NBS Measurement Services:

Victor R. Weidner

Jack J. Hsia

U.S. Department of Commerce

National Bureau of Standards
Center for Radiation Research

The Center for Radiation Research is a major component of the National Measurement Laboratory in the National

Bureau of Standards. The Center provides the Nation with standards and measurement services for ionizing

radiation and for ultraviolet, visible, and infrared radiation; coordinates and furnishes essential support

to the National Measurement Support System for ionizing radiation; conducts research in radiation related

fields to develop improved radiation measurement methodology; and generates, compiles, and critically

evaluates data to meet major national needs. The Center consists of five Divisions and one Group.

Atomic and Plasma Radiation Division

Carries out basic theoretical and experimental research into the

spectroscopic and radiative properties of atoms and highly ionized

species; develops well-defined atomic radiation sources as radiometric

or wavelength standards; develops new measurement techniques and

methods for spectral analysis and plasma properties; and collects,

compiles, and critically evaluates spectroscopic data. The Division

consists of the following Groups:

• Atomic Spectroscopy

• Atomic Radiation Data

• Plasma Radiation

Radiation Physics Division

Provides the central national basis for the measurement of far ultraviolet, soft x-ray, and electron radiation; develops and disseminates

radiation standards, measurement services, and data for for these radiations; conducts theoretical and experimental research with electron,

laser, ultraviolet, and soft x-ray radiation for measurement applications; determines fundamental mechanisms of electron and photon interactions with matter; and develops advanced electron- and photon-based

measurement techiques. The Division consists of the following Groups:

Far UV Physics

Electron Physics

Photon Physics

Radiometric Physics Division

Provides national measurement standards and support services for ultra- • Spectral Radiometry

violet, visible, and infrared radiation; provides standards dissemination • Spectrophotometry

and measurement quality assurance services; conducts research in optical • Radiometric Measurement Services

radiation, pyrometry, photometry, and quantim radiometry; and develops

spectroradiometric and spectrophotometric standards and calibration

procedures. The Division consists of the following Groups:

Develops,

Radiation

operates,

Source

and

and

improves

Instrumentation

major NBS radiation

Division

facilities ' • Accelerator

^

Research

including the electron Linac and race track microtron; develops, • Linac Operations

designs, and builds electronic and mechanical instruiientation for • Electronic Instrimentation

radiation programs and facilities; provides national leadership • Mechanical Instrunentation

in the standardization of nuclear instrunentation; and develops

new competence in radiation sources and instrimentation. The

Division consists of the following Groups:

Ionizing Radiation Division

Provides primary national standards, measurement services, and basic

data for applications of ionizing radiation; develops new methods of

chemical and physical dosimetry; conducts theoretical and experimental

research on the fundamental physical and chemical interactions of

ionizing radiation with matter; provides essential standards and measurement support services to the National Measurement Support

System for Ionizing Radiation; and develops and operates radiation

sources needed to provide primary radiation standards, fields, and

well-characterized beams of radiation for research on radiation

interactions and for development of measurement methods. The Division

consists of the following Office and Groups:

Nuclear Physics Group

Engages in forefront research in nuclear and elementary particle physics;

performs highly accurate measurements and theoretical analyses which

probe the structure of nuclear matter; and improves the quantitative

understanding of physical processes that underlie measurement science.

• Office of Radiation Measurement

• Radiation Theory

• Radiation Chemistry and Chemical

Dosimetry

• Neutron Measurements and Research

• Neutron Dosimetry

• Radioactivity

• X-Ray Physics

• Dosimetry
NBS MEASUREMENT SERVICES

SPECTRAL REFLECTANCE

Victor R. Weidner

Jack J. Hsia

Center for Radiation Research

National Measurement Laboratory

National Bureau of Standards

Gaithersburg, MD 20899

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued July 1987
Library of Congress Catalog Card Number: 87-619843

National Bureau of Standards Special Publication 250-8

Natl. Bur. Stand. (U.S.), Spec. Publ. 250-8, 142 pages (July 1987)

CODEN: XNBSAV

Commercial products— materials and instruments— are identified in this document for the sole pur- pose of adequately describing experimental or test procedures. In no event does such identification imply recommendation or endorsement by the National Bureau of Standards of a particular product; nor does it imply that a named material or instrument is necessarily the best available for the purpose

it serves.

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1987

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 Bureau

of Standards are intended to assist the makers and users of precision

measuring instruments in achieving the highest possible levels of

accuracy, quality, and productivity, NBS offers over 300 different

calibration, special test, and measurement assurance services. These

services allow customers to directly link their measurement systems to

measurement systems and standards maintained by NBS. These services

are offered to the public and private organizations alike. They are described in NBS Special Publication (SP) 250, NBS Calibration Services

Users Guide .

The Users Guide is being supplemented by a number of special

publications (designated as the "SP 250 Series") that provide a detailed description of the important features of specific NBS

calibration services. These documents provide a description of the:

(1) specifications for the service; (2) design philosophy and theory;

(3) NBS measurement system; (4) NBS operational procedures; (5)

assessment of measurement uncertainty including random and systematic

errors and an error budget; and (6) internal quality control procedures

used by NBS. These documents will present more detail than can be

given in an NBS calibration report, or than is generally allowed in

articles in scientific journals. In the past NBS has published such

information in a variety of ways. This series will help make this type

of information more readily available to the user.

This document (SP 250-8), NBS Measurement Services: Spectral

Reflectance, by V. R. Weidner and J. J. Hsia, is the eighth to be

published in this new series of special publications. It describes the

instrumentation, standards, and techniques used in the measurement of

spectral reflectance over the ultraviolet, visible, and near-infrared

spectral ranges, from 220 to 2500 nm (see test number 38060S in the

SP 250 Users Guide). Inquiries concerning the technical content of

this document or the specifications for these services should be

directed to the authors or one of the technical contacts cited in

SP 250.

The Center for Radiation Research (CRR) is 1n the process of publishing

21 documents in this SP 250 series, covering all of the calibration

services offered by CRR. A complete listing of these documents can be

found inside the back cover.

NBS would welcome suggestions on how publications such as these might

be made more useful. Suggestions are also welcome concerning the need

for new calibration services, special tests, and measurement assurance

programs

.

George A. Uriano Chris E. Kuyatt

Director Director

Measurement Services Center for Radiation Research

i i i
ABSTRACT

This documentation describes the instrumentation, standards, and techniques used in the measurement of spectral reflectance over the ultraviolet,

visible, and near infrared spectral ranges. The documentation is divided

into three parts. Part I describes the guiding philosophy for maintaining

reference and transfer spectrophotometers for spectral reflectance measurements, and standards and services that are available. Part II describes the

NBS high accuracy reference spectrophotometer including specially developed

accessory ref lectometers. This instrument provides the basis for the

development of absolute NBS standards of diffuse and specular reflectance.

Part III describes the NBS transfer spectrophotometer, a high precision

commercial spectrophotometer used for calibrating Standard Reference

Materials (SRMs) such as diffuse reflectance and specular reflectance

standards. The transfer instrument relies on master standards that are periodically calibrated on the high accuracy reference spectrophotometer

described in Part II. The transfer instrument is also used for performing

special measurements on samples submitted by other laboratories in industry

and government. References containing details and equations are reproduced

in the appendices.

Key Words: diffuse reflectance; spectrophotometers; spectrophotometry;

spectral reflectance; specular reflectance

iv
TABLE OF CONTENTS

Page

ABSTRACT iv

I. Measurement Philosophy, Available Standards, and Services. ... 1 A. Measurement Philosophy 1 B. Available Standards 1 C. Description of Services 1

II. Reference Spectrophotometer for Spectral Reflectance 4

A. Description of Instrumentation 4

1. Basic Instrument 4

2. 6°/Hemi spherical-Reflectance Accessory 6

3. Specular-Reflectance Accessory 6

4. 45°/0°-Ref lectance-Factor Accessory 10

B. Instrument Calibration and Internal Quality Control .... 10

1. Wavelength Calibration 12

2. Linearity of the Photometric Scale 12

3. Stray Radiant Power 14

4. Instrument Sensitivity Function 14

5. Detector Stability 15

C. Establishment of the Reflectance Scales and Calibration

of Master Standards and Uncertainties 15

1. e'/Hemispherical Reflectance . 15

2. Specular (Regular) Reflectance 18

3. 45V0° Reflectance Factor 19

D. Measurement Procedures for Test Samples 20

1. 6°/Hemispherical Reflectance 20

2. Specular (Regular) Reflectance 20

3. 45V0'' Reflectance Factor 20

E. Safety 21

III. Transfer Spectrophotometer for Spectral Reflectance 21

A. Description of the Instrument 21

B. Instrument Calibration 23

1. Wavelength 23

2. Linearity 23

3. Stray Radiation , 23

C. Calibration of Standards 23

D. Operational Procedures and Uncertainties 27

E. Calibration Report of Test 28

F. Safety 28

References 30

V
TABLE OF CONTENTS (cont'd)

Appendix A: A Report of Calibration

Appendix B: Development of an NBS Reference Spectrophotometer for Diffuse

Transmittance and Reflectance

Appendix C: NBS Specular Ref lectometer - Spectrometer

Appendix D: NBS-45°/Normal Ref lectometer for Absolute Reflectance Factors

Appendix E: Establish a Scale of Directional - Hemispherical Reflectance

Factor I: The Van den Akker Method

Appendix F: Reflection Properties of Pressed Polytetraf luoroethylene Powder

Appendix G: Laboratory Intercomparison Study of Pressed

Polytetraf luoroethylene Powder Reflectance Standards

vi
Table of Contents (continued)

