antibody complexes formed in solution. The concentration of the unknown analyte is determined by use of

appropriate calibration materials. Since only relative

nephelometric measurements are required, absolute

standardization of instrumentation has not been necessary for internal laboratory accuracy. However,

while lack of standardization has not been deleterious

in internal accuracy, comparison of data between

laboratories and day to day internal laboratory instrumental quality control has been difficult at best.

Poorly defined protein standards make the definition

of a more standardized measuring system an acute

problem.

II. Application of Light Scattering to

Immunochemistry

Quantitative immunochemical methods used since

the 1930's include immunoprecipitation in solution

[1]

1 and in a gel matrix [2]. Both approaches rely on

the formation of a precipitate for the quantitation

of the analyte. The methods are time consuming and

are considered relatively tedious and expensive. The

resurgence of nephelometric methods for the measurement of the extent of immunochemical reactions

beginning in 1969 to date, can be traced to the improvement in efficiency and sensitivity provided by

this approach.

Manual and Flow Nephelometry. Fluorometers have

been used almost exclusively to make 90° equilibrium

light scattering measurements when following immunochemical reactions. Numerous manual methods

for the measurement of urine, serum and cerebrospinal fluid proteins have been reported [3-5]. Continuous flow systems have made automation of immunochemical reaction measurements feasible.

Kinetic Light Scattering. The introduction of the

centrifugal analyzer [6] has provided an automated

instrument capable of precise kinetic measurement.

The centrifugal analyzer has been applied to the

1 Figures in brackets indicate the literature references at the end of this paper.

95
automated kinetic measurement of antigen antibody

reactions. Centrifugal analyzers have been used to

measure scatter from antigen antibody complexes

at 90° [7] and at angles between 15 and 30 degrees [8],

with the smaller angles providing greater sensitivity

due to the large complex size.

Solid Phase Light Scattering. Recently Giaver [9] described the use of a solid phase protein preparation

for the monitoring of immunochemical reactions.

Protein or carbohydrate antigens were adsorbed onto

a glass slide coated with small spheres of indium

metal (~ 1000 A in diameter). Incubation of the

plates in an antiserum specific for the adsorbed

antigen results in reaction between antigen and

antibody causing a variation in the protein coat

thickness on the metal spheres resulting in an increase

in the amount of light scattered from areas of the

plates at which a reaction has occurred. This technique can detect, by visual inspection, a reaction on

a bovine albumin coated slide at an antibody concentration of 10~ 4g/l.

Mie Scattering. Application of light scattering to

the detection of rheumatoid factor provides a more

sensitive and potentially quantitative means of

measurement [10]. A homogeneous distribution of

latex spheres whose particle diameter is approximately equal to the wavelength of light used for

analysis, will produce characteristic maxima and

minima intensities when scattering is observed at

different angles. Any agglutination of human IgG

coated spheres by rheumatoid factor will result in a

loss of homogeneity of particle size and the characteristic maxima and minima intensity pattern, with

changes in maxima slopes being related to the

concentration of rheumatoid factor.

Quasi-Elastic Light Scattering. The use of quasielastic light scattering holds the potential for measurement of antigen or antibody at a concentration

of a few micrograms per liter, making this technique

competitive with RIA in terms of sensitivit}"[ll].

Broadening of laser spectral line widths caused by

changes in the diffusion coefficient is used as an

extremely sensitive means of detecting agglutination

of antigen coated latex spheres.

III. Instrumental Standardization

The diverse methods and instrumentation just

reviewed would require a versatile material for

instrumental standardization. Here I consider the

types of standards that have been used and some of

the most recent commercial materials marketed for

calibration.

Reflecting Diffusers. Several materials used as

reflecting diffusers for measurement of primary

beam intensity are outlined in table 1. These

materials are useful for calibration of the instrument

with respect to primary beam intensity, but do not

provide the analogous calibration situation one

encounters when using suspended scattering particles.

Neutral filters for primary beam attenuation are usually necessary when using this approach. These

filters represent an additional variable and possible source of error. Transmitting Diffusers, Flashed Opal Glass, is simply a white glass fused with clear glass. The two

types of glass are drawn simultaneously from their

respective tanks and fused immediately as they cool.

The drawing is done by mechanical means and

results in a reproducibly smooth surface. Opal

Glass, is blown white glass. Manual manipulation

results in a more variable product with a more irregular surface than the flashed opal glass.

Table I. Reflecting diffusers [12]

Material Description R'

a. Vitrolite White structural glass ground

with #320 carborundum

0. 816

b. MgC03 Block scraped with straight

edge

. 964

c. MgO Layer (0.5 mm) smoked onto

MgCO-3 from burning chips

. 990

d. Casein paint #1 Commercial brand, painted on Vitrolite

. 885

B Absolute reflectance

When dealing with reflecting diffusers, it should

be noted that depending on the angle of measurement and the type of phototube used, polarization

effects caused by these diffusers can produce variation in the absolute intensity measured.

Amorphous Solid Scattering Materials. Zimm [13]

has described the preparation of a polystyrene

methyl acrylate material and its use as a scattering

standard. The material is prepared by adding 5

percent methyl acrylate to the polystyrene when the

polymerization is half complete. The mixture results

in an opalescent material suitable for scattering or turbidity measurements. Zimm observed that_ the

turbidity measurements were temperature sensitive

as would be expected for an amorphous solid. Zinc

oxide suspended in an acrylic resin has also been

used as a standard. This preparation is also sus- ceptible to temperature fluctuation.

Liquid Scattering Materials. Liquid turbidity standards have been used in industry for several years.

The most commonly used material being a preparation known as Formazin [14]. Formazin, produced

from a reaction between hydrazine sulfate and hexamethylenetetramine, is a suspension of relatively

large particles which exhibit angular dependent

light scattering and unsuitable sedimentation

properties.

Other suspensions that have been used include

silver iodide, silver sulfide, and barium sulfate, also

known as McFarland's standard. These suspensions

show only transient stability and should be used

with care. Solutions of polystyrene prepared in organic

solvents have been used as calibration material for

96
scattering photometers, and provide a relatively

stable standard when appropriately sealed and not

subjected to excessive ultraviolet radiation.

An aqueous standard, in the form of highly cross linked spherical beads of styrene divinylbenzene, is available commercially from AMCO Service Company 2 (4151 Middlefield Road, Palo Alta, CA

94303). Particle size ranges from 0.1 to 0.8 p.

The suspension is reported to be temperature, time

and pressure stable and to possess superior sedimentation characteristics relative to Formazin.

Several advantages of the styrene divinylbenzene

suspension make it attractive as a nephelometric

standard: (1) the suspension can be infinitely diluted

in an aqueous medium, (2) it can be accommodated

in both manual and automated systems now in use

for nephelometric or light scattering measurement

and (3) it is nonreactive with glass vessels.

Ludox® is a commercial colloidal suspension of

silica marketed by the Dupont Chemical Corporation. Ludox has gained popularity in recent years for

calibration purposes because of its ease in handling.

There are several forms of Ludox,® each having its

own unique physical and chemical properties.

Ludox® stability depends on silica solid content,

temperature, size and surface area of silica particles,

pH, particle charge, and salt concentration and

character. The specific effect of each parameter is

dependent on the Ludox® system under consideration. Ludox® can react with glass vessels if not

properly stabilized. A detailed discussion of the

chemical properties can be found in the Dupont

technical publication entitled, Properties, Uses,

Storage and Handling of Ludox Colloidal Silica.

IV. Applicability of Standardization

The following aspects of nephelometric immunochemical analysis would benefit directly from instrumental standardization.

Quality Control. The antigen antibody reaction

is intricate, producing antigen antibody complexes

with different characteristics at different antigen

antibody ratios. Quality control in essentially all clinical laboratories consists of the measurement

of one or two reference sera or plasma per assay

representing discrete ratios in restricted zones of

the calibration curve. Instrumental standards would

provide a means of monitoring results in all zones without resorting to multiple reference measurements in each set of analyses.

Data Comparison. Currently the criteria for method

acceptance consists of the evaluation of the clinical

applicability of results generated by the method.

Comparison cannot now be made on an analytical

basis except by semiquantitative means due to

the lack of reference methods and instrumental

standardization.

2 In order to adequately describe materials, it was occasionally necessary to identify the company and commercial products by name and trademark. In no

instances does such identification imply endorsement by the National Bureau of Standards, nor does it imply that the particular product is necessarily the best

available for the purpose.

Calibrator and Reagent Evaluation. A reference

scattering material is necessary to allow for evaluation of both calibrators and biological reagents.

These materials can vary from source to source and lot to lot.

The brief discussion of variables intrinsic to

immunochemical methodology demonstrates the

applicability of an instrumental standard to provide

a point of reference for improved overall quality

control, method comparison and quality control of

reagents and calibrators.

V. Summary

Amorphous solid scatterers such as described by

Zimm or liquid scatterers, such as a polystyrene

solution or styrene divinylbenzene suspension, seem

to be the most reliable and practical material for

routine use based on the experience of this investigator.

Low molecular weight polystyrene samples (300-

500,000 g/mol) dissolved in an organic solvent can

serve as a scattering standard in both automated

and manual systems and provide scattering independent of the angle of measurement. As

mentioned earlier, scattering from the solutions can

be relatively low and the sensitivity of the instrumentation should be considered. The stability of the

individual scattering components with regard to

temperature, pressure and also the sedimentation

characteristics would be superior.

Styrene divinylbenzene and Ludox® suspensions

exhibit relatively high scatter even at 90° and can

be diluted in an aqueous medium eliminating

refractive index differences that might arise when

comparing an organic solvent standard and an

aqueous standard in an absolute measurement.

Styrene divinylbenzene and Ludox® need to be

evaluated with respect to long term stability in

reference to this type of application.

An amorphous solid scatterer made up of polystyrene and methyl acrylate or zinc oxide in an

acrylic resin can provide a suitable standard for

manual instrumentation if the temperature variation

fluctuation is closely controlled.

Considerable work remains to be done with respect

to the evaluation of long term stability and comparison of different light scattering standard materials before specific recommendations can be

advanced.

VI. References

[1] Heidelberger, M., and Kendall, F.E., A quantitative

theory of the precipitin reaction. J. Exp. Med. 62, 467

(1935).

[2] Mancini, G., Carbonara, A.O., and Heremans, J.E.,

Immunochemical quantitation of antigens by single

radial immunodiffusion, Immunochem. 2, 235 (1965).

[3] Ritchie, R.F., A simple, direct, and sensitive technique

for measurement of specific protein in dilute solution,

J. Lab. Clin. Med. 70, 512 (1967).

97
[4] Savory, J., and Killingsworth, L.M., Measurement of

immunoglobulins in cerebrospinal fluid employing

nephelometric immunoprecipitin techniques, Clin.

Chim. Acta 43, 279 (1973).

[5] Alper, C.A., Automated nephelometric determination of serum haptoglobin, C'3 and ^-antitrypsin. In Advances in Automated Analysis, Technicon International

Congress. 1970, 1, C.E. Barton, et al., Eds. (Thurman

Assocs, Miami, Fla. 33132, 1971), p. 13.

[6] Anderson, N.G., Computer interfaced fast analyzers,

Science 166, 317 (1969).

[7] Tiffany, T.O., Parella, J.M., Johnson, W.F., and Burtis,

C.A., Specific protein analysis by light scatter measure- ment with a miniature centrifugal fast analyzer, Clin.

Chem. 20, 1055 (1974).

[8] Buffone, G.J., Cross, R.E., Savory, J., and Soodak, L., Measurement of laser-induced near front surface light

scattering with a parallel fast analyzer system, Anal.

Chem. 46, 2047 (1974).

[9] Giaver, J., The antigen-antibody reaction: A visual

observation, J. Immunol. 110, No. 5, 1424 (1973).

[10] Blume, P., and Greenberg, L.J., Application of differential light scattering to the latex agglutination assay

for rheumatoid factor, Clin. Chem. 21, 1234 (1975).

[11] Cohen, R.J., and Benedeck, G.B., Immunoassay by light

scattering spectroscopy, Immunochem. 12, 349 (1975).

[12] Brice, B.A., Hawler, M., and Speiser, R., Photoelectric

light scattering photometer for determining high

molecular weights. J. Opt. Soc. Am. 40, 768 (1950).

[13] Zimm, B.H., Apparatus and methods for measurement

and interpretation of the angular variation of light

scattering; Preliminary results in polystyrene solutions,

J. Chem. Phys. 16, 105 (1948).

[14] Standard Methods for the Examination of Water and

Waste Water (American Public Health Assoc., 13th

ed., p. 349-356, 1971).

(Paper 80A4-905)

98
Part 3. Ultraviolet Absorption Spectrometry

NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 466, Standardization in Spectrophotometry and Luminescence

Measurements, Proceedings of a Workshop Seminar Held at NBS, Gaithersburg, Md., November 19-20, 1975 (issued May 1977).

Errors in Spectrophotometry and Calibration

Procedures to Avoid Them

A. G. Reule

Carl Zeiss, 7082 Oberkochen, Germany

(May 26, 1976)

Based on simple principles, spectrophotometry nevertheless demands a lot of precautions to avoid errors. The following properties of spectrophotometers will be discussed

together with methods to test them:

Spectral properties—wavelength accuracy, bandwidth, stray light; photometric linearity;

interactions between sample and instrument—multiple reflections, polarization, diver- gence, sample wedge, sample tilt, optical path length (refractive index), interferences.

Calibration of master instruments is feasible only by complicated procedures. With

such a master instrument standards may be calibrated which greatly simplify performance

checks of instruments used for practical work. For testing high quality spectrophotometers

the use of emission lines and nearly neutral absorbing solid niters as standards seems to be

superior, for some kinds of routine instruments the use of absorption bands and liquid

filters may be necessary.

Key words: Bandwidth; calibration; errors in spectrophotometry; interferences; multiple

reflections; photometric linearity; polarization; sample characteristics; stray light; wavelength accuracy.

I. Introduction

The comparison of measured results of different

optical parameters reveals considerable differences

in accuracy. There is no difficulty in stating refractive indices to within 5 decimals and tables of line

spectra quote wavelengths to within 6 to 7 significant

digits. In contrast, the transmittance of an object can be indicated to within 0.1 percent only, and even

this allows merely statements as to random but not

to systematic errors. In 1973 the College of American Pathologists

carried out a comparative test. A number of solutions

was sent out and measured with spectrophotometers

in 132 different laboratories. The results showed coefficients of variation in absorbance of up to 22

percent. When the test was repeated in 1974, the

coefficients of variation among 135 laboratories still amounted to maximally 15 percent; although 24

laboratories had been excluded by a special test

because their photometers had more than 1 percent

stray light at 240 nm. This corresponds to a coefficient of variation in transmittance of up to 11

percent (table I) [l]. 1

1 Figures in brackets indicate the literature references at the end of this paper.

It is thus not surprising that spectrophotometer

users call for standards to test their instruments.

These tests and many similar ones have been and

are still carried out with solutions having several

wide transmission maxima and minima. As refer- ences for photometric and wavelength accuracy of

the instruments, measuring wavelengths are sometimes stipulated for the extremes and for values on

the slopes of the transmission curves, although such

an inference is often impossible. The author

would therefore suggest separate tests for wavelength

accuracy and photometric accuracy, even for routine

work. Only then will it be possible to prove by a

test not only the unreliability of measurements, but

also to derive quantitative parameters suitable for

correction of the results. The individual sources of error are, of course, dealt with and eliminated separately if instruments and equipment are tested in

laboratories issuing and calibrating standards.

The individual sources of error and possible test

methods are discussed in the following, with special

consideration of two points of view: fundamental

tests for specific errors in the standards laboratories

and tests by the average users of spectrophotometers

in clinical or analytical laboratories.

The result of a spectrophotometric measurement

is expressed by two numbers: wavelength and trans99
Table I. Best, medium and worst values selected from table I group A of Beeler and Lancaster [1]

C.V. = Coefficient of Variation

St. D. = Standard Deviation

T, AT/T=2.303AA, and AT have been calculated from A and AA/A given by B. and L.

Solution Cone. Wav. AA/A A T AT/T AT

p. = potassium mg/1 nm c.v.% % c.v.% St.D.%

Acid p. dichromate 20 380 11. 1 0. 109 77. 8 2. 79 2. 17

Alkaline p. chromate 40 300 15. 1 . 151 70. 9 5. 25 3. 72

Alkaline p. chromate . 40 340 9. 2 . 318 48. 3 6. 74 3. 25

Acid p. dichromate 60 328 5. 0 . 432 38. 0 4. 97 1. 88

Acid p. dichromate 100 366 5. 8 . 855 14. 0 11. 42 1. 59

Acid p. dichromate 100 240 2. 8 1. 262 5. 47 8. 14 0. 45

mittance. The transmittance of a sample as a function of the wavelength is generally expressed by a

curve. Since the transmittance may vary more or

less strongly with wavelength, both the spectral

characteristics and the accuracy of the photometric

result must be considered. Three groups of characteristics are therefore discussed: spectral characteristics, genuine photometric characteristics, and

optical interactions between sample and photometer.

In practice there are other sources of error, such

as environmental effects on photometer and sample,

temperature, line voltage fluctuations, vibrations,

contamination, or heating of the sample by the

photometer. All these factors may impair the measured result, and ways and means are Known to test

and eliminate them. They are therefore disregarded

in the following discussion.

There are numerous publications about tests of

this kind, and each individual problem has been

discussed in the relevant literature. This paper gives a survey of the problems and discusses methods the

author would like to recommend or to warn against.

The study is limited to photometers for Uv, VIS,

and near IR. A good survey of the literature published until 1972, especially regarding tests for

photometric linearity, is included in the proceedings

of the Conference on Accuracy in Spectrophotometry

and Luminescence Measurements, held at the National Bureau of Standards in March 1972 [2],

particularly in the contributions of Clarke [3],

Mavrodineanu [4], and Sanders [5].

II. Testing the Spectral Characteristics

A. Accuracy of the Wavelength Scale

The wavelengths of a great number of emission

lines within the ultraviolet and visible spectral

regions are known exactly. Standards or industrial

laboratories which have to supply the data for such

scales encounter no difficulties in testing wavelength

scales. Two facts deserve special mention:

(a) Even in regions without absorption the dispersion of prism materials is not as homogeneous as

may be expected. Thorough tests therefore require

measurements at a great number of wavelengths

(fig- 1).

(b) The fundamental errors of a sine bar mechanism (fig. 2), which is commonly used for rotation

of gratings, should be covered by checks at four

wavelengths. This does not apply, however, to

periodic errors of the lead screw or its bearing, which

sometimes cause surprising discrepancies (fig. 3).

A single wavelength suffices to test an instrument

supplied free of defects by the manufacturer, because

it is unlikely that the tested wavelength remains

unchanged in case of damage during shipment or other sources of error. This is not true, however, if the user or the manufacturer's maintenance service

carries out adjustments, which generally requires the

checking of two to three wavelengths. This is not

necessary in case of special designs (fig. 2a).

If the user wants to check the wavelength in

instruments equipped with a deuterium source, he

should use the emission lines of deuterium. Note the

differences between deuterium and hydrogen lines

(table II). However, many light sources contain in

addition to deuterium higher or lesser amounts of

hydrogen, which cause errors if the resolving power

of the instrument is not adequate to separate the

lines (fig. 4).

Error of a preliminary wavelength scale

following a smooth dispersion curve

for glass F2

1,0-

0.5-

' i

1 1 1 1 r 2000 2500 \nm

500

Figure 1. Irregularities in the dispersion of a prism made of

F-2 glass (Schott).

Shown are differences between actual transmitted wavelengths and readings of a preliminary wavelength scale following a smooth dispersion curve. Projection

scale with 50x magnification see figure 2. 1 mm on the groundglass screen corre- sponds to about 0.038 nm near 400 nm and about 5.5 nm near 1500 nm.

100
In an instrument without a deuterium source the

aforementioned average user cannot be expected to

equip it with a line source to check the wavelength;

therefore absorption bands must be used for the test. The bands of the well-known didymium glass are not

suited for wavelength checking because they are too

wide, temperature-dependent and because didymium

glass may contain varying amounts of several absorbing rare earths.

Figure 2. Different wavelength display systems.

To the left: (a) (Micro) projection scale rigidly connected with prism, (b) Wavelength cam and scale fixed to cam. To the right: (c) Sine bar mechanism,

(a) nonlinear, high uniformity of different instruments of the same type, no

backlash, no wear, no parallax

(b) can be made linear in X or v, less uniform, subject to backlash, wear and

parallax (a projection system in connection with a cam avoids parallax only)

(c) linear in X, uniform, subject to backlash and, less pronounced, to wear and

parallax. Periodic errors possible (see fig. 3).

Holmium in aqueous solution has rather sharp

absorption bands. Most of the bands of holmium

glass are at nearly the same wavelengths as for

holmium solutions but are somewhat wider with one

striking difference near 450 nm (fig. 5). Because the

glass matrix seems to influence Ho absorption there

arises the question whether the wavelengths of

absorption maxima of Ho-glass are the same for all melts.

In single-beam instruments only narrow bands

measured with small bandwidth allow the determination of absorption maxima by simply scanning the

wavelength. If the bands or bandwidths are wider,

the positions of the maxima are shifted due to the

spectral variation of signal in the empty instrument

(fig. 6). This can be avoided by using an absorption

or transmission maximum near the maximum of the

instruments' response curve, which is achievable by

special interference filters (fig. 7). We found such

interference niters to be most helpful for wavelength

checks of instruments with bandwidths between 2

and 10 nm. The filters must, of course, be most

carefully produced, and the wavelength of maximum

transmittance given for each individual filter.

B. Bandwidth

Bandwidth is best checked by recording the signal

as a function of wavelength, when the monochromator is irradiated with an isolated emission line (fig.

8). Bandwidths well above the limit of the resolving

power produce the well known triangle, whereas

bandwidths approaching the limit of resolving power

result in a rounded curve.

X 1 1 ,^nn^ D F r?

.] . ... .

0 0 D

0 0*00 0 CO0 0 c 0

-1

-11

-I?

o o

0 0 0

oo o

0 0

0 « 0 0 0 0

0 0

0 0 0 0

X 0 0 0 •

0 0 0 0

0 0

0 0 0 0

0 09 0

-s < Periodic error of sine bar mechanism 5/2920

. . . ..... . . . ^ . . .

Figure 3. Periodic error of a sine bar mechanism (in this case due to an unsuitable ball bearing).

x measured lines (Hg), + and 0 best fitting curve.

101
Table II. Emission lines of hydrogen and deuterium

tjXX r-i xJ

a 656. 285 nm 656. 100 nm

0 486.133 485. 999

double beam

Dq 485,999 nm

single beam

H

n

486,133 nm

7\\=0,2nm

H0CI3 - solution

Figure 4. Line emission of a commercial deuterium source showing D and H lines.

\nm

360 370 360 370

The H/D intensity ratio is likely to increase with age.

