NIST Measurement Services:

NATL INST. OF STAND & TECH R.I.C.

AlllDS M7blb7

M!ST

REFERENCE FUBUCATIONSlj

Spectral Reflectance

NIST

Special

Publication

250-48

P. Yvonne Barnes

Edward A. Early

Albert C. Parr

Optical Properties of Materials:

Bidirectional Reflectance Distribution Function

Directional - Hemispherical Reflectance Factor

Reflectance Standards:

First Surface Mirrors

Tiles and Polished Glasses

Diffusers and Pressed Powders

Wavelength Standards:

Rare-Earth Mixture

U.S. Department of Commerce

QC Technology Administration

jl OQ National Institute of Standards and Technology

U57

0.250-48

998
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'At Boulder, CO 80303. ^Some elements at Boulder, CO.
NIST MEASUREMENT SERVICES:

Spectral Reflectance

p. Yvonne Barnes

Edward A. Early

Albert C. Parr

Optical Technology Division

Physics Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-0001

March 1998

U.S. DEPARTMENT OF COMMERCE

William M. Daley, Secretary

Technology Administration

Gary R. Bachula, Acting Under Secretary for Technology

National Institute of Standards and Technology

Raymond G. Kammer, Director

/
National Institute of Standards and Technology Special Publication 250-48

Natl. Inst. Stand. Techno!. Spec. Publ. 250-48, 153 pages (Mar. 1998)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1998

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
PREFACE

The calibration and related measurement services of the National Institute of Standards

and Technology are intended to assist the makers and users of precision measuring

instruments in achieving the highest possible levels of accuracy, quality, and

productivity. NIST offers over 300 different calibrations, special tests, and measurement

assurance services. These services allow customers to directly link their measurement

systems to measurement systems and standards maintained by NIST. These services are offered to the public and private organizations alike. They are described in NIST Special

Publication (SP) 250, NIST Calibration Services Users Guide.

The Users Guide is supplemented by a number of Special Publications (designated as the

"SP250 Series") that provide detailed descriptions of the important features of specific

NIST calibration services. These documents provide a description of the:

(1) specifications for the services; (2) design philosophy and theory; (3) NIST

measurement services; (4) NIST operational procedures; (5) assessment of the

measurement uncertainty including random and systematic errors and an error budget;

and (6) internal quality control procedures used by NIST. These documents will present

more detail than can be given in NIST calibration reports, or than is generally allowed in

articles in scientific journals. In the past, NIST has published such information in a

variety of ways. This series will make this type of information more readily available to the user.

This document, SP250-48 (1998), NIST Measurement Services: Spectral Reflectance, is a revision of SP250-8 (1987). It describes the instrumentation, standards, and techniques

used to measure spectral reflectance over the ultraviolet, visible, and near infrared

wavelengths for Standard Reference Materials 2003, 2011, 2015, 2016, 2023, 2026, and

2044 and for Special Test 38060S. Inquiries concerning the technical content of this

document or the specifications for these services should be directed to the authors or to one of the technical contacts cited in SP250.

NIST welcomes suggestions on how publications such as this might be made more

useful. Suggestions are also welcome concerning the need for new calibration services,

special tests, and measurement assurance programs.

Peter L.M. Heydemann Katharine B. Gebbie

Director Director

Measurement Services Physics Laboratory

iii
ABSTRACT

This document describes the instrumentation, standards, and techniques used at the National Institute of Standards and Technology to measure spectral reflectance over

the ultraviolet, visible, and near infrared wavelength ranges. The organization is as follows. Part I describes the motivation for maintaining reference and transfer

spectrophotometers for spectral reflectance measurements, the basics of reflection, and

the standards and services that are available from NIST. Part II develops the necessary

theory of reflection, beginning with basic definitions and equations and ending with the

relevant measurement equations for the experiments described in this documentation.

The NIST Spectral Tri-function Automated Reference Reflectometer is described in

Part III. This instrument provides the basis for the development of absolute NIST

standards of diffuse and specular reflectance. Part IV describes the NIST transfer

spectrophotometers, high precision commercial instruments used for calibrating Standard

Reference Materials such as diffuse reflectance and specular reflectance standards. The

transfer instruments rely on master standards that are periodically calibrated on the high

accuracy reference reflectometer described in Part III. References containing details are reproduced in the appendices.

Key words: bidirectional; diffuse reflectance; reflectance; spectrophotometer;

spectrophotometry; spectral reflectance, specular reflectance

iv
TABLE OF CONTENTS

Abstract iv

1. Introduction 1

2. Theory 4

2.1 Basic Definitions and Equations 4

2.2 Measurement Equations 8

2.2.1 Bidirectional Reflectance Distribution Function 8

2.2.2 Directional - Hemispherical Reflectance 10

3. Reference Instrument - STARR 12

3.1 Description 12

3.1.1 Basic Instrument 12

3.1.2 Source System 14

3.1.3 Goniometer 16

3.1.4 Integrating Spheres 18

3.2 Calibration 20

3.2.1 Source System 20

3.2.2 Goniometer 21

3.2.3 Integrating Spheres 22

3.2.4 Detectors 22

3.3 Operation 22

3.3.1 Source System 23

3.3.2 Bidirectional Reflectance 23

3.3.3 Directional - Hemispherical Reflectance 28

3.4 Uncertainties 30

3.4.1 Introduction 30

3.4.2 Bidirectional Reflectance 31

3.4.3 Directional - Hemispherical Reflectance 37

4. Transfer Instruments - Spectrophotometers 40

4.1 Description 40

4.2 Calibration 42

4.3 Operation 44

4.4 Uncertainties 45

Acknowledgments 46

References 47

V
Appendix A: Sample Report of Test for Bidirectional Reflectance Distribution Function

Appendix B: Sample Report of Calibration for Spectral Reflectance

Appendix C: Sample Report of Test for 0°/45° Reflectance Factor

Appendix D: Sample Report of Test for 6°/Hemispherical Reflectance

Appendix E: NIST High Accuracy Reference Reflectometer - Spectrophotometer (copy

of Ref 1)

Appendix F: Establishing a Scale of Directional - Hemispherical Reflectance Factor I: The Van den Akker Method (copy of Ref. 23)

Appendix G: Reflection Properties of Pressed Polytetrafluoroethylene Powder (copy of

Ref 26)

Appendix H: Laboratory Intercomparison Study of Pressed Polytetrafluoroethylene

Powder Reflectance Standards (copy of Ref 27)

Appendix I: 45°/0° Reflectance Factors of Pressed Polytetrafluoroethylene (PTFE)

Powder (copy of Ref 28)

Appendix J: A Wavelength Standard for the Near Infrared Based on the Reflectance of

Rare-Earth Oxides (copy of Ref 29)

vi
LIST OF FIGURES

Figure 2.1 Geometry of incident and reflected elementary radiant beams 5

Figure 3.1 Schematics of the STARR instrument 13

Figure 3.2 Components and optical path of the STARR source 14

Figure 3.3 Goniometer system of the STARR instrument 16

Figure 3.4 Detection system on the goniometer of the STARR instrument 17

Figure 3.5 Integrating sphere of the STARR instrument 19

Figure 3.6 Sample mount of the STARR goniometer 24

Figure 3.7 Specular reflectance as a function of wavelength 27

Figure 3.8 45°/0° reflectance factor as a function of wavelength 27

Figure 3.9 BRDF as a fiinction of reflected angle at 632.8 nm 28

Figure 3.10 6°-hemispherical reflectance factor as a function of wavelength 30

Figure 4. 1 Integrating Sphere Assembly of the Lambda 19 42

Figure 4,2 Spectrum of wavelength standard 45

vii
LIST OF TABLES

Table 1 . 1 Available NIST Standard Reference Materials and Calibration

Services for spectral reflectance and wavelength standards 2

Table 3.1 Wavelength ranges of components used in the STARR source 15

Table 3.2 Wavelength ranges of detectors used in the STARR instrument 19

Table 3.3 Wavelengths of emission lines and absorption bands used to calibrate

the wavelength scale of the STARR instrument 20

Table 3.4 Relative sensitivity coefficients for bidirectional reflectance

measurements 32

Table 3.5 Relative expanded uncertainties (k = 2) for the bidirectional reflectance

of a white PTFE plaque 33

Table 3.6 Relative combined expanded uncertainties, in percent, (k = 2) for the

bidirectional reflectance of a white PTFE plaque 33

Table 3.7 Relative expanded uncertainties (k = 2) for the bidirectional reflectance

of a green tile 34

Table 3.8 Relative combined expanded uncertainties, in percent, (k = 2) for the

bidirectional reflectance of a green tile 34

Table 3.9 Relative sensitivity coefficients for 6° - hemispherical reflectance

measurements 38

Table 3.10 Relative expanded uncertainties (k = 2) for the 6° - hemispherical

reflectance of a PTFE plaque 39

Table 3.11 Relative combined expanded uncertainties {k - 2) for the 6° - hemispherical reflectance of a PTFE plaque 39

Table 4.1 Wavelengths of emission lines and absorption bands used to calibrate

the wavelength scale of the Gary 5E transfer spectrophotometer 43

Table 4.2 Wavelengths of emission lines and absorption bands used to calibrate

the wavelength scale of the Lambda 1 9 transfer spectrophotometer 43

Table 4.3 Standard uncertainties of spectral reflectance values for the transfer

spectrophotometers in the visible wavelength region 46

viii
1. Introduction

Spectral reflectance measurements provide important information about the

optical properties of many materials. NIST strives to provide the best possible standards

for diffuse and specular reflectance as well as special services and a research program to support the national requirements for these measurements. For this purpose, the Optical

Technology Division of NIST maintains a primary reference laboratory for spectral

reflectance with specialized instrumentation and trained personnel. This primary

laboratory is responsible for realizing the absolute scales of diffuse and specular

reflectance.

The Optical Technology Division has designed, built, and characterized a new

high-accuracy reference instrument for reflectance, designated the Spectral Tri-function

Automated Reference Reflectometer (STARR) [1]. The STARR instrument is devoted to the highest accuracy measurements such as those required for maintaining master

standards. It is designed to deliver greater measurement speed and accuracy, improved

mechanical stability, and higher optical throughput than the previous reference

instrument. The three functional operations of the STARR instrument are absolute

measurements of bidirectional, specular (regular), and directional - hemispherical

reflectance.

In support of the STARR instrument, two high-precision commercial

spectrophotometers with reflectometer accessories are maintained as transfer instruments

and are calibrated with primary reference standards from the STARR instrument.

Standards calibrated by the transfer instruments under commonly used spectral and

geometrical conditions are issued as Standard Reference Materials (SRMs) [2].

Reflectance standards available as of June 1997 are listed in table 1.1. Special

calibrations and tests are supplemental measurement services that are provided to the

optical radiation measurement community upon request and within the guidelines

outlined in the NIST Calibration Services Users Guide SP-250 [3].

In general, reflection is the process by which radiant flux (or power), incident on a

stationary surface, leaves that surface from the incident side without a change in

wavelength; spectral reflectance is the fraction of the incident radiant flux that is reflected

as a function of wavelength. A related quantity is the reflectance factor, which is simply

the ratio of the reflected radiant flux to the radiant flux that would be reflected by an ideal

diffuse sample irradiated and measured in exactly the same manner.

Reflectance is often categorized as specular or diffuse. For specular reflectance,

also termed regular reflectance, the angle of reflection is equal and opposite to the angle

of incidence. This is what occurs ideally with mirrors. For diffuse reflectance, the

radiant flux is reflected at all angles within the hemisphere bounded by the plane of the

sample, except in the direction of the specular reflection angle.

There are also directions assigned to the incident and reflected radiant fluxes. If

the radiant fluxes are confined within solid angles along fixed directions, the term

1
Table 1.1 Available NIST Standard Reference Materials* and Calibration Services for

spectral reflectance and wavelength standards

SRM

Number Description

2003

2011

2023

2026

2015

2016

2044

1920a

38060S

Specular reflectance standards

1st Surface Aluminum Mirror 5.1 mm diameter 250 nm to 2500 nm

1 St Surface Gold Mirror 5.1 mm diameter 600 nm to 2500 nm

2nd Surface Aluminum Mirror 5.1 mm diameter 250 nm to 2500 nm

Black Glass (NG-9) 5.1 mm diameter 250 nm to 2500 nm

Diffuse reflectance standards

Opal Glass 2.5 cm x 5 cm x 0.64 cm 400 nm to 750 rmi re-certification

Opal Glass 10 cm x 10 cm x 0.64 cm 400 nm to 750 nm re-certification

White Diffuser, SpectralonTM 51 mm diameter 250 nm to 2500 nm

Wavelength standards

Rare-Earth Mixture 5 1 mm diameter 740 nm to 2000 nm

Special test BRDF, Specular Reflectance, Reflectance Factor

' NIST Special Publication 260 "NIST Standard Reference Materials Catalog 1995-96" p. 107, March

1995.

"directional" is applied to the reflectance. On the other hand, if the radiant fluxes are in

all directions on the incident side of the sample, the term "hemispherical" is applied to the reflectance.

In terms of these concepts of spectral reflectance, NIST provides the following

types of spectral reflectance measurements:

1. Spectral bidirectional reflectance-distribution function (BRDF), which is the ratio of

the reflected radiance at a given angle to the incident irradiance from another given angle,

both angles being measured in the same plane. From this, the bidirectional spectral

reflectance and the bidirectional spectral reflectance factor can be calculated. Note that

the widely used 45°/0° reflectance factor (where the angle of incidence is 45° and the

angle of reflection is 0°) is a specific instance of the more general BRDF [4,5,6].

2. Spectral specular (regular) reflectance, which is the ratio of the reflected radiant flux

to the incident radiant flux, the reflection being without diffusion in accordance with the

2
laws of optical reflection. While this measurement is classified separately from BRDF, it

is actually another specific instance [4,5,6].

3. Spectral directional - hemispherical reflectance factor, which is the ratio of the total

reflected radiant flux to that reflected by a perfectly reflecting diffuser, the angle of

incidence being 6° from normal and the reflected flux being collected over the entire

hemisphere [4,5,6].

Spectral reflectance measurements on submitted samples are available at cost. Preliminary discussion with NIST staff is required before submission. When high

accuracy or a special geometry is required, the STARR instrument is used. The transfer

instrument provides most of the measurements unless they can be performed only by the

STARR instrument.

The STARR instrument can provide two conditions for spectral reflectance

measurements: bidirectional and directional - hemispherical. The spectral range is 200

nm to 2500 nm and the sample size that can be accommodated is 5 cm to 30 cm, square

or round. For bi-directional reflectance, the incident angle can range from 0° to 80°

within the horizontal plane, while any reflected angle in that same plane greater than 5°

from the incident beam can be achieved. Note that the incident and reflected angles can be adjusted to measure 45°/0° reflectance factors and specular reflectances. For

directional - hemispherical reflectance, a choice of integrating spheres allows incident

angles of 0° (specular component excluded) or 6° (specular component included).

The transfer spectrophotometers can provide several conditions for reflectance

measurements [7,8]. The minimum sample size is 2.5 cm, round or square, while the

maximum sample size is approximately 15 cm. The spectral range is 200 nm to 2500 nm. The specular reflectance of mirrors can be measured for a 6° angle of incidence only.

The angle of incidence is 6° for measuring both specular reflectance and directional - hemispherical reflectance. In addition, the directional - hemispherical reflectance can be

measured with the specular component either included or excluded.

3
2. Theory

2.1 Basic Definitions and Equations

This section is concerned with stating the basic definitions and deriving the

general equations which specify reflectance in terms of the beam geometry of both the

incident and reflected radiant flux. In the next section, these general equations are applied to the specific geometries used with the STARR instrument to determine the

corresponding measurement equations. The approach is based upon the concepts

presented in Ref. [9].

The derivation of the general equations begins by considering a relatively large area of reflecting surface irradiated by a well-collimated beam of incident radiation and

examining the radiation reflected from a point well within the irradiated area. Only the

geometry of this situation is considered, namely the spatial parameters of position and

direction of all rays. Other radiation parameters, such as wavelength, time, polarization,

and fluorescence, are not discussed in this section, although they may be important in

actual measurements of reflectance. Specifically, the wavelength and polarization

parameters are included in the next section.

Let radiant flux be incident on a surface from the direction {9„ (f\), within the

element of solid angle d<5Ji, as shown in figure 2.1. The total irradiated surface area is A-^. The portion of the incident radiant flux which strikes an element of area dA-, centered on

the point {x„ is denoted by d^j. The reflected radiance in the direction {0„ (})^ at the

point (Xf, which comes from dO^ is dZ^. In general, dL, is directly proportional to A0^,

so that

The factor of proportionality S will, in general, depend upon the location of the point at which the incident flux strikes, the location of the point at which the ray of radiance dZ^

emerges, and the directions, so that

This basic proportionality function S is called the bidirectional scattering-surface

reflectance-distribution function (BSSRDF), and is a property of the reflecting surface.

This treatment is completely general, with no simplifying assumptions other than

those of geometrical optics and ignoring all but spatial parameters. No assumption is made about the mechanism involved other than that there is some form of interaction

between radiation and matter by which some of the flux incident at (Xj, emerges as

reflected flux from (x^, y,), quantitatively expressed by the function S. To obtain more

tractable expressions, some simplifying assumptions will be made that will still cover a very wide range of the cases of interest.

di:, = 5 d0i . (2.1)

(2.2)

4
Figure 2.1. Geometry of incident and reflected elementary radiant beams.

A convenient flat surface is chosen as a reference plane to represent the reflecting

surface. Then the polar angles ^are angles from the reference-plane normal, and azimuth

angles ^ are angles from an arbitrary reference direction in the reference plane, as shown

in figure 2.1. Also, assume that the surface is uniformly irradiated over the entire part of

the area from which there is a significant contribution to the reflected flux at (jc^, y,), so

that the incident radiance depends only on direction,

L = Liea) . (2.3)

The incident flux d<Z>j on the element of area 6A^ is

dcZ>i = L -cosd: -do), -dA-

(2.4) = dE.-dA.

where dE^ is the incident irradiance and dca, is the solid-angle element which confines the

incident radiance. Summing the contributions to the reflected radiance at (x^, y^) from the

entire incident flux in the direction {6^, <!>) and within the solid-angle element da\ by

integrating eq (2.1) over the entire irradiated area yields

5
, (2.5)

Assume further that the scattering properties of the sample are uniform and

isotropic across the reference plane, so that the scattering function S does not depend on

the location of the point of observation {x„ y^, but still depends on the distance r between

(Xj, y^ and {x„ y). Equation (2.5) simplifies to

dL, = dE,-m,(lK,e,,(f>;) (2.6)

where

f,-\s{e„(l>-,e„(l>;,r)-M, (2.7)

and

r = [{x,-x^' + {y,-y^'r • (2-8)

Thus, for uniform irradiance over a large enough area of a uniform and isotropic

surface, the basic quantity that geometrically characterizes the reflecting properties of that

surface is the bidirectional reflectance-distribution function (BRDF) given by

m, (Ik, e„ (/>,) = dLX0, <k, <t>. i <dEie„ <^) . (2.9)

Note that the BRDF can have any value fi^om zero to infinity, and that real measurements

involve finite, rather than infinitesimal, intervals of the parameters, yielding average

values of BRDF over those intervals.

Reflectance p is the ratio of reflected radiant flux to incident radiant flux. From

conservation of energy, it follows that reflectance may have values only in the interval

from zero to one, inclusive. A general expression for reflectance can be written readily in

terms of BRDF. First, the element of projected solid angle d/2 is given by the product of

an element of solid angle do) with the cosine of the angle 6 between the normal to the

surface and the direction associated with 6.0), so that di7 = cos^ • dco. In general, the

radiant flux incident through a solid angle o>^ onto a surface element dA^ is

d0,^dA-\Lie,,(j>yda . (2.10)

Similarly, the flux reflected by the surface element dA into a solid angle co, is

6
(2.11)

Now, the reflected radiance into the solid angle o)^ is

LiO„ <!>;) = jdl,(^., (I>^ 0. (I>r\ Ed (2.12)

which, using eq (2,9), gives

m, (p:) = ld£i(^„ (!>:) -m, <i>., e„ </>:) . (2.13)

Expressing the incident irradiance in terms of the incident radiance in eq (2.13), eq (2.1 1)

becomes

d0 = AA-\ \m, (Ik, e,, <p:) me, (f^) d/3, • da . (2.14)

The general expression for the reflectance p of a surface with an arbitrary

configuration of beam geometry with respect to direction is obtained from the ratio of

eq (2.14) to (2.10),

^ \lfMA-A,^r)-m0iA)-^^i-d^r . (2.15)

The only condition placed upon up to this point is that it be uniform over a sufficiently

large area. If it is further specified to be uniform and isotropic within the incident beam,

the constant value of can be brought outside the integrals in eq (2. 15), leaving

Pi0,j,;0,,<p^) = i\/ o,)- l\fMJrAM-dnrda (2.16)

where

a = Ua

.

Reflectance factor R is the ratio of the radiant flux reflected by a sample surface to

that reflected by an ideal perfectly diffuse standard surface irradiated in exactly the same

way as the sample. For an ideal surface,

M0„(P,;0„^,) = \/n, (2.17)

so using eq (2.14) the ratio of reflected flux to ideally reflected flux is

7
d^r/d^Hd= — f

• (218)

Assuming, as before, that Zj is isotropic within the full solid angle of incidence <y„ can

be brought out of the integrals, leaving

i?(^i,^z>i;^„^zJ,) = (7://25A)- jj/r(^„^z>i;^„^zJ,)-d/2i-d/2, . (2.19)

2.2 Measurement Equations

2.2.1 Bidirectional Reflectance Distribution Function Measuring the BRDF of a sample is one of the primary functions of the STARR instrument. As shown in the

previous section, other quantities can be calculated from the BRDF. In particular, the

bidirectional reflectance dp is given by

dp(6^,<p.,O^,</>,) = M0„^,-A,A)-dO^ (2.20)

and the bidirectional reflectance factor R is given by

Ri0i,(/>^;O„(/>,) = n-fM,<Pi;0„(^,) . (2.21)

In addition, the BRDF as measured by the STARR instrument is also a function of

wavelength A and incident polarization a. Therefore, these two parameters are included

in/, yielding

= dl, (^i ,

^zJ. ; , ^zJ,

; A; 0-) / d£i (^. ,

^z), ; /I; 0-)

From eq (2.22), determining the BRDF of a sample for given values of the

parameters involves measuring both the incident irradiance dE, and the reflected radiance

dL^. The light source generates a uniform, collimated, monochromatic, linearly polarized

beam of cross-sectional area A^. To measure the incident irradiance, the sample is removed from the beam and the detector is positioned so that the beam underfills its field

stop. Therefore, all of the light in the beam is incident on the detector. To measure the

reflected radiance, the sample is placed in the beam at an angle 6^ between the direction of

the beam and the sample normal. The detector is then positioned a distance D from the

center of the illuminated area on the sample to the aperture stop, which has circular crosssectional area A^. Again, the field stop of the detector is underfilled by the image of the

illuminated area. The line joining the center of the illuminated area and the center of the

aperture stop makes an angle 0^ with the sample normal.

The signal Si(A,; d) from the detector recorded during the measurement of the

incident irradiance is given by

8
S;iA; a) - UX- a) dOiX; a) , (2.23)

where cr) is the responsivity of the detector to the incident flux d0j(A; d). Note the

explicit dependence of these values on the wavelength and polarization parameters. The

incident flux in terms of irradiance dE^{A,\ d) is given by

d(?i(/l;cT)-d£i(^;o-)-d4i, (2.24)

where d^j is the area of illumination. Therefore, using eqs (2.23) and (2.24), the incident

irradiance is

diE;{X;cj) =

'^'^^''^^

. (2.25)

Likewise, the signal S,{0,, (f>;, 0^, ^4; X', cr) from the detector recorded during the

measurement of the reflected radiance is given by

Sie,, ^- e,, (f)- A; d) = i?,(A; cr) d0Xd, 0,, A; a), (2.26)

where RX^^; cr) is the responsivity of the detector to the reflected flux d0Xdi, d„ ^'^

(7). The signal and flux now depend on the angles of reflection. The reflected flux in

terms of radiance dZ^^i, ^4' ^'^ cr) is given by

doie,, 4^- 0„ (t>- X; (J) = dix^i, (Ik, (I>.\ ^; o) • d^^ • ^ , (2.27)

where again dA-^ is the area of illumination and is the solid angle from the center of that area to the aperture stop of the detector, given by

Q^=\dQ, = A,-zQ^ejD' . (2.28)

Note the dependence of the reflected flux upon the angle of reflection 6,. Combining

eqs (2.26) to (2.28) yields the reflected radiance, given by

dX,W,^,;^„AU;<.) = ^if^^^-^-— (2.29)

The BRDF is simply the ratio of eq (2.29) to eq (2.25). The area of illumination

d/lj cancels, yielding

S-{a;(J) A^(/l;cr) ^^•cosfc'^

9
The regular reflectance p{0,, (f>;, 6„ (/);, A; o), for which the special conditions 65. = -6^ and

^4 = -<^, apply, is easily obtained from eq (2.30) by multiplying by the solid angle i?,, resulting in

. (2.3,)

2.2.2 Directional - Hemispherical Reflectance The other primary function of the

STARR instrument is to measure the directional - hemispherical reflectance of a sample.

This reflectance includes both the specular and the diffuse components of the reflection.

The sample to be measured is placed at a port of an integrating sphere. The incident

beam strikes the sample, and the signal from a detector at another port is measured. The

sphere is then rotated so that the beam strikes the sphere wall at the same angle at which

it struck the sample, and again the signal is recorded. The sample is then replaced by a sample with a known reflectance, and the procedure is repeated.

In the following, the subscript x refers to the sample with the unknown

reflectance, s to the sample with a known reflectance, and w to the wall of the integrating

sphere. For pairs of subscripts, the first member is the object that the incident beam is striking, while the second is the sample that is at the port. For example, the subscript ws

on a quantity refers to its value when the beam strikes the wall and the sample with the

known reflectance is at the port. All the quantities are functions of wavelength and

polarization, so this dependence is not shown explicitly in the following equations. For

any of the four measurements described above, the signal S is given by

(2.32)

where R is the responsivity of the detector and cZ> is the reflected flux.

For the four measurements that are used to calculate the reflectance of the sample,

the reflectances, in terms of the definitions from eq (2.15) and the signals from eq (2.32), are given by

0 S 1 Pws=— , (2.33) 0i,ws R 0i,ws 0 S 1 0. R 0 ' ^ ^ ^

1,WX WX 1,WX S 1 p = and (2.35) 0i,ss Rss 0i,ss p^^=-i^=^.— 0 S 1

. (2.36) 0 R 0. 1,XX TiX l.XX

10
Taking ratios for the signals measured with the samples with known and unknown

reflectances, eqs (2.33) to (2.37) become

y\x noA^ws S S R R O _ ^xx ^ws -"-wx -'*-ss i,wx 1^

/'wx /^ss "^wx "^ss ^xx ^^s ^i,xx l.WS

1,SS (2.37)

To solve for the reflectance of the sample, p^^, some assumptions have to be made in

order to obtain this value from eq (2.37). The reflectance of the wall must remain stable

during the two times when it is struck by the incident beam, so that = p^^. The

responsivity of the detector and integrating sphere must also remain stable over the course of the measurements, and additionally it must be independent of the sample, so

that R^ = /?xx '^ws ^ -^ss- Finally, the incident radiant flux must remain stable, both on

the wall and on the sample so that cZ> ^ = 0^^^ and 0^^^ = 0^^^, respectively. With these

assumptions, which are closely realized in practice, eq (2.37) can be solved for p^^, with

the result

Ax = Ass ws

ss

(2.38)

Converting from reflectance to reflectance factor, eq (2.38) becomes

= ^ss

• ws

ss

(2.39)

where R^^ and R^^ are the known and unknown reflectance factors, respectively.

11
3. Reference Instrument - STARR

3.1 Description

3.1.1 Basic Instrument The Spectral Tri-function Automated Reference Reflectometer

(STARR) is designed to perform absolute spectral measurements of bidirectional,

specular, and directional - hemispherical reflectance [1]. The instrument, consisting of a

source, goniometer, integrating sphere, and detectors, is located on a vibration isolation

table in the center of a light-tight room with black walls and ceiling and special air filters in the room ventilation system. A schematic of the instrument is shown in figure 3 . 1 (a)

with all the major components labeled. A computer is located in an adjacent room and is interfaced to the data acquisition and control electronics and devices to provide fully

automatic operation of the instrument.

The source of the incident radiant flux provides a collimated, monochromatic

beam of light with a known polarization over a spectral range of 200 nm to 2500 nm. The goniometer positions the sample and the detector for measurements of bidirectional

reflectance. The sample holder on the goniometer centers the face of the sample on the

axis of rotation, which is perpendicular to the plane of the paper in figure 3.1(a). The

goniometer varies the angle of incidence from 0° to 80°, and the sample can be translated

in two orthogonal directions perpendicular to the direction of the incident beam. The

detector on the goniometer rotates on the same axis of rotation as the sample to measure

both the incident and the reflected radiant flux, which is shown schematically in

figures 3.1(b), and 3.1(c), respectively. The absolute reflectance can be calculated from

the measured fluxes as detailed in the previous section. The reflected angle can have any

value greater than 5° from the incident beam.

Two integrating spheres are used for directional - hemispherical reflectance

measurements [10,11,12]. One sphere is used for an incident angle of 0°, while the

incident angle of the other sphere is 6°. For both spheres the sample is mounted at a port

opposite the entrance port of the sphere. The integrating spheres collect the reflected

radiant flux over nearly the entire hemisphere, and a portion of this flux is measured by a

detector attached to the sphere. The incident beam geometry for these measurements is shown in figure 3.1(d). By measuring pairs of signals, the reflectance of the sample can

be calculated as detailed in the previous section.

12
Figure 3.1. Schematics of the STARR instrument showing top views

of the major components (a) and the geometrical

arrangements for measuring the incident directional flux

(b), the reflected directional flux (c), and the reflected

hemispherical flux (d). The conventions for the incident

and reflected angles are also shown in (c).

13
3.1.2 Source System The source system consists of an illuminator, a monochromator, a

limiting aperture, a collimator, a chopper, and a polarizer. The components of the source,

as well as the optical path, are shown in figure 3.2.

Monochromator

Filter Wheel

Flat Mirror

Chopper Parabolic Mirror

Figure 3.2. Top view of the components and optical path of the source of radiant flux for the STARR instrument.

The lamp housing contains two sources. A 150 W ultraviolet-enhanced xenon arc (Xe) lamp is used for ultraviolet wavelengths from 200 nm to 400 nm, and a 100 W

quartz-tungsten-halogen (QTH) lamp is used for visible and infrared wavelengths from

400 nm to 2500 rmi. Each source is operated by a separate regulated power supply used

in conjunction with a light intensity controller to reduce the effects of electronic

fluctuations and lamp aging. The operating conditions for each power supply are set manually. The Xe lamp is monitored by a light intensity controller equipped with a UV

bandpass filter to optimize the stability in this spectral range. The QTH lamp is monitored by another light intensity controller. A concave collection mirror in the lamp

housing rotates to select either of the two lamps and focuses the radiant flux from the

lamp through a filter onto the entrance slit of the monochromator.

The lamp housing is attached to the monochromator with a five-position filter wheel assembly. This filter wheel contains a series of cut-on (long-pass) filters which are used for order-sorting to eliminate higher-order wavelengths from passing through the

monochromator. The 1/4 mjl?>.9 monochromator has a four-grating turret equipped with

14
three 600 lines/mm ruled gratings blazed at 200 nm, 400 nm, and 1000 nm, and a 150 lines/mm ruled grating blazed at 4000 nm. This last grating is not used on a regular

basis, but is reserved for future upgrades into the mid-infrared spectral region. The

monochromator also has an internal shutter for blocking the beam of light for darkcurrent measurements. The filter wheel, shutter, and grating turret are controlled by the

monochromator microprocessor. The proper filter and grating for a given wavelength are automatically selected based on information stored in the monochromator non-volatile

memory. The wavelength ranges covered by the various lamps, filters, and gratings are

listed in table 3.1. The radiant flux exits the monochromator through a 1 mm circular

aperture. The fuU-width-at-half-maximum spectral bandwidth is 7 nm for a 1 mm wide

entrance slit and 10 nm for a 2 mm wide slit using the grating ruled at 600 lines/mm.

Table 3.1 Wavelength ranges of components used in the STARR

source

Component Wavelength range [nm]

Lamp

Xenon arc 200 to 400

Quartz-tungsten-halogen 400 to 2500

Filter

#1, no filter 200 to 350

#2, 309 nm cut-on 350 to 550

#3, 495 nm cut-on 550 to 900

#4, 780 nm cut-on 900 to 1 600

#5, 1 600 nm cut-on 1 600 to 2500

Grating

#1, 200 nm blaze 200 to 500

#2, 400 nm blaze 200 to 1 600

#3, 1 000 nm blaze 600 to 2500

The radiant flux exiting the monochromator passes through a baffle and is incident on a 51 mm diameter 15° off-axis parabolic mirror. The flux is collimated into a beam by this mirror and is then directed by a 51 mm diameter flat mirror through the

remaining components of the source system. The collimated beam has a diameter of

approximately 14 mm and a divergence of less than 1°. Both mirrors are mounted on

three-axis high-resolution angular orientation holders with precision micrometers. The

optical chopper is used at infrared wavelengths when a phase-locked signal is required for a sufficient signal-to-noise ratio. A Glan-Taylor polarizer is used to obtain linear

polarization of the beam either perpendicular (s) or parallel (p) to the plane of incidence.

15
The polarizer is automated and computer controlled. The beam passes through a final

baffle before exiting the source system.

3.1.3 Goniometer The goniometer used to position the sample for bidirectional

reflectance measurements has four independent positioning stages. A mechanical

drawing of the goniometer, showing the sample holders and detector, is shown in

figure 3.3. The sample holder, designed and manufactured by NIST, is attached to a twoaxis linear positioning system. This positioning system is used to center the sample in the

incident beam, raster-scan the sample, and position the sample out of the path of the beam

when making a measurement of the incident beam radiant flux.

Rotary

Stages

^^^^^^^^^^^^^^^^^^

Figure 3.3. Front view of the goniometer system of the STARR

instrument showing the sample holder, stages, and

detector mount.

The linear positioning system is mounted on a rotation stage used to rotate the

sample with respect to the incident beam. In figure 3.3, the axis of rotation is in the plane

of the paper. The relatively thin profile of the sample holder and positioning system

gives the goniometer a range of incident angles from 0° to 80° while maintaining

mechanical rigidity. The detector system is attached to a light-weight rigid arm which is mounted on a second rotation stage. This second rotation stage is independent of and

coaxial with the sample rotation stage. This allows the detector to rotate around the

sample holder at a constant distance of 672.6 mm from the sample rotation axis to the

solid-angle limiting aperture. These two rotation stages are precisely aligned, which was

16
achieved through high precision machining of a heavy-duty stainless steel chassis. The

resolution and repeatability of the rotation stages are 0.001° and 0.01°, respectively. All

four stages are fitted with servo motors controlled by a four-axis motion controller

interfaced to the computer.

A drawing of the detector system and the optical path for reflected radiant flux is shown in figure 3.4. The detector system consists of a precision circular aperture, a fused

silica lens with a focal length of 150 mm, and several stray-light reducing baffles

mounted in a 5 1 mm diameter cylindrical housing with the detector mounted at the end.

Two precision apertures, one 31.85 mm in diameter and the other 44.42 mm in diameter, can be manually interchanged. For measurements of the incident radiant flux, which is in a collimated beam, the precision aperture is underfilled and the lens converges the beam

so that the detector is also underfilled. For measurements of the reflected radiant flux, the

precision aperture is the aperture stop and defines the collection solid angle, and the

detector is the field stop. The entire image of the incident beam upon the sample is within the field of view of the detector system for incident angles as large as 60°.

Lens Detector

1 \

I i A

Precision Aperture Baffles

Figure 3.4. Cross-section of the detection system on the goniometer

system of the STARR instrument.

Three detectors are manually interchangeable and mounted at the end of the

cylindrical housing, allowing the detectors to be changed without needing to re-align the

system. A uv-enhanced silicon (Si) photodiode, with dimensions 10 mm by 10 mm, is used for the spectral range of 200 nm to 1 1 00 nm. A germanium (Ge) photodiode

thermoelectrically cooled to -20 °C mounted on a 38 mm diameter integrating sphere

coated with polytetrafluoroethylene (PTFE) is used for the spectral range of 800 nm to 1600 nm. The flange surrounding a 10 mm diameter entrance port of the integrating

sphere fits into the end of the cylindrical housing. This same integrating sphere and

thermoelectric cooling is used with an indium arsenide (InAs) photodiode for the spectral

range of 1000 nm to 2500 nm.

The output current of the detector is converted to a voltage using a low-noise

transimpedance amplifier. The output voltage of this amplifier is measured directly by a

17
seven and one-half digit digital voltmeter for the Si and Ge detectors. For the InAs

detector, the incident beam is chopped and the output voltage is measured with a lock-in

amplifier. The output signal of the lock-in is measured with the voltmeter.

3.1.4 Integrating Spheres Two separate integrating spheres are used to measure

directional - hemispherical reflectances. Both integrating spheres are constructed of

aluminum, have diameters of 30 cm, and are lined with a 10 mm thick coating of PTFE to a density of 1 g/cm^ The spheres have 50.8 mm diameter sample ports, 38 mm diameter

entrance ports, and 48 mm diameter detector ports. A cross-section of one of the spheres

is shown in figure 3.5. The two spheres are identical except for a difference in the fixed

angle at which the incident beam strikes the sample. In one sphere, the incident angle is 0°, so that the specular component of the reflected flux is excluded by the detector. In the

other sphere most of the specular component is included in the measurement since the

incident angle is 6°. Both spheres are mounted on a rotation stage so that the entrance

port is centered on the incident beam and placed on the axis of rotation. Rotations of the

spheres about this axis allow the incident beam to alternately strike the sample and the

sphere wall.

The sample is pressed against the outside of the sample port and supported by

adjustable tabs, and then secured with a spring-type clamp. The surface of the sample is located slightly inside the radius of curvature of the internal surface of the integrating

sphere to allow as much of the diffusely reflected flux as possible to be included in the

measurement. The incident beam has a diameter of 20 mm when it illuminates the

sample. The area of the integrating sphere illuminated by the incident beam is built up so

that direct reflection of the flux to the sample port is prevented.

The detector port is located 90° from the entrance and sample ports. Direct

reflections from the sample to the detector are prevented by a collar, coated with PTFE, at the detector port, as shown in figure 3.5. The appropriate detector for the spectral range

is mounted at the detector port. The same Si and Ge detectors that are used with the

goniometer are used with the integrating spheres. For longer wavelengths, a liquid

nitrogen cooled indium antinomide (InSb) detector is used for the spectral range 900 nm

to 2500 nm. As with the goniometer, the output currents of the Si and Ge detectors are amplified and measured by the voltmeter. The chopper is used with the InSb detector, so

the lock-in is also included in the detection circuit. A summary of the spectral ranges of

the detectors used for the different reflectance configurations is given in table 3.2.

18
Detector

Figure 3.5. Cross-section of the integrating sphere used for 6° - hemispherical reflectance measurements with the STARR

instrument.

Table 3.2 Wavelength ranges of detectors used in the

STARR instrument

Detector Wavelength range [nm]

Bidirectional reflectance

Si 200 to 1100

Ge 800 to 1700

InAs 1200 to 2500

Directional - hemispherical

reflectance

Si 200 to 1100

Ge 800 to 1700

InSb 900 to 2500

19
3.2 Calibration

3.2.1 Source System Wavelength calibration consisted of comparing the wavelength

indicated by the monochromator to the true wavelength. This was accomplished by

measuring the emission lines of spectral line sources [13,14] and the absorption bands of

some materials [15,16]. These emission lines and absorption bands are listed in table 3.3.

A low-pressure emission line lamp was mounted in place of one of the lamps in

the lamp housing, and the detector on the goniometer arm, either Si or IilA^s, was rotated

to intercept the beam emerging from the source. The monochromator was scanned

through the wavelength regions of the emission lines of the lamp and the signal was

recorded at small wavelength intervals. This was repeated for all the emission lamps

listed in table 3.3. Likewise, the absorption band materials were mounted in the beam

emerging from the source, and scans of the monochromator were performed as before.

Table 3.3 Wavelengths of emission lines and absorption bands used to calibrate the

wavelength scale of the STARR instrument

Source Wavelength [nm]

Emission lines

Hg 253.65, 334.15, 435.83, 546.07, 1014.0,

1529.5

He 587.56,667.81

Cd 508.58, 643.85

Absorption bands

Polystyrene (0 . 6 mm) 2 1 44

1 ,2,4-trichlorobenzene (0.5 mm) 1 660.6, 2 1 52.6, 2494

Didymium glass (6 mm) 1 067

The indicated wavelength of the monochromator was given by the centroid of the

resulting signal. The difference between the indicated wavelength and the true wavelengths of the emission lines and absorption bands was used to correct the indicated

wavelength and thereby calibrate the wavelength of the monochromator. The standard

uncertainty in wavelength from this calibration was 0.1 nm at ultraviolet and visible

wavelengths and 0.5 nm at infrared wavelengths.

The stray radiation present in the monochromator was determined by filling the

entrance slit with the light from a HeNe laser operating at 632.8 nm. The emerging beam

was again incident on the Si detector, and the signal was recorded as the wavelength was

scanned. The fraction of stray radiation decreased from approximately 80 x 10"^ at

20
600 nm to 0.5 x 10'^ at 400 nm. A similar level of stray radiation was found at wavelengths longer than that of the laser and using methods with filters [17,18].

The stability of the Xe source was measured with the beam emerging from the source incident on the Si detector. Signals from both the beam and background were measured at wavelengths from 200 nm to 400 nm for 30 min. The relative standard

deviation of the net signal was 0. 1 percent over this time. A similar measurement was

performed with the QTH lamp at visible and infrared wavelengths using the Si and Ge

detectors, and the relative standard deviation of the net signal varied from 0.01 percent to 0.02 percent.

3.2.2 Goniometer Calibration of the goniometer involved aligning the sample holder

and incident beam with the axis of rotation. The axes of the two rotation stages were machined to be aligned by the hardware that mounts them to the optical table. Likewise,

the sample holder was designed and machined so that the front surface of the sample is vertical and coplanar with the axis of rotation.

To align the horizontal position of the sample holder on the axis of rotation, an

alignment jig with a cross-hair at the center was mounted in the sample holder. An

alignment telescope viewed the jig, and the horizontal position of the sample holder was

adjusted so that the cross-hair did not translate upon rotations of the sample holder. The

center of the sample holder was positioned on the axis of rotation to within 0. 1 mm.

The incident beam was centered on the axis of rotation and made normal to the

sample in several steps using an alignment mirror mounted on the sample holder. For

alignment in the vertical plane, the tilts and translations of the source mirrors were

adjusted until the beam was retroreflected from the alignment mirror. The translations of

the source mirrors in both the vertical and horizontal planes were adjusted to center the

beam on the alignment mirror. Finally, the rotation of the alignment mirror was adjusted

using the sample rotation stage so that the incident beam was retroreflected, which set the zero for the angle of incidence within 0.1°.

The area of the aperture stop of the detector system was determined using the

NIST High Accuracy Aperture Comparator [19], and has an assigned relative standard

uncertainty of 0.05 percent. The distance from the sample to the aperture stop was

measured using a precision inside-micrometer. This distance was measured at five

different detector arm angles at 45° intervals and varied by less than 0.1 mm.

The zero of the detector rotation stage was set by centering the detector system on

the incident beam. An alignment mirror was then placed in the sample holder and rotated

to retroreflect the incident beam. The sample holder was rotated in 10° steps and the

detector was positioned to the appropriate angle to intercept the specular reflection of the

beam. The distance from the center of the detector to the center of the reflected beam was

measured for each angular setting. This procedure was repeated several times. The

largest measured displacement of the beam from the detector center was 1.0 rrmi,

corresponding to an angle of 0.1° at the distance from the sample to the receiver.

21
3.2.3 Integrating Spheres Calibration of the integrating spheres simply required that

the incident beam be perpendicular to the entrance port of the sphere, pass through the

center of this port upon rotation of the sphere, and strike the center of the sample port at the correct angle. The angle of incidence was set by designing the center of the sample

port to be at an angle of either 0° or 6°, in the horizontal plane, from the diameter of the

sphere passing through the center of the entrance port. The mount for the sphere was

designed so that the entrance port was centered on the axis of rotation. Using translations

and rotations of the sphere, the incident beam was centered on both the entrance and

sample ports using cross-hairs at these ports and aligned perpendicular to the entrance

port by retroreflecting the beam with a mirror over this port. The alignment was checked

by rotating the sphere and verifying that the incident beam struck the correct portion of

the sphere wall.

3.2.4 Detectors The linearity of the detectors was determined using a combination of

multiple apertures and neutral density filters [20,21]. A double aperture mechanism

consisting of two adjacent semicircular apertures, each with its own shutter, was placed in

the sample holder and positioned such that both apertures were overfilled by the incident

beam. The signal due to light passing through aperture "A" was measured and designated

V^. The signal due to light passing through aperture "B" was measured and designated

Vq. Finally, the signal due to light passing through both apertures simultaneously was

measured and designated V^. A neutral density filter was then used to attenuate the

beam, and the above measurement sequence was repeated. This process continued using

successively higher density filters until the attenuated beam could no longer be measured.

These measurements were repeated at several wavelengths. The data were analyzed to determine at what signal level the relationship Vf^+ V^= was no longer satisfied to within the uncertainty of the measurement. For all detectors, it was found that the above

relationship was satisfied until the noise floor of the detector system was reached.

Therefore, the nonlinearity of the detectors was significantly less than 0.01 percent.

Since the Si detector is used without an integrating sphere, its response uniformity

was measured in the NIST Detector Comparator Facility [22]. The response uniformity

of the other detectors was not determined since they use an integrating sphere. The peakto-valley nonuniformity of the Si detector was as high as 1 percent at 1000 nm and

0.6 percent at 250 nm. However, comparing the areas of the detector illuminated by the

incident and reflected beams, the effect of these nonuniformities is less than 0.01 percent

for the STARR instrument. The nonuniformity would contribute uncertainty only for

measuring samples with a significant nonuniform spatial distribution of reflected radiant

flux, which was not a measurement that the system was designed to perform.

3.3 Operation

Determining the reflectance of a sample requires several steps, namely setting up

the source and detection systems, aligning the sample, and performing the measurements.

Since the source system is common to both the goniometer and the integrating spheres, its setup is described first, followed by descriptions of the setup and operation for the two

types of reflectance measurements. Samples are usually measured in batches, i.e. several

22
samples of the same type are measured in sequence. Therefore, the instrument setup is performed once prior to the batch run, and then the samples are measured. The spectral

range of the measurement determines the lamp and detector combination. In some cases, more than one of either may have to be used.