LIST OF TABLES Page

1. Available NBS Standard Reference Materials for Spectral

Reflectance and Wavelength Standards 2 2. Emission lines and absorption bands used to calibrate the

reference spectrophotometer wavelength scale 13

3. Summary of Estimated Uncertainties of Spectral Reflectance

Values for NBS Reference Spectrophotometer 17

4. Emission lines and absorption bands used to calibrate the

transfer spectrophotometer wavelength scale 24

5. Linearity check of the photometric scale of the transfer

spectrophotometer at 770 nm for the PMT and PbS Detectors 25

6. Stray radiation measurements on the transfer spectrophotometer. . . 26

7. Summary of Estimated Uncertainties of Spectral Reflectance

Values for NBS Transfer Spectrophotometer 29

vi i

*
TABLE OF CONTENTS (cont'd)

Page

LIST OF FIGURES

Fig. 1 Pictorial diagram of spectrophotometer optica! system 5

Fig. 7. Diffuse reflectance integrating sphere showing detector

position 7

Fig. 3 Exit aperture optics and beam switch 8

Fig. 4 Specular reflectance accessory 9

Fig. 5 Schematic of the 45V0° reflectance accessory 11

Fig. 6 The auxiliary sphere system for determination of an absolute 16

reflectance scale.

vi i i
I. Philosophy, Available Standards and Measurement Services

A. Measurement Philosophy

Spectral reflectance measurements provide information on the properties

of many materials. NBS 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 mesurements. For this

purpose NBS 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 instrumentation for realizing these reflectance scales

consists of a high-accuracy reference spectrophotometer with several special

ref lectometer accessories. The reference spectrophotometer is devoted to the

highest accuracy measurements such as those required for maintaining master

standards. In support of the primary reference instrumentation, a high

precision commercial spectrophotometer with a ref lectometer accessory is

maintained as a transfer instrument. The transfer instrument is calibrated

with master standards from the primary laboratory.

Standards calibrated by the transfer instrument under commonly used

spectral and geometrical conditions are issued as Standard Reference

Materials (SRMs). Special calibrations and tests are supplemental services

to the public.

B. Available Standard Reference Materials

The reflectance and wavelength standards listed in Table 1 are available as SRMs as of 1986. They can be obtained from the Office of Standard Reference

Materials, Room B311, Chemistry Building, National Bureau of Standards,

Gaithersburg, MD 20899.

C. Description of Services (SP250, Item 38060S, Old Number 7.8A)*

NBS provides the following three types of spectral reflectance

measurements:

1. eVhemispherical spectral reflectance [1] - the ratio of the total

reflected radiant flux to that reflected by a perfectly reflecting

diffuser (same as to that of the incident flux), the angle of incidence

being 6° from normal and the reflected flux being collected

hemispherical ly.

2. Specular (regular) spectral reflectance [1] - the ratio of the reflected

radiant flux to the incident flux, the reflection being without diffusion

in accordance with the laws of optical reflection as in a mirror.

*NBS Special Publication 250, NBS Calibration Services User Guide, 1986-1988

Edition.

1
Table 1

Available NBS Standard Reference Materials* for

Spectral Reflectance and Wavelength Standards

Specular Reflectance Standards

SRM No. Description

2003d First surface aluminum mirror, 5.1 cm diameter,

wavelength range: 250 - 2500 nm.

2011 First surface gold mirror, 5.1 cm diameter,

wavelength range: 600 - 2500 nm.

2023 Second surface aluminum mirror, 5.1 x 5.1 cm,

wavelength range: 250 - 2500 nm.

"

' Diffuse Reflectance Standards

SRM No. Description

2015 Opal glass, 2.5 x 5 x 0.64 cm,

wavelength range: 400 - 750 nm.

2016 Opal glass, 10 x 10 x 0.64 cm,

wavelength range: 400 - 750 nm.

2019b White ceramic tile, 5.1 x 5.1 cm,

wavelength range: 350 - 2500 nm.

2021 Black porcelain enamel tile, 5.1 x 5.1 cm. wavelength range: 280 - 2500 nm.

Wavelength Standards

SRM No. Description

2034 Holmium oxide solution (transmittance only),

wavelength rnage: 240 to 640 nm.

1920 Rare-Earth mixture (reflectance only)

wavelength range: 740 to 2000 nm.

2009 Didymium glass mounted in a cuvette holder, (transmittance only)

wavelength range: 400 to 750 nm.

2010 Didymium glass, 5.1 x 5.1 cm, (transmittance only)

wavelength range: 400 to 750 nm.

*NBS Special Publication 260 "NBS Standard Reference Materials Catalog

1986-87" p. 100,101, June 1986.

2
3. 45V0° spectral reflectance factor [1] - 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 angle of

incidence being 45° from normal and the angle of viewing being at the

normal direction.

Spectral reflectance measurements on submitted samples are available at

cost. Preliminary discussion with NBS staff is required before submission.

When high accuracy or a special geometry are needed, the reference instrument

is used. The transfer instrument provides most of the measurements unless

they can only be done on the reference instrument specular-reflectance and

45°/0°-ref lectance factor accessories.

The reference spectrophotometer can provide the following conditions for

reflectance measurements:

e 6°/hemispherical reflectance with specular component included, from 220

to 2500 nm. Sample sizes of 5 cm to approximately 30 cm (round or square) can be accommodated.

e Specular (regular) reflectance, from 250 to 2500 nm. The samples can be

measured for sample beam incidence angles ranging from 5° to approximately 80°. Measurements are made with the sample beam polarized both

horizonally and vertically. The average of these two measurements is

the sample reflectance for an unpolarized beam. The samples can range

in size from 50 mm to approximately 108 mm (round or square). Second

surface mirrors, with the first surface to second surface thickness

greater than 2 mm, can only be measured at near normal incidence.

o 45°/0° reflectance factor, from 380-770 nm. This wavelength range can

be extended into the ultraviolet and near infrared by calibrating the

system as described in reference 5. Measurements are made with the

sample beam polarized both horizontally and vertically. The average of

these two measurements is the reflectance for an unpolarized beam. The

samples can range in size from 50 mm to 108 mm (round or square).

The transfer spectrophotometer can provide the following conditions for

reflectance measurements:

e 6° /hemi spheri cal reflectance. This geometry includes the specular and

diffuse reflectance of the sample to give the total hemispherical

reflectance.

o 0°/hemispherical reflectance. This geometry measures the diffuse

reflectance with the specular component of the reflected sample beam

excluded from the measurement.

• Specular reflectance of mirrors for 6° incidence only.

For the transfer spectrophotometer, the spectral reflectance data are referenced to absolute scales of reflectance through the use of transfer

3
standards. The wavelength range is 220 to 2500 nm for diffuse reflectance

measurements and the range is 250 to 2500 nm for specular measurements.

The uncertainties associated with the various types of reflectance measurements performed by means of the transfer spectrophotometer depend on wavelength range, sample parameters, and various other instrumental considerations. Discussions of these uncertainties are included in Part III.

Colorimetric terms can be computed from 10 nm interval reflectance data

for CIE Standard Illuminants [2] A, C, and Dss •

The minimum sample size for the transfer spectrophotometer is approximately 2.5 cm (round or square). The maximum size is approximately 15 cm.

1 1 . Reference Spectrophotometer for Spectral Reflectance

rA. Description of Instrumentation

The instrument has been described in detail in previous publica"

tions [3,4,5,6], which are included as Appendices B,C,D,E. A brief

description of the instrumentation is given in this section.

1. Basic Instrument [3]

The spectrophotometer (Figure 1) consists of the source optics, a monochromator, power supplies, control and data acquisition systems, and

specialized reflectance accessories.

The instrument is equipped with three sources: (1) a 150 watt xenon arc

lamp for the ultraviolet spectrum below 325 nm; (2) a 100 watt tungsten strip

lamp for the visible spectrum; and (3) a 500 watt tungsten lamp for the visible and near infrared. These sources are powered by regulated DC power

supplies. An off-axis parabolic mirror collects and collimates the radiation

from the source. Polarizers or a chopper for infrared measurements can be

placed in this collimated beam. The polarization condition of the horizontally or vertically polarized beam is not altered by the optical components

before entering the reflectance accessories.

Another off-axis parabolic mirror refocuses the collimated beam at the

entrance slit of a quartz Ebert prism predi sperser. The beam passes from the

predisperser through the entrance slit of a 1-meter focal length CzernyTurner monochromator with an effective aperture of f/8.7. Two gratings are used with the monochromator, depending on the spectral range. The grating

used for the near ultraviolet and visible spectral range is blazed to give a maximum efficiency at 500 nm; the near infrared grating is blazed for a maximum efficiency at 1250 nm. Both gratings are 150 grooves/mm and with a linear despersion of 6.66 nm/mm. A triangular bandpass can be set

selectively to 2, 5, 10, or 20 nm with equal entrance and exit slit widths.

The wavelength drive can be operated manually or driven by a computercontrolled stepper motor.

4
a: S

inN 2 u a • S *» uz c

asK

^5

>»

I.

Oi

-i->

a.8UV

a.

to

1.ou

a.

01

at 5
A dedicated microcomputer with interface boards is used to control the

instrument, acquire data, and perform data reduction.

2. e'/Hemispherical-Ref lectance Accessory

6°/Hemi spherical reflectance measurements are made with a 30 cm diameter

integrating sphere. The design of this sphere is illustrated in Figure 2.

The sphere has a 3.8 cm diameter beam entrance port, a 5 cm diameter detector

port, and a 5 cm diameter sample port. The sample port is attached to the

sphere 6° from the tangent. The sphere is coated with pressed

polytetraf luoroethylene (PTFE) powder. The detector is located 90° from the

other two ports. There is a shutter between the detector and the detector

port to protect the detector when the room lights are turned on and to provide a means of cutting off the signal in order to check the dark current

level. The detector port has a cylindrical collar that extends into the

sphere. This collar, which is also coated with PTFE powder, restricts the

field of view of the detector to prevent direct viewing of the sample and

reference beam first reflections.