100-

%

Figure 6. Spectral transmittance of Holmium chloride solution as in figure 5 measured in a double-beam instrument (ZEISS

DMR 10) at 0.2 nm (left) and 2 nm (right) bandwidth (curves

above), and in single-beam mode (turves below).

In single-beam mode the error is less than 0-05 nm at 0.2 nm bandwidth. At 2 nm bandwidth the double-beam curve shows a shift of 0.1 nm of the minlmim

due to skewness of the true transmittance. The single-beam minimum is shifted by 0.15 nm from the double-beam minimum (0.25 nm from the true one) due to skewness of the empty instrument signal.

50-

%

5i.O 550 560 SiO 550 560 U0 450 460 470

Figure 5. Spectral transmittance of Holmium in aqueous solution

(1.14 9 H02O3 in 100 ml 0.2 N HC1; 1 cm) and as an absorbing

constituent of glass.

Part with the greatest differences; minor differences are observed with the

other bands.

Figure 7. Spectral transmittance of an interference filter for

wavelength calibration measured at 0.2 nm and 2 nm bandwidth

in double-beam mode (curves below) and single-beam mode

(curves above).

There is no difference in the position of the maxima up to 2 nm bandwidth; 0.4 nm shortwave shift at 5 nm.

102
/I single beam signal

Figure 8. Bandwidth determination with isolated emission lines.

Recorded in single-beam mode with ZEISS DMR 10 Recording Spectrophoto- meter and mercury line 546.07 nm. Abscissa scale expansion changed to give

nearly equal widths of the tour larger bandwidths; ordinate expansion, voltage

adjustment and neutral niters used to make amplitudes nearly equal. Nominal

bandwidths ("spectral slit widths") set to 5-2-1-0.4-0.2 and below 0.1 nm.

The aforementioned deuterium lines are less

suited for the determination of the bandwidth, be- cause of other lines and continuous background in

their vicinity.

The dip between two emission lines can be easily

interpreted only if both lines are of equal intensity

and if the transmission profile of the monochromator

is symmetrical.

Absorption bands are generally not sufficiently

pronounced or isolated. The only definite conclusion

that can be derived from the resolution of two bands

is that the bandwidth is smaller than the distance

between the two.

As far as the author knows, previous comparative

tests did not include bandwidth checks by the user. There is little danger of corresponding changes in

good instruments. If a check by the user is necessary,

the separation of absorption bands is probably the

most convenient procedure.

C. Stray Light

In this connection the term stray light refers to

heterochromatic stray light; that is, light of wavelengths outside the bandpass of the monochromator.

Due to scattering, a fraction of this light passes

through the monochromator, while outside the

monochromator this light follows the regular path.

In Germany the expression "Falschlicht" is used,

similar to "false light," sometimes used in the U.S.,

to distinguish this unwanted radiation from radiation

scattered by the sample or sample compartment

optics and deviating from the regular path. The

fraction of the signal (electric current) which is due

to stray light falling on the detector is important

for the measurement. This is called the stray light

ratio and is especially large at the ends of the spectral

range of the instrument, where slit width or amplification must be large. However, with a. single monochromator this stray light ratio does not change as the

slit width or the amplification changes [6].

There are various methods to determine the stray

light ratio, of which the different versions of the

absorption method, the slit height method, and

Preston's method are of practical relevance.

The absorption method requires a substance that

is completely opaque within the region of two bandwidths and is completely transparent outside this

region. If the stray light occurs exclusively at the

longwave or shortwave side, like at the ends of the

spectral range, the substance may only have a longwave or shortwave cutoff.

There is no substance which provides an ideal step

function transmittance at one wavelength, but

there are a number of substances having sharp

cutoffs or narrow absorption bands in the center of

the spectral range. Sharp shortwave cutoffs can, for

instance, be produced with chlorides, bromides, and

iodides (fig. 9). A 15 g/1 aqueous solution of sodium

chloride has, for instance, at 200 nm and 1 cm path

length a transmittance of less than 0.1 percent. The

cutoff is temperature-dependent, and even at low

temperatures the concentration fulfills the requirements well. Generally the solution is selected as follows: a solution with suitable cutoff is measured in

low concentration so that the transmittance lies between 20 and 50 percent (there is only little influence

of stray-light) and the required concentration or path

length is calculated. If the aforementioned sodium

chloride solution is, for instance, used to test a double

monochromator, 2 cm instead of 1 cm path length

are used.

There are no substances with similarly steep longwave absorption cutoffs, but interference barrier

filters are of some help. The true transmittance of

l

1 t

1 1 r 210 220 230 nm

200

Figure 9. Determination of stray-light ratio and its variation

with the slit height using KBr solutions in 1 cm cells.

The true transmittance ot 0-005 Nsolution (dotted lin%) is calculated from the transmittance of 0.0005 Absolution.

103
each filter must, of course, be measured in a double

monochromator. The instrument user may carry out

checks with absorbing solutions and interference

barrier filters.

Slit height variation is the second method for

stray-light tests [6]. Contrary to its independence of

slit width, the stray-light ratio decreases linearly

with the slit height, provided the heights of the

entrance and exit slits are reduced simultaneously.

For a quantitative determination all parts of the slit must contribute uniformly to radiant flux and signal.

This requirement is hardly ever met, and reduction

of the slit height therefore only reduces the straylight ratio without allowing its quantitative determination. Some manufacturers equip their instruments with facilities to change the slit height, thus

offering the user the possibility of estimating and

reducing the stray light (fig. 9).

In Preston's method [7] one half each of the en- trance and exit slits is covered. If the covering is such that an image of the free part of the entrance

slit is produced on the free part of the exit slit, the

transmitted radiation still contains signal light and

stray light. Owing to the reduced slit height the

stray light ratio is about fifty percent less than

originally. If the other half of the exit slit is covered,

only stray-light leaves the monochromator, which

can be quantitatively determined. The accuracy of

the determination is impaired, though, because for

safety reasons the covering must be larger than the

part of the slit through which the signal light passes.

As this method requires manipulations in the slit plane, it usually cannot be applied by the instrument

user.

III. Testing Linearity

A. Representation of Linearity Errors

Two methods of representation are in use which

are both based on the fact that the photocurrent

?'max (or the equivalent readout on an instrument)

which corresponds to a maximum value <£max of the

radiant flux is stipulated as a reference point. If

ia is the dark current, the following equation should

hold for a current i Ua which has a strict linear

relationship with the radiant flux 3> (fig. 10)

{iun—id)l{imM—id)=4>l4>n (1)

Differences between the actually measured value

i and the value i liD derived from the equation are

called linearity errors

Ai=i—

iin- (2)

Both methods express the linearity error as a

fraction of a measured result, usually in percent.

The two methods differ in that the error is referred

either to the maximum value or to the actual

reading i (fig. 1 \) . In both cases the determined errors or derived corrections are valid only for measureFigure 10. Nonlinearity of detector response (vertical distance

between the characteristic curve giving the current i as a function of the incident radiant power <f> and the straight line)

'A ma x Figure 11. Expression of the nonlinearity by Ai/i mai or Ai/i.

ments which are based on the radiant flux <£max. Which method is chosen depends on the user. In

practice the reference to the maximum value is somewhat easier for the correction of transmittance,

because the correction term can be added directly.

Reference to the individual value has advantages

if the transmittance is low or for measurements of

absorbance A, because the following equation holds:

AA=0.434 (Ai/i).

B. Photomultiplier Characteristics

(3)

Most precision spectrophotometers are equipped

with photomultipliers as detectors. Their characteristics; such as, spectral sensitivity of the cathode,

dependance of gain on voltage, voltage drop at the

anode resistor, variations of sensitivity across the

cathode or with direction of incidence etc. are so well known that they will not be discussed here.

We should like to mention just a few effects which

are not so well known. The first is the temperaturedependent sensitivity of the cathode [8] (table III).

If a radiant flux of 10 nW falls on a cathode with a metal substrate, the rate of temperature increase

due to absorption of radiation is approx. 0.5 x 10~B

°C/s. This value is so small that even with irradiation over extended periods the sensitivity does not

change markedly due to the temperature increase

104
Table III. Variation of photocathode sensitivity with temperature [8]

Photocathode Blue Red

Ag 0 Cs -0. 24 %/°C -0. 14 %/°C

Sb Cs -0. 48 + 0. 64

Multialkali -0. 22 -0. 24

caused by the radiation. However, the temperature

rise time of cathodes on glass or quartz substrates

(as in end-on types) may reach values which are

interfering, yet are still too slow to reach thermal

equilibrium.

Another troublesome characteristic of detectors is that the current generated depends not only on the

present but also on the previous irradiation, an

effect which is known as memory effect. Most

detectors have memory effects of some tenths of a percent for a duration of a few seconds, if they are covered for a few seconds after long exposure to

light. This holds true even when the anode currents

are kept to values between 10~ 8 to 10" 7 A. Some detectors show much larger memory effects. The effect

is not only noticeable upon irradiation with con- tinuous light, but also if the light is chopped at 50

Hz. Only recently, we observed a change of the

signal amplitude in light pulses of 5 ms width and

15 ms dark time, dependent on whether or not

pulses of equal amplitude and width were interspaced between these pulses. The change in amplitude

of the original pulses amounted to —1.3 percent and

covered a period of approximately 5 s (fig. 12) [9]. In keeping the measuring accuracy below 10"4

of the maximum current, there is the danger that

these memory effects affect not only the measurement

of the sample under test but also the methods for linearity tests. It will be difficult to distinguish between

memory effect and nonlinearity. All readings must

be done in a sequence of time which is exactly

stipulated and reproducible. Residual memory effects

in the results may be recognized by changing the

time between readings.

Figure 12. Short-term memory effect of photomultipliers.

The multiplier is at first illuminated with light pulses which result in the

current given by the solid lines. If equal light pulses (dashed lines) are interposed between the first ones, the current amplitude is reduced by an amount which

depends on multiplier type and spocimen. With pulses giving a current amplitude

of 10"' A a reduction of —1.3 percent was observed, which took about 5 s to reach the new level.

C. Light Addition Methods

As indicated elsewhere [10, 11], there are no samples the transmittances of which are known with

sufficient reliability without photometric measurement. The standards laboratories must therefore

determine the linearity of the instruments by special

test methods. The addition method is the basic

procedure for the design of an equidistant scale of

any measuring parameter. Different versions of the

method are in use in photometry [12]. There are setups with several apertures and setups with several

light sources. The setups with two apertures (fig. 13)

[13, 3, 4], with many apertures [14, 5], and with two

light sources (fig. 14) [15, 10] are especially important

in practice (the first—to the author's knowledge—and

one or two recent papers are cited respectively)

Setups with two or several apertures have the advantage of needing only one light source, that is the

one in the instrument under test. Neither is additional optics required in the beam path, so that the

state of polarization of the radiation remains unaffected. However, the light in the instrument is

reduced considerably by the aperture diaphragms, so that the method can only be applied if there is sufficient light available and if the cross section of the

light beam is large. For these reasons, these methods

cannot be applied to commercial instruments with

small beam cross sections or other beam geometries

(e.g., variable apertures, rotating sectors and mirrors,

modulators etc.) that would be perturbed by the

Figure 13. Arrangement for the double-aperture method.

K, V, O 0

*)

Figure 14. Arrangement for the supplementary-light method.

105
insertion of additional apertures. For example, an

existing variable aperture stop may cause incomplete

illumination of an inserted double aperture arrangement and, thus, render it useless. If, as another ex- ample, in an instrument using chopped light, the

shape of the intensity versus time (as can be observed

by an oscilloscope) is changed by an inserted double

aperture other than merely in amplitude, linearity

cannot be tested this way. Methods using two or several apertures however are well suited for testing

the linearity of special equipment the design of which

allows the use of the aperture method.

To guide the light beam the method with two

sources requires more optical parts and a semitransparent plate which may change the state of

polarization. However this method can be adapted

to commercial instruments as demonstrated by the

author, even in a double-beam instrument [10].

D. Other Methods

As mentioned before [10, 11, 16], tests based on

Lambert's or Beer's laws alone are inadequate.

At least one point of the photometer scale must be

established in another way. The same is true of the

method discussed in detail in reference [11], in which

neutral density niters or perforated screens are measured for varying attenuations of the beam.

Rotating sectors are not suited to test photometer

scales of equipment with detectors having response

times which are short compared with the open and

dark periods of the sector [5, 10]. The detector

signal changes between the dark period and the full

value; the part of the characteristic curve which is essential for the measurement of an absorbing sample

is not passed (fig. 15). The test can be made with a rotating sector only if the open and dark periods

of the sector are short compared with the response

time of the detector (in the IR range, for instance).

Figure 15. Current from a nonlinear fast detector illuminated

through a rotating sector.

With the sector set to 40 percent open time the light pulses (shown below the

dectector characteristics) will cause current pulses with 40 percent on time (shown

to the right of the detector characteristics), i.e., strict linearity . A sample of 40 percent transmittance illuminated with continuous light will cause a current amounting to about 50 percent of that without sample and showing striking

nonlinearity.

Inspired by a theoretical treatment of Hansen,

who introduced the derivative of flux with respect to

reading [17], Ploke [18] has applied a simple method

to test the linearity of detectors. A weak, chopped

radiation is supplied to the detector under test,

and is measured with a lock-in amplifier. Additional

unchopped light is then supplied to the detector

and the signal of the lock-in amplifier is observed,

which approximates the derivative of reading with

respect to flux. Each change of the signal is interpreted as a curvature of the characteristic curve and thus as a nonlinearity. This holds true if there is no memory effect and if the characteristic curve is the same for continuous and chopped radiation. In

other cases the distinction of nonlinearity, frequency

dependence and memory effect becomes difficult.

The same disadvantage applies to the following

method.

Jung [19] states an interesting method to determine

the nonlinearity from the beat frequency of two

radiations chopped at different frequencies. Although

this method is interesting for testing multipliers, it is not suited for the direct calibration of a photometer.

Jung also describes a method to improve the linearity

of multipliers [20], which uses chopped measuring

light and adds unchopped light to the weaker of the

two light portions until the mean photocurrents

are equal in both cases. The amount of added un- chopped light need not be measured. However,

Jung's own theoretical treatment of the method reveals

that only the nonlinearity which is proportional to

the radiant flux is rendered completely ineffective.

Higher-order components of nonlinearity are re- duced, but not eliminated. For this reason Jung's

method can be assumed to improve linearity,

although it does not eliminate the necessity to

measure it. The difficult testing of photometer linearity can

only be carried out in standards laboratories. They

must provide standards of known transmittance

which are then applied by the user to test his photometers. The interaction between sample and photometer must be considered for the calibration of the

standards and for their use.

IV. Interaction Between Photometer

and Sample

A. Definition of True Transmittance

If the transmittance of a specific sample is measured in several photometers with defined linearity or known nonlinearity and arithmetically corrected,

this would not be a guarantee for consistent results.

This is due to a number of interactions between

sample and photometer. The values obtained by

measurements in a linear photometer cannot be

regarded as true transmittance.

Corresponding to international standards _ or- ganizations, we start with the theoretical definition

of the internal transmittance of a homogeneous

106
sample limited by parallel plane surfaces. This

internal transmittance r t is defined as the ratio of the

outgoing radiant flux at the inside of the exit surface

to the incoming radiant flux at the inside of the

entrance surface. The radiation is assumed to be a

quasi-parallel, sufficiently monochromatic light beam

perpendicular to the boundary surface of the sample

(fig. 16). A reflectance of the radiant flux of the

amount r is assumed, owing to the refractive index

discontinuity at the boundary surface. It follows

that the transmittance determinable from the outside is, for a single passage of the radiation,

T=Ti(l-r)2

. (4)

The radiant flux reflected by the inner exit surface

returns to the entrance surface where it is again

partially reflected. The result of the infinite series

of multiple reflections is a somewhat higher

transmittance.

The first question is to what extent these multiple

reflections will become effective in the photometer.

Even in photometers with a collimated beam the

light is not exactly parallel. The more it is reflected

the more it diffuses and finally does not reach the

detector any more. Therefore, in practice, an infinite

number of reflections need not be considered; the

first back and forth path in the sample alone produces

the transmittance

r=r < (l-r) 2 (l +r i2 r

2 ). (6)

For normal glass, r is approx. 0.04 (4%). Although

the first back and forth reflection will change the

transmittance of an absorption-free sample (r*=l)

by about 0.16 percent, the following would result

in only 2.5X10"4 percent and can be neglected.

The thickness of absorbing glasses used as standards

is typically about 2 mm. Even in photometers

with focused beam the expansion of the light beam

over this distance is not large enough so that an

appreciable part of the reflected light would be

lost. Thus, it is justified to define the transmittance

according to the eq (6). After elimination of the causes of error mentioned, it can be expected that

photometers with correct display will also measure

this value, which does not differ from (5) within the

stipulated measuring accuracy. The flux reflectance

r was used for the calculation; thus possible interferences of coherent light are not considered for the

definition. They will be disucussed further.

B. Obliquity Effects

Not all rays passing through the sample in a photometer are parallel. This applies not only to commercial photometers with focused beams, but also to

photometers with a collimated beam. The aperture

limiting the divergence must have a finite diameter

if energy is to pass. Deviation of the rays from the

normal on the sample surface causes path length

and reflection errors. If the optic axis is perpendicular to the surface

and if the path length for the maximum external

angle of incidence <p max does not exceed (1 + e) of

the path length for normal incidence (fig. 17)

the following equation must hold

<pL^2n2 e (7)

where n is the refractive index of the sample.

If the light beam at the sample has a cross section

A, this determines the light gathering power. From

this value, the spectral radiance L\ of the light source and the bandwidth AX used for measurement,

the radiant flux, and finally the number A

T

( of

photoelectrons per unit time at the cathode can be

calculated as follows

Nt =Lx -A\-A-w^-T-q/hv (8)

where q is the quantum yield of the cathode, t the

transmittance of the entire optical system including

the efficiencjr of a sphere (if any), h Planck's constant,

and v the frequency of light. Due to shot noise, the

T =—

%

(l-r) :

1-r2 zf

Figure 16. Influence of surface reflections on the transmittance

of a homogeneous, isotropic, optically clear sample with plane

parallel surfaces passed by a nearly parallel beam of light. Figure 17. Path length error caused by oblique incidence.

107
relative precision for a measurement with an integrating period t is

AiV 1 =

(9)

Numerical values are given in table IV. As can be

seen from the table, difficulties are to be expected

only if one tries to limit errors substantially below

10-4

. The obliquity is generally greater in commercial

photometers. The photometer reads an average

value Ti- It must be considered, however, that the

instrument does not average the path lengths or absorbances, but transmittances. For a sample with

an internal transmittance t<0 for normal incidence,

if traversed by a light beam containing rays of

obliquity <p with a weight factor g(cp) the following

equation holds

7,= fg(<p)e {lD T<0) /cos { * ln) dep. (10)

Developing both the cosine and the exponential

function in power series and truncating after the

first term, yields the following result

r,= r <0 [l-ln (l/r,o)-^2 /<7(?)V-^]- (H)

When measuring samples which attenuate due to

absorption (not reflection) such a photometer seems

to read a linearity error referred to the maximum

value of

A7r=-^-2

- T 10 -ln (1/t 10 ) fg(<p)-<p

2 -d<p (12)

or a linearity error referred to the corresponding

individual value of

Ar</r,= ~-ln (l/r< 0) fgt») (13)

If 9 (<p) contains all beams within a circular cone with the maximum aperture <pmax (corresponding to

the geometry of a point source irradiating a circular

aperture, or corresponding to collimated light if the

aperture limiting the divergence appears under the

aperture angle <pmax seen from the lens) the function

g(<p) with due consideration of the normalizing

condition

fg(<p)-(fo=\

has the form

so that

flf(p)=2<p/<9i

fg(<p)-<P

2 -d<p--

max

2 /2

(14)

(15)

(16)

The curves in figure 18 are calculated with

<Pmax =0.05 and n=1.5 to illustrate the eqs (12) and

(13). The errors have been calculated by Hansen

and Mohr for two apertures of finite size [21].

If the sample is tilted by the angle ^ towards the

optic axis, which may be necessary because of multiple reflections, Mielenz [22] stated for a point

source and a square aperture the equation

ATi'' 3¥2

" Tl0 ' ln (VrfoW-.+l.S *2

) (17)

The reflection error is caused by oblique rays

which are reflected differently than normal rays. The

reflection of the component polarized parallel with

the plane of incidence decreases, while the reflection

of the perpendicularly polarized component increases.

The effects are oppositely equal for small angles,

which means that they cancel when unpolarized

light or a symmetrical cone is used. Mielenz indicates

the following equation [22] for the tilted sample

n

(18)

Table IV

Shot noise influence on precision of transmission measure- ments if the cone angle <pmax is limited by acceptable path

length error e. Calculated from eq (9) with AX=1 nm, g=0.1,

A = 0.196 cm2 (beam diameter 0.5 cm), n = 1.5

for X = 400 nm with t = 0.1 and L\ =2 mW/cm2 sr nm (Tungsten coil) and

for X=200 nm with t=0.01 and Lx = 0.8 mW/cm2 sr nm (Deuterium lamp).

If the measuring time is assumed to be 1 s for 100 percent

transmittance or 10 s for 10 percent transmittance, relative

precision remains the same.

e Vmax AN/N AAVAT rad deg (400 nm) (200 nm)

lO-3 6. 71 10"2 3. 84 3. 0 10-° 2. 1 10~5 10"1 2. 12 10-2 1. 215 0. 95 10"5 6. 7

10-»

10-5 6. 71 10"3 0. 384 3. 0 10"5 2. 1 10"4

C. Influence of Bandwidth

If the bandwidth used for measurement is not

small enough to assume that the transmittance of

n-1.5

Figure 18. Apparent nonlineariiy due to oblique incidence cal- culated from eqs {12) and (IS) for a circular cone with the aperture angle <t>maz—0.06 and n=1.5.

108
the material within the bandwidth is constant, the

spectrophotometer will supply an average value of

the transmittance within the bandwidth, which is based on the internal transmittance

T i =fg(\)-T i (\)-d\ (19)

where g(\) is the weight with which the individual

wavelengths contribute to the total signal. If onlyone sample is measured, the conditions are fully

described by this equation. However, the situation is

This equation is similar to equation (11) in the

preceding paragraph, and shows the same dependence

on transmittance. If non-neutral standards of the

same material but with different thicknesses are measured in photometers with different bandwidths,

differences are liable to occur between the measurements in accordance with figure 18.

D. Interreflections

Every photometer contains reflecting surfaces

before and after the sample. Even if attempts are made to avoid such surfaces, which will be discussed

further below, light source and detector themselves

will become effective as surfaces of this kind. In

commercial photometers the sample is generally

arranged between plane or convex windows. The

radiant flux will then not simply pass through the

sample^ but there are interreflected portions, as shown in figure 19, For the radiant flux passing

through a sample with the transmittance n and the

reflectance i?, (reflectance of the entire sample,

both front and rear surface) it follows that

Q^o-rAl+RviRa+RJ+Ra-RbW]. (22)

where 0O is the radiant flux passing without reflection,

and Ra , Rb are the reflectances at the surfaces in the

photometer. Consequently the radiant flux

4>=<M1 +RaR>] (23)

passes through the empty photometer. If a second

sample (r2 , R2 ) is measured relative to the first

sample (tu RJ, the ratio of the radiant fluxes is

<h/4n= riT,[i

(R1 ~R2 )

• (Ra+Rb

) -Ra -Rb

• (Tl»-

2

2 )].