3.3.1 Source System Setting up the source system first involves checking the

wavelength calibration of the monochromator. As described in section 3.2 above, the

wavelength is calibrated using the spectral lines of emission lamps. If there is an obvious

discrepancy between this wavelength calibration and the one stored in the computer

program, the new wavelength calibration is stored in memory and used in the program

that operates the instrument.

The lamp appropriate for the spectral range of the measurement is turned on, the

mirror in the lamp housing is turned to the appropriate position, and the lamp is allowed

to warm up for at least an hour. The power to the lamp is adjusted manually to 1 50 W for

the Xe arc lamp and 96 W for the QTH lamp. The grating is observed during the warm

up period to verify that it is fully illuminated by the lamp.

3.3.2 Bidirectional Reflectance In most cases the sample, whether measuring diffuse or specular reflectance, is mounted in a holder. The sample holder attaches to the sample

mount of the goniometer, shown in figure 3.6. The top bracket is attached to two parallel

rails, allowing it to adjust vertically. When the sample holder is in place, the weighted

top bracket pushes down on the holder and keeps it in place.

A similar holder with a glass plate, scribed with a cross-hair at the center is used

to align the sample holder and the goniometer. This holder is referred to as the alignment

jig. The jig is placed in the sample mount and adjusted so that the center is on the axis of

rotation, shown in figure 3.6. The holder is designed so that the front of the sample, and

hence the front of the glass plate of the alignment jig, is in the plane indicated in

figure 3.6. With the incident beam striking the alignment jig, the two linear translation

stages of the goniometer are adjusted so that the cross-hair of the jig is centered in the

beam to within 0.2 mm. The absolute positions of these stages are recorded by the

computer program to set the position of the center of the sample. Next, the rotation stage

attached to the sample mount is adjusted so that the retroreflected beam returns to the exit

slit of the monochromator to within 0.1°. The absolute position of this stage is recorded

to set the position of zero rotation for the sample. The position of the alignment jig in the

sample mount is indexed appropriately, the jig is removed, and a sample is put in its place. Using these techniques, the front of the sample is placed on the axis of rotation to within 0.1 mm.

The alignment procedure for the detector is as follows. Using the linear stage, the

sample is translated horizontally until the incident beam is clear of the sample and falls on the detector. This position of the linear stage is also recorded by the computer. Then,

the detector and front baffle tube are removed from the cylindrical housing. An

alignment jig is placed over the front of the housing and the position of the housing is adjusted using tilt and translation stages and the rotation stage attached to the housing so

23
Figure 3.6. Sample mount of the STARR goniometer.

that the incident beam falls on the centers of both the alignment jig and the hole for the

detector. The absolute position of the rotation stage is recorded to set the position of zero

rotation for the detector. The front baffle tube and detector are reattached to the housing.

The operating parameters for the detector are determined prior to the

measurements. With the incident beam falling on the detector, the signal is monitored at selected wavelengths in the spectral range of the measurement. The gain on the

transimpedance amplifier is adjusted so that the maximum signal is less than 1 1 V. The

number of power line cycles of the voltmeter, either 1 0 or 1 00, and the number of voltage

readings recorded by the computer, between 3 and 20, are determined so that the standard

deviation of the signal is less than 0.0002 V. The same parameters are used for all the

measurements of the samples in the batch. The incident and reflected angles and

wavelengths are entered in the computer program.

Since the incident beam, sample normal, and measured reflected beam are all in

the same horizontal plane, the azimuth angles (t\ = (f)^ = Q dUQ not included in the following

equations. From eq (2.29), assuming the responsivity of the detector remains constant

24
over the time period of the measurement, the BRDF for a fixed linear polarization of the

incident beam is given by

(3.1)

where ^ is the incident angle, 0^ is the reflected angle, A is the wavelength, a is the

polarization, is the signal from the incident radiant flux, is the signal from the

reflected radiant flux, D is the distance from the sample to the aperture stop, and is the

circular area of the aperture stop. Defining the geometrical factor by

a^ = A,- COS0,/ (3.2)

simplifies eq (3.1) to

/,(.,;.,.;.) = ^fff).-L. (3.3)

The BRDF of unpolarized light is given by the average of the BRDFs obtained for

the two orthogonal polarizations of the incident beam, denoted by s and p, so that

fMA-^^) = \[f:i0rA-^^-,^) + fM-A-,^-,p)] (3.4)

Note that the reflectance p is given by

P=a-fr (3.5)

and the reflectance factor R is given by

R-n-f,. (3.6)

From eqs (3.3), (3.5), and (3.6), measurements of BRDF, reflectance, and

reflectance factor require measurements of the signals from the incident and reflected

radiant flux. Net signals are used in all the calculations, and are the signal obtained with

the shutter on the monochromator closed (i.e. no light from the source) subtracted from

the signal obtained with the shutter open. For fixed incident and reflected angles,

wavelength, and polarization, the following measurement sequence is performed. The

sample is horizontally translated out of the path of the incident beam, the detector is rotated into the path of the incident beam, and the net incident signal is measured. The

sample is then translated into the incident beam and rotated to the appropriate incident

angle, the detector is rotated to the appropriate reflected angle, and the net reflected signal

S, is measured. The net incident signal is measured again, and the two values are averaged to obtain the final incident signal.

25
The signals, together with the distance, area, and angle, are used in eq (3.3) to calculate BRDF, from which the reflectance and reflectance factor can also be calculated

by using eqs (3.5) or (3.6), respectively. Equation (3.3) assumes that the source is a

point, while in fact the beam has a diameter of at least 14 mm on the sample. Therefore,

eq (3.3) is modified to account for the actual projected area of the incident beam on the

sample for each angle of incidence.

In terms of a nested loop structure, the measurement sequence for the signals

described above is the irmermost loop. The next outer loop varies the reflected angles,

the next loop the incident angles, the next loop the wavelengths, and the outermost loop

the polarization. The spatial uniformity of BRDF can be determined for = 0 by raster scanning the sample. The loop that translates the sample horizontally and vertically occurs between the loops controlling the incident and reflected angles.

The performance of the instrument is checked by measuring the BRDF of check

standards similar to the type of sample under test. The number of times a check standard

is measured depends upon previous experience with the samples measured in the batch.

If similar samples have been measured previously, the check standard is measured only

once. Otherwise, the check standard is measured both before and after the samples of the

batch have been measured. The check standards are porcelain enamel on steel, a Russian

opal, difftise aluminum, and pressed PTFE.

Representative reflectances are plotted in figures 3.7 to 3.9. The specular

reflectances of various mirrors as a function of wavelength are shown in figure 3.7. The

45°/0° reflectance factor of PTFE as a function of wavelength is shown in figure 3.8,

while the BRDF of PTFE at 632.8 nm as a function of reflected angle is shown in

figure 3.9. Appendices A, B, and C are sample reports of BRDF, specular reflectance,

and 45°/0° reflectance factor measurements, respectively.

26
Figure 3.7. Specular reflectance as a function of wavelength for the

SRMs listed in the legend. The relative expanded

uncertainties of the reflectances, approximately

0.1 percent, are within the sizes of the symbols.

1.050

1.025

1.000

0.975

0.950

300 400 500 600

Wavlength [nm]

700 800

Figure 3.8. 45°/0° reflectance factor as a function of wavelength

for a PTFE plaque. The vertical bars are the expanded

uncertainties of the reflectance factor.

27
0.40

0.28

0.26 ^

'

'

'

'

I I '

' -80 -60 -40 -20 0 20 40 60 80

Reflected Angle [°]

Figure 3.9. BRDF as a function of reflected angle at 632.8 nm for a PTFE plaque at the indicated incident angles. The

relative expanded uncertainties of the BRDF, less than

0.2 percent, are within the sizes of the symbols.

3.3.3 Directional - Hemispherical Reflectance The sample to be measured is placed at the sample port of the integrating sphere. Three aluminum slides surrounding the sample

port are adjusted to center the sample in the port, and a spring-type clamp is used to hold

the sample against the port. The position of the incident beam is checked to verify that it passes through the center of the entrance port and strikes the center of the sample. The

appropriate detector is attached to the detector port of the integrating sphere.

The operating parameters for the detector are determined prior to the

measurements in the same manner as for the bidirectional measurements. The gain,

number of power line cycles, and number of readings obtained from this procedure are then used for all the measurements of the samples in the batch.

From eq (2.39), assuming the responsivity of the detector and integrating sphere

remains constant over the time period of the measurement and including the wavelength

dependence, the reflectance factor of the sample is given by

R^a) = RSXyf^M^ (3.7)

28
where is the reflectance factor of the standard, 5*^^ and .S"^ are the signals obtained with

the sample at the port and the incident beam striking the sample and wall, respectively,

and and S^^ are the signals obtained with the standard at the sample port and the

incident beam striking the standard and wall, respectively. The primary standard is a set of three flat PTFE samples of the same type that were calibrated for absolute spectral

directional - hemispherical reflectance factor using the techniques described in

Ref. [1 1,23,24]. Working standards of Vitrolite, Russian opal, white enamel, and a white

tile were calibrated using the PTFE samples [23] and are used for measurements of

similar samples.

The signals obtained with either a sample or a standard at the sample port are obtained in the same manner. At a fixed wavelength, and with no polarization of the

beam, the net signal from the incident beam striking the target area of the integrating

sphere wall is measured. The sphere is then rotated so that the incident beam strikes the

sample at the sample port, and the net signal, S^^ or S^^, is measured. Finally, the sphere is rotated back so that the incident beam again strikes the target area, and the net signal is measured. The two net signals obtained with the beam incident on the target area are averaged to obtain the signal or S^,.

The signals are measured at each wavelength specified in the computer program.

In general, the three PTFE standards are measured, then the sample, and finally the three

PTFE standards again. The average reflectance factors and measured signals of the

standards are used in eq (3.7), along with the signals obtained from the sample, to calculate the reflectance factor of the sample. Representative 6° - hemispherical

reflectance factors as a function of wavelength are shown in figure 3.10, and Appendix D

is a sample report of a 6° - hemispherical reflectance factor measurement.

29
1.05

1.00

0.95

0 0.90 o^0.85

o1 0.80 o§0.75

. I 0.70

'

' 0.65

0.60

350 400 450 500 550 600 650 700 750 800

Wavelength [nm]

Figure 3.10. 6° - hemispherical reflectance factor as a function of

wavelength for the materials listed in the legend. The

^ relative expanded uncertainties of the relectance factor,

' approximately 0.3 percent, are within the sizes of the

symbols.

3.4 Uncertainties

3.4.1 Introduction The approach to the uncertainty analysis follows the guidelines

given in Ref. [25]. This section details the basic definitions and equations used in the

uncertainty analysis, while their application to reflectance measurements are given in the

following two sections.

In general, the purpose of a measurement is to determine the value of a measurand

y, which is obtained from n other quantities x/ through the functional relationship /, given

by

y =Axi, X2, Xi, x„) . (3.8)

The standard uncertainty of an input quantity x/ is the estimated standard deviation

associated with this quantity and is denoted by w(x/). In addition, the relative standard

uncertainty is given by / Xj. The standard uncertainties may be obtained using either a Type A evaluation of uncertainty, which is based on statistical analysis, or a Type B

evaluation of uncertainty, which is based on other means.

30
The estimated standard uncertainty in the measurand y is the combined standard

uncertainty u^(y). To first order, and assuming that the standard uncertainties of each

input quantity are uncorrelated, u^(y) is given by the law of propagation of uncertainty,

2

/=1 u\x,). (3.9)

where dfI dxi is the sensitivity coefficient. For additive functional relationships, eq (3.9)

is convenient for calculating the combined standard uncertainty. However, for

multiplicative functional relationships, the relative combined standard uncertainty

u^(y) / y'ls more convenient, and is given by

, (3.10)

where (1 / y) (dfI dxi) is the relative sensitivity coefficient. The expanded uncertainty U

is given by k-uj(y), where k is the coverage factor and is chosen on the basis of the desired

level of confidence to be associated with the interval defined by U. For the purpose of

this publication, k = 2, which defines an interval having a level of confidence of

approximately 95 percent.

3.4.2 Bidirectional Reflectance Four measurement equations are relevant for

determining the functional relationship of the input quantities to the measurand for

bidirectional reflectance. These are stated in terms of BRDF for convenience and their

extension to reflectance and reflectance factor can be easily determined fi^om eqs (3.5)

and (3.6).

The first measurement equation relates the BRDF to the signals and the

geometrical quantities, and is given by eq (3.1),

f,ie-0-Z;a) = ^^f^--^ . (3.11)

The second equation relates the signal from the reflected radiant flux to the incident flux,

and is given by

5,(^i;^,;>^;c7) = i?(A) y^(^i;^,;A;o-) /2,-^i(/l;o-) . (3.12)

Finally, the incident beam is not monochromatic at a single wavelength A but also has

contributions from other wavelengths A', so that 0^ = 0j(/l, A,'). Therefore, the signals

depend on the spectral properties of the incident flux, the BRDF, and the detector

responsivity. The measurement equations for the signals from the incident and reflected

fluxes are given by

31
SiiA) = jR(A')-0^{X,A')-dA' and (3.13)

S,(A) = \R(A')-fM;0,;A')- n,-0^(A,X'ydA' , (3.14)

where the integrals are over all wavelengths A'.

The components of uncertainty associated with bidirectional reflectance are conveniently divided among those arising from the source, the goniometer, and the

detector. These com.ponents are evaluated using eqs (3.11) to (3.14), and the relative

sensitivity coefficients resulting from them are given in table 3.4. These coefficients are derived below, followed by their application to representative measurements of two types

of samples, one a white PTFE plaque and the other a green tile. Note that the STARR

instrument was designed to measure white samples, not colored samples. Therefore, the

green tile serves to illustrate uncertainties that are nearly zero for the white plaque. The

resulting relative expanded uncertainties are given in tables 3.5 and 3.7, while the relative

combined expanded uncertainties are given in tables 3.6 and 3.8.

Table 3.4 Relative sensitivity coefficients for bidirectional

reflectance measurements

Component of uncertainty Relative sensitivity coefficient

Source stability, 0^ 1 / 0,

Wavelength, A (!//){dfjdX)

Stray light, 5'3,(A) -qiX))l{\+qiX))

Angle of incidence, 6^ 0 /y^'

Angle of reflection, 0^ tan 6^ Aperture area, 1 /A,

Distance, D 21

D

Signal, incident, \IS,

Signal, reflected, MS,

32
Table 3.5 Relative expanded uncertainties {k = 2) for the bidirectional reflectance of a white PTFE plaque

Component of Relative expanded

uncertainty Type uncertainty [%]

Wavelength [nm]

200 400 800 1200 1600

Source stability A 0.20 0.20 0.04 0.04 0.04

Wavelength B 0.04 <0.01 <0.01 <0.01 <0.01

Stray-light B <0.01 <0.01 <0.01 <0.01 <0.01

Signal, incident A 0.18 0.06 0.06 0.02 <0.01

Signal, reflected A 1.66 0.22 0.16 0.06 0.22

Angle [°] 0 15 30 45 60 75

Angle of reflection B 0 0.08 0.16 0.28 0.48 1.04

Aperture area B 0.10

Distance B 0.06

Table 3.6 Relative combined expanded uncertainties, in percent, {k = 2) for the

bidirectional reflectance of a white PTFE plaque

Angle of reflection Wavelength [nm]

200 400 800 1200 1600

0 1.69 0.32 0.21 0.14 0.25

15 1.69 0.34 0.23 0.16 0.26

30 1.69 0.36 0.26 0.21 0.30

45 1.71 0.43 0.35 0.31 0.38

60 1.75 0.58 0.52 0.50 0.54

75 1.98 1.09 1.06 1.05 1.07

33
Table 3.7 Relative expanded uncertainties {k = 2) for the bidirectional reflectance of

a green tile

Component of Relative expanded

uncertainty Type uncertainty [%]

Wavelength [nm]

400 500 600 700

OUUIL-C oLdUlllLj' A 0 90 0.02 0.02 0 04

TV Ct V wl^Xlj^ LIX B 0.16 0.36 0.22 0.18

Stray-light B 3.66 0.16 <0.01 <0.01

Signal, incident A 0.88 0.02 <0.01 0.32

Signal, reflected A 2.72 1.32 1.96 1.36

Angle [°] 0 15 30 45 60 75

Angle of reflection B 0 0.08 0.16 0.28 0.48 1.04

Aperture area B 0.10

Distance B 0.06

Table 3.8 Relative combined expanded uncertainties, in percent,

{k = 2) for the bidirectional reflectance of a green tile

Angle of reflection Wavelength [nm]

[deg] 400 500 600 700

0 4.65 1.38 1.98 1.41

15 4.65 1.38 1.98 1.42

30 4.66 1.39 1.98 1.42

45 4.66 1.41 2.00 1.44

60 4.68 1.46 2.03 1.49

75 4.77 1.73 2.23 1.76

The three components of uncertainty arising from the source are an uncertainty

from the stability of the source, an uncertainty in wavelength, and an uncertainty from

stray light. From the measurements detailed in section 3.2.1, the flux in the beam

emerging from the source had a standard deviation that depends on wavelength. Using

34
eq (3.14), the relative sensitivity coefficient of the reflected signal due to the incident flux

is 1 / (Pj. The expanded relative standard uncertainty in BRDF due to instability of the source is given in tables 3.5 and 3.7 at selected wavelengths.

The maximum error in wavelength is 0.1 nm for wavelengths shorter than

1000 nm, and 0.5 nm for longer wavelengths. The uncertainty in BRDF due to these

uncertainties in wavelength is determined by the dependence of f,{^0;, 6;, X; cr) on

wavelength, with a relative sensitivity coefficient of (1 / /) (5/^ / dX). For example, the

BRDF of a white sample is virtually independent of wavelength, therefore the relative

sensitivity coefficient is nearly zero. In contrast, the BRDF of a colored sample changes

rapidly at certain wavelengths, and therefore the relative sensitivity coefficient is finite at those wavelengths. The relative expanded uncertainties in BRDF due to errors in

wavelength, assuming a rectangular probability distribution, are given in tables 3.5 and

3.7 at selected wavelengths.

The spectral dependencies of the measured signals are given by eqs (3.13) and

(3.14). Ideally, the signals are due only to radiant flux within the bandwidth of the

source, either 7 nm or 10 nm about the wavelength setting of the monochromator.

However, because of stray light in the source, there is radiant flux at other wavelengths,

which contributes to the measured signal. An equation for estimating the uncertainty due

to stray light and a method for calculating this contribution are given below.

Let S^{X) be the measured signal from the incident flux at wavelength setting X of

the monochromator. This signal is the sum of the signal S^ ^^{2) due to light within the

bandwidth A/l and the signal S-, J^X) due to stray light. Let q^{X) = S^^iX) I S^J^X) be the

ratio of the signal due to stray light to the signal due to flux within the bandwidth. Then,

SiX) = S,UX)-[\+qm. (3.15)

Similarly, the measured signal from the reflected flux is given by

SiX) = S,^,^{X)-[\+qm- (3-16)

Using eqs (3.15) and (3.16) for the measured signals and eq (3.1 1) for the dependence of

BRDF on the signals, and showing only the wavelength dependence explicitly, the

relative change in/(/I) due to stray light is given by

isfM)

(3 17)

fM) l+^i(^)

To estimate the signals due to flux within the bandwidth and due to stray light,

eqs (3.13) and (3.14) are expanded in terms of the two contributions to the measured

signal, so that

35
jR(A')-0;{X,Z') dr and (3.18)

A-AA

Si,s\W= j/?(A')-<^i(A,A')-dA'+ jRiZ')-0i(A,A')-dA' . (3.19)

0 A+AA

A+AA

'^r,bwW= Ji?(A')-/r(^')-A-<^i(^^')-dA' and (3.20)

A-AA

A-AA 00

5,^^,(^)= Ji?(A')-/,(;i')- A-^ia'^')-dA'+ Ji?(;i')-/r(>^')-A •^i(A,A')-dA'

0 A+AA

(3.21)

Additionally, the incident flux 0,{X, X') is the product of the flux 0^^) of the lamp and

the slit-scattering function z(A, A') of the monochromator and the other optics, so that

0,{A, M)=0lX)-z{X, X') (3.22)

For purposes of estimating the contribution of stray light to the measured signal, the slit- scattering function is assumed to have the form

2(A,A')='

1 for X-^X<X' <x + ia

0 for X'<X.cut -on (3.23)

10

-5

otherwise

where is the cut-on wavelength of the appropriate order-sorting filter. The actual

BRDF is assumed to be given by the measured BRDF.

The ratio q^{X) for the incident beam can be calculated using the responsivities of

the detectors, the relative spectral output of the sources, and eqs (3.18), (3.19), (3.22), and

(3.23). Since the corresponding ratio for the reflected beam, qJiX), depends on the BRDF

of the sample, from eqs (3.20) and (3.21), these were calculated for the two examples of a white PTFE plaque and a green tile. The corresponding expanded relative standard

uncertainties using eq (3.17) are given at selected wavelengths in tables 3.5 and 3.7. Note

that if/(A) does not depend on wavelength, q<i^X) = qJi^X) and the uncertainty due to stray

light is zero. This situation is closely approximated by the white PTFE plaque.

The components of uncertainty arising from the goniometer are errors in the

incident and reflected angles. The zero angle of incidence was determined to within 0.1°

from the retroreflected beam and to within 0.1° from differences between the alignment

mirror and the sample surface. The resolution and repeatability of the incident angle are

36
0.001° and 0.01°, respectively. Assuming a rectangular probability distribution for these

errors, the combined standard uncertainty in the angle of incidence is 0.08°. Since the

uncertainty in BRDF due to an uncertainty in incidence angle 9^ depends upon the

properties of the sample, the relative sensitivity coefficient is given by (1 //) • (5/ / dO^.

This uncertainty is not included in the tables 3.5 and 3.7 since the dependence of BRDF

on the angle of incidence was not determined for these samples.

As detailed in section 3.2.2., the angle of reflection is determined to within 0.1°.

Differences between the alignment mirror and the sample surface are also within 0.1°.

Again assuming a rectangular probability distribution for these errors, the combined

standard uncertainty in reflected angle is 0.08°. Using eq (3.11), the relative sensitivity

coefficient due to the angle of reflection is tan^^. The resulting relative expanded

uncertainties at selected angles of reflection are given in tables 3.5 and 3.7.

The components of uncertainty arising from the detector are uncertainties in the

aperture area, distance from aperture to sample, and noise in the signal. The relative

expanded uncertainty in the aperture areayl^ is taken to be 0.10 percent, while the relative

sensitivity coefficient calculated from eq (3.1 1) is 1 /^p

For the distance, the sample holder is aligned on the axis of rotation of the

goniometer to within 0.1 mm, as detailed in section 3.2.2; the distance from the sample to the aperture is measured to within 0.1 mm, again as detailed in section 3.2.2; and the

sample is placed in the sample holder to within 0.1 mm. Assuming rectangular

probability distributions for all of these errors, the combined standard uncertainty in the

distance is 0.1mm. Using eq (3.11), the relative sensitivity coefficient due to the

distance is 2 / Z), which results in a relative expanded uncertainty of 0.06 percent at a

distance of 650 mm.

Again using eq (3.11), the relative sensitivity coefficients due to the signals are

l/^i and 1 / for the signals from the incident and reflected flux, respectively. The

standard deviations of the mean for the net signals are propagated through to the final

signals to obtain the expanded relative standard uncertainties. These are listed at selected

wavelengths in tables 3.5 and 3.7. Note that the relative expanded uncertainties in the

reflected signals are greater than those from the incident signals since the fluxes are

significantly smaller in the former case than in the later. The relative combined expanded

uncertainties given in tables 3.6 and 3.8 are obtained from the root-sum-square of the

uncertainties listed in tables 3.5 and 3.7, respectively.

3.4.3 Directional - Hemispherical Reflectance Only two measurement equations are needed for determining the functional relationship of the input quantities to the

measurand for direction-hemispherical reflectance. They are analogous to eqs (3.11) and

(3.12). The first relates the reflectance factor of the sample, R^, to the signals and the

reflectance factor of the standard, i?^, and is given by eq (3.7), which is repeated here

37
The second equation relates any signal S{A) from the reflected flux in the integrating

sphere to the incident flux C^A), and is given by

SiA) = ^iA)-R{Ji)-0(X) , (3.25)

where is the responsivity of the integrating sphere and detector and R(A) is the

reflectance factor . Since the reflectance factor of a sample is always determined relative to that of a standard with nearly the same reflectance factor, there is no uncertainty

associated with stray light, as detailed in the previous section. Therefore, the analogues

to eqs (3.13) and (3.14) are not included in the measurement equations for directional - hemispherical reflectance factor.

The components of uncertainty associated with directional - hemispherical

reflectance are conveniently divided among those arising from the source (stability and

wavelength), the detector (signals), and the standard (reflectance). These components are evaluated using eqs (3.24) and (3.25), and the relative sensitivity coefficients resulting

from them are given in table 3.9. These coefficients are derived similarly to those listed

in table 3.4, so the derivation will not be repeated below. There is a factor of 2 associated

with the coefficient for the source stability since there are two ratios of signals in

eq (3.24). The resulting expanded relative standard uncertainties for a representative

PTFE plaque are given in table 3.10 and the expanded combined relative uncertainties are given in table 3.1 1.

Table 3.9 Relative sensitivity coefficients for directional

hemispherical reflectance measurements

Component of uncertainty Relative sensitivity coefficient

Source stability, C?> 2/0,

Wavelength, A (l/pJ-idpJdX)

Signal, wall and standard, S^^

Signal, wall and unknown, I /

Signal, standard,

Signal, unknown, S^^

Reflectance of standard, 1/A

38
Table 3.10 Relative expanded uncertainties {k = 2) for the 6° - hemispherical

reflectance of a PTFE plaque

Component of Relative expanded

uncertainty Type uncertainty [%]

Wavelength [nm]

200 400 800 1200 1600

0.40 0.40 0.08 0.08 0.08

0.04 <0.01 <0.01 <0.01 <0.01

0.50 0.30 0.12 0.06 0.08

0.18

Source stability A

Wavelength B

Signals A

Standard B

Table 3.11 Relative combined expanded uncertainties {k = 2) for

the 6° - hemispherical reflectance of a PTFE plaque

Wavelength [nm]

Relative combined

expanded uncertainty [%]

200 0.67

400 0.53

800 0.23

1200 0.21

1600 0.21

i

39
4. Transfer Instrument - Spectrophotometers

4.1 Description

Two commercial spectrophotometers, a Varian-Cary 5E and a Perkin-Elmer

Lambda 19,^ are used as transfer instruments and are calibrated with primary reference

standards from the STARR instrument. The reflectance standards issued as SRMs are

calibrated on these transfer spectrophotometers. Since these are commercial instruments,

the descriptions will be limited to the features that are pertinent for understanding their

operation. Additional details can be found in the users' manuals [7,8].

Both transfer spectrophotometers are double beam instruments with transmittance

and reflectance capabilities. They are equipped with microprocessors with programmable

features under external computer control. Both use a double monochromator with ordersorting filters for wavelength selection, and are purged with purified nitrogen gas. The

Varian-Cary 5E, hereafter referred to as the Gary 5E, is equipped with a Diffuse

Reflectance Attachment (DRA), while the Perkin-Elmer Lambda 19, hereafter referred to as the Lambda 19, is equipped with an Integrating Sphere Assembly (ISA).

The spectral wavelength range of the instruments is 200 nm to 2500 nm. This

range is conveniently divided into three regions, the ultraviolet (200 nm to 400 nm), the

visible (400 nm to 700 nm), and the near-infrared (700 nm to 2500 nm). The sources, order-sorting filters, gratings, and detectors are automatically controlled so that

continuous spectral scans can be made through the full wavelength range of the

instrument. A deuterium lamp is the source for the ultraviolet wavelength range, while a quartz-tungsten-halogen lamp is used at other wavelengths. One grating is used for the

ultraviolet and visible ranges, while the other grating is used for the neai--infrared range.

Likewise, a photomultiplier tube (PMT) detector is used for the ultraviolet and visible

ranges while a lead sulfide (PbS) detector is used for the near-infrared range. The

spectral bandwidth in the ultraviolet and visible ranges is adjustable from 0.1 nm to 3.8 nm (3.0 nm) on the Gary 5E (Lambda 19), and in the near-infi-ared range is adjustable

from 1.0 nm to 14.3 nm (20 nm) on the Gary 5E (Lambda 19).

The integrating sphere of the DRA on the Gary 5E has a diameter of 1 1 0 mm.

The PMT is mounted above the sphere and views the sphere interior through an elliptical

aperture. The PbS detector port is adjacent to the PMT port. Baffles attached to the top

of the sphere interior block first reflections from the sample to the detectors. The sphere

interior and baffles are coated with pressed PTFE powder.

The reference beam enters the sphere through a port 22 mm high by 12 mm wide

located 90° from the sample port. The reference beam target area is located on the

^ Certain commercial equipment, instruments, or materials are identified in this paper in order to specify

the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the

materials or equipment identified are necessarily the best available for the purpose.

40
opposite side of the sphere. The sample beam is nearly collimated and enters the sphere

through a rectangular port approximately 30 mm high by 20 mm wide. The sample port

is opposite this entrance port and is 22.5 mm in diameter. An image of the exit slit of the

monochromator is formed at the sample plane. The width of this image may vary,

depending on the bandwidth setting. The image height is about 1 5 mm at the maximum

exit slit height. The image height can be decreased by reducing the exit slit to one-third

of its maximum height.

The section of the sphere at the sample port can be turned in the plane of this port.

In one position of this section the sample plane is tilted so that the sample beam is incident at 6° from the normal. This angle allows the specular component of the reflected

sample beam to be trapped in the sphere. In the other position, this section is turned

180°. In this configuration the sample beam is normal to the sample plane and the

specular component returns along the axis of the sample beam and passes back out of the

sphere through the sample beam entrance port. This allows only the diffuse component

of the reflected beam to be measured.

The ISA on the Lambda 19 was custom-designed for high precision by the NIST

staff A top view diagram of the ISA is shown in figure 4.1. The integrating sphere of

the ISA has a diameter of 220 mm. The PMT is mounted above the sphere and views the

sphere interior through an circular aperture. The PbS detector port is adjacent to the PMT

port, and each port is symmetrically placed with respect to the sample and reference

ports. There are appropriate baffles designed to block the first sample reflection to the

detectors. The sphere interior and baffles are fabricated from SpectralonTM.

There are two entrance ports, one for the reference beam and the other for the

sample beam. The sample beam enters the sphere through a port with a diameter of

22 mm located nearly opposite to the 22 mm diameter sample port. The ports for the

reference beam and reference sample are similar. The incidence angle of the center of the

beams is 6°. The removable reference sample is freshly prepared high purity PTFE. The

centers of all the ports except those of the detectors lie along the horizontal great circle of

the sphere. The integrating sphere design accommodates not only measurements for

which the specular beam is included in the measurement result, but also measurements

for which the specular beam is excluded from the result. This is achieved by removing a

set of plugs on the integrating sphere so that the specular component of the beam exits the

sphere through these ports. These plugs were machined to complete the spherical shape

of the wall.

The sphere wall is brought to a knife edge at the sample and reference ports to completely collect the hemispherically scattered light from the sample and the reference.

Since SpectralonTM is a volume diffuser and will transmit light to a depth of several

millimeters, the outer sphere shell directly behind the SpectralonTM wall was painted with

BaS04 around the sample and reference ports to attempt to achieve the highest possible

reflectance.

41
(a) Specular excluded mode

(b) Specular included mode

Figure 4.1. Top view of the Integrating Sphere Assembly of the

Perkin-Elmer Lambda 1 9 transfer spectrophotometer

configured for reflectance operating in the specular

excluded (a) and specular included (b) modes.

4.2 Calibration

While emission lamps can be placed in the source compartment of the Gary 5E,

the same is not true of the Lambda 19. Therefore, both emission lines and absorption

bands are used to calibrate the wavelength scales of the Gary 5E, while only absorption

bands and the emission lines of deuterium are used for the Lambda 19. The lines and

bands used for the Gary 5E are listed in table 4.1, while those for the Lambda 19 are

listed in table 4.2. The maximum error in the wavelength scale is 0.1 nm in the

ultraviolet and visible wavelength ranges and 0.5 rmi in the near-infrared for both

instruments. The deuterium lamp is used to check the wavelength scales on a routine

basis.

42
Table 4.1 Wavelengths of emission lines and absorption bands used to calibrate the

wavelength scale of the Gary 5E transfer spectrophotometer

Source Wavelength [nm]

Emission lines

Hg 253.65, 334.15, 435.83, 546.07, 1014.0,

1529.5

Dj 486.0, 656.10, 1312.2^'^, 1968.3<^\

2624.4^^)

Ne 703.24

Xe 881.94,979.97

Kr 1816.73

Absorption bands

1,2,4-trichlorobenzene (0.5 mm) 2152.6

Holmium oxide (SRM 2034) 241.0, 249.8, 278.1, 287.0, 333.5, 345.5,

361.4, 385.4, 416.1, 451.3, 467.8, 485.3,

536.5, 640.5

Rare-Earth oxide (SRM 1920) 799.0,886.7, 1132.4, 1260.8, 1535.4,

1682.2, 1757.8, 1847.0, 1932.5, 1970.8

^^^These wavelengths are the 2nd, 3rd, and 4th order lines of the 656.1 nm line.

Table 4.2 Wavelengths of emission lines and absorption bands used to calibrate the

wavelength scale of the Lambda 1 9 transfer spectrophotometer

Source Wavelength [nm]

Emission lines

D2 486.0, 656.10, 1312.2^^^ 1968.3^^^

2624.4^^)

Absorption bands

Didymium glass 1067.0

Holmium oxide (SRM 2034) 241.0, 249.8, 278.1, 287.0, 333.5, 345.5,

361.4, 385.4, 416.1, 451.3, 467.8, 485.3,

536.5, 640.5

Rare-Earth oxide (SRM 1920) 799.0,886.7, 1132.4, 1260.8, 1535.4,

1682.2, 1757.8, 1847.0, 1932.5, 1970.8

^^^These wavelengths are the 2nd, 3rd, and 4th order lines of the 656.1 nm line.

43
The presence of stray light in the transfer spectrophotometers sample beam was

checked using a number of solutions and glass fihers that have sharp cut-off absorption

features in different spectral regions. The techniques for measuring stray radiation are described in ASTM and other publications [17,18]. The level of stray radiation was

checked for spectral bandwidths of 1.0 nm and 3.6 nm. The results of these

measurements indicate that the level of stray light is not significant for the transfer

spectrophotometers, especially since samples are always calibrated using a reference with

the same spectral characteristics.

The linearity of the detectors on both instruments was determined with a set of

transmittance standards [21]. These transmittance standards were calibrated on the NIST

reference transmittance spectrophotometer at 546 nm and 770 nm. The measured

transmittances and resulting differences with the transmittances of the standards are used

to correct for the non-linearity of the detectors.

4.3 Operation

The SRMs listed in table 1.1 are calibrated on the transfer spectrophotometers

using master standards as a means for transferring the absolute reflectance scale from the

fundamental measurements of these quantities on the STARR. Pressed PTFE powder is preferred as a master standard for diffuse reflectance (SRMs 2015, 2016, and 2044)

because the absolute reflectance of this material is well documented [26,27,28]. Other

transfer standards used are master first surface aluminum and gold mirrors, second

surface aluminum mirrors, and Black Glass for calibrating SRMs 2003, 201 1, 2023, and

2026. The wavelength SRM 1920a is also calibrated on the Gary 5E as described in

Ref [29], and the reflectance of this standard as a function of wavelength is shown in

figure 4.2.

The instrument parameters are set after a 2 h warm up period. The wavelength

calibration is checked during this time by running the instrument test procedure with the

deuterium emission lines. Data for determining the reflectance of a sample are recorded

in the following sequence. Prior to beginning a measurement, a sample of PTFE is placed at the sample port and a spectral scan is performed. The resulting signals from

this scan are used to adjust the fluxes in the reference and sample beams so that they are nearly equal. Then a master standard, either for specular or directional - hemispherical

reflectance, is placed at the sample port. A spectral scan of the master standard is performed, recording the signals as a function of wavelength for both the reference and

the sample beams. In the notation of section 2.2.2, now including the wavelength

dependence, these are the signals S^X'^) ^ssi'^)-' respectively. The sample to be

calibrated is then placed at the sample port, and another spectral scan is performed. This

yields the signals S^(/i) and S^^(A,). If additional samples are to be calibrated, they are measured in turn. The master standard is measured again, then background

measurements are made by placing a large black cavity at the sample port and performing

a spectral scan.

44
1.0

0.5

0.4 V

0.3 '

'

I

'

'

I — I

'

'

I

'

I

'

I

'

'

I

'

I

'

'

I

'

' 600 750 900 1050 1200 1350 1500 1650 1800 1950 2100

Wavlength [nm]

Figure 4.2. Reflectance as a function of wavelength for the rare-earth

mixture wavelength standard SRM 1920a.

The corrected, net signals are calculated in two steps. First, the net signals are obtained by subtracting the background signals. Then, the signals from the master

standards are corrected for nonlinearity of the detector and for drift in the instrument by

linearly interpolating these signals to the time when the sample to be calibrated was

measured. The reflectance or reflectance factor of the sample is calculated from eq (2.38) or (2.39) using the corrected, net signals and the known reflectance or reflectance factor

of the master standard. Note that eqs (2.38) and (2.39) are valid for the both the doublebeam transfer spectrophotometers and the single-beam STARR instrument.

4.4 Uncertainties

The expanded uncertainty {k = 2) in diffuse and specular reflectance obtained

through these measurements and data reduction procedures is generally 0.003. The

components of uncertainty arise from the source stability and wavelength, non-linearity

and noise in the detector, and reflectance of the master standard. The standard

uncertainties associated with these components in the visible wavelength region are given

in table 4.3, along with the expanded uncertainty of the reflectance.

There are some sample-related features that can cause errors that are not corrected

for in the data reduction. Examples of such error sources are large sample nonuniformity,

surface characteristics such as parallel grooves, surface waves and dimples that scatter the

specular component, and thin coatings that cause interference effects. If any of these

45
features, or others that could affect the measurements, are observed on the sample, a note

is made in the calibration report.

Table 4.3 Standard uncertainties of spectral reflectance values

for the transfer spectrophotometers in the visible

wavelength region

Component of uncertainty Standard uncertainty

Source stability 0.5 X

10"'

Wavelength 0.2 X

10-'

Detector linearity 0.7 X

10"'

Signal noise 0.8 X

10-'

Reflectance of standard 0.5x10-'

Combined Standard Uncertainty 1.3 X

10-' Expanded Uncertainty (k = 2) 2.6 X

10-'

Acknowledgments

The success of the Measurement Services and Standard Reference Materials for

spectral reflectance detailed in this Special Publication benefited from the efforts of

Robert D. Saunders, James E. Proctor, Jack J. Hsia, and Thomas A. Germer, who helped

with the design, construction, and characterization of the STARR instrument.

46
References

[I] James E. Proctor and P. Yvonne Barnes, "NIST High Accuracy Reference

Reflectometer-Spectrophotometer," J. Res. Natl. Inst. Stand. Technol. 101, 619

(1996).

[2] Standard References Materials Catalog 1 995 - 1 996, NIST Special Publication 260.

[3] NIST Calibration Services Users Guide, NIST Special Publication 250.

[4] F. A. Jenkins and H. E. White, Fundamentals of Optics, 3rd Edition, McGraw-Hill,

NY (1957) p. 521.

[5] ASTM Compilation, ASTM Standard on Color and Appearance Measurements, 5th

Edition (1996).

[6] International Commission on Illumination, International Lighting Vocabulary,

Publication CIE No. 17.4 (1987).

[7] Perkin-Elmer Reference Guide to the Lambda 19 UV-VIS-NIR Spectrophotometer.

[8] Varian-Cary 5E UV-VIS-NIR Spectrophotometer's Reference Guide.

[9] F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, and T. Limperis,

"Geometrical Considerations and Nomenclature for Reflectance," U.S. NBS

Monograph 160(1977).

[10] W. H. Venable, Jr., J. J. Hsia, and V. R. Weidner, "Development of a NIST

Reference Spectrophotometer for Diffuse Transmittance and Reflectance," National

Bureau of Standards (U.S.) Tech Note 594-1 1 (1976).

[II] G. Goebel, B. Caldwell, and H. K. Hammond III, "Use of an Auxiliary Sphere with

Spectrophotometer to Obtain Absolute Reflectance," J. Opt. Soc. Am. 56, 783

(1966).

[12] J. A. Van den Akker, L. R. Dearth, and W. W. Shillcox, "Evaluation of Absolute

Reflectance for Standardization Purposes," J. Opt. Soc. Am. 56, 250 (1966).

[13] Craig J. Sansonetti, Marc L. Salit, and Joseph Reader, "Wavelengths of Spectral

Lines in Mercury Lamps," Appl. Opt. 35, 74 (1996).

[14] CRC Handbook of Chemistry and Physics, 3rd Edition, CRC Press, Inc. (1982).

[15] W. H. Venable, Jr. and K. L. Eckerle, "Standard Reference Materials: Didymium

Glass Filters for Calibrating the Wavelength Scale of Spectrophotometers - SRM

2009, 2010, 2013, and 2014," U.S. NBS Special Publication 260-66 (1979).

[16] Devinder Gupta, Lan Wang, Leonard H. Hanssen, Jack J. Hsia, and Raju U. Datla,

"Standard Reference Materials: Polystyrene Films for Calibrating the Wavelength

Scale of Infrared Spectrophotometers - SRM 1021," NIST Special Publication 260-

122(1995).

[17] American Society for Testing and Materials, "Standard Test Method for Estimating

Stray Radiant Power Ratio of Spectrophotometers by the Opaque Film Method,

ASTM E3 87-84," Annual Book of ASTM Standards, Section 14.01, 469 (1985).

[18] K. D. Mielenz, V. R. Weidner, and R. W. Burke, "Heterochromatic Stray Light in

UV Absorption Spectrometry: A New Test Method, " Appl. Opt. 21, 3354 (1982).

[19] J. B. Fowler and G. Deszi, "High Accuracy Measurement of Aperture Area Relative

to a Standard Known Aperture," J. Res. Natl. Inst. Stand. Technol. 100, 277 (1995).

[20] K. D. Mielenz and K. L. Eckerle, "Spectrophotometer Linearity Testing using the

Double-Aperture Method," Appl. Opt. 11, 2294 (1972).

47
[21] K. L. Eckerle, V. R. Weidner, J. J. Hsia, and K. Kafadar, "Measurement Assurance

Program Transmittance Standards for Spectrophotometric Linearity Testing:

Preparation and Calibration," J. Res. Natl. Bur. Stand. (U.S.) 88, 25 (1983).

[22] C. L. Cromer, G. P. Eppledauer, J. E. Hardis, T. C. Larason, and A. C. Parr,

"National Institute of Standards and Technology Detector-Based Photometric

Scale," Appl. Opt. 32, 2936 (1993).

[23] W. H. Venable, Jr., J. J. Hsia, and V. R. Weidner, "Establishing a Scale of

Directional - Hemispherical Reflectance Factor I: The Van den Akker Method," J. Res. Natl. Bur. Stand. 82, 29 (1977).

[24] W. Budde, W. Erb, and J. J. Hsia, "International Intercomparison of Absolute

Reflectance Scale," Color Research and Application 7, 24 (1982).

[25] Barry N. Taylor and Chris E. Kuyatt, "Guidelines for Evaluating and Expressing the

Uncertainty of NIST Measurement Results," NIST Technical Note 1297 (1994).

[26] V. R. Weidner and J. J. Hsia, "Reflection Properties of Pressed

Polytetrafluoroethylene Powder," J. Opt. Soc. Am. 71, 856 (1981).

[27] V. R. Weidner, J. J. Hsia, and B. Adams, "Laboratory Intercomparison Study of

Pressed Polytetrafluoroethylene Powder Reflectance Standards," Appl. Opt. 24,

2225 (1985).

[28] P. Yvonne Barnes and Jack J. Hsia, "45°/0° Reflectance Factors of Pressed

Polytetrafluoroethylene (PTFE) Powder," NIST Tech Note 1413 (1995).

[29] Victor R. Weidner, Patricia Y. Barnes, and Kenneth L. Eckerle, "A Wavelength

Standard for the Near Infrared Based on the Reflectance of Rare-Earth Oxides," J. Res. Natl. Bur. Stand. 91, 243, (1986).

48
Appendix A

REPORT OF TEST

38060S Bidirectional Reflectance Distribution Function (BRDF)

of

One White Target

Submitted by:

Any Company

Attn: Yura Customer

Any Street

Any Town, Any State Zip Code-0000

(See your Contract No. 000000-000 Dated Month Day, Year)

1. Description of Test Item

The test item submitted was an encased white target, 50.8 mm by 50.8 mm and identified by the

letter "A".

2. Description of Test

Bidirectional Reflectance Distribution Function (BRDF) measurements as a fiinction of wavelength were made using the NIST Spectral Tri-function Automated Reference Reflectometer (STARR). The

collimated light beam (< 1° divergence) was centered on the sample in the plane of incidence. The

reported results are the averaged values from measurements made at two orthogonal polarizations.

The measurements were made at each specified wavelength for the geometrical conditions illustrated

in Figure 1. The spectral bandpass was 10 nm. A quartz-tungsten-halogen lamp was used as the source and a silicon photodiode was used as the detector. The average projected solid angle of the

limiting aperture of the detector was determined for each viewing angle by measuring the distance

between the limiting aperture and the specimen plane, and the diameter of the aperture.

Laboratory Environment:

Temperature: 21 °C ± 0.6 °C

Relative Humidity: 35% ± 0.6%

Test Date: Month Day, Year

NIST Test No.: Division Number/Test Folder Number-Year Page 1 of 4
REPORT OF TEST

Any Company

38060S BRDF

Since the illuminated area of the specimen is not a point source, the average projected solid angle

of the illuminated area was determined for computing the BRDF values. The circular receiver

aperture subtended a half angle of approximately 1 .4° at the center of the sample. When the light

beam is incident on the test specimen at an angle of 60°, the major and minor axes of the illuminated area are 28 rmn and 14 mm. When the light beam is incident on the test specimen at an angle of 0°

(normal incidence), the illuminated area has a diameter of 14 mm. The distance from the center of

the illuminated area to the center of the limiting aperture of the detector is approximately 673 mm.

The diameter of the limiting aperture is 31.85 mm.

The BRDF of the test item is computed from the ratio of the signal from the reflected flux to the

signal from the incident flux, divided by the projected solid angle and the cosine of the angle of

reflection. The BRDF values for both polarizations are averaged to obtain the reported values. The

results of the data reduction are listed in Tables 1 and 2. The expanded uncertainty (^2) for the

BRDF values listed in Tables 1 and 2 is 0.004.