The exit slit optical system is illustrated in Figure 3. The exit slit

of the monochromator is located in a light-tight diaphragm built into the

partition between two rooms. The beam exiting the monochromator enters into

a dark room. A 15" off-axis parabolic mirror near the exit slit collects and

collimates the beam. This parabolic mirror is mounted on a mechanism

designed to rotate the mirror 180" clockwise or counterclockwise about the

beam axis. This is accomplished by the action of a small piston. When the

mirror is in one position, the collimated beam is directed through the en- trance port of the integrating sphere to the sample port. When the mirror is

rotated to the second position, the same beam is directed at a different

angle through the same entrance port to an area of the integrating sphere

wall. This area of the wall is between the sample and detector ports. The

sphere coating at this area of the wall is shaped as shown in Figure 11 of

Appendix B, so that first reflections from the reference beam cannot be seen from the sample port. The measurement procedures will be described in

Section II.D.l.

3. Specular-Reflectance Accessory

The specular ref lectometer illustrated in Figure 4 is designed to

measure the spectral reflectance of mirrors and other polished surfaces as a function of angle of incidence and polarization. This instrument is set up

in a dark room adjacent to the room containing the reference spectrophotometer. The collimated beam formed by the exit slit optics of the reference

spectrophotometer is directed horizontally to the specular ref lectometer.

The ref lectometer has two stepper motor driven turntables, one for the sample

and a second for the tracking mirror and detector averaging sphere. The two

turntables operate independent of each other but share a common axis of

rotation (see Fig. 4). Samples are mounted on a two position slider that moves them in and out of the beam. When the sample is out of the beam, the

tracking mirror intercepts the beam and directs it into an integrating

(signal averaging) sphere at the center of rotation of the detector

turntable. This sphere rotates with the turntable but the detector is

6
7
EXIT APERTURE OPTICS

Figure 3. Exit aperture optics and beam switch.

8
POSITION OF

TRACKING MIRROR

FOR INTERCEPTION

OF SPECULAR SAMPLE BEAM

PHOTOMULTIPUER DETECTOR —

(STATIONARY)

AVERAGING SPHERE AND

TRACKING MIRROR TURNTABLE

COLLIMATED

INCIDENT I Vv

POSITION OF

TRACKING MIRROR FOR INTERCEPTION OF INCIDENT BEAM

BACKGROUND SHUTTER

SAMPLE

TURNTABLE

SAMPLE

SLIDER

Fig. 1. General scheme of the NBS specular reflectometer showing the relationship of the sample turntable and beam-tracking turntable and detector systems.

TRACKING MIRROR

INTERCEPTING SAMPLE BEAM \^

TRACKING MIRROR

-INTERCEPTING

INCIDENT BEAM

COLLIMATED

INCIDENT BEAM

Fig. 2. Horizontal x section through the plane of the sample beam,

specular sample, and the tracking mirror that orbits the sample.

PHOTOMULTIPLIER DETECTOR

AREA VIEWED

BY DETECTOR

(BELOW DASHED LINE)

COMMON AXIS OF

ROTATION FOR SAMPLE

AND TRACKING MIRROR

SHUTTER

AVERAGING 'SPHERE

Figure 4 Specular Reflectance Accessory
designed to remain stationary over the axis of rotation because the response

of the photomul It ipl ier tube, even with magnetic shielding, may change if

moved tnrough local variations in ambient magnetic fields. The limiting

aperture of the detector system is the entrance port in the averaging sphere.

A baffle tube extends from the limiting aperture to near the tracking mirror.

The system is programmed to measure the reflectance of a test mirror at

required angles of incidence. The tracking mirror moves to the correct

position to intercept and direct the beam into the averaging sphere below the

detector. Before the specular reflectance of a sample can be measured, the

alignment of the turntables and sample are checked by means of the sample

beam and a laser to assure that the sample beam always passes through the

center of the detector limiting aperture. The sample turntable is aligned so that the sample beam reflects back on itself when normal to the sample plane.

The axis of rotation of the sample turntable is moved to the center of the

sample beam. The tracking- mirror turntable axis of rotation is aligned to

the same axis of rotation as the sample. The tracking mirror is adjusted to

reflect the beam through the center of the limiting aperture. Measurements

of specular reflectance are completely automated by means of the computer

controlled stepper motors and the signal processing systems. The

measurements are monitored by an operator to check the system alignment

before and after each measurement at a given wavelength and polarization.

4. 45V0''-Ref lectance Factor Accessory

The 45°/0° reflectance factor accessory illustrated in Figure 5 is

designed to measure the absolute reflectance factor for a sample illuminated

at 45° incidence and viewed by a detector at normal incidence. The sample is

mounted on a two position slider on a turntable so that the sample plane is

vertical and the axis of rotation is at the center of the collimated sample

beam. The sample beam is diffusely reflected at the sample. The detector

system consists of a limiting aperture and shutter attached to a signal

averaging sphere, and a detector. Attached to this sphere at 90° from the

optical axis (normal to the sample plane) is a second averaging sphere with a photomult ipl ier detector. The reason for using two spheres is to have a uniform receiver system in order to measure a small light spot from a black

glass and a larger light spot of a diffuser for the calibration of master

standards (see II, C, 3). The measured reflectance signal depends on the

size of the limiting aperture and its distance from the sample plane, and is

small compared to the intensity of the incident beam. The 45°/0° reflectance

of a sample is compared to a white porcelain enamel plaque master standard

mounted in the second position of the two position slider. Calibration of

the standard is done by a step-down technique, requiring measurements of the

ratio of two fluxes and some linear dimensions. The step-down technique also

involves measuring the specular reflectance of a polished piece of black

glass at 22.5° incidence. These absolute specular reflectance measurements

are done on the reference specular ref lectometer . Additional details of

the establishment of the scale and measurement procedures will be given in

Sections II. C. 3 and II. D. 3.

B. Instrument Calibrations and Internal Quality Control

Since the best available standards may change over long periods of time,

the instrument measuring reflectance must itself serve as a reference. For

10
Figure 5a

Sft

Figure 5b

Figure 5. Schematic of the A5*/0* Ref lectometer

.

Fig. 5a: Top view with top sphere not shown, for clarity.

S: Sample, LA: Limiting Aperture, DA: Detector assembly,

SA: Aperture between spheres.

Fig. 5b: Front view of two-sphere Receiver Assembly.

AS: Averaging Sphere, SH: Shutter, D; Detector,

LA: Limiting Aperture, SA: Aperture between spheres.

11
this purpose, the reference spectrophotometer must be monitored for changes

in performance. The five parameters which can affect the accuracy of measurement are wavelength calibration, linearity of the photometric scale,

stray radiant power, instrument sensitivity function, and detector

stabi 1 ity.

1, Wavelength Calibration

The wavelength scale error is determined by measuring the emission

lines [7] of spectral line sources and the absorption bands of some materials. These emission lines and absorption bands are listed in Table 2.

The low-pressure arc-emission-line lamps are mounted at the source

position of the reference spectrophotometer and imaged on the entrance slit

of the predisperser. All the listed emission lines are relatively intense

and isolated from other intense lines. The monochromator is scanned through

the wavelength region of the emission line and the signal is recorded at

small wavelength intervals. These data are used to compute the centroid for

the emission line. The natural bandwidth of the spectral line is much

narrower than the instrument bandwidth. The spectrum of the emission line is

recorded as a triangular function with the peak representing the measured

wavelength of the line. Using these techniques, the wavelength scale error

can be determined to an uncertainty of 0.2 nm for a 10-nm bandpass in the

near ultraviolet and visible spectrum. Since the uncertainties are upper

bounds, they may be regarded as having a 99.7% confidence level {3a). All

upper bounds in this publication will be of 3o uncertainty. It is standard

procedure to check the wavelength scale in the wavelength region of interest

before using the instrument. This is usually done with the Hg source.

The near infrared wavelength scale is more difficult to check and the

uncertainties in the wavelength scale are larger because of a lack of

reliable emission lines. Hg emission lines, polystyrene absorption bands,

and the absorption bands of 1,2,4-trichlorobenzene are used in the 1000 to

2500 nm wavelength range. The uncertainty of the wavelength scale in the near infrared is about 1 nm. Various factors can affect the wavelength

calibration: temperature changes, problems with the wavelength drive

mechanism, changing of gratings, and shifting of the optical table.

Therefore, it is advisable to recalibrate the wavelength scale before each

use of the instrument.

2. Linearity of the Photometric Scale

The non-linearity of the photometric scale is the deviation of the

observed signal from a linear scale of signal attenuation ranging from 100%

of the incident signal to the lowest level that can be measured. The

non-linearity of the reference instrument photometric scale is determined

through the use of a double aperture technique [8]. For reflectance

measurements, the detector non-linearity needs to be considered only for

signals between 100% and 1% since there are few requirements to measure

materials having smaller reflectances. The non-linearity (3a) of the

photomultiplier detector is generally in the range of 1 x 10"^ to 9 x 10"^ of

the unattenuated incident beam. This magnitude is small compared to other

12
Table 2

Emission Lines and Absorption Bands Used to Calibrate the Reference

Spectrophotometer Wavelength Scale.

Emission Lines :

Hg: 253.65 nm, 334.15 nm, 435.83 nm, 1014 nm, 1529.5 nm.

He: 587.56 nm, 667.81 nm. Cd: 508.58 nm, 643.85 nm.

Absorption bands of Materials :

Polystyrene (0.6 mm): 2144 nm. 1,2,4-trichlorobenzene (0.5 mm): 1660.6 nm, 2152.6 nm, 2494 nm. Didymium glass (6 mm): 1067 nm).

13
errors that affect measurements of reflectance, so that a non-linearity

correction need not be applied if it remains in this range. The non- linearity of a lead sulfide infrared detector used on the reference instrument was also tested by the double aperture technique. In this wavelength

range the random noise is large enough to mask the magnitude of the

non-1 inearity.