(24)

If, however, the second sample is measured in the

empty instrument, it follows that (^=1, Rt =0)

&/0i=r2[l +R2

• (Ra+Rb)-RaRb (l-Ti

2)]. (25)

In all these equations R, Ru R2 , Ra and Rb are treated as small quantities; powers higher than R2 are neglected.

different if a thicker sample of the same material is

measured, which has not only a different internal

transmittance but also another wavelength dependency. Terming the absorption coefficient at a mean

wavelength a„, and that at a different wavelength

a(X), and the difference of the two values Aa(A),

and defining

a(\)=Aa(\)/a0 , (20)

it follows for the average value of the internal transmittance that

(21)

Ra T,R Rb

, 0o

. r

^ <t>0 -R0 -R-T

- <P0 -Rb-R-T

* <t>oRa -Rb -v

3

Figure 19. Interreflections in a transmission photometer.

J?» is the reflection coefficient for all optical surfaces before the sample for light incident from the sample side, Rb that for all surfaces behind the sample. R is the reflection coefficient, t the transmittance of the total sample. 00 is the radiant power flowing directly from source to detector (without interreflections).

Due to these reflections the ratio of the radiant

fluxes deviates from the value of the actual transmittance. Part of the reflections can be rendered

ineffective by tilting the sample. The errors caused

by the tilt must then, of course, be considered. Apart

from the errors mentioned in section IV-B, these are the influences of a lateral displacement of the light

beam. Mielenz [22] gave a good example, and subsequently Mielenz and Mavrodineanu [23] developed

a method to determine {Ra -{-Rb ) by sample tilting.

However, tilting the sample affects only the term

(Ra+Ri,), and does not permit the measurement of

Ra Rf An upper limit for this term may be estimated

from

Ra'Rb < \(Ra +Rb)

2

- (26)

For direct evaluation of Ra Rb the following procedure is suggested here: a sample of approx. 58

percent transmittance (the function t(1 — t

2

) has its

maximum at rw =l/V3 =0.577) is measured in the

photometer under test. It is tilted so that the reflections by the sample do not impair the result, i.e.,

the term (Ra -\-Rb) is eliminated. Two weakly absorbing plates with a transmittance tp of approx.

76 percent each are tilted opposite to each other and

are placed before and after the sample so that their

reflections are excluded, and that they do not cause

interreflections with the tilted sample. The opposite

Ti =fg(\)-e^to)ii+^n.d\=ri0 [1-ln (l/r i0 )-fg(X)-a(X)-d\].

109
inclination cancels possible beam shifts. For the first

measured ratio of the radiant fluxes it follows that

W*i =rM [1-Ra •£» • (1- tm2 )}, (27)

while the second measurement yields the following

radiant fluxes

03=00- Tp

2 [l + rP*-Ra-Rb], (28)

04=00- Tp

2

-

M[1 + TM

2

-

p

i -Ra -Rb\. (29)

The ratio of these is

04/03= rM[\ - r/ .Ra Rb

• (l-rM

2 )] (30)

and consequently the difference of these ratios is

04/03-02/01 =TM • (1 - tm2

) ( 1 - rp

4

)

• Ra R„. (31

)

RaRb can be calculated from this equation. The

reason for the proposed transmittance of 76 percent

of the auxiliary plates is the difference 1 — r v

i in eq

(31) and the decrease by r p

2 of the total radiant flux.

The function t

2 (1 — r

4

) has its maximum near

r7) =l/V3 =0.76.

The user of a commercial photometer cannot

carry out such tests. He cannot work in the cell compartment without windows because of the

danger of damage to optical surfaces by spilled

chemicals or vapors. If the manufacturer has not

eliminated the reflections, the user has to take the

instrument as it is. Most spectrophotometers, however, are used to measure solutions. A cell with solution is measured relative to another one containing

the solvent. Equation (24) states the "transmittance

of the solution relative to the solvent." The errors tend to cancel, though not completely. Actually the user wants to determine the internal transmittance.

If the solvent does not absorb, it follows from the

above mentioned definition of true transmittance

(equation 5 or 6) that

r2/r1 =ri [l-r2 .(l-r12

)]. (32)

For the reflection of the solvent

#i=r[l-Kl-r)2

] (33)

and the reflection of the solution

R2 =r[l+{l-ry- Ti

2

]. (34)

If these terms are entered in equation (24) it follows

that

^/4>l = Ti .[l-(l- T 2). {r2 +(Ra+Rb) . r . Ra+Rt)]]

(35)

The user calculates with the simple formula

02/0i =t{

. Due to the multiple reflections in the

instrument (provided they have not been eliminated

by the manufacturer) he will experience an apparent

nonlinearity according to eq (35) of

Ar4 = - r ,

• (1 - r

2 )

• {

2 + (Ra +Rb )r+Ra Rb )

. (36)

Though higher, it is of the same kind as that expressed

in eq (32) for a reflection-free photometer with the

following apparent nonlinearity

Ar^-Tiil-T 2)-^. (37)

The errors are so small that they are negligible in

practice. Only very few cases are known to the

author where the reflection within the sample was

considered according to eq (32) or (37) for analytical

applications. Consequently also the somewhat larger

error due to eq (36) may be tolerable.

When designing instruments for standards laboratories, multiple reflections should be avoided.

Mielenz achieved this by imaging with off-axis

parabolic mirrors. This doubtless reduces multiple

reflections to values which are neglegible even for

most exacting demands with regard to measuring

accuracy. However, such an arrangement should

always be checked for multiple reflections. Not only

must the sample be placed exactly perpendicular to

the optic axis, but aberrations must also be kept

small and apertures must be blackened. One of these

apertures is the monochromator exit slit, and it may

be difficult to eliminate reflections from its sharp

edges (fig. 20). In Mielenz's instrument, a blackened

monochromator exit aperture was used successfully.

To avoid reflections the instrument designer can

equip the instrument with off-axis mirrors (see

above), tilt lenses and windows, or provide them with

antireflection coating (which is, however, possible

only for a limited spectral range). As far as the linear

function of the photometer can be influenced, he

can correct the apparent linearity error resulting

from eq (35). In 1953 the author did this for ZEISS's

ELKO II photometer. 2 The apparent errors ac- cording to eq (36) were eliminated together with the

apparent errors from eq (12) which depend similarly

on the transmittance, and possible genuine linearity

errors [17]. They were eliminated by so-called cor- rectors described by Hansen [24] (figs. 21, 22).

The following numerical value was determined for

correction :

Ar ( =+0.0084ri (l-T( 2 ).

The above considerations reveal a danger in testing photometers with multiple reflections by standards which are calibrated against air. Multiple

reflections do not only supply higher absolute values

than actually available of the linearity error, but

compared with the error involved in the measurement

> In order to describe materials and experimental procedures adequately, it was occasionally necessary to identify a commercial product by the manufacturer's name. In no instances does such identification imply endorsement by the National Bureau of Standards.

110
D ~ n - oU /o 10%

10%

J Filter perpendicular

b b Filter tilted c

c Slit edges blackened

bOO

Figure 20. Interreflections in a system with collimated beam

(simplified drawing of an arrangement studied by the author

for other reasons).

The tilted lenses correspond to Mielenz's proposal of off-axis concave mirrors to eliminate the term R (i?«+i?b) in eqs (22) to (25). The interreflective term

i?b has a very high value in the straight beam from left to right because of the high reflectance of the plate in front of detector 1 (signal i\) and a very low one

for the beam to detector 2 (signal ii) because there is no reflecting plate and interreflections are attenuated by the low reflectance of the inclined beam splitting

plate. At wavelengths below 600 nm the short cutoff filter suppresses interreflec- tions in both beams, and the variation of the ratio nth with the wavelength shows

the influence of interreflections. The filter was at first perpendicular to the beam axis (a), then tilted .(b), and

finally the small reflecting edges of the slit were carefully blackened. The ratio

\iLh arbitrarily set to 100 percent in one case, shows in curve a below 600 nm the

influence of the front surface of the filter and above 620 nm the influence of both

surfaces and of the slit edge. Curve b shows above 620 nm the influence of the slit edge alone. In an actual photometer the effects will be smaller depending on the lower

reflection values of the detector, but assuming a reflection of 1 percent, the in- tended accuracy of 10_i will still leave amounts for consideration.

AT; - 0.0081, -Xi -i^-Ti

2

)

o - r

Figure 21. Correction of interreflections arid oblique incidence

applied to ELKO II photometer. Correction is positive because

of the negative error.

of solutions against solvent this error has the opposite

sign (compare eqs 25 and 35). If standards are used

which are pairs of equally reflecting, yet differently

absorbing substances, the errors caused by multiple

reflections when measuring the standards and the

samples themselves will be at least approximately

equal, and the error caused by a multiple reflection

will be eliminated at least approximately by the

linearity correction.

Horr 1

Kott U

+0,5%

0

-05%

Figure 22. Correctors for the linearity adjustment of the ZEISS

ELKO II photometer designed by Hansen [24]. The instrument is operated according to the "optical null" principle with a measuring diaphragm (shown in the drawing) consisting of 4 dark sectors of 45°

central angle each, and 4 variable sectors with maximum 45° open angle. Corrector

1 is rotatable around an axis A perpendicular to the diaphragm plane, corrector 2 around an axis B parallel to the diaphragm plane. Also shown (as curves) are the

linearity changes brought about by the correctors.

E. Interference

The calculation of multiple reflection given in

section IV-D is based on the reflection coefficient

of the radiant flux. With strictly collimated and

monochromatic light, there will be interferences

111
at the parallel surfaces. The transmittance of such

a sample will show periodic maxima and minima

as a function of the wavelength. This is well known

from IR instrument applications, but is also observed

in the visible under special conditions. Mielenz

has stated corresponding formulae [22]. These interferences are generally regarded as disturbances

in spectrophotometries measurements and are eliminated, if possible. There are three ways to achieve

this: sufficiently large bandwidth, varying thickness

of the sample, and sufficiently large aperture angles.

If the sample has a thickness d and a refractive

index n, the interference maxima at the wavelength

X will be at wavelength intervals of

A\j=\2/(2nd). (38)

For a glass sample (n = 1.5) of 1 mm thickness this

yields at 500 nm a distance of 0.08 nm, and at

1000 nm as much as 0.33 nm. To average the interferences the photometer bandwidth A\h should be

at least ten times the distance between interference

maxima, [28] that is

AXs >10AX/ =10X2/(2nd) (39)

which means that at 1000 nm the bandwidth must

be at least 3 nm for a thickness of 1 mm, or that

at 1 nm bandwidth the thickness must be at least

3 mm.

To get from one inference maximum to the next

by changing the thickness, the change of thickness

must be

Ad=\/2n. (40)

If again 10 interference maxima (Fizeau fringes) are to be averaged [28], a thickness change of 3.3 nm

is necessary at 1000 nm. Provided this is to be below

10~5 of the thickness, the sample should be at least

33 cm thick. Even if constancy of the thickness to

within only 10-4 of its value is required, the required

sample thickness would still be 3.3 cm. Interferences can thus not be compensated by intentional variation of the sample thickness over the measuring area

unless the accuracy requirements are low.

The same applies to the compensation of interference by the use of larger aperture cones. The

relation of oblique beam passage and change in path

length has been derived in section IV-B. The same

limits as mentioned above are true because, although

with oblique rays (Haidinger rings) the change of

the transmitted layer is desirable to compensate the

interference, it is undesirable for the constancy of

absorption. Interferences cannot be effectively compensated by the aperture cone in collimated-beam

photometers of standards laboratories, however, the

larger cone in commercial photometers causes freedom fiom interferences.

To calibrate standards of high accuracy, several

measurements must be made at intervals of approx.

% of the wavelength difference indicated in eq (38),

followed by averaging over one period of the interference, if interferences are detected.

The small increase in transmittance of gray

glasses over the years may also be considered as an

interference phenomenon. It is due to the formation

of surface layers by a kind of aging, which have a

reflection-reducing effect. For this reason, gray

glasses should not be used alone but in combination

with other glass types. It has up to now not been

possible to obtain glass of equal refractive index

and chemical composition which changes with time

in the same manner as gray glasses.

F. Polarization

As a rule, the light in commercial photometers

is partially polarized. The horizontal and vertical cross sections of the light beams being of different

shape, this polarization affects the reflection at

oblique incidence. If such a photometer is tested

with standards having surfaces similar to those

of the cells used for measurement, the error caused

by polarization is corrected together with the linearity error. An instrument with rotational symmetry of the

beam cross section must be used to calibrate the

standards. If this proves impossible, measurements

must be made in the two preferred polarization

directions.

To avoid systemmatic errors in partially polarized

light, the standards should be free from birefringence,

strain or optical activity.

G. Beam Shift Errors

As mentioned before, the sensitivity of all known

photomultiplier tubes depends considerably on the

position on the cathode and on the direction of

incidence. If the beam is shifted when the sample is

brought into the beam path, errors occur which

differ even with instruments of the same type.

Shifts of the light beam on the cathode may be due

to wedge errors, tilt errors or focusing errors. This

changes the cross section of the light beam at the

cathode. If collimated light passes through the

sample, the tilt and focusing errors will not shift

the beam cross section in the focal plane of the

collimator but the direction of the beams. If the

light beam falls directly on the detector the cross section on the detector should not be too small. This

is the reason for producing an image of the pupil

on the detector. However, even with collimated

light the sample may cause changes of the pupil

image.

The best solution is to eliminate the dependency

of the sensitivity on place and direction. This can be

achieved with an averaging sphere, which because of

its low efficiency has so far only been used in special

equipment. Whether or not the progress made in

designing averaging spheres [25] will make them suitable for commercial spectrophotometers remains to

be settled.

112
V. How Can Routine Spectrophotometry Be

Improved?

Whoever wants to improve spectrophotometry

must know the inherent sources of error. According

to the author there are enough means to test the

spectral characteristics. But, to test the linearity of

the transmittance scale, standards are required which

must be issued by a standards laboratory. As far as the author knows there are being offered only two

types of standards which are calibrated according to

independent and published procedures: the gray

glasses and solutions issued by NBS and the gray

glasses of ZEISS (see note [26]).

A standards laboratory will be responsible for the

increase in accuracy up to a technically feasible

limit. Important progress has recently been made in

this respect. Yet the errors mentioned at the beginning are about 3 orders of magnitude above the

accuracies obtained in standards laboratories. It

would be an important step forward if an accuracy

of a few tenths of a percent were achieved for routine

applications. Standards with transmittances guaranteed to within approx. 0.1 percent will do. They

must be easy to handle and to clean and must, of

course, be stable. They should also be neutral. Gray

glasses meet these specifications for the visible spectral range, but the formation of a surface layer impairs the stability of the values with time. Changes

of up to 1 percent of actual transmittance have been

observed by us within ten years. If a material of

higher stability is not found, it should be tried to

calibrate these glasses with reference to a similar

absorption-free glass, which would eliminate most of

the time-dependency [27]. This would best meet

practical requirements, and would ensure the

smallest influence by multiple reflections.

Gray glasses cannot be used in the UV. Blackened

quartz glass being commercially available, attempts

should be made to produce quartz glass which

absorbs in the UV almost independent of the wavelength.

Vaccum-deposited, neutrally transmissive metal

coatings can be used within a much wider spectral

range than glasses. In spite of this the author

doubts their usefulness even for moderate accuracy

requirements, because they reflect too much light.

Even if such filters are tilted (by means of a suitable mount, for instance) to eliminate part of

the errors due to multiple reflection, this may cause

errors in commercial spectrophotometers, because

the reflected light is much stronger than the reflection

at glass surfaces; even a reflection on to a black

surface may cause measuring errors. Furthermore,

these coatings are very sensitive, but in spite of this

the author would not recommend cementing with a

coverglass, because all cementing agents are known

to increase their UV absorption with time.

Solutions, even if they are transported in sealed

ampouls, are still problematic with regard to durability, contamination and the cells required for their

use. Other means not being available at present,

they are to the author's knowledge the onlv solution

for the UV.

Photometers with fixed cells to measure liquids

continuously or in cycles should be tested with

reference to gray glasses. These usually can be

inserted, because the cells must be removable for

cleaning and replacement. Liquids are needed in the

visible spectral range to test such photometers only

if the cell cuts off the beam path and an additional

gray glass cannot be provided.

The improvement of routine spectrophotometry is more a problem of instruction of the user and provision of suitable equipment than of improving the

accuracy in the standards laboratories.

The author thankfully acknowledges the assistance

of K.D. Mielenz and R. Mavrodineanu in revising

the English text. His participation at the workshop

seminar held Nov. 1975 at Gaithersburg was sponsored by NBS.

VI. References and Notes

[I] Beeler, M. F., Lancaster, R. C, Am. Journ. of Clinical

Pathology 63 Suppl. 953-959 (1975).

[2] Mavrodineanu, R., Shultz, J. I., Menis, 0., (editors),

Nat. Bur. Stand. (U.S.), Spec. Publ. 378, 268 pages

(May 1973); J. Res. Nat. Bur. Stand. (U.S.), 76A

(Phys. and Chem.), No. 5, (Sept.-Oct. 1972); No. 6, (Nov.-Dec. 1972).

[3] Clarke, F. J. J., reference [2], pp. 1-29

[4] Mavrodineanu, R., reference [2], pp. 30-51

[5] Sanders, C. L., reference [2], pp. 63-79

[6] Reule, A., Coll. Spectr. Int. XVI, Preprints 1, 107-113

(1971)

[7] Preston, J. S., Journ. Sci. Instr. 13, 368 (1936)

[8] Hamamatsu TV Co. Ltd. Data Sheets No. 14E (Aug.

1969)

[9] Wiedmann, K., Personal communication (Carl Zeiss,

Oberkochen, 1975).

[10J Reule, A., Appl. Opt. 7, 1023-1028 (1968)

[II] Reule, A., Zeiss-Mitt. 1, 283-299 (1959)

[12] See references cited in [3], [4], [5] and Korte, H., Schmidt,

M., Lichttechnik 6, 355-359 (1954)

[13] Buchmiiller, F., Kbnig, H., Bull. Schweizer Electrotechn.

Verein 28, 89-99 (1937)

[14] Preston, J. S., Cuckov, F. W., Proc. Phys. Soc. (London)

48, 869-880 (1936)

[15] Elster, J., Geitel, H., Wied. Ann. 48, 625-635 (1893).

[16] Hawes, R. C, Appl. Opt. 10, 1246-1253 (1971).

[17] Hansen, G., Mikrochim. Acta 1955, 410-415.

[18] Ploke, M., Personal communication (Zeiss Ikon A. G.,

Kiel, 1961).

[19] Jung, H. J., Z. Angew. Physik 30, 338-341 (1971);

see also reference [2], 72.

[20] Jung, H. J., Z. Angew. Physik 31, 170-176 (1971);

see also reference [2], 75.

[21] Hansen, G., Mohr, E., Spectrochim. Acta 3, 584-598

(1949).

[22] Mielenz, K. D., reference [2], 81-93.

[23] Mielenz, K. D., Mavrodineanu, R., J. Res. Nat. Bur.

Stand (U.S.), 77A (Phys. and Chem.), No. 6, 699-703

(Nov.-Dec. 1973).

[24] Hansen, G., Optik 8, 251-277 (1951).

25 Mielenz, K. D., Mavrodineanu, R., Cehelnik, E. D.,

Appl. Opt. 14, 1940-1947 (1975).

113
[26] In the discussion Dr. Clarke pointed out, that by N.P.L.,

Teddington, U.K. since many years transmittance

standards, though not being offered for sale, are calibrated on request. The double aperture method is used for qualifying linearity.

Dr. Bril (Philips) reported that standards were available

from International Commission on Glass, Charleroi,

Belgium but the author could up to March '76 not get

any more information.

[27] The apparently obvious solution, to use a thinner and a

thicker glass of the same melt, is wrecked by the fact,

that either one of these glasses had to be to thin as that it could be handled in a routine laboratory, or the

photometric scale would be checked starting at a considerably smaller flux than present in normal use.

[28] Note added in proof:

If to = 2AX*/AX/, the influence of interferences

cancels for to = 2, 4, 6 . . . and reaches relative

maxima for to = 1, 3, 5 . . . with an amplitude

of 4/m2 r2 times the transmission modulation

for to <<7. Because to cannot be made an even number for all wavelengths simultanously, one

has to deal with uneven to as the worst case. The condition AX A/A\j=10 given in the text to=20 and reduces the effect of interferences

to 1/100. In many cases to = 3 will do, giving a

reduction of interferences to about 1/20.

Similar considerations hold true for Fizeau

fringes and Haidinger rings.

(Paper 80A4-906)

114
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 466, Standardization in Spectrophotometry and Luminescence

Measurements, Proceedings of a Workshop Seminar Held at NBS, Gaithersburg, Md., November 19-20, 1975 (issued May 1977).

Standardization in Transmission Spectrophotometry in the

Visible and Ultraviolet Spectral Regions*

A. R. Robertson

Division of Physics, National Research Council,

Ottawa, Ontario, Canada K1A OR6

(May 26, 1976)

In an instrument as complex as a spectrophotometer there are many potential sources

of error. Because of this it is useful to have available standard materials whose spectral

transmittances are known accurately. Periodic measurement of such standards provides a

useful indication of whether a spectrophotometer is producing accurate results.

If the spectral transmittance functions of these standards are chosen suitably, the

measurements can provide diagnostic information to indicate what type of error is occurring.

Among the factors that most often lead to errors in spectrophotometry are the slit-width,

the wavelength scale, the photometric scale, and stray radiation. Suitable material standards can provide indications of the occurrence of these errors. However it is sometimes difficult to identify a particular error since often several errors will occur at the same time.

Several sets of standards for testing spectrophotometers are available or can be constructed easily. Most of these are glass filters, but interference filters, perforated screens, and rotating sectors are also used. Liquid niters have some advantages, especially in the

ultraviolet where glass filters absorb too strongly to be useful. However difficulties in preparing and handling liquid niters can introduce uncertainties.

It is important that standard materials are insensitive to environmental conditions

(such as temperature) and that they are stable over a long period of time. Unfortunately,

many of the materials with the most suitable spectral characteristics are least suitable in these respects, and it would be very useful if new and better materials could be developed.

Key words : Errors in spectrophotometry ; photometric scale ; slit width ; spectral trans- mission; spectrophotometer standards; stray light; wavelength scale.

I. Introduction

A spectrophotometer is an extremely complex

instrument and there are many potential sources of

error. Tests are available that will detect the pres- ence of each type of error but they are usually rather

inconvenient to use in practice. It is often more

convenient to have available a set of material

standards whose spectral transmittances are known

accurately. If the spectral transmittances are chosen

carefuUy, measurement of them can provide a useful

check on the performance of the instrument. There

is no need to modify or make any additions to the

instrument because the tests can be made with the

instrument in the mode in which samples are nor- mally measured.