4. General Information

1) The encased test samples were measured in the "as received condition" and the front surface

alignment was at the encasement.

2) Spatial uniformity was not assessed.

3) This test report may not be reproduced except in frill without the written consent of this

3. Results

Laboratory.

Prepared by: Approved by:

P. Yvonne Barnes

Optical Technology Division

Physics Laboratory

Robert D. Saunders

For the Director,

National Institute of

Standards and Technology

Test Date: Month Day, Year

NIST Test No.: Division Number/Test Folder Number-Year Page 2 of 4
REPORT OF TEST

Any Company

38060S BRDF

TABLE 1

White Target A

ANGLE OF INCIDENCE: 0°

WAVELENGTH: 800 nm

ANGLE OF VIEWING

[degrees] BRDF

60

40 0.300

20 0.300

0 0.310

-20 0.320

-40 0.340

-60 0.400

Test Date: Month Day, Year

NIST Test No.: Division Number/Test Folder Number-Year Page 3 of 4
REPORT OF TEST

Any Company

38060S BRDF

TABLE 2

White Target A

ANGLE OF INCIDENCE: 45'

ANGLE OF VIEWING: 0"

Wavelength

[nm] BRDF

400 0.323

500 0.323

600 0.323

700 0.323

800 0.323

900 0.323

1000 0.323

Test Date: Month Day, Year

NIST Test No.: Division Number/Test Folder Number-Year Page 4 of 4
Appendix B

REPORT OF CALIBRATION

38060S Spectral Reflectance

of a

First Surface Aluminum Mirror SRM 2003

Series D

Submitted by:

Any Company

Attn: Yura Customer

Any Street

Any Town, Any State Zip Code-0000

(Purchase Order No. 00-0000-00 dated Month Day, Year)

1. Description of Calibration Item

Standard Reference Material (SRM) 2003 consists of a low thermal expansion glass substrate,

5.1 cm in diameter and 0.9 cm thick, onto which aluminum has been vacuum deposited. SRM 2003

is supplied with a threaded protective aluminum container fitted with a Teflon insert. The insert has

been constructed so that it does not impinge upon the calibrated surface. The top or lid of the

container bears a label that identifies the type of SRM and the Series Number. The SRM is placed

face down in the bottom half of its container.

2. Description of Calibration

The reflectance measurements as a function of wavelength were made using the NIST Spectral Trifimction Automated Reference Reflectometer (STARR). The nearly collimated light beam

illuminated an area of approximately 14 mm in diameter and was centered on the sample in the plane

of incidence. Measurements were made using a 6°16° geometry. Measurements were made with

light polarized parallel and perpendicular to the plane of incidence. The reported results are the

averaged values of measurements made at the two polarizations.

Laboratory Environment:

Temperature: 23°C ± 0.6°C

Humidity: 50% ± 0.6%

Calibration Date: Month Day, Year

NIST Test No.: Division Number/Test Number-Year Page 1 of 4
REPORT OF CALIBRATION

Any Company

38060S Spectral Reflectance of a First Surface Aluminum Mirror

SRM 2003 was calibrated over the wavelength range of 250 nm to 2500 nm as follows: 50 nm

intervals over the range of 250 nm to 1000 nm, 100 nm intervals over the range of 1000 nm to 1300 nm, and 200 nm intervals over the range of 1300 nm to 2500 nm. The spectral bandpass was

approximately 1 0 nm.

The following sources and detectors were used: a xenon arc lamp and a silicon photodiode detector over the range of 250 nm to 400 nm, a tungsten source and a silicon photodiode detector over the

range of 450 nm to 1 100 nm, and a quartz-tungsten-halogen lamp and an indium-aresenide detector over the range of 1 100 nm to 2500 nm.

3. Results

The reflectances are listed in Table 1. The expanded uncertainties (^2) of the reflectances are 0.005 for wavelengths shorter than 350 nm, 0.003 for wavelengths from 400 nm to 2000 nm, and

0.005 for wavelengths longer than 2000 nm. The expanded uncertainties include increased random

noise at wavelengths below 350 nm and above 2000 nm. Contributors to the Type A uncertainty are

spatial uniformity over an area with diameter 20 mm and surface conditions, source stability, and

signals. Contributors to the Type B uncertainty are the receiver system non-linearity and nonuniformity, scattered flux, angular setting, and view factor uncertainties.

4. General Information

1) SRM 2003 is not durable. Airborne particulates, aromatics, laboratory conditions, and improper

handling may adversely affect the surface conditions. If the delicate aluminum surface becomes

contaminated it cannot be restored to its original reflectance by cleaning.

2) It is strongly recommended that a face mask be worn to prevent fogging or contaminating the

mirror with vapors or particles from the mouth or nose. It is further recommended that all fmgers/thumbs be covered with a lint-free glove i.e., nylon or latex types to prevent latent

fingerprints on mirror surfaces. If and only if dust must be removed, be extremely careful when

using a very clean air bulb and use it so that no condensation is generated by a high velocity air

flow over the mirror's calibrated surface.

3) The data in Table 1 are valid for a 6° angle of incidence only.

4) This report may not be reproduced except in full, without written permission from this

Laboratory.

Calibration Date: Month Day, Year

NIST Test No.: Division Number/Test Number-Year Page 2 of

4
REPORT OF CALIBRATION

Any Company

38060S Spectral Reflectance of a First Surface Aluminum Mirror

Prepared by: Approved by:

P. Yvonne Barnes

Optical Technology Division

Physics Laboratory

(301) 975-2345

Robert D. Saunders

For the Director,

National Institute of

Standards and Technology

(301) 975-2355

References

[1] Linford, R.M.F., Strouse, E.A., Optical Coatingsfor Space Laser Communications System,

SPIE, Vol. 150, Laser and Fiber Optics Communications, pp 55 - 61, (1978)

[2] Hass, G., Filmed Surface for Optics, JOSA, Vol. 45, No. 1 1, pp 1070 - 1073 (1957).

[3] Hass, G., Hunter, W.R., Tousey, R., Influence of Purity, Substrate Temperature, and Aging

Conditions on the Extreme Ultraviolet, JOSA, Vol. 49, No. 6, pp 593 - 602 (1959).

[4] Hass, G., Tousey, R., Reflecting Coatingsfor the Extreme Ultraviolet, JOSA, Vol. 49, No. 6,

pp 593 -602 (1959).

[5] Hass, G., Waylonis, J.E., Optical Constants and Reflectance and Transmittance of

Evaporated Aluminum in the Visible and Ultraviolet, JOSA, Vol. 51, No. 7, pp 719 - 722

[6] Bennett, H.E., Silver, M., Ashley, Infrared Reflectance ofAluminum Evaporated in

Ultraviolet, JOSA, Vol. 51, No. E.J., 7, pp 719 - 722 (1961).

[7] Hass, G., Reflectance and Preparation ofFront Surface Mirrorsfor Use at Various Angles of

Incidence from the Ultraviolet to the far Infrared, JOSA, Vol. 72, No. 1, pp 27 -39 (1982).

[8] Taylor, B.N., and Kuyatt, C.E., Guidelinesfor Evaluating and Expressing the Uncertainty of

the NIST Measurement Results, NIST Technical Note 1297 (1994)

[9] Taylor, B., Guidelinesfor the Use ofthe International System of Units (SI), NIST Technical

Note 811 (1995).

(1961).

Calibration Date: Month Day, Year

NIST Test No.: Division Number/Test Number-Year Page 3 of 4
REPORT OF CALIBRATION

Any Company

38060S Spectral Reflectance of a First Surface Aluminum Mirror

Table 1

First Surface Aluminum Mirror, SRM 2003, Series D

Wavelength [nm] Reflectance

250 0.883

300 0.901

350 0.904

400 0.903

450 0.899

500 0.899

550 0.898

600 0.895

0 88?

700 0.870

750 0.854

800 0.855

850 0.887

900 0.916

950 0.924

1000 0.934

1100 0.955

1200 0.962

1300 0.965

1500 0.966

1700 0.967

1900 0.967

2100 0.967

2300 0.967

2500 0.967

Calibration Date: Month Day, Year

NIST Test No.: Division Niunber/Test Number-Year Page 4 of 4
Appendix C

REPORT OF TEST

38060S 45°/0° Reflectance Factor

of a

White Diffiiser Tablet

Submitted by:

Any Company

Attn: Yura Customer

Any Street Any Town, Any State Zip Code-0000

(Reference Purchase Order Number: 00-0000-00 dated Month Day, Year)

1. Description of Test Item

The test item submitted was a plaque of pressed polytetrafluoroethylene.

2. Description of Test

The reflectance factor measurements as a function of wavelength were made using the NIST Spectral

Tri-function Automated Reference Reflectometer (STARR). The nearly collimated light beam was

centered on the sample in the plane of incidence. The reported results are the averaged values from

measurements made at two orthogonal polarizations. The spectral bandpass was 10 nm. A quartztungsten-halogen lamp was used as the source and a silicon photodiode was used as the detector. The

average projected solid angle of the limiting aperture of the detector was determined by measuring

the distance between the limiting aperture and the specimen plane, and the diameter of the aperture.

Laboratory Enviroimient:

Temperature: 21 °C ± 0.6 °C

Relative Humidity: 49 % ± 0.6 %

Test Date: Month Day, Year

NIST Test No.: Division Number/Test Folder Number-Year Page 1 of 3
REPORT OF TEST

Any Company

38060S 45°/0° Reflectance Factor

Since the illuminated area of the specimen is not a point source, the average projected solid angle

of the illuminated area was determined for computing the reflectance factors. The circular receiver

aperture subtended a half angle of approximately 1.4° at the center of the sample. When the light

beam is incident on the test specimen at an angle of 45 °, the major and minor axes of the illuminated area are 19.8 mm and 14 mm. When the light beam is incident on the test specimen at an angle of

0° (normal incidence), the illuminated area has a diameter of 14 mm. The distance from the center

of the illuminated area to the center of the limiting aperture of the detector is approximately 673 mm.

The diameter of the limiting aperture is 3 1 .85 mm.

The results of the data reduction are listed in Table 1 . The expanded uncertainty (^2) for the

values listed in Table 1 is 0.004.

4. General Information

1) The reflectance factor of the sample is the ratio of the reflectance of the sample to the

reflectance of a perfect Lambertian diffuser under the same measurement conditions. The

45°/ 0° reflectance factor is the reflectance factor for 45° incidence and 0° viewing.

2) The test samples were measured in the "as received condition",

3) Spatial uniformity was not assessed.

4) The test report may not be reproduced except in fiill without the written consent of this

3. Results

Laboratory.

Prepared by: Approved by:

P. Yvonne Barnes

Optical Technology Division

Physics Laboratory

(301) 975-2345

Robert D. Saunders

For the Director,

National Institute of

Standards and Technology

(301)975-2355

Table 1

Test Date: Month Day, Year

NIST Test No.: Division Number/Test Folder Number-Year Page 2 of 3
REPORT OF TEST

Any Company

38060S 45°/0° Reflectance Factor

Reflectance factor Rasa function of wavelength /I for 45° incident angle and 0° viewing angle

of the pressed PTFE plaque

[nm] R(45°/0°) [nm] i?(45°/0°) [nm] i?(4570°)

380 1 All

1.01

525 1.015 670 1.015

385 1 All1.01

530 1 A 1 ^ 1.015 675 1.015

390 1 All

1.01

535 1.015 680 1.015

395 1 All

1.01

C A f\ 540 1.015 685 1.015

400 1 All1.01

C A C 545 1 Air*

1.015

/'A A 690 1 A 1 ^ 1.015

405 1 All1.01

c C f\ 550 1 A 1 ^ 1.015 695 1.015

410 1 A 1 1 1.01

c c c 555 1 A 1 C 1.015 ^AA 700 1 A 1 ^ 1.015

415 1 All

1.01

C /'A 560 1 A 1 ^ 1.015 705 1 A 1 ^ 1.015

420 1 A 1 1.012 eye 565 1 A 1 C 1.015 ^ 1 A 710 1.015

425 1 A 1 1.012 C ^A 570 1 Air* 1.015 715 1 A 1 ^ 1.015

430 1 A 1 O 1.012 575 1 A 1 ^ 1.015 720 1.015

435 1 A 1 1.012

^ O A 580 1.015 725 1.015

440 1.012 585 1.015 730 1.015

445 1.012 590 1.015 735 1.015

450 1.012 595 1.015 740 1.015

455 1.012 600 1.015 745 1.015

460 1.012 605 1.015 750 1.015

465 1.012 610 1.015 755 1.015

470 1.012 615 1.015 760 1.015

475 1.012 620 1.015 765 1.015

480 1.012 625 1.015 770 1.015

485 1 A 1 1.012 630 1 A 1 ^ 1.015 775 1 A 1 ^ 1.015

490 1.012 635 1.015 780 1.015

495 1.012 640 1.015

500 1.012 645 1.015

505 1.012 650 1.015

510 1.015 655 1.015

515 1.015 660 1.015

520 1.015 665 1.015

Test Date: Month Day, Year

NISTTestNo.: Division Number/Test Folder Number-Year Page 3 of 3

Appendix D

REPORT OF TEST

38060S 6°/Hemispherical Reflectance Factor

of

One White Diffuser Plate and

One Aluminum Diffuser Plate

Submitted by:

Any Company

Attn: Yura Customer

Any Street Any Town, Any State Zip Code-0000

(Reference Purchase Order Number: 00-0000-00 Dated Month Day, Year)

1. Description of Test Items

The materials submitted for this test are identified as follows:

1. White Diffuser plate (7.6 cm by 12.7 cm)

2. Aluminum Diffuser (7.6 cm by 12.7 cm)

2. Description of Test

The reflectance factor measurements as a fiinction of wavelength were made using the NIST

Spectral Tri-function Automated Reference Reflectometer (STARR). Three specimens of freshly

pressed polytetrafluoroethylene (PTFE) powders were prepared and then measured before and

after the test specimens. Measurements were made at the twelve specified wavelengths, with the

specular beam included in the measurement of 6°/hemispherical reflectance factor. The sample

beam illuminated an area with diameter 20 mm in the center of the specimen. The spectral

bandwidth was 10 nm.

Laboratory Envirormient:

Temperature: 23 °C ± 0.6 °C

Relative Humidity: 40% ± 0.6%

Test Date: Month Day, Year

NIST Test No.: Division Number/Test Folder Number-Year Page 1 of 4
REPORT OF TEST

Any Company

38060S 6°/Hemispherical Reflectance Factor

3. Results of Test

The average of the PTFE measurements and the absolute reflectance factor (relative to that of a

perfect diffuser) of the PTFE was used to adjust the measured reflectance factor of the test items

to the absolute reflectance scale. The results of the data reduction are listed in Tables 1 and 2.

The expanded uncertainty (k=2) for the 6°/hemispherical reflectance factor values listed in

Tables 1 and 2 are as follows: 0.005 for the measurements at 230 nm and 252 nm, 0.003 for the

measurements from 273.5 nm to 400 nm. The factors that contribute to this uncertainty are the

variation in reflectance factor of freshly pressed PTFE specimens, the increased random noise at the shortest wavelengths, and random noise in the measurements.

4. General Information

1 ) The test samples were measured in the "as received condition".

2) The test report may not be reproduced except in full without the written consent of this

Laboratory.

Prepared by: Approved by:

P. Yvonne Barnes

Optical Technology Division

Physics Laboratory

Robert D. Saunders

For the Director

National Institute of

Standards and Technology

Test Date: Month Day, Year

NIST Test No.: Division Number/Test Folder Number-Year Page 2 of

4
REPORT OF TEST

Any Company

38060S 67Hemispherical Reflectance Factor

Table 1

67Hemispherical Reflectance Factor

Specimen: WHITE DIFFUSER PLATE

Wavelength [nm] Reflectance Factor

230 0.885

252 0.921

273.5 0.942

283 0.947

292.2 0.958

301.9 0.966

312.5 0.969

331.2 0.977

339.8 0.979

350 0.983

375 0.983

400 0.990

425 0.990

Test Date: Month Day, Year

NIST Test No.: Division Number/Test Folder Number-Year Page 3 of 4
REPORT OF TEST

Any Company

38060S 6°/Hemispherical Reflectance Factor

Table 2

6°/Hemispherical Reflectance Factor

Specimen: ALUMINUM DIFFUSER

Wavelength [nm] Reflectance Factor

230

252

273.5

283

292.2

301.9

312.5

331.2

339.8

350

375

400

425

Test Date: Month Day, Year

NIST Test No.: Division Number/Test Folder Number-Year

0.409

0.442

0.468

0.475

0.482

0.489

0.496

0.507

0.511

0.516

0.526

0.530

0.533
Appendix E

Volume 101, Number 5, September-October 1996 Journal of Research of the National Institute of Standards and Technology

[J. Res. Natl. Inst. Stand. Technol. 101, 619 (1996)] NIST High Accuracy Reference

Reflectometer-Spectrophotometer

Volume 101 Number 5 September-October 1996

James E. Proctor and

P. Yvonne Barnes

National Institute of Standards and Technology,

Gaithersburg, MD 20899-0001

A new reflectometer-spectrophotometer has been designed and constructed using

state-of-the-art technology to enhance

optical properties of materials measure- ments over the ultraviolet, visible, and

near-infrared (UV-Vis-NIR) wavelength

range (200 nm to 2500 nm ). The instru- ment. Spectral Tri-function Automated

Reference Reflectometer (STARR), is capable of measuring specular and

diffuse reflectance, bidirectional reflectance

distribution function (BRDF) of diffuse

samples, and both diffuse and non-diffuse

transmittance. Samples up to 30 cm by

30 cm can be measured. The instrument and its characterization are described.

Key vfords: bidirectional; diffuse; hemispherical; monochromator; reflectance; reflectometer; scatter; spectrophotometer; specular.

Accepted: April 2, 1996

1. Introduction

The Optical Technology Division of the Physics

Laboratory at the National Institute of Standards and

Technology has designed and constructed a new reflec- tometer-spectrophotometer to replace the previous generation Reference Reflectance Instrument (RRI) [1]. The new instrument, the Spectral Tri-function Auto- mated Reference Reflectometer (STARR), delivers higher accuracy, greater speed of measurement, and

greater functionality than the previous instrument. The

STARR is capable of measuring spectral reflectance (specular and diffuse) at incidence angles up to 80° from

sample normal, and observation angles from within 5° of the incident beam to 80° from sample normal. Spectral transmittance can be measured for incident and observation angles up to 80° from sample normal. The

receiver (detector system) has an aperture stop, the area of which has been accurately measured, which remains

at a fixed distance from the illuminated spot on the sample for all observation angles. This allows the STARR to make high accuracy bidirectional reflectance

distribution function (BRDF) [2] measurements. In all operating modes, a sample up to 30 cm by 30 cm can be

raster-scanned to measure sample spatial uniformity.

The key improvements over the RRI include greater

mechanical stability, higher precision positioning,

higher source system throughput, improved detector per- formance, larger sample holder, sample raster-scanning

capability, increased measurement speed, and improved

air filtering for a cleaner laboratory environment.

2. Reflectometer Design

Two major problems with the previous instrument

(RRI) were poor mechanical stability and low signal

levels in the ultraviolet (UV) spectral region. To ensure

exceptional mechanical stability, heavy duty precision

linear and rotary stages were used in the new design. All components of the STARR are mounted on a 3.6 m by

1.2 m by 0.3 m thick vibration isolated optical table.

619
Volume 101, Number 5, September-October 1996 Journal of Research of the National Institute of Standards and Technology

This table is located in the center of a light-tight room

with black walls and ceiling. Special air filters have been

incorporated into the room ventilation system to provide

a clean environment. This room also houses all of the STARR electronic components. The instrument is fully

automated and is controlled by a computer in an adja- cent room. Figure 1 shows the source optics and

monochromator mounted at one end of the optical table, the reflectometer-spectrophotometer near the center of

the table, and a hemispherical reflectometer located at the far end of the optical table. This hemispherical

reflectometer attachment, which is currently under

development, will be used for measuring directional- hemispherical reflectance factor, and will not be dis- cussed further in this paper.

Hemispherical STARR Goniometer

Reflectometer \

Lamp Housing Monochromator

\Optical Tible

Fig. 1. Top view of the Spectral Tri-function Automated Reference

Reflectometer (STARR) facility.

machining of a heavy duty stainless steel chassis which was fabricated, along with most of the other custom

components, in the NIST Fabrication Technology

Division's main shop. All four stages are fitted with

servo motors controlled by a four axis motion controller.

Sample Holder

Reference Sample Holder

Receiver

Fig. 2. Front view of the STARR goniometer.

To ensure adequate signal in the UV spectral region, the optical system was designed to minimize reflective

losses. An optical system composed of n first surface

reflective optics will have an overall effective reflec- tance (output flux divided by input flux, assuming no

other loss mechanisms) of peff where

The STARR goniometer has four independent positioning stages. The sample holder, shown in Fig. 2, is attached to a two axis linear positioning system which

gives the range of motion needed to raster-scan the

entire 30 cm by 30 cm sample area, as well as to position either of two reference samples for measurement.

This positioning system is mounted on a rotation stage

used to rotate the sample with respect to the incident

radiation. The relatively thin profile of the sample holder and positioning system gives this system its large working range of incident angles while maintaining rigidity.

The receiver system is mounted on a light weight,

rigid arm, which is mounted on a second rotation stage. This rotation stage is independent of and coaxial with

the sample rotation stage. This allows the receiver to

rotate around the sample holder at a constant radius of

672.6 mm (from the sample rotation axis to the receiver

limiting aperture). These two rotation stages are precisely aligned. This is achieved through high precision

n

i= 1

where p, is the reflectance of the first element, and p„ is the reflectance of the nth element. If we assume, for

illustrative purposes, that all of the elements have the same reflectance p, then this simplifies to

Peff = P".

Thus, if n is large, the overall effective reflectance of the optical system can be quite low, even for relatively high

reflectance optics. The optical system for the RRI

included 14 first surface reflective elements, while the STARR includes only 7 such elements. This provides a

significant improvement in overall effective reflectance over die RRI.

620
Volume 101, Number 5, September-October 1996 Journal of Research of the National Institute of Standards and Technology

3. Source System

The lamp housing (Oriel 7340 Monochromator

niuminator') contains two sources. A 150 W ultraviolet enhanced xenon arc lamp is used for the 200 nm to 400 nm spectral range, and a 100 W quartz-tungstenhalogen (QTH) lamp is used for the 400 nm to 2500 nm

spectral range. The xenon arc is monitored by a detector based light intensity controller (Oriel 68850 Light Intensity Controller) equipped with a UV bandpass filter to optimize the stability in this spectral region. This intensity controller provides feedback to the arc lamp power

supply (Oriel model 68805) to stabilize the lamp intensity. The stability of the xenon arc was measured with

and without the intensity controller. For this measurement, the receiver was positioned to measure the incident beam, and the beam and background were measured from 200 nm to 400 nm in 10 nm steps. This

process was repeated ten times over a period of several hours. The intensity stabilizer improved the xenon arc

stability by a factor of 5, reducing the relative experimental standard deviation of the measured intensity

from 0.5 % to 0.1 %. The QTH lamp is operated by a high stability power supply (Oriel 68830 Radiometric

Power Supply). The lamp housing has a collection mirror which focuses the radiation on the monochromator entrance slit, and matches the//# of the monochromator. The collection mirror can be rotated to select either of the two lamps. The lamp housing is coupled to the 1/4 meter// 3.9 monochromator (Oriel 77700 Multi- spec 257) through a five position filter wheel. This filter wheel holds a series of cut-on (long-pass) filters, used to eliminate higher order wavelengths (order sorting). The

monochromator has a four-grating turret equipped with

three 600 lines per millimeter ruled gratings blazed at 200 nm, 400 nm, and 1000 nm, respectively, and a 150

lines per millimeter ruled grating blazed at 4000 nm

(included for possible extension of the working range beyond 2500 nm). The filter wheel and the grating turret are controlled by the monochromator microprocessor.

The filter and grating selection information, after being

optimized experimentally, is stored in the monochromator nonvolatile memory. The proper filter and grating

are automatically selected for any given wavelength. As

the radiation exits the monochromator through a 1 mm

circular aperture, it is collimated by a 5 1 mm diameter

off-axis parabolic mirror. The radiation is then directed by a 51 mm diameter flat mirror through a series of

' Certain commercial equipment, instruments, or materials are identi- fied in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

baffles, an optical chopper, a Glan-Taylor polarizer, and

a final baffle before exiting the source system along the

optical axis of the instrument. A 1 mm monochromator entrance slit is used for UV

and visible (Vis) measurements. The spectral bandpass was evaluated using emission line measurements and

found to be approximately 7 nm at 550 nm. A 2 mm

entrance slit is used for near-infrared (NIR) measure- ments to improve signal to noise ratio, resulting in a

slightly larger spectral bandpass in this region. A 1 mm

diameter circular exit aperture is used for all measurements.

4. Receiver System

The STARR receiver system consists of a precision

circular aperture with an area of 796.84 mm^ [3], a fused silica lens, and several baffles mounted in a 51 mm diameter cylindrical housing. The precision

aperture is the limiting aperture of die receiver and

defines the collection solid angle for BRDF measurements. The lens has two functions in this system. First,

it condenses the nearly collimated 1 4 mm diameter

beam onto the detector such that the detector is underfilled. Second, the lens images the sample plane of

the goniometer onto the detector, giving the STARR

receiver a well-defined field of view.

Two detectors are utilized in the STARR receiver. A

10 mm by 10 mm silicon photodiode is used for the

spectral range of 200 nm to 1 100 nm. A 1 mm diameter

thermoelectrically cooled photovoltaic indium arsenide

photodiode coupled to an averaging sphere is used for the spectral range of 900 nm to 2500 nm. The receiver system was constructed in such a way that the baffles,

limiting aperture, and fused silica focusing lens remain

fixed on the detector arm, while the detectors are inter- changeable. This design permits the interchanging of

detectors without the need to realign the system. A low

noise transimpedance amplifier (TIA) is used with both

detectors. When using the silicon photodiode, the output

of the TIA is measured with a seven and one-half digit

digital voltmeter (DVM). When using the indium

arsenide photodiode, an optical chopper is used in conjunction with a lock-in amplifier. The output of the lock-in amplifier is measured with the DVM.

The linearity of the detectors was measured using a combination of multiple apertures and neutral density

filters. A double aperture mechanism consisting of two

adjacent semicircular apertures, each with its own shutter, was placed in the sample holder and positioned such

that both apertures were overfilled by the incident beam.

The signal due to light passing through aperture "A"

was measured and designated Va- The signal due to light

621
Volume 101, Number 5, September-October 1996 Journal of Research of the National Institute of Standards and Technology

passing through aperture "B" was measured and desig- nated Vb- Finally, the signal due to light passing through

both apertures simultaneously was measured and designated Vab- a neutral density filter was then used to attenuate the beam, and the above measurement

sequence was repeated. This process continued using

successively higher density filters until the attenuated beam could no longer be measured. These measure- ments were repeated at several wavelengths. The data were analyzed to determine at what signal level the relationship Va + Vb = Vab was no longer satisfied to within the uncertainty of the measurement. For both

detectors, it was found that the above relationship was

satisfied until the noise floor of the detector system was

reached. That is, no measurable nonlinearity was found

at signal levels above the noise floor. Since the silicon photodiode is used without an aver- aging sphere, its response uniformity was measured in the NIST Detector Comparator Facility to determine if the detector was suitable for use in the STARR receiver. Table 1 shows the nonuniformity of this detector at four wavelengths. While the nonuniformity is as high as 1 %

in the NIR and 0.6 % in the UV, because the detector is underfilled, and because these nonuniformity figures

represent extreme values which are limited to very small

portions of the detector active area, the effect of these nonuniformities is insignificant. Due to the imaging

characteristics of the receiver system, this nonuniformity would only contribute significantly to the measure- ment error when measuring a sample with a significantly nonuniform spatial distribution of reflected energy, such as measuring near-specular BRDF of a

mirror. This is not the type of measurement that this system was designed to perform. The nonuniformity of

this detector will not contribute significantly to the measurement uncertainty for the types of measurements

to be performed.

Table 1. Silicon photodiode response non-uniformity

Wavelength Detector response non-uniformity

250 nm 0.6%

500 nm 0.2%

800 nm 0.4%

1000 nm 1.0%

5. Measurement Results

For the purpose of this work, four types of samples were selected to demonstrate the capabilities of the new

instrument: (1) A first-surface-aluminum-coated mirror,

representative of the Standard Reference Material

(SRM) 2003 used in industry to calibrate the photometric scale of spectrophotometers; (2) a porcelain enamel

on steel tile which is used for colorimetric measure- ments of chromatic British Ceramic (BCRA) tiles; (3) an NG-9 black glass, representative of SRM 2026,

which is also used to calibrate the photometric scale of

spectrophotometers; and (4) a GL-2 black glass which

was used to expand the dynamic range of the photomultiplier tube detector system used in the previous

generation instrument for low level measurements in the

ultraviolet region. All of these samples were chosen for

their long history of stable, repeatable measurements.

Additionally, a freshly pressed plaque of Polytetrafluoroethylene (PTFE) resin was measured using an

angle of incidence of 45° and angle of observation of 0° with respect to the sample normal (customarily denoted

as 45°/ 0° geometry). This type of sample is currently

being developed as a working standard for 45°/0° BRDF

[4].Measurements results given herein represent two

types of measurement geometries: specular reflectance

factor {SRF) using 6°/ 6° geometry, and bidirectional reflectance distribution function {BRDF) using 45°/0°

geometry.

The SRF is measured by setting the angle of inci- dence (the angle between the incident radiation and the sample normal) to 6° and measuring the specularly re- flected flux at 6° on the other side of the sample normal.

The incident flux i<P,) and the reflected flux (0^) are measured, and the ratio of these measurements gives the specular reflectance factor.

SRF =0,10, . BRDF is defined as the differential ratio of the reflected radiance {L,) to the incident irradiance (£i) and can be

expressed as BRDF = dLr/dEi

For practical measurements conditions [5], this can be

expressed as BRDF= 0J{0, (OrCOSdr) ,

where 0, is the reflected flux collected by the receiver,

0\ is the flux incident on the sample, 6, is the angle of

observation, and (o, is the solid angle subtended by

the limiting aperture of the receiver where, to a good

approximation

(o,= TTrVR^

where r is the radius of the receiver limiting aperture

and R is the distance from the sample to the receiver

limiting aperture.

622
Volume 101, Number 5, September-October 1996 Journal of Research of the National Institute of Standards and Technology

Table 2 lists the components of relative standard

uncertainty, the relative combined standard uncertainties, and the expanded uncertainties for these measure- ments [6]. The incident and reflected flux measure- ments each have a relative standard uncertainty of

0.10 %. These values arise from statistical variations in repeated flux measurements made over a period of

approximately 5 h using the xenon arc lamp and light

intensity controller, and are due to lamp drift, amplifier

noise and drift, voltage measurement noise, and other

contributions. The receiver limiting aperture area was

determined using the NIST High Accuracy Aperture

Comparator, and its uncertainty was assigned based on

the uncertainty budget of the comparator. The distance from the sample plane to the receiver limiting aperture was measured using a precision inside-micrometer. This

distance was measured at five different detector arm

angles at 45° intervals. This measured distance varied by

0.05 mm. The inside micrometer had a standard uncertainty of 0.05 mm. These values are small compared to the overall distance, so for simplicity these were added together and treated as a standard uncertainty of 0.10 mm, or 0.02 % of the distance. The uncertainty in the solid angle of detection was calculated by

combining in quadrature the uncertainties in the receiver

limiting aperture area and the distance from the sample

plane to the receiver limiting aperture (with appropriate

weighting factors). This yielded a relative standard uncertainty in the solid angle of detection of 0.075 %.

To check the angular accuracy of the goniometer system,

the receiver was centered on the incident beam and the receiver angle counter was set to 0°. A first surface mirror was then mounted in the sample holder and

positioned so as to retro-reflect the incident beam. The

sample angle counter was then set to 0°. The sample

holder was rotated in 10° steps and the receiver was

positioned to the appropriate (theoretical) angle to inter- cept the specular reflection of the beam. The distance from the center of the receiver to the center of the reflected beam was measured for each angular setting.

This procedure was repeated several times. The largest

measured displacement of the beam from the receiver center was 0.5 mm. Because the center of the beam

could be estimated to 0.5 mm, this was added to the measured displacement for a maximum displacement of

1 .0 mm. At a distance from sample to receiver of

672.6 mm, this corresponds to a relative standard uncertainty in the receiver angle of 0.09°. The rotary stages

used in the STARR goniometer have an angular resolution of 0.001° and an angular standard uncertainty and

Ikble 2. Relative combined standard uncertainties, expanded uncertainties, and their components

Components of the relative standard uncertainties.

Source of uncertainty Relative standard uncertainty

Incident flux measurement, 0.10%

Reflected flux measurement, <P, 0.10%

Receiver limiting aperture area, A 0.05 %

Distance from sample to receiver, R 0.02 %

"

Solid angle of detection, to. 0.075 %

Angle of observation, 6, 0.09° cosd, 6,-0° «0.001 %

6,- 15° 0.042 %

6, - 30° 0.091 %

«r-45° 0.157%

flr-60° 0.272 %

6,-15° 0.586 %

Relative combined standard uncertainties and expanded uncertainties for coverage factor k-2

Uc{SRF) U{SRF)

SRF measurements 0.14% 0.28 %

u,{BRDF) U(BRDF)

BRDF measurements 6,-0° 0.160% 0.320 %

6,-15° 0.165% 0.330 %

6, - 30° 0.184% 0.368 %

6,-45° 0.224 % 0.448%

6,-60° 0.316% 0.632 %

6,-15° 0.607 % 1.214%

" This is the only type B component of the combined standard uncertainty. All other components are type A.

623
Volume 101, Number 5, September-October 1996 Journal of Research of the National Institute of Standards and Technology

repeatability of 0.01°. These are small compared to the measured receiver angular relative standard uncertainty

of 0.09 %, and in fact, such stage-induced errors are included in the measurement of the receiver angular

relative standard uncertainty.

Figure 3 shows the specular reflectance of an SRM

2003 first-surface-aluminum-coated mirror at 6°/6°

geometry. Measurements made on the STARR and RRI

agree to within their respective measurement uncertainties.

Figure 4 shows the BRDF of a white porcelain

enamel on steel plaque at 45°/0° geometry. It is interest- ing to note that the RRI data for this sample were

obtained in 1977 while the STARR data were obtained

in 1995. Measurements made on the two instruments agree to within their respective measurement uncertainties over most of the spectral range measured. Considering that nearly 20 years elapsed between these measurements, the agreement is remarkable, and demonstrates

the excellent long term stability of this sample. The

1.00 T

0.95

0.90 V

0.85 - -

0.80250 500

5 5

i

^

^ \ ^ ''il \ \ \ III

a STARR

o RRI

H

750 1000 1250 1500 1750 2000 2250 2500

Wavelength (nm)

Fig. 3. Specular reflectance factor of a first-surface-aluminum-coated mirror using a 6° angle of incidence and a 6° angle of observation (6°/6° geometry) as measured by the STARR and the Reference Reflectance

Instrument (RRI).

0.35 T

0.30 -

-

i 0.25

0.20 - -

0.15

a STARR

o RRI

^^^^^^

380 440 500 560

Wavelength (nm)

620 680 740

Fig. 4. BRDF of a porcelain enamel on steel tile using a 45° angle of incidence and a 0° angle of

observation (45°/0° geometry) as measured by STARR and by RRI.

624
Volume 101, Number 5, September-October 1996 Journal of Research of the National Institute of Standards and Technology

slight differences in the UV data could easily be due

to aging of the sample or differences in cleaning

techniques.

Figure 5 shows the SRF of NG-9 black glass (SRM

2026) at 6°/6° geometry. At some wavelengths the agreement between the instruments is excellent, while at other wavelengths they differ by several percent. Other

types of black glass samples, such as GL-2, show much

better agreement. A period of approximately 2 years elapsed between the RRI and STARR measurements, so

further studies of NG-9 stability and the effects of clean- ing procedures should be performed.

Figure 6 shows the SRF of GL-2 black glass at 6°/ 6°

geometry. This sample was used in the RRI as a refer- ence sample for low level reflectance measurements in the UV spectral region, and was chosen for its long

0.050 T

0.045 -

Z 0.040 -

aIt 0.035 ,• •

I ^ ^ f i J 5

Q STARR

o RRI

-H

1250

0.030 '

250 -+—

500 —H750 1000 1500 1750 2000 2250 2500

Wavelength (nm)

Fig. 5. Specular reflectance factor of NG-9 black glass using 6°/6° geometry as measured by STARR and by RRI.

0.060 T

0.055 • STARR

oRRI

0.050

0.045 • - I 0 0

0.040230 250 270 290 310 330 350 370 390

Wavelength (nm)

Fig. 6. Specular reflectance factor of GL-2 black glass using 6°/6° geometry as measured by STARR

and by RRI.

625
Volume 101, Number 5, September-October 1996 Journal of Research of the National Institute of Standards and Technology

measurement history and demonstrated long term

stability. The agreement between the two instruments is excellent except for the 230 nm and 250 nm data. The

RRI was known to have marginal low-level measure- ment performance at 250 nm. The RRI was not designed

to operate at 230 nm, and at this wavelength, measure- ment performance was very poor. Figure 7 shows the BRDF of pressed PTFE as measured by the STARR. Because this sample was freshly

pressed for measurement on the STARR, no direct comparison can be made with the RRI. However, the

results of the STARR measurements are in agreement

with RRI measurements of similar samples.

6. Conclusion

The Reference Reflectance Instrument (RRI) had

been in service at NIST for nearly 2 decades, performing specular reflectance and BRDF measurement

services, as well as calibration of numerous SRMs. The

Spectral Tri-function Automated Reference Reflec- tometer (STARR) was designed to replace the aged RRI,

and to enhance the range of measurements that could be

performed to include larger samples, raster-scanning of

samples for uniformity, and spectral transmittance. The new instrument has been designed to provide these

capabilities, as well as to provide greater speed of

measurement, and more stable and accurate positioning.

The STARR source system was designed to deliver higher flux to the sample and more reliable alignment

than the previous system. Care was taken in the optical

layout to minimize the number of optical elements in the source system. The STARR source system (including

the lamp housing, monochroroator, and beam steering

optics) has 7 first surface reflective elements versus 1

4

for the RRI. This allows the STARR source system to maintain optical performance longer in the presence of

degradation of optical elements. As an example, if the reflectance of the elements degrades to 0.8, the effective reflectance of the seven elements would be 0.8' = 0.202,

while the same degradation in the RRI would result in an effective reflectance of 0.8'" = 0.044. During a 1 year testing period of the STARR, the mechanical stability of the system was shown to be

excellent. During this period, frequent checks of the optical alignment demonstrated that the instrument

maintained proper alignment for extended periods. The

system required re-alignment only as a direct result of

making changes to the optical components to improve

performance. The longest period between optical system

changes was 6 months, and during this time, no alignment adjustments were needed.

The STARR receiver system was designed to give

better detector performance over a broader spectral range than that of the RRI. The STARR can measure

reliably at 200 nm, while the RRI could not perform

below 250 nm. Even at 250 nm, the measurement per- formance of the RRI was marginal.

Two limitations of the STARR were found during

testing. First, the Glan-Taylor polarizer has fairly low

transmittance in the 200 nm to 350 nm spectral region.

A UV grade polarizer will be evaluated for use in this

0.36 T

0.34 -

0.32 -

0.30 • -

0.28 - -

5 5

5

5 5 5 5 5 5 555555

0.26220 240 260

-I——I 1 h

280 300

+-

320

Wavelength (nm)

340 —I H360 380 H 1 400

Figure 7. BRDF of pressed Polytetrafluoroethylene (PTFE) using 45°/0° geometry as measured by STARR.

626
Volume 101, Number 5, September-October 1996 Journal of Research of the National Institute of Standards and Technology

spectral region. Second, while the indium arsenide

phododiode has excellent responsivity and linearity, it is only available in sizes which are too small for use in the STARR receiver without some diffuser or light gathering mechanism. Several approaches to improve NIR

performance are being considered. A 2 mm diameter InAs detector can be fabricated, but due to the relatively

low shunt impedance of these detectors, it is not clear

that the larger area will result in better performance. A

nonimaging concentrator may be used to collect more

flux from the averaging sphere and concentrate it onto

the detector. Additional optical elements may be used to refocus the receiver at reduced image size directly onto

the InAs photodiode, eliminating the need for the aver- aging sphere. Other detector technologies may also be

evaluated. The design goals for the STARR were to build an

instrument which would perform all of the measure- ments of the former RRI, to perform these measure- ments with higher accuracy and greater speed, and to handle much larger samples. The STARR performs all of the measurements of the RRI, with additional capabilities, such as raster scanning of large samples, and

transmittance measurements. Improvements in the detector system have reduced the radiometric uncertainties of these measurements. The accuracy of positioning and

mechanical stability of the new system provide reduced

geometrical uncertainties. High accuracy measurement

of the receiver limiting aperture reduce both radiometric

and geometric uncertainties. Many measurements which took several days on the RRI can be performed in a matter of hours on the STARR.

Acknowledgments

The authors wish to express special thanks to Albert

C. Parr for initiating this project, for the support and

encouragement needed to achieve our goals, and for many valuable suggestions; Robert D. Saunders and

Christopher L. Cromer for their support and technical guidance; Jack J. Hsia for many useful discussions; and Sally Bruce, Thomas Larason, Joel Fowler, Clara

Asmail, and Thomas Germer for calibrations and other

contributions to this effort.

7. References

[1] Victor R. Weidner and Jack J. Hsia, NBS Measurement Services: Spectral Reflectance, NIST Special Publication 250-8, (1987).

[2] F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, and

T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, NIST Monograph 160 (1977).

[3] Joel B. Fowler, High Accuracy Measurement of Aperture Area

Relative to a Standard Known Aperture, J. Res. Natl. Inst. Stand. Technol. 100 (3), 277-283 (1995).

[4] P. Yvonne Barnes and Jack J. Hsia, 4570° Reflectance Factors of

Pressed Polytetraflouroethylene (PTFE) Powder, NIST Technical Note 1413 (1995).

[5] John C. Stover, Optical Scattering: Measurement and Analysis

2nd edition, SPIE Press (1995) pp. 19-22.

[6] Barry N. Taylor and Chris E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST Technical Note 1297 (1994).

About the authors: James E. Proctor is an Electronics

Engineer and P. Yvonne Barnes is a Physical Scientist in the Optical Technology Division of the NIST Physics

Laboratory. The National Institute of Standards and

Technology is an agency of the Technology Administration, U.S. Department of Commerce.

627

Appendix F

JOURNAL OF RESEARCH of the National Bureau of Standards Volume 82, No. 1 , July-August 1 977

Establishing a Scale of Directional-Hemispherical Reflectance

Factor I: The Van den Akker Method

William H. Venable, Jr., Jack J. Hsia, and Victor R. Weidner

Institute for Basic Standards, National Bureau of Standards, Washington, D.C. 20234

(May 22, 1977)

A thorough study and error analysis was made of the Van den Akicer or "auxiliary sphere" method of determining a scale of directionaJ-hemispherical reflectance factor. The effects of a non-Lambertian distribution of

the reflected radiation, including retroreflection, were included in this study. Three working standards were

measured to an uncertainty in reflectance of less than ±0.0015 and these will be used as a basis for a new, more

accurate NBS scale of 6°-hemispherical reflectance factor. The new scale and the NBS scale established in 1965

are in agreement to within the uncertainly of ±0.005 assigned to the 1965 scale.

Key words: Absolute reflectance; diffuse reflectance; error analysis; reflectance; reflectance factor; spectrophotometry. Foreword

We have arranged this paper in a way which should

accomodate readers who have an interest in this work from

three quite different points of view:

1. Those who must make decisions based upon the results of the measurements are addressed principally in the Summary which directly follows this foreword. The

material in parts I. and V.B. would also be of interest

to such readers.

2. Those who wish to use the Van den Akker auxiliary

sphere method for determining absolute reflectance should find the material in parts II, III, and V.A. to be

of particular interest, and part IV can be read superficially, if at all, in order to glean a few technological

ideas.

3. Those who are interested in a detailed understanding of the way in which these measurements are carried out at NBS and in a detailed discussion of the error analysis

should, after a careful reading of parts II and III, place

their emphasis on part IV.

Summary

Of the light or other optical radiation incident upon a surface in a given direction and at a given wavelength, a

fraction is reflected from the surface. This fraction is called the spectral directional-hemispherical reflectance of the surface, and measuring it accurately is important in two different classes of applications:

1. Applications in which the value of the reflectance is of

direct importance. Such applications include radiative energy transfer as in solar energy devices, lighting

system engineering, calibrating radiometers in remote

sensing satellites, and formulating the pigmentation in paints and other flnishes.

2. Applications in which the actual value of the reflec- tance is of secondary importance, but for which the basis of measurement must be extremely stable in time. These applications include quality control in auto- mated production and specifications involving color or appearance of finished products. For such applications, the instruments which are used are calibrated with material standards, and the laboratories supplying

these standards must be able to measure reflectance

directly in order to measure the standards and verify their stability.

The economic benefits derived from having this portion of the measurement system under control are very large, coming in the form of an accumulation of modest benefits over a very

large base of application [1].' In order to realize these advantages, it is important that the uncertainty in the measurements be commensurate with the uniformity and stability of the reflectance of the surfaces encountered in practice. For a number of applications, it is important to measure

directional-hemispherical reflectance factors near 1 with an

uncertainty in the neighborhood of ±0.001. The present extensive work on spectral directional-hemispherical reflec- tance was undertaken at NBS for two reasons. First, the stated uncertainty of ±0.005 for the NBS reflectance factor scale established in 1965 [2]* was too large for many of the applications for which we were called upon to standardize the measurements. Second, and even more disturbing, intercomparisons between the scales of national standardizing laboratories in connection with the work of the International Standardization Organization (ISO) revealed differences as great as 0.015 between the measured value of reflectance of the same

samples. Such a large difference can have serious economic

consequences in international trade in finished goods such as paper. As a first step in this work, we have investigated in great

detail the Van den Akker auxiliary sphere method of deter- mining spectral directional-hemispherical reflectance which

' Figum in brackets indicate the literature references on page 49.