3. Stray Radiant Power

The level of stray radiation present within a selected 10 nm bandpass

is checked by two tests.

The first test method uses glass filters. The transmittance of a sharp

cut-off seleniijn orange glass filter that passes about 90% at the wavelengths

above 600 nm and nearly zero below 550 nm is measured below the cut-off.

Then a second selenium orange glass filter is added and the transmittance of

the combined filters is measured. By comparing the transmitt ances measured

with one and two filters, the amount of stray radiation from wavelengths

above 600 nm can be determined. In this case the stray radiation at 400 and

500 nm is 5 X 10"^ and 3 x 10"*+ respectively. A similar test is done with

cobalt blue filters to check stray radiation at 600 nm, where the cobalt

glass has a strong absorption band. The filter passes approximately 80% in

the 350 to 450 nm range and 90% above 700 nm. By the filter addition technique, the stray radiation from wavelengths below and above 600 nm is found

to be approximately 1 x 10"*^ of the detector output for the total incident

radi at ion.

A second stray radiation test is made with a 632.8 nm He-Ne laser. This

test shows that the stray radiation drops off from 84.0 x 10"^ at 600 nm to

0.5 X 10"^ at 400 nm. A similar level of stray radiation is found on the

long wavelength side of the laser line.

4. Instrument Sensitivity Function

The term "instrument sensitivity function" is used here to describe the

relative signal output of the spectrophotometer without the test sample as a function of wavelength. It is the resultant of the spectral distribution of

the source, the spectral response of the detector, and the spectral

properties of the gratings, prisms, mirrors, and other optical components.

The instrument sensitivity function introduces a shift in the wavelength away

from the desired wavelength setting. This effect can exceed 1 nm if the

slope of the instrument function curve is steep. The effect of a steep slope

in the instrument function curve is a red shift if the slope is positive and

a blue shift if it is negative.

Wavelength scale corrections are made by estimating the magnitude of the

shift using the following equation [9]:

d = aw2/6,

14
where

d = wavelength shift,

a = slope of the curve normalized at the center of a triangle,

w = full width at half-height of the triangular passband.

5. Detector Stability

In all of the data taking procedures for the reference spectrophotometer, signal drift is monitored as a function of time. The 100% signal is

measured before and after the samples are measured. The sample and background measurements are averaged to compensate for signal drift. If the

standard deviation of three measurements is larger than 1 x 10"^ of the 100%

signal, the measurements are repeated. The sudden appearance of a large

standard deviation sometimes warns of a malfunction or equipment failure.

C. Establishment of Reflectance Scales, Calibration of Master Standards,

and Uncertainties

1. 6VHemispherical Reflectance [6, 10]

The absolute NBS scale of 6°/hemispherical reflectance is established through the application of the double sphere system illustrated in

Figure 6. This technique was first described by Van den Akker [11] and was

also used by Goebel [12]. The term double sphere comes from the use of a sphere sample attached to the measuring integrating sphere of a spectrophotometer. The NBS system uses a 30 cm diameter integrating sphere illustrated

in Figure 2. This same sphere is identified as the detector sphere in figure

6. The sample or "auxiliary sphere" is approximately 30 cm in diameter (a

20-cm diameter auxiliary sphere yielded the same reflectance scale within the

measurement uncertainty). There is one port in this sphere. The spheres are attached to each other so that the sample beam can enter the auxiliary

sphere. The auxiliary sphere is coated with a 10 mm thick pressed PTFE

powder. Three flat specimens of the same coating are also prepared for

direct measurement at the sample port of the detector sphere. From these

measurements and measurements of the reflectance of the auxiliary sphere, and some measurements of the areas of the auxiliary sphere port and surface area

of the sphere coating, the absolute reflectance of the coating material of

the auxiliary sphere is computed. As the computations involve numerous equations and geometrical factors, the reader is referred to Appendix E for

detai Is.

Discussions of systematic and random errors associated with the measurements of diffuse reflectance are given in Appendices B and E. A representative estimation of uncertainties (3a) are given in Table 3. The uncertainty

due to the double-sphere measurement, which is for hemispherical incidence

and hemispherical viewing h/h, is 0.0005. The uncertainty due to the conversion from h/h reflectance to 6°-incidence and hemispherical viewing reflectance (6Vh) is 0.0002. The uncertainty due to the retrof lection correction

is 0.0001. A typical noise level is 0.0015. The over- all uncertainty for

the determination of absolute diffuse reflectance and the assigned values of

15
K 3 uj

u 7 < B w t h- < I 6 p ui > a o 1

1- ^ -J

i*J <

<2 I o ^ K «

Q. 2 o > Z ti. d uj uj X K K 3 lU 3 < O

UJ OC (0 X O 9 H U. < oc

+-> o

<u

<0

I/) >»

«/t v

I.

a.

to

16
Table 3

Summary of Estimated Uncertainties of Spectral Reflectance Values for

NBS Reference Spectrophotometer [A representative analysis in the visible

Spectral region]

6°/ Hemispherical Reflectance (6°/h)

Double Sphere (h/h)

h/h — 60/h

Retroref lection

Random Noise

Correction

5.0 X 10^

2.0 X

10-'+ 1.0 X

10-'+ 1.5 X 10-3

Total Uncertainty* (3a) 1.6 X 10-3

Specular Reflectance

Wavelength

Stray radiation

Linearity

Detector response

Random Noise

5.0 X

10-'+ 3.0 X

10-'+ 1.0 X

10-^+ 1.0 X 10-^

1.5 X 10-3

Total Uncertainty* (3a) 1.7 X 10-3

45V0°Reflectance Factor

Wavelength

Uniformity of the receiver system

Stray radiation

Scattering

Black glass

Angular setting

Linearity

View factor

Random Noise

5.0

5.0

3.0

1.5

1.7

1.5

1.0

5.0

1.5

10-'+

10-'+ 10-'+ 10-3

10-3

10-3

10-^

10-'+ 10-3

Total Uncertainty* (3a) 3.2 X 10-3

*Square root of sum of squares

17
reflectance for the master standards are believed to be no greater than

±0.002 {3a). The published results of an international inter- comparison of

the absolute reflectance scale [13] support this finding. The smallest un- certainties are representative of measurements made in the visible spectrum.

The uncertainties for the near ultraviolet and near infrared vary from ±0.005

(3a) to ±0.010 (3a), depending on the wavelength range. They increase near the wavelength operating limits of the spectrophotometer due to limitations

of the detectors, light sources, and optics.

The absolute reflectance of pressed PTFE powder was determined by the

double-sphere technique for the ultraviolet, visible, and near infrared

spectral ranges^°. The absolute reflectance of this material is greater than

96% from 200 to 2500 nm and greater than 99% from approximately 350 nm to

1800 nm.

Although the pressed PTFE powder serves as an absolute reflectance

standard, it is desirable to have working standards of a more permanent

nature. These are hard durable materials that remain stable and can be

easily cleaned without affecting their spectral reflectance. Five master

standards have been calibrated for G^/hemispherical reflectance. These are:

(1) Russian opal glass: (2) Vitrolite opal glass; (3) porcelain enamel on steel; (4) white ceramic (SRM 2019); and (5) black porcelain enamel on steel

(SRM 2021). Each of these standards has been calibrated relative to a perfect diffuser by measuring them relative to the high purity PTFE at the

time the double-sphere absolute technique is realized. Periodic comparison

of their reflectance relative to the pressed PTFE standards indicate that

they are stable to within an uncertainty better than ±0.005 (3o).

2. Specular (Regular) Reflectance [4]

The absolute specular reflectance measurements are made in the following

sequence: background, incident flux, reflected flux, incident flux, background. The sequence is performed three times with the sample rotated

clockwise to the desired angles of incidence and three times with the sample

rotated counterclockwise to the same angles of incidence. For each clockwise

and counterclockwise sequence, the background is first subtracted from the

measured data of incident and reflected fluxes and the ratio of the reflected

flux to the incident-flux is computed. The ratios are averaged for the three

cycles and the standard error is computed.

After the measurements for both vertically and horizonally polarized

incident beams for a given wavelength, the average of the two polarizations

and the overall standard error are computed.

The components of the estimated uncertainty are as follows. The

uncertainty due to the wavelength scale is 0.0005. The uncertainty due to

the stray radiation is less than 0.0003. The uncertainty due to the

non-linearity is less than 0.0001. The uncet^tainty due to the detector

response at different tracking-mirror positions is 0.0001. And the

uncertainty due to a typical random noise level is 0.0015. The overall

uncertainty for specular reflectance measurements is less than ±0.002 (3a)

for the wavelength range 320 to 800 nm (see Table 3). Below 320 nm the

18
uncertainty increases to about ±0.005 (3o) at 250 nm. The uncertainty in the

near infrared is ±0.002 (3a), except for wavelengths below 850 nm and above

2000 nm where it increases to about ±0.005 (3a). Some brief discussions of

the checks on the instrument performance are given in Appendix C.

The specular reflectance accessory of the reference spectrophotometer is

used to calibrate master aluminum and gold mirrors for the wavelength range

250 to 2500 nm. These master mirrors are used to calibrate SRM mirrors on the transfer spectrophotometer. These mirrors are selected from an uncalibrated stock of SRM mirrors when a new batch is received from the

manufacturer. A batch usually consists of about 30 mirrors that are coated

at the same time. The new mirrors are aged under laboratory conditions in

glass covered containers (Petri dishes) for about one year before being

calibrated. New master mirrors are calibrated at approximately two year

intervals because under the best of care the mirrors become contaminated and

cannot be restored to their orignal reflectance by cleaning.