In general, departure of the measured transmittance from the true transmittance will indicate

the presence of an error, but will not indicate the

type of error, (photometric, wavelength, silt-width,

stray radiation, etc.). However, if the spectral

transmittances of the standards are chosen appropriately, it is sometimes possible to use the measurements to diagnose what type of error is occurring.

•National Eesearch Council Paper No. 15510.

The spectral transmittances must be chosen so that

the error in question will have the maximum effect

while other errors have very little or no effect.

A problem is that two different errors will sometimes

have the same or similar effects on the measured

transmittances making it difficult to interpret the

measurements, but nevertheless, departure of the

measured transmittances from the true transmittances will always be an indication of problems even

when diagnostic information cannot be derived.

If the standards are calibrated in one instrument

and then used in another instrument of different

design the situation may be very complex, and it

will be quite difficult to determine exactly what is

causing differences in the results from the two

instruments, especially when more than one factor

is involved. Standards are often much more valuable

when they are used to detect changes in the performance of a single instrument. Periodic measurement of standard materials will give an early

warning of problems that may be developing from

dirty optical components, from wear of mechanical

components, from aging of the source or detector

or from any other cause. Standards are also useful

115
HDD £DD EDD

WRVELENGTH (nm)

700

Figure 1. Spectral transmittances of the NBS 2100 series of five colored-glass

filters for checking the performance of spectrophotometers [1].

in detecting and correcting faulty calibration or faulty experimental technique.

As well as having the desired spectral transmittance curves, materials to be used as standards

must have certain other properties. They must be

stable with respect to time, temperature, humidity

and other environmental parameters; they must be

uniform, nonscattering, nonfluorescent, and nonpolarizing; and they must be easy to handle.

An example of a set of standards that is very

useful in detecting and diagnosing errors in the

visible spectral region is the 2100 series of five

colored-glass niters issued by the National Bureau

of Standards [l].

1 The spectral transmittances of

these filters are shown in figure 1

II. Use of Standards to Determine Different

Types of Error

In this section some of the many types of error that can occur in spectrophotometry are discussed.

Material standards that can indicate the presence

of each type of error are described. Errors that can

occur with special types of samples such as samples

that fluoresce or that change the state of polarization of the measuring beam are not discussed.

A. Photometric Errors

Photometric errors can conveniently be divided

into two types: errors of the endpoints of the photometic scale (0% and 100% transmittance) and

failure of readings taken from the photometric

scale to be linearly related to the amount of radiation striking the photodetector. Endpoint errors

1 Figures in brackets indicate the literature references at the end of this paper.

can be detected easily by measurements with an

opaque sample and with an empty sample compartment, but linearity is more difficult to check. A

survey of methods of measuring photometric linearity

has been given by Sanders [2]. The most fundamental method is the flux addition or superposition

method. The simplest form of this is the doubleaperture method described by Clarke [3] and by

Mielenz and Eckerle [4]. The method requires

special equipment and there are several systematic

errors that may occur, so it is more convenient

in routine work to use standards of known transmittance. To reduce or eliminate the effect of other

errors, these standards should have a transmittance

that does not vary with wavelength, but this is

difficult to achieve in practice.

Filters made of metal screens with a large number

of small holes have been suggested but there are problems with diffraction effects and with dirt

accumulating in the holes [5]. In addition the position

of the screens in the measuring beam is critical,

especially if the cross-section of the beam is small or nonuniform. Rotating sectors are sometimes used

but they may be too large to fit into the sample

compartment and, in any case, their use depends on

the assumption that the photo-electronic system

obeys Talbot's law, an assumption that may not

always be valid. Interference filters can be made

spectrally neutral, but they reflect rather than absorb

the untransmitted radiation so they may introduce

stray radiation errors. In addition, pin-holes and

other nonuniformities in these filters can cause errors. Colored glass filters with an approximately

neutral spectrum are probably the most satisfactory

materials for checking photometric scales, but they

too have some disadvantages. The spectral transmittances of a set of neutral glass filters that has been

used at the National Research Council are shown in

figure 2. A calibrated set of three similar filters is

116
I .

D . B

y

K>Z

K

h

h

I

inz

i

c

h

HDD SEE EDO

WRVELENETH ( nm)

7DD

Figure 2. Spectral transmittances of ten neutral glass filters that have been used

to check photometric scales.

available from the National Bureau of Standards [7]. Such filters can be used with the least uncertainty

to check for changes in the photometric linearity of a single instrument. When they are used to compare

two different instruments, the uncertainties are higher because geometrical differences between the

two instruments may lead to different effective

pathlengths through the filters. A disadvantage of

these materials is that they are not perfectly neutral,

so that wavelength and bandwidth errors may

affect their transmittance, unless only the flat parts

of the spectral transmittance curve are used, but

even then stray radiation errors may influence the

results. Another disadvantage is that the filters are not always stable over long periods of time[6].

Surface films of silicon oxide may form[7, 8] and

there may be some leaching of metal oxides from

the surface caused by the action of the atmosphere or by cleaning agents [3]. It must be noted that colored glasses can only be

used to check a photometric scale if the transmittances of the glasses have been established in

advance with an instrument whose linearity has

been checked by a fundamental method such as the

double aperture method. There is no way that they can be used on their own to establish photometric

linearity [.6]. It is sometimes assumed fallaciously that

if the transmittances of two thicknesses of the same

filter material (or two thicknesses or two concentrations of a liquid) obey the Lambert-Beer law

(after suitable correction for surface reflections),

then the instrument is linear. The justification of

this fallacy is made as follows. Let the true spectral

internal transmittances of two filters of the same

material be Tj(X) and T2 (\), the thicknesses di(X)

and d2 (\), and the spectral absorptivity a (A), then

7V(\):= 10-^0°

and

r2 (x)=io-^a(X)

Thus the ratio of the spectral absorbances ^4i(X)

and A2 {\) is M\)Jog10 T1 (\) _d1 A2 (X) log10 T2 (X) d2

It is then assumed that if the ratio of the measured

spectral absorbances is djd2 the photometric system

is linear. This is not necessarily true. It is possible

that the photometric system is such that the measured spectral internal transmittance T'(X) is given

by

T'{\) =[T{\)Y

where x^l. In this case the measured spectral

absorbance will be given by

A'(X) = -log10 T'(\)

=-xlog10T(\)

=xA(\)

and the relation

A' 1 (\) _di

A'2 (\) d2

will hold, despite the nonlinearity. Apart from this,

the Lambert-Beer law is often not obeyed, especially

if the measuring beam is not collimated so that the

pathlength is not exactly equal to the thickness of

the filter.

117
B. Wavelength Errors

A survey of methods of checking the accuracy of

the wavelength scales of spectrophotometers has

been given recently by Alman and Billmeyer [9]. The best method for a spectrophotometer with a narrow waveband is the line spectra method, but for

instruments with a wide waveband the linear filter

method [10] is preferable. Again, however, these

methods require auxiliary equipment and modifications to the spectrophotometers so it is convenient

to have glass filters available with clearly defined

transmittance minima that can be used as a simple

check on the wavelength scale.

Two of the most commonly used materials are didymium [11] and holmium oxide glasses [12, 13].

One difficulty with these glasses is that the positions

of the transmittance minima vary with both the

width and the shape of the waveband transmitted by

the spectrophotometer. The problem is especially

bad when a minimum is not symmetrical or consists

of two slightly separated individual minima. Holmium oxide is better than didymium in this respect

but there is still some uncertainty if the waveband

is not very narrow. The effect of temperature on these filters is to

increase or decrease the transmittances at the

minima without changing the wavelengths significantly [14].

Both types of filter can be used with rather less

uncertainty to check for changes in the performance

of a single instrument, than to check one instrument

relative to another. However it is sometimes difficult

to distinguish wavelength errors from other types of error such as the error caused by the response of the

recording mechanism being too slow to follow the

changes of transmittance. An example of the latter

is shown in figure 3. The broken line represents the

WAVELENGTH ( nm ) Figure 3. Spectral transmittance of a didymium glass measured

with low and high damping of the recording system of a Zeiss

DMC25 spectrophotometer.

The direction of scan is from high to low wavelengths.

measurement of a didymium filter measured with a fast-responding recorder and the full line represents

the measurement of the same filter with a slowly

responding recorder. (The direction of scan is from

high to low wavelengths in both cases.)

C. Bandwidth

No spectrophotometry measurements are ever made with radiation of a single wavelength. There is

always a finite band of wavelengths distributed

around the nominal wavelength. The width and

shape of this band is determined by the widths of

the slits of the monochromator and by the spectral

power of the source, the spectral transmittance of

the optics, and the spectral responsivity of the photodetector. The exact width and shape of the waveband

is difficult to measure, but departures from a narrow

band can be detected by measuring standards such

as a didymium glass with several transmittance

minima of different shapes. Figure 4 shows the

spectral transmittance of such a filter measured on a

Zeiss 2 DMC 25 spectrophotometer with 2.5 nm and

10 nm bandwidths. With the wider bandwidth the

minima are broadened, the wavelengths of some of

the minima are shifted, and some double minima are not resolved.

It is important to check for changes of the bandwidth of a spectrophotometer, especially in those

instruments, such as the Cary 14, in which the slits are adjusted automatically to maintain a constant

reference signal. In such instruments, changes of the

bandwidth can indicate instrumental defects such

as the accumulation of dirt or the deposition of

films on the optical parts.

WAVELENGTH ( nm ) Figuee 4. Spectral transmittance of a didymium glass measured

on a Zeiss DMC25 spectrophotometer with narrow and wide

slits.

2 In order to adequately describe materials and experimental procedures, it was

occasionally necessary to identify commercial instruments. In no instance does such identification imply endorsement by the National Bureau of Standards.

118
D. Stray Radiation

Two types of stray radiation should be distinguished. The first is stray radiation of the same

wavelength as is being measured, but which reaches

the detector without passing through the sample. It

is caused by reflections and scattering between the

various optical and mechanical components including the sample itself. It can be detected by

measuring an opaque sample. If the measured

spectral transmittance is not zero, stray radiation

may be present, although an error of the 0 percent

end-point of the photometric scale will have the

same effect. Scattering or reflection by the sample

can be exaggerated by painting the opaque sample

white, or replacing it by a mirror.

The second type of stray radiation has wavelengths different from that of the measurement

beam. It too can arise from unwanted reflections

and from scattering by dirt, scratches and other

defects in optical components. Another common

cause is unwanted orders of diffraction in grating

instruments. The effect of this stray radiation is often exaggerated greatly at the ends of the wavelength range because here the photodetector may be

much more sensitive to the wavelengths of the stray

radiation than to the measurement wavelength.

This type of stray radiation can be detected readily

by cut-off or band-pass filters that have zero transmittance for some wavelengths and high transmittance for others. Stray radiation of the former

wavelengths will lower the measured transmittance

at the latter, and vice-versa.

E. Nonuniformity of Photodetector

If the response of the photodetector is not uniform across its surface, errors will occur whenever

a sample causes a change in the irradiated area,

either by shifting it across the photodetector or by

increasing or decreasing the area by altering the

focus of the measurement beam. Such errors can

usually be detected by measuring clear glass or quartz filters of different thicknesses or with a wedge

shape. The errors should be avoided by using a

suitable diffuser to increase the uniformity of the

detector response [15].

F. Inertia Errors

The recording mechanism of a spectrophotometer

often has significant inertia and lags or leads changes

in spectral transmittance as the instrument scans through the spectrum. Mechanical or electrical malfunctions can often develop to cause such inertia

even if the instrument was originally free from the

problem. Errors caused by inertia can be detected

readily by measuring standard meterials whose spectral transmittance varies rapidly with wavelength.

An example is shown in figure 5. In this case, measurement of the NBS 2100 series of filters and a didymium glass indicated very slow response in the

400 500 600 700

WAVELENGTH ( nm

Figure 5. Spectral transmittances of the NBS 2100 series of

filters and a didymium glass with a General Electric Hardy

spectrophotometer functioning properly (full line) and with

the same spectrophotometer with a malfunction causing poor

response in the red part of the spectrum (broken line).

The direction of scan is from low to high wavelengths.

red region of the spectrum, but the response in the

rest of the spectrum was satisfactory.

III. Standards for the Ultraviolet

Most of the examples of diagnostic standards given

in the preceding section were for the visible spectrum.

Exactly the same principles apply in the ultraviolet

sprectrum, but there are greater difficulties in finding

suitable materials. In particular most glass filters

cannot be used below about 350 nm because of their

strong absorption below this wavelength. For this

reason, liquid standards such as solutions of potassium chromate, copper sulphate, and cobalt ammonium sulphate have often been used [16]. Recently

a number of other solutions have been suggested [17].

Unfortunately, variations in the preparing and handling of such liquid standards introduce some extra

uncertainties so glass standards are preferable if they

have appropriate spectral transmittance functions.

IV. Conclusions

Material standards provide a very useful and con- venient way to check the performance of a spectrophotometer and to diagnose malfunctions, although

they can never completely replace more fundamental

methods of checking for errors. Materials are available with some of the desired properties, especially

for the visible spectral region. However most of the

presently available materials do have some drawbacks. Often the spectral transmittance functions are

less than ideal and in many cases they are instable to

environmental conditions such as temperature and

are not sufficiently permanent over long periods of

time. For these reasons it is very desirable that new

and better standard materials should be developed

in the future.

119
V. References

[1] Keegan, H. J., Schleter, J. C. and Judd, D. B. Glass

niters for checking performance of spectrophotometerintegrator systems of color measurement, J. Res.

Nat. Bur. Stand. (U.S.), 66A (Phys. and Chem.),

No. 3, 203-221 (May-June 1962).

[2] Sanders, C. L., Accurate measurements of and corrections for nonlinearities in radiometers, J. Res. Nat.

Bur. Stand. (U.S.), 76A (Phys. and Chem.), No. 5, 437-453 (Sept.-Oct. 1972).

[3] Clarke, F. J. J., High accuracy spectrophotometry at the National Physical Laboratory, J. Res. Nat.

Bur. Stand. (U.S.), 76 A (Phys. and Chem.), No. 5, 375-403 (Sept.-Oct. 1972).

[4] Mielenz, K. D. and Eckerle, K. L., Spectrophotometer

linearity testing using the double-aperture method,

Appl. Opt. 11, 2294 (1972).

[5] Vandenbelt, J. M., Investigation of screens as spectrophotometric absorption standards, J. Opt. Soc. Am.

52, 284 (1962).

[6] Hawes, R. C, Technique for measuring photometric

accuracy, Appl. Opt. 10, 1246 (1971).

[7] Mavrodineanu, R., An accurate spectrophotometer

for measuring the transmittance of solid and liquid

materials, J. Res. Nat. Bur. Stand. (U.S.), 76 A

(Phys. and Chem.), No. 5, 405-425 (Sept.-Oct. 1972).

[8] Blevin, W. R., Ageing of neutral glass filters, Optica

Acta 6, 99 (1959).

[9] Alman, D. H., and Billmeyer, F. W., Jr., A review of

wavelength calibration methods for visible-range

photoelectric spectrophotometers, J. Chem. Ed. 52,

A281 and 52, A315.

[10] Van den Akker, J. A., Wavelength calibration of spectrophotometers, J. Opt. Soc. Am. 33, 257 (1943).

[11] Gibson, K. S., and Keegan, H. J., Calibration and operation of the General Electric recording spectrophotometer of the National Bureau of Standards, J. Opt.

Soc. Am. 28,372 (1938) . [12] Vandenbelt, J. M., Holmium filter for checking the wavelength scale of recording spectrophotometers, J. Opt.

Soc. Am. 51, 802 (1961).

[13] McNeirney, J., and Slavin, W., A wavelength standard

for ultraviolet-visible-near infrared spectrophotometry,

Appl. Opt. 1,365 (1962).

[14] Dodd, C. X., and West, T. W., Spectral transmittance

properties of rare-earth glasses, J. Opt. Soc. Am.

51,915 (1961).

[15] Mielenz, K. D., Mavrodineanu, R., and Cehelnik, E. D.,

Efficient averaging spheres for visible and ultraviolet

wavelengths, Appl. Opt. 14, 1940 (1975).

[16] Schleter, J. C, Standards for checking the calibration of spectrophotometers (200 to 1000 nm), NBS Letter

Circular LC-1017 (Jan. 1967).

[17] Burke, R. W., Deardorff, E. R., and Menis, O., Liquid

absorbance standards, J. Res. Nat. Bur. Stand. (U.S.),

76A (Phys. and Chem.), No. 5, 469-482 (Sept.-Oct.

1972).

(Paper 80A-907)

120
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 466, Standardization in Spectrophotometry and Luminescence

Measurements, Proceedings of a Workshop Seminar Held at NBS, Gaithersburg, Md., November 19-20, 1975 (issued May 1977).

Acidic Potassium Dichromate Solutions as

Ultraviolet Absorbance Standards*

R. W. Burke and R. Mavrodineanu

Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234

(May 18, 1976)

The absorbances of five concentrations of potassium dichromate in 0.001 M perchloric

acid have been determined at eight wavelengths in the ultraviolet on the National Bureau

of Standards Institute for Materials Research high-accuracy spectrophotometer. Four of the

wavelengths—235, 257, 313, and 350 nm—correspond to absorbance maxima or minima in

the HCr04 ~ spectrum and are useful wavelengths for checking the accuracy of the absorbance

scale of narrow bandpass spectrophotometers. Although partial dimerization of HCr04 ~

to CviOi" produces small positive deviations from Beer's law at these wavelengths, the apparent absorptivities calculated for each concentration are reproducible to one part in a thousand. The estimated uncertainties in the absorptivity values are ±0.7 percent at 0.1 absorbance (A) and ±0.2 percent near A = l. These uncertainties include all known sources

of possible systematic error and the 95 percent confidence level for the mean. The remaining

four wavelengths used for measurement are near two predicted isosbestic points in the

HCr04 _/Cr2 07TM spectra. The absorptivities at 345 nm are sufficiently independent of concentration that this wavelength can be used for checking absorbance linearity to one part

in a thousand over the range A = 0.2-1.

Key words: Absorbance linearity; accuracy; acidic potassium dichromate solutions; calibration of ultraviolet spectrophotometers; liquid filters; transfer standards; ultraviolet absorb- ance standards.

I. Introduction

At present, there are no certified standards

available from the National Bureau of Standards

(NBS) for checking the accuracy of the absorbance

scale of spectrophotometers throughout the ultraviolet. The number of analytical applications in

this

_ important region of the spectrum, however,

continues to increase relatively sharply and the

need for such standards is becoming increasingly

acute.

The area with perhaps the most serious need for

ultraviolet absorbance standards at the moment is clinical chemistry. Workers in this field, for example,

frequently use molar absorptivity as an index of

purity of their biological standards. Only recently,

Burnett [1]

1 has discussed the importance of ac- curate molar absorptivity measurements in the

clinical laboratory. He especially emphasizes the

need for spectrophotometric accuracy in clinical

enzymology. Not only must the molar absorptivity

of the substrate or enzyme-catalyzed reaction

product be known accurately but also the individual

absorbance measurements on the test sample must

be accurate. This dual requirement for accuracy

•This work was supported in part by the National Institute of General Medical Sciences.

1 Figures in brackets indicate the literature references at the end of this paper.

in this instance arises because high-purity and wellcharacterized enzyme preparations are not yet

routinely available for use as standards.

A program has been under way at NBS in the

Institute for Materials Research (IMR) since 1969

for the development and issuance of visible and

ultraviolet transfer standards for use as Standard

Reference Materials (SRM's). Two such standards

are currently available: (1) SRM 930, consisting of a

set of three neutral Schott NG glass filters and (2)

SRM 931, an empirical inorganic solution available

at three concentrations in 10-ml ampoules. Neither of

these SRM's meets the present needs for absorbance

standards in the ultraviolet. The glass filters do not

transmit below about 350 nm while the inorganic

solution is certified only at one wavelength in the

ultraviolet (302 nm) and with an uncertainty of ± 1 percent. Transfer standards capable of being certified throughout the range of 200-350 nm and with a smaller uncertaintj^ are being investigated, however.

The most promising solid filter at the moment for

this purpose is the metal-on-quartz type. Some

recent experiences with this filter are discussed jn the

paper immediately following [2]. Of the chemical or

liquid-type filters that have been proposed, the

weakly acidic potassium dichromate system is considered the best. A critical evaluation of this

system, as well as several other candidate materials,

was presented in a previous paper [3].

121
In this paper, we present absorptivity values for

five concentrations of potassium dichromate in

0.001 M perchloric acid. These concentrations effectively span the absorbance range of A=0.1-1.

when measured in 10 mm cuvettes. The absorptivities were calculated fiom transmittance measurements at eight wavelengths in the ultraviolet on the

IMR high-accuracy spectrophotometer. Four of the

wavelengths—235, 257, 313 and 350 nm—correspond

to absorbance maxima and minima in the HCr04 _ spectrum and are useful wavelengths for checking

the accuracy of the absorbance scale of narrow

bandpass spectrophotometers. Although partial dimerization of HCr04 ~ to Cr207 = produces small positive deviations from Beer's law at these wavelengths,

the apparent absorptivities calculated for each concentration are reproducible to one part in a thousand.

The estimated uncertainties in the absorptivity

values are ±0.7 percent at 0.1 absorbance (A) and

±0.2 percent near A=l. These uncertainties include

all known sources of possible systematic error and

the 95 percent confidence level for the mean. The

remaining four wavelengths used for measurement

are near two predicted isosbestic points in the

HCr04 ~/Cr207 = spectra. The absorptivities at 345 nm

are sufficiently independent of concentration that

this wavelength can be used for checking absorbance

linearity to one part in a thousand over the range

A=0.2-l.

II. Experimental Procedure

The potassium dichromate (K2 Cr2 07 ) used in this

study was a special lot of analytical reagent grade

material obtained from the J. T. Baker Chemical

Company.2 Drying studies performed at 105 °C

indicated that the surface moisture of this material

was less than 0.01 percent. No measurement of

possible occluded water was made. However, a recent paper [4] by Yoshimori and Sakaguchi has

shown that K2 Cr2 07 typically contains 0.01 to 0.02

percent occluded water which can be removed only

by crushing and drying at 350 °C.

Coulometric assay of the undried potassium

dichromate gave a purity, expressed as an oxidant,

of 99.972 ±0.005 percent at the 95 percent confidence level. Emission spectroscop}^ indicated that

the only significant elemental impurities present

were sodium and rubidium. Their concentrations

were estimated to be 0.02 and 0.03 percent,

respectively.

The concentrations of the K2 Cr2 07 solutions used

throughout this study are expressed on a weight/

weight basis. Milligram samples of K2 Cr207 were

weighed to the nearest microgram on a microbalance.