29
has been used in the past at NBS, improving upon the techniques and providing the necessary corrections to make

the measurements precise and accurate to within ±0.0015 to the best of our knowledge. This step has been completed and

is reported in this paper. The new and former NBS scales of measurement agree to well within the combined measurement

uncertainties. As a second step, we plan to investigate the techniques

used by the other major national laboratories and to work with our colleagues in these laboratories to determine the cause of

the discrepencies which have been encountered internationally. As part of this step, we have already completed a set of measurements using a second method of determination, the

Sharp-Little method. The results obtained with that method

are in good agreement with those reported in this paper and

are to be published soon in another paper in this same series. We have visited the National Research Council Laboratories

in Canada (NRC) for detailed discussions of these results. We

also plan to conduct experiments with the Korte method

currently used by the Physikalisch-Technische Bundesanstaldt (PTB) in Germany and possibly with one or two other approaches less commonly used. The scale of directional-hemispherical reflectance as currently established will be disseminated through standards

supplied through the NBS Office of Standard Reference

Materials and through commercial secondary standards laboratories in the United States. The improvements in tech- niques which have been developed as a result of this work

will be submitted to the appropriate committees of ASTM,

ANSL and TAPPI for possible incorporation in standard

procedures. When the international discrepancies have been

ehminated, we will be working with NRC, PTB, and possibly

other laboratories as standardizing laboratories for ISO re- flectance measurements.

I. Introduction

Directional-hemispherical (d/h) reflectance factor measurements are important in a wide variety of applications. If the results of these measurements are to be a useful tool for technical communication, the measurements must be made

accurately. Most reflectometers are not capable of measuring

d/h reflectance factor directly, but can only compare the reflectance factors of two objects. The calibration of such

instruments is accomplished by measuring a standard object

which has a known reflectance factor. To see that accurately

measured reflectance standards are available to the measure- ment community is one of the primary responsibilities of the spectrophotometry group of the Radiometric Physics Section

of the Institute for Basic Standards.

In the development and production quality control of fin- ished products in which appearance is an important factor, the measurement of reflectance should be accurate to within ±0.002. This level of accuracy or better is also important to rapidly evaluating the stability of reflecting materials under

weathering and ageing. These two types of applications are

the ones which commonly call for the lowest measurement

uncertainty. It is difficult to produce highly reflecting sur- faces for which the reflectance is reproduced to better than ±0.001 and the reflectance of most surfaces is not even

uniform to this degree. Therefore, a reflectance measuring

capability for which the uncertainty is less than ±0.001 is both necessary and sufficient for a national standardizing

laboratory. The work described in this technical note is part of an effort to reduce the uncertainty in diffuse reflectance

factor measurements at NBS from an estimated ±0.005,

which it has been in the recent past, to ±0.001.

The National Bureau of Standards (NBS) has established

its scale of d/h reflectance factor in 1965 through an extensive series of measurements by Goebel, Caldwell, and Hammond [2]. At that time, Vitrolite [3] glass standards [4] to calibrate the General Electric Recording Spectrophotometer

(GERS) [5] (Cat. 5962004 G28 No. 732986) were measured.

Until recently, that instrument has been used for most reflec- tance measurements made at NBS. The reflectance of the

Vitrolite standards has been shown to be very stable by measurements made over a period of thirty years relative to freshly prepared MgO surfaces [6]. In 1974, the scale of measurement was rechecked using the same apparatus used

in the 1965 experiments and the agreement was within the experimental error associated with the measurements.

In April of 1974 and through the following year, it was

determined from measurements made on a number of samples

that there was a systematic difference between the scales of measurement being used by NBS and the National Research

Council Laboratories of Canada (NRC). This difference was

approximately 0.015 at the short wavelength end of the

visible spectrum and decreased more or less regularly to approximately 0.01 at the long wavelength end of the spec- trum (table I). A similar intercomparison between NRC and

Physikalisch-Technische Bundesanstalt of Germany (PTB)

[7] revealed only slight differences between the measure- ments being made by these laboratories (table II). Since the NBS uncertainty at that time is conservatively estimated to be

±0.005 and the NRC uncertainty is conservatively estimated

to be ±0.003, the difference is clearly significant.

Table I

Data from an intercomparison between NRC and NBS of reflectance measurements on a sprayed BaS04 coating*. (June 1975) (Spectral directional (6°)-hemisphericai reflectance).

Reflectance Wavelength

NRC NBSt Difference (NRC-NBS)

400 0.961 0.975 0.014 420 .963 .975 .012 440 .966 .978 .012 460 .970 .980 .010 480 .970 .981 .011 500 .972 .981 .012 520 .972 .985 .013 540 .972 .985 .013 560 .974 .984 .010 580 .975 .985 .010 600 .975 .985 .010 620 .976 .982 .006 640 .975 .986 .011 660 .976 .985 .009 680 .976 .985 .009 700 .977 .985 .008 720 .978 .985 .008 740 .979 .985 .007

* Samples prepared at NRC.

t Data from NBS test 232. 14/49D.

The methods used by NBS, NRC, and PTB are all differ- ent. In any such case of disagreement between measurements, all measurements and methods are logically suspect

30
Table II

Data from an inlercomparison between NRC and PTB of reflectance measurements on a pressed BaSO^ tablet [7] (Spectral Hemisphericaldirectional (0°) reflectance factor).

Reflectance Wavelength

NRC PTB Difference (PTB-NRC)

370 0.961 0.965 0.004 380 .969 .971 .002 390 .974 .976 .002 400 .977 .979 .002 420 .982 .983 .001 440 .985 .984 -0.001

460 .986 .985 -0.001 480 .987 .986 -0.001

500 .987 .987 0

550 .988 .988 0 600 .988 .988 0

650 .987 .988 0.001 700 .987 .989 .002 750 .987 .988 .001

until the cause of the difference is located. However, since

the NRC and PTB measurements were in close agreement, it seemed reasonable to investigate the method used by NBS

first. A Diffuse Transmittance and Reflectance Reference

Spectrophotometer [8], which will be referred to by the acronym DRS for convenience, was completed at NBS in October 1975. This has been used to make detailed measure- ments of all aspects of the Van den Akker auxiliary sphere

method for realizing an absolute scale of d/h reflectance

factor [9], which was the method used to establish the NBS

scale. The results of this investigation are reported in this paper. As a result of this investigation a new NBS scale of diffuse reflectance factor measurements for 6° incidence and hemispherical collection has been established which is believed to be accurate to within ±0.0015. The new scale of reflectance

factor differs by less than 0.002 from the scale formerly used

by NBS. Since this investigation revealed no cause for the discrepancy between national laboratories, we are undertaking a thorough examination of the methods used by the other

laboratories. The results of that work are to be reported in future papers.

II. Definitions

A. Directional-Hemispherical Reflectance

One quantity to be measured is the spectral d/h reflec- tance, p (U, P, \) at a point on a plane surface. Using the notation described in NBS Technical Note 594-9 [10], this quantity can be expressed in terms of a generalized scattering function 5 as:

p (U, P, X) = // 5 (U, P; u, p, \) u-da du) (1)

where S(U, P; u, p, \) is the radiance emerging from the sample surface at point p in direction u due to a unit flux striking the sample at point P in direction U. It is assumed

that the sample is non-fluorescent so that all of the radiation can be confined to a very narrow band at wavelength k. The

integral with respect to the solid angle, oj, in which the radiation emerges is taken over the entire hemisphere of

directions and the integral with respect to the area a from

which the radiance emerges is taken over the entire area from

which the flux emerges. For the uniform, isotropic samples to be discussed in this paper, the d/h reflectance can be repre- sented by p(r, K), where F is the angle between the direction of incidence u and the surface normal.

B. Directional-Hemispherical Reflectance Factor A typical d/h reflectometer has an entrance port which

subtends at the sample a circularly shaped solid angle to' which in magnitude is on the order of lO""* steradians. None

of the flux falling into &)' reaches the detector, and therefore the instrument does not compare d/h reflectances of the samples as just defined but rather compares "directional- hemispherical" reflectance factors [11] F(T, ,A) for collection over the entire solid angle except for a»'. That is to say, the

retroreflected flux is excluded from the measurement. To a very good approximation.

F{r, \)

ff'S(U, P; u, p, k)u-dad(i}

//'[8(P - p)/n]a-dadai

(2)

where the prime on the integral indicates integration over the

entire hemisphere except for (o' and 8(P — p)/7r is the

idealized scattering function S for an ideal diffuse reflector.

It is the quantity F(r, k) in which we are most interested when calibrating a reflectometer, and determining this quantity for several working standards is the object of the work

reported in this paper.

III. An Overview of the Method

The method to be described for determining d/h reflec- tance factor is more complex than the method for measuring

d/h reflectance originally proposed by Van den Akker. In the

original method, it was assumed that d/h reflectance is independent of the direction of incidence. Since this is not

sufficiently correct for many surfaces, additional measure- ments are needed in order to accurately determine the d/h

reflectance using this approach. Also, the relationship be- tween d/h reflectance and the reflectance factor as measured

by an instrument must be determined. However, for simplicity, we will continue to call the entire process the Van den

Akker method.

Although this method is simple in principle and is potentially one of the most accurate methods, the descriptions of it in the literature are usually given in terms of involved summations of infinite series. These descriptions tend to cloud

the simplicity of the method and to lead to a misunderstanding of it. Therefore, before describing the details of the measurements as performed at NBS, we will first provide a

brief overview of the method in terms of four main steps. The

first and last steps were used in the original Van den Akker

method, and we have added the additional steps to take into account the variation of p(r, k) with F and the difference between p(F, k) and F(F, k). The primary nieasurement in the Van den Akker method is a measurement of the reflectance of the wall of an integrating

sphere (fig 1) under the irradiation it receives in the sphere.

We will call this reflectance the Van den Akker reflectance

PtJik). A flux is introduced into the sphere by reflecting a collimated beam of radiation from the back of the sphere.

31
REFLECTOMETER

SPHERE ^

REFLECTOMETER

SAMPLE PORT

RADIUS

HEMISPHERE ASSEMBLY FLANGi REMOVEABLE

TARGET

SECTION

POLISHED BEVELLED PORT EDGE

STAINLESS STEEL PORT PLATE /

(.6 mm THICK 1^

ALUMINUM SPHERE SHELL

Figure I. Sphere used for measuring Van den Ahker reflectance.

Most of the radiation which strikes a given area of the sphere

wall has undergone many reflections. In a sphere of this type,

the average number of times a photon will have passed into the sphere wall and been reflected before it is absorbed or escapes would be between fifty and one-hundred. Because

the reflection from the sphere wall is very diffuse, any asymmetry in the way the photons are introduced is dispelled

in one or two reflections and the distribution of radiance, L,, striking the wall has two characteristics properties. First, the

irradiance is very nearly uniform over the sphere wall. This

follows from the fact that a perfectly Lambertian (radiance

constant with respect to direction) reflected flux would pro- duce a uniform irradiance over the sphere wall. Since the

distribution of the reflected flux is very nearly Lambertian,

the distributon over the sphere wall of incident photons which

have been reflected more than two or three times is for all practical purposes uniform. This phenomenon is well-known

and forms the basis for the many applications of integrating

spheres in which the sphere is used as a flux averaging

device. Another property of the spherical geometry which is less often noticed is that a photon which leaves the sphere

wall at an angle 6 will next strike the sphere wall at the same

angle. Thus, after one or two reflections, an angular distribution of radiance Lg (f), will be set up which represents, to within a proportionality constant, the incident and emerging

radiance at any point on the sphere wall. Unlike the distribution of irradiance over the wall area, the distribution of the radiance with respect to the angle does not become uniform

with angle but takes on a distribution determined by the

bidirectional reflectance properties of the wall coating.

The remaining steps in the method relate the Van den

Akker reflectance to the d/h reflectance factor and provide a method of using this reflectance data to calibrate an instru- ment. The four steps in the Van den Akker method can be

outlined as follows:

A. Determining the Van den Akker Reflectance Pv(X)

A sphere with a single port (see fig. 1) is lined with a

highly reflecting white coating, radiation is introduced into the port in a collimated beam, and, from measurements made

of the flux re-emerging from the port and of the flux reflected

from the target area, the Van den Akker reflectance p^'^ is determined. A flux 4>o (A.) is introduced into the sphere in a

collimated beam which strikes the target area of reflectance

Pt (F, \), providing a nearly Lambertian source of radiation which emits a flux 0oPr- A fraction f of this flux passes out through the port as a nearly collimated beam, and the re- maining portion falls on the sphere wall and is reflected with

reflectance Py, the average reflectance of the sphere wall,

excluding the port. This flux, the strength of which is given

by 0oPf (1 " f)p'vi acts as a radiation source which is uni- formly distributed over the sphere wall. This flux is the source of radiant energy for the total flux <^>i(X) striking the sphere boundary. A fraction / of A.^ passes out through the

port, and a fraction (1 — p'y) of the remaining (1 — f) is ab- sorbed in the sphere wall or otherwise lost and is not returned

to the sphere. In equilibrium, the flux lost from «^,- out the

port and into the walls is replaced by the uniformly dis- tributed source, from which an equilibrium flux balance

equation can be obtained: 0opki -fip'v = <t>i[f + (1 -m - p'v)]- (3)

If the flux </>o is the sample beam flux from a dual beam

reflectometer, a signal 4's(^) is obtained with the sphere in the sample position:

Qs - h[<f>/(i -/') + 4>oPtAi -/")] (4)

where /' is the fraction of the lambertian flux which escapes

from the ports of the reflectometer sphere and /" is the corresponding fraction of the nearly collimated beam which

emerges from the sphere as a result of the first reflection from

the back of the Van den Akker sphere. With the target area from the back of the sphere placed directly on the reflectometer sample port as a sample, a signal ^/(A.) is obtained:

(5)

It is arranged that the angle of incidence F at which <}>o strikes the target when Qt is measured is the same as when Qg

is measured. Equations (3), (4), and (5) can be solved to obtain an expression for p'„ in terms oi Qt, Qs,f, f and /".

Pv

1 - {fQi/Qs)ii/a - g))

1-/

/her

a

f<J' - f") Qt

(1-/) Q,

(6)

(6a)

If a were 0, this would be the usual form cited for the Van

den Akker reflectance. The factor 1/(1 — a) takes into account that the first reflection of the incident beam from the

target in the sphere emerges nearly collimated whereas the remaining flux emerging from the sphere is nearly Lambertian. If the reflectometer handled both fluxes in the same

way, i.e., if/' and /" were equal, this term would be zero. However, it is usually the cause that /" is very much larger than /' and this contribution must be included.

' Tu ktfep ihe writing unclullered, the functinmii dfpendence (if euch quantity ii ihuwn only when

it it inlnxiuced and ul key points in the devrlupment.

32
An additional modification must be made in the original

Van den Akker equation to take into account the effect on

of the retroreflectance of the sphere wall. This modification,

which results in only a small adjustment pp but which greatly

complicates the form of eq (6), is discussed in detail in appendix A.

Since (1 ~y)(l ~ Pv) in eq (3) represents the portion of </)j which is lost everywhere but out of the port, it follows that the reflectance pp' is the average reflectance over the sphere area excluding the port. To relate pp to a property of the sphere

coating, it is important that the sphere coating be uniform and

completely cover all of the sphere area except for the entrance port. If it is necessary to have cracks or other gross imperfections in the coating, the losses in such imperfections must be estimated and Pp must be suitably corrected in order

to obtain the Van den Akker reflectance pp of the sphere

coating.

B. Adjustment from Van den Akker Reflectance Pp(X) to d/h Reflectance p(r, X)

In order that the need for the next steps be more readily

understood, pp will be interpreted in terms of the directional- hemispherical reflectance, p, as defined in eq (1).

Pv =

ir/2 27T

I UY) piT) cos(r) sin(r) dT

JT/2 27r I L,{T) cos(r) sin(r) dT

(7)

where ^,(r) is the radiance associated with <f>i at the incident angle T and explicit indication of the dependence on wavelength has been omitted for clarity. As we have indicated, pp

is just the weighted average over all directions of incidence F

of the d/h reflectance. The weighting function LgiT) cosF

sinT is proportional to the irradiance of the sphere wall per

unit angle at the angle F. If the d/h reflectance were inde- pendent of angle of incidence, one can see from equation (7) that Pp and p{F) would be identical. However, in any real sphere coating, piT) is not quite constant and this variation must be taken into account if d/h reflectance is to be deter- mined from Pp.

The flux. <^j. striking the sphere wall is composed of radiation most of which has undergone many reflections. As

has already indicated, the radiance LgiT) striking the wall in one location emerged-from the wall at the same angle at some

other location. When the irradiance of the wall is uniform and

if the generalized scattering function S of the coating were known, the function L, could be determined by solving the

integral equation

PvL,siy) = 27r [

Jo

«2

LID Sir, y) cosF sinT «/F. (8)

Because the irradiance of the sphere wall is uniform, the self radiance distribution, L,, can be determined to within a

constant by measuring the radiance, Lg(y), emerging from the sphere coating through the port with an uncalibrated gonioreflectometer. The relative signal Ng from the gonioreflectometer as a function of the angle of observation y can be related

to L,{y) as

Ls(y, X) = fc,(X) /V„(7, X^cos(-y) (9)

where ki is a constant of proportionality.

To complete the adjustment, information about the form of p(F, X) is obtained. A flat sample of the sphere wall coating

is prepared in the same way as the sphere wall coating and its relative d/h reflectance is measured. The corrected reflec- tometer signal [12] Nq is proportional to the d/h reflectance.

p(F, X) = MX) /Vc(F, X). (10)

The constant Ic^ can be expressed in terms of measured

quantities by simultaneous solution of eqs (7), (9). and (10).

A2(X) =

Pr(A)JyVg(F, X) sinF dr _ Pp(X)

//Vc(F, X) /v„(r, X) sinF dr ~

yvcCx)

(11)

where A'g is the weighted average of A'c(F, X) with weighting

function Ng{r, X) sinF. With the value of A:2 determined, the d/h reflectance for any wavelength and angle of incidence can be calculated from the relative d/h reflectance data by using eq (10). However, we prefer to use an expression forp(r, X) which takes the form of a small adjustment of the Van den

Akker reflectance. By substituting the expression for from eq (11) into eq (10) and using some algebraic manipulation, one can put eq (10) into the form

p(F, X) = Pp(X) [1 + C(F, X)] (12)

, Ncir, X)

ar, X = - 1. A^g(X)

C. From d/h Reflectance p(r, k) to d/h Reflectance

FactorF(r, k)

If the generalized scattering function S for direction;; of incidence and reflectance both falling within the reflectometer entrance port (retroreflectance at entrance angle F) were

equal to the average of S over all directions of viewing, then

the reflectance p(F, X) and the reflectance factor F(F, X) will be equal. However, for the usual type of sphere coating, S in the retroreflective direction has been observed to be as much

as 50 percent above the average at small angles of observation [13]. Therefore, the bidirectional reflectance factor F(U, u X) must be determined over the extent of the solid angle co' surrounding the incident direction U and the relationship

between F(r, X) and p(F, X) determined from eqs (1) and (2) as

p(F, X) - -

I F(U, u)cosy dco Fir, X) = ( 13) ^1 — — O)' cos^^

where the integral inoj is taken overa>'. (Note thatF(U, u) =

TT / S (U, u)da.)

33
D. Determining the Directional-Hemispherical Reflec- tance Factor of Standards and Other Samples

The dih reflectance factor F[Y, X) as determined in the preceding four steps is the dIh reflectance factor of the sphere

wall coating. The final step is to use this information to measure a stable standard reflector which can then be used to calibrate a djh reflectometer. One of the methods used by

Van den Akker [9] was to compare the standard directly with

sections of the sphere wall which were hoped to be representative. Another method is to prepare a large number of samples using the same materials and preparation techniques

that were used in coating the sphere itself and comparing

these to the standard. In either case, the djh reflectance

factor Fe(r, X) of the standard is calculated from the previously determined djh reflectance factor F(r, X) of the sphere

wall as

Fe(r, X) = F(r, X) ^M^J^ (14)

S QIT, X)

where Qc is the reflectometer signal for the standard and Qi is the reflectometer signal for the ith one of the n samples which

are taken to represent the sphere wall. In day-to-day use, the djh reflectance factor Fj(r, X) of a sample can be measured

by comparison to the stable standard.

F,(r, X) = F,(r, X) ^4f^ (1^)

where the reflectometer readings Qx and Qc are taken close

together in time in order to minimize the effects of instrument

drift.

IV. The Measurements as Currently Made at

NBS

The overview in the preceding section describes in general

the way that djh reflectance can be determined by the Van

den Akker method. Three determinations of the djh reflec- tance of a set of standards has been made using the DRS.

Through the experience gained in these determinations, a procedure for making the measurements with this instrument

has been worked out. That procedure is described in this section to give a documented starting point for future im- provements in the method and the data from these three determinations provide the basis for the current NBS scale of

6°//i reflectance factor. Three different materials were used as sphere coatings for the determinations. In the first determination, the sphere was

coated with BaS04 powder [.3, 14] from a stock which had

been on our laboratory shelf for some time and had been

opened on previous occasions. This was used to obtain experience with the method and to obtain an idea of some of

the difficulties which might be encountered with a material which was slightly contaminated and which had a slightly lower reflectance than the best quality coatings. In the sec- ond determination, the sphere was coated with Halon [3, 1.5] powder, and in the third determination a fresh lot of reagent

grade BaS04 powder [3, 16] was used. The advantages and

disadvantages of each coating will be brought out in the

discussion of the measurement errors in the description of each of the three main measurement steps.

A. Determining the Van den Akker Reflectance Pt)(^)

The design of the spheres used to determine the Van den

Akker reflectance of the sphere coating material is shown in figure 1. In some of his earlier work using this method. Van

den Akker used a sphere with many removable sections in order to sample at many points the actual sphere coating

being measured. However, the presence of many removable

sections provides an uneven substructure for the sphere

coating, creating a potential for dark rings and even cracks in the coating at the border of each removable section. Therefore, we decided to have only the target area removable and to rely on reproducing the coating for a representative sampling.

The sphere coating is made by packing the powder into the aluminum sphere shell with an electrically driven hammer

which has a Teflon [3] head (fig. 2). The hammer is mounted

on a stand and each hemisphere of the sphere is mounted in turn on a gimbal which allows it to be rotated about a point a

fixed distance behind the hammer. In this way, a hemisphere

of constant interior radius R is packed uniformly in a mechanical way. A plastic ring attached to the flange of each

hemisphere as it is being packed allows the packing jig to be

aligned the same for both hemispheres and allows the coating

to be built up to full thickness at the edge of the hemisphere.

In this way, when the plastic ring is removed and the sphere

is joined, a uniform sphere coating of interior radius R results which has no crack at the plane where the hemispheres join.

Figure 2. Apparatus used to produce the sphere coaling.

1 . Detennining the Uncorrected Van den Akker Reflectance p'„

The fraction / introduced in eq (6) is taken as that portion

of the area of the sphere of radius R which is occupied by the port of radius r, i.e., f

^ {\ - {\ - (rlRmil. (16)

Associated with each determinaton off there is an estimated

random error, as defined in appendix B. A random error 8R

arises from our inability to pack the sphere to the same radius

34
R from one determination of reflectance to the next and from

the inability to measure the average/? exactly. This gives rise

to a random error 8f which is given by:

8f =

2(1 - {rlR)^y

8R. (17)

A systematic error arises from any error in measuring r and

from assuming that the measured r is the effective r. Both of these can be taken into account in terms of an uncertainty Ar

in the effective port radius. The estimated systematic error A/

is given by

r/R')

2(1 - {r/R)y

(18)

The reflectance of the sphere was measured using the DRS

with the 6°/h (specular included) general purpose integrating

sphere [17]. In this mode of operation, the instrument is a dual beam reflectometer with a capability of highly accurate measurements of relative 6°/h reflectance factor, i.e., the instrument measures a quantity Q which is proportional to the 6°/h reflectance factor of the sample appearing in the plane of

its sample port. With the sphere in place as a sample, a

reflectance value which will be called is measured. As is described in detail in the Technical Note on the DRS [18], a

correction must be made for the small amount of radiation which does not enter the sphere port but instead is reflected from that portion of the sphere port plate which shows in the reflectometer sample port or is reflected from the sphere wall

of the reflectometer itself. In order to correct for this scattered

radiation, a second reflectance measurement is made with the

auxiliary sphere port plate in place without the sphere behind

it, i.e., with most of the sample beam of the reflectometer passing out into the room and being lost. The reflectance value Qp obtained in this manner must be subtracted from Q's in order to obtain a reflectance value proportional to the

radiation being returned from inside the sphere. Most of the radiation emerging from the sphere passes freely back

through the port into the reflectometer sphere. A small

fraction of it, however, will strike the polished beveled edge

of the auxiliary sphere port and will, thereby, suffer a slight loss as it returns to the reflectometer sphere. To correct for

this loss, we measured the relative reflectance ^/ of a flat plate of the same stainless steel from which the auxiliary

sphere port plate was made. Since Qf in the reflectometer is approximately the reflectance of the sample relative to the sphere wall which in turn has a reflectance nearly 1, Q/was

approximately the reflectance of the stainless steel plate for 6° incidence. The radiation coming from the sphere which

strikes the beveled edge strikes it at near grazing incidence.

Since the reflectance from a metal surface near grazing

incidence is higher than the near-normal reflectance, we

chose to represent the reflectance from the beveled edge by (1

-f 2Qf)/3. This estimate is based on the general shape of the

reflectance curves for metals [19] and on the port dimensions

(fig. 3) [20]. Under this assumption, if the projected solid angle subtended by the beveled edge of the port averaged

over the port area is cOp, an expression for the corrected sphere reflectance Qs can be written as

9. = («-W/[i-^^^i^]. (19)

POLISHED BEVELED PORT EDGE

(STAINLESS STEEL)

SPHERE WALL LINING

Figure 3. Cross section detail ofpolished beveled port edge.

Associated with this determination of Qg, there is a random

error 8Q g arising from the random errors in measuring Q'$i Qp, and Qf. Because of the smallness of a>e, the denominator in eq (19) is approximately 1 and the small random error

in Qf\\as little effect on the total random error. Therefore

(20)

Also associated with the determination of is a systematic

error A^, which arises from the uncertainty in Oig and from

the approximation used in estimating the effective reflectance

of the beveled edge of the port. The systematic uncertainty in the beveled edge correction is estimated to be one-half as

large as the correction itself, so that

The reflectance of the removable target was measured

using the same instrument. In this case a value Q't was

obtained which also included a small contribution due to stray radiation from the sample beam which is reflected from

the reflectometer sphere wall and from that portion of the

target which is outside the region occupied by the auxiliary

sphere port. A correction for this contribution was obtained

by measuring Qg with a sample in the port made of the same

material as the target but which has a hole in it the size of the

port in the auxiliary sphere. Note that in this measurement,

the beveled edge is not present, since the stainless steel port structure depicted in figure 3 is part of the auxiliary sphere.

The corrected relative reflectance of the target Qt is obtained

Qt = Q't- (22)

An expression for the random error associated with this determination of ^( is determined in a straightforward fashion and resembles eq (20).

8Qt = [8q;' + 8Qiy". (23)

The values of/, Qs, and obtained above were used in eq

(6) (more specifically, eq (A7)) to calculate values of Pk(A.),

35
the Van den Akker reflectance of the sphere wall in its entirety. The random error in pj, is obtained from eq (6) as

Sp;=[((l -QtlQm -fffT

+ {{fiQm -f)f m

The systematic error in Py is given similarly by:

Ap; = [((i -QjQm -j)'f^f

(24)

(25)

where g is only that portion of the systematic uncertainty

in given by eq (21). Note that the contribution to the systematic error in Qs and Qt due to systematic errors in the DRS are omitted because these errors are very small [21] and

because they tend to cancel when the ratio QtlQ s is taken in determining p|, from eq (6). Therefore there is no ^Qi term in eq (25).

2. From Uncorrected Van den Akker Reflectance p'„ to Corrected Van

den Akker Reflectance p„

The quantity pj, as determined in the preceding section is the average Van den Akker reflectance of the sphere wall. In oxder to obtain the Van den Akker reflectance of a thick coating of the sphere wall material, it is necessary to correct

pl, for the effect of the crack around the removable target section and for translucency in the sphere wall coating.

a. Th* Gap Araund Ih* Tai9*t

Since the target portion of the sphere is removable, there is a narrow gap in the sphere wall around the target. The gap

acts as a light pipe between two aluminum surfaces, so that the effective reflectance of the gap is essentially zero. Therefore, in order to relate the measured Van den Akker reflec- tance p'v to the Van den Akker reflectance of the wall

coating, the loss in the gap must be accounted for:

Pv kti\- 2r,ir/(4/f2 - r")] (26)

where r, is the radius of the target, W is the width of the gap, r

is the radius of the entrance port, and kt is a transluency

correction factor as determined in section IV. A.2.b. below. The systematic error associated with the crack correction is estimated to be one-half the magnitude of the correction. The

total systematic error in p„ is given by

^Pv = Pv

rtW

are depicted in figure 4. The coating in the sphere is, on the average, about 4 mm thick, so that the reflectance of a barium sulfate sphere wall is equal to the reflectance in the

limit of a very thick wall, p^c [22]. Therefore, for these

coatings kt = \. However, in the case of Halon, the wall is not thick enough and a correction was made based on the data

in figure 4. In this correction, the thickness of the coating at any point was taken to be the distance from the surface to the aluminum substrate at that point, and a translucence correction factor was obtained by a calculation having the follow- ing form:

Pio

(28)

where Px is the relative reflectance for the coating thickness

at a given point, Pio is the relative reflectance for a 10 mm thick coating

(assumed equal to p»),

dA is an element of the sphere wall area, and the integral is taken over the entire area of the sphere

wall.

1 002

1 000

998

996

994

992

990

988

986

I

§

8

O

I- A A nm HALON X nm 1 BaS04

400 o 400 •

550 550

700 A 700

J L

4 6 THICKNESS (mm)10

Figure 4. Reflectance of wall coalings as Junction of thickness.

(Nurmalized to give a reflectam:e of approximately 1 for thick samples.)

b. Trantlucency of f^he Wall Coating

The relative reflectance as a function of thickness was

measured at each of three wavelengths on samples of each

type of coating material. The results of these measurements

It is estimated that the coating thickness measurements

might have been in error by as much as V2 mm for the 4 mm

thickness. Therefore the calculation of eq (28) was redone

using 3.5 and 4.5 mm for the average coating thickness over

the main sphere wall in order to obtain an estimate of the random uncertainty 8kt of this correction. An expression for

36
the random error in Po as given by eq (26) is

Since using the distance from the coating surface to the aluminum substrate as its thickness is only a rough approximation in the regions of the port and of the target boundary, a systematic error will be introduced by that approximation. An

estimation of this uncertainty was obtained by calculating k'l — P4/P1O1 and estimating the systematic error as (/cj — k()/2. We assumed the translucency correction to be approximately

independent of wavelength. The data in figure 4, for 1 mm

thickness indicates that this may not be exactly correct. Therefore, there may be a wavelength dependent systematic

error of approximately ±0.0005 in ^^ with the positive error associated with short wavelengths and the negative error with long wavelengths.

The Halon coatings used in our apparatus had a density of 0.8 g cm~^. Grum [23] refers to a coating of Halon which is opaque at 2 mm thickness. However, from the description of the pressure under which the coating was formed, his coat- ings are probably much denser than ours.

3. Sample Curvature and Sphere Size

Questions have been raised concerning the effect of the

size of the sphere upon the Van den Akker reflectance. Possible errors may arise due to the inability of the measuring

instrument to properly compare the reflectance of curved and

flat surfaces, either due to the difference in the relative areas

of the port and the remainder of the sphere wall or due to a change in the reflectance of the wall coating with curvature. This question has been addressed experimentally in two

different ways. The relative 6°//i reflectance of curved and

flat samples was measured directly. The average relative reflectance at 550 nm of four concave BaS04[14] samples

from the first determination was 0.9826 ± 0.0027 and the average reflectance of two flat samples of the same material was found to be 0.9834, and the uncertainty is probably of the same order of magnitude. The difference of 0.0008 is probably not significant. In the second test, the Van den Akker reflectance was

determined using two different sized spheres, one with a 95

mm interior radius and the other with a 146 mm interior radius. Both spheres were coated with the type of BaS04 [6] used in the third determination. The Van den Akker reflec- tances for these two determinations are given in table III. It can be seen that there is no significant difference between the

results from the two spheres.

4. Results and Error Analysis

The Van den Akker reflectances p^ determined for each

coating at twenty-five nanometer intervals over the wavelength range 400 nm to 750 nm are given in tables IV, V and

VI, and are pictured in figure 5. A listing of typical values used in the calculations for the Van den Akker reflectance is shown in table VII, and representative calculations of the random and systematic uncertainties in p„ are presented in tables VIII and IX respectively. The only known wavelength

dependency of these uncertainties is in the random errors.

Table III

Comparison of ih e Van den Akker re fleclance of p„ of the walls of two

different size spheres coaled with BaSO^ (16].

Wavelength

Sphere rad lus R

Diiterence in p^ (nm)

14.6 cm 7. O 1 171

4-OU n 425 .9771 .9769 0.0002 450 .9789 .9788 .0001 475 .9802 .9801 .0001

500 .9813 .9812 .0001 525 .9823 .9821 .0002 550 .9829* .9828 .0001 575 .9834 .9832 .0002

600 .9836 .9835 .0001 625 .9838 .9836 .0002 650 .9838 .9836 .0002 675 .9aS7 .9836 .UUOi OOOl

700 .9836 .9835 .UUOl 725 .9835 .9833 non9

750 .9832 .9831 .UOUl onoi

* For this value. 6p„ = 2. 1 x 10'^ Table IV

First Determination BaS04 [14] Wavelength

(nm) Van den AkkerReflectance p„

p(6°, \) F{6\ X)

400 0.9661 0.9606 0.9599 425 .9688 .9638 .9631 450 .9721 .9675 .9668 475 .9744 .9703 .9696 500 .9767 .9728 .9721 525 .9788 .9752 .9745 550 .9806t .9774* .9767@

575 .9823 .9793 .9786 600 .9835 .9807 .9800 625 .9845 .9818 .9811 650 .9852 .9826 .9819 675 .9858 .9834 .9827 700 .9864 .9840 .9833 725 .9869 .9846 .9839 750 .9873 .98.50 .9843

t ep„ is 2.3 X lO-" (6p„ = 2.1 x lO"" and Ap„ = 1.1 x lO"").

* ep is 9.8 X lO-* (8p = 9.5 x 10-* and Ap = 2.3 X lO"*). @eS is 1.01 X 10"' (SF = 9.5 x lO"" and AF = 3.3 x lO"").

Table V

Second Determination Halon [15] Van den Akker ,,o .

, r-i<iO \

.

an, „ p(6 . \ f16 , \) nellectance p„

t €p„is9.0 X 10-'{8p„= 7.3 X 10-* and Ip,. = 5. 1 x 10"*).

* ep is 9.6 X lO-^Sp = 7.9 X lO"" and Ap = 5.5 X IQ-" ). @6F is 9.7 X lO-" (dF = 7.9 X IQ-* and Af = 5.6 X lO"*).

400 0.9961 0.9930 0.9927 425 .9961 .9932 .9929 450 .9961 .9933 .9930 475 .9960 .9934 .9931 500 .9959 .9935 .9932 525 .9958 .9935 .9932

5.50 .9957t .9935* .9932®

575 .9956 .9935 .9932 600 .9955 .9935 .9932 625 .9954 .9935 .9932 650 .9952 .9934 .9931 675 .9951 .9934 .9931 700 .9950 .99.33 .9930 725 .9949 .9932 .9929 750 .994S .9931 .9928

37
Table VI

Third Determination BaS04 [16] Wavelength

(nm) Van den AkkerReflectance pp

p(6°, X) F(6°, \)

400 0.9744 0.9695 0.9688 425 .9771 .9732 .9725 450 .9789 .9757 .9750 475 .9802 .9775 .9768 500 .9813 .9791 .9784 525 .9823 .9804 .9797 550 .9829t .9813* .9806@

575 .9834 .9819 .9812 600 .9836 .9822 .9815 625 .9838 .9824 .9817 650 .9838 .9824 .9817 675 .9837 .9822 .9815 700 .9836 .9819 .9812 725 .9835 .9815 .9808 750 .9832 .9808 .9801

t epr is 2.3 X lO-" (5p„ = 2.1 X lO"* and Ap„ = 1.1 x IQ-"). * ep„ is 2.1 X 10-' (Bp = 2.1 X 10"' and Ap = 2.3 x 10"^). @6F is 2.1 X 10"' (SF = 2.1 X 10"' and AT = 3.3 X 10-*).

The smallest random error is in the central region of the spectrum, where the product of the source intensity and the receiver sensitivity is maximum. At the short wavelength end

of the spectrum, there is an increase in uncertainty in Qt and

()s associated with a decrease in source intensity, while at the long wavelength end of the spectrum there is an increase in uncertainty associated with a decrease in receiver sensitivity.

However, because the random error associated with/ dominates the overall uncertainty, we will cite only error figures at 550 nm for p„ as representing the entire spectrum.

The total uncertainty in determining the Van den Akker

reflectance is obtained by adding the random and systematic

uncertainties in quadrature. The total uncertainty in the Van

den Akker reflectance is 0.0002 for the BaS04 coating. It can

be seen that this uncertainty is very small, confirming the

results of the error analysis by Goebel, et al., [2]. The larger

uncertainty for the Halon coating is due to the transluscence

of the coating and is introduced in the extrapolation to the reflectance of a thick enough layer rather than being caused

by an uncertainty in the measurement. This additional uncer-

.95I 1 1 I i 400 500 600 700 750

WAVELENGTH (nm)

Figure 5. Van den Akker reflectance of three coatings.

{The height of the symbols X represent the tola! uncerlainty. Height of the symbols 0 and A

represents approximately 4 times the total uncertainty.) The associated solid curves show p(6*, k) for each coating.

tainty would not exist if the Halon coating were twice as

thick.

B. Adjustment from Van den Akker Reflectance p^k) to 6°lh Reflectance p(6°, X)

The second main step is the transition from Pt)(A.) to p(6'', K). As was pointed out in section III, this step is an intrinsic part of the determination which is needed because the sphere

coating is a real material and not an ideal Lambertian reflector. For this reason it is not proper to regard this step as a

correction. However, for the type of sphere coatings being

examined, the departure from Lambertian reflection is small and the difference between p„ and p is small. For this reason, we will refer to the transition step from p„ to p as an

adjustment in order to emphasize the small size of the change

with respect to the quantity being changed.

Table VII

Typical Values Used in Calculating the Van den Akker Reflectance Pg{K — 550 nm) for BaS04 [14]. Symbol Reference Equation Value Comments

(a) r (16) 12.70 mm measured with inside caliper and micrometer.

(b) R (16) 146 mm measured with steel rule.

(c) / (16) 1.90 X 10"^ calculated using r and R above.

(d) <?i (19) 8.731 X 10"' measured reflectance of auxiliary sphere.

(e) Qp (19) 1.24 X 10"' measured with stainless port open to dark room.

(0 Q, (19) 7.0 X 10-' measured reflectance of stainless steel port plate.

(g) <"e (19) 3.78 X 10-2 calculated from dimensions of port structure [17]. radians

(h) Q, (19) 8.630 X 10-2 calculated using Q',, Qp, Qf, and (Ug above.

(i) <?; (21) 9.832 X 10-' measured reflectance of target.

(j) Qe (21) 1.36 X 10-* measured with reflectometer port open into dark room.

(k) Q, (21) 9.831 X 10-' calculated using Q', and Qe above.

(1) p; (6) and (A7) 9.805 X 10"' calculated using/, Q, and Qi from lines (c), (h) and (k) above respectively. (m) r, (26) 25.4 mm measured with micrometer caliper.

(n) W (26) 0.17 mm measured with traveling microscope.

(o) h, (26) I BaS04

(0.9974) (Halon determination only).

(P) Pi- (26) 9.806 X 10-' calculated using p„, r,, W, and A, above.

38
Table VIII

Calculation of the Random Error in the Van den Akker Reflectance

Symbol Reference Equation Value Comments

(a) SR (17) .8 mm Uncertainty in packing sphere coating to constant ra- dius.

(b) Sf (17) 2 X 10"' Calculated from SR above.

(c) sq; (20) 7 X 10"' Uncertainty from 3 measurements.

(d) dQ, (20) 7 X 10-'' Roundoff uncertainty.

(e) 8^1. (20) 1 X 10-" Calculated from SQ', and SQp as given above.

(0 8q; (23) 2 X 10-" See comment on (d) above.

(g) 8Q, (23) 7 X 10-' See comment on (d) above.

(h) 6^, (23) 2.1 X 10"" Calculated from 8Q', and 5^, above.

(i) Sp'p (25) 2.1 X 10-" Calculated from Sf, and from (c), (g) and (j) above.

(j) St, (27) (7 X 10-")* CorrespKinds to an uncertainly in coating thickness of 0.5 mm.

(k) 5p„ (27) 2.1 X 10-"

(7.3 X 10-")* Calculated from Sp„ and

Sh, above. Halon coating only.

Table IX

Calculation of the Systematic Error in the Van den Akker Reflectance

Symbol Applicable Equation Value Comments

(a) Ar (18) 0.03 mm Uncertainty in measuring port ±.01 mm. Another

contribution is uncertainty in amount scattered back

from port lip, which is estimated.

(b) A/ (18) 9 X 10-" Calculated from Ar above.

(c) (21) 2 X 10-3 rad

(d) A^. (21) 1.1 X 10"" Calculated from Aa>, above and from Qf, &>„ and Q,

from entries {[), (g) and (h) in table VII.

(e) (25) 9.7 X 10-* Calculated from A/ and AQ, from (b) and (d) above.

(0 Ah, (27) (5 X 10"")1* Wavelength dependent error ±.0005 estimated from

fig. 4; uncertainty due to tapered edges of coating ±0.0001.

(g) r,W

(R^ + r^)

(27) 5 X 10-= Calculated using/?, r, r,, W from (a), (b), (m), and (n) in table VII.

(b) Apo (27) 1.1 X 10-"

(5.1 X 10-") * Calculated using Ap^, A^t, and the gap uncertainty as given in (e), (0 and (g) above respectively. Halon coating only.

1. Determining the Relative Self-Radiance Nj;(-y)/cos y

For each type of sphere coating, the relative self-radiance l^giy)/cos y was determined as a function of angle of emergence. A 75 mm radius sphere was coated using the same

procedure as was used when coating the spheres for the Van

den Akker reflectance determinations. This sphere was irra- diated through its single port and the flux emitted from the

port past a knife-edge was observed at a number of angles.

The geometry of this measurement is illustrated in figure 6.

The instrument used was the NBS-Gaertner goniophotometer

illustrated in figure 7. The source aperture permitted colli- mation to within 0.25° of the optical axis, and the receiver was collimated to within 0.6° of the optic axis. All three coatings were measured with a Vx-illuminant C [24] spectral

weighting, the centroid of which falls at approximately 550

nm. In addition, the coatings from the second and third determinations were measured using a 550 nm low pass

interference filter, which resulted in a centroid of spectral

weighting at 450 nm, and using a 600 nm high pass filter which resulted in a centroid spectral weighting at approxi39
COLLIMATEO

RECEIVER

COLLIMATEO BEAM

COLLIMATEO SOURCE

Figure 6. Arrangement of knife-edge apparatus for measuring A',('y).

mately 700 nm. No distinction between the measurements

under different spectral weightings were observed, indicating

that L^y) depends principally on the geometrical nature of

the surface. The relative magnitude of the observed flux divided by the cosine of the observation angle is shown in figure 8. Also shown in figure 8 are measurements made by

scanning, with a telescopic detector, the interior of a 20 cm

radius sphere coated with Halon. These latter measurements,

believed to be much more accurate (±0.001) than the knife- edge measurements, extend only to 45°. Because of the method used to produce the coating by hammering, there is reason to expect an increase in Ng(y)/cos (y) as y approaches

90° because of a slight glossiness in the surface. However, it appears that this effect is not nearly as great as the measurements using the knife-edge indicate. Two possible sources for the difficulties at large y are reflections from the comer of the knife-edge and scattered light from the receiver optics. At

large y, the flux to be measured is small, so that small amounts of stray radiation can cause large errors. Fortunately, this uncertainty in IVfJi,y)/cos y results in only a small

uncertainty in determining C(r, \). A discussion of our

ui i. o

o

Uj'

u

z

< I. o

<

a:

.4

-J I 2

(A

UJy I.I <

o 1.0

1 1

|St o BaS04

J 2n<* X HALON

Z'^ A BaS04

HALON (telescope meas.)

X

A 04

O

ANGLE OF VIEWING Y(DEG.)

Figure 8. Normalized self-radiance at 550 nmfor each of three coating

materials.

choice of function to represent Nj(y) will be deferred to part IV. B. 3 in which C(r, k) is calculated.

2. Determining the Relative Directional-Hemispherical Reflectance

The relative directional-hemispherical reflectance of a sample of each of the three coatings was measured with the

RECTANGULAR STOP a SHUTTER

Figure 7. NBS-Gaertner goniophotometer.

40
DRS using the special measurement accessory apparatus for this purpose [12]. A diagram of this measurement accessory

is reproduced from that reference in figure 9. The reflectance values were measured for radiation polarized with the electric vector in the plane of incidence and perpendicular to the plane of incidence. The average of the relative reflectance for the two polarizations was determined as a function of angle of incidence for each material for each of three wavelengths,

450 nm, 550 nm, and 750 nm. The data were fitted with a

quadratic function, using a least-squares fitting program, to obtain the A'c(r, \) shown in figure 10. These curves were used to determine the adjustment function C(r, \) of eq (12). The general trend is for the reflectance to increase as the angle of incidence approaches grazing. The amount of the increase is greater for the materials with lower reflectance.

1.015 —

SAMPLE

SUSPENSION ROD

ENTRANCE PORT

APERTURE

SAMPLE TURNTA8L£

STEPPING MOTOR CONTROLLED)

SAMPLE HOLDER

AT SPHERE CENTER

BEAM size:

10 MM SQUARE

FOR lO-NM BAND-PASS

(HEIGHT ADJUSTABLE)

OPAQUE WHITE CAP

ON TRANSPARENT

PLEXIGLAS ROD

PHOTOMULTIPUER

DETECTOR

SHUTTER

PHOTO-CATHODE

DIRECTIONAL - HEMISPHERICAL REFLECTANCE

( 45 CM DIA. SPHERE )

Figure 9. Integrating sphere for measuring relative directional-hemispherical reflectance as a function of angle of incidence.

3. Determining C(T, k)

For each type of coating, the function C was e\aluated

using in eq (13) the/V^/y) and A'c^T, k) data from parts 1. and

2. above for each of the three wavelengths 450, 550, and 750

nm. Actually three sets of C were calculated for each of three

interpretations of the highly uncertain data iorNJ^y) in figure

8 above in order to evaluate the effect of that uncertainty. We

wish to distinguish between the data taken from measure- ments of the radiance from the sphere wall and the interpretations of this data which are used as incident radiance values

in calculating C(T, X). We will do this by using a lower case y in NiJ{y)/cos y to indicate the data obtained directly from

the measurements and by using an uppercase F in NJ,r)/cos r to indicate the processed data used as the relative radiance

distribution incident on the sphere wall when we calculate C(r, X). The first set of C{r, X) was calculated assuming that

oz

< 1.000 a

1.007

_i

u.UJK

O

UJN 1.000 ^ 1.012 2

1.000

!* RUN

(B0SO4 )

30 60 ANGLE OF INCIDENCE P (DEC.)