The master aluminum mirrors are calibrated at 25 nm intervals from 250

to 400 nm, 50 nm intervals from 400 to 1000 nm, 100 nm intervals from 1000 to

1300 nm, and at 250 nm intervals from 1500 to 2500 nm. They are also

calibrated at the laser wavelengths of 632.8 and 1060 nm. The mirrors are measured at angles of incidence of 6°, 30°, and 45°, for vertically and

horizontally polarized incident beams. The master gold mirrors are calibrated in a similar way for wavelengths above 600 nm.

3. 45°/0° Reflectance Factor [5]

Because the detector accepts only a small solid angle of the total

hemispherical reflection, the calibration of diffuse reflectance standards

for 45°/0° reflectance factors involves comparing a very small reflected flux

to a large incident flux. A step-down technique must be used to attenuate

the incident beam by means of a calibrated polished black glass with an absolute specular reflectance of about 4% for a 22.5° angle of incidence.

This black glass is mounted in the sample holder so that the light reflected

by it enters the limiting aperture of the detection system. A white

porcelain enamel plaque to be calibrated as a 45°/0° diffuse reflectance

standard is also mounted in the sample holder. Alternate readings are taken

with the collimated beam incident on the white plaque and the black glass.

The reflectance of the white plaque is adjusted to the specular reflectance

embodied in the black glass. The reflectance factor of the white plaque is

obtained by dividing this adjusted reflectance by the geometrical factor [5]

of the limiting aperture.

The overall uncertainty (3a) in the measured 45°/0° reflectance factor

is about 0.003. A representative analysis of estimated uncertainties are summarized in Table 3. The uncertainty due to the wavelength error is

0.0005. The uncertainty for the receiver system (uniformity) to receive the

specularly and diffusely reflected radiation is less than 0.0005. The

uncertainty due to the radiation scattering in the accessory is 0.0015. The

uncertainty due to the black glass specular reflectance is 0.0017. The

uncertainty due to the angular setting is 0.0015. The uncertainty due to the

non-linearity is less than 0.0001. The uncertainty due to the view-factor

19
determination is less than 0.0005. And the uncertainty due to a typical

random noise level is 0.0015. Appendix D provides some brief discussion of

the instrument performance.

A Vitrolite opal glass is used as a check standard for monitoring the

long term performance of the 45°/0° ref lectometer. Any change in the

measured ratio of the reflectance of the Vitrolite check standard to the

master porcelain enamel plaque serves as a warning that the absolute scale

has changed. Such a change could indicate that there is an alignment

problem, or that one or both of the standards have aged.

D. Measurement Procedures for Test Samples

1. 6VHemispherical Reflectance

Measurements of 6°/Hemispherical reflectance are done with a ratio

technique, switching the incident collimated beam back and forth between

sphere wall and sample holder. Three measurements are necessary: background

signal with the beam blocked near the monochromator exit slit, reflectance of

the sample relative to the sphere wall, and reflectance of a master standard

relative to the sphere wall.

Data are first .recorded in the following order: background, sample,

sphere wall, sample, background. This cycle is performed three times for

each wavelength. To compensate for signal drift for each cycle, the two

sample measurements are averaged and the two background measurements are averaged; the background is subtracted from the sample and sphere wall

signals, and then the reflectance of the sample relative to the sphere wall

is computed. The results of the three measurements are averaged, and a standard deviation of the averaged ratio is computed.

This procedure is repeated for the master standard, and then the

relative reflectance of the sample is adjusted to the absolute scale embodied

in the master standard. The reflectance of the sphere wall need not be known

but must be stable throughout the measurements.

2. Specular (Regular) Reflectance

Calibration of samples requiring a high accuracy are performed on the reference spectrophotometer. The measurement procedures are the same as discussed in Section II. C. 2.

3. 45V0° Reflectance Factor

Data for measurements of 45°/0° reflectance factors are recorded in the

sequence: background, white plaque master standard, test sample, white

plaque master standards, background. This sequence is repeated two times for

each wavelength and polarization. The preliminary data reduction involves

subtracting the background from the other measurements and computing the

ratio of the test sample reflectance to the reflectance of the master white

plaque. The 45°/0'' absolute reflectance factor of the sample is obtained by

multiplying this ratio by the 45°/0° absolute reflectance factor of the

master white plaque.

20
E. Safety

The main hazards in the spectrophotometry laboratory are due to radiation from He-Ne lasers, xenon arcs, and spectral line sources. Laser signs

are posted to alert personnel of possible hazards. The xenon arc is shielded

to protect personnel from UV radiation, possible injury due to lamp explosion, or injury from hiqh voltages. Ozone gas produced by the xenon arc is

removed by an exhaust system. Similar precautions are taken with spectral

line sources that produce UV radiation. Personnel wear protective goggles

when working with light sources that emit harmful optical radiation.

There are also electrical hazards due to lamp power supplies and high

voltage power supplies for detectors. Approved grounded cables are used on

all electrical equipment.

III. Transfer Spectrophotometer for Spectral Reflectance

The transfer spectrophotometer is a commercial double beam instrument

[14] with transmittance and reflectance capabilities. It is equipped with

microprocessors with programmable features. It is also connected to an external computer with software to control the spectrophotometer and perform

data reductions.

The wavelength range is from 200 to 2500 nm for diffuse reflectance

measurements. The spectral bandwidth can be set to any fixed value between

0.1 and 3.6 nm for the wavelength range 200 to 900 nm when using the photomultiplier detector. The bandwidth, in the near infrared, may range from

less than 1 nm to a maximum of 14.3 nm, depending on the available signal.

The photometric scale can be recorded in percent reflectance or optical density (= - logio p, where p is a reflectance). The optical density scale

ranges automatically to 4.5 and can be extended to about 6 in the ultraviolet

and visible spectral ranges by attenuating the reference beam with photoetched nickel screens. In the near infrared the upper limit of the optical

density scale is approximately 3.

A. Description of the Instrument

The wavelength range is divided into three operating ranges based on the

selected source and detector combination. These are the ultraviolet (200 to

400 nm); visible (340 to 900 nm); and near infrared (700 to 2500 nm). The

instrument has two gratings; one for the spectral range 200 to 900 nm and one

for the 700 to 2500 nm near infrared. There is a deuterium lamp for the near ultraviolet wavelength range below 340 nm and a tungsten-halogen source for

the spectral range 340 to 2500 nm. The deuterium lamp also serves as a wavelength calibration source with the instrument operated in the single beam

mode. The gratings, sources, and order separating filters are automatically

controlled so that continuous spectral scans can be made through the full

wavelength range of the instrument. A number of instrument systems can be

checked with computer routines stored in the microprocessor. A detailed

description of all instrument controls and features is given in the operators

manual supplied by the manufacturer. The measurement parameters are

21
continually displayed on the control panel monitor. Selected wavelengths,

bandwidth, scan speed, scale expansion, and other parameters are shown on the

monitor, and warning messages flash on the screen to alert the operator of

problems or instrument parameters that are out of range.

The sample compartment is insulated and the temperature can be con- trolled within ±0.2°C in the range 15°C to 40^0 by circulating water from a control bath. The temperature of a sample can be monitored by means of a thermocouple probe in the sample compartment. The temperature is displayed

on the control panel monitor and can be recorded on the thermal printer.

The spectrophotometer has a chart recorder and a thermal printer for

recording digital spectral data and instrument parameters. There are features for automatic repeat scans. The photometric scale baseline calibration

can be stored in memory so that baseline corrections can be made continuously

during a spectral scan.

The operation of the spectrophotometer can be controlled from the external computer that controls all instrument parameters and records spectral

data. Additional software is used to perform data averaging, conversion of

optical density to reflectance or vice versa, computing colorimetric terms,

and other data manipulations.

The integrating sphere of the diffuse reflectance accessory is approximately 100 mm in diameter. The photomult ipl ier detector (PMT), a Hamamatsu

tube, is mounted above the sphere and views the sphere interior through an elliptical aperture. The lead sulfide (PbS) detector port is adjacent to the

PMT port. There are baffles attached to the top of the sphere interior that

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 that is 22 mm high

and 12 mm wide and is located 90° from the sample port. The reference-beam

target is located about 33 mm inside the sphere.

The sample beam is nearly collimated and enters the sphere through a rectangular port of approximately 30 mm height and 20 mm width. 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 15 mm when the exit slit height is set to full

height. The image height can be reduced by reducing the exit slit to 1/3

full height.

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

of this sample 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°. 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

22
sample beam entrance port so that only the diffuse component of the reflected

beam is measured. The solid angle subtended by the sample beam entrance port

at a distance of 100 mm from the center of the sample extends approximately

15" in the vertical plane and 10° in the horizonal plane.

The integrating sphere described above is also used to make specular

reflectance measurements of mirrors and other specular reflectors. Since

measurements of specular reflectance on this device are not absolute, a master standard must be measured along with the test sample. The relative

reflectance of the test sample is adjusted to the absolute scale embodied in

the master standard. The master standard is either a first surface aluminum

mirror, first surface gold mirror, or a second surface aluminum mirror that

has been calibrated on the reference specular ref lectometer [4]. The

integrating sphere geometry allows only for 6° incidence for specular

reflectance measurements on the transfer spectrophotometer.

B. Instrument Calibration

1. Wavelength

Emission lines [7] and absorption bands used to calibrate the

transfer spectrophotometer wavelength scale are listed in Table 4. The

wavelength scale uncertainty is ±0.1 nm {3a) in the near ultraviolet and

visible, and ±1.0 nm (3a) in the near infrared. The deuterium lamp mounted

in the spectrophotometer, is used to check the wavelength scale on a day-to-day basis at the wavelengths listed in Table 4.

2. Linearity

The linearity of photometric scales for the PMT and PbS detectors

for diffuse reflectance measurements has been determined with a set of

transmittance standards[15] . These transmitt ance standards have been

calibrated on the NBS reference transmittance spectrophotometer at 770 nm. The results of linearity check for both detectors of the reflectance

accessory are given in Table 5. The data in Table 5 are used to correct for

non-linearity of measurements.