After dissolution in distilled water shown to be free

of reducing impurities (see Discussion) , 1 ml of 1 M

perchloric acid was added and the solutions were

2 In order to describe materials and experimental procedures adequately, it is occasionally necessary to identify the sources of commercial products by the manufacturer's name. In no instance does such identification imply endorsement by the National Bureau of Standards, nor does it imply that the particular

product is necessarily the best available for that purpose.

diluted approximately to volume in 1-liter volumetric flasks. Each flask was fitted with a doubleribbed Teflon stopper (Kontes Glass Company,

Vineland, New Jersey) to prevent evaporation. The

weight of each solution was determined on a singlepan top-loading balance having a sensitivity of 0.01 g. NBS-calibrated weights were used to establish the

accuracy of the balances. The concentrations of the

solutions were then calculated after correcting all weights to vacuum. A solvent blank was prepared by

diluting 1 ml of 1 M perchloric acid to 1 liter with

distilled water.

The Institute for Materials Research highaccuracy spectrophotometer was used for performing

the transmittance measurements which, in turn, were

converted to absorbance. The design and construction of this instrument have been described in detail

by one of us (RM) in reference [5] and will not be

repeated here. Similarly, the quartz cuvettes used

are also of NBS design and construction and have

been described previously [6]. These cuvettes are currently available through the NBS Office of

Standard Reference Materials as SRM 932. Each

cuvette is certified for path length and parallelism to

±0.0005 mm.

Prior to use the cuvettes were cleaned by soaking

in concentrated (18 M) sulfuric acid for several hours.

In order to minimize the heat of mixing, they were

then transferred consecutively to 12, 6 and 3 M

sulfuric acid before rinsing with distilled water. After

rinsing thoroughly, the cuvettes were air-dried under

an inverted Petri dish that served as a dust-protective

cover. For sample measurements, five calibrated cuvettes

were placed in separate holders in the rotating

sample compartment [5] of the IMR high-accuracy

spectrophotometer and a reference filter (inconelon-quartz) was placed in a sixth position. The

cuvettes were left in their respective holders for

the duration of the experiment. All transmittance/

absorbance measurements were made relative to

air in a temperature-controlled room at 23.5 ±0.3

°C. The transfer of solvent blank and sample solutions to and from these cuvettes was made by means

of borosilicate, Pasteur-type, disposable pipettes.

After being rinsed with the test solution, a final

transfer for measurement could be made in 10-15

seconds, after which time the cuvette was immediately stoppered with a snugly-fitting Teflon

stopper.

Six sets of solutions having nominal concentrations of 20, 40, 60, 80 and 100 mg K2 Cr207 /kg

were prepared. Each concentration within a set

was measured a minimum of six times at the eight

wavelengths of interest. The absorbance, A——log

(^sampie/^Biank), was computed for each wavelength

and concentration from the average of the six

transmittance measurements (T). Absorptivities

were then calculated after correcting the absorbances

for systematic errors due to cuvette path length,

beam geometry and internal multiple reflections.

No correction was applied for the reflections discussed by Mielenz and Mavrodineanu [7] from

122
internal components such as the lenses and slit jaws because these are adequately compensated

for by the blank. A detailed account of these corrections and calculations will be given in an NBS 260

Special Publication which is now in preparation.

III. Discussion and Results

The ultraviolet absorbance spectrum of a 40 mg

kg-1 solution of potassium dichromate in 0.001 M

perchloric acid is shown in figure 1. The four wavelengths selected for certification of absorptivity of

this absorbing system, namely 235, 257, 313 and

350 nm, are also indicated. The maxima and minima

are sufficiently broad that serious restrictions are not placed upon instrumental spectral bandwidth

requirements. The half bandwidths of the 257 and

350 nm peaks, for example, are approximately 60

nm so that an instrumental spectral bandwidth of

3 nm or less is sufficient for obtaining at least 0.999

of the maximum peak intensities.

1.0

o

z

<o

0.8 -

0.6

0.4

0.2

i i i

257

K

2 Cr2 0 ? = 40 mg/kg

\ 235

350

\

313 / \

i

250 300 350 WAVELENGTH, nm

400

The first experiment performed on the IMR highaccuracy spectrophotometer was the determination

of the rinse behavior and reproducibility of the

transmittance/absorbance measurements of the solvent blank. In the initial studies, measurements

were made at 235 nm only, since any problems

associated with the transfer of solution were expected

to be the greatest at the shortest wavelength used.

The results obtained for the five cuvettes employed

are shown in figure 2. All exhibit a similar rinse

pattern, attaining a minimum and constant absorb- ance value after 5-6 rinses (the term rinse as used

here and throughout the remainder of this paper

refers to the exchange of one cuvette volume for a second one). Once the blank measurements were in

control, similar absorbance measurements were

then made on the first series of K2 Cr207 solutions.

Five concentrations having nominal concentrations

of 20, 40, 60, 80 and 100 mg K2 Cr2 07 /kg were

measured. Table I summarizes the results of these

measurements together with the final solvent blank

values for 235 nm. The cycle of measurements shown

here was then extended to the other seven wave5.50

5.40

5.30

5.20

5.00

4.90

X

X

" O Q

*

X

—e o 0

•

a u

3 4 5 6 7

NO. OF RINSES

18

26

Figure 1. Absorbance spectrum of K2 Cr2 07 in 0.001 M per- Figure 2. Apparent absorbances of the blank solvent in the five chloric acid. curvettes used

Nos. 14, 16, 18, 25, and 26 ref. [6].

Table I. Reproducibility of absorbance measurements at 285 nm for a cycle of solvent and sample runs

Solvent Sample Sample Solvent

Cuvette No.

After 5 rinses After 5 rinses After 7 rinses After 5 rinses

14 0. 05198 0. 30128 0. 30141 0. 05213

16 . 05099 . 55052 . 55057 . 05093

18 . 05310 . 80066 . 80074 . 05321

25 . 05002 1. 04863 1. 04855 . 05022

26 . 05064 1. 30351 1. 30333 . 05065

Ref. filter °

. 55913 . 55925 . 55936 . 55922

° Inconel-on-quartz.

123
lengths of interest. In all, six sets of K2 Cr2 07 solutions were measured. Typically, two volleys consisting of three transmittance/absorbance measurements

were made on each of the 30 solutions. The first

volley was made after rinsing the cuvettes, initially

containing solvent, with five rinses of sample and

was repeated again after two additional rinses.

Since no systematic increase in absorbance was ever observed when the results of the first volley of

measurements were compared to the second, the six

measurements were invariably averaged. The absorbances were obtained by subtracting the solvent

blank values from the sample readings. After applying appropriate corrections for beam geometry and

internal multiple reflections, the corrected absorbances C<4corr) were used to calculate the desired

absorptivities, using the relationship

Absorptivity—^l corr/6c,

where 6=internal light path in cm and c=concentration of K2 Cr2 07 solution in g kg-1

. The absorptivities

computed for the five concentrations of K2 Cr2 07 solutions used are summarized in table II. The values

tabulated were determined from least-squares plots

of the experimental values and were subsequently

normalized to the concentrations shown. The

uncertainties given include all known sources of

possible systematic error and the 95 percent (2a)

confidence interval for the mean. The random

component of these uncertainties, based on standard

deviations computed from residuals resulting from

fitting the data to the various concentration levels

for each wavelength, is 0.07 percent at the 2a level.

It is observed that all absorptivities in table II

increase with increasing K2 Cr207 concentration.

These deviations from Beer's law are produced by the

fact that, in weakly acidic media, chromium (vi) ions

exist as two distinct absorbing species—HCr04 ~ and

its dimerization product, Cr207 =

. The equilibrium between these two species may be represented as

2HCrOr =Cr207 =+H2 0 (1)

and the corresponding dimerization constant, KD, is given by

[Cr2 07 =] ^D [HCrOr]2 {

'

Although eq. (2) predicts that the formation of Cv2 0^

is strictly a quadratic function of K2 Cr2 07 concentration, the value of KD —32.9 (mol kg-1

) -1 obtained

previously [3] is of such magnitude that the percentage of total chromium present as the Cr2 07 = ion is very nearly a linear function of the K2 Cr207 concentration for the range of solutions studied. Calculated values of HCr04 ~/Cr207 = speciation in this

system are given in table III.

Table III. HCr04 _/Cr2 07=

speciation in 0.001 M perchloric

acid solutions of K2 Cr2 07 .

K2 Cr2 07 Percent Cr as Percent Cr as Cone, g kg-1 HCr04 - Cr2 07=

0. 020 99. 10 0. 90

. 040 98. 22 1. 78

. 060 97. 38 2. 62

. 080 96. 56 3. 44

. 100 95. 77 4. 23

The direction and magnitude of the expected

deviations from Beer's law for the acidic potassium

dichromate system can be ascertained when the

speciation data in table III are combined with the

spectral characteristics of the _ two chromium (vi)

species. Figure 3 shows the relation of the absorbance

spectra of the HCr04 ~ and Cr2 07 =

ions. At wavelengths of 235, 257, 313 and 350 nm, the Cr2 Or ion

is shown always to have a larger absorptivity than

the HCrOr ion. Hence, the measured absorptivities

at these wavelengths should increase with increasing

K2 Cr2 07 concentration.

From the same argument, the data in figure 3 also

suggest that there are two wavelengths near 320 and

345 nm where Beer's law is obeyed. In an attempt to

determine these isosbestic points experimentally,

absorbance measurements were also made on the

Table II. Absorptivities of K2 C2 07 in 0.001 M perchloric acid at 23.5 °C

Absorptivity, kg g

_1 cm 1

K2 Cr2 07 Cone, g kg-'

235(1. 2)»nm 257(0.8)nm 313(0.8)nm 350(0.8)nm Uncertainty c

"0. 020

. 040

. 060

. 080

. 100

12. 243

12. 291

12. 340

12. 388

12. 436

14. 248

14. 308

14. 369

14. 430

14. 491

4. 797

4. 804

4. 811

4. 818

4. 825

10. 661

10. 674

10. 687

10. 701

10. 714

0. 034

022

020

<*. 020

d

. 019

° Nominal concentration; all weights corrected to vacuum.

6 Wavelength and, ( ), spectral bandwidth.

c Includes estimated systematic errors and the 95 percent confidence interval for the mean.

d For wavelength of 313 nm, the uncertainty is reduced to half of these values for K2 Cr2 07 concentrations of 0.040,

0.080 and 0.100 g

kg-i.

124
4000

E

2000

3o

250 300 350 WAVELENGTH, nm

400

Figure 3. Absorbance spectra of the HCrOv ion and its dimerization -product, Cr2 07=

same solutions used above at 322, 323, 345 and 346

nm. The corresponding absorptivity values are given

in table IV. Although small systematic deviations

from Beer's law are still present, the absorptivities

calculated for 345 nm are sufficiently constant that

the acidic K2 Cr2 07 system can be used at this wavelength, over the concentration range shown, to check

the absorbance linearity of narrow bandpass spectrophotometers to one part in a thousand.

The variation of absorptivity of the acid K2 Cr2 07 system with temperature is the smallest that we

have observed for any liquid filter that we have

studied to date. For the four wavelengths recommended for checking the accuracy of the absorbance

scale—235, 257, 313, and 350 nm—the absorptivities

decrease with increasing temperature. Over the range

20-30 °C, the corrections are, respectively, —0.05,

—0.05, —0.02, and —0.05 percent per degree Celsius.

The —0.02 percent correction found at 313 nm cor- responds closely to the correction predicted from the

thermal expansion of the solvent. Until further evaluation can be made of the temperature dependence

of 345 nm wavelength recommended for checking

absorbance linearity, measurements should be re- stricted to 23.5 ±1 °C.

Several considerations were involved in the selection of perchloric acid for acidifying the K2 Cr2 07 solutions. First, perchloric acid was preferred over

the sulfuric acid which has been used traditionally

because perchlorate ion, unlike sulfate, has no tendency to form mixed complexes with chromium (vi)

species. Secondly, the choice of 0.001 M acid rather

than 0.01 Mwas based on two factors : (1) the 0.001 M

acid represented a practical compromise for minimizing conversion of HCr04 ~ to either H2 Cr04 or Cr04 = and (2) the lower acid concentration substantially lowered the oxidation potential (~13 percent)

of the chromium (vi) ions and hence improved the

solution stability of the proposed K2 Cr207 standards.

A final point that needs to be emphasized concerns

the quality of the distilled water used for preparing

the standard solutions. Acidic potassium dichromate

is a potential oxidant and consequently the distilled

water used must be shown to be free of reducing

impurities in order that the absorptivity data given

in this paper be valid. A simple but yet definitive

test is outlined in figure 4. In this study a 500-fold

dilution of a 100 mg kg-1 standard solution of

K2 Cr2 07 was made with the distilled water in question and its absorbance measured at 350 nm. Not

only did the measured absorbance agree with the

predicted value, thus indicating no reduction of

chromium (vi), but also subsequent measurements

showed that this K2 Cr2 07 solution standard should

be stable for at least two months provided it is adequately protected against evaporation. In instances

where this test shows the distilled water to be sus- pect, it is recommended that the water be redistilled

from alkaline potassium permanganate in order to

preoxidize the impurities.

Finally, the general use of solid and liquid transfer

standards for calibrating the absorbance scale of a

precision commercial spectrophotometer is illustrated in figure 5. The measurements on the glass

0.0025

0.0020

Is

g | 0.0015 - 500-FOLD DILUTION OF 100 mg K

2 Cr2 0

7/kg

2 4 6 8 10 12 14 "' go I 30 DAYS AFTER PREPARATION

Figure 4. Test of the distilled water for reducing impurities.

Table IV. Absorptivities of K2 Cr2 07 in 0.001 M perchloric acid near two predicted isosbestic wavelengths; temperature S3. 5 °C

Absorptivity, kg g

_1 cm-1

K2 Cr2 07 322 (0.8) b nm 323 (0.8) nm 345 (0.8) nm 346 (0.8) nm

Cone, g kg"1

a 0. 020 5. 845 6. 065 10. 593 10. 615

. 040 5. 842 6. 062 10. 595 10. 621

. 060 5. 838 6. 059 10. 598 10. 627

. 080 5. 835 6. 056 10. 600 10. 632

. 100 5. 831 6. 053 10. 602 10. 638

"Nominal concentration; all weights corrected to vacuum.

bWavelength and, ( ), spectral bandwidth.

125
<

0.4 0.6 ABSORBANCE

Figure 5. Correction AA for the absorbance scale of a precision

commercial spectrophotometer.

filters were performed at 440 nm while the K2 Cr2 07 measurements were made at 350 nm. At both wavelengths the absorbances measured on the precision

spectrophotometer are high and should be corrected

by subtracting the appropriate AA values.

IV. Conclusion

Following widespread use in the collaborative

testing of spectrophotometers for more than 25 years,

the absorptivities of the acidic potassium dichromate

system have now been determined with a known

accuracy from measurements performed directly on

the NBS Institute for Materials Research highaccuracy spectrophotometer. Later this year, crystalline K^C^Oy, together with detailed instructions on

preparing solutions from it, will be available from*

NBS through its Office of Standard Reference

Materials as an SRM. In conjunction with the calibrated quartz cuvettes previously issued (SRM 932),

it is believed that this material will provide a valid

check of the accuracy of the absorbance scale of

narrow bandpass spectrophotometers in the ultraviolet from 235-350 nm.

The authors gratefully acknowledge the assistance

of the following persons at NBS during various

phases of this work: K. D. Mielenz, for helpful

discussions of fundamental spectrophotometric parameters; G. Marinenko, for performing the coulometric assay; J. A. Norris, for the the emission

spectrographic analyses; H. H. Ku, for the statistical

analysis of the data; and R. W. Seward, for supplying through the Office of Standard Reference Materials the samples of potassium dichromate.

V. References

[1] Burnett, R. W., J. Res. Nat. Bur. Stand. (U.S.), 76A

(Phys. and Chem.), No. 5, 483-489 (Sept.-Oct. 1972).

[2] Mavrodineanu, R., J. Res. Nat. Bur. Stand. (1976), in

press.

[3] Burke, R. W., Deardorff, E. R., and Menis, O., J. Res.

Nat. Bur. Stand. (U.S.), 76A (Phys. and Chem.),

No. 5, 469-482 (Sept.-Oct. 1972).

[41 Yoshimori, T. and Sakaguchi, N., Talanta 22, 233-238

(1975).

[5] Mavrodineanu, R., J. Res. Nat. Bur. Stand. (U.S.), 76

(Phys. and Chem.), No. 5, 405-425 (Sept.-Oct. 1972).

[6] Mavrodineanu, R., and Lazar, J. W., Nat. Bur. Stand.

(U.S.), Spec. Publ. 260-32, 26 pages (Dec. 1973), and

in Clin. Chem. 19, 1053-1057 (1973).

[7] Mielenz, K. D., and Mavrodineanu, R., J. Res. Nat.

Bur. Stand. (U.S.), 77A (Phys. and Chem.), No. 6, 699-703 (Nov.-Dec. 1973).

(Paper 80A4-908)

126
NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 466, Standardization in Spectrophotometry and Luminescence

Measurements, Proceedings of a Workshop Seminar Held at NBS, Gaithersburg, Md., November 19-20, 1975 (issued May 1977).

Considerations for the Use of Semi-Transparent Metallic Thin Films

as Potential Transmittance Standards in Spectrophotometry*

R. Mavrodineanu

Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234

(May 20, 1976)

Various characteristics of evaporated metal-on-fused silica niters are discussed in

relation to their optical transmission properties. Special metal holders provided with shutters were designed to be used with these niters, and are described in detail. Transmittance

measurements, performed in various conditions, are reported and indicate that the evaporated metal-on-fused silica filters might present an acceptable material as transfer standards

in spectrophotometry.

Key words: Evaporated metal-on-quartz; filters, transmittance; neutral filters; standard

reference materials; transmittance characteristics; ultraviolet-visible filters.

The use of solid materials, in the form of glass

filters and of solutions of inorganic and sometime

organic compounds, to test the correct functioning

of spectrophotometers is a common practice [l].

1 A

variety of materials are available from the National

Bureau of Standards (NBS) which can be used as transfer standards to verify the accuracy of the

transmittance scale and the short and long term

stabilities of conventional spectrophotometers. Two

Standard Reference Materials (SRM's) have been

issued by NBS for the verification of the accuracy

of the transmittance scale; these are SRM 930 and

SRM 931.

SRM 930 is a solid material which consists of a

set of three glass filters having nominal transmittance of 10; 20; and 30 percent. They are certified

for transmittance in the visible spectral range from

400 nm to 635 nm. A detailed description of this

SRM is given in NBS Special Publication 260-51

[2]. SRM 931 is a liquid standard which consists

of a solution of cobalt and nickel in dilute perchloric

acid contained in glass ampoules [3]. The transmittance of these solutions is certified from 302 nm

to 678 nm and should be used in conjunction with

curvettes having a known light path; such curvettes

are available from NBS as SRM 932 [4].

_ Both SRM's 930 (the glass filters) and 931 (the

liquids) are limited in their spectral transmittance

range and require the use of spectral bandpasses,

from 2.2 nm to 6.5 nm for the glass filters and from

1.0 nm to 6.5 nm for the liquid filters depending

of wavelength, when accurate transmittance values

are sought.

"This work was supported in part by the National Institute of General

Medical Sciences.

1 Figures in brackets indicate the literature references at the end of this paper.

The need to provide similar transfer standards, but

with expanded spectral range to the ultraviolet and

with less stringent spectral bandpass requirements,

has resulted in an investigation to find adequate

materials for this purpose. Such materials should

fulfill the following conditions: (a) be transparent

in the spectral range of interest, usually between 200

nm and 800 nm; (b) have a transmittance independent of wavelength (optically neutral) ; (c) have

a spectral transmittance independent of temperature

(d) have low reflectance and be free of interferences;

(e) be nonfluorescent; (f) be stable, homogeneous,

and free of strain; (g) have mechanical stability for

the size used (thickness, length, width) and be easy

to fabricate b}^ conventional techniques used in optical shops; (h) be simple to use in conjunction with

the conventional spectrophotometers available today

in analytical laboratories; (i) be readily available

and relatively inexpensive. Thus, various solid

materials were examined and the final choice was

the evaporated metal-on- (non-fluorescent) fused

silica type filter. The transmission characteristics of such filters are illustrated in figure 1 and are compared with that

of three glass filters and Ronchi ruling on glass.

The major limitation of the evaporated metal-onquartz filters results from their intrinsic property of

attenuating the incident radiation by reflecting

rather than absorbing part of it. As a consequence

of this property, this type of filter could generate

stray radiations in the sample compartment of conventional spectrophotometers and is susceptible to

produce interreflections when used with instruments

equipped with lenses.

To determine the practical value of such filters as a

transfer transmittance standard, comparative meas127
Ll) u

<

cro

cn

CD<

CORNING

8364

CHANCE

ON-10

SCHOTT

NG-4

Table I. Comparison between the percent transmittances (%T)

measured on three inconel-on-silica filters at NPL and NBS

EVAPORATED METAL ON QUARTZ

[INCONEL]

RONCHI RULING ON GLASS

100 LINES/in.

200 300 400 500

X. NANOMETERS

600 700

Figure 1. Spectral characteristics for five transparent

materials from 200 nm to 700 nm.

urements were performed with the National Physical

Laboratory in England (NPL), and the results are given in table I. In this case the inconel-on-fused

silica filter was protected by a clean fused silica

plate held in place with an organic cement. Except

for a filter which showed some mechanical flaws in its

structure, the reproducibility of transmittance measurements was as good as that obtained for the

absorbing glass filters (table II). The error which

would result from positioning the inconel-on-fused

silica was measured by rotating from 0° angle to

3°—6°—and 9°. From the results obtained (table

III) it can be concluded that in the case of the highaccuracy spectrophotometer used at NBS a positioning error within 3° can be tolerated.

The interreflection error affecting the measurements when a filter is inserted in the radiation path

between the two lenses of a spectrophotometer

was examined in detail [5]. The measured error for a glass filter established for the high-accuracy spectrophotometer was one or two 10 -4 transmittance

units; a value which is about four times larger was

found for an evaporated metal-on-fused silica filter. It should be mentioned here that both the positioning

and interreflection errors are, for a given material,

instrument dependent.

As a result of these considerations a decision was

made to produce a limited number of sets of evaporated inconel-on-fused silica and to test these filters

in actual measurements performed on the conventional spectrophotometers manufactured in the

United States.

One of the filters from a set is shown in figure 2. From left to right one can see the main body of the

filter holder made from an aluminum alloy anodized

black. This body is provided with dove-tail grooves

which can accept a front and rear shutter made

NBS, %T

Wavelength NBS, %T NPL, %T

nm average

1 2

450. 0 24. 87 24 88 24. 876 24. 93 CCA A

550. 0 23! 78 23. 82 23. 80 23. 86

650. 0 23. 38 23. 39 23. 386 23. 46

450. U 49. 35 49. 33 49. 34 49. 56

550. 0 47. 60 47. 60 47. 81

650. 0 46. 85 46. 85 46. 85 47. 14

450. 0 72. 17 72. 20 72. 185 72. 30

550. 0 72. 05 72. 11 72. 08 72. 20

650. 0 72. 20 72. 34 72. 27 72. 33

Average difference between NBS and NPL percent T

values = —0.30 percent

5 This filter had a flaw in the form of a crack which was

sometimes visible and other times invisible. The larger differ- ences found in the measurements of this filter may be due to

this flaw.