Figure 10. Relative directional-hemispherical reflectance NgiF, K) as a

function of angle of incidence F for each of three coatings at three wavelengths.

A'fl(7)/cos y is independent of y. This provides a lower limit on C. The second was calculated by using 1 {ot l\l Jl,y)fcos y

between 0 and 45°. To obtain the A^g('y)/cos y above 45° in this approximation, a straight line was drawn through the knife-edge experiment data from 0 to 45° and the amount by

which the experimental data for greater than 45° fell above

this line was added to 1 to obtain Nj(y). (See fig. 11 for a diagram illustrating this procedure for the Halon data in fig. 8.) The set ofNg^y) obtained in this way were consistent with

the more accurate data from the telescopic detector scan and

the C(r, X) calculated with these Nj(y) are used as the accepted values. Finally, as an upper limit, C's are calculated using the unmodified knife-edge experiment data given

in figure 8. The functions CiV, X) corresponding to the accepted values, are plotted against T for each of the three materials at each of three wavelengths in figure 12. (See

appendix C for details of the calculations leading to this figure.)

Since the goal of this section is to determine p(6°, X) at 25 nm intervals over the wavelength range 400 nm X 750

nm, we need values of C(6°, X) at these wavelengths. Since

the large amount of data required would make impractical

determining all of these values of C(6°, X) in the way de- scribed above, we choose to determine C(6°, X) from the data

at the three wavelengths 450, 550, and 750 nm by interpolation and extrapolation. This determination is based on the

definition of C(6°, X) which comes from eq (12)

C(6°, X) =

yVc(6°. X)

Nr. - 1. (30)

41
1.5

81.4

uj 1.3-

o

0= 1.2

a I.I

1.0

HALON

Ng (P ) cos r

upper limit

straight line through first - three points o

Ng(r)/cos r lower limit

I I 30 60

ANGLE OF VIEWING Y (DEG.) 90

Figure 11. An illustration of the three assumptions used in interpreting

the NB(y) data from the knife-edge determiruUions.

Making use of this, we can write a correction factor C'(6*', X) which is a rough approximation to C(6°, X) as:

(32)

Since C and C are approximately equal, their ratio is a smoothly varying function of wavelength. Therefore, we de- termined y(X) as

such that

y(x) =

C(6°, X)

C'(6°, X)

(33)

(34)

at the wavelengths 450 nm, 550 nm and 750 nm. We then determined C(6°, X) at other wavelengths as

C(6°, X) - ;(X)C'(6°, X) (35)

30 60 ANGLE OF INCIDENCE V (DEG.)

Figure 12. C[V, X) as a function of r at three wavelengths for each of

three coatings.

where C'{6°, X) is calculated from expression (32) using

values o(N(,i6°, X) and/Vc(45°, X) measured with the relative d/h reflectance instrument [12]. The values of C(6°, X) .so determined are plotted in fig. 13.

-.001

|S' RUN (BaS04)

2nd RUN (HALON)

3rd RUN (BaS04)

-.006L 400

_L 500 600 WAVELENGTH (nm) TOO 750

Figure 13. C{6°, X) as a function of wavelength for each of three coatings

.

4. Results ond Error Analysis

Since the weighing to determine /Vg(X) is heaviest at 45°, it follows that

/Vc(X) - /Vc(4.5°, X). (31)

The three sets of values forC(6°, X) determined above were used in eq (12) to calculate p(6°, X) for the three wall materials. The results of this calculation are shown in the

third columns of tables IV. V and VI and by the line curves in

fig. 5.

42
From eq (12) one can determine a propagation of error formula for the random error 8p(6°, A.) as:

8p(6°, A.) = [8p„(A.)2 + 5yVc(6°, + 8/Vc{X)^]"^ (36)

In this form p„, Ng and Na_are each assumed to be 1, and

errors common to Nq and Nq are ignored, since these will effectively cancel when the ratio is taken. Therefore the only

errors to be included in eq (36) are the independent errors in the various quantities. The principal independent uncertainty

in Ng is that due to the uncertainty in the self-radiance measurements as shown in appendix C. The principal random

uncertainty in is due to the noise in the d/h data. Since

the value of N(^6°, K) was obtained through a rather indirect procedure involving curve fitting, it is difficult to establish a good theoretical basis for the error estimate. Therefore, we

sought a reproducible way of estimating the error which

depended as little as possible on arbitrary judgment. Since most of the curves involved fitting through ten to fifteen points with a quadratic function with two independent parameters, there is almost no likelihood that a point taken from the curve will depart from the most probable value by more than

the root mean square deviation of the individual points with

respect to the curve. Therefore, we will use this deviation as

the estimated random uncertainty. In determining Ng, two

such fittings are involved, one to the original data as a

function of angle and one to the C{A.) data used in the

interpolation. A summary of the random error analysis for the p^X) to p(6°, X) adjustment is given in table X. The only source of systematic error which we have identified for this adjustment step is an uncertainty in the measure- ment of Ng due to the correction which is made for the entrance port of the reflectometer. This results in an uncertainty in C(r, A.) of 2 X 10""* independent of wavelength.

The total uncertainty in p(6°, \) for a given determination

is obtained by adding 5p(6°, X) and Ap(6°, X) in quadrature.

The additional uncertainty introduced in making the adjustment from Pp(X) to p(6°, X) is of the same order of magnitude

as the uncertainty in Pu(X) itself. Particularly noteworthy is the large increase in uncertainty in the third determination.

The barium sulfate used in this determination had a rather "sticky" consistency which made it difficult to pack it into a uniform smooth surface, and this may have had an effect upon the noise in the Ng{^, A.) data from this surface.

C. Adjustment from d/h Reflectance p(6°, X) to d/h

Reflectance Factor f(6°, A.)

In order to determine the bidirectional reflectance factor in the retroreflective direction, apparatus was set up as customarily used for measuring the coefficient of luminous intensity of retroreflective sheeting (See fig. 14). Since the retroreflect- ance of the sphere coatings is essentially spectrally nonselective over the visible wavelength range [13] we measured the luminous reflectance factor for CIE illuminant A as being

representative of the entire spectrum to within the uncertainty

of the retroreflectance measurements.

SAMPLE SURFACE

Figure 14. Diagram of apparatus used in retroreflectance measurements.

Table X

Calculation of the errors in the p„{K) to p(6°, \) adjustment (See equation (36) and the accompanying discussion).

Symbol BaS04 [14] Halon [15] BaS04 [16] Comments

(a) 2.1 X 10-" 7.3 X 10-" 2.1 X 10-" See Table VIII.

(b) 0.5 X 10-" 0.5 X 10"" 0.5 X 10-" See Appendix C.

(c) 6Af,(6°, k) 7 X 10-" 3 X 10-" 20 X 10-" Component due to Titling angular data

for A'c(r. X).

(d) 6/V,(6°, X) 6 X 10-" 3 X 10-" 5 X 10-" Component due to fitting wavelength

data to C'(X).

(e) SAf,(6°, k) 9.2 X 10-" 4.3 X 10-" 21 X 10-" Quadrature combination of (c) and (d) above.

(f) 8p(6°, A) 9.5 X 10-" 7.9 X 10-" 21 X 10-" Quadrature combination of (a), (b) and

(c) above.

(g) Apr 1.1 X 10-" 5.1 X 10-" 1.1 X 10-" See Table IX.

(h) AC 2 X 10-" 2 X 10-" 2 X 10-" Associated nilh d-h reflectometer port correction.

(i) Ap(6°, X) 2.3 X 10-" 5.5 X 10-" 2.3 X 10-" Quadrature combination of (g) and (h) above.

43
To make the measurements, the receiver was placed in the sample position and a signal Nk proportional to the normal

illuminance Ir on the sample was measured.

(37)

The receiver was then moved to a position a distance d away

from the sample and, on the same scale of measurement and

using the same receiver aperture, signals N^fi), which is in the same way proportional to the illuminance /(/3) on the

receiver due to the radiation reflected from the sample, was

measured with the entire sample area A in view. From the

basic definition for reflectance factor, it follows that the

reflectance factor Fp(/3) can be determined from

/Vr(/3) N„ (P cos (T) cos {T + 13}

(38)

The value of F^'ifi) so determined as a function of observation

angle f3 is given for BaS04 and for Halon in fig 15. (See

appendix A, sec. A. 2 for further discussion of these data and

the evaluation of the integrals.) The retroreflectance factor F6°()8) was found to be essentially independent of the angle

which the plane of observation makes with respect to the plane of incidence. Therefore, the integral in eq (13) be- comes

F(U, u) cos y to = 2ttcos6° fy' Fei 13)13 d 13 (39)

and (t)' in (13) becomes

to' = 27r/5"''/3r/i8 (40)

where r is the radius of the reflectometer entrance port and d'

is the distance in the reflectometer sphere from the sample to the plane of the entrance port. The p{6°, X) data were adjusted to F(6°, k) using eq (13). In general, the difference

p(6°, K) - F(6°, k) is 0.0007 for BaS04 and 0.0003 for Halon. The estimated systematic uncertainty in this adjust- ment is approximately one-third of its value in each case. These uncertainties, added in quadrature with the uncertainties in p(6°. A.) yield the total systematic uncertainty in F{6°, X.). The values of F(6°, A.) for the three coatings are given in the third columns of tables IV, V, and VI.

D. Determining the d/h Reflectance Factor of Working

Standards

The d/h reflectance factor F{6°, A.) determined in IV. C. above is the average for the wall coating used in the Van den

Akker sphere. Since this coating is neither permanent nor

readily accessible, the reflectance factor Fc(6°, \) is deter- mined for working standards made of glass, ceramic, or some

other permanent material. The value of Fc is assigned as indicated in eq (14) and the accompanying text. Specifically, we will denote by Fcj(6°, A.) the reflectance factor for stan- dard c as obtained from the yth determination. Equation (14) takes the form: F (41)

where

coating.

A) is the reflectance factor for the jth wall

42 -

6' ANGLE OF INCIDENCE 0 1st BaSO-»

X 2nd Holon

OBSERVATION ANGLE

Figure 15. Retroreflective bidirectional reflectance factor for 6" inci- dence as a Junction of observation angle.

Qc is the measured relative reflectance of working stan- dard c, and

Qj is the average of the measured relative reflectance for several representative samples of the y th wall coating.

The relative reflectances and Qj were found by experiment

to be independent of the polarization of the incident radiation

for the working standards and sphere coatings used. It follows

that the random error in Fcj is given by:

8Fr + if)'

(42)

The largest new contribution to the uncertainty which is introduced in this step is 8Qj. This is due to the variability

between the representative samples and the resulting uncertainty in whether these samples properly represent the sphere

coating. If the values of Qc and differ significantly a small

correction for instrument non-linearity must be made in the

ratio QclQi- With this non-linearity is associated a small

contribution to the systematic uncertainty.

\ iQc/Qj) I + (43)

Three different working standards are currently used. These are identified and described in appendix D. The values

of Fc.j for each of these standards for each of three determinations are given in tables XI, XII and XIII, and sample

calculations for the uncertainties appear in table XIV.

44
Table XI

Reflectance Factor of Working Standard 1 (Russian Opal Class, Polished)

Wavelength

(nm)

F,

,

F,' , 1.3 F,

,

'1.2 F, ,

400 0.9793 0.9734 0.9738 0.9759 0.9753 423 0.9781 0.9739 0.9743 0.9756 0.9753 450 0.9803 0.9765 0.9779 0.9781 0.9781 475 0.9841 0.9807 0.9812 0.9822 0.9819 500 0.9854 0.9823 0.9846 0.9836 0.9838 525 0.9856 0.982

1

0.9845 0.9836 0.9838

C\ OQQ7 U. vozo U. VooC) 575 0.9810 0.9785 0.9805 0.9796 0.9798 600 0.9792 0.9761 0.9785 0.9775 0.9777 625 0.9777 0.9742 0.9769 0.9757 0.9760 650 0.9770 0.9745 0.9774 0.9756 0.9761 675 0.9771 0.9751 0.9772 0.9759 0.9763 700 0.9761 0.9736 0.9761 0.9747 0.9750 725 0.9742 0.9718 0.9741 0.9728 0.9732 750 0.9716 0.9687 0.9711 0.9699 0.9702

5 2.2 X 10-» 1.6 X 10-' 2.7 X 10"' 1.3 X 10"' 1.2 X 10-' A 3.3 X 10-* 5.5 X 10-* 3.3 X 10-^ 5.5 X 10"" 5.5 X 10-» 6 2.2 X 10"' 1.7 X 10-» 2.7 X 10"^ 1.4 X 10-' 1.3 X 10-'

Ml 4.5 6.0 3.7 w 10.5 14.2

Table XII

Reflectance Factor of Working Standard 2

(Vitrolite)

Wavelength

(nm) f2.t l^i,2 F2.3 1^2.2 F2,3

400 0.9100 0.9049 0.9049 0.9071 0.9065 425 .8944 .8901 .8907 .8920 .8916 450 .9006 .8977 .8981 .8990 .8987 475 .9140 .9116 .9083 .9126 .9114 500 .9192 .9169 .9178 .9179 .9179 525 .9242 .9204 .9226 .9221 .9222 550 .9245 .9222 .9243 .9232 .9235 575 .9215 .9190 .9213 .9201 .9204 600 .9160 .9125 .9155 .9140 .9145 625 .9099 .9066 .9085 .9080 .9082 650 .9050 .9027 .9043 .9037 .9039 675 .9035 .9013 .9040 .9023 .9028 700 .9010 .8991 .8999 .8999 .8999 725 .8959 .8939 .8953 .8948 .8949 750 .8893 .8867 .8882 .8878 .8879

5 2.2 X 10-' 1.6 X 10-' 2.3 X 10-' 1.3 X 10-' 9.8 X lO"" A 3.2 X 10-* 5.3 X 10-* 3.2 X 10-* 5.3 X lO-" 5.3 X 10-*

e 2.2 X 10-' 1.7 X 10"' 2.4 X 10-' 1.4 X 10-' 1.1 X 10"' w 4.5 5.9 4.2 W 10.4 14.6

The systematic uncertainty associated with the Fc for a

particular standard is, by definition, independent of the number of determinations which are made. However, the random uncertainty associated with a given Fc can be re- duced by taking the average of the F^'s from a number of determinations. We maintain a running weighted average F(.j of the results of all determinations from 1 through j by means

of the calculation

where the weighting factor Wc, j for the y'th determination of

is

u;c.i = 1/100 eFc, (45)

where cFc.j 's the total uncertainty in F^^j as is given in appendix B. The weighting factor Wcj for the average of the j

determinations is

Wcj = i wc.i . (46)

WcJ-lfcJ-l + WcJ^c

w, (44)

cj

45
Table XIII

Reflectance Factor of Working Standard 3

(Porcelain Enamel 80-1)

Wavelengtn

(nm) ^3.8 3 J ^3.2

400 0.7615 0.7573 0.7571 0.7591 0.7585 425 .7936 .7911 .7915 .7922 .7920

Qf\AO .ouiy .oUoU 4/5 .OVlZ 0A01 .oUol .8079

cnA .oIUd -oU to .oiUi .ouyu .OWO

Ql Aii QAQA .oi/yo DDU .OUOO .(HRiO 575 .8063 .8045 .8071 .8053 .8058 600 .8030 . .8017 .8032 .8022 .8025 625 .7990 .7969 .7994 .7978 .7983 650 .7949 .7937 .7960 .7942 .7947 675 .7926 .7911 .7925 .7917 .7919

700 .7909 .7900 .7927 .7904 .7910

725 .7885 .7869 .7886 .7875 .7878 750 .7855 .7839 .7860 .7846 .7850

5 2.1 X 10-' 1.5 X 10-3 2.3 X 10-' 1.3 X 10-' 1.1 X 10-'

3.0 X 10-" 4.7 X lO"" 3.0 X 10-" 4.7 X 10"" 4.7 X 10-" e 2.2 X 10-' 1.6 X 10-' 2.3 X 10-' 1.4 X 10-' 1.2 X 10"' w 4.6 6.2 4.2 W 10.8 15.0

Table XIV

Calculat ion of the Uncertainties in the p(6°,X) to F{6°,\) and F(6°,X) to F^, i(6°. X) steps as determined for Working Standard No. 2.

Value Symbol Comments

BaS04 [14] Halon [15] BaSO, [16]

fiF(6°, X) 9.5 X 10-" 7.9 X 10-" 2.1 X 10-' See table X, entry (f). (a) (=5p(6°, \))

(b) 0.9767 0.9932 0.9806 See tables IV. V. and VI.

(c) 2.7 X 10-" 8.7 X 10-" 3 X 10-" From three measurements in each determination.

(d) Qc 0.929833 0.931036 0.92922 Measured.

(e) 2 X 10-' 1.2 X 10-' 1.2 X 10-' From measurements on a number of samples.

(0 Qj 0.985022 1.00283 0.985982 Measured.

(g) Fz. > .9245 0.9222 0.9243 Calculated from (b), (d) and (f) above in equation (41).

(h) ^2. J 2.2 X 10-' 1.6 X 10-' 2.3 X 10-' Calculated from equation (42) and (a) through

(g) above.

(i) -1 X 10-" -1 X 10-" -1 X 10-" From reference [17].

(j) 3.3 X 10"" 5.6 X 10-" 3.3 X 10-" From tables IV, V, and VI.

(k) ^2. J 3.2 X 10-" 5.3 X 10-" 3.2 X 10"" Calculate from equation (43) and (b), (d), (0.

(i) and (j) above.

(1) «f2. i 2.2 X 10-' 1.7 X 10-' 2.4 X 10-' Quadrature combination of (i) and (k) above.

(m) "Jr. j 4.5 .5.9 4.2 Calculate from equation (45) using (I) above.

(n) 10.4 14.6 Calculate from equation (46) using (m) above.

(o) Fc.j 0.9232 0.9235 Calculate from equation (44) using (g) and (m)

above.

(pi 1.3 X 10-' 9.8 X 10-" Calculate from equation (47) using (g), (m).

(n), and |o) above.

(q) 5.3 X 10-" 5.3 X 10-" Largest entry from (k) above.

(r) 1.4 X 10-' 1.1 X 10-' Quadrature combination of (p) and (q) above.

46
The random uncertainty in the F is given by

S^cj = t:. (47)

The values oiFc,i andF^.a appear in tables XI, XII, and XIII along with the Fcj. The results of these three determinations

are also displayed by way of summary in figure 16.

V. Conclusions

A. Precautions and Pertinent Parameters

In the work reported in this paper, a large number of potential sources of error in determining reflectance factor using the Van den Akker method were investigated in order

to evaluate the magnitude of their importance. Many of these sources of uncertainty were of little importance in themselves

and even cumulatively were of importance only to a laboratory seeking the highest accuracy possible. For a laboratory

for which a total uncertainty on the order of ±0.005 is tolerable, a number of the detailed steps described in section IV are not necessary. In this section we will briefly describe

precautions which should still be taken in the case of such

truncated measurement procedures and make suggestions for possible improvements in the overall procedure.

1 . Determining the Van den Akker Reflectance Pc(X)

In an experiment designed and carried out with reasonable

care, the Van den Akker reflectance p„ can be determined

very accurately. The principal strong point in this method is the insensitivity of the basic measurement accuracy to uncertainties in any of the measured parameters such as the port diameter, the sphere diameter, or the ratio of the reflectance

of the sphere to the reflectance of the wall sample. The

sensitivity to such parameters is kept lowest by using a large

sphere with a small port (low f) and by using a highly

reflecting coating in the sphere so that the sphere reflectance

is still reasonably high.

Considerable care should be taken however to make the sphere coating in such a way that the Van den Akker reflec- tance can be related meaningfully to the reflectance of a sample of the coating. This means that a coating should be

chosen the reflectance of which is uniform and very repro- ducible. It is especially important that no cracks appear in the finished coatings and that the coating should be thick enough to be opaque. In this regard, it is probably best not to incorporate a removable port in the Van den Akker sphere at

all, but rather to rely upon the reproducibility of the coating

and use the average Q from several separate samples of coating for in eq (6).

2. Adjustment from the Van den Akker Reflectance pp to the d/h

Reflectance p(6°, X)

As can be seen from figure 13, the magnitude of this adjustment was in no case greater than —0.006. Since p(T,

X) can never be greater than 1, it follows that this adjustment

will be smaller for samples for which py closer to 1. It also is clear that the need for this adjustment comes about from the

rise in reflectance at near-grazing incidence. This rise is due

to the specular reflectance of the slightly glossy surface which

is produced in pressing. For this reason, a coating technique

which produces a rougher or more matted coating is to be

preferred if no adjustment is to be made. It is probably the roughness of the coating that Goebel, et al., [2] produced by

scraping which led to the rather remarkably good agreement

between their results, which are the basis of the earlier NBS

scale of F(6°, \), and the present adjusted results. (See fig. 17 and the discussion in section V.C. which follows.) An

error of as much as 0.01 in the upward direction can result from assuming and p to be equal, and an adjustment based on relative dih reflectance measurements A' 0(1, A.) should be

made if an uncertainty of less than ±.01 is desired. In all but

the highest accuracy work, it is safe to assume the self- radiance is Lambertian, i.e., Nj(y, \)/cos y is constant.

It should be pointed out that in every case p„ and P45'>/ft are very nearly equcd, as can be determined from the Ci V, A.) curves in figure 12. Therefore the Van den Akker method is especially well adapted for calibrating measurements of di- rectional-hemispherical reflectance at 45° incidence.

3. Adjustment from d/h Reflectance p(6°, X) to d/h Reflectance Factor

f(6°, X)

Since most reflectometers compare reflectance factor F(6°,

\) rather than reflectance p(6°, X), it is in principle necessary

to make an adjustment. However, since the solid angle

subtended at the sample is small compared to the total hemisphere, any departure from Lambertian reflectance by

the sphere coating would have to be large if the difference between p and F is to be significant. In the sphere coating

materials ordinarily in use, the reflectance factor departs

greatly from 1 only for small solid angles of collection at very small observation angles /3 (fig. 14). Therefore in general p is less than 0.001 higher than F and this adjustment can be

ignored or estimated from data in the literature [13]. Note that if the object of the measurement is to determine

the radiative transfer properties of the sphere coating itself, then p is the quantity of interest and the adjustment to F

should not be made. This would be the case, for example, if the coating were being studied in order to determine the

radiative heat transfer to the coating material.

4. Determining the d/h Reflectance Factor F(6°, X) of Working

Standards

Next to the adjustment from p^ to p, it is this step which

contains the highest potential for error. These measurements

are meaningful only to the extent that the samples of coating

with which the working standards are compared are repre- sentative of the sphere wall coating. It is for this reason that the sphere coating and the samples should be prepared in precisely the same way and that reproducibility of reflectance

is an important requirement of the coating. It is also this reason that favors Van den Akker's original technique of having many removable sections in the sphere wall itself, provided that the presence of such removable sections does

not give rise to irregularities in the sphere coating.

B. The Present NBS Scale of d/h Reflectance

Factor F(6°, X)

The present NBS scale of spectral d/h reflectance factor is maintained by means of three carefulK preserved working

standards which have been evaluated at 25 nm intervals. The

reflectance factor data for the first three determinations are given in tables XI, XII and Xlll. Figure 16 provides a

47
WORKING STANDARD NO. I (RUSSIAN OPAL GLASS)

• l«t RUN (BaS04)

X 2"<* RUN (HALON)

O RUN (BaS04) ^ AVERAGE |«ta2fKlRUN • WORKING STANDARD NO. 2

(VITROLITE) • . • • •

400 500 600

WAVELENGTH (nm)

700 750

Figure 16. Reflectance factor differeru es for the measurement of three working standards in three refleclaru e scale determinations.

graphical record of the establishment of the average value lor the three determinations. The representative error bars given

to the left of the diagram actually were derived for 550 nm,

but are fairly representative of the entire spectral range. The

zero line in each case represents the average for the three determinations, and the shaded area represents the range of

the total uncertainty of that average. Although the distribution of the points in general is consistent with the uncertainty

levels which have been assigned, there is a lack of consist- ency from standard to standard between the relative values from pairs of determinations. For example, for working stan- dard No. 1 (Russian opal glass), the third determination

reflectance values are consistently lower than those of the

first determination, whereas, for the other two working stan- dards the first and third determinations yielded values which

were more nearly equal (fig. 16). This difference in general

behavior is too large to be explained by the uncertainties in the measured values of Qc in expression (41). The most

straightforward explanation for this difference is a slight drop

in the reflectance of the working standard No. 1 during the

interval between the second and third determinations. A

better knowledge of the stability of the working standards will be obtained as more data are gathered from additional deter- minations. The results of the work reported in this paper document the

establishment of a scale of djh reflectance factor at 25 nm

intervals over the wavelength range 400 to 750 nm. The error analysis indicates that for high quality, uniform samples with

reflectance greater than 0.5 there is only a very small probability that our measured reflectance factor values will be in error by more than 0.(X)15.

C. Relationship to Other Scales

In order to determine the relationship between the newly

established NBS scale of dih reflectance factor and the former one, we measured the three working standards on the NBS scale established in 1965. The results of this comparison are summarized in figure 17. In this figure, the data

points indicate the departure of the old scale from the new for each working standard. The departure of the average value of

the spectral 6°//i reflectance factors for the three standards on

the 1965 scale from the same average on the new scale is shown by the light continuous line (GE average). The shaded

area in the figure represents the uncertainty of the new scale,

and the error bar on a central point indicates the uncertainty

attributed to the 1965 scale. On the average, the old scale appears to depart from the new by about 0.002 at the short wavelength end of the range with the magnitude of the departure diminishing as the wavelength increases.

.005

uj -.005

-.01

-.015

• RUSSIAN OPAL GLASS X VITROLITE + ENAMEL 80-1

""•^^ GE AVERAGE

NRC VALUE

400 500 600 WAVELENGTH ( nm )

700 750

Figure 17. Comparison ofpresent NBS scale ofFe-_^ {taken as zero line) to previous i\BS scale and to Results of an tntercomparison with NRC.

In 1974, measurements were made of several samples of pressed BaS04 and matte ground Russian opal glass at the National Research Council Laboratories (NRC) in Canada

and at NBS on the 1965 NBS scale. The heavy line in figure 17 (NRC value) departs from the light line (GE average) by

the difference between the averages of the reflectance values determined in the intercomparison. In this way, the present

NBS scale and the NRC scale of 1974 are compared indirectly. The rather noisy appearance of the difference can very

48
probably be attributed to the imprecision of the NBS GE

spectrophotometer.

The clashed line at approximately —0.004 indicates the combined error for this comparison. Since the NRC value

differs from the present NBS value by over twice that amount,

it is clear that at least one of these scales is in error by an amount greater than that claimed for it. At the time of this writing, work is under way on a new direct intercomparison

between the present NRC and NBS scales of directional- hemispherical reflectance factor and on joint efforts to deter- mine the cause of any differences.

D. Looking Ahead

We have already begun work on a determination of djh

reflectance factor by the Sharp-Little method [25, 26]. Most

of the data have been obtained, and detailed analysis will be

begun soon. Preliminary results indicate that the reflectance

factors of the three working standards obtained by that method agree with those obtained by the Van den Akker

method to well within the uncertainty of 0.0015. Therefore, it appears that the present NBS scale is accurate to within the uncertainty reported in this paper. Mainly because of the slight instability and non-uniformity

of the working standards, it is doubtful that an uncertainty in F(6°, \) of less than 0. 1 percent of its value can be achieved on a practical, routine basis by any technique which relies on such standards. However, these working standards are more

stable and more uniform than most samples encountered in practice. For this reason, we believe the newly established

NBS scale oidjh reflectance factor to be sufficiently accurate and precise to serve the current needs for such measurements

in science and industry.

VI. References

[1] Venable, William H. Jr., The National Measurement System for Spectrophotometry (Part of NBS Special Publication series 445,

currently being prepared for publication.)

[2] Goebel, David G., Caldwell, B. Patrick, Hammond, Harry K., Ill, Use

of an auxiliary sphere with a spectrophotometer to obtain absolute

reflectance, J. Opt. Soc. Amer. 56, 7a3 (1966).

[3] Certain products are mentioned in this paper by brand name or manufacturer for purposes of identification. This in no way implies recommendation or endorsement by the National Bureau of Standards.

[4] Keegan, Harry J., and Gibson. Kasson S., On the use of working

standards of didymium and Vitrolite glasses for spectrophotometric measurements. J. Opt. Soc. Amer. 34, 770 (Dec. 1944). (abstract).

[5] J. Opt. Soc. Amer. 28 (Oct. 1938). (Issue devoted to early develop- ment of recording spectrophotometer).

[6] NBS Letter Circular 1050 (June 1970). Preparation and Colorimetric

Properties of a Magnesium-Oxide Relectance Standard.

[7] Private communication from W. Erb., Physikalisch-Technische Bundesanstalt.

[8] Venable, William H. Jr., Hsia, Jack J., and Weidner, Victor R.. Development of an NBS reference spectrophotometer for diffuse reflectance and transmitance, Nat. Bur. Stand. (U.S.), Tech. Note

594-11. 47 pages (Oct. 1976).

[9] 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).

[10] Venable, William H. Jr., and Hsia, Jack J., Describing spectrophotometric measurements, Nat. Bur. Stand. (U.S.), Tech. Note 594-9, 50 pages (Nov. 1974).

[11] International Lighting Vocabulary, Publication CIE No. 17 (E-1.1) 1970, section 45-20-201.

[12] Section III.B. of reference [8] above.

[13] Egan, W. G., and Hilgeman, T., Retrorefleclance measurements of photometric standards and coatings. Applied Optics 15, 184.5 (1976).

[14] BaS04 manufactured by Mallincrodt Chemical Works (Reagent powder

for X-ray diagnosis) #3808. [3] [15] Halon tetrailuoroethylene powder manufactured by Allied Chemical

Co. Type G-80, Lot 463169 Drum 31. [3] [16] BaS04 manufactured by J. T. Baker Chemical Co. #.5-10.30 (5.53- 1011) (analytical Reagent) [3]. [17] See section III. A. of reference [8] above.

[18] See Appendix C of Reference [8] above.

[19] Jenkins, F. A., and While, H. E., Fundamentals of Optics, 3rd edition (McGraw-Hill, N. Y., 1957) pg. 521, figure 25M.

[20] Jakob, Max, Heal Transfer, Volume II, p. 14 (John Wiley and Sons, N. Y., 1963), (oijn = 1 -/,2).

[21] See section III. A. 4 of reference [8] above.

[22] Kubelka, Paul, New contributions to the Optics of Intensely Light- Scattering Materials. Part I, J. Opt. Soc. Amer. 38, 448 (1948).

[23] Grum, F. and Saltzman, M.; P-75-77 New While Standard of Reflectance. Compte Rendu 18*^ Session, Londres 1975, CIE Publication No. 36, 91 (1976).

[24] Colorimetry, Publication CIE No. 15 (E13. 1) 1971. pages 81 and 93.

[25] Sharp, C. H. and Little, W. F. , Measurement of Reflection Factors, Transactions l.E.S. 15, 802 (1920).

[26] Budde, Wolfgang, and Dodd, C. X., Absolute reflectance measure- ments in lhe£>/0° Geometry, Die Farbe 19, 94 (1970).

[27] Hapke, Bruce W., A theoretical photometric function for the lunar

surface. Journal of Geophysical Research 68, 4571 (1963).

[28] Bom, M., and Wolf, E., Principles of Optics, 3rd Edition, (Pergamon

Press, New York, 1964), p. 399.

VII. Appendix A. Accounting for

Retroreflectance

Retrorefleclance refers to the tendency of objects to preferentially reflect radiation back in the direction from which it is incident. This can arise from several causes. If a focussing

element such as a small dielectric sphere directs radiation onto a reflecting surface at or near its focal point, the

reflected radiation will be returned back into the direction from which it came. This type of retroreflectance can be very

directional, i.e., most of the radiation returns within a few

tenths of a degree of the angle from which it came. A second,

much less directional retroreflectance effect, results from the

fact that shadows are not visible from the direction of inci- dence. This mechanism is important only for surfaces which

are not highly reflecting, so that the radiation is not re- reflected out of the shadows. In the case of the highly

reflecting coatings being used in the spheres in this experiment, the highly directional retroreflectance dominates.

1 . The Effect of Retroreflectance

In order to obtain an estimate of how the presence of retroreflectance will affect a determination of the Van den

Akker reflectance p^, we will use a simple model in which most of the radiation is reflected in a Lambertian distribution but a small retroreflected fraction fr appears above the Lambertain background. The effect which the retroreflectance has upon the flux (see III. A.) striking the sphere boundary

can be seen by going one step backwards in determining the source of <^j. The flux <f)i comes from the walls by reflection,

and the incident radiation for this reflection is from the sphere walls, but not from the port. Therefore, in the pres- ence of retroreflection the irradiance on the sphere boundary

is higher on the wall coating than in the port. The makeup of can be determined by noting that, in this model, the flux incident upon the walls (which also comes from the walls) is either absorbed or reflected. The total reflected flux, which is

<f>i, is made up of two parts

(t>i = (l>r + 4>'i (Al)

49
where (f>r is the retroreflected fraction of the reflected flux

<l>r=fr<i>i (A2)

and (f>i is the diffusely reflected fraction

(t>i = a -/Hi. (A3)

With thie model, the power balance equation, equation (3) of

part III. A., takes on the following form. p;(i+/rp;)(i-/)pA (A4) = 4>j+ [(1 -Ml+Mi - p'v)

where p< is reflectance of the target exclusive of the aug- mented reflection in the retro direction, which is lost through

the port of the measuring instrument in every case. The

relative reflectance Qg of the sphere is

Qs = k[<j>ifi\ -/') + <t>o{l + frPv)pJ{l - /")] (A5)

and the relative reflectance of the target is, as before

Q, = k(l>oPt{l-f'). (A6)

Equations (A2), (A3), (A4), (A5), and (A6) can be solved to obtain an expression for p„ in the following form:

l-/(l-/r):

1 Pv l-/(l-/r) l-« (A?)

where

^ f/(l + P'vfr)[f' -n ^ #.(l-/rP3

"

I (1-/) l-Pv[l-A^-fr)]}Qs

(A7a)

Comparing (A7) with (6), it is seen that /in the dominant first term is replaced hyj{l — fr)- This in essence states that the

fraction the flux escaping from the port has been reduced

relative to the flux lost to the walls by an amount proportional

to the retroreflected fraction. The correction term a for the singular treatment of the first target reflection when the target

is in the auxiliary sphere is also modified by the retroreflec- tance, making the form of this term so complicated that a closed solution in terms of the measurement parameters is not

practical. We solve the equation iteratively, using as a first approximation for p'„ the value obtained from (A7) with a =

0. Taking the retroreflectance into account has a very small

effect on the calculated value of py. For example, if fr —

0.001, the effect of not ignoring this in the case of a sample

for which p'„ =0.98 is to reduce the calculated />p by

approximately 10~®. Note that p'„ must be the total reflec- tance, including retroreflectance, since 1 — p„ represents

loss of radiation by absorption.

2. Models for Retroreflective Mechanisms

Our measurements of retroreflective bidirectional reflec- tance factor, the data for which are shown in figure 15, were

limited to observation angles greater than 0. 1°. Therefore we

sought a model which could be used to interpolate our data to 0° observation angle so that we could evaluate the integral in eq (39). A model based on shadowing was developed by Hapke [27]

to explain the retroreflective phenomena observed from the lunar surface. This model, which was quite successful in Hapke's application, was used by Egan and Hilgeman [13] in an effort to quantitatively evaluate the retroreflectance which

they observed from barium sulfate paint and other highly

reflective white coatings. Other possible mechanisms for producing retroreflectance include cube comer reflectors formed from broken cubic crystals and retroreflectance by

focussing, as occurs in glass beaded retroreflecting sheeting.

In the following paragraphs we will treat special cases of each

mechanism.

a. Shadowing

The Hapke model includes as one of its basic assumptions

that the absorbance of the scattering particles is very high. In

this way, there will be a considerable contrast between the radiance coming from shadowed areas in which the radiation undergoes several reflections and the radiance reflected from an unshadowed area. Although there is relatively little loss in highly reflecting materials such as barium sulfate or Halon, it

is still possible for an initial first surface reflection to add to the background of multiply reflected radiation in a preferential manner. In order to estimate the order of magnitude of the non-diffuse reflection, one can use layers of close-packed

spheres as a model for the many randomly oriented particles

in the coating. Referring to one such sphere as shown in figure 18a, one can calculate the reflectance factor for such

an array as follows. The bidirectional reflectance factor is given by

/^(U, u)

ttL[u)

F(U)

(AS)

where ^(U) is coUimated irradiance incident in the direction U and iL(u) is the reflected radiance in the direction u, both averaged over a sufficiently large area of the sample. In the case of retroreflectance, we set the unit vectors U and u

equal. The average reflected radiance is given by definition

Un) =

<!>(&>, A)

aj(u)Acosy

(A9)

where (o{u) is an element of solid angle oriented in the

direction (u), A is the area of the surface over which the average is being taken, and 4>(aj, A) is the flux reflected from

area S into solid angle w. Collimated incident radiation will come to a virtual focus at a point / which is r/2 from the outer

surface of the sphere. The solid angle it) is defined in terms of

a small arbitrary area a on the sphere

4a

,2 (AlO)

The flux reflected from this area into <ti is given by

<|) = pEa/cosy (All)

50
where p is the reflectance of the sphere surface. (Note that since we are treating retroreflectance, a is chosen so that it is centered on a radius in the direction of E, and therefore the

direction of incidence is normal to a.) The areaA occupied by

this sphere in a hexagonal close-packed array is

6r2 (A12)

Using expressions (A9), (AlO), (All), and (A12) above in (A8) one obtains under conditions of retroreflectance:

F (U,u) =

7T 'cosV = 0.227p/cos2 7. (A13)

This would be roughly the maximum amount of additional

bidirectional reflectance factor which might occur in the

retro-direction under ideal conditions of shading by sur- rounding particles. The cos^ term in the denominator is an

artifact of the "array of spheres" model we are using. In the continuous surface being represented by the array of spheres

model, the projected surface area goes as cos^ so that the cos^ term should be omitted.

b. Cube corners

In the ideal case, the bidirectional reflectance factor for a cube comer reflector would be infinite at zero observation

angle and zero at all other observation angles. However,

imperfections in the cube comers and diffraction tend to spread the reflected radiation out so that bidirectional reflec- tance factor has meaning in describing reflection by cube

comers. For the model for maximum reflectance, we will assume that the cubes are perfect and that diffraction is the limiting factor. For near normal incidence the total retrore- flectance from a close-packed array of cube comer reflectors

is

(A14)

where pi is the reflectance of the cube faces and pj is the reflectance of the entrance surface. For a perfect intemal comer p, is 1 and p2 is roughly 0.05, so that pt is roughly

0.9. For an external comer (cube comer "hole"), pa = 0 and

Pi is roughly 0.05 so that p, is roughly 1.25 X 10~* in that case. The reflected radiance is distributed in the diffraction paltem associated with the reflecting faces treated as apertures. For this order of magnitude calculation, we will assume

the pattem to be that of a circular aperture of effective radius

[A

r — \ — where A is the area of the entrance surface. The

radiance in such a pattem would be given by [28].

EA 2Ji{x)

(A15)

where

X = 2TTr sin {p)IK

from which it follows that the reflectance factor is given by

2Jix)

Pt- (A16)

The data in figure 15 suggest that the particle sizes are such

that the central bright spot would subtend an angle of about 1°

for BaS04. The edge of the central bright spot falls at at =

3.8. For an effective wavelength of approximately 550 nm, it follows that the particle size would have to be such that r —

20 fJLva. Thus, the reflectance factor at /3 «^ 1° would be

roughly

F(/3) = 10V^ (A 17)

c. Focussing retroreflectors

If the index of refraction of a bead is such that the radiation passing through it comes to a focus behind it, a suitable

reflector may be placed at the focal point (I in fig. 18c.) and

the radiation will be reflected back through the bead into a collimated retroreflected beam. Here, the spreading of the

reflected radiance can be brought about either by diffraction, poor focussing, or both. The diffraction limiting case in the previous paragraph can be applied to the Halon data in figure

15. In this case, the central bright spot appears to subtend an

angle of about 0.5° which corresponds to an effective lens radius of r —40 fim. If one assumes a refractive index of 1.5

so that the radiation will come to a focus on the back of the bead and from experience with cheap cameras assumes that

ENTRANCE

SURFACE

CUBE FACE

REFLECTING

SURFACE

Figure 18. Diagrams for estimating magnitude of retroreflectance by

various means.

51
the diameter of the effective lens area is roughly one-eighth of

the diameter of the bead, it follows from expressions (A12)

and (A16) that a closely packed array of such spheres would

have a reflectance factor for ^ 1 of

F(/3) = 6 X lO^p, (A18)

for a specular reflector of reflectance pt located at I and

F(/3) - lOp, (A19)

for a diffuse reflector of reflectance Pt at I.

3. Interpolating the retroreflectance data

From the foregoing analysis, one can make the following

deductions, assuming that the 0.5 excess reflectance factor is caused by only one mechanism:

a. Shadowing cannot by itself account for the observed

retroreflectance.

b. At least 6 X 10~^ of the area is effectively taken up

with inside comer cube retroreflectors.

c. At least 0.4 of the area is effectively taken up with

outside comer cube retroreflectors.

d. At least 1.6 x 10~^ of the area is effectively taken up

with focusing sphere retroreflectors backed by specular

reflectors of reflectance 0.05.

e. At least 5 X 10~^ of the area is effectively taken up

with sphere retroreflectors backed by diffuse reflectors of reflectance 1.

Since the mechanisms are not mutually exclusive, it is ex- pected that all will operate to some extent in pressed powder

samples. However it is highly unlikely that cube corner

reflectors will be formed in Halon, so it would be expected

that the mechanism in d. or e. above would predominate. Even though the cleavage of a crystal in such a way that it forms an inside comer cube reflector is not very likely,

mechanism b. probably predominates in the BaS04 powder.

Shadowing will contribute some effective retroreflectance in both cases. The predominate mechanisms appear to depend on the sum of the diffraction pattems associated with a number of

reflectors, each with a different effective aperture, and the

statistical distribution of the aperture sizes is unknown.

Therefore we chose to use an emperical fitting function. The

function

F03) = 1 + exp(a + 6/3'^) (A20)

was found to fit the data adequately. Fitting all BaS04 data, we obtained

a = -0.393

b = -0.966

c = 0.57

and fitting the first seven points of the Halon data we obtained

a = 1.18

b = -3.41

c = 0.21

These fitting functions are shown as solid curves in figure 15. The average of the function Fiji) for BaS04 over the range 0 :S /3 S 0.5° is 1.42 which is in good agreement with the data of Egan and Hilgeman [13]. The difference values for p{6°, X) — F(6°, X.) were obtained by using the fitted functions in eqs (39) and (40) with r = 1.9 cm and d' = 29A cm.

In each case, the contribution from the region of extrapolation

(|j8| < 0.1°) was only a small part of the total flux in the

retroreflected component, so the choice of fitting functions was not critical. A crude measurement "f BaS04 using a beam splitter yielded p(6°, X) - F(6°, X) = 0.0006 which is in good agreement with the value of 0.0007 obtained from the data in figure 15.

Vlli. Appendix B. Interpretation of Error

Statements

The error analysis in this paper involves three distinct classes of errors. The first class of error is the measured

random error. This type of error appears as noise in the measurements and is evaluated by making each measurement

several times and performing the usual error analysis on the

results. For this type of error, we will cite three times the standard deviation of the mean. The second class of error is the estimated random error. This class of error contributes to the outcome in the same way

as the measured random error, but, either because of the inconsequential effects of the error or because of experimental difficulties which would be involved in evaluating it, we

choose to estimate the size of the error instead of determining

it by making several measurements. In making such an

estimate, we choose to estimate the smallest range of uncertainty within which the correct value will fall with a very high

probability, i.e., an intuitive ninety-five times out of a hundred. For this type of error, we will cite the size of the estimated error itself. The estimation process is carried out in such a way that the sign of the error is indeterminant. If it is known that a particular cause of error will result in an error which is always of one sign, we will correct the measured

value to a most probable value and reduce the magnitude of the estimated random error appropriately. The estimated

random error is combined in quadrature with the measured

random error to obtain the total random error. All random

errors, whether measured or estimated, will be denoted by

the symbol 8. The third type of error is the estimated systematic error, indicated by the symbol A. This error is like the estimated

random error in all respectes except one, namely it is not independent from determination to determination, i.e., it will affect all determinations in the same way. It should be

pointed out that this does not mean that the sign of the measurement is known, but only that the sign of the effect is known to be fixed from determination to determination. For example, in correcting for the reflection of radiation from the beveled lip of the sphere, we estimate that the radiation will be reflected with an average reflectance intermediate be- tween one and the normal reflectance of the stainless steel. (See discussion preceding (19).) If the actual reflectance is less than our estimated value, determinations of reflectance made using this estimate will result in p„ values which are all slightly higher than if the estimates were correctly made. In the course of many determinations, the total random error will be reduced, but the systematic error will remain. Since the

52
sign of the systematic errors is not known, systematic errors from independent causes will be added in quadrature, and at each point in the analysis at which it is desirable to estimate a

total uncertainty, the systematic error and the total random

error will be added in quadrature. However, when proceeding

to combine the results of several determinations, we will first combine the random errors in the ordinary way and add the largest systematic error in quadrature at the end. In this way,

the calculated systematic error is not reduced by repeating

the measurements. The total uncertainties so calculated are

to be regarded as determining a range within which we expect

the correct value to fall with a probability of approximately

0.95. This total uncertainty will be indicated by the symbol

e.

IX. Appendix C. Calculating C(r, X.)

The integrals in (11) are evaluated in closed form after

fitting the experimental data for Ng and /Vg.

/. Fitting Ng(T, k)

The data for A'c were fitted by an expression of the form:

/Vc(r, \) = aoik) + a,(\)n + a2(\)P. (CI)

An even function of F was used, since we have assumed the directional-hemispherical reflectance of the coatings does not depend on the angle of azimuth of the incident direction, but depends only on the angle of elevation. The coefficients in (CI), as determined by a least squares fitting of the experimental data are given in table CI.