3. Stray Radiation

The presence of stray radiation in the transfer spectrophotometer

sample beam was checked, using a number of solutions and glass filters that

have sharp cut-off absorption features in different spectral regions. The

techniques for measuring stray radiation are described in ASTM and other

publications [16,17], The level of stray radiation was checked for spectral

bandwidths (SBW) of 1 nm and 3.6 nm. The results of these measurements are given in Table 6, and indicate that the level of stray radiation is not

significant in this spectrophotometer.

C. Calibration of Standards

Many of the Standard Reference Materials (SRMs) listed at the beginning

of this documentation are calibrated on the transfer spectrophotometer, using

23
Table 4

Emission Lines and Absorption Bands Used to Calibrate the Transfer

Spectrophotometer Wavelength Scale.

Emission Lines :

Hg: 253.65 nm, 334.15 nm, 435.83 nm, 1014 nm, 1529.5 nm.

D : 486.0 nm, 656.10 nm, 1312.2 nm, 1968.3 nm, 2624.4 nm.

^ Note: the last 3 wavelengths for D are 2nd, 3rd, and 4th order

lines of, the 656.1 nm line and are observed with the near

infrared grating.

Ne: 703.24 nm. Xe: 881.94 nm, 979.97 nm. Kr: 1816.73 nm.

Absorption Bands of Materials:

1 ,2,4-trichlorobenzene (0.5 nm): 2152.6 nm. Holmium oxide (SRM 2034): 241.0 nm, 249.8 nm, 278.1 nm, 287.0 nm 333.5 nm, 345.5 nm, 361.4 nm, 385.4 nm,

416.1 nm, 451.3 nm, 467.8 nm, 485.3 nm. 536.5 nm, 640.5 nm. Rear-Earth Oxide (SRM 1920): 799.0 nm, 886.7 nm, 1132.4 nm 1260.8 nm,

1535.4 nm, 1682.2 nm, 1757.8 nm, 1847.0 nm,

1932.5 nm, 1970.8 nm.

24

It
Table 5

Linearity Check of the Photometric Scale of the Transfer Spectrophotometer at

770 nm for the PMT and PbS Detectors.

Reflectance Mode:

Fi Iter No. Reference Value PMT Difference PbS Difference

1-1 0.9185 0.9207 +0.0022 0.9208 +0.0023

1-2 .6644 .6651 + .0007 .6659 + .0015

1-3 .4787 .4789 + .0002 .4795 + .0008

1-4 .3289 .3284 - .0005 .3290 + .0001

1-5 .1674 .1671 - .0003 .1669 - .0005

1-6 .0500 .0495 - .0005 .0489 - .0011

1-7 .01163 .01129 - .00034 .01041 - .00122

25
Table 6

Stray Radiation Measurements on the Transfer Spectrophotometer

Wavelength* Filter/ Observed Stray Radiation level

nm Sol ut ion 1 nm SBW 3.6 nm SBW

200 KCl 3.38 X 10 o 5.75 X 10-7

215 NaBr 3.54 X 10 ' 1.90 X 10-5

245 Nal 4.36 X 10 ' 1.17 X 10-6

318 Acetone 5.01 X 10-7 3.89 X 10-6

380 NaN02 2.04 X 10-6 1.47 X 10-5

512 Red #222 2.39 X 10-6 2.88 X 10-6

568 Red #3059 8.91 X 10-7

660 Methylene Blue 3.89 X 10-6

671 Methylene Blue 4.16 X 10-6

688 Red #3002 5.12 X 10-7

^Central wavelength of the incident beam. At these wavelength settings, the

filter in the sample beam should be opaque. Any observed transmittance

signal is attributed to stray radiation from other wavelengths.

26
master standards as a means for transferring the absolute reflectance scale

from the basic or fundamental measurements of these quantities on the

reference spectrophotometer documented in Part II.

Pressed PTFE powder is preferred as a master standard for diffuse

reflectance because the absolute reflectance of this material is well

documented [10,18]. Other transfer standards used are: (1) a master white

ceramic tile used for calibrating NBS SRM 2019 and a black porcelain enamel

master tile used for calibrating SRM 2021; (2) master first surface aluminum

and gold mirrors and second surface aluminum mirrors used for calibrating

SRM's 2003, 2011, and 2023.

D. Operational Procedures and Uncertainties

The instrument parameters are set after a 30 minute warm-up period. The

wavelength scale is checked at this time by running the instrument test

procedure with the deuterium emission lines. The baseline is set before any

measurements are recorded. In setting up the baseline calibration, a white

diffuser is placed at the sample port of the reflectance attachment

integrating sphere. The instrument scans the spectral region to be measured

and stores the data required to correct the sample measurements for gross

baseline fluctuations. As long as subsequent measurements are made for the

same parameters, the recorded baseline information in the computer will be

used. If the operator changes a critical parameter, a warning message will

be displayed on the monitor screen and a new baseline must be established.

Data are recorded in the sequence: 100%, transfer standard, zero, test

samples, zero, transfer standard, 100%. The zero measurements are made with

a large black cavity at the sample port of the integrating sphere. The 100%

and standard measurements are made at repeated intervals when many test

samples have to be measured. Most samples are compared to a freshly prepared

PTFE standard of known absolute reflectance, prepared as described in

reference [18]. A black diffuse standard such as NBS SRM 2021 porcelain

enamel standard is used as a transfer standard for dark samples. Similar

sequences are measured when measuring specular reflectance except that the

reference standard is a mirror.

Diffuse reflectance data are corrected to an absolute scale as follows:

(1) Test sample and standard data are corrected for linear drift by

performing measurements in a time-symmetrical sequence and

subsequent averaging.

(2) Any zero calibration error is subtracted.

(3) The ratio of the reference value of the transfer standard to the

measured value of the transfer standard is multiplied by the

measured value of the test sample to adjust the test sample data to

an absolute scale.

The uncertainty (3o) in the diffuse reflectance data obtained through

these measurements and data reduction procedures is generally 0.005. A

27
similar uncertainty exists for the specular reflectance data. The

photometric scale uncertainties arise from factors such as the master

standard, non-linearity of the photometric scale, stray radiation, random

noise, and sample related uncertainties. The uncertainty due to the master

standard is 0.0015. The uncertainty due to the non-linearity is less than

0.003. The uncertainty due to the stray radiation is less than 0.00002. The

uncertainty due to the random noise varies with a number of instrumental

operational parameters. The upper bound of noise may be as small as 0.0002

to as much as 0.02 depending on such things as spectral bandwidth, wavelength

range, and available reference signal. A typical noise level is 0.0025.

When random noise is relatively high, the effects of the noise on the

measurements is reduced by averaging 10 measurements at each wavelength. As

stated in Section III.B.l, the wavelength scale uncertainty is ±0.1 nm (3a)

in the ultraviolet and visible spectral range and ±1.0 nm (3o) in the near

infrared. For a typical neutral filter, the uncertainty of transmittance in

the visible region due to wavelength scale is 0.0005. A correction for

wavelength scale error is usually not required for neutral samples. The

influence of wavelength error on the overall uncertainty depends on the rate

of change in reflectance versus change in wavelength. The stability of the

photometric scale over a period of three hours is better than 0.003. The

drift is linear and can be minimized by recording the 100% calibration at

shorter time intervals and correcting for changes in this calibration. The

estimated uncertainties are summarized in Table 7.

Some sample-related uncertainties cannot be corrected for in the data

reduction. Examples of such uncertainties are: large sample nonuniformity;

surface features such as parallel grooves; surface waves and dimples that

scatter the specular component; and thin coatings that cause interference

effects in the recorded data

E. Calibration Report of Test

The Report of Test (see Appendix A) is an important documentation of

service performed. The report includes: purpose of the test; description of

the test sample; description of the instrumentation, measurement parameters,

and procedures; data reduction and uncert anit ies; comments and references;

and tables of data and results. Records of these tests are kept for at least

ten years.

F. Safety

The hazards and safety precautions in the transfer spectrophotometer

laboratory are the same as those discussed in Part II for the reference

spectrophotometer laboratory.

28
Table 7

Summary of Estimated Uncertainties of Spectral Reflectance Values for

NBS Transfer Spectrophotometer [A representative analysis in the visible

region]

Wavelength 5.0 X

10"'+ Stray radiation 2.0 X 10"^

Linearity 2.2 X 10-3

Master Standard 1.5 X 10-3

Random noise 2.5 X 10-3

Stability (Drift) 1.5 X 10-3

Total Uncertainty (3a) 4.1 X 10-3

(Square root of sum of squares)

29
REFERENCES

*{References included in the Appendices)

[1] International Commission on Illumination, International Lighting

Vocabulary, Publication CIE No. 17 (E-1.1) 1970.

[2] International Commission on Illumination, Colorimetry, Publication CIE

No. 15.2 (TC-1.3) 1971.

*[3] Venable, W.H. Jr., Hsia, J.J., and Weidner, V.R., Development of an NBS

reference spectrophotometer for diffuse transmittance and reflectance.

National Bureau of Standards (U.S.) Tech Note 594-11, October 1976. 47

pages. (Appendix B)

*[4] Weidner, V.R. and Hsia, J.J., NBS specular ref lectometerspectrophotometer, Appl. Opt. 19, 1268 (April 15, 1980).

(Appendix C)

*[5] Hsia, J.J. and Weidner, V.R., NBS 45''/normal ref lectometer for absolute

reflectance factor, Metrologi a _17 , 97 (1981). (Appendix D)

*[6] Venable, W.H., Jr., Hsia, J.J. and Weidner, V.R., Establishing a scale

of directional-hemispherical reflectance factor I: The Van den Akker

Method, J. Res. Nat. Bur. Stand. (U.S.) 82, p. 29 (July-August 1977).

(Appendix E)

[7] CRC Handbook of Chemistry and Physics, 63"^^ Edition, CRC Press,

inc. (1982-1983).