Table II. Comparison between the percent transmittances

(%T) measured on three Schott NG-4 glass filters at NPL

and NBS

Wavelength

nm

NBS, %T

March 12,

1971

NBS, %T

May 18,

1971

NBS, %T

average

NPL, %T

February

1971

440. 0 12. 92 12. 91 12. 915 12. 93

465. 0 14. 965 14. 98 14. 973 15. 01

590. 0 11. 70 11. 64 11. 67 11. 67

635. 0 12. 72 12. 68 12. 70 12. 72

440. 0 19. 625 19. 58 19. 603 19. 62

465. 0 22. 385 22. 35 22. 367 22. 43

590. 0 19. 06 18. 95 19. 005 19. 01

635. 0 20. 455 20. 37 20. 41 3 20. 47

440. 0 32. 89 32. 86 32. 875 32. 98

465. 0 35. 52 35. 54 35. 53 35. 66

590. 0 31. 165 31. 10 31. 133 31. 21

635. 0 32. 565 32. 52 32. 543 32. 62

Average difference between NBS and NPL percent T

values = —0.19 percent

Table III. Percent transmittance (%T) measured on a Schott

neutral glass filter 2 mm thick, and an inconel-on-fused silica

filter 2 mm thick at 690 nm, for normal incidence and for the angle of 3°; 6°; and 9°

%T

^\ Filter Schott Inconel-on-fused silica NG-4

Angle \. Glass

Front Back

0° 28. 13 29. 91 29. 87

3° 28. 10 29. 98 29. 87

6° 28. 03 29. 84 29. 82

9° 27. 98 29. 92 29. 90

128
1III

3| 4j 5| 6| ' 7

III IIIIIHII II

9 : lOl 111 12' IV 14' 15

Figure 2. Filter holder with shutters. From left to right: front and rear view of the holder body provided with dove-tail grooves; retaining spring with nylon screw and washer; filter; two shutters; front view of the filter holder with front shutter; rear view of the filter with rear shutter; filter holder with both shutters closed.

from a black plastic (Delrin 2 ). The last three units

illustrate the holder with these shutters on. A more

detailed dimensional drawing of the filter holder is shown in figure 3. The shutters provide two functions

one is to protect the filter from contamination, the

other to detect if stray radiant energy (SRE) is produced in the spectrophotometer compartment

as a result of reflections generated by the incident

beam on the semi-transparent metal layer. The

determination of stray radiant energy generated

in the sample compartment of the spectrophotometer,

due to the reflecting propreties of these filters, may

be assessed as follows: A background signal may be

measurable when the instrument shutter at the

photomultiplier tube is closed. Another slightly

higher background signal may be detectable with

the instrument shutter open and with the filter

placed in the beam, in the sample compartment, with

both sliding shutters closed. Both of these signals

should be very small. A third signal may be detected

when the front sliding shutter at the filter holder is removed and the rear sliding shutter is closed. If

under these circumstances a signal is detected, it is very likely due to SRE produced by reflections re- sulting from the semi-transparent mirror which

scatter from the walls of the cell compartment. This

should also be low in magnitude. The transmittance

of the filter is measured where both sliding shutters

at the filter holder are removed.

2 In order to describe materials and experimental procedures adequately, it was

occasionally necessary to identify commercial products by manufacturer's name

or label. In no instance does such identification imply endorsement by the National Bureau of Standards, nor does it imply that the particular product or equipment is necessarily the best available for that purpose.

Under these circumstances a source of systematic

error can be from multiple reflections between the

lenses in the instrument and the filter surfaces [5]. An indication of the existence and magnitude of such

interreflection phenomena can be obtained by comparing the differences between the transmittance

measurements and the certified values for SRM 930

and 931 to the corresponding differences for the

inconel-on-fused silica filters.

Each set is made from three filters and one blank

placed in individual metal holders which are provided with the front and rear sliding shutters. The

selection of inconel as the semi-transparent metal

layer was made on the basis of its relatively good

optical neutrality in the spectral range from 250 nm

to 700 nm. The fused silica substrate is of optical

quality and non-fluorescent. All the silica niters,

including the blank, were ground and polished at the

same time and together to a parallelism of 0.02 mm

and a flatness of less than 2 fringes (mercury 546.1

nm). The nominal dimensions are 30.5 mm by 10.4

mm by 2 mm thick, and the nominal transmittances

of these filters are 1 percent; 20 percent; 30 percent;

and 90 percent.3 The transmittances of each set were

measured at 250 nm, 300 nm, 340 nm, 400 nm, 440

nm, 465 nm, 500 nm, 546.1 nm, 590 nm, and 635 nm.

Sets of these filters were sent to the manufacturers

of spectrophotometers for evaluation and tests on

the individual instruments. The results of these

s The filter holders and the evaporated inconel-on-fused silica filters were made

in the NBS Instrument Shops.

129
-}>0t ±^ -1 \ \ t ^

1 \

1

CUT COHStR OWVeWVE.^

Figure 3. Details of the filter holder with shutters.

Nominal dimensions are in millimeters.

Table IV. Percent transmittance (%T) measured on four inconel-on-fused silica filters at 10 wavelengths and on the NBS-IMR

high-accuracy spectrophotometer and on two conventional instruments A and B

% T

^\Wavelength

nm

Instruments^

250 300 340 400 440 465 500 546 590 635

NBS-IMR

High-accuracy

Spectrophotometer

1. 45

21. 39

28. 68

91. 42

1. 81

21. 27

29. 92

92. 34

1. 86

20. 33

30. 20

92. 66

1. 94

18. 93

29. 96

92. 90

2. 04

18. 33

29. 70

93. 01

2. 13

18. 09

29. 55

93. 05

2. 27

17. 90

29. 44

93. 11

2. 49

17. 83

29. 44

93. 16

2. 70

17. 86

29. 49

93. 19

2. 90

17. 95

29. 57

93. 23

Spectrophotometer A

1. 53

21. 37

28. 67

91. 59

1. 84

21. 24

29. 87

92. 60

1. 93

20. 31

30. 19

93. 32

2. 00

18. 91

29. 95

93. 20

2. 12

18. 29

29. 70

93. 30

2. 20

18. 07

29. 58

93. 30

2. 34

17. 89

29. 49

93. 42

2. 55

17. 82

29. 46

93. 46

2. 75

17. 84

29. 52

93. 50

2. 95

17. 92

29. 60

93. 58

Spectrophotometer B

1. 49

21. 6

28. 8

91. 4

1. 85

21. 5

30. 0

92. 6

1. 90

20. 5

30. 2

92. 6

1. 97

19. 1 30. 0

93. 1

2. 07

18. 5

29. 9

93. 3

2. 16

18. 3

29. 7

93. 3

2. 31

18. 1 29. 5

93. 3

2. 53

18. 0

29. 5

93. 3

2. 83

18. 3

29. 9

93. 9

3. 06

18. 5

30. 0

93. 9

tests will permit to establish the usefulness of these

niters as SRM's in spectrophotometry.

In the mean time comparative measurements were

performed on two conventional spectrophotometers

available at NBS, and the results are assembled in

table IV. These results are preliminary measurements

and should be considered with caution. The data

seem to indicate, however, that the evaporated

metal-on-fused silica niters may be an acceptable

material for use as transfer standards in

spectrophotometry.

Note.—The semi-transparent metallic surface of the filters described in this paper is not protected from environmental

exposure and careless handling. A solution to this problem was found recently. It consists in placing on top of the fused

silica plate carrying the semi-transparent evaporated metal

layer a clear fused silica plate, about 1.5 mm thick, adequately

ground and polished, to achieve an optical contact with the

evaporated semi-transparent metal layer surface. The two

fused silica plates are slightly beveled, and an optical cement

is applied to protect the edges. Under these conditions the

two fused silica plate assembly, with the semi-transparent

evaporated metal layer in between, behaves optically as if

it were a single semi-transparent plate, and provides full protection of the metal layer. Several sets of these new filters were made for evaluation in actual working conditions.

130
References

[1] Rand, R. N., Practical spectre-photometric standards,

Clin. Chem, 15, 839-863 (1969).

[2] Mavrodineanu, R., and Baldwin, J. R., Glass niters as a

standard reference material for spectrophotometry—

selection, preparation, certification, use, SRM 930,

Nat. Bur. Stand. (U.S.), Spec. Publ. 260-51, 118

pages (Nov. 1975).

[3] Burke, R. W., Deardorff, E. R., and Menis, O., Liquid

absorbance standards, J. Res. Nat. Bur. Stand.

(U.S.), 76A, (Phys. and Chem.), No. 5, 469-482

(Sept.-Oct. 1972).

[4] Mavrodineanu, R., and Lazar, J. W., Standard quartz

cuvettes for high accuracy spectrophotometry, Nat.

Bur. Stand. (U.S.), Spec. Publ. 260-32, 26 pages (Dec.

1973) and Clin. Chem. 19, (9) 1053-1057 (1973).

[5] Mielenz, K. D., and Mavrodineanu, R., Reflection

correction for high-accuracy transmittance measure- ments on filter glasses, J. Res. Nat. Bur. Stand. (U.S.),

77A (Phys. and Chem.), No. 6, 699-703 (Nov.-Dec.

1973).

(Paper 80A4-909)

131

NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 466, Standardization in Spectrophotometry and Luminescence

Measurements, Proceedings of a Workshop Seminar Held at NBS, Gaithersburg, Md., November 19-20, 1975 (issued May 1977)

Structure-Related Optical Characteristics of Thin Metallic

Films in the Visible and Ultraviolet

H. E. Bennett and J. L. Stanford

Michelson Laboratories, Naval Weapons Center

China Lake, California 93555

(November 20, 1975)

Surface irregularities and crystalline order strongly influence both the scattered light

and absorption of metallic films. These effects extend through all spectral regions but are

particularly important in the visible and ultraviolet. Scattered light arises from several

scattering mechanisms. Macroscopic irregularities such as dust, scratches and particulates

are typically much less important than are microirregularities only a few tens of angstroms

in height but covering the entire surface. For metals such as silver and aluminum, which

have plasma edges in the ultraviolet, the excitation of surface plasmons resulting from these

microirregularities causes additional incoherently reemitted or "scattered" light. Surface

plasmon excitation also causes increased absorption in some wavelength regions. These

effects are enhanced by dielectric overcoating layers, which both increase the absorption

and scattering.and shift the wavelength at which the peak occurs. Surface plasmon excitation

is particularly important in the ultraviolet region, where the dielectric overcoating applied

to prevent formation of an oxide film on aluminized mirrors, for example, can significantly

change the mirror reflectance. Plasmon excitation is made possible by a momentum conserving process associated with material inhomogeneities and hence can presumably be

caused by crystalline disorder in the metal surface as well as surface irregularities. If the

disorder is present on a sufficiently fine scale, it also affects the band structure of the metal

and hence its optical absorption. Examples of the effect of film structure on the optical

properties of evaporated and sputtered metal films will be given.

Keywords: Absorption; dielectric layers; irregularities; metallic thin films ; microirregularities

overcoating; plasmons; scatter.

I. Introduction

The optical characteristics of opaque metal films

which are of most interest are the fraction of the

light which is either absorbed or scattered by the

films. The most commonly assumed mechanism for

light scattering consists of reflection from numerous

tiny scratches, dust particles and other surface

blemishes which act as tiny mirrors oriented at

various angles to the surface normal. This picture

has marginal merit in the infrared, where scattering

from particulates and surface blemishes usually is dominant, but is not the important mechanism for

light scattering from optical surfaces in the visible

and ultraviolet regions of the spectrum. To the ex- tent that it is a geometrical optics phenomenon,

scattering from surface blemishes such as scratches

will be independent of wavelength. Particulate scattering, however, is largely a diffraction phenomenon.

Closely related is resonant scattering and absorption

associated with the polarization characteristics of

individual irregularities in the metal surface. To the

approximation that these irregularities are independent, i.e., that the scattering from one irregularity is unaffected by the presence of its neighbors,

we may compute the resultant scattering and absorption approximately from the Mie scattering

theory. Particulate scattering and scattering from

large "macroirregularities" can usually be regarded

in this way. However the dominant source of scattered light for good optical surfaces in the visible

and ultraviolet regions is closely spaced microirregularities only a few tens of angstroms in height.

These microirregularities scatter and absorb collectively and cannot be regarded as independent. They

can be treated statistically, and give rise to several

interesting phenomena.

When monochromatic electromagnetic waves are

incident on a smooth metal surface they induce

virtual surface currents within the skin depth of the

metal. The currents are virtual since the electrons

in the metal have too much inertia to couple to the

wave, but they have the same wave vector along

the surface as the incident wave. Thus the radiation

from these currents must also have the same wave

vector along the surface as the incident wave, and the

radiation leaves the surface in the specular direction.

When surface irregularities are present, the current

distribution is modulated according to the distribution of surface heights as well as their correlation

133
along the surface. Additional tangential components

are thus introduced into the wave vector of the cur- rent distribution producing nonspecular or scattered

light. If we confine ourselves to total integrated

scatter (TIS) and ignore its angular dependence or

polarization at nonnormal incidence, the scattering

caused by perturbation of the virtual current distribution can be described by classical diffraction

theory in the Kirchhoff integral approximation. This

effect is the most important source of scattered light

in the visible and ultraviolet wavelength regions.

Actual surface currents can exist in the skin depth

of the metal but their allowed phase velocity is lower than that of the virtual currents induced on a smooth surface by an incident light wave and thus

no coupling occurs. However when microirregularities are present, coupling can in some cases occur and

these surface charge waves can absorb energy from

the incident light. These surface charge waves are quantized into units termed surface plasmons with

a fixed energy-wave vector relationship. Once

excited they may decay thermally into single

electron excitations or they may radiate because of

their acceleration along the curved surface irregularities. Surface plasmons are strongly affected by

the presence of a dielectric layer on the metal surface. Both absorption and scattering are often greatly

enhanced, a result which has significant implications

since protective dielectric overcoating layers must

be used to prevent oxidation of aluminum reflectors

in the ultraviolet or sulfide formation on silver

reflectors used at longer wavelengths. To minimize

surface plasmon related absorption and scattering

in such cases the mirror must be extremely smooth.

Other structure-related mechanisms also affect

the optical properties of metals. Both mechanical

abrasion and the inherent disorder in polycrystalline

films of vacuum evaporated or sputtered metals

result in increased absorption. The crystalline imperfections in such metal samples modify the electron energy band structure, permit excitation of

surface plasmons by the incident electromagnetic

fields, and affect the motion of conduction electrons.

In the latter case the effect is greatest in the infrared,

where the optical properties of metals are determined

by the mean free path and number of conduction

electrons.

In the visible and ultraviolet the response of single

electrons in metals to incident light is influenced

significantly by interband electron transitions. Because the energy band structure results directly

from the regularity of the lattice structure, lattice

distortion produced by mechanical abrasion or

polycrystalline film growth affects the optical re- sponse of metals. The optical properties of metals

thus prepared are notoriously nonreproducible in

the visible and ultraviolet. In addition to single

electron effects, the inhomogeneities resulting from

the disorder permit absorption via excitation of

collective electron oscillations, namely, surface plasmon excitation. The combination of these two effects can significantly reduce the reflectance of metals in

the visible and ultraviolet through increased

absorption.

Surface irregularities can also affect the mean free

path of the conduction electrons near the metal

surface. The conduction electrons have a de Broglie

wavelength associated with their energy and may be

thought of as a wave motion incident on the metal

surface from inside. If the surface is perfectly smooth

they reflect specularly and there is no change in their

mean free path between collisions, i.e., the electronsurface interaction does not represent a collision in

the specular case. If the conduction electrons are

diffusely reflected, however, as the}' will be if surface

microirregularities are present which are not adequately screened by the surface electron cloud, reflection from the surface does represent a collision and

the electronic mean free path will be decreased with

consequent increase in absorption. This "anomalous

skin effect" [1]

1 is important in the infrared region

of the spectrum [2]. Surface microirregularities as well as macroirregularities may modify the optical properties of a metal

surface through resonant scattering and absorption

of light associated with resonance effects in the

polarization characteristics of individual irregularities. These effects are equivalent in many ways to

scattering from small dispersed particles and may be

calculated in the first approximation using Rayleigh

or Mie scattering theory.

In this paper we will first discuss briefly the

theoretical predictions for optical absorption and

scattering in metal surfaces due to structure-related

mechanisms. Those which appear to be most important in the visible and ultraviolet regions are scattering and absorption from isolated microirregularities, and diffraction effects from correlated ir- regularities including the optical excitation of surface

plasmons. We will then discuss instrumentation for

measuring scattering, absorption, and surface structure, and finally will show some experimental results

for silver and aluminum surfaces.

II. Theory

A. Light Scattering and Absorption by Isolated

Irregularities

If we assume that we can treat each scattering

center independently, the scattering may be computed using the Mie theory. Consider first nonabsorbing irregularities. Assuming spherical

scattering centers and defining x as x=2ira/X where

a is the particle radius, X the wavelength and n the

index of refraction, the ratio Qs of scattering to

geometrical cross section of the scatterer for nx

<0.8 is [3]

The Rayleigh l/\4 law for x «1 follows from eq

(1). For x >>1, Qs =2. In the region iMa somei Figures in brackets indicate the literature references at the end of this paper.

134
times complicated resonance occurs. E. D. Bailey [4] has suggested the universal scattering curve shown

in fig. 1 as a first approximation to this resonance.

If the index of refraction of the scattering center

is in the 1.3-1.4 range, the resonance then occurs when the diameter of the scattering center is approximately equal to the wavelength. Dust particles are probably largely nonabsorbing.

If the index of refraction of the scattering center

is complex, as would be the case if scattering were

occuring from an asperity on the metal surface

rather than from a dust particle, both absorption

and scattering would occur. The ratio Qe of extinction cross section to geometrical cross section,

which includes both scattering and absorption,

would then be given by [3]

Qe =-im[4x {gy+i! *

3 (S+£)

2 ri*+27n2 +38\ ~| 4 8

2n2 +3 J J 3

nn

2 +2 (2)

5

4

3

2

0

0.01 0.1 1 10

Figure 1. Theoretical prediction of scattering cross section Q,

as a function of the ratio of particle diameter d to wavelength X

times a function of index of refraction. The graph is calculated for spherical, nonabsorbing particles. The effective area of each scattering center is wd'Q,li.

where the complex index n=n—ik and k is the

extinction coefficient. The term in brackets gives the

absorption and the second term the scattering as in

eq (1) except that now n is complex. A resonance would still occur in this case, but as k increases the

short wavelength side of figure 1 will fall off less

rapidly than for the nonabsorbing case.

B. Scalar Scattering Theory

In addition to particulates and other isolated

irregularities on an optical surface, there are also

closely spaced irregularities, often having very small

deviations from the mean surface level (MSL) , which

scatter and absorb collectively. The effect of these

interdependent irregularities may be understood by

considering the surface current induced by an

incident electromagnetic wave. Figure 2 illustrates

the surface charge wave which would be induced if the electrons in the metal could move rapidly enough.

These charge waves are virtual states under most

conditions since the charge density waves which can

actually exist within the skin depth of a metal have

phase velocities u/k0 which are less than the velocity

of light c/n in the dielectric in contact with the metal

Metal

Induced phase velocity wlk

Q s'mB - c/nsin# I Surface plasma phase velocity

ojI k < c/n

Figure 2. Surface charge wave induced by the electric field of an incoming electromagnetic wave.

The dashed lines indicate maximum field strength. The induced charge wave

is virtual since its phase velocity is > the velocity of light, and a real surface plasma wave must have a phase velocity < c/n.

surface, whereas, as seen from figure 2, the phase

velocity of induced surface charge waves is greater

than c/n. The component of the wave vector of this

induced virtual surface charge wave is k0 sin 0 where

k0 is the wave vector of the incident light and 8 the

angle of incidence. The radiation from this induced

current must also have the same wave vector component along the surface in order to satisfy the

boundary conditions associated with the fields.

Therefore, the radiation from the surface leaves in

the specular direction. However if irregularities were

present on the surface, the current distribution

would be modified according to the heights of these

irregularities as well as their correlation along the

surface. Additional tangential components are thus

introduced into the wave vector of the current distribution producing nonspecular or "scattered" light.

An example of the effect of correlated surface

irregularities on light reflected from a surface is

furnished by a reflection grating with groove spacing

d shown in figure 3. The wave vector K associated

with the grating grooves is K=2ir/d. If light with

wave vector k0 is incident on the grating, in the N—0

order, the light is reflected specularly and has a component of its wave vector along the surface of k0 sin0 as in the case for the smooth surface. In other orders

the magnitude of the wave vector is unchanged

(i.e., the wavelength of light reflected in various

directions is the same) but the component of the

135
grating constant

d

= 2^/K

N=3 N=4

Figure 3. Momentum transfer from a grating surface to a

light beam.

ko is the vector of the incident light, N the order of interference, d the line spacing on the grating, and K the wave vector for the grating surface.

wave vector along the surface of the grating is increased by multiples of K, the wave vector asso- ciated with the grating surface. Photons in the light

incident on the grating have energies of ho> and

momenta of hk0. The photons reflected from the

grating have the same energy but the component of

their momenta along the surface has been altered

by integral multiples of the momentum KK associated

with the grating surface. The effect of a rough surface can thus be interpreted as supptying an additional

tangential momentum component to the reflected

photon without changing its resultant energy or

total momentum hK0 = fio)/c. The momentum which

the surface can supply is determined by the statistical character of its surface irregularities.

The angular dependence and polarization of scattered light requires an involved theoretical analysis

[5,6]. However, if we confine ourselves to total integrated scatter from irregularities which are large

laterally relative to the wavelength of light, the scattering caused by perturbation of the virtual surface

current distribution can be described quite simply

by classical diffraction theory in the Kirchhoff integral approximation[7-9]. A statistical representation

of the surface irregularities is sufficient to make the

calculation. Of primary importance is the height

distribution function of surface irregularities about

the MSL. Interferometric analyses using fringes of

equal chromatic order (FECO interferometry) indicate that the height distribution function of real

optical surfaces is very nearly Gaussian[10]. For a

surface with a Gaussian height distribution the ratio

of the specularly reflected light R to the total reflectance R0 is[8] ^ e -(4.5/X) 2

( 3 ) -"0

where 5 is the rms value of the height of surface

microirregularities about the MSL. Equation (3) is exact [9] for all values of 5/X and expresses the

fraction of the reflected light which is reflected

coherently from different points on the surface.