2. Fitting Ng(T, \)

Since the experimental data for A^j,(7, X)/cos (y) were found

to be nearly independent of wavelength, only one function Ng{V) is needed for each type of coating. However, since

there was such a large uncertainty in the Ng{r) data, three

sets of Ng{T) were fitted as described in part IV. B. 3. in the main text. The form used for the fitting the data was:

iv„(r)/cosr = i biV. (C2)

i=0

Table CI

Coefficients for llie expansion of/VclF, \) in even powers of the angle of incidence F in radians at three different wavelengths for three sphere wall coatings.

Coating Wavelength oo

a,* X 10^ at* X lOf 450 0.999942 5.99 0.438 BaS04 [14] 550 .99978 4.40 0.159 750 1.00011 3.27 -0.00814

450 0.999875 3.97 -0.172

Halon[13] 550 1.00004 4.17 -0.985

750 1.00027 3.68 -1.20

450 0.999829 4,08 0.405 BaSO^ [16] 550 1.00047 1.43 0.741 750 1.00012 3.91 -0.471

* The second and third digits are not significant but are kept to avoid round-off error in further calculations.

In the case of the original knife-edge data, the values of the

coefficients, as obtained by least squares fitting, are given in table CII as describing the "upper limit" curve. In the

original data, the least uncertainty was associated with the r = 0 reading. Therefore, all data were normalized to the F = 0 reading and bo was taken to be 1 when the data were

fitted. Because of the symmetry in azimuth. 6, and 63 are taken to be zero.

In the accepted data, A'j,(r)/cos F was taken as 1 up to F =

7r/4. To obtain the remaining part of this curve we obtained

Ngiy) according to the expression

Ng{y)/cosy= I + Ca- (C3)

The difference data Ng{y) — N'g(y) using the data for the angles tt/S (60°), 57r/12{75°) and 177r/36(8.5°) were fitted using the form

/V,(7)/(cos 7) = 1 + 6 ;( F - + 6;(F - j)\ (C4)

4 4

After bi and 62 were determined, these were used to obtain

the bi in the expression (C2).

3. Calculating C(F, X)

With the expressions (CI) for A'g(F, \) and (C2) for A'g(F,

X) substituted into eq (11), the integrals in that equation can

be evaluated in closed form in terms of integrals of the form

A = /o'^ F' cos F sin YdT (C5)

for the upper and lower limit functions, and

I'i = in'* F* cos F sin TdT (C6)

and

I.' = cos F sin F^/F (C7)

for the accepted value functions. The values of these integrals are given in table CIII, and the resulting values of A'c(X) are given in table CIV. It can be seen from table CIV that the difference between the various assumptions concerning the self-radiance has a very small effect on the value of Ng ^11 cases. Therefore only the accepted value of .'Vg will be used in each case to calculate C(F, X). The results of the scanning

which has been done to date with the telescopic detector indicate that the real value probably lies toward the lower

limit from the accepted value. On this belief, we will assign

the largest difference between an accepted value and a lower

limit value, 0.00005, as the magnitude of the uncertainty in Nq due to the uncertainty in evaluating the self-radiance by

measuring Ng.

X. Appendix D. The Three Working Standards

The properties which standards for reflectance factor measurements should have is a subject over which there is much

diversity of opinion. By definition, reflectance factor is re- flectance relative to the reflectance of a totally reflecting

Lambertian reflector, both measured on the same instrument. Based on this definition, the best standard for calibrating an

53
Table CII

Coefficient for the expansion of yVj( Fj/cosF in powers of the angle of incidence F in radians for three different sphere coatings and three different assumptions concerning the self-radiance distribution.

Coating Curve Type L"0 0 J ^ L\JU fcj X 100 63 X 100 64 X 100

upper limit 1 0 7.0 0 -1.1

( accepted; BaSOi [14] { r<7r/4 1 0 0 0 0

^ r>7T/4 1.03 -1.240 -12.4 16.7 -5.33

lower limit 1 0 0 0 0

upper limit 1 0 5.3 0 6.1

/ accepted; Halon [15] } r<7r/4 1 0 0 0 0

\ r>Tr/4 1.45 -219 405 -339 107

lower limit 1 0 0 0 0

upper limit 1 0 3.8 0 1.6

{ accepted; BaS04 [16] } r<7r/4 1 0 0 0 0

\ r>7r/4 1.17 -120 271 -248 79

lower limit 1 0 0 0 0

Values of the

1.

integrals in Table CIII equations (C5), (C6), and (C7) for nine values of

I li /.' 0 0.50000 0.25000 0.25000

1 .39270 .12500 .26770

2 .36685 .07135 .29550

3 .37990 .04382 .33608

4 .42147 .02819 ..39328

5 -49129 .01872 .47257

6 .59443 .01273 .58170

7 .74046 .00882 .73164

8 .94416 .00614 .93802

Table CIV

Values of the weighted averages No (X) for each of three coatings for three wavelengths and three different assumptions concerning the self-radiance

distribution.

Determination number

Wavelength K Upper limit Accepted

value Lower limit

BaSOn [14] 450 1.00486 1.00479 1.00476

5.50 1.00343 1.00338 1.00336

7.50 1.00244 1.00240 1.00239

Halon [15] 450 1.00294 1.00282 1.00277 550 1.00233 1.00225 1.00223

7.50 1.00175 1.00170 1.00169

BaS04 [16] 450 1.00343 1.00335 1.00333 550 1.00173 1.00168 1.00167

7.50 1.00253 1.00247 1.00247

instrument to measure reflectance factor would be a totally reflecting Lanibertian reflector, or the closest thing to it which could be obtained. The Halon and barium sulfate sphere linings which were used in the work described in this paper were very close to this ideal.

However, if reflectance factor measurements are going to be of use in practical applications, the instrument must be

defined as part of the specification of the measurement. It is for this reason that we have defined the measurements as carefully as possible in terms of integrals describing the incident radiation and the instrument response. We believe

the properties of our reference reflectometer are very close to those specified in the definition for directional-hemispherical

reflectance factor which we have used, and furthermore, we

believe the geometrical properties of that instrument to be

stable in time. In order to confirm this, however, we feel that

it is important to have several working standards representing

the gamut of the highly reflecting materials which we would

be measuring with this instrument. It is also important that several different types of working standards be used in order

to be able to detect changes in the optical properties of any one of them. As a means of retaining our scale of measure- ment in day-to-day measurements and as a means of comparing one determination with another, we are using the follow- ing working Standards:

Working Standard No. 1 —This standard is a piece of MC20 opal glass purchased in September 1970 from

Mashpriborintorg

Smolenskaja pi., 32/34

121200, Moscow, G-200

U.S.S.R.

The piece used is 99 mm by 99 mm and is 20 mm thick. It is marked MC-20-2 for identification and is usually referred to as the Russian Opal Glass. The side which is measured has a very flat, highly polished surface. Working Standard No. 2 — This standard is a piece of

Vitrolite glass which was manufactured by

Libbey Owens Ford

1701 E. Broadway

Toledo, Ohio 43605

The exact date of manufacture of this particular piece of glass

is unknown, but it has been at least twenty years since any

glass of this type has been manufactured. The piece used is

54
100 mm by 100 mm and is 11 mm thick. It is marked V6-D1

for identification. The side which is measured is flat and

highly polished.

Working Standard No. 3 — This standard is a porcelain

enamel on steel plaque which was made around 1946 by

The Harshaw Chemical Co. Division of Kewanee Oil Company

1933 E. 97th St. Cleveland, Ohio 44106

The plaque used is 108 mm by 108 mm and is marked 80-1

for identification. The surface which is measured is smooth

and non-porous, but it has a slight ripple or "orange peel"

texture. These three working standards cover the range of reflec- tance factor from nearly 1 to approximately 0.8, which is the range generally used for standards to calibrate the gain

setting of reflectometers. In addition, the Vitrolite standard is slightly translucent. Recent tests have shown our instrument

to be insensitive to this amount of translucence, but if this should change the difference will be noticeable in the measurements obtained using this standard as compared to the

others. Because of the rippled surface in the porcelain en- amel standard, the surface reflection from this standard is spread out more than that from the other two standards which

have flat surfaces. Therefore, differences in the way the instrument handles specular reflection may show up in the

relative measurements of this standard with respect to the

others. (The most sensitive test of the way the instrument

treats specular reflectance is made by measuring a specular

mirror. We intend to use this procedure as soon as we have

the capability to measure the reflectance of a mirror with the necessary accuracy.)

The cleaning procedure used is an important part of maintaining working standards of reflectance. Our present ap- proach is to use a procedure which will disturb as little as possible the layers of oxides and other surface films characteristic of the materials. Therefore, we store the standards in dessicators and before each measurement we wash them with

a mild nonfluorescing soap, rinse them thoroughly with hot water, rinse them with distilled water, and blot them dry with

soft tissue paper. Any lint which remains on the surface is removed by gently brushing with a soft brush.

55

856 J. Opt. Soc. Am./Vol. 71. No. 7/JuIy 1981 Appendix G V, R. Weidner and J. J, Hsia

Reflection properties of pressed

polytetrafluoroethylene powder

Victor R. Weidner and Jack J. Hsia

Radiometric Physics Division, National Bureau of Standards, Washington, D.C.

Received December 18, 1980; revised manuscript received February 12, 1981 The reflection properties of pressed polytetrafluoroethylene powder have been under investigation by the Radiometric Physics Division at the National Bureau of Standards for the past five years. This material has a great potential use, both as a standard of diffuse reflectance and as a coating for integrating spheres for applications in re- flectance spectrophotometry and other signal-averaging devices. It possesses certain physical and optical properties that make it ideal for use in these applications. Techniques are given for preparing reflection standards and

coating integrating spheres with the pressed powder. The effects of powder density and thickness on its reflec- tance are reported, and observations of possible problems with fluorescence that are due to the presence of contaminants in the powder are discussed. The absolute reflectance (6°/hemispherical reflectance factor relative to a perfect diffuser) is reported for the spectral range of 200-2500 nm. The directional/hemispherical reflectance factor

relative to 6°/hemispherical reflectance is given for several wavelengths in the ultraviolet and visible spectrum and

for angles of incidence between 5 and 75°. The bidirectional reflectance factor is reported for 300, 600, and 1500 nm at angles of incidence of -10, -30, -50, and -70° and at viewing angles at 10° intervals from -80 to +80°.

INTRODUCTION

The reflection properties of pressed polytetrafluoroethylene

(PTFE) powder^ in the ultraviolet, visible, and near-infrared

spectral regions, combined with certain desirable physical

characteristics, make this material exceptionally useful when

there is a need for a good white diffuser or a standard of diffuse

reflectance. The diffuse reflectance of pressed PTFE powder

is remarkably high over the spectral range of 200-2500 nm and

is probably higher than that of any other known material, its reflectance being 99% or higher over the spectral range of 350-1800 nm. It is particularly useful as a coating for inte- grating spheres commonly used in diffuse reflectance spec- trophotometry. Historically, the most commonly used materials for this purpose have been magnesium oxide and bar- ium sulfate powders or barium sulfate paint.^ Much has been

written on the optical properties of these materials, and the advantages and disadvantages of their use in spectrophotometric applications have been experienced by nearly everyone

involved with reflectance spectrophotometry. Certainly, there is no longer any advantage in coating integrating spheres

by the old method of burning magnesium and collecting the magnesium oxide smoke. The standards that still specify that

reflectance measurements be reported on a photometric scale

relative to smoked magnesium oxide should be rewritten to specify that reflectance measurements be reported on an absolute reflectance scale (relative to a perfect diffuser^). A

review of publications on properties and reflection values of material reflection standards is given in Ref. 2. The purpose of this paper is to make available the technical findings of several years of research on the optical properties of pressed PTFE powder. Other authors'* have reported on

the potential usefulness of this material as a reflection stan- dard. The spectrophotometry group of the Radiometric

Physics Division at the National Bureau of Standards (NBS)

began studies of the reflection properties of pressed PTFE

powder in 1975. At that time, this group was engaged in constructing a new reference spectrophotometer for diffuse re- flectance^ along with a number of accessory devices for measuring diffuse reflectance. These accessory devices include

integrating spheres for measuring 6°/hemispherical reflec- tance factor, 45°/0° reflectance factor, and directional/

hemispherical reflectance factor and a specular reflectometer.^ At the same time, a more accurate absolute diffuse reflectance

scale was being established by the auxiliary sphere or Van den

Akker method.^ A technique was developed for coating in- tegrating spheres with the PTFE powder, and extensive measurements of the optical properties of this material were

carried out over a five-year period. The results of these

studies are reported here along with some descriptive details of the techniques used in preparing reflection standards from

PTFE powder and its application to integrating spheres.

PREPARATION

The PTFE powder is somewhat lumpy as it comes in a shipping drum. It can be prepared for optical-coating purposes by reducing it to a uniform low-density powder. This can be

accomplished with a blender or other chopping device, preferably one with stainless-steel blades and a glass container. The powder should be kept in glass containers and handled

with tools made of materials such as stainless steel that are

less likely to contaminate the material. The powder will ad- here to itself on pressing, but it does not adhere well to metal,

glass, or plastic. One technique for making it adhere to metal

(or other materials) is first to coat the metal with a thin film

of high-vacuum silicone grease. Once this is done, the powder

can be pressed into place in thicknesses varying from 1 to 10 mm without much difficulty. The silicone grease has a low

volatility and does not affect the reflection properties of the

Reprinted from Journal of the Optical Society of America,

Vol. page 856, .July, 1981 Copyright © 1981 by the Optical Society of America and reprinted by permission of the copyright owner
V. R. Weidner and J. J. Hsia Vol. 71, No. 7/July 1981/J. Opt. Soc. Am. 857

Fig. 1. The NBS integrating-sphere-coating apparatus showing the hemisphere manipulator with the electronically controlled tamping

head used to press the PTFE powder into the hemisphere with a uniform radius.

PTFE powder because it contacts only a thin layer at the powder-metal interface. PTFE powder has been successfully applied to integrating

spheres ranging in diameter from a few centimeters to 45 cm

and to large, flat surfaces used as reflection standards. The

coatings are not affected by conditions of high humidity be- cause the pressed powder repels water. Exposure to highintensity ultraviolet radiation,'* such as that encountered near

a xenon arc, will slightly degrade the reflection properties of the coatings in the ultraviolet spectral region. The reflectance

will be degraded as a result of contamination from smoke,

dust, or other contaminants that may be present.

The time required for coating an integrating sphere of 20-cm diameter with a 6-mm-thick coating is typically about

4 h. This includes preparing the PTFE powder with a

blender, trimming up the finished coating around the ports,

and assembly of the usual two hemispheres. At NBS, spheres

up to 45-cm diameter are coated with the aid of a special

hemisphere manipulator (Fig. 1) that enables the technician

to rotate and pivot the hemisphere about the center point of the sphere and pack the PTFE powder into the curvature of the hemisphere with a light pressure, using hand tools such

as a stainless steel spoon or a round-bottom glass flask. In some special applications, such as in the preparation of an

auxiliary sphere for determining the absolute reflectance of the sphere coating, the radius of curvature of the coating

surface is carefully controlled by tamping the PTFE powder

under an electronic tamping head before it is rolled to a final

finish. A retainer ring is attached to the hemisphere flange

during the coating procedure to retain the powder at the open

edge of the hemisphere. When the coating is completed, this retaining ring is removed, and the two completed hemispheres

are attached to each other by means of the flanges. The

PTFE coating expands slightly at the hemisphere edge when

the retaining ring is removed. This is an advantage because

it results in the formation of a tight fit when the two hemispheres are combined to form the sphere.

As with any sphere-coating material, PTFE powder has its advantages and disadvantages. Some practice is required in

order to master the coating techniques. The powder should

be packed in lightly at first, to a depth of approximately 2-3

times the desired final thickness before it is pressed to a finish. The application of added powder to an already hard-pressed

coating may result in a peeling and separation of the material

into layers. The best results are obtained with a sand-blasted

or ground-glass pressing tool, such as a round-bottom flask of small diameter. The coating should be done in a relatively

clean, dust-free environment because the PTFE coating

usually becomes electrostatically charged during the pressing

and will hold small specks of dirt or lint. These can be picked

up or removed with a small, clean artist's brush. PTFE powder is very fine and easily mixes in the air about

the working area. Although the powder is believed to be

nontoxic, it is a good practice to use a dust mask to avoid unnecessary breathing of the material. PTFE may form toxic gases at thermal decomposition

temperatures above 400°C. These toxic products may be

produced inadvertently by contact of the fine powder with a flame or other high-temperature source. For further infor- mation on the safe handling of fluorocarbon resins, refer to Ref. 8. It should be noted that there are U.S. patents dealing with

the use of fluorocarbons as coatings for integrating spheres.

These U.S. patents are given in Ref. 9.

DENSITY

The reflectance of PTFE powder is influenced by the density

to which the powder is pressed. This relationship is illus- trated in Fig. 2, in which the results of a number of measure- ments of reflectance versus powder density are plotted. The

reflectance scale in this illustration is a relative one with the

data normalized at a density of 1.0 g/cm^, because this is the

density at which the powder reflectance is the highest. There seem to be no noticeable wavelength-related effects for wavelengths less than 2000 nm. The vertical bars in Fig. 2 show the spread in reflectance values at the 10 selected

1.005

- 1.000

0.985

1

0.980

PTFE POWDER

• 300 to 1800 nm

(overage of 10 wavelengths) V" 2000 nm V (overage of 2 runs) ^

0.5 1.0 1.5 2.0

DENSITY (g/cm3)

Fig. 2. Pressed PTFE powder reflectance as a function of powder

density (10-mm thickness). '
858 J. Opt. Soc. Am./Vol. 71. No. 7/July 1981 V. R. Weidner and J. J. Hsia

Table 1. Reflectance of Pressed PTFE Powder (0.8 g/cm^) Relative to That of a 10-mm-Thick Layer at Each Wavelength

Thickness Relative Reflectance (mm) 400 nm 550 nm 700 nm

1 0.991 0.989 0.986

2 0.995 0.994 0.993

4 0.998 0.998 0.997

6 1.000 1.000 0.999 8 1.000 1.000 1.000 10 1.000 1.000 1.000

wavelengths. The maximum reflectance is obtained by

compressing the powder to a density of from 0.8 to 1.2 g/cm^.

The loose powder has a density of approximately 0.5 g/cm^.

A sample of the pressed powder having the maximum reflec- tance can easily be prepared by compressing 2-2.5 volumes

of loose powder into 1 volume. This results in a pressed

sample that is rather soft. A sample compressed to a density

of 2 g/cm^ will have a much harder surface and slightly lower

reflectance. Higher densities require higher pressures, and

a mechanical press must be used. As is shown in Fig. 2, the

reflectance does not vary much with change in powder density

for the density range of 0.8-1.2 g/cm^. Repeated preparation

of pressed samples having reflectances that are the same to within a few tenths of a percent can easily be achieved, and

a fresh sample can be prepared in minutes. At wavelengths

greater than 2000 nm the reflectance drops more rapidly with

increasing powder density.

THICKNESS

The diffuse reflectance of pressed PTFE powder is influenced by the thickness of the powder layer. Its translucency is such

that at least a 6-mm thickness at a density of approximately

1 g/cm^ is required to obtain maximum reflectance. Table

1 shows the influence of thickness on the reflectance of PTFE

powder at 400, 550, and 700 nm. These measurements were made with an aluminum backing having a reflectance of ap- proximately 60%. Later measurements in the infrared out

to 2500 nm indicate that 6- to 8-mm thicknesses and a density of 1 g/cm'' are adequate in order to achieve maximum diffuse reflectance values for the pressed powder. Coatings this thick are not required in applications where the coating is used in a signal -averaging sphere. However, when the PTFE powder

is used as a reflection standard, a 10-mm thickness will be

certain to give the maximum reflectance at all wavelengths.

FLUORESCENCE

There has been no clear evidence to show that the PTFE

powder itself fluoresces. However, coatings made from PTFE

powder show a very weak fluorescence. This fluorescence may be associated with a slight contamination from the plastic

bag used to contain the PTFE powder in its shipping drum.

As a test of the contribution of fluorescence to the reflectance of PTFE powder, a specimen was first measured on a double- beam reflectance spectrophotometer with the use of monochromatic illumination of the PTFE powder and then with

polychromatic illumination. In Table 2 the normalized dif- ference D between the reflectances obtained by these two modes of illumination is given as D = (Rm — Rp )lfifj, where

Rm is proportional to the reflectance of the PTFE powder

sample relative to that of an aluminum mirror with monochromatic irradiation and Rp is the same relative reflectance with polychromatic irradiation. There appeared to be a slight

amount of fluorescence with excitation at wavelengths less than 290 nm and emission in the wavelength range of 310-350 nm. Subsequent measurements with a spectrofluorometer'^

confirmed these conclusions. The levels of fluorescence observed may be negligible for most radiometric and spectrophotometric applications.

However, in applications in which a small amount of fluores- cence can cause a significant error, it would be wise not to use any kind of pressed -powder coating without first checking for the presence of fluorescence that is due to contaminants,

especially when ultraviolet radiation below 300 nm is in- volved.^^

REFLECTION PROPERTIES

The 6°/hemispherical reflectance factor of a diffuse reflec- tance standard is probably the most important calibration. The term 6°/hemispherical reflectance refers to a measure- ment geometry in which the sample is illuminated by a coUi- mated source incident upon the sample at 6° from the normal

Table 2. Data from Fluorescence Check

Wavelength Wavelength

(nm) D (nm) D

250 0.019 500 0.000 260 0.016 510 -0.002

270 0.022 . 520 0.000 280 0.018 530 0.000 290 0.005 540 0.002

300 -0.004 550 0.000 310 -0.018 560 0.000 320 -0.011 570 0.000 330 -0.021 580 0.005 340 -0.015 590 0.001

350 -0.009 600 0.006 360 -0.007 610 0.004 370 -0.006 620 0.001 380 -0.003 630 0.001 390 -0.002 640 0.000

400 -0.006 650 -0.002 410 -0.002 660 0.000 420 -0.002 670 -0.002

430 0.002 680 -0.002 440 0.002 690 -0.006

450 0.000 700 -0.003 460 0.002 710 -0.004 470 -0.002 720 -0.003

480 0.002 730 0.002 490 0.002 740 -0.008

750 -0.007
V. R. Weidner and J. J. Hsia Vol. 71, No. 7/July 1981/J. Opt. Soc. Am. 859

Table 3. 6° /Hemispherical Reflectance Factor of a 10-mm-Thick Pressed PTFE Powder Relative to a Perfect

Diffuser

A A A (nm) p (nm) p (nm) p

200 0.962° 950 0.994 2140 0.964 210 0.964- 1000 0.994 2150 0.965 220 0.967 1050 0.994 2160 0.967 225 0.968 1100 0.994 2170 0.970 230 0.969 1150 0.994 2180 0.973

240 0.971 1200 0.993 2190 0.975 250 0.973 1250 0.993 2200 0.977 260 0.976 1300 0.992 2210 0.977 270 0.978 1350 0.991 2220 0.978 275 0.979 1400 0.991 2230 0.978

280 0.980 1450 0.992 2240 0.977 290 0.982 1500 0.992 2250 0.977 300 0.984 1550 0.992 2260 0.976 310 0.985 1600 0.992 2270 0.976 320 0.987 1650 0.991 2280 0.975

325 0.988 1700 0.990 2290 0.974 330 0.988 1750 0.990 2300 0.972 340 0.989 1800 0.990 2310 0.971 350 0.990 1850 0.986 2320 0.970 360 0.990 1900 0.985 2330 0.968

370 0.991 1950 0.984 2340 0.966 375 0.991 2000 0.981 2350 0.965 380 0.991 2010 0.979 2360 0.964 390 0.992 2020 0.978 2370 0.963 400 0.993 2030 0.976 2380 0.963

450 0.993 2040 0.975 2390 0.962 500 0.994 2050 0.973 2400 0.962 550 0.994 2060 0.972 2450 0.961 600 0.994 2070 0.971 2500 0.960 650 0.994 2080 0.970

700 0.994 2090 0.969 750 0.994 2100 0.968 800 0.994 2110 0.967 850 0.994 2120 0.966 900 0.994 2130 0.964

" Extrapolated.

and in which the reflected flux is averaged by an integrating

sphere-detector system. An angle of 6° off the normal is commonly used to allow for including the specular component

in the measurement. The 6° /hemispherical reflectance factor of samples of PTFE powder pressed to a thickness of 6 mm or more with a density of 0.8-1.2 glcm? is very reproducible. For a set of samples made at different times from different lots of PTFE

powder, a standard deviation of less than 0.001 in measured

reflectance was found for the wavelength range of 400-750 nm.

Further measurements will have to be made in order to es- tablish what this deviation will be in the ultraviolet and in- frared regions. The 6°/hemispherical reflectance factor of pressed PTFE powder is given in Table 3 for a PTFE coating 10 mm in thickness and having a density in the range of 0.8-1.2 glcm^. The data listed in Table 3 are plotted in Fig. 3. These

data are reported on an absolute reflectance scale (relative to a perfect diffuser) and were obtained by the auxiliary sphere

100

96 . 6VHEMISPHERICAL REFLECTANCE

OF PTFE POWDER

95

200 500 1000 1500 2000

WAVELENGTH (NM)

2500

Fig. 3. The 6°/hemispherical reflectance factor (relative to a perfect

diffuser) of 10-mm-thick, l-g/cm''-density pressed PTFE powder.
860 J. Opt. Soc. Am.A'ol. 71. No. 7/July 1981 V. R. Weidner and J. J. Hsia

Table 4. Directional/Hemispherical Reflectance Factor of Pressed PTFE Powder for a 10-mm-Thick Coating

(Relative to Hemispherical Reflectance at 6° Incidence)

Angle

of Incidence

Reflectance 250 nm 300 nm 350 nm 450 nm 600 nm 7.50 nm

6° 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 10° 1.0003 1.0002 1.0001 1.0001 1.0001 1.0001 15° 1.0009 1.0005 1.0004 1.0002 1.0002 1.0002 20° 1.0017 1.0010 1.0007 1.0004 1.0004 1.0004 25° 1.0026 1.0015 1.0011 1.0007 1.0006 1.0006 30° 1.0038 1.0022 1.0015 1.0010 1.0008 1.0008 35° 1.0052 1.0030 1.0021 1.0013 1.0011 1.0011 40° 1.0066 1.0038 1.0026 1.0016 1.0014 1.0014 45° 1.0082 1.0047 1.0032 1.0020 1.0017 1.0017 50° 1.0099 1.0056 1.0038 1.0023 1.0020 1.0020 55° 1.0117 1.0065 1.0044 1.0026 1.0023 1.0023 60° 1.0134 1.0074 1.0049 1.0029 1.0025 1.0025 65° 1.0153 1.0083 1.0054 1.0031 1.0027 1.0027 70° 1.0170 1.0090 1.0058 1.0032 1.0028 1.0029 75° 1.0186 1.0097 1.0061 1.0032 1.0029 1.0029

1.025

1.020

UJ P 1.015

UJ

u_ <

UJ -I

CE UJ

oc.

I.OlO

1.005

1.000

DIRECTIONAL/HEMISPHERICAL

REFLECTANCE OF

PTFE

POWDER

/250

/(NM)

>^300'

^--350

450 *^750

6" 20" 40» 60" 75°

ANGLE OF INCIDENCE

Fig. 4. The directional/hemispherical reflectance factor of pressed

PTFE powder as a function of angle of incidence and wavelength.

method.^ These absolute reflectance data are believed to be

accurate to within ±0.002 on the basis of the analysis of the known sources of error as discussed in Ref. 7. The directional/hemispherical reflectance factor of pressed

PTFE powder given in Table 4 shows how the hemispherical

reflectance of the material varies as a function of the angle of

incidence. These measurements were made by means of an

integrating sphere accessory to the NBS reference spectrophotometer for diffuse reflectance. This accessory consisted

of a 45-cm-diameter sphere designed so that the sample can

be mounted in the center of the sphere where it can be rotated

to control the angle of incidence. The measurements were made at several wavelengths in the ultraviolet and visible spectra for both vertically and horizontally polarized sample

beams. The results listed in Table 4 and illustrated in Fig. 4 are an average of the two polarizations. The values for ei- ther polarization did not vary by more than ±0.5% from the

average. The most noticeable changes in reflectance as a

function of angle of incidence occur in the ultraviolet spectral

region. The data are relative to the 6°/hemispherical re- flectance factor values. The bidirectional reflectance factor of pressed PTFE

powder listed in Table 5 shows how the reflectance varies over

a wide range of viewing angles for four different angles of in- cidence. These measurements were made by means of the NBS specular reflectometer.^ This instrument is ordinarily

used for specular reflectance measurements as a function of angle of incidence. It can be used to measure the bidirectional reflectance of a diffuse sample in the plane of the incident

sample beam. Measurements were made at 300, 600, and

1500 nm for angles of incidence of —10, —30, —50, and —70°.

The angles of viewing were selected at 10° intervals from —80

to -f 80°. The bidirectional reflectance data reported in Table

5 are an average of the vertical and horizontal polarizations.

The values for either polarization varied from this average by

as little as ±0.2% to as much as ±20% depending on the combination of beam incidence and viewing angle. These data

are relative to the reflectance values obtained at 0° (normal)

viewing. The results listed in Table 5 are representative of the bidirectional reflectance of a "rough" surface prepared by

pressing the PTFE powder with a coarsely ground glass plate.

Samples pressed with a polished glass plate exhibit slightly

higher values of reflectance, particularly at viewing angles

greater than 75°. Figure 5 illustrates the bidirectional re- flectance properties of pressed PTFE powder at 600 nm.

Similar results are shown for barium sulfate powder in Fig.

6. Further studies of the reflection properties of pressed PTFE

powder are being made at NBS. Among these properties are the 45°/0° or 0°/45° reflectance factors for the visible spectral

region. The results of these studies will be published at a future date.
V. R. Weidner and J. J. Hsia Vol. 71, No. 7/July 1981/J. Opt. Soc. Am. 861

Table 5. Directional/Directional Reflectance Factor (Bidirectional Reflectance) of lO-mm-Thick Pressed PTFE

Powder

Angle Angle of Incidence

of Viewing

300 nm 600 nm 1500 nm

-10° -30° -50° -70° -10° -30° -50° -70° -10° gnhr -30° -50° -70°

-80° 0.763 0.792 0.872 1.148 0.743 0.761 0.827 1.048 0.702 0.830 0.820 1.045 -70° 0.836 0.867 0.937 0.822 0.840 0.898 0.760 0.882 0.855 -60° 0.882 0.914 0.980 1.074 0.872 0.891 0.946 1.019 0.819 0.918 0.886 1.000 -50° , 0.919 0.949 1.022 0.909 0.931 0.987 0.875 0.952 0.992 -40° 0.946 0.979 1.000 0.996 0.939 0.967 0.982 0.974 0.920 0.974 0.936 0.980 -30° 0.967 0.993 0.982 0.963 0.980 0.971 0.959 0.945 0.980 -20° 0.988 1.005 0.991 0.981 0.986 0.998 0.984 0.974 0.978 0.980 0.966 0.985 -10° 1.000 0.994 0.988 0.998 0.991 0.983 0.990 0.982 0.995 0° 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 10° 0.991 1.001 1.008 1.021 0.991 1.002 1.012 1.027 0.998 1.005 1.010 1.010 20° 0.982 1.001 1.022 1.052 0.983 1.003 1.027 1.067 0.986 1.012 1.018 1.060 30° 0.970 0.999 1.036 1.098 0.971 1.004 1.048 1.125 0.971 1.015 1.040 1.155 40° 0.960 0.997 1.056 1.163 0.957 1.004 1.076 1.212 0.942 1.018 1.066 1.270 50° 0.943 0.996 1.085 1.265 0.938 1.002 1.114 1.343 0.895 1.022 1.100 1.440 60° 0.921 0.992 1.125 1.426 0.914 1.000 1.168 1.549 0.832 1.030 1.155 1.695 70° 0.882 0.974 1.167 1.691 0.872 0.985 1.227 1.897 0.754 1.035 1.235 2.075 80° 0.817 0.937 1.214 2.190 0.802 0.946 1.291 2.551 0.660 1.040 1.340 3.090

5.0

4.0-

Ul UJ 3.0-

o

o

I-uj2 >

0-

PTFE

POWDER

(600 NM)

ANGLE OF INCIDENCE;

-10° -30° -50°

-70°

"rough"

0-

J_J I I I L ' -80° -40° 0° 40° 80°

ANGLE OF VIEWING

Fig. 5. The bidirectional reflectance factor at 600 nm of pressed

PTFE powder having a rough surface finish.

5.0

UJ

UJ UJ

4.0-

3.0

- -10°

-30°

I- -50°

-70°

6^

9 ^

2.0

1.0

BARIUM SULFATE

POWDER

(600 NM)

ANGLE OF INCIDENCE:

"rough"

-80° -40° 0° 40° 80°

ANGLE OF VIEWING

Fig. 6. The bidirectional reflectance factor at 600 nm of pressed

barium sulfate powder having a rough surface finish.

REFERENCES

1. The polytetrafluoroethylene powder used in these investigations

is manufactured by Allied Chemical Company. The material is commonly referred to by the trade name Halon and is further

identified as type G-80 tetrafluoroethylene resin. The commercial name of this material is given here for purposes of identification only and in no way implies endorsement by the National Bureau of Standards.

2. Bureau Central de la Commission Internationale de I'Eclairage, Review of Publications on Properties and Reflection Values of Material Reflection Standards (Paris, 1979), CIE Publication 46 (TC-2.3), pp. 15-72.

3. The term "perfect diffuser" is defined in Bureau Central de la Commission Internationale de I'Eclairage, International Lighting

Vocabulary (Paris, 1970), CIE Publication 17 (E-1.1), p. 95.

4. F. Grum and M. Saltzman, P-75-77 New White Standard of Reflectance (Paris, 1976), CIE Publication 36, 91.

5. W. H. Venable, J. J. Hsia, and V. R. Weidner, "Development of an NBS reference spectrophotometer for diffuse reflectance and

transmittance," Nat. Bur. Stand. U.S. Tech. Note 594-11, 47 pp.

(1976).

6. V. R. Weidner and J. J. Hsia, "NBS specular reflectometer- spectrophotometer," Appl. Opt. 19, 1268-1273 (1980).

7. W. H. Venable, J. J. Hsia, and V. R. Weidner, "Establishing a scale of directional-hemispherical reflectance factor I: the Van den Akker method," J. Res. Nat. Bur. Stand. 82, 29-55, (1977).

8. E. I. Du Pont de Nemours and Company, Inc., Fluorocarbons

Division, Teflon Fluorocarbon Resins—Safety in Handling and

Use (Wilmington, Del., 1970), pp. 1-10. This publication ref- erences technical papers dealing with the thermal decomposition

of fluorocarbons and associated safety problems.

9. The following U.S. patents are assigned to J. A. Seiner of PPG

Industries, Inc., Pittsburgh, Pa.: U.S. Patent No. 3,956,201, May

11, 1976, and U.S. Patent No. 3,764,364, October 9, 1973.

10. From uncorrected emission spectra supplied by K. Mielenz and

R. Velapoldi using the reference spectrofluorimeter in the NBS

Center for Analytical Chemistry.

11. R. D. Saunders and W. R. Ott, "Spectral irradiance measurements: effect of UV produced fluorescence in integrating

spheres," Appl. Opt. 15, 827-828 (1976).
Appendix H

Reprinted from Applied Optics, Vol. 24, page 2225, July 15, 1985

Copyright © 1985 by the Optical Society of i^erica and reprinted by permission of the copyright owner.

Laboratory intercomparison study of pressed polytetrafluoroethylene powder reflectance standards

V. R. Weidner, J. J. Hsia, and B. Adams

The object of this paper is to present results of several experiments relating to the preparation and use of pressed polytetrafluoroethylene (PTFE) powder as a diffuse reflectance standard for the 200-2500-nm spectral range. These experiments include two round-robin intercomparisons involving nine laboratories. These round-robin experiments provided data on the variability of the reflectance of pressed PTFE reflec- tance standards prepared in different laboratories. Results of these measurements provided insight into the problems associated with the PTFE standards and helped to establish what practices needed to be stan- dardized to improve interlaboratory agreement for diffuse reflectance measurements.

I. Introduction

The object of this paper is to present the results of

several experiments relating to preparation and use of

pressed polytetrafluoroethylene (PTFE) powder as a

diffuse reflectance standard for the 200-2500-nm

spectral range. The usefulness of this material as a reflectance standard was first reported by Grum and

Saltzman.-'^ Further investigations into the reflection

properties of pressed PTFE powder were reported by

the authors.^ As a result of the growing need for improved diffuse reflectance standards for the UV, visible,

and near IR, and the interest shown in this material, the

Inter Society Color Council (ISCC, Subcommittee 22)

has suggested that a laboratory intercomparison be

conducted to study the methods of preparation and

uniformity of reflectance of pressed PTFE powder. In addition to these round-robin experiments, the results of some closely related PTFE investigations at the

National Bureau of Standards (NBS) are also in- cluded.

II. Round-Robin Intercomparisons

Two round-robin experiments were conducted in spring 1984. The first experiment yielded results that

established a need for further control over the experiment. Therefore, a second round robin was initiated. The design of the two experiments and the resulting

data provided some insight into the problems associa*

The authors are with U.S. National Bureau of Standards, Radiometric Physics Division, Gaithersburg, Maryland 20899. Received 18 January 1985.

with the use of PTFE reflectance standards and also

helped to establish what practices needed to be stan- dardized to improve the interlaboratory agreement for reflectance measurements.

A. Round-Robin Experiment 1 Six laboratories participated in this experiment. A

quantity of PTFE powder sufficient to prepare two

pressed plaques was sent to each laboratory. The

PTFE powder was provided by NBS. It was mixed

thoroughly by means of a glass blender and shipped in sealed glass jars. NBS also provided 50-mm diam by

10-mm depth holders with covers for the participating

laboratories to use in preparation of the pressed PTFE

specimens. The instructions requested that the laboratories weigh the powder holders before and after pressing the powder to be used in the pressing because

the object was to determine what variations in reflec- tance would result if this part of the experiment were

uncontrolled.

The participating laboratories were accustomed to using commercial powder presses and encountered some

difficulty in using the holders provided by NBS. Because of this, some laboratories submitted additional

pressed specimens in their own holders. As a result, more specimens were returned to NBS for analysis than

had originally been planned on. However, this turned

out to be useful because it provided a larger sampling

for comparison.

Measurements of the spectral reflectance of the re- turned PTFE specimens were made at NBS and are reported in Table I. A white ceramic tile of known

spectral reflectance was used to compare the PTFE

specimens and place the measurements on an absolute

scale for the 400-2500-nm wavelength rang For the

15 July 1985 / Vol. 24, No. 14 / APPLIED OPTICS 2225
Table I. Round-Robin 1; Spectral Reflectance of Pressed PTFE Powder

VV dVcicIlg til (nm) 1 I 2 9 Laboratory

2 2

0 QO0o

250 0.973 0.973 0.931 0.935 0.962 0.967 0.922 0.983 0.984 300 0.984 0.984 0.963 0.963 0.974 0.975 0.956 0.988 0.988 350 0.990 0.990 0.984 0.984 0.983 0.983 0.977 0.992 0.992 400 0.993 0.993 0.991 0.991 0.985 0.986 0.984 0.993 0.993 500 0.992 0.992 0.992 0.991 0.988 0.987 0.989 0.993 0.993 600 0.993 0.993 0.993 0.993 0.990 0.990 0.992 0.994 0.994 700 0.993 0.993 0.993 0.993 0.987 0.988 0.991 0.993 0.993 800 0.993 0.993 0.993 0.993 0.988 0.988 0.992 0.993 0.993 1000 0.992 0.992 0.992 0.992 0.986 0.987 0.991 0.993 0.993 1200 0.989 0.989 0.989 0.989 0.983 0.984 0.988 0.991 0.991 1500 0.987 0.987 0.987 0.987 0.979 0.983 0.987 0.987 0.987 2000 0.978 0.978 0.978 0.978 0.960 0.962 0.976 0.979 0.980 2100 0.962 0.963 0.962 0.962 0.933 0.935 0.960 0.964 0.965 2200 0.967 0.967 0.965 0.966 0.946 0.948 0.963 0.967 0.967 2300 0.965 0.966 0.965 0.964 0.940 0.943 0.963 0.966 0.968 2400 0.960 0.960 0.959 0.959 0.923 0.926 0.956 0.961 0.960 2500 0.960 0.960 0.960 0.960 0.922 0.924 0.958 0.960 0.960 Density (1.05) (0.94) (1.16) (1.15) (1.65) (1.64) (1.04) (0.87) (0.81) (g/cm3)

Wavelength Laboratory Average Standard

(nm) 3 3 4 4 5 5 6 of 16 dev.

250 0.978 0.977 0.947 0.955 0.960 0.960 0.983 0.9619 0.0195 300 0.984 0.984 0.964 0.976 0.968 0.967 0.987 0.9753 0.0106 350 0.990 0.990 0.976 0.982 0.977 0.976 0.990 0.9847 0.0059 400 0.990 0.990 0.978 0.983 0.982 0.978 0.993 0.9877 0.0054 500 0.992 0.992 0.978 0.983 0.983 0.980 0.992 0.9886 0.0049 600 0.992 0.992 0.981 0.986 0.983 0.981 0.993 0.9900 0.0046 700 0.992 0.992 0.976 0.983 0.980 0.977 0.993 0.9886 0.0061 800 0.992 0.992 0.975 0.982 0.977 0.975 0.990 0.9881 0.0068 1000 0.990 0.990 0.974 0.981 0.974 0.971 0.988 0.9866 0.0075 1200 0.987 0.987 0.972 0.980 0.967 0.964 0.988 0.9836 0.0085 1500 0.985 0.985 0.966 0.976 0.957 0.954 0.986 0.9800 0.0111 2000 0.976 0.976 0.934 0.962 0.905 0.900 0.977 0.9824 0.0262 2100 0.960 0.960 0.893 0.937 0.845 0.832 0.962 0.9372 0.0430 2200 0.964 0.965 0.913 0.945 0.879 0.873 0.965 0.9475 0.0313 2300 0.964 0.964 0.903 0.945 0.860 0.848 0.964 0.9430 0.0386 2400 0.958 0.958 0.872 0.928 0.814 0.796 0.956 0.9279 0.0536 2500 0.957 0.957 0.862 0.923 0.795 0.781 0.948 0.9242 0.0592 Density (1.18) (1.23) (1.77) (1.67) (2.05) 2.10 (1.15) (g/cm^)

measurements at wavelengths of <400 nm the data were

adjusted to an absolute scale by comparison of the

specimens to a freshly prepared PTFE specimen. The

absolute reflectance of this specimen was assumed to be that of the published data for the 6°/hemispherical

reflectance of pressed PTFE powder (see Ref. 2). The

average reflectance of the sixteen specimens and the

standard deviations are listed in the last two columns

of Table I. The approximate densities of the specimens

are listed at the bottom of the table. The densities of the pressed PTFE specimens listed in Table I varied from ~0.8 to 2 g/cm^. The data indi- cate that the reflectances are less for the higher density

specimens. Two specimens submitted by laboratories

2, 4, and 5 have densities that exceed 1.5 g/cm^. At

these higher densities the reflectance decreases at longer

wavelengths in the 2000-2500-nm range. Similar ef- fects have been reported for other compacted powders.'^

These specimens also have slightly lower reflectances

at shorter wavelengths.

There are some larger variations in specimen reflec- tances at wavelengths <300 nm in the UV. These dif- ferences do not correlate with variations in specimen

densities. This is a wavelength range in which the

specimen reflectance may be easily altered by con- tamination. Since all the PTFE powder originated

from the same source, it is assumed that these variations

in the UV reflectance are the result of some change in the sample purity that took place during the round

robin.

The variation in reflectance for the visible spectral range, shown in Table I, is small for all the specimens

having densities of <1.5 g/cm^. Because the PTFE

reflectance is so reproducible in the visible spectrum,

it is clear that the material can be used as a diffuse re- flectance standard in this range. To improve the re- producibility of spectral reflectance measurements for pressed PTFE powder in the UV and near IR, the

density of the pressed specimens must be controlled,

and care must be taken to maintain material purity.

2226 APPLIED OPTICS / Vol. 24, No. 14 / 15 July 1985
Table II. Round Robin 2; Spectral Reflectance of Presssed PTFE Powder

Wavelength Laboratory

(nm) 1 1 o

I 2 2 \3 3 4 5 5

200 0.959 0.963 0.948 0.946 0.947 0.959 0.960 0.888 0.963 0.961 250 0.972 0.974 0.966 0.967 0.968 0.972 0.972 0.923 0.969 0.967 300 0.984 0.984 0.982 0.976 0.977 0.984 0.984 0.962 0.983 0.982 350 0.989 0.990 0.988 0.989 0.990 0.989 0.991 0.983 0.989 0.988 400 0.992 0.992 0.992 0.992 0.993 0.991 0.993 0.987 0.991 0.990 500 0.993 0.993 0.993 0.993 0.993 0.993 0.993 0.987 0.992 0.991 600 0.993 0.993 0.993 0.993 0.993 0.991 0.993 0.986 0.991 0.991 700 0.993 0.993 0.993 0.993 0.993 0.991 0.992 0.986 0.991 0.991 800 0.993 0.993 0.993 0.993 0.993 0.991 0.993 0.985 0.991 0.990 1000 0.994 0.993 0.993 0.993 0.993 0.990 0.991 0.986 0.991 0.988 1500 0.992 0.991 0.991 0.991 0.991 0.989 0.989 0.983 0.987 0.986 2000 0.981 0.981 0.981 0.980 0.980 0.980 0.979 0.974 0.978 0.975 2100 0.970 0.965 0.970 0.967 0.971 0.969 0.969 0.963 0.967 0.963

u.y (O u.y / 6

C\ QQ1 0.976 0.982 0.974 0.977 u.ybo U.y / i U.y lb 2300 0.970 0.973 0.971 0.967 0.970 0.967 0.967 0.961 0.967 0.968 2400 0.968 0.962 0.962 0.964 0.964 0.962 0.960 0.953 0.952 0.951 2500 0.964 0.960 0.960 0.960 0.960 0.962 0.961 0.946 0.954 0.955 Density (0.905) (0.990) (0.835) (0.920) (0.800) (1.025) (1.025) (0.920) (1.085) (1.08) (g/cm3)

Wavelength Laboratory Average Standard (mm) 6 7 7 8 8 9 9 01 17 Dev.