[8] Mielenz, K.D. and Eckerle, K.L., Spectrophotometer linearity testing

using the double-aperture method, Appl. Opt. II, 2294 (1972).

[9] Venable, W.H., Jr. and Eckerle, K.L., Standard Reference Materials:

Didymium Glass Filters for Calibrating the Wavelength Scale of

Spectrophotometers - SRM 2009, 2010, 2013, and 2014, NBS Special

Publication 260-66, p. 54 (October 1979).

*[10J Weidner, V.R. and Hsia, J.J., Reflection properties of pressed

polytetraf luoroethylene powder, J. Opt. Soc. Am. _71» 856 (1981).

(Appendix F)

[11] Van den Akker, J. A., Dearth, L.R. and Shillcox, W.W., Evaluation of

absolute reflectance for standardization purposes, J. Opt. Soc. Am.

56, 250 (1966).

[12] Goebel, G., Caldwell, B., and Hammond, H.K. Ill, Use of an auxiliary

sphere with spectrophotometer to obtain absolute reflectance, J. Opt.

Soc. Am. 56, 783 (1966).

30
REFERENCES (cont'd)

[13] Budde, W., Erb, W., and Hsia, J.J., International intercompar i son of

absolute reflectance scale. Color Research and Application, _7, 24

(1982).

[14] Varian-Cary Model 2390 UV-VIS-NIR spectrophotometer.

[15] Eckerle, L., Weidner, V.R., Hsia, J.J., and Kafadar, K., Measurement

assurance program transmittance standards for spectrophotometric

linearity testing: Preparation and Calibration, J. Res. Nat. Bur.

Stand. 88, 25 (January-February 1983).

[16] Mielenz, K.D., Weidner, V.R., and Burke, R.W., Heterochromatic stray

light in UV absorption spectormetry: A new test method, Appl. Opt. _21^, 3354 (1982).

[17] American Society for Testing and Materials, Standard Test Method for

Estimating Stray Radiant Power Ratio of Spectrophotometers by the

Opaque Filter Method, ASTM E387-84, Annual Book of ASTM Standards,

Section 14.01, p. 469-4890, 1985.

*[18] Weidner, V.R., Hsia, J.J., and Adams, B., Laboratory i ntercompar i son study of pressed polytetraf luoroethyl ene powder reflectance standards,

Appl. Opt. 24, 2225 (1985). (Appendix G)

31

(cv. u^) APPENDIX A

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF gTANDARDS

Gaithersburg, MD 20899

REPORT OF CALIBRATION

for

Spectral Reflectance

of

One Gold Mirror

Su knitted by:

(Reference Purchase Order No. 55883 dated September 20, 1985.)

1

.

Purpose

The purpose of this test is to measure the spectral reflectance of one gold mirror over the spectral range 250 to 2500 nm.

2. Material

The gold mirror submitted for measurement by Inc. is approximately 27 mm in diameter, identified by serial number 2007-9.

3. Measurements of Spectral Reflectance

Measurements of spectral reflectance of the gold test mirror, NBS

Master Standard aluminum mirror #31 and NBS Master Standard gold mirror

#16 were made by means of a Gary Model 2390 recording spectrophotometer.

The Gary Model 2390 is equipped with an integrating sphere reflectance

attachment with sample and reference beams. Measurements were made in

the area approximately 8 mm by 12 mm at the center of each mirror.

The measurements of the test mirror and NBS Master Standard aluminum

mirror #31 were made over the wavelength range 250 to 800 nm using a deuterium source and tungsten source in combination with a photomul tip! ier

detector. The spectral band pass was 1-nm. The measurements of the test

mirror and NBS Master Standard gold mirror #16 were made over the wavelength range 800 to 2b00 nm using a tungsten source and lead sulfide

detector. The spectral band pass varied from 2-nm to approximately 13-nm.

NBS Test No.: 534/235956-86

Date: November 4, 1985 Page 1 of 5

A-1
REPORT OF CALIBRATION

The absolute reflectance of specular mirrors cannot be obtained

directly by this technique. However, by comparing the reflectance of

the test mirror to the reflectance of a standard mirror of known absolute

reflectance, the measurements made on this relative scale can be used to

obtain the absolute reflectance of the test mirror. NBS Standard #31 is

a first surface aluminum mirror and NBS Standard #16 is a first surface

gold mirror that are periodically calibrated by means of the high accuracy

reference specular ref lectometer-spectrophotometer. Each Master Standard

reflectance scale was last determined in April 1985. The uncertainty in

the Master Standards reflectance values is ±0.002. The reflectance

values of the master standards were determined with a collimated beam

incident on the mirror at 6 degrees from the normal. The assigned re- flectance values of the standards are an average of two sets of measurements made with horizontally and vertically polarized sample beams. The

angle of incidence for the measurements made with the Gary reflectance

attachment is also 6 degrees from the normal.

4. Data Reduction and Results

The data of spectral reflectance oiF the test mirror and NBS Master

Standards were recorded at 25 nm intervals. These data were corrected

for small variations in the zero calibration and converted to equivalent

values of spectral reflectance. The values of the test mirror are adjusted to an absolute reflectance scale by the ratios of the assigned

reflectance values and the measured reflectance values for the NBS Master

Standards #31 and #16. Note that these spectral reflectance values should

only be considered valid for the condition of illumination in which the

incident sample beam is approximately 6 degrees from the normal to the

plane of the mirror. The results of the data reduction are listed in

table 1, these data were plotted and smoothed. The reflectance values

listed in Table 1 are believed to be uncertain by no more than ±0.005.

(An equivalent uncertainty of 3a, or at 99.7% confidence level).

Prepared by: Approved by:

Patricia Y. Barnes

Radiometric Physics Division

Center for Radiation Research

Jack J. Hsia

Radiometric Physics Division

Center for Radiation Research

NBS Test No.: 534/235956-86

Date: November 4, 1985 Page 2 of 5
REPORT OF CALIBRATION

Spectral Reflectance, Gold Mirror - Serial Number 2007-9

TABLE 1

wave 1 eng un Ref 1 ec tanc

(nm)

cDU u. ^yb

. J4 1

300 .346

325 .342

. J jU

. OHO

400 .360

425 .363

. JDO

H/ 0

500 .453

525 .671

pnn . ouu

0/0

600 .906

625 .931

Qd7

0/ 3 . 3 DO

700 .963

725 .968

7 cn Q7n

77C 079 . y /

1

800 .973

825 .973

ODU Q7T

O/ 3 974

974

925 .974

950 .974

975 .974

1000 .974

1025 .975

1050 .975

1075 .975

NBS Test No.: 534/235956-85

Date: November 4. 1985 Page 3 of 5

A-3
REPORT OF CALIBRATION

Spectral Reflectance, Gold Mirror - Serial Number 2007-9

TABLE 1 (continued)

Wavelength Reflectance

11 00 .975

1125 . 975

1150 .975

1175 .975

1 200 . 975

1225 n "7 c

. 975

1250 .975

1275 .975

1 'inn 07 C 07 C

. y / 0

1350 .975

1375 .975

1 Ann 07 . y / D Q7 C

. y / D 1450 .975

1475 .975

\ bOO . 975

1 c o c

1 525 . 975

1550 .975

1575 .975

1600 .975

1625 .975

1650 .975

1675 .976

1700 . 976

1725 .976

1750 .976

1775 .976

1800 .976

1825 .976

1850 .976

1875 .976

1900 .976

1925 .976

1950 .976

1975 .976

NBS Test No.: 534/235956-86

Date: November 4, 1985 Page 4 of 5

A-4
REPORT OF CALIBRATION

Spectral Reflectance, Gold Mirror - Serial Number 2007-9

TABLE 1 (continued)

Wavel ength Reflecta

(nm)

2000 .976

2025 .976

2050 .976

2075 .976

2100 .976

2125 .976

2150 .976

2175 .976

2200 .976

2225 .976

2250 .976

2275 .976

2300 .976

2325 .976

2350 .976

2375 .976

2400 .976

2425 .976

2450 .977

2475 .977

2500 .977

NBS Test No.: 534/235956-86

Date: November 4, 1985 Page 5 of 5

A-5

APPENDIX B

Optical Radiation Measurements:

Development of an NBS Reference Spectrophotometer

for Dififuse Transmittance and lleflectance

William H. Vcnablc, Jr., Jack J. Hsia, and

Victor R. Weidncr

UJS. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretory

Edward O. Vetter, Und«r S«cr«tory

Dr. Betsy Ancker-Johnson, Auisiani S^cfiary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acfing Director

Issued October 1976

Optical Physics Division

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

B-1
National Bureau of Standards Technical Note 594-11

Nat. Bur. Stand. (U.S.), Tech. Note 594-1 1. 47 pages (Oct. 1976) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1976

For sale by the Superintendent of Documents, U.S. (Order by SD Catalog No. C 1 3.46:594- 1 1). (Add 25 percent additionalGovernment Printing Office, Washington, D.C. 20402

Stock No. 003-003- Price $1.15

for other than U.S. mailing).

B-2
This 1s the eleventh Issue of a series of Technical Notes entitled

OPTICAL RADIATION MEASUREMENTS. The series will consist primarily of

reports of progress In, or details of, research conducted In radlometry,

photometry and spectrophotometry In the Optical Radiation Section and

the Radiometric Physics Section of the Optical Physics Division.

The level of presentation In OPTICAL RADIATION MEASUREMENTS will

be directed at a general technical audience. The equivalent of an undergraduate degree In engineering or physics, plus familiarity with the

basic concepts of radlometry and photometry [e.g., G. Bauer, Measurement

of Optical Radiations (Focal Press, London, New York, 1965)], should be

sufficient for understanding the vast majority of material In this

series. Occasionally a more specialized background will be required.