However as 5/X—»1 an increasing amount of incoherently reflected or scattered light falls very

near to the specular direction and cannot be separated

from it experimentally. Therefore eq (3) is most

useful in describing the experimentally observed

scattered light for <5/X<<l. In this case the exponent

may be expanded, giving the scattered light AR as

Afl=i?0 (47rcVX)

2

. (4)

Two precautions must be observed in using eq (4)

(1) the rough surface total reflectance must be used

for R0 . It may or may not be equal to the smooth

surface reflectance, and (2) scattering from surface

plasmon excitation and decay must be excluded,

i.e., scattering measurements to determine 5 must be

taken in wavelength regions where surface plasmon

excitation is not important.

Figure 4 shows the fractional scattering AR/B0 predicted by eqs (3) and (4) as a function of wavelength and surface roughness. The solid diagonal

lines give the theoretically predicted scattering

levels. The dashed vertical lines show typical

roughness values for superpolished optical surfaces,

high quality glass optics and high quality metal

optics polished by conventional techniques. In the

photographic infrared typical metal coated glass

mirrors will scatter about 0.1 percent of the reflected

light. This value quadruples in the visible region and

in the near ultraviolet approaches 1 percent. At

shorter wavelengths it increases still further, although

in the vacuum ultraviolet the situation is unclear.

In the intermediate and far infrared scattered light

caused by microirregularities becomes quite low and

other types of scattering become important.

10.0 -

5.0

I

2- 0

E

a

z

in 1.0 >

<s

0.5

SCATTERED L GHT

1 1 | 1 1

./j super polish J

I

normal polish

I— 1 1

1 / normal polish /

S 1

1 //

' /

f (glass) \/f (metal)

/l0"e

1

1 // 1 /

/ 1 /

/ 1 / 1

1 //

L/io- 4 /I /

/ I /10"3 / I / / I

'< //

i /

/icr2

1

/ I / / l / / i /

! ,

J/kt1

1 1 2 5 10 20 ROUGHNESS A

50 100 200

Figure 4. Theoretical predictions for scattering as a function

of roughness and wavelength.

136
C. Optical Excitation of Surface Plasmons (13)

The "scalar scattering theory" described above

predicts a monotonic increase in scattering with

decreasing wavelength. Several years ago we and

others [11-13] found that slightly rough metal

surfaces can exhibit resonant absorption in the

spectral range near the metal's surface plasmon

frequency. Accompanying this resonant absorption

is increased scattering which also occurs predominantly in the surface plasmon region. These phenomena may be interpreted in terms of optical

excitation of surface plasmons, [14], which then

decay either thermally (absorption) or radiatively

(scattering). Surface plasmons may be excited

optically in either thin metal films, where the surface

oscillations at the two surfaces can couple, or in

thick films (i.e., significantly thicker than the optical

penetration depth of the light, which for the best

conductors is a few tens of nm). We will consider

only the thick film case here.

The allowed surface charge waves which may exist

on a conducting surface may be obtained directly

from Maxwell's equations, which may be written in

Gaussian units as [15]

VXE=-

0 (5)

0 (6)

1 dH

(7)

c dt

.01, • N T-I i - (ei—te2)E

c (8)

where ej and e 2 are the real and imaginary parts of

the complex dielectric constant e and the other symbols have their usual significance. Choosing a co- ordinate system at the metal-dielectric interface in

which x is directed into the metal along the surface

normal and y and z are in the plane of the interface,

Maxwell's equations are satisfied by the transverse

magnetic (TM) wave solution

E=E(x)eHat -^z) (9)

where Ey =Hx =0 at z=0. From eqs (5), (8) and the

wave equation given by V X V X E, we obtain

E — _i_ dEx k0 dx

Hv {x)=^Ex

d

2 Er -(«~?) Ex=0.

dx2

Solving eq (12) gives

Ex =Eme-«

2o-°

2

<>n<°2

> 1/2x z>0

(10)

(11)

(12)

where subscripts m and d refer to the metal and

dielectric respectively. Ez and Hy can be calculated

from using eqs (10) and (11). The TM surface

charge waves are evanescent with phase velocity

o}/k0 . Boundary conditions are that eEx and dEJdx

are continuous across the metal-dielectric interface,

giving

C \tm +ed J

1/2 (14)

Equation (14) is a general relation giving the wave

vector of the surface charge wave in terms of the

complex dielectric constants of the metal and

dielectric. Note that a resonance can occur if ei = — e d whereem =ei— ie2 and that it will be strongest when

e 2 =0 i.e., damping is minimized. For real metals em

is a complicated function. However, for a free electron

metal with no damping

=ei=

2/a2 to. /CO (15)

where up is the plasma frequency. Substituting in

eq (14) we obtain the dispersion curve for surface

charge waves at a free electron metal-air interface:

w =a; P {0.5+(W2 +[0.25-t-(^)4

] 1/2

} 1/2 (16)

where k p =oi p/c. Letting k—><*> we see that there will

be a maximum frequency usp which the plasmon

can have where

o> sp =ccp/(l + e dy

/2

. (17)

For a metal-air interface, then, the maximum frequency which surface plasmons in a free electron

metal can have is w p/V2.

Equation (16) is plotted in figure 5 as the solid

line. Note that the k0 value for the surface plasma

waves is always larger than that of the incident

light waves having the same energy and becomes

very much larger near the limiting frequency.

The density of allowed states is highest in this

energy region. The momentum which must be

furnished by the surface for coupling to occur is, for

normally incident light, all of that to the left of the

surface plasma wave dispersion curve, since the

wave vector of normally incident light has no

component parallel to the surface and the wave

vector of the surface wave is entirely in the surface.

For grazing incidence light, only the difference

between the "light line" <x>=ck kQ and the dispersion curve need be supplied and in the "retardation

region" where w<<co5 p they approach coincidence.

In the grating illustrated in figure 3 an order of

interference could occur for which light would be

diffracted at a grazing angle. If the frequency of the

light were in the retardation region, coupling could

then occur and energy would be absorbed by the

grating from the beam to excite surface plasma

waves. This situation does occur and is the origin

137
Figure 5. Dispersion curves for light waves and surface plasma waves at a

metal-dielectric interface where the dielectric has a refractive index of unity

(solid lines) and an index of n^>l (dashed lines).

Surface wave modes exist for all values of « below a limiting frequency a,p but the density of states

is highest near u,p . As the index increases w, p decreases and the ft values for the surface waves remain

larger than those associated with the light waves.

of the Woods anomalies in diffraction gratings.

[11, 16].

A dispersion curve analogous to eq (16) can also

be calculated from eqs (14) and (15) when the dielectric is not air. Such a curve is shown in figure 5

as the dashed line with its associated "light line."

The effect of increasing e d is to lower co s „ and move

the frequency associated with a given k0 to lower

values. Thus when a dielectric is deposited on a metal surface without affecting the resultant k 0 values, we would expect resonances in absorption

or scattering to move to longer wavelengths.

Calculating the coupling probability between

incident photons and surface waves resulting from

surface roughness is a difficult quantum mechanical

problem. It has been attacked by Elson and

Ritchie [17] by means of a perturbation calculation in

which damping is neglected. They obtain the

probability that a photon of energy hu incident

normally on a rough surface will be converted into a surface plasmon, which may be written as the

decrease in reflectance of the specular beam ARsp where

^iXFo^KCifer) <i8)

where g is the surface structure factor, which is the

two dimensional Fourier transform of the autocovariance function of the surface roughness. In

general, as the autocovariance length a of the sur- face irregularities becomes longer the momentum

spectrum of surface roughness becomes more concentrated toward the origin in k0 space and the

probability for photon-surface plasmon conversion

becomes lower. Thus the optical excitation of surface

plasmons will be relatively weak for gently rolling

surfaces and much stronger for more jagged surfaces.

In addition it will increase with the square of the

rms height of surface irregularities and will also

increase as the wavelength of the incident light

decreases. Theoretical absorption curves calculated

from eq (18) for optical excitation of surface plasmons

on a free electron metal surface having Gaussian

height distribution and autocovariance functions

are shown in figure 6 for various values of a. As a

becomes larger relative to \ p the peak absorption

decreases but the wavelength range over which an

effect occurs becomes longer. Thus although the

magnitude of effect is less for a gently rolling surface

than for a jagged one, the wavelength range over which the effect may be important should increase.

III. Experimental Procedure

In order to accurately measure scattering and

absorption in the visible and ultraviolet regions and

to relate them to surface structure, various nonstandard instruments are required. Four types of

instruments which have been of particular help at

Michelson Laboratory are the NWC Scatterometer

and the Optical Evaluation Facility for measuring

scattered light, the NWC Absolute Reflectometers

for measuring reflectance, and the NWC FECO

Scanning Interferometer for determining the structure of optically polished surfaces. A brief description

of these instruments follows.

138
Figure 6. Absorption in a free electron metal caused by surface

plasmon excitation.

Xpis the limiting wavelength for surface plasmon excitation, a the autocovari- ance length and 5 the rms surface roughness, both assuming a Gaussian model, and Ai? the increase in absorption for wavelength X. Calculations are based on the Crowell- Ritchie model.

Figure 7. Schematic diagram, of Scatterometer

The symbols are defined in the text.

A. NWC Scatterometer

Figure 7 gives a schematic diagram of the NWC

Scatterometer [18]. Mirrors are indicated by M,

lenses by L, slits by E, apertures by A, the adjustable

diaphragm by D, the photomultiplier by PM, and

its shutter by Sh, and the dispersing prism by P.

In operation dispersed light from either a high pressure xenon arc Xe or a tungsten filament W is used.

Alternatively, a low pressure mercury arc Hg may

be used as a monochromatic source with the aid of

filters F. The light is collimated and a pencil beam

1 mm in diameter passes through A3 to strike

sample S, a plane circular sample 3.86 cm in diameter,

at an angle of incidence of 15°. Specularly reflected

light passes out along the axis of internally aluminized cone C of semivertex angle 18°45' and is re- flected by Mg to PM. It may be entirely blocked

by B, which is situated at the focus of A3 and re- moves all light within a half angle of 37' of the

specular direction. Light scattered within 20° of the

specular direction strikes M8 directly and is focussed

at A5. At larger scattering angles light is reflected

from C to M8, which then images the virtual object

formed by reflection from C as a ring which can be

blocked off by rotating aperture A4 . By manipulating

B, D, and A4 light scattered into all angles or into a range of angles between 37' and l%° to 20°, may

be ratioed to total sample reflectance. Advantages

of this instrument are that it uses mirror optics and

thus is nearly independent of wavelength, it does

not rely on having a Lambertian surface as does an

integrating sphere, and it is sufficiently efficient to

measure scattering levels down to below 10

5 when

care is taken to ensure that the detector and electronics are linear over this dynamic range. A three

polarizer unit [19] is helpful for such linearity

investigations.

B. Optical Evaluation Facility

For measuring scattered light from flat or curved

samples of various shapes up to 40 cm in diameter the

Optical Evaluation Facility shown schematically in

figure 8 is useful. This instrument, which is somewhat

more straightforward in concept than the Scatterometer, utilizes Coblentz spheres, indicated by C,

and pyroelectric detectors D to measure scattered

light in either reflection (for opaque samples) or transmission (for semitransparent ones). Back-scattering from transparent samples can also be measured. Approximate reflectance measurements can be

made by using for comparison a reflectance standard

R„ that has been calibrated in the absolute reflectometer. Over 20 laser lines ranging from the ultraviolet

through the intermediate infrared are available, and

by utilizing rotatable detector D2 bidirectional re- flectance distribution function (BRDF) measurements may also be taken. In addition to the pyroelectric detector a silicon detector for added sensitivity in the- visible region is mounted on D2

. Sample movement and data reduction are automated

and computer controlled so that a sample surface can be scanned automatically to determine scattering

levels as a function of position on the surface.

C. NWC Absolute Reflectometer

For making absolute spectral reflectance measurements the principle shown in figure 9 is employed.

Light is reflected at nearly normal incidence from

the sample S to a spherical mirror whose center

of curvature is at the center of the sample surface.

The mirror reimages the beam on the sample where

it is again reflected and passes out to the detector.

This scheme has several advantages. Most important

139
0.3507 0.5208 0.7525

0.3564 0.5309 0.7931 0.4762 0.5682 0.7993 „

0.4825 0.6471 0.4880 (Ar) 0.6764

Fl cure 8. Schematic diagram of the Optical Evaluation Facility

showing lasers and available laser lines, mirrors M, lens L,

spatial filter SF, attenuation filters F, chopper Ch, diaphragm

d, beam collector B, Coblenlz spheres C, pyroelectric detectors D, samples S and R.

Figure 9. Principle of double reflection absolute reflectometti showing cancellation of beam deviation caused by sample

tilt.

is cancellation of beam deviation resulting from

sample tilt. If the sample is tilted to S', as shown in

the figure, the beam is deviated through twice the

tilt angle and strikes mirror M8 at a slightly different

place. A spherical mirror used at its center of curvature images an object at the same place regardless

of where the light beam from the object strikes the

mirror surface, so M8 reimages at the same point for

position S' as it does for position S. Since the sample

is plane, on the second reflection the beam tilt introduced on the first reflection is exactly cancelled.

M8 has a long focal length to give a relatively large

effective / number, so that both S and S' are within

the focal range of the mirror. Thus, in our reflectometers one can reach in, tilt the sample manually

and observe no change in the beam at the detector

position even when it is viewed with a high power

microscope. In this way the most common cause

of systematic error in reflectance measurements is eliminated.

Figure 10 shows a schematic diagram of one of our three absolute reflectometers [20, 21]. The

sample is mounted at S and can be removed from the

beam, in which case light falls on Mn , a mirror nearly

identical to M8 , and returns to follow the same

optical path as for the sample-in position. The

optical path length is the same for sample-out

and sample-in, so no differential atmospheric absorption can occur and the same areas of the same mirrors are used for both cases with the exceptions of

M8 and Mu . By optically interchanging them by

rotating the sample about a vertical axis in the

plane of its surface, possible systematic errors resulting from differences in M8 and Mn are

cancelled.

Another advantage of a double reflection from the

sample is that the beam is not reversed side to side.

When a single reflection is used and the detector

swung from the straight through, sample-out position

to the reflected light position to make an absolute

reflectance measurement, the beam is reversed side

to side on the detector. Any nonuniformities in the

detector or intervening optics will introduce a systematic error into the measurement. In a double

reflection the beam is reversed twice so this error is eliminated. A similar argument can be made for the

plane of polarization if it is not in the vertical

direction.

The reflectometer shown in figure 10 uses mirror

optics entirely so that measurements can be made

from 0.3 to 30 p.m. A double-pass monochromator is

used to minimize light scattering in the infrared

from wavelengths shorter than that used. For

ultraviolet measurements double passing is less

effective and a second absolute reflectometer shown

in figure 11 employs a double monochromator. This

reflectometer also has fewer reflections. The angle of

incidence for both instruments is about 5°. For

unpolarized light the reflectance at 5° differs from

that at normal incidence by less than one part in

104 for all real materials. A third absolute reflectometer consisting of a one-meter grating monochromator, a single sample reflection and a rotatable

sodium salicylate-coated light pipe-photomultiplier

detector system is used for measurements in the

vacuum ultraviolet [20].

D. FECO Scanning Interferometer

In order to compare observed values of scattering and absorption caused by surface irregularities

with theoretical predictions, a direct measurement of

surface structure is required. The FECO Scanning

Interferometer which was developed by J. M. Bennett of our laboratory [10, 20] is shown schematically

in figure 12. Studies of individual irregularities and

statistical surface characterization can be performed

with this instrument. The sample to be measured

forms the top half of the interferometer I and is illuminated in reflection by xenon arc lamp Z.

140
Figure 10. Schematic diagram of absolute reflectometer for use in visible and infrared wavelength

regions employing -principle illustrated in figure 9: sample S, transmission sample T, mirrors M,

lens L, thermocouple detectors D, photomultipler P, slits E, chopper C, visible light source A,

globar (infrared source) G, and filter F.

FECO SCANNING INTERFEROMETER

SIGNAL MINI- TELE- AVERAGER COMP TYPE

Figure 11. Schematic diagram of absolute reflectometer for use

in the ultraviolet and visible wavelength regions employing

principle illustrated in figure 9: sample S, mirrors M, prisms

P, lead sulfide detector PbS, photomultiplier detector PM,

slits E, chopper C, hydrogen H2 or tungsten W sources.

Figure 12. Schematic diagram of FECO Scanning Interferometer.

The image detected by the slow scan TV camera is shown at right center and a

single scan line is shown above it: interferometer I, xenon arc Z, lenses L, beam

splitter B, silt S and prism P.

FECO fringes contouring the surface are formed in

the focal plane of a slow scan TV camera along with

reference wavelengths for determining fringe position as indicated in the right portion of the figure.

The output of the TV camera is fed to a computer

system to provide the height distribution function,

slope distribution function and autocovariance function characterizing the surface irregularities. The

height of the spectrometer slit defines the 1 mm length

of the long narrow section of the sample which is

evaluated; the lateral resolution of the system is

2 p.m. By translating the sample sideways the projected slit can be made to sweep out an area on the

sample surface for statistical characterization.

IV. Results

A. Scalar Scattering

The height and slope distributions for a superpolished Cervit flat [10], as determined using the

FECO Scanning Interferometer are shown in figure

13. A Gaussian curve having the same area as the

histogram giving the experimental data is also shown.

141
CERVIT

DISTANCE FROM MEAN SURFACE LEVEL (X) SLOPE (X/mm)

Figure 13. Height and slope distribution functions for a superpolished Cervit

optical flat obtained with the FECO Scanning Interferometer.

The smooth curves are Gaussians that have the same area under the curves as the measured

histograms.

LIGHT SCATTERED FROM COPPER MIRROR

2.0

I

C3

<

w 1.0

O SCATTEROMETER

OPT. EVAL. FAC.

[THEORY FOR 5 = 31A*

0.7 WAVELENGTH (Mm)

Figure 14. Scattered light as a function of wavelength for a

polished copper mirror.

The circles represent the hemispherical scatter measurements taken on the

facatterometer and the squares measurements taken on the Optical Evaluation

b acuity. The solid curve is the hemispherical scattering predicted by the scalar scattering theory.

The fit is quite good so that eq (3) can be used to

calculate the scattering level. Both glass and polished

metal surfaces examined thus far do have height

distribution functions that are nearly Gaussian [10],

although their autocovariance functions are strongly

non-Gaussian [10]. Figure 14 shows the light scattered from a polished copper mirror. The circles

represent data taken with the NWC Scatterometer

and the squares data that are taken with the Optical

Evaluation Facility. The agreement between the two

instruments is quite good. The solid line is the scattering level predicted by eq (3) for a 31 A rms

surface. Agreement here is also quite good.

The rms roughness of an optically flat surface can

be determined independently by using the FECO

Scanning Interferometer. A comparison of values for

polished glass surfaces [22] obtained from scattered

light measurements and FECO interferometry is given in table I. Agreement again is quite good.

For some polished metal samples the agreement

between FECO and scattered light measurements is not as good as that shown in table I. Reasons may

be that the surface is gently rolling with a long

autocovariance length, that optical excitation and

reemission of surface plasmons is occurring, that the

height distribution function is not quite Gaussian,

that contributions to scattered light are being made

by irregularities too small to be resolved by the

Table I. Comparison of rms roughness values of polished glass

surfaces obtained from FECO interferometry and from

scattered light measurements

Sample

o ^FECO (A)o ^SCAT (A)

TJLE Quartz 10. 2 8. 4

ULE Quartz 12. 6 9. 9

ULE Quartz 12. 7 12. 5 Fused Quartz 11. 0 10. 2 Fused Quartz 16. 7 16. 4

Fused Quartz 17. 3 17. 3 BK-7 Glass 19. 3 19. 1

142
FECO system, that a significant contribution to the

scattering process is being made by scratches, etc., or for some other as yet unsuspected reason. For

most optical surfaces, however, the agreement between predicted and actual scattering behavior m

the visible and ultraviolet regions based on eq. (3)

is excellent.

At infrared wavelengths the agreement between

experimentally observed scattering levels and those

predicted by eq (3) may be excellent or may be like

that illustrated in figure 15. The circles represent the

minimum scattering levels obtained from measurements at ten positions on an aluminized polished

dense flint glass sample. The bars represent average

values. The difference between the average and

minimum values is indicated by the square points.

Since an exponential becomes a straight line on

log-log paper, the predictions of eq (3) are represented

by the diagonal line. In the visible and ultraviolet

regions there is good agreement between experiment

and the theoretical predictions for a 29.5 A rms

surface. However, in the infrared the experimental

points begin to deviate from theory and approach a nearly constant value which coincides with the

variations from point to point on the surface. When

this surface was examined under a microscope using

oblique illumination, about 103 particles/mm2 were

observed as scattering centers as well as various

sleaks and scratches. We believe that the additional

infrared scattering observed on this sample resulted

from a change in dominant scattering mechanism

from microirregularities to scratches and particulates. Scattering from both particulates and scratches

should be nearly constant in the visible region where

both would be expected to have dimensions larger

than a wavelength. The variation from point to

point on the surface of this sample is an order of

magnitude less than the scattering caused by microirregularities, which suggests that scattering from

<

10-' -

ioAV-MIN SCATTERING

(103 particles/mm2

)

THEORY FOR 29 b m

-v

RMS ROUGHNESS X

9.5 X \

0.4 J I I I I I 1.0 2.0 4.0 WAVELENGTH (urn)

_l I I I l_ 10.0

Figure 15. Scattering from an aluminized polished dense

flint glass mirror.

The open circles are minimum scattering values obtained for 10 points across the

surface; averages of the 10 values are indicated by the crossbars. The open

squares are the differences between these average and minimum values. The

solid line is a fit to the minimum values and the straight dashed line gives

scattering levels predicted by eq (4).

scratches and particulates is negligible in the visible

and ultraviolet. However, with increasing wavelength microirregularity scattering decreases and the

scratch and particulate scattering becomes dominant.

The slight hump in the scattering curve shows

up even more prominently when the average deviation in scattering from this sample is plotted in

figure 16. A resonance would be expected for particulate scattering when the wavelength nearly equals

the particle diameter [4] as seen in figure 1. If the

particulate has an index of refraction of 1.5 and is not strongly absorbing, this resonance should occur

at a particle diameter to wavelength ratio of about

0.7 according to figure 1, or at a wavelength of 1.4

yum if a 1 iim particle diameter is assumed. The

observed resonance in figure 16 is in this wavelength range and may thus be caused by dust

particles on the mirror surface, which if largely

Si02 would have an index of about 1.5. That typical

dust particles in our laboratory have a diameter

of about 1 jum is shown by assembling the FECO

Scanning Interferometer. Dust particles are used as spacers and the minimum order of interference

which normally is possible is about 4, which would

correspond to a 1 diameter dust particle. From

these data we conclude that scattering from dust

and scratches may be important in the infrared,

but for good clean optical surfaces microirregularity

scattering is the dominant scattering mechanism

in the visible and ultraviolet wavelength regions.

B. Surface Plasmon Excitation

Microirregularities can give rise to scattered light

not only through classical diffraction but also through

surface plasmon excitation and reemission. This

mechanism also introduces additional absorption.