200 0.898 0.823 0.905 0.905 0.911 0.954 0.949 0.9317 0.0382 250 0.968 0.920 0.950 0.921 0.929 0.971 0.970 0.9576 0.0204 300 0.985 0.968 0.975 0.977 0.979 0.983 0.982 0.9792 0.0063 350 0.990 0.984 0.986 0.988 0.989 0.989 0.989 0.9883 0.0021 400 0.993 0.988 0.988 0.991 0.992 0.992 0.992 0.9911 0.0018 500 0.993 0.988 0.989 0.992 0.993 0.993 0.993 0.9919 0.0020 600 0.993 0.987 0.988 0.992 0.993 0.993 0.993 0.9915 0.0023 700 0.992 0.987 0.988 0.992 0.993 0.993 0.993 0.9914 0.0023 800 0.992 0.987 0.988 0.991 0.993 0.992 0.993 0.9912 0.0024 1000 0.992 0.987 0.988 0.991 0.991 0.991 0.993 0.9910 0.0024 1500 0.989 0.985 0.984 0.988 0.988 0.990 0.990 0.9885 0.0027 2000 0.980 0.976 0.975 0.979 0.980 0.979 0.980 0.9787 0.0023 2100 0.965 0.962 0.962 0.972 0.973 0.972 0.971 0.9677 0.0038 2200 0.979 0.961 0.971 0.974 0.979 0.980 0.982 0.9753 0.0055 2300 0.965 0.967 0.974 0.965 0.972 0.967 0.968 0.9682 0.0032 2400 0.966 0.957 0.956 0.964 0.965 0.957 0.952 0.9597 0.0055 2500 0.959 0.948 0.953 0.957 0.962 0.961 0.962 0.9579 0.0051 Density (0.900) (0.845) (0.830) (0.900) (0.890) (0.900) (0.895) (g/cm3)

B. Round-Robin Experinnent 2.

It was decided at the ISCC meeting in Apr. 1984 that a second round-robin experiment should be undertaken

and that each participant would try to submit pressed

PTFE specimens of 0.9 ± 0.05-g/cm^ density in their own holders. All the participants received a new supply

of PTFE powder from NBS. The six laboratories that

participated in the first round robin also took part in the

second, and three more laboratories joined in the ex- periment.

The returned specimens were measured relative to a freshly prepared PTFE specimen. The data were

then adjusted to an absolute reflectance scale based on

the 6° /hemispherical reflectance of PTFE previously

published.2 It was necessary to place all the measure- ments on an equal scale for comparison. The white

ceramic tile used in round robin 1 to establish the absolute scale was not used since the same scale could be

established with a fresh PTFE specimen. The freshly

prepared PTFE specimen served to accomplish that

purpose. Results of the spectral analysis of the pressed

PTFE specimens for round-robin experiment 2 are shown in Table II. The PTFE specimens ranged in density from ~0.80

to 1.08 g/cm'^ for the second round robin indicating that

the density can be controlled at or near 0.9 ± 0.1 g/cm'^.

This is a small spread in density, considering that most

of the powder presses used to prepare these specimens

are not well designed for controlling the density of the

finished specimen.

Controlling the density of the specimens resulted in a smaller spread in the reflectance values than those

reported in the first round robin. This is especially true

for reflectance values in the wavelength range between

2000 and 2500 nm. The reflectance data at 250 nm

show less variation than reported in the first round

robin. However, the variation in the UV is still large

and cannot be reduced by controlling the PTFE density.

15 July 1985 / Vol. 24, No. 14 / APPLIED OPTICS 2227
Some of the variation in reflectance for the PTFE

specimens listed in Tables I and II can be attributed to random noise. At wavelengths below 250 nm the noise

level is approximately ±0.003. In the near-IR range of

2000 to 2500 nm, the noise is as high as ±0.010.

The data submitted by laboratories 4 and 7 for the

second round robin show lower reflectances by ~0.5%

than the other specimens. The reason for this is not

clear. However, these specimen holders have a 0.2-mm

raised metal ridge that causes a gap between the surface

of the PTFE and the plane of the sample port of the

reflectometer integrating sphere. This condition may

contribute toward this observed lowering of the measured reflectance of the three PTFE specimens.

However, 0.5% is a larger difference than would be ex- pected for an 0.2-mm gap. Data will be presented in a

later part of this paper that show how the reflectance

of PTFE appears to decrease as the gap between the

measured surface and port increases.

C. Conclusion of the Round-Robin Experiments

The round-robin experiments emphasize the need for some degree of standardization in the techniques used

to prepare reflectance standards from PTFE powder.

They also indicate that this material can be a useful and

convenient diffuse reflectance standard if these techniques are followed.

NBS has found through experiment that pressed

PTFE powder of ~1 g/cm^ produces a reflectance

standard with reflectance values that are reproducible

to ±0.01 in the 200-300-nm wavelength range, ±0.005

for the 300-2000-nm wavelength range, and ±0.01 for the 2000-2500-nm wavelength range. Larger variations

in the reflectance are possible, however, if the material

is contaminated or if the specimen holders are not filled so that the measured surface is in contact with the plane

of the sample port of the reflectometer. The data from

these round-robin experiments confirm these findings.

III. Additional Experiments Relating the PTFE

Reflectance

A. Influence of Specimen Positioning at the

Reflectometer Sample Port The influence of specimen positioning at the reflec- tometer sample port is demonstrated by the experimental results shown in Fig. 1. The data show how the

diffuse reflectance of a specimen of pressed PTFE

powder is influenced by controlling the spacing between

the specimen plane and the plane of the sample port.

The data are shown for measurements at 300, 550, and

1800 nm. Measurements with no spacing between the

specimen and sample port are set equal to 100%, and

measurements at increasing distance between the

specimen and port are plotted relative to the zero spacing data. The sample beam illuminated an area of

^l-cm diameter in the center of a port of 2.3-cm di- ameter. The results plotted in Fig. 1 show that the ef- fects are about the same at different wavelengths. The

measured reflectance is ~1% lower if the spacing were

lOOi

5? I00<

100'

300 nm

- 550 nm

-

-

1800

1 1 1 1 1 1 1 1 I 1 1 1 1 1 0 0.5 1.0 1.5 DISTANCE FROM PORT (mm)

Figure 1. Measured diffuse reflectance of a pressed PTFE powder

specimen is influenced by varying the spacing between the plane of the specimen and the plane of the integrating sphere port. The effect

is shown for measurements at 300, 550, and 1800 nm.

1 mm. A spacing of 0.1 or 0.2 mm seems to have little effect on measured reflectance. However, an error of

0.5% could be introduced by a spacing as small as 0.7 mm. The results may vary for different instruments

because the effect can be influenced by the ratio of the

beam diameter to the port diameter and thickness of the

port rim. One problem when the PTFE specimen is in contact with the sample port is of course that of damaging the standard. This occurs if the standard slips across the port during mounting and can only be

avoided by allowing a small spacing between the spec- imen and port. The other solution is to prepare fresh

samples when required and always allowing contact between the specimen and port.

B. Comparison of PTFE from Two Manufacturers

A comparison of the diffuse reflectance of pressed

PTFE powder from two manufacturers was made to see

if significant differences existed between them. The

relative differences in the spectral reflectance of the two

types of PTFE are shown in Table III. The differences

reported are not significant since they fall within the

random uncertainties associated with sample preparation and measurement.

C. Reproducibility of the Absolute Reflectance of Pressed PTFE Powder using the Double-Sphere Method

The best values of spectral reflectance of pressed

PTFE powder as determined at NBS are reported in Ref. 2. The values are reported for the 6°/hemispherical reflectance factor (relative to a perfect diffuser).

The reproducibility of the reflectance values for pressed

PTFE powder as determined by the double-sphere

technique was tested by repeating the experiment three

times and computing the standard deviation for the

three trials. Details of the double-sphere technique are reported in Refs. 2, 4, and 5. The standard deviations

for three trial runs using this technique are reported in

2228 APPLIED OPTICS / Vol. 24, No. 14 / 15 July 1985
Table III. Differences In Spectral Reflectance of PTFE Obtained from

Manufacturers A and B WW 1 tU 3vclGngtn iVlCaoUl iX^PnQI irPITIPtl t CIlICllI/ (nm) differences uncertainty

oUU +0.004 ±0.005

+0.003 ±0.005

0\J\J +0.002 ±0.005

DUU +0.002 ±0.005

700 +0.001 ±0.005

+0.001 ±0.005

+0.001 ±0.005

lUUU 0.000 ±0.005

1 luU 0.000 ±0.005

1200 +0.001 ±0.005

ioUU -0.002 ±0.005

1 Ann +0.001 ±0.005

iOUU -0.002 ±0.005

—0.001 ±0.005

1700 -0.001 ±0.005

1 son -0.002 ±0.005

u.uuu ±u.uuo

2000 -0.003 ±0.005

2100 -0.002 0.010 2200 -0.001 0.010

2300 -0.012 0.010 2400 -0.003 0.010 2500 -0.002 0.010

Table IV. Standard Deviation for Three Independent Determinations of the 6°/Hemispherical Reflectance Factor of Pressed PTFE Powder by the Double-Sphere Technique for Measuring Absolute Reflectance

Standard deviation Wavelength of three (nm) determinations

200 0.0014 210 0.0014 220 0.0012 230 0.0008 240 0.0008

250 0.0011 300 0.0007 350 0.0003 400 0.0002 500 0.0003

600 0.0004 700 0.0005 800 0.0006 900 0.0006 1000 0.0006

1100 0.0006 1200 0.0006 1300 0.0006 1400 0.0008 1500 0.0007

1600 0.0007 1700 0.0008 1800 0.0007 1900 0.0006 2000 0.0004

2100 0.0005 2200 0.0005 2300 0.0007 2400 0.0007 2500 0.0006

PLEXIGLAS PLUNGER

POWDERSTAINLESS ^ STEEL

CYLINDER

LOCKING

RING

POWDER

RECEPTACLE

Fig. 2. Powder press is designed to provide a means for controlling the density of pressed PTFE diffuse reflectance standards. The

preferred density is 1 g/cm^.

Table IV. Each of the three trials represents independent determinations in which the auxiliary sphere was recoated with the pressed PTFE powder for each

determination. The PTFE powder for two of the trial runs came from a drum of the powder that was the

source of supply for the round-robin experiments described earlier. A third trial run was made with PTFE

powder from a newer drum that had never been opened

before. The resulting data indicated no differences in reflectance for the PTFE powder from these two

drums.

iV. Recommended Procedures for Preparing and

Using Pressed PTFE Powder as a Reflectance

Standard

It is suggested that the following procedures and

precautions be followed to improve the reproducibility

of diffuse reflectance measurements and increase

agreement among laboratories using pressed PTFE

powder as a reflectance standard:

(1) Store the powder in sealed glass containers.

(2) Prepare the powder for use by pulverizing it into a uniform consistency in a glass blender with stainless

steel blades.

(3) Use stainless steel spoons to transfer the

powder.

(4) Press the powder into holders that have a depth

of 10 mm.

(5) Press the powder to a density of '~1 ± 0.1 g/cm^.

A l-g/cm^ density results in a firmer and less fragile

specimen than lower densities. This can be done very

conveniently with a powder press of the design shown

in Fig. 2. This press is designed with a metal cavity of

10-mm depth. The diameter of this cavity will depend

on the diameter of the sample port of the reflectometer

integrating sphere. It should be made slightly larger

than the diameter of the port. A stainless steel cylinder

of the same inside diameter as the PTFE cavity is press

fitted into a locking ring that can be locked onto this cavity with three thumbscrews. The PTFE powder is introduced into the stainless steel cylinder after it is locked onto the receiving cavity. To obtain a pressed

PTFE reflectance standard of 1 g/cm^, the volume of the

receiving cavity must be determined in cubic centimeters. The pressing operation is done with a Plexiglas

15 July 1985 / Vol. 24, No. 14 / APPLIED OPTICS 2229
plunger made for a sliding fit into the stainless steel cylinder. The plunger is designed so that when fully

inserted into the cylinder, it just reaches the plane of the

cavity opening. The plunger surface can be roughened

by sandblasting if a coarser surface on the pressed

PTFE is desired. However, this will not significantly

affect the reflectance of the specimen. The pressure

required to produce a standard of 1 g/cm^ can easily be

achieved by force of hand. A protective cover can be

provided for storing the standard. This powder press

and powder receptacle are not available commercially

but can be made easily in a small machine shop.

(6) When measuring the PTFE reflectance standard,

make sure it is pressed against the sample port of the

integrating sphere so that no gap exists between the

standard and port.

(7) Prepare fresh standards every day if necessary

to avoid using soiled or damaged reflectance stan- dards.

(8) Prepare at least three fresh standards when

making reflectance measurement in the UV and use an

average value of reflectance for these standards.

V. Remarks

The results of the round-robin experiments reported

in Tables I and II should not be used as reference data

for the absolute reflectance of pressed PTFE powder.

Even the reported averages appearing in these tables

are not considered good for reference purposes because some of the submitted specimens had significantly lower

reflectances. Refer to the 6° /hemispherical reflectance

data published in Ref. 2 for the absolute reflectance of

PTFE powder.

The following laboratories participated in the

round-robin experiments described in this paper:

Burlington Industries, Corp. Research & Development,

Greenboro, N.C.; E. I. Dupont Co., Troy, Mich.; Hunter

Associates, Reston, Va.; Macbeth Division, KoUmorgen

Corp., Newburgh, N.Y.; Munsell Color Science Laboratory, College of Graphic Arts and Photography,

Rochester Institute of Technology, Rochester, N.Y.; National Research Council of Canada, Ottawa, Canada;

Pacific Scientific, Gardner/Neotec, Silver Spring, Md.;

The Sherwin-Williams Co., Chicago, II., National Bureau of Standards, Radiometric Physics Division,

Gaithersburg, Md.

References

1. F. Grum and M. Saltzman, P-75-77 New White Standard of Reflectance, CIE Publication 36, (Paris, 1976), p. 91.

2. V. R. Weidner and J. J. Hsia, "Reflection Properties of Pressed

Polytetrafluoroethylene Powder," J. Opt. Soc. Am. 71, 856

(1981).

3. E. Schatz, "Effects of Pressure on the Reflectance of Compacted

Powders," J. Opt. Soc. Am. 56, 389 (1966).

4. W. H. Venable, J. J. Hsia, and V. R. Weidner, "Establishing a Scale of Directional-Hemispherical Reflectance Factor I: The Van den Akker Method," J. Res. Natl. Bur. Stand. 82, 29 (1977).

5. D. G. Goebel, B. P. Caldwell, and H. K. Hammond III, "Use of an

Auxiliary Sphere with a Spectroreflectometer to Obtain Absolute

Reflectance," J. Opt. Soc. Am. 56, 783 (1966).

2230 APPLIED OPTICS / Vol. 24, No. 14 / 15 July 1985
Appendix I

NIST Technical Note 1413

45""1

0"" Reflectance Factors of Pressed

Polytetrafluoroethylene (PTFE) Powder

p. Yvonne Barnes and Jack J. Hsia

Radiometric Physics Division

Physics Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-0001

July 1995

U.S. Department of Commerce

Ronald H. Brown, Secretary

Technology Administration

Mary L. Good, Under Secretary for Technology

National Institute of Standards and Technology

Arati Prabhakar, Director
National Institute of Standards U.S. Government Printing Office

and Technology Washington: 1995

Technical Note 1413

Natl. Inst. Stand. Technol.

Tech. Note 1413

23 pages (July 1995)

CODEN: NTNOEF

For sale by the Superintendent of Documents

U.S. Government Printing Office

Washington, DC 20402
Table of Contents

Abstract 1

1. Introduction 1

2. Sample Pressing Method 2

3. 45°/0° Reflectometer 3

4. Measurements 3

4.1 Operator Variability 4

4.2 Material Variability 4

4.3 45°/0° Reflectance Factor and Uncertainty 4

5. Remarks 5

6. References 5

Tables and Figures 7

Appendix A. General and advance preparation information for pressing

PTFE samples 12

Appendix B. Reprint, NBS 45%ormal reflectometer for absolute

reflectance factors 13

iii
List of Tables

1. Operator Variability : Each laboratory returned two pressed PTFE

samples; alpha-numerics indicate the laboratory (A - J) or the

sample (1 - 2). The quantity reflectance factor minus the average

for the twenty samples is shown for each sample at the

measurement wavelengths. The Type A uncertainty (k = 2) for the

20 measurements is shown in the last row 7

' 2. Material Variability : Pressed PTFE samples from four drums;

each drum was manufactured at a different time. The quantity

reflectance factor is shown for each drum at the measurement

wavelengths. The mean and Type A uncertainty (k = 2) for the

measurements of the four drums are shown in the last two

rows 8

3. 45°/0° Reflectance Factors of Pressed PTFE Powder (1 g/cm^) 9

List of Figures

1 . PTFE powder presser designed to produce a sample with spatial

uniformity in density and in appearance 10

2. 45°/0° reflectometer system (Top view) 11

iv
4570" Reflectance Factors of Pressed

Polytetrafluoroethylene (PTFE) Powder

p. Yvonne Barnes and Jack J. Hsia

Radiometric Physics Division, National Institute of Standards and Technology,

Gaithersburg, MD 20899, USA

Abstract

Pressed polytetrafluoroethylene (PTFE) powder is used for 45°/0° reflectance factor

standards. The radiometric and spectrophotometric measurement community such as the Council for Optical Radiation Measurements (CORM) has demonstrated the need

for such a standard and its application to quality control and quality assessment. This

publication briefly describes the instrumentation used for the 45°/0° reflectance factor

measurements of pressed PTFE powder from 380 nm to 770 nm. Also, the variations

of 45°/0° reflectance factor with sample preparation and materials are discussed. The

expanded uncertainty at a coverage factor of two for the 4570° reflectance factors of

pressed PTFE powder ranges from 0.009 to 0.017.

Keywords

Diffuse Reflectance, 4570° Reflectance Factor, Polytetrafluoroethylene resins. Pressed

PTFE powder, PTFE, Reflectance Factor

1. INTRODUCTION

Over the years, the Radiometric Physics Division at the National Institute of Standards

and Technology (NIST) has investigated [1,2] the reflection properties of

polytetrafluoroethylene (PTFE) resins, in a form of granular molding powder. NIST

has established the 6°/hemispherical reflectance factor scale of pressed PTFE powder

[3] and provided general preparation information on pressing PTFE powder (Appendix

A). Recently, standards organizations, government agencies, national laboratories,

optical material industries, and instrument manufacturers have expressed the need for a 45°/0° reflectance factor standard in a report on critical problems and projected

national needs in optical radiation measurement by the Council for Optical Radiation

1
Measurements [4]. Although these requirements span the ultraviolet, visible and near

infrared spectral regions, most of the requests for calibration are 45°/0° reflectance

factors in the visible wavelength region.

The reflectance factor of a sample is defined [5] as "the ratio of the radiant flux

reflected in the directions delimited by the cone to that reflected in the same directions

by a perfect reflecting diffuser identically irradiated." This cone is formed by the

receiver limiting aperture and with apex at the center of the sample surface. A perfect

reflecting diffuser is an ideal (no loss) lambertian (uniform in all directions) diffuser.

The 45°/0° reflectance factor is the reflectance factor measured at 45° incident angle

and normal viewing angle. The governing equations and the description of how the

reflectance factor is measured are given in Reference 6 and a reprint is included in

Appendix B. The reflectance factor measurement method (see app. B) using a stepdown technique and a view factor calls for the measurements of the ratio of two fluxes

and, in addition, some linear dimensions.

In order to develop the pressed PTFE powder as an intrinsic standard, studies of the

major factors that affect the measured values were performed. This publication

describes the sample pressing method and briefly described the 45°/0° reflectometer

for reflectance factor measurements of the samples from 380 nm to 770 nm. Also, the

variations of 45°/0° reflectance factor with sample preparation and materials are discussed. Finally, a table is presented for 45°/0° reflectance factors and their

associated uncertainties of pressed PTFE powder from 380 nm to 770 nm at every

10 nm.

2. SAMPLE PRESSING METHOD

This section describes the method used to prepare a diffuse PTFE sample that is uniform in both appearance and density (approximately 1 g/cm^). After practice and

familiarity with the presser (see fig. 1) [7], a sample can be made quickly, frequently,

and with consistent results. For the best results and ease of processing, 25 g of

PTFE powder is placed in a blender with sharp blades. The PTFE powder is pulverized until it appears light, airy and powder-like.

Referring to Figure 1, the diameter of the poly(methyl methacrylat) plunger is 51 mm;

the height of the funnel is 75 mm; and the receptacle is 10 mm in depth. The end area of the plunger is pre-treated by pressing it on some amount of PTFE powder to reduce

the influence of hydrocarbons in the plunger material. The following steps are followed to press a sample: 1) the funnel and the receptacle are assembled; 2) 25 g of

pulverized PTFE powder is scooped into the funnel; 3) the pre-treated plunger is inserted into the funnel and manually pressed downward until it stops; 4) the plunger

is withdrawn slowly to overcome the suction created by the close fit of the funnel and

the plunger; 5) the receptacle is separated from the funnel by loosening the set screws;

6) the pressed sample is then imprinted with a sheet of pre-treated sandpaper by hand

with minimum pressure. Some general information on PTFE powder and preparation

2
is provided in Appendix A. The safety aspects in handling and use of PTFE powder

are listed in Reference 8.

3. 4570° REFLECTOMETER

The overall instrument consists of a source system and a 4570° reflectometer [6,9,10].

The source system consists of a tungsten ribbon-filament lamp, mirrors, polarizer,

predisperser, monochromator, and other mirrors. The source system provides a nearly

coUimated, polarized output with 10 nm band pass. The configuration of the 4570°

reflectometer is shown in figure 2. Details of the receiver system are shown in

figure 2 of Appendix B.

Referring to figure 2a in Appendix B, the incident beam illuminates at 45° from the

sample normal an area 21 mm by 21 mm at the center of the sample (S). Due to the

change of the optical arrangement of the source system after the publication of the

paper in Appendix B, the larger light beam still provides a 10 nm band pass. The

receiver system views the entire sample at 0° from the sample normal. In figure 2b of

Appendix B, two 15 cm diameter averaging spheres (AS) are mounted together

vertically and the photomultiplier (D) is attached to the upper sphere. A precision

circular limiting aperture (LA) on the lower sphere subtends a half angle of 2.8° from

the center of the sample. This double-averaging sphere detection arrangement

provides a uniform receiver system for both of the required measurement geometries: a small light beam reflected from a specular black glass plate and a larger diffusely

reflected light beam from a diffuse sample.

4. MEASUREMENTS

Due to the low signal levels associated with this type of bidirectional reflectance

factor measurement, a step-down technique is used to reduce the required dynamic

range for measurements and to reduce measurement uncertainty. A specular black

glass plate with a regular (specular) reflectance value of about 0.04 is employed. The

22.5°/22.5° regular reflectance of the black glass is measured, using a specular

reflectometer [11], with light polarized parallel and perpendicular to the plane of

incidence at each wavelength. The flux of the pressed PTFE sample is then measured

relative to the flux of the black glass plate with the 45°/0° reflectometer for each

polarization state. This relative value of the pressed PTFE sample, the specular

reflectance of the black glass plate and the projected solid angle of the receiver

limiting aperture are used to calculate the 45°/0° reflectance factor according to Eq

(9) in Appendix B.

The 45°/0° reflectance factors of pressed PTFE powder were performed on ten freshly

pressed samples. These samples were prepared by one operator, taken from one batch

of PTFE powder, and measured over the visible spectral range. The standard

deviation for these measurements for a coverage factor (k) of 2 was less than 0.001

3
indicating a good repeatability. There was no spectral dependence. The Type B

uncertainty [12] for k = 2 was 0.0027 for the visible spectral region [6]. The

contributors to Type B uncertainty were receiver system non-linearity and nonuniformity, scattered flux, and angular setting and view factor uncertainties.

4.1 Operator Variability

A study was conducted to investigate variability in the results when ten different

laboratories prepared samples. Each laboratory received an instruction sheet, a

presser, a container with pulverized PTFE powder, and a pre-labeled box with packing

material to return the pressed PTFE samples to NIST. Each laboratory pressed two

samples with the proper amount of PTFE powder needed to prepare a sample of

1 g/cm^ in density, 51 mm in diameter and 10 mm in thickness. No measurements

were required from the laboratories and all twenty samples were returned to NIST for

measurements. Results of this study are reported in Table 1, which shows the

difference of the reflectance factor for each sample from the mean value of 20 samples

at each of the five wavelengths. The Type A uncertainty (k = 2) of these differences

for the 20 samples range from 0.006 to 0.012 in the wavelength region from 380 nm to 770 nm.

4.2 Material Variability

The variability in the results due to the composition of the PTFE powder was studied

by making samples from four different drums of PTFE powder. The Ausimont', type

G-80 and type Algoflon F5 PTFE powder were used in this investigation. Each of

these powders was produced at a different time with different lot numbers. The

samples were made as described above and measured at seven wavelengths. The

quantity reflectance factor for each drum at the measurement wavelengths is shown in

Table 2. The Type A uncertainties (k = 2) for measurements of four drums range

from 0.013 to 0.001 for the wavelength range from 380 nm to 770 nm.

4.3 45°/0° Reflectance factor and uncertainty

The 45°/0° reflectance factors of pressed PTFE powder of samples from four drums in

Table 2 were averaged at each of the seven wavelengths and these values were

' Certain commercial instrument or materials are identified in this paper in order to specify adequately the procedure. In no case does such identification imply

endorsement or evaluation by the National Institute of Standards and Technology.

4
interpolated by spline fit for other wavelengths. These values are reported in Table 3

together with the expanded uncertainties for a coverage factor of 2. These

uncertainties include the type B uncertainty, statistical measurement uncertainty,

operator to operator variations, and material to material variations. The standard

deviations (k = 2) range from 0.017 to 0.009 for wavelengths from 380 nm to 770 nm.

5. REMARKS

The results of this investigation show that the expanded uncertainties of the 4570°

reflectance factors of pressed PTFE powder mainly due to two factors, one is the

material variability which is larger at the shorter wavelengths and the other is the

operator variability. Furthermore, these expanded uncertainties are about twice those

of the 6°/hemi spherical reflectance measurements [2].

The following laboratories participated in the PTFE powder pressing study described

in this publication: Biospherical Instruments, San Diego, CA; Byk-Gardner, Silver

Spring, MD; Datacolor, Lawrenceville, NJ; Hughes, Danbury, CT; Hunter Lab,

Reston, VA; Jet Propulsion Laboratory, Pasadena, CA; Labsphere, North Sutton,

NH; Miles Lab, Elkart, IN; Munsell Color Science Laboratory, Rochester Institute of

Technology, Rochester, NY; University of Arizona, Tuscon, AZ.

Both the 45°/0° reflectometer and the specular reflectometer used in this investigation

were replaced in 1995 by a new Spectral Tri-function Automated Reference

Reflectometer (STARR) incorporating new detectors and electronics. Preliminary

intercomparisons between the old and new instruments on 4570° reflectance factor

show measurements agreeing to within 0.002.

6. REFERENCES

[1] V. R. Weidner and J. .J. Hsia, J. Opt. Soc. Am., 71, 856 (1981).

[2] V. R. Weidner, J. J. Hsia and B. Adams, Appl. Opt., 24, 2225 (1985).

[3] F. E Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg and

T. Limperis, NBS Monograph No. 160 (1977) p. 9.

[4] Council for Optical Radiation Measurements: CORM Fifth Report on Pressing

Problems and Projected National Needs in Optical Radiation Measurements (1989).

[5] Commission International de I'eclairage: International Lighting Vocabulary, CEE

Publ.No. 17.4 (1987).

[6] J. J. Hsia and V. R. Weidner, Metrologia, 17, 97 (1981). (A reprint is attached as Appendix B.)

5
[7] American Society for Testing and Materials: Standard Practice E259-93, ASTM

Annual Book of ASTM Standards 06.01 (1994) p. 709

[8] E.I. Du Pont De Nemours and Company, Inc., Fluorocarbons Division,

Teflon Fluorocarbon Resins - Safety in Handling and Use (1970)

[9] W. H. Venable, Jr., J. J. Hsia and V. R. Weidner, NBS Tech. Note 594-1 1 (1976).

[10] V. R. Weidner and J. .J. Hsia, NBS SP 250-8 (1987).

[11] V. R. Weidner and J. .J. Hsia, Appl. Opt., 19, 1268 (1980).

[12] B. B. Taylor and C. E. Kuyatt, NIST Tech. Note 1297 (1994) p. 2.

6
Table 1. Operator Variability : Each laboratory returned two pressed PTFE

samples; alpha-numerics indicate the laboratory (A - J) or the sample (1 - 2). The

quantity reflectance factor minus the average for the twenty samples is shown for each

sample at the measurement wavelengths. The Type A uncertainty (k = 2) for the 20

measurements is shown in the last row.

Wavelength [nm]

380 450 600 700 770

Al 0.002 0.004 0.002 0.003 0.004

A2 0.004 0.006 0.003 0.001 0.003

Bl -0.001 0.001 0.000 0.000 -0.007

B2 -0.005 0.000 -0.001 0.000 -0.001

CI 0.009 0.006 0.004 0.004 0.005

-0 005 -0 005 -0 004 -0 006 -0 005

Dl 0.001 0.002 0.001 0.001 0.002

D2 0.007 0.004 0.003 0.002 0.002

El -0.003 0.002 0.002 0.003 0.004

E2 -0.004 -0.004 -0.005 -0.006 -0.006

Fl 0.000 -0.011 -0.004 0.008 0.004

F2 -0.001 0.000 0.001 0.001 0.001

Gl -0.002 -0.004 -0.004 -0.004 -0.005

G2 0.009 0.005 0.002 0.002 0.004

HI -0.012 -0.006 -0.006 -0.008 -0.007

H2 0.010 0.001 0.000 0.001 0.002

11 -0.003 0.000 0.002 -0.001 0.000

12 0.006 -0.002 0.002 0.002 0.005

Jl -0.010 -0.007 -0.005 -0.007 -0.004

J2 0.003 0.007 0.006 0.008 0.006

std dev 0.012 0.010 0.006 0.008 0.008

(k = 2)

7
Table 2. Material Variability : Pressed PTFE samples from four drums, each drum

was manufactured at a different time. The quantity reflectance factor is shown for each

drum at the measurement wavelengths. The mean and Type A uncertainty (k = 2) for the

measurements of the four drums are shown in the last two rows.

Wavelength [nm]

Drum 380 420 470 550 630 700 770

1 1.005 1.008 1.011 1.013 1.012 1.013 1.016

2 1.001 1.006 1.009 1.011 1.012 1.012 1.017

3 0.993 0.999 1.003 1.007 1.010 1.011 1.016

4 1.007 1.010 1.011 1.012 1.013 1.013 1.017

mean 1.002 1.006 1.009 1.011 1.012 1.012 1.017

stddev 0.013 0.010 0.008 0.005 0.002 0.002 0.001

(k=2)

8
Table 3. 45°/0° Reflectance Factors of Pressed PTFE Powder (1 g/cm^)

wavGiGngin nGllGCianCG uncGriainiy

fnml Factor k = 2

380 1.002 0.017

390 1.003 0.017

400 1.005 0.016

410 1.006 0.016

420 1.006 0.015

430 1.007 0.015

440 1.007 0.015

450 1.008 0.014

460 1.008 0.014

470 1.009 0.014

480 1.009 0.014

490 1.009 0.013

500 1.010 0.013

510 1.010 0.012

520 1.010 0.012

530 1.010 0.011

540 1.011 0.011

550 1.011 0.011

560 1.011 0.011

570 1.011 0.010

580 1.011 0.010

590 1.011 0.010

600 1.011 0.010

610 1.011 0.009

620 1.012 0.009

630 1.012 0.009

640 1.012 0.009

650 1.012 0.010

660 1.012 0.010

670 1.012 0.010

680 1.012 0.011

690 1.012 0.011

700 1.012 0.011

710 1.013 0.011

720 1.014 0.011

730 1.015 0.011

740 1.015 0.011

750 1.016 0.011

760 1.016 0.011

770 1.017 0.011

* The total uncertainty consists of the instrument uncertainty, material and operator variations.

9
PLUNGER

FUNNEL

POWDER

RECEPTACLE

Figure 1 . PTFE powder presser designed to produce a sample with spatial

uniformity in density and in appearance.

10
Figure 2. 45*/0" Reflectometer System

(Top View)

11
APPENDIX A. General and Advance Preparation Information for

Pressing PTFE Samples

a. PTFE presser: Since there are no commercially available PTFE pressers that

met our specifications, a simple PTFE presser was designed and fabricated at NIST (Refer to fig. 1 ). The presser consists of three parts: a plunger that was

constructed of poly(methyl methacrylate), a funnel of sufficient size to hold

bulk PTFE powder before pressing, a receptacle designed to fit into the

specimen holder of the 45°/0° reflectometer. This plunger was preconditioned

by pressing against clean PTFE powder.

b. Commercial blender: PTFE powder naturally clumps together as aggregates.

An Osterizer [13] blender was used to pulverize PTFE powder into a flufty

powder-like appearance. This type of commercial blender was chosen because

it could be attached to glass jars and the blades could be sharpened in the

machine shop.

c. Alternative devices: A stainless sifter or a flour sifter may be used instead of a commercial blender.

d. Static charge: PTFE powder acquires an electro-static charge throughout the

pulverization process and will coat the glass blending jar and blades.

e. Utensils: Only stainless steel, glass, and porcelain materials or containers

should be used to handle PTFE powder. The ultra-violet spectral reflectance

factors of a pressed PTFE sample are affected by the hydrocarbons in plastic

materials.

f. Containers of PTFE powder: PTFE powder is usually shipped by the

manufacturer in drums of either 20 kg or 45.5 kg. The powder is packed in a

plastic bag. Only the PTFE in the center portion of the drum is used, thus

avoiding the powder that came in contact with the plastic bag.

g. Preconditioned sandpaper: A sheet of 1 50 grit size sandpaper was rubbed with

a piece of sintered ( in an electric furnace at 370 °C for 1 hour) PTFE, and

shaken repeatedly so that the loose particles would fall off and not be

embedded to the surface of the sample.

h. Ceramic tile: Use a ceramic tile or a similar type of object to evenly distribute

the applied force over the preconditioned sandpaper on the sample area.

12
i. Laboratory conditions: PTFE powder is contaminated by airborne particles

and smoke due to the electro-static charge (see sec. d above).

j. Safety: Obtain a Material Safety Data (MSD) sheet from the manufacturer of

PTFE powder. Safety precautions and safety issues are the sole responsibility

of users.

k. PTFE sample: A pressed sample of PTFE is durable and will not fall out of the

receptacle. A sample may be positioned vertically, and if necessary it may also

be inverted and tapped lightly so that the loose particles would fall off.

1. Cleaning. A clean camel-hair brush can be used to remove pieces of lint on the

sample surface.

APPENDIX B. Reprint, NBS 45°/Normal Reflectometer for Absolute

Reflectance Factors

(see next six pages)

13

Metrologia 17, 97-102 (1981)

metrologia

© by Springer Verlag 1981

NBS 45°/Normal Reflectometer for Absolute Reflectance Factors

Jack J. Hsia and Victor R. Weidner

National Bureau of Standards, Washington, DC 20234, USA

Received: March 25, 1981

Abstract

A 45°/nonnal reflectometer has been constructed and

tested for calibrating the absolute reflectance factor of

diffuse samples over the 380—770 nm spectral range

using polarized radiation. The measurement equations

have been derived for the method used. The method

using a step-down technique and view factor calls for the measurements of the ratio of two fluxes and, in addition, some linear dimensions. The uniformity of the

receiver system is achieved by means of a double-sphere

signal averager. Uncertainties of the absolute-reflectancefactor measurements obtained with this system are estimated to be ±0.3% of the measured value. For all the samples that have been tested, the 45°/normal re- flectance factor was found to be higher than the 6°/hemispherical reflectance factor. The higher reflect- ance values for 45°/normal geometry were confirmed by

additional gpnioreflectometer measurements.

1. Introduction

Measurements of the diffuse reflecting characteristics of materials are of basic importance in radiometry,

photometry and colorimetry as well as many other

fields of science, technology and industry.

The International Commission on Illumination

(Commission Internationale de TEclairage - CIE) re- commended that starting in 1969, in colorimetric measurements of opaque materials, the perfect diffuser was to be taken as the primary reference standard. There

is no existing material having diffuse reflection properties corresponding to the perfect diffuser with sufficient approximation. Therefore, the characteristics of all physical standards actually employed in comparison measurements must be established by techniques

through which their absolute reflectance factors can be determined. The measurements involve not only the determination of the ratio of radiometric quantities but

also the determination of linear dimensions.

The four geometries recommended by the CIE are 45°/normal, normal/45°, diffuse/normal, and normal/

diffuse. The method and instrumentation to realize the NBS scale of directional-hemispherical reflectance

factor has been described in [ 1 ]. For the 45°/normal and normal/45° reflectance

factor measurements, there exists a large ratio of the incident flux to the reflected flux contained in a small

solid angle. Various step-down techniques have been

used by several National Laboratories [2—8] to insure

sufficient accuracy over this wide dynamic range. The purpose of this paper is to describe the method

and the instrumentation used to establish the NBS scale of absolute reflectance factor in the 45°/normal geo- metry.

2. Measurement Equations

An absolute reflectance factor is defined [9, 10] as the

ratio of the radiant flux reflected in the directions bounded by a given cone with the apex at a point of the

surface under test to that reflected in the same directions by a perfect reflecting diffuser identically irradiated. The term "perfect reflecting diffuser" means the ideal

(lossless) lambertian (uniform in all directions) diffuser.

If the solid angle of the cone approaches zero, or 2n

steradians, the reflectance factor approaches radiance

factor or reflectance, respectively.

The reflectance factor of sample x, R^, can be ex- pressed as

f^LiU,A)S^iUM,^)riu,X) U-dA dni/ dadcj dX

" ~

f^L(U,X) K«,a) U dA dn u-da du>dk (1)

where L is the incident radiance; 5^ and 5,^ are the

scattering functions of the sample and of the ideal sur- face, r is the relative responsivity of the receiver; U and u are the direction vectors of travel of the incident and

emergent radiation; dn and dcj are elements of solid angle oriented in the direction U and u; dA and da are elements of area through which the energy passes on to the sample and emerges from the sample ; d A is the ele- ment of wavelength; and the symbol /" indicates inte0026-1394/81/0017/0097/$01.20
gration with respect to n variables. In general, the nomenclature (especially the symbols) used here is that of reference [11]. There it is more completely defined

and discussed.

If there is no interaction between the wavelength

dependence and the geometrical dependence of the incident radiance and of the responsivity, the functions

are separable. For any source function CXA) and

luminous efficiency function V{X), Eq. (1) can be

written as

m)vi^) (2)

[f^L(Lf) S^iUji,^) K«) U-dA dn u da doj] dX

[S^^f^LiU) r(u) U-dA dfi u da doj] dx

^

/CTa) VjX) R^(A) dA

^

la^) ViX) dX (3)

The spectral reflectance factor R^{X) is expressed as

f^'LiU) 5x(t/^,X) K") U-dA dn u da doj (4)

S^JL{U) liu) U-dA dQ. u da dw

For a receiver system with uniform responsivity

within the cone, , r{u) = r within cj and tip) /c\ = 0 outside of cj. The scattering function of a perfect diffuser could be

written as S-^=b{P-p)lTr (6)

where P and p are position vectors on the testing surface

for incident space and the emergent space, respectively.

Thus (4) can be expressed as

It ^JX) (7)

cjp *j(A)

where cOp = u-dfl dcj is the projected soUd angle of

the cone onto the surface to be measured.

4>x = L{U) S^{Up,X) U'dA dHu-dfldcj is the reflect- ed radiant flux for the sample that enters the Umiting re- ceiver aperture, and

<t)j = L{U) 8{P ~ p) U-dA dn is the incident radiant

flux.In radiation heat transfer [12, 13], cj^/tt (or fi-2) is named the view factor (alternatively designated as the form factor, configuration factor, geometrical factor, or

angle factor) representing the fraction of the radiant flux leaving a diffuse surface that is entering the limiting

aperture. In other words, fi-2 is the fraction of the in- cident flux reflected from (1) a perfect diffuser that is entering the (2) limiting aperture. The spectral reflect- ance factor can now be expressed as

IC(A)=

' (8)

Equation (8) clearly indicates that the reflectance fac- tor is the ratio of the reflected flux (into the limiting

aperture) to that of a perfect diffuser. If another sample

S with known reflectance is used to step down' the in- cident flux, the reflectance factor of sample x can be

calculated as

1

fi- *x(^)*i(I)-^s

(9)

where 4>3 and are the flux and the reflectance of the step-down sample S, respectively. The view factor will be expressed in detail below. For a circular limiting aperture (diameter D) which

is parallel to the sample surface at a distance d, and for A<4 1

, a small portion of the illuminated area, and the

distance between a point in AA 1 and the central normal

(on the sample surface) to the circular area of the

limiting aperture being c, (see Fig. 1) the view factor can be expressed [14] as: fA^i-^2 = ll-J/K]/2,

where J = 1 + - K= [G''+2G^(1-B^) + (l+B^)^]''^

B=DI2d

G = cjd

(10)

COA2

AAl

Fig. 1. Schematic for view factor (Eq. 10) Determination

When the illuminated area is very small and is at the

central normal to the circular area of the limiting aperture, the view factor becomes

ft-2=fA^,-^2=[l+4^/V/)']-' (11)

and when the illuminated area is finite, the view factor is

or f,-2 =

A/II

A2

if A/1 1 is selected to be sufficiently small.

(12)

(13)

' Procedure described in Sect. 5

98
3. NBS Reference Spectrophotometer

The 45°/normaI reflectometer is an accessory to the NBS reference spectrophotometer for reflectance [15].

The light source, monochromator, electronics and other

associated equipment are located in a system control room. The exit slit housing of the monochromator is attached to a light-tight diaphragm in a wall, which

allows the exit light beam or sample beam to enter a second room where the various reflectance-measuring

devices, such as the specular reflectometer or the 45°/

normal reflectometer, are installed. The advantages of

this arrangement are that the second room can be used

as an experimental dark chamber, while the light source,

electronics and control systems are isolated from the experimental area. The sample beam emerging from the

exit slit of the monochromator can be controlled to provide a spectral bandpass of 2, 5, 10, or 20 nm. For a 10-nm bandpass, the light beam has a cross section 10 by

18 mm at the sample position.

To measure spectral reflectance factor over the

visible wavelength range of the monochromator, the system employs a tungsten strip lamp and a photomultiplier detector. A complete description of the spectrophotometer is given in an earlier publication [15]. Data have been pubUshed [16, 1 7] on the large effect of polarization on the reflectance factor. Therefore, the NBS design includes a polarization-insensitive receiver system and the measurements are made with polarized

incident light. The final result is the average of measure- ments made with light polarized perpendicular and

parallel to the plane of incidence.

4. 45°/Normal Reflectometer

The light beam from the source system is incident on a sample at 45° from normal and the reflected flux at nor- mal to the sample is collected and measured. The sche- matic of the instrument is shown in Fig. 2. The 45°/normal rather than the normal/45° geometry was chosen,

because the distance between the limiting aperture and

Fig. 2 a and b. Schematic of the 45 /normal Reflectometer. a Top view with top sphere not shown, for clari- ty. S: Sample, LA: Limiting Aperture, DA: Detector

assembly, SA: Aperture between spheres; b Front view

of the two-sphere Receiver Assembly, AS: Averaging

Sphere, SH: Shutter, D: Detector, LA: Limiting

Aperture, SA: Aperture between spheres

the sample surface and, in tum, the view factor could

be determined more accurately. Because the step-down technique with a polished black glass is used to obtain the absolute reflectance fac- tors of a diffuse sample, the instrument should be able

to measure accurately both the specularly and the

diffusely reflected light beams. This requires that the re- sponsivity of the receiver system be uniform over its aperture area. To fulfill the above requirement, the photomultiplier is equipped with a double-sphere signal averager. The spheres are approximately 1 5 cm in diameter. The

sphere coating is a fluorocarbon powder, which is a nearly perfect diffuser of very high reflectivity. The two

spheres are mounted together vertically and are designed

to allow the inside curvature of the sphere coating to meet at the center of the port between the two spheres.

The photomultiplier is mounted horizontally on the upper sphere. The spheres are attached to a stepping- motor-controlled vertical sUde for alignment and scanning purposes. The lower sphere has a circular limiting

aperture facing the sample. To prevent scattered radia- tion, other than that directly from the sample, reaching

the limiting aperture, no component is placed between

the surfaces of the sample and the limiting aperture. A

black felt is placed on the top surface of the rotation arm to further reduce scattered radiation. The sample holder, which can hold two samples, is mounted on a two-position slide that moves 12.5 cm be- tween positions and is pneumatically driven. The slide

is mounted on a stepping-motor-controlled turntable. The detector assembly is on an arm attached to another

independently-controlled tumtable having the same axis of rotation as that of the sample tumtable.

The signal processing of the output from the photomultiplier utilizes a current-to-frequency converter that can integrate the detector output over a selected time

interval, and a digital counter. The digital data from the counter are transferred to a computer for analysis.

5. Measurement Procedure

Before a measurement is performed, the instrument is

first aligned. The sample holder can be adjusted normal

to the incident Light beam with the aid of a flat mirror

in the sample position. The sample holder is then turned

22.5° from the normal position toward the limiting

aperture. The limiting aperture is adjusted to center on

the reflected light beam which is 45 from the incident

light beam. A thin mirror, with the reflecting surface

facing the limiting aperture, is held against the limiting

aperture. The limiting aperture is aligned so that the

light is reflected back to the exit slit of the monochromator. Thus the limiting aperture is aligned normal to the reflected Ught beam 45° from the incident beam.

The diameters of the limiting aperture were meas- ured at eight places by using a shadow profile projector before the aperture was mounted on the lower sphere.

The circularity has been checked by a deviation plotter.

The average diameter is 38.238 mm. The distance be99
tween the surfaces of the limiting aperture and the sample is determined when the sample holder is turned

45° from the normal position. A thin glass plate is placed over the limiting aperture. The distance between

this glass plate and a flat surface at the sample position

is measured with an inside micrometer. The thickness of

the glass plate is added to the micrometer measurement

to give the total distance which in this case is 381.89 mm. The view factor can thus be calculated using (10)

and (13).

The spectral 22.5° specular reflectances of a piece

of polished black glass are first determined with the specular reflectometer [18] with light polarized per- pendicular and parallel to the plane of incidence. This

piece of black glass is then used to step down the in- cident flux to determine the 45°/0° reflectance factors of a sample. The flux of the sample in 45°/0° geometry

is compared to the flux of the black glass in the 22.5°/ 22.5° geometry. The reflectance factor of the sample

can thus be calculated using (9). The measurements are performed with polarized light, and the final result is the average of measurements made with light polarized

perpendicular and parallel to the plane of incidence.

6. Performance

It is beyond the intent of this paper to describe in detail the various checks that were made on the performance

of the monochromator, other components of the spectrophotometer, and the reflectometer, except to mention briefly the magnitudes of errors associated with

this portion of the system, since they do influence the accuracy of measurements of reflectance factor. Infor- mation regarding some of these investigations is presented in [15]. Wavelength scale uncertainties, receiver linearity, receiver uniformity, scattered radiation, angular setting

uncertainty, and view factor uncertainty are involved

in checking the performance of the instrument.

The wavelength scale of the monochromator was

checked by measuring the emission lines [18] of several line-source lamps and the instrument function, then

determining the centroid wavelengths. Uncertainty in the wavelength scale is 1 nm or less for a 10 nm bandpass. Corrections for these errors are made by adjustment of the wavelength-scale setting to compensate for differences between the wavelength counter and the

true wavelength.

The linearity of the receiver system was measured by

the light addition method with a double aperture apparatus [20, 21]. The results indicate the receiver system is linear to better than ±0.1% and the nonlinearity is corrected for measured data. Even though the receiver system utiUzes double

spheres as an averager device, there is still a slight nonuniformity causing 0.05% uncertainty in comparing the

fluxes of specularly and diffusely reflected beams.

Radiation scattered off the components between

the exit slit of the monochromator and the limiting

aperture of the receiver system causes errors in a

reflectometer. The room containing the reflectometer

is lined with a black felt material to absorb scattered

radiation. All mechanical components, including the sample holder and the limiting aperture, are black

anodized to reduce the scattered radiation. Some

interreflections between the limiting aperture and the sample and between the sphere coating and the sample

are unavoidable. The scattered radiation caused by the

interreflection is determined to be less than 0.05% of

the reflected radiation. The 0.05° uncertainty of the angular setting of the sample holder contributes to 0.1 5% uncertainty in deter- mining the ratio of the reflected fluxes of the sample

and the piece of black glass. The uncertainties in determining the diameter of

the limiting aperture, the distance between the sample

surface and the limiting aperture, and the dimensions of

the light image size on the sample surface result in an

uncertainty of about 0.05% for the view factor. An analysis of the various sources of error that may

affect the accuracy of reflectance factor measurements

on the NBS 45°/normal reflectometer indicates that the

final uncertainty in these measurements will be of the order of ±0.3% of the measured value.

7. Ratio of R(4S°/Normal) TO R(6°/Hemispherical)

with Specular Component Excluded

The hemispherical reflectance factor R(0°/h) of a diffuser for normally incident light can be calculated from

the angular variations of reflectance factors R(0 Id)

using the following expression:

jr/2

R(07h)= ^

/ R(O°/0) cose sine 2nde

(14)

/ cose sine lirde

0

Divided by R(0°/45°), Eq. (14) can be written as:

R(0°/h) = 2 f sinfl cos^de (15)

R(0°/45°) i R(0°/45°)

In terms of measurable quantities, (15) can be rewritten

as:

n/2

where

§^^0^=2 / B(O°/9)sinecos0d0 (16)

R(0 /45 ) ^

B(O°/0) = ^0°/g)/cosg

<K0°/45°)/cos45'

(17)

with ^ as the reflected flux from the sample.

The two working standards, vitrolite glass and porcelain enamel plate, one pressed BaS04 sample, and one

pressed fluorocarbon sample were measured on the gonioreflectometer at 550 nm with 10 nm bandpass.

The incident angle was 0° and the angles of viewing were from 5° to 85 at 10° intervals. Measurements were

100
made with light polarized parallel and perpendicular to

the plane of incidence. B(0°/d)'s were calculated for each polarization and the averages obtained.

Average B(O°/0)'s at the discrete intervals were fitt- ed by the least-squares method. Individual data did not

deviate from the fitted curve by more than ±0.001 and

were typically within 0.0005 of the fitted curve. The

curve fittings were done by using a six-parameter equation:

5 B(0»= Z (18)

i = 0

Inserting (18) into (16), we have

R(0°/h) _

R(0°/45°)

where

li=/o^^0* sine cose d0 (20)

The values [1] of the integrals Ij are (from i = 0 to 5): 0.50000, 0.39270, 0.36685, 0.37990, 0.42147, and

0.49129. With the values of Ij and bj, R(0°/h)/R(0°/

45°) can be predicted using (19).

Six deg.-hemispherical reflectance factors, R(6°/h),

with specular component excluded and 45°/normal re- flectance factors, R(45°/0°), were also measured for the four samples. R(6°/h) will not be different significantly

from R(0°/h), and R(45°/0°) is equal to R(0°/45°)

according to the Helmholtz reciprocity principle.

The measured values of R(45°/0°), R(6°/h) and the

ratio of the measured values and integrated ratios are given in Table 1 . The measured and integrated values of

the ratios agree to 0.005. These ratios are consistent with references [4, 22, 23] in that the values of 45°/

normal reflectance factors are higher than the values of

the 6°/h reflectance factors. And in the cases of vitrolite and enamel samples the ratios are about four percent

higher than unity.

Table 1. Comparison of R(45°/0°) and R(6°/h)* (at 550 nm)

Measured Value R(45°/0°)/R(6°/h)

Sample R(45°/0°) R(6°/h)* (b)/(a) Integrated**

(b) (a)

BaS04 0.987 0.982 1.005 1.002 Fluorocarbon 1.009 0.994 1.015 1.01 1 Vitrolite 0.922 0.884 1.043 1.044 Enamel 0.875 0.839 1.043 1.040

Specular component excluded

** Integration using normalized gonioreflectance data

8. Summary

A 45°/normal reflectometer spectrophotometer was constructed for calibrating the absolute reflectance factor of

diffuse samples over the 380-770 nm spectral range. The measurement equations were derived and the measurements were made as a function of wavelength with

a polarized light beam. The system performance was examined for such parameters as wavelength scale uncertainties, receiver system linearity and uniformity,

scattered radiation, angular setting and view factor uncertainties. Uncertainty in the measurements of reflect- ance factor will be of the order of ±0.3% of the measured value. Measured ratios of the 45°/normal re- flectance factor to the hemispherical reflectance factor with specular component excluded were found to be

greater than one for all the samples that have been test- ed. The higher reflectance values for 45°/normal geo- metry were confirmed by additional gonioreflectometer measurements.

References

1. W.H. Venable Jr, J.J. Hsia, V.R. Weidner: Establishing a scale of directional-hemispherical reflectance

factor. I: The Van den Akker method. National Bureau of Standards (US). J. Res. 82, 29-55 (1977)

2. J.S. Preston, G.W. Gordon-Smith: A new determination of the luminance factor of magnesium oxide.

Proc. Phys. Soc. B65, 76-80 (1952)

3. F.J.J. Clark, G.E.V. Lambert, J.M.B. Sparrock, F.A.

Gargorth: Research on absolute reflectance standards at the National Physical Laboratory. Proc. Symp, Color Measur. Ind. 25-40, 1967 (The Color

Group, London)

4. F.J.J. Clark, F.A. Garforth, D. Parry: Goniophotometric and polarization properties of the common

white reflection standards. Nat. Phys. Lab. Rep.

MOM 26 (1977)

5. W. Erb: Bestimmung des spektralen LeuchtdichteKoeffizienten fiir die Messgeometrie 45 /Normal.

Die Farbe 20, 1 79- 186 (1971)

6. L. Morren: Mesure absolute des facteurs de lumi- nance et de reflection. LUX No. 45, 448-453

(1967)

7. V.E. Kartahevskaya, S.P. Skachkova: New method

of the luminance factors and total reflectances for the standard plates of the Institute of Metrology.

Svetsteknika 1, 16-19 (1966); also available as translation NRC TT-1 265

8. Commission Internationale de I'^clairage: Absolute

methods for reflection measurements. CIE Publication Nos. 44 and 46 ( 1 979)

9. Commission Internationale de I'dclairage: Colori- metry, official CIE recommendations. CIE Publication No 15 (1971)

10. F.E. Nicodemus, J.C. Richmond, J.J. Hsia, J.W.

Ginsberg, T. Limperis: Geometrical considerations

and nomenclature for reflectance. Nat. Bur. Stand. (US). Monogr. 160(1977)

11. W.H. Venable, Jr, J.J. Hsia: Describing spectrophotometric measurements. Nat. Bur. Stand. (US).

Tech. Note 594-9 (1976)

101
12. E.M. Sparrow, R.D. Cess: Radiation heat transfer (augmented edition) p. 121. New York: McGrawHill Book Company, 1978

13. F.E. Nicodemus (ed.): Self-study manual on optical radiation measurements: Part I — Concepts,

Chap. 4 and 5 p. 97. Nat. Bur. Stand. (US). Tech.

Note 910-2 (1978)

14. M. Jakob: Heat transfer. Vol. II p. 11. New York:

John Wiley and Sons Inc., 1 957

15. W.H. Venable, Jr, J.J. Hsia, V.R. Weidner: Development of an NBS reference spectrophotometer for diffuse transmittance and reflectance. Nat. Bur. Stand. (US). Tech. Note 594-1 1 (1976)

16. A.R. Robertson: Effect of polarization on reflect- ance factor measurements. Appl. Opt. 11, 1936-

1941 (1972)

17. D.C. Cramer, M.E. Bair: Some polarization characteristics of magnesium oxide and other diffuse re- flectors. Appl. Opt. 8, 1597-1605 (1969)

18. V.R. Weidner, J.J. Hsia: NBS specular reflecto- meter-spectrophotometer. AppL Opt. 19, 1268—

1273(1980)

19. C.E. Hodgman (ed.): Handbook of Chemistry and

Physics, 44th. edn, pp. 2892, 293 1

, 2961

.

The Chemical Rubber Publishing Co. 1962-1963

20. K.D. Mielenz, K.L. Eckerie: Design, construction,

and testing of a new high accuracy spectrophotometer. Nat. Bur. Stand. (US). Tech. Note 729 (1972)

21. K.D. Mielenz, K.L. Eckerie: Spectrophotometer

linearity testing using the double-aperture method.

Appl. Opt. 11 2294(1972)

22. V.E. Kartachevskaya, H. Korte, A.R. Robertson:

International comparison of measurements of luminance factor and reflectance of white diffusing

samples. Appl. Opt. 14, 2694-2702(1975)

23. A.R. Robertson, W.D. Wright: International comparison of working standards for colorimetry. J. Opt.

Soc. Am. 55, 694-706 (1965)

102
Appendix J

Journal of Research of the National Bureau of Standards

A Wavelength Standard for the Near

Infrared Based on the Reflectance

OfRare-Earth Oxides

Volume 91 Number 5 September-October 1986

Victor R. Weidner,

Patricia Y. Barnes, and

Kenneth L. Eckerle

National Bureau of Standards

Gaithersburg, MD 20899

This work describes the techniques used

to prepare and analyze a reflectance wavelength standard composed of three

rare-earth oxides. A mixture of dyspro- sium oxide (DyjOi), erbium oxide

(Er.jOi), and holmium oxide (HoiOi)

provides a pressed powder specimen ex- hibiting a near infrared reflectance spec- trum characterized by many discrete absorption minima in the wavelength

range 700 to 2000 nm. The object of

this activity was to develop a wavelength standard for improving the accuracy of reflectance measurements in the near infrared. The reflectance minima

of the rare-earth oxide mixture was ana- lyzed for the effects of varying spectral resolution and temperature. The uncertainties associated with the various parameters affecting the measurements

and the determination of the location of

the reflectance minima have been analyzed. The overall uncertainty in the location of these reflectance minima is believed not to exceed ± 1 nm.

Key words: dysprosium oxide; erbium

oxide; holmium oxide; near infrared re- flectance; rare-earth oxides; spectral bandwidths; wavelength calibration; wavelength standard.

Accepted: February 28, 1985

1. Introduction

This work describes the techniques used to pre- pare and characterize a reflectance wavelength

standard composed of three rare-earth oxides. A

mixture of dysprosium oxide (DyjOj), erbium oxide

(EraOj). and holmium oxide (H02O3) provides a pressed powder specimen exhibiting a near infrared

reflectance spectrum characterized by many dis- crete reflectance minima in the wavelength range

700 to 2000 nm. This wavelength standard is primarily intended for checking the wavelength accu- racy of spectrophotometric instrumentation

designed for measuring diffuse reflectance in the near infrared.

About the Authors: Victor R. Weidner, Patricia Y. Barnes, and Kenneth L. Eckerle are with the

Radiometric Physics Division in NBS' National

Measurement Laboratory.

2. Experimental

2.1 Instrumentation

Measurements of spectral reflectance of the rare- earth oxide mixture were made by means of a Varian-Cary Model 2390 recording spectrophotometer [1]'. The optical system of this doable beam

instrument consists of a filter predisperser and a double-pass monochromator with UV-VIS and

near IR gratings. A deuterium lamp is used as a source for the ultraviolet spectral range. The visi- ble and near infrared source is a tungsten-halogen

lamp. The deuterium lamp also serves as a wavelength scale calibration source when the instrument

is operated in a single beam mode, providing emission lines at 486.0 and 656.1 nm in the visible specFigures in brackets indicate literature references.

243
Journal of Research of the National Bureau of Standards

trum and 2"^ and 4'^ order lines of the 656. 1 nm

line with the near infrared grating.

The spectrophotometer is equipped with an inte- grating sphere diffuse reflectance reflectometer.

This device is capable of measuring total hemispherical reflectance over the wavelength range

200 to 2500 nm, using a photomultiplier detector

for the ultraviolet and visible spectral range, and a lead sulfide detector for the near infrared. When

operating with the lead sulfide detector, the refer- ence mode (which determines the method used to control the reference signal level) operates at constant gain. The constant gain is maintained by varying the spectral bandwidth as a function of

wavelength. The available range of spectral bandwidth settings is approximately 1 to 14 nm when

using the diffuse reflectance attachment. The noise

associated with the recording of a spectrum in- creases as the spectral bandwidth is narrowed and

the spectral resolution must be sacrificed in order

to maintain reasonable noise levels when recording

spectra near the extreme short and long wavelength range of the lead sulfide detector. In order

to record a spectrum over the full near infrared

spectral range at approximately constant resolution, the gain must be reset every 25 to 50 nm. When constant resolution is not important, a complete scan of the near infrared range can be made at a fixed gain setting. For the measurements described in this work, the control of spectral resolution was of primary importance and gain settings were varied to provide a number of fixed spectral

bandwidths for analysis of the effects of resolution on the location of the wavelengths of minimum re- flectance of the rare-earth oxide mixture.

2.2 Materials

2.2.1 Rare-Earth Oxides. The rare-earth oxides

of dysprosium, erbium, and holmium were selected

for preparation of the reflectance wavelength studies after extensive measurements of the near in- frared reflectance spectra of numerous rare-earth

oxides. None of the single component rare-earth

specimens analyzed exhibited enough absorption

bands to serve as a wavelength standard for the full

700 750 800 850 900 900 960 1000 1050 1100 WAVELENGTH (nm) WAVELENGTH (nm)

1.0

0.9

0.8

UJu

i

G 0.7

UJ

_i

b.bJ"=0.6

0.5

04

—1—1—1—1—

1—1—1

\—

r

1

1 1 1 1

1 1 1 T ~

hY\ / ^

- \ kWf I / Et Er kDy

k>

Er

1 1 1 1 1 1 1 1 1

1 .

1 1 1 1500 1550 1600 1650 WAVELENGTH (nm) 1700

0.6

0.5-

0.4 J—I—I—I—I—I—I I I I I I I I I I I l_J_ 1700 1750 1800 1850 WAVELENGTH (nm) 1900

244
Journal of Research of the National Bureau of Standards

700 to 2500 nm spectral range and none showed

any promise at wavelengths much beyond 2000 nm. The oxides of dysprosium, erbium, and

holmium were selected because their infrared ab- sorption bands occurred at various wavelengths

throughout the 700 to 2000 nm spectral range with

a minimum of overlapping of the bands attributed

to each oxide. The disadvantage of mixing the

three component rare-earth oxides was the loss of some intensity of depth of the individual absorption

bands. The reflectance spectra of the three component rare-earth oxide mixture is illustrated in fig- ures 1-1 through 1-7 for a nominal spectral

bandwidth of 4 nm. The absorption features se- lected for analysis are numbered 1-37 and the rare- earth oxide attributed to each of these absorption

features is identified by the elemental symbols Dy,

Er, and Ho appearing with each band number.

The three rare-earth oxides were mixed in equal

parts by weight. The purity of each rare-earth oxide was indicated by the manufacturer [2] to be

99.99 percent. The specimens are identified by lot numbers; (Dy: lot no. Dy-0-4-018), (Er: lot no. Er0-4-028), and (Ho: lot no. Ho-0-4-007). Each rare- earth oxide was weighed in portions of 2 g ±0.01g.

These were combined to form a total weight of 6 g. After throughly mixing the three components, the

mixture was pressed into an aluminum cavity having a depth of 0.5 cm and diameter of 2.85 cm. This

produced a specimen with a powder density of ap- proximately 2 g/cm\ The powder specimen was

provided with a sapphire window of 1.5 mm thickness. This window retained the powder and protected it against damage and contamination.

Sapphire was selected as a window material be- cause it is essentially free of absorption features in the near infrared.

2.3 Measurement Techniques

2.3.1 Calibration of the Spectrophotometer

Wavelength Scale. The spectrophotometer wavelength scale error was evaluated by measuring the

emission lines of the following elements: neon at 703.24 nm, xenon at 881.94 and 979.97 nm, mercury

at 1013.97 and 1529.58 nm, and krypton at 1816.73

1100 1150 1200 1250 WAVELENGTH (nm) 1300

1.0

0.9

0.41300

1 1 1 1 1

1—1—

r

1 I1 1 I I

1 1 1 1 T

i)

Dy

^'

E1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r 1 1 1350 1400 1450 WAVELENGTH (nm) 1500

1900 1950 2000 2050 WAVELENGTH (nm) 2100

Figures 1-1 through 1-7-Beginning upper left at a wavelength

700 nm the near infrared spectral reflectance of a rare-earth oxide mixture composed of DyjOj, EriOi, and HoiOi in equal

portions by weight compressed to a density of Ig/cm'.

245
Journal of Research of the National Bureau of Standards

nm. [3] In addition to these, the absorption band of

1-2-4 trichlorobenzene at 2152.60 nm [4] was also measured.

The wavelength scale of the spectrophotometer was calibrated at the beginning of the study and

again after completion of the spectral analysis of

the rare-earth oxide spectra. The day-to-day

stability of the instrument wavelength scale was

monitored by recording the 2"'' order emission of

the 656.1 nm deuterium line at 1312.2 nm after a nominal warm-up time of 1 hour. The record of

this day-to-day stability check is illustrated in fig- ure 2 for the time period of November 13 to December 24. The data in figure 2 show that the

1.0

K O.Oi

-1.0

••• •••••••• • • • • • • • •

Instrument Wovelength Scole Stability in Infrared

Nov. 30 Dec, 24 DATE

Figure 2-The day-to-day record of the stability of the spec- trophotometer wavelength scale in the near-infrared.

wavelength scale was stable to ±0.2 nm during

this time interval. The wavelength error was evaluated by scan- ning the emission lines at a rate of 0.01 nm/sec. and

recording the resulting spectrum on a scale of 0.2 nm/cm. The recorded emission peaks were bi- sected, using a proportional divider, to determine

the wavelengths at the center of the recorded trian- gular lines. Using this technique, the wavelength

scale was read to the nearest 0.01 nm. The wavelength errors were evaluated for spectral bandwidths of 2, 3, 4, 5, and 10 nm. The differ- ences between the published or "true" wavelengths

of the emission lines as determined from the measurements on the spectrophotometer, are plotted in figures 3-1 and 3-2 for analysis of the instrument

wavelength error. The data points were found to be closely grouped for the measurements at spectral bandwidths of 2, 3, 4, and 5 nm. The data

points for the 10 nm spectral bandwidth measure- ments were somewhat separated from the others. For this reason the analysis of the 2, 3, 4, and 5 nm

bandwidth data are illustrated in figure 3-1 and the

10 nm bandwidth data in figure 3-2. Since the dayto-day wavelength scale stability check indicates a possible point spread of 0.4 nm, this grouping of

the bandwidth data into one group for the 2, 3, 4, and 5 nm measurements seemed reasonable.

+2.5

e +2.0

+1.5

<s +1.0 z

+0,5

Figure 3-1 (upper) and Figure 3-2- The wavelength scale calibra- tion results for the selected

spectral bandwidths showing

the data point spread (vertical

bars), data point averages (open

circles on the vertical bars), the

linear least-squares fit to the data point averages (sloping

solid straight line).

WAVELENGTH SCALE CALIBRATION FOR 2, 3,4, and 5 nm BANDWIDTHS

5 ~———

X« Xe ——-

Hg

- J (POINT SPREAD)

0 (AVERAGE) TCB

1 1 1 1 1 ' '

1 1 1 1 1 1 700 1000 1500 WAVELENGTH (nm)

2000

+ 2.5

6+2.0

Xo +1.0

UJ§ +0.5

WAVELENGTH SCALE CALIBRATION FOR 10 nm BANDWIDTH

:Ne

I Hg

L 1 ri

Kr

X« Xe

Straight Line Fit i TCB

J

( POINT SPREAD j

0 ( AVERAGE

)

1 1 1 1 1 1

1 1 1 1 1 1 L

1 700 1000 1500 WAVELENGTH (nm)

2000

246
Journal of Research of the National Bureau of Standards

The spread of data points in figures 3-1 and 3-2 is indicated by the vertical bars. The average of the

data points within the vertical bar is indicated by

the open circle on the bar. A linear least-squares fit of the the average data points, (represented by the

open circles), is shown as a straight line across the

graph. This line was taken as a indication of the wavelength scale error of the spectrophotometer

for these spectral bandwidths over the near in- frared spectral range 700 to 2150 nm. This linear least-squares fit represents a nominal wavelength

correction. The data spread bars shown in figures

3-1 and 3-2 are sometimes completely above or be- low the least-squares fit. Repeated measurements

probably would not improve the fit because of hidden factors that influence where a particular emission line will appear, A mathematical estimation of the uncertainty in the calibration of the instrument wavelength scale can be derived from the sum of the following observed uncertainties:

The wavelength scale uncertainty (a) is: a=2d + r + v where:

2c? = twice the standard deviation of

the linear least-squares fit for the emission

line wavelengths,

r = l/2 the range of the data point spread

for the worst case for location of an emission line, v=the day-to-day stability of the

wavelength scale. For the 2, 3, 4, and 5 nm spectral bandwidths:

a = ±0.57 nm

For a 10 nm spectral bandwidth:

a = ±0.66 nm. Other uncertainties associated with the overall

determination of the wavelengths of minimum re- flectance of the rare-earth oxide mixture will add

to these uncertainties. These uncertainties will be

discussed in section 2.3.4. 2.3.2 Spectral Bandwidths. The spectral bandwidth settings used in the analysis of the rare-earth oxide mixture were selected to provide data on the

effect of changing resolution on the location of the

reflectance minima that are characteristic of this material in the near infrared. The spectral bandwidths in the near infrared are controlled by adjusting the reference signal gain. This adjustment

involves the monochromator slit width mechanism

which in effect controls the spectral bandwidth or

resolution. The bandwidth is displayed on the in- strument control panel. In order to check the validity of the spectral bandwidth readout on the display panel, a series of measurements were made

of the half-band widths of the mercury emission

line at 1014 nm for nominal bandwidth settings of

2, 3, 4, 5, and 10 nm. In the single beam mode of

operation the gain can be adjusted without changing the selected bandwidth. The half-band width is determined by scanning the emission line with the

gain adjusted until the peak of the emission is ap- proximately 100 percent. The measured width of

the recorded emission spectra at half the peak

height is an indication of the spectral bandwidth. A

comparison of the nominal spectral bandwidth, as indicated on the instrument display panel, and the

measured half-band width of the mercury emission

spectra is given in table 1. The comparison shows

that the actual bandwidths are less than the nominal bandwidths for the 2, 3, 4, and 5 nm settings

and the same for the 10 nm setting. 2.3.3 Determination of the Wavelength of Minimum Reflectance. The spectral reflectance of the

rare-earth oxide mixture is shown in figures 1-1 through 1-7 for a nominal spectral bandwidth of 4 nm. The number of observed absorption bands

varies as a function of the spectral bandwidth set- ting selected for recording the spectrum. There are 37 reflectance minima identified in the figures.

Most can be observed at bandwidths less than 4 nm. Only a few can be observed at 10 nm spectral

bandwidth.

The reflectance spectra of the mixture of rare- earth oxides was recorded on a chart with a wavelength display of 0.5 nm/cm and a wavelength scan range of 0.05 nm/sec. This speed is a relatively

slow scan rate for these absorption bands so that the effect of recorder inertia error is essentially

eliminated as a source of wavelength scale error. The reflectance was measured with a sapphire

window between the rare-earth oxide mixture and

the sample port of the integrating sphere of the

reflectometer. The 100 percent (baseline) calibra- tion was set with a pressed powder Halon (polytetrafluoroethylene) specimen, also covered by a sapphire window. The near infrared spectral re- flectance of a sapphire window covered Halon

Table 1. Comparison of the spectral bandwidths as indicated by

the instrument readout (A) with the spectral bandwidths as derived from the half-height bandwidth measurements of the 1014 nm Hg emission line (B).

Spectral Bandwidths

(A) (B)

2 nm 1.4 nm

3 2.6 4 3.6 5 4.6 10 10.0

247
Journal of Research of the National Bureau of Standards

specimen versus an uncovered Halon Specimen

(100 percent) is shown in figure 4. The spectral

transmittance of the sapphire window is also shown in figure 4. The determination of the wavelengths of minimum reflectance of the rare-earth mixture was ac- complished through an analysis of the recorded

spectral curves. The location of the wavelengths of

minimum reflectance for a given absorption band was graphically determined by bisecting the ab- sorption band. The technique is illustrated in figure

5. The horizontal grid lines of the chart paper that intersect the two slopes of the absorption band are bisected by means of a proportional divider. The

points of bisection locate a line between the two

slopes that intersects the minimum reflectance

point, (usually at the lowest point of the curve).

The wavelength at this point of intersection was

taken as the measured wavelength of minimum re- flectance for the absorption feature. The true wavelength of the minimum was determined by ap- plying a wavelength correction to this measured

value. This correction was discussed in section

2.3.1. Various uncertainties are associated with

these assigned true wavelengths. These will be dis- cussed in section 2.3.4. 2.3.4 Accuracy of the Wavelengths of Minimum

Reflectance. The overall uncertainty in the location

of the wavelengths of minimum reflectance is believed to be no greater than ± 1 nm. This conclusion is based on the reproducibility of the following

calibration parameters:

a) The uncertainty of the calibration of the

spectrophotometer wavelength scale using

1.0

0.9

IL.

(£O

0.8

z

<

I0.7

0.6

0.5

REFLECTANCE OF

SAPPHIRE WINDOW

WITH HALON BACKING

TRANSMITTANCE OF

SAPPHIRE WINDOW

J_J I I L_J_ ' ' L 700 1000 1500

WAVELENGTH (nm)

2000

Figure 4-The spectral transmittance of the sapphire window

used to cover the rare-earth oxide pressed powder specimen, and the spectral reflectance of a sapphire window covering

the Halon diffuse reflectance standard.

t

UJO

o

UJ

_J

li. UJ

q:

Die no Jr cut fVE

(-

e-

'—

r f

—-/

\

w/kVELEI H OF

RE

m

FL EC

1—

CE

<- 0.! nn /c

WAVELENGTH

Figure 5-The wavelengths of minimum reflectance are deter- mined by bisecting the recorded absorption feature as illus- trated in this example.

the emission lines of Ne, Xe, Hg, and Kr,

and the absorption band of 1-2-4 trichlorobenzene, and the day-to-day instabilities of the instrument; (±0.57 nm

and ±0.66 nm depending on the spectral

bandwidth).

b) The imprecision of the graphical technique

for deriving the measured wavelengths of

minimum reflectance; (±0.41 nm), (twice

the largest standard deviation), (see table 2). c) The maximum observed temperature effect; (±0.15 nm).

A mathematical estimation of the overall uncertainty (T) in the location of the wavelengths of

minimum reflectance can be derived from the

square root of the sum of the independent errors squared:

T = Va' + b' +c'

where:

a = uncertainty in the instrument wavelength

scale.

248
Journal of Research of the National Bureau of Standards

Table 2. Ten measurements of the reflectance minima for each

of three absorption bands at a spectral bandwidth of 4 nm, showing the spread of values obtained by the graphical location of the minima. The average, standard deviation, and stan- dard error for the ten values are also given. These

measurements are for 25 °C.

Measurement

No. Band No. 14 (DyjO,)

Band No. 23 (Er^Oi)Band No. 32 (H02O1)

1 1261.00 1 535.68 1 847.09

2 1260.93 1535.65 1847.00

3 1261.15 1535.70 1846.77 4 1261.00 1535.70 1847.00

5 1261.03 1535.60 1846.73 6 1261.20 1535.65 1846.78 7 1261.08 1535.63 1846.50

8 1260.93 1535.60 1846.70

9 1260.93 1535.69 1846.73

10 1261.00 1535.70 1846.43

Average 1261.03 1535.66 1846.77

Standard

Deviation 0.09 0.04 0.21

Standard Error 0.03 0.01 0.07

Note: The data in this table have not been corrected for the wavelength scale error of the spectrophotometer.

6 = twice the standard deviation for the graphical determination of the minima,

c=the largest observed temperature effect.

For spectral bandwidths of 2, 3, 4, and 5 nm: r=±0.72 nm

For a spectral bandwidth of 10 nm: r=±0.79 nm. These uncertainties are for a 95 percent confidence

level. Some other possible uncertainties are dis- cussed in the conclusion.

3. Measurements

3.1 Influence of the Sapphire Window and the Baseline Calibration

In measuring diffuse spectral reflectance, some

reference must be used to establish a 100 percent

level (baseline). In this double beam spectrophotometer, the reference beam enters the integrating

sphere and is incident on a Halon target. The sample beam enters through another port and is inci- dent on the sample. In order to establish a 100

percent level calibration curve, a sample of pressed

Halon is placed at the sample port. The 100 percent

level is established by the ratio of the sample

(Halon) reflectance to the reference beam signal

(also Halon). The instrument records this baseline

in a computer memory. When the Halon sample is replaced by a test specimen, the reflectance of the

specimen is recorded relative to this stored baseline or 100 percent level. This method is called the substitution method. The reflectance of the test speci- men is a relative measurement. Halon is used to

establish the 100 percent level because its absolute

reflectance is very high and it has no significant

absorption features that would introduce a distor- tion in the recorded spectra. The absolute reflec- tance of the test specimen can be obtained by

adjusting the relative measurement to the absolute

reflectance of the Halon [5]. In this study a sapphire window is placed over

the rare-earth oxide test specimen. This window is 1.5 mm thick. A similar window is placed over the

Halon sample during the recording of the 100 per- cent level. By using a sapphire window on both the

Halon and the rare-earth oxide specimens, the ef- fects of the window reflectance and absorbance are cancelled out in the baseline calibration. The sapphire window has no absorption bands in the near infrared that would influence the determination of the wavelength of minima reflectance of

the rare-earth oxide mixture. The absolute reflec- tance data for Halon [5] also show that it can be

used as a baseline standard for purposes of this in- vestigation.

3.2 Influence of Spectral Bandwidth

The effects of spectral bandwidth on the location

of the rare-earth oxide reflectance minima are shown in table 3. The absorption bands are numbered from 1 at approximately 742 nm to 37 at ap- proximately 2005 nm. Measurements were made at nominal spectral bandwidths based on the instru- ment display readout of this parameter. However,

the data listed in table 1 indicate that the spectral

bandwidths were less than the nominal values for

all but the 10 nm setting.

The blank spaces in table 3 are blank for the fol- lowing reasons: (1) The noise level was too large to make reliable measurements. This was the case for bands 1, 2, 36, and 37 at the 2 nm spectral bandwidth setting. (2) Two adjacent bands merged to- gether because the selected spectral bandwidths

did not resolve the two bands. This was the case

for bands 24 and 25 at 3 nm spectral bandwidth. (3) The band became too shallow due to the large

spectral bandwidth. This case occurs for many of

the bands at 5 and 10 nm spectral bandwidths.

Table 3 does not give a clear picture of the exact

effects of changing spectral bandwidth on the location of the the wavelengths of minimum reflec249
Journal of Research of the National Bureau of Standards

Table 3. The adopted wavelengths of minimum reflectance for the rare-earth oxide mixture at 25 °C and for spectral bandwidths (SBW) of 2, 3, 4, 5, and 10 nm.

lare-earth Band SBW SBW SBW SBW SBW

oxide No. 2 nm 3 nm 4 nm 5 nm 10 nm

DyiO.i 1 743.0 743.4 743.4 2* 799.0 799.0 798.6 798.0 3* 887.2 886.9 886.7 886.7 886.5

A4 907.5 907.3 EriOj 5 970.6 971.3 971.6 971.6 0 979.6 980.8 980.8 980.8 7 1012.

y

lUl J.Z luiz.y 1012.8 DyiOi 8 1064.7 1065.0 1065.0 1064.9 9 1095.6 1096.0 1 AnA T 1 AAA A iuyo.4

HoiOi 10* 1 1 il.l 1 ML.i 1 1 jZ.4 1 1 jz.y 1 132.9 11' 1 148.

1

1 148.4 \ \ AQ ^

1 148. J 1 148. /

1 1 /I 0 A

1 148.6

1 TIZ 1 1 m n t 1 m "7

1 lyz.v 1 1 AT A 1 lyz.y

1 J \li\J.L IZJU.Z 1 Z jU.Z 1 Z jU. J

1 >1 4t 1 1 A IzOl.U 1 zou.y 1Z0U.8 1 TAA Q

1 ZOu.8 1 7 A 1 0 1Z01.8

1 c

1

J

1 JZU. / 1 jzU. / 1 JZU.8 1 17A 7 1 jZU. /

1 lOA 7

1 JZU.Z triUi 10 1 A 0 1 J A 1430.4 I4j0. /

1 /

1 /I A 1 "7 14ol. / 140 1 .y

1 /I AT 1 140Z.Z

IB 1 /IT 1 "> 14/1.

Z

\ A^\ A 14/1.0 \ A^\ A 14/ 1.0

1 Qly 14 / /.4 1 ym A 14 / /.O 14 / /.J I4V4.0 14V4.y I4y j.u 21 1 jUj.4 1 ^

1 jUJ. J 1 jUj. J ioIL 1 J lo.u 1 c 1 A n I J lO.U 1 J 1 j.y 1 C 1 C 7 ID 1 J. / ZJ' 1 J

1 ^ 1 ^ A 1 J J j.O 1 JJJ.O 1 A 1 JJJ.4 1 J J4.0 /4 1 j44. / Zj 1 ^A Q 1 ZD 1 <c< 1 IDDD.U ICC/1 0 OT 1 J / /.I 1 J / /.Z 15 / /.Z Zo lOl 1.0 1 A 1 1 7 101 1 . /

1 A 1 1 "7 1011./ 1 A 1 1 Q 101 1 .y 29 1642.7 1642.7 1642.5 1642,5 30* 1682.6 1682.3 1682.2 1682.2 1681.4

J111 1 / J / .u 1757.8 1757.9 1 1 J 1 .0 17S7 (\ H020., 32* 1847.5 1847.3 1846.9 1847.0 1847.3 33 1874.3 1874.0 1873.8 1874.0 34 1885.0 1885.3 1885.7 1885.5 35* 1930.9 1931.6 1932.2 1932.5 1935.5 36* 1970.6 1970.7 1970.8 1970.8 37 2004.5 2005.9 2005.8 2006.3

The uncertainty in the wavelengths of minimum reflectance are believed to be no greater than ± 1 nm.

* (preferential bands)

tance for the rare-earth oxide absorption bands be- cause some of the uncertainties discussed in section

2.3.4 are large enough to mask the bandwidth ef- fects. However, the apparent shift in the wavelengths of the minima are sometimes larger than

the overall uncertainty. Therefore, all the results are listed in the table. For purposes of checking the wavelength scale of a reflectance spectrophotometer there are many

reflectance minima listed in table 3. A few of the

minima might be considered as being preferable be- cause the absorption bands are observed at bandwidths as large as 10 nm. These bands are marked

with an asterisk after the band number in the table.

3.3 Influence of Temperature

All the data listed in table 3 was obtained at a temperature of 25 °C ±0.5 °C. The effects of temperature on the location of the wavelengths of minimum reflectance of the rare-earth oxide mixture were studied by analyzing one absorption band for each of the three rare-earth components. The results are shown in table 4 for bands 14, 23, and 32,

at 20 °C, 25 °C, and 30 °C. These measurements were made with a spectral bandwidth of 4 nm. Because these measurements did not prove or dis- prove the effects of temperature, and effect was as250
Journal of Research of the National Bureau of Standards

Table 4. The observed effects of temperature on the wave

lengths of minimum reflectance for 20 °C, 25 °C, and 30 °C. The temperature effects are not revealed by the observed dif- ferences because of larger uncertainties discussed in section

2.3.4.

(spectral bandwidth = 4 nm)

Band No. 14 Band No. 23 Band No. 32 Temperature (DyjO,) (ErjO,) (HojO,)

20°C 1260.8 nm 1535.7 nm 1847.0 nm

25 °C 1260.8 1535.6 1846.9 30°C 1261.0 1535.5 1846.7

sumed based on the largest differences observed

for the data in table 4 for purposes of estimating the

overall uncertainty (see sec. 2.3.4).

3.4 Influence of Instrument Sensitivity Function

The instrument function is the relative sensitivity

of the instrument as a function of wavelength as observed in the single beam mode of operation

with no sample in the beam. The instrument sensitivity is influenced by a number of parameters such

as the energy output of the source as a function of

wavelength, grating efficiency, reflection of mirrors, transmission of windows, and spectral re- sponse of the detector. The near infrared

instrument sensitivity of the Varian-Cary 2390

spectrophotometer, increases from 700 nm to ap- proximately 1 1 50 nm, then decreases with increasing wavelength. There are some local variations in

this sensitivity curve due to absorption features as- sociated with optics and atmospheric conditions.

The effect of the instrument sensitivity function on

the wavelengths at which absorption features ap- pear for a specimen being scanned is to shift the

scale to longer wavelength when the instrument

sensitivity is increasing from shorter wavelength to longer wavelength (positive slope) and to shift the

scale to shorter wavelength when the instrument

sensitivity is decreasing from shorter wavelength

to longer wavelength (negative slope). The amount

of wavelength shift increases as the slope becomes

steeper with changing wavelength.

The shift in wavelength due to the influence of

the instrument sensitivity can be determined to a

close approximation, using the following equation:

o

where:

dX=the wavelength displacement,

a=the slope of the sensitivity curve normalized at the center of a triangle,

w=the width at the half-height of the geometrical passband.

The wavelength shift is greater for very wide

spectral bandwidths and almost negligible for very narrow spectral bandwidths. The effect of instru- ment sensitivity function is not cancelled by operating the instrument in a double-beam mode. The

measured location of emission lines such as those

described in section 2.3.1 is not influenced by the

instrument sensitivity function because the emission lines are relatively narrow with respect to the

spectral bandwidth.

The data for the reflectance minima listed in table 3 and 1 have been adjusted for the influence

of the instrument sensitivity function. The amount

of adjustment varied from zero where the sensitivity slope was essentially flat to as much as 0.26 nm

where the slope was steep and the spectral bandwidth was 10 nm. For all but 10 of the values listed

in these tables, the wavelength shift due to the in- fluence of the instrument sensitivity function was

less than 0.1 nm.

4. Results

4.1 Reflectance of the Rare-Earth Oxide Mixture

The general reflectance spectrum of the rare- earth oxide mixture is illustrated in figures 1-1 through 1-7 for a nominal spectral bandwidth of 4

mm. The absorption bands are numbered in order

to associate the data listed in the tables with the

spectral features illustrated in the figures.

4.2 Numerical Results

Most of the absorption bands appearing in fig- ures 1-1 through 1-7 were analyzed and the recom- mended values for the wavelengths of minimum

reflectance are listed in table 3 for the indicated

spectral bandwidths. Preferred bands are identified by asterisks after the band numbers in the table.

5. Other Measurements

A check of the reflectance of the EriOi absorption bands at approximately 1012 nm (Band No. 7) and 1535 nm (Band No. 23), and Dy203 band at approximately 1260 nm (Band No. 14) was made

on the NBS Reference spectrophotometer for dif- fuse reflectance [6]. This spectrophotometer uses a

1 -meter monochromator equipped with a prism

predisperser. The spectral bandwidth was set at 5

251
Journal of Research of the National Bureau of Standards

nm or 10 nm. The reflectometer is a 30 cm diameter integrating sphere with a lead-sulfide detector.

Measurements are recorded with the wavelength

drive set at fixed wavelengths. At each wavelength

setting the signal is processed by a current-to-fre- quency converter and integrated over a 4 second

time interval. The reflectance of the sample is measured relative to the sphere wall which is coated

with a spectrally neutral white diffuser [5]. The wavelength correction for the reference

spectrophotometer was determined by measuring

the emission lines of a Hg lamp at 1013.97 nm and

1529.58 nm. These measurements indicate that the

reference instrument wavelength scale was reading too high by +0.82 nm at 1014 nm and +0.35 nm at 1530 nm for a 5 nm spectral bandwidth. The reflec- tance minima of the EraOs bands at approximately

1012 nm and 1535 nm are close to the Hg emission

wavelengths. The sample reflectance was measured at 0.2 nm intervals. From these data, the re- flectance minima for band numbers 7, 14, and 23 were determined to be 1012.9 nm, 1260.7 nm and

1535.5 nm respectively for a spectral bandwidth of

5 nm after correcting for the wavelength scale error. Band No. 23 was determined to be at 1534.5

nm for a 10 nm spectral bandwidth.

A comparison of reflectance minima results for bands 7, 14, and 23 as determined on the VarianCary and Reference spectrophotometers, indicates that a wavelength bias of approximately 1 nm exists between the two instruments after the wavelength

scale has been corrected for all known sources of

error (see table 5). Measurements of the reflectance

minima made by the Instrumental Research Laboratory [7], of the U.S. Department of Agriculture

(USDA) indicate a similar wavelength bias between their spectrophotometers and the VarianCary instrument used in this work. Repeated

measurements on the Varian-Cary instrument after

1.5 years indicate that the bias remains constant. Because of the strong evidence for this wavelength

bias and confidence in the wavelength accuracy of

the NBS Reference spectrophotometer, and the

Table 5, A comparison of the data for reflectance minima numbers 7, 14, and 23 as determined on the Varian-Cary spec- trophotometer and the NBS Reference spectrophotometer.

Reflectance Minima

Varian-Cary Reference Difference Band SBW Instrument Instrument No. (nm) (1) (2) (2)-(l)

7 5 1011.8 1012.9 -1.1

14 5 1259.8 1260.7 -0.9

23 5 1534.4 1535.5 -1.1

23 10 1533.6 1534.5 -0.9

supporting evidence from the USDA, the data in table 3 has been adjusted to correct for the VarianCary near infrared wavelength scale bias. The

over-all uncertainty of ±1 nm given in section

2.3.4 remains the same for these adjusted reflec- tance minima.

6. Conclusion

In addition to those uncertainties discussed

above there are also other factors that might intro- duce uncertainties affecting the results of this study. Although these have not been quantitatively

investigated, they include: 1) purity of the rare- earth oxides. 2) variation in the ratios of the three

rare-earths that are mixed to form the specimen,

and 3) variation in the density of the pressed powder. All three of these factors can be controlled to a high degree of precision in the preparation of the

three-component rare-earth mixture used in this study. The purity of the individual constituents is sufficiently high (99.99%) so that it is not likely that slight variations in this parameter will affect the location of the wavelengths of minimum reflec- tance. The ratios of the three rare-earth components was established by careful weighing. For a weighing of 2 g, an uncertainty of ±0.01 g is too

small to have much effect on the location of the

wavelengths of minimum reflectance. Mixing of

the three components must be thorough, however,

to avoid inhomogeneities.

Figures 1-1 through 1-7 should only be used as a key to the appearance of the reflectance spectra.

Refer to table 3 for the numerical values. The re- flectance data shown in the figures should not be

used for purposes of a reflectance standard. The

absolute reflectance of pressed Halon [5] has been

established for this type of calibration. A wavelength standard based on the diffuse re- flectance of a mixture of three rare-earth oxides has

been analyzed and calibrated for the near infrared

spectral range 700 to 2000 nm. The reflectance

minima obtained from a mixture of Dy203, Er203,

and HO2O3 have been determined for nominal spectral bandwidths of 2, 3, 4, 5, and 10 nm. The principal sources of error influencing the accuracy of the

assigned wavelengths of the reflectance minima are

the calibration of the spectrophotometer wavelength scale and the imprecision in the techniques

used to record and estimate these minima.

This proposed wavelength standard should

provide a useful means for checking the accuracy

of the near infrared wavelength scale of spec- trophotometers equipped with suitable accessories

252
Journal of Research of the National Bureau of Standards

for measuring diffuse reflectance if the required

wavelength accuracy does not have to be better than ±1 nm. An uncertainty of ± 1 nm for this near infrared

wavelength standard is less accurate than current wavelength standards for the ultraviolet and visible spectral ranges. A wavelength standard based on a solution of Ho20.i in perchloric acid [8] provides 14 transmittance minima for wavelength scale calibra- tion in the ultraviolet and visible spectrum. The

overall uncertainty for this wavelength standard is ±0.1 nm for the location of the transmittance minima.

References

[1] Certain commercial equipment or products are metioned

in this paper in order to adequately document the work.

In no case does this imply that the equipment or product

is being endorsed by the National Bureau of Standards or

that it is necessarily the best equipment or product for the

application.

[2] The rare-earth oxides were obtained from Research

Chemicals, a division of Nucor Corp., Phoenix, Arizona.

[3] CRC Handbook of Chemistry and Physics, 63rd Edition, CRC Press Inc., (1982-1983).

[4] Acquista, N., and E. K. Plyler, Calibrating Wavelengths

in the Region from 0.6 to 2.6 Microns, J, Res. Natl. Bur.

Stand., Vol. 49, 13-16 (July 1952).

[5] Weidner, V. R., and J. J. Hsia, Reflection Properties of Pressed Polytetrafluoroethylene Powder, J. Opt. Soc. Am., Vol. 71, 856-861, (July 1981).

[6] Venable, W. H. Jr., J. J. Hsia, and V.R. Weidner, Devel- opment of an NBS Reference Spectrophotometer for Diffuse Transmittance and Reflectance, Natl. Bur. Stand., Tech. Note 594-11, October 1976.

[7] Memorandum from: Dr. Karl H. Norris and William R. Hruschka, Instrumentation Research Laboratory, USDA,

BARC-W, Beltsville, MD 20912.

[8] Weidner, V. R.; R. Mavrodineanu, K. D. Mielenz, R. A.

Velapoldi, K. L. Eckerle, and B. Adams, Spectral Trans- mittance Characteristics of Holmium Oxide in Perchloric Acid Solution, J. Res. Natl. Bur. Stand., 90-2 (1985).

253 »U.S. GOVERNMENT PRINTINO OFFICE: 1998-433-235/93211



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