Figure 17 shows the near ultraviolet reflectance of

silver deposited on substrates of varying roughness.

A large increase in absorption with increasing roughness is observed at wavelengths slightly longer than

the limiting wavelength for surface plasmon excitation, which for silver occurs at about 3390 A where

1—i—i—i—

0.4

i

' I I 1—1-

1.0 2.0 4.0 WAVELENGTH lum)

i I I I l_10.0

Figure 16. Average deviation in scattering from 10 points on

the dense flint sample of figure 15.

Values obtained from same measurements as those shown in figure. 15.

143
ENERGY floi (eV)

WAVELENGTH X (A)

Figure 17. Normal incidence reflectance of silver for surfaces

of various roughnesses.

As the roughness increases the reflectance decreases.

ei=— 1. By subtracting the rough surface reflectance

from the smooth surface reflectance the additional

absorption introduced by the rough surface is obtained. The results for various surface roughnesses

are shown in figure 18. The absorption peak occurs between 3500 and 3550 A for this type of rough surface, which was produced by evaporating increasingly thick films of CaF2 on an initially smooth substrate. Roughness values are shown under each

absorption curve; the initial roughness of the fused

o quartz substrate was 12 A rms. A comparison of

roughness values for CaF2 -coated substrates as determined from light scattering measurements and

interferometrically is given in table II. The slightly

lower values obtained from FECO measurements for

the thicker CaF2 films probably result from contributions to scattered light by crystallites too small to

be resolved by the interferometer. The agreement

between these two independent measurement techniques is still quite good.

The shape of the absorption curve which would be

predicted if plasma excitation occurred at e x = — 1 is given by the dotted curve in figure 18. A silver

sulfide film only 9 A thick would be enough to cause

the observed shift in the resonance to longer wavelengths, but careful ellipsometric studies of the

growth of silver sulfide on silver [23, 24] have established that the observed shift does not result from

silver sulfide contamination. It probably occurs because the momentum required from the surface

to excite a plasmon at the limiting wavelength

would be much larger than that for plasmons in the

retardation region (see fig. 5).

The growth of a surface film such as Ag2 S on the

silver surface will move the plasma resonance to

longer wavelengths and, if the film is absorbing,

will damp it. Figure 19 shows the measured change

in plasmon-induced absorption of silver on a rough

surface as the sulfide film grows [23]. Sulfide film

thicknesses r were determined ellipsometrically. They

could also be computed from the shift in peak posiENERGY tiu (eV)

WAVELENGTH X (A)

Figure 18. Optical absorption by rough silver coaled surfaces

resulting from surface plasmon excitation.

The roughness value in A for each surface is given near the absorption peak.

The dotted line shows the expected position of the absorption peak if there were

no retardation effects.

Table II. Comparison of rms roughness values for superpolished optical flats coated with evaporated calcium fluoride

films of various thicknesses as determined from FECO inter- ferometry and scattered light measurements

CaF2 Thickness (A)

o ^FECO (A)

O 5scat (A)

0 11 10

875 12 13

1750 16 19

2625 19 26

3.8 ENERGY Jftw (eV)

3.4 3.0

i

1 1 1

1 r

WAVELENGTH X (A) Figure 19. Optical absorption by tarnished silver surfaces

resulting from surface plasmon excitation.

The r values give the thicknesses of the different silver sulfide tarnish films.

144
tion of the absorption resulting from changes in the

dispersion relation for a metal-thin film-air interface.

The average difference between the values of r

o obtained by these two techniques was only 1 A in

this case.

If the surface film is nonabsorbing, it not only

moves the absorption peak to longer wavelengths

but may also significantly enhance the absorption

by surface plasmons [25]. In figure 20 the solid line

represents the reflectance of silver deposited on a very smooth substrate and the circles and triangles

silver deposited on a slightly rough and moderately

rough substrate. When a 250 A thick film of A1 2 03 was deposited on the silver the slightly rough surface

had the reflectance indicated by the squares and the

moderately rough surface that indicated by the

diamonds. Not only do the reflectance minima move

to longer wavelengths but they are also greatly

enhanced. This effect is of considerable importance

for aluminized mirrors used in the vacuum ultraviolet. The protective MgF2 overcoat used to

prevent oxidation of the aluminum coating can

significantly reduce mirror reflectance above 1600

A through enhanced absorption by surface plasmons

unless the mirror surface is extremely smooth. A

similar effect is seen for silvered quartz back surface

reflectors. The mirror often has a golden appearance

because enhanced surface plasmon absorption re- duces the reflectance in the blue region of the

spectrum. By intentionally roughening the back

surface the reflectance of silver in the blue region

of the spectrum can be reduced nearly to zero. Although most of the increase in absorption observed on rough silver surfaces is found at wave1 1

- / /

1 I^J-o-K^)

$ /

J

±=b-0

- fffa

few

f X

i

i

[ *

\> V

/

i

i i

1 1 1 1

1 1 1 3200 3600 4000 4400 4800 WAVELENGTH X (A)

Figure 20. Normal incidence reflectance of slightly rough

(circles) and moderately rough (triangles) silver surfaces. The reflectances of the same surfaces after being coated with a 250 A thick layer

of AI2O3 are shown by the squares and diamonds, respectively.

lengths longer than the limiting wavelength for sur- face plasmon excitation, some increase in absorption

is also observed at shorter wavelengths. Figure 21

shows the increase in absorption extending from the

visible region into the vacuum ultraviolet. Also

plotted is a line proportional to the reciprocal of the

optical penetration depth. Although this line has no

apparent relation to the observed absorption to the

right of the surface plasmon limiting wavelength

\ sp it does fit that to the left of this wavelength rather

well. In particular it reproduces both minima jn the

ultraviolet reflectance data at about 1400 A and

3200 A. In addition, it has approximately the exponential dependence to the left of the volume plasmon

wavelength X 6 found experimentally by Hunderi and

Beaglehole [26] and verified by these measurements.

The magnitude of this additional absorption for

\<X(, for samples with varying degrees of roughness

is directly proportional to the ration between the

rms roughness and the penetration depth. The intensity penetration depth for Ag in the interband region

is about 150 A. A 20 A rms surface roughness will

have a peak to valley height of irregularities of 50 A

or more, roughly a third of the penetration depth.

Rougher surfaces will have irregularities which are an even larger fraction of the penetration depth. The

band structure of a material derives its character

from the regular crystalline array of the atoms. Modification of this array near the surface of the crystal

should modify the band structure of the material

somewhat. A possible explanation for this additional

absorption is that the surface roughness introduces a perturbation of the band structure at the surface of

the crystal where its optical behavior is determined.

Interband transitions would be expected to be

significantly affected by this perturbation, hence the

anomalous absorption in the interband region for

silver. Intraband transitions should be much less

affected, as appears to be true for silver in the free

carrier region.

ENERGY hu (eV)

10.0 6.0 4.0 3.5 3.0 2.5 2_0 15

Figure 21. Comparison of the roughness induced increase in

absorption at normal incidence for silver and the reciprocal

of the optical penetration depth.

Note the agreement in minima both at 3200 A and 1400 A.

145
0.030

5 0.020

o

Hi

ceLU

0.010

1 r

\

T T

\ 700A* MgF2

/ \ 1,200a* MgF2

THEORY

. SILVER

\ 150X MflF.

w

0.30 0.40 WAVELENGTH (microns)

0.50

Figure 22. The lo7ig-dashed curve is the wavelength dependence of the ratio of

the total scattered light to the incident light for a "rough" {21.5 A rms) silver surface calculated from scalar scattering theory. Other curves are the difference between measured values and the calculated curve; solid curve is for a bare silver surface, and other dashed curves are for silver surfaces coated with the indicated thicknesses of magnesium fluoride.

In addition to additional absorption, surface

plasmon excitations can also cause significant

increases in scattered light [18]. Figure 22 shows the

effect for silver deposited on a CaF2 -roughened substrate having 5=21.5 A. The scattering level calculated for this surface from equation (3) is shown by

the long-dashed line. The triangles and solid line

show the additional scattering which was observed

on the uncoated silver surface. When the surface

was coated with various thicknesses of MgF2 the

scattering level rose again and then declined as a re- sult of an interference effect. The peak scattering

level was over an order of magnitude higher than that

predicted from classical scattering theory for this

relatively smooth optical surface.

C. Mechanical Abrasion and Surface Damage

Figure 23 shows the decrease in reflectance of bulk

copper caused by mechanical abrasion [27]. Both

copper samples were cut from the same OFHC

copper block; one was electropolished, and the other

mechanically polished on a silk-covered pitch lap.

Both surfaces were optically flat and the electropolished data, which is in good agreement with other

optical measurements on high quality bulk copper

surfaces and copper films evaporated under good

deposition conditions, is representative of the intrinsic reflectance spectrum of copper. The mechanically polished surface has a reflectance spectrum

which differs in shape from that of the electropolished

sample and is lower by as much as a factor of two.

Differences in reflectance persist to 30 /xm in wavelength, the limit of the measurements, but are largest

in the visible and ultraviolet regions.

Germanium is an even more graphic example of

the importance of structure on the optical properties

of absorbing materials. In the visible and ultraviolet

region it is highly absorbing, strong interband transitions are occurring and the casual observer would

think it was a metal. Germanium can be deposited

in thin films either in a crystalline or an amorphous

state. The reflectance spectra for both cases [28] are shown in figure 24. It is not obvious from the

optical spectra that we are even dealing with the

same material. However, the amorphous film can be

recrystallized by annealing at high temperatures

and its reflectance curve then reverts to that for the

crystalline case. The crystalline structure of evaporated metal

films is quite complex and its effect on the optical

properties is a story in itself. Sputtered metal films are even more complicated and it has been believed

that the sputtering process is so uncontrollable that

the highest reflectance metal films could not be ob146
1.00

0.80

1 1 1 1

1 I 1 —|

1 [ 7—

1

i

--O

/ ^

-

\ y

J

/

/

/

/

/ J

f> & electropolished

/ o mechanically

S polished

f 1 J J

// -X/

/ / - y

i i i 1 1 1 1 1 0.4 0.6 0.8 1.0 WAVELENGTH X (microns)

Figure 23. Reflectance of electropolished copper (triangles)

and mechanically polished copper (circles) from 0.3 to 1.0 nm.

Both samples were cut from the same high-purity ingot.

UJ

or

0.70

' 4.399 ev 2.284 ev

1 1 2 .109 ev

-o o- ELECTROPOLISHED

SINGLE CRYSTAL

0.60 —a— -o- AMORPHOUS FILM

0.50 0-aD' 000—o\

\~°"-o- / \ \ 3&- \

No -a

0.40 1 1 1 1 1 1 1 0.3 0.4 0.5 0.6 0.8 1.0 WAVELENGTH, X (microns)

Figure 24. Reflectance of electropolished germanium (circles)

and an amorphous germanium film (squares) from 0.26 to 1.0 urn.

tained using it. Sputtered silver, aluminum, and

copper films have now been produced [29, 30] which

have essentially the same reflectance as those produced by evaporation.

The kind of difficulty which is typically found in

experimentally obtaining the theoretical optical

properties of overcoated metal films is illustrated in

figure 25. In this case an aluminum film was deposited

by evaporation and then overcoated with a lead

fluoride film [31]. The dashed line shows the refleco u i i i I I I I

i i i i i I 0.3 0.4 0.5 0.7 1.0 2.0 3.0 5.0 WAVELENGTH \ (microns)

Figure 25. Measured reflectance (solid curve) and calculated

o reflectance (dashed curve) for an 8869 A film of lead fluoride on aluminum.

The optical constants used in the calculations were determined from measure ments on evaporated films of the two materials.

tance spectrum which should have been obtained

based on the optical constants of the two .materials.

The solid line shows that actually obtained. The

difference is probably due in large part to the optical

excitation of surface plasmons. In aluminum the e l curve has a much more gradual shape than for silver,

and surface plasmon effects are thus important over

a much larger wavelength range. Other factors

(which probably were not important) were conventional scattering caused by particulates, and surface

roughness and structure-related conventional absorption in both the metal and the dielectric. Notice

that the discrepancy between predicted and actual

optical performance becomes larger as we go to

shorter wavelengths. This example is t3r pical of the

problems faced by the optical designer in the visible

and ultraviolet regions of the spectrum.

V. Conclusions

Surface irregularities and ciystalline order strongly

influence both light scattering and absorption of

metal surfaces. These effects are more pronounced

in the ultraviolet than at longer wavelengths. Although scattering from isolated irregularities such as dust, scratches and other surface blemishes occurs, it

is typically much less important for optically polished

surfaces in the visible and ultraviolet regions than

scattering from closely spaced microirregularities. In

addition to classical scattering from these microirregularities, which if polarization and angular dependence are ignored can be calculated from scalar

scattering theory, scattering resulting from surface

plasmon excitation and reemission can be very important. It is enhanced by a nonabsorbing dielectric

coating, and in limited wavelength regions can exceed

classical scattering levels by over an order of magnitude. Surface plasmon excitation also causes addi147
tional absorption, which is also enhanced by a dielectric coating. This effect is particularly important

in the vacuum ultraviolet where aluminum, for

example, must be coated with a nonabsorbing dielectric such as magnesium fluoride to prevent oxidation. Crystalline disorder at the metal surface introduces significant additional absorption, presumably

both through surface plasmon excitation and band

structure modification. For optimum optical performance of metal surfaces in the visible and ultraviolet regions of the spectrum it is thus essential

that they have an absolute minimum of surface

roughness and as undistorted a lattice structure as

possible.

VI. References

[1] Reuter, G. E. H., and Sondheimer, E. H., Proc. Roy.

Soc. (London) A195, 336 (1948) ; Sondheimer, E. H.,

ibid. A224, 260 (1954); R. B. Dingle, Phvsica 19,

311 (1953); R. B. Dingle, Appl. Sci. Res. B3, 69

(1953).

[2] Bennett, H. E., Bennett, J. M., Ashley, E. J., and

Motyka, R. J., Phys. Rev. 165, 755 (1968).

[3] van de Hulst, H. C, Light Scattering by Small Particles

(John Wiley and Sons, Inc., New York, 1957), p. 270.

[4] Orr, C, Jr., and Dallavalle, J. M., Fine Particle Measurement (The Macmillan Co., New York, 1959), p. 119.

[5] Kretschmann, E., and Kroger, E., J. Opt. Soc. Am. 65,

150 (1975); Maradudin, A. A., and Mills, D. L., Phys. Rev. Bll, 1392 (1975); Elson, J. M., Phys.

Rev. B12, 2541 (1975); Celli, V., Marvin, A., and

Toigo, F., Phys. Rev. Bll, 1779 (1975).

[6] Elson, J. M., J. 'Opt. Soc. Am. 66, 682 (1976).

[7] Davies, H., Proc. Inst. Elec. Engrs. (London) 101,

209 (1954).

[8] Bennett, H. E., and Porteus, J. 0., J. Opt. Soc. Am. 51,

123 (1961).

[9] Porteus, J. O., J. Opt. Soc. Am. 53, 1394 (1963).

[10] Bennett, J. M., Statistical Characterization of Mirror

and Window Surfaces, in Laser Induced Damage in

Optical Materials: 1974 (Nat. Bur. Stand. (U.S.),

Spec. Publ. 414, 157-162 pages (Dec. 1974).

[11] Teng, Ye-Yung, and Stern, E. A., Phys. Rev. Letters

19, 511 (1967).

[12] Jasperson, S. N., and Schnatterly, S. E., Bull. Am.

Phys. Soc. 12, 399 (1967); ibid. 13, 989 (1968);

Jasperson, S. N., and Schnatterlv, S. E., Phys. Rev.

188, 759 (1969).

[13] Stanford, J. L., Bennett, H. E., Bennett, J. M., Ashley

E. J., and Arakawa, E. T., Bull. Am. Phys. Soc. 13'. 989 (1968).

[14] See Ritchie, R. H., Surf. Sci. 34, 1 (1973) for a review of

this field. [15] Jackson, J. D., Classical Electrodynamics (John Wiley and Sons, Inc., New York, 1962)', p. 618.

[16] Ritchie, R. H., Arakawa, E. T., Cowan, J. J., and

Hamm, R. N., Phys. Rev. Letters 21, 1530 (1968).

[17] Elson, J. M., and Ritchie, R. H., Phys. Stat. Sol. (b)

62, 461 (1974).

[18] Bennett, H. E., Stanford, J. L., and Bennett, J. M.,

Scattering From Metal Surfaces Used in Space

Applications, in Space Optics (National Academy Sci.,

Washington, D.C., 1974), pp. 717-738.

[19] Bennett, H. E., Appl. Opt. 5, 1265 (1966).

[20] Bennett, H. E., and Bennett, J. M., Precision Measurements in Thin Film Optics, in Physics of Thin Films,

G. Hass and R. E. Thun, Eds. (Academic Press, New

York, 1967), Vol. 4, pp. 1-96.

[21] Bennett, H. E., and Koehler, W. F., J. Opt. Soc. Am.

50, 1 (1960).

[22] Bennett, J. M., (private communication)..

[23] Stanford, J. L., J. Opt. Soc. Am. 60, 49 (1970).

[24] Bennett, J. M., Stanford, J. L., and Ashlev, E. J., J. Opt. Soc. Am. 60, 224 (1970).

[25] Stanford, J. L., and Bennett, H. E., Appl. Opt. 8, 2556

(1969).

[26] Hunderi, O., and Beaglehole, D., Phys. Letters 29A, 235

(1969).

[27] Bennett, H. E., Influence of Surface Roughness, Surface

Damage and Oxide Films on Emittance, in Symposium

on Thermal Radiation of Solids (National Aeronautics

and Space Administration SP-55, Washington, D.C.,

1965), pp. 145-152.

[28] Donovan, T. M., Ashley, E. J., and Bennett, H. E.,

J. Opt. Soc. Am. 53, 1403 (1963).

[29] Bennett, J. M., Green, A. K., Burkardt, L. A., Ashley,

E. J., and Dancy, J. H., Effects of Deposition Techniques on Optical Properties, in High Energy Laser Mirrors

and Windows, Semi-Annual Report No. 6, Sep 1974-

Mar 1975, ARPA Order 2175 (Naval Weapons Center,

China Lake, California, 1975), pp. 5-23.

[30] Temple, P. A., and Burge, D. K., and Bennett, J. M.,

Optical Properties of Mirrors Prepared by Ultraclean

dc Sputter Deposition, in Laser Induced Damage in Optical Materials: 1976 Nat. Bur. Stand. (U.S.), in press.

[31] Bennett, J. M., Ashley, E. J., and Bennett, H. E., Appl. Opt. 4, 961 (1965).

(Paper 80A4-910)

148
Index of Key Words

Absorbance linearity

Absorption

Absorptivity

Accuracy

Acidic potassium dichromate solutions Actinometry

Aminocoumarins 33

Antibodies 95

Antigens 95

Bandwidth 99

Barium sulfate 75

Bi-directional radiometry 87

Biological polymers 95

Calibration of spectrophotometers

99,

121 Calorimetry 25

Lanopies 87

Carbazine dyes 33

Cathode-ray excitation 13 Chromatography 41

Color matching 41 Color measurement 41 Continuum models 57

Correction factors 21

Deuterium effect 33

Dielectric layers 133

Diffuse reflectance 41, 57, 75, 87

Diffuse reflectance spectra 57, 75

Diffuse reflectance standards 41, 75, 87

Diffuse transmittance 87

Errors in spectrophotometry

99,

115

Evaporated metal-on-quartz filters 127

Excited states 33

Fluorescence 1 Fluorescence lifetime 1 Fluorescence spectrum 1 Fluorescence standards 1

Immunochemical analysis 95

Interferences 99

Irregularities 133

Kubelka-Munk functions 41

Laser dyes 33

Light scattering 95

Liquid filters 121 Luminescence 13, 21, 25

Luminescence standards 13

Magnesium oxide 33, 75

Metallic thin films 133

Micro-irregularities 133

Molecular fluorescence parameters 1 Molecular structure 33

Multiple reflections 99

Neutral filters 127

Observed (technical) fluorescence parameters 1 Opal glass 75 Oxazine dyes 33

Overcoating 133

Phosphors 13

Photo-acoustic spectrometer , 25

Photometric linearity 99

Photometric scale . 113

Piezo-calorimeter 25

Plasmons 133

Polarization 1, 99

Polymers 95

Proteins 95

149
Quantum efficiency or yield 1. 13, 21, 25, 33

Quantum-flat actinometer 21 Quenching 33

Radiant efficiency 13, 21 Radiant flux 75

Radiative and non-radiative transition probabilities 1 Radiative transfer 37

Real fluorescence parameters 1 Reflectance (see diffuse reflectance)

Sample characteristics 99

Scatter 133

Scattering coefficients 57

Scattering surfaces 87

Semi-transparent metallic thin films

127,

133

Slit width 115

Solid standards 95

Spectral transmittance 115

Spectrophotometer standards 115

Standard Reference Materials 127 Standards calibration 75

Statistical models 57

Stray light

,99,

115

Technical (observed) fluorescence parameters 1 Thin layer chromatography 41 Transducers 25

Transfer standards 121 Transmittance filters 127 Transmittance characteristics 127

Triplet formation 25

UV absorbance standards 121 UV excitation 13 UV-visible filters 127

Wavelength accuracy 99

Wavelength scale 115

Xanthene dyes 33

X-ray excitation 13

150

ft U. S. GOVERNMENT PRINTING OFFICE : 1977 O - 236-905
NBS-TRA ire v. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS SP-466

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Standardization in Spectrophotometry and

Tj_i limn LiJii uicV) JtCJitc <z c e^T\ c I'lcaoQiTT*^Tn^7ii" ux CJiLCJi toq Pthppp^ i n (tc c\ ~f~ "f~ V» o y r i ULCCUlllto UJ. Lilt; Workshop Seminar held at NBS, Gaithersburg , MD,

Nov. 19-20, 1975

5. Publication Date May 1977

6. Performing Organization Code

7. AUTHOR(S)

K.D. Mielenz, R.A. Velapoldi R . Mavrndinpann e>r]*

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as 9.

13. Type of Report & Period

Covered

Final

14. oponsonng Agency Code

15. SUPPLEMENTARY NOTES

Library of Congress Catalog Number: 77-4739

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

This volume contains 15 papers presented at the Workshop Seminar on

Standardization in Spectrophotometry and Luminescence Measurements

organized by the Analytical Chemistry Division, Institute for Materials

Research, at the National Bureau of Standards, and held from November 19

to 20, 1975.

These papers discuss the problems encountered where accurate measurements

are required in the fields of luminescence quantum yields, diffuse

reflectance spectroscopy, and ultraviolet absorption spectrometry. They

also define the needs for standardization of measurements in these fields

and suggest materials that could be used as Standard Reference Materials.

Considerations on some applications of such standards in the field of

environmental pollution and health are included.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Accuracy; critical parameters; diffuse reflectance; fluorescence;

instrumentation; luminescence; quantum yield; spectrophotometry;

Standard Re fe r e nc e Mat e rials ;—standardization

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