Even In such Instances, however, a careful reading of the assumptions,

approximations, and final conclusions should permit the non-specialist

to understand the gist of the argument if not the details.

At times, certain cornnercial materials and equipment will be

Identified In this series in order to adequately specify the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply

that the material or equipment identified is necessarily the best

available for the purpose.

Any suggestions readers may have to improve the utility of this

series are welcome.

Henry J. Kostkowski, Chief

Optical Radiation Section

National Bureau of Standards

Jack L. Tech, Chief

Radiometric Physics Section

National Bureau of Standards

iii
TABLE OF CONTENTS

Paee

I. INTRODUCTION.

.....

1

II. SPECTROPHOTOMETER DESIGN ......... 3

A. LiSht Sources ................. 3

B. Source Optics 3

C. Predisperser . 3

D. Monochromator 5

1. Description ..... 5

2. Calibrations and Tests 5

a. Wavelength calibration 5

be Stray radiant energy

.....

6

E. Exit Slit Optics 7

111. MEASUREMENT ACCESSORY SYSTLMS 7

A« General Purpose Integrating Spheres 9

1» Description 9

2. Definition of the Measurement ..... 9

3. Reflectance Measurement Procedure 13

4. Evaluation . 14

a. Detector linearity ..... . 14

b. Sample induced non-linearity 16

c. Polarization effects 16

d. Angular dependence of response 16

e. Sample Plane to port Plane displacement effect 17

B. Inteeratine Sphere for Measuring Relative Directional-Hemispherical

Reflectance as a Function of Angle 17

1. Description 17

2. Measurement Procedure 19

3. The Entrance Port Correction 19

C. Auxiliary Spheres for Determination of the Absolute Reflectance Scale .... 20

D. Bidirectional Diffuse Reflectance Factor Accessory System 20

IV. SUMMARY ........ 20

APPENDIX As Sample-Induced Non linearity

...

23

1. Wall Retro-Reflectance Non linearity 23

2. Flat-Sample Non linearity 24

3. Baffle-Induced Non linearity

.....

25

4. Combinations of Sample-Induced NonI inearities . 27

APPENDIX Bs Method of Evaluating SamP I e-Induced Nonlinearity 28

APPENDIX Cs Correcting for Scattered Radiation in Incident Beam 29

B-4
TABLE OF CONTENTS (cdntlnu«d) PMt

APPENDIX Di Ttst for Polarization Effects X

APPENDIX Et Estimation of Samp I «-DcPcndent Non linearity 31

1. SPhcrs Without Baffit 31

2. Sphere With Baffle 31

APPENDIX Ft Estimating Error Due to Antfular Dependence of Response 35

1. Surface Reflection 35

2. Body Reflection 36

APPENDIX 6t Focusintf the Exit Slit Optics 39

V. REFERENCES 41

V

B-5
DEVELOPMENT OF AN NBS REFERENCE SPECTROPHOTOMETER

FOR

DIFFUSE TRANSMIHANCE AND REFLECTANCE

William H. Venable, Jr., Jack J. Baia and Viator R. Veidner

A new reference spectrophotometer, designed primarily

for the analysis of diffuse transmlttance and reflectance,

has been developed In the Institute for Basic Standards at

NBS. The spectrophotometer consists of a broadband monochromator with optional bandpasses of 2, 5, 10, and 20

nanometers. The exit aperture of the monochromator Is

provided with special mirror optics to colllmate and switch

the beam for optional use as a reference or sample beam.

These colllmated beams are directed Into a dark room where

a variety of sample mounts, light gathering devices, and

detectors can be installed. Measurements for which provisions

have been made or are being planned Include directionalhemispherical reflectance as a function of angle of Incidence,

diffuse transmlttance, haze, and bidirectional reflectance

factor. This Technical Note describes the design of the

instrument in detail, and gives the results of the performance tests and detailed error analyses which have been

carried out to date.

Key Words: Bidirectional reflectance factor; diffuse refleotanoet

diffuse transmittancet reflectance; spectrophotometry.

I. INTRODUCTION

Improving the accuracy and usefulness of spectrophotometric measurements made throughout the scientific and industrial conmunity is a fundamental purpose of the spectrophotometry

group of the Radiometric Physics Section of NBS. One type of spectrophotometric measure- ment in which a substantial improvement is needed is that of the interaction of light with

turbid media. The principal quantities which are to be measured are directional -hemispherical

reflectance and transmittance, bidirectional reflectance factor, and bidirectional transmlttance factor. However, in order to measure these accurately, one must determine the effects

of a number of related parameters such as translucency and reflections at the sample boundaries.

A reference spectrophotometer for diffuse reflectance and transmittance measurements

has been constructed at NBS utilizing a modular design and state of the art components. This

design allows flexibility in investigating the many aspects of the measurements and it can

be adapted to additional types of measurements in the future. The instrument consists of a monochromatic source radiator which projects the radiation into an adjoining darkroom. This

radiation source is described in part II of this Technical Note. A number of specialized

sample mounts, light gathering devices, and detection systems can be installed in the darkroom for performing specific measurements. For brevity, these will be called the "accessories". Several of them are described in part III. The experiments are controlled and the

data is gathered and analyzed by a mini-computer which is interfaced with the instrument

using a modular interactive data acquisition system (MIDAS)[1]^ developed in part at NBS [2]. A block diagram showing the general arrangement of the experiment control and data gathering

system is shown in figure 1.

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

1

B-6
B-7
II. SPCCTROPHOTOHETER DESIGN

The general layout of the optical system of the spectrophotometer is shown In figure 2. The source, alignment laser» and monochromator are mounted on a surface plate with their

optic axes horizontal and parallel to the surface of the plate. The exit aperture of the

monochromator is attached to a light tight diaphram in a partition that separates the room containing the monochromator and source optics from the dark chamber in which are located

the exit aperture optics and the accessories. The accessory pictured in figure 2 is an integrating sphere for directional -hemispherical reflectance measurements. The electronics

and control systems are located in the same room as the monochromator, leaving the dark

chamber free of all sources of light except the beam from the monochromator. The dark

chamber is lined with black felt to absorb stray radiation.

A. Light Sources

The light source ordinarily used with the Instrument for the spectral range 400 to 800

nanometers is a tungsten lamp with a 14 mn long by 2 mm wide ribbon filament (GE Microscope

Illuminator, TIO bulb, SR-8 filament, 6V, ISA [1]). The tungsten lamp is powered by a regulated supply operated in the constant voltage control mode. This lamp operates in the

temperature range of 2100 K to 2900 K. Other sources such as deuterium lamps or xenon arcs can be substituted for operation in the ultraviolet and visible spectral ranges. A heliumneon laser is used to align the optical components in the system. The source and the optical

system used to direct the radiation into the monochromator are enclosed in a cover to reduce

air currents which can affect the stability of the source.

B. Source Optics

Associated with the light source is an optical bench on which are located mirrors for

introducing the radiation into the predisperser and monochromator. The light from the

tungsten source is collected and collimated by a 52 mm diameter, 15° off-axis parabolic

mirror, having a focal length of 178 mm. The collimated beam of radiation is directed to a flat mirror near the end of the optical bench. The beam is directed by the flat mirror to

a second 15° off-axis parabolic mirror which in turn focuses an image of the source on the

entrance aperture of the predisperser. The use of mirrors rather than lenses in the system

reduces interreflections, improves throughput of radiation in the UV and IR spectral ranges,

and eliminates wavelength dependent focusing. The mirrors have been coated with MgF2 in

order to maintain their reflectance to greater than 80% down to 180 nm wavelength. The offaxis parabolic mirrors are mounted in micrometer controlled angular orientation devices which

are in turn mounted on micrometer cross fed slides for ease of alignment. Polarizers can be

inserted into the collimated beam for controlling the intensity of the light or its plane of

polarization. The polarizers are mounted in stepping motor driven rotators for independent

programmable rotation of each polarizer in the beam.

The two off-axis parabolic mirrors used in the source optics along with a third off-

- axis parabolic mirror located at the exit slit of the monochromator were specially made for

this instrument. They were tested [3] at 15° off-axis with a shearing interferometer at

wavelength 577 nm. Collimated light with wavefront deviations no greater than 1/20 wavelength from a plane wave was incident on the parabolic mirror at an angle of 15° ± 0.25°

with respect to the test system optical axis. This arrangement simulated the application

for the mirror in which a light source at the mirror focus will produce a nearly collimated

light. These mirrors were found to be within the diffraction limited performance desired.

(In tlie strictest sense, off-axis parabolic mirrors cannot be diffraction limited because

of their inherent astigmatism and coma.) The mirror focal lengths fell within the ±2 mm

tolerances placed on them. The fringe pattern for these three mirrors and two additional

mirrors that were prepared from the same parabolic mirror are the same to within 1/10 of a fringe when comparing the superpositioned interferogram negatives.

C. Predisperstr

The predisperser is an Ebert prism instrument with a 2 iran entrance slit (McPherson

608M1 [1]). The purpose of the predisperser is to eliminate higher order wavelengths and

reduce stray light in the monochromator. It has a range of 180 nm to 2600 nm. The focal

length of the collimating and focusing mirrors is 15.2 cm with a horizontal aperture ratio

3

B-8
(A 2

UJu (T. UJ

1-

Ul o UJ

UJ o o z

REF Ul o

crX

UJ CL

L_ o

UJ Ul q:

0) oc 3 l3

U- UJ

IJ- Q. o CO e

(/) >>

l/> o

-fj io

a.o

i- +jo

(UD-O

s-o

•pu

0)

sB-9
of f/6. The predlsperser wavelength drive is synchronized with the wavelength drive of the

monochromator.

D. Monochromator

1. DtscrlPtion

The monochromator is a 1-meter Czemy-Turner system with an effective aperture of f/8.7

(McPherson 2051 [1]). Its useful wavelength range is from 200 nm to more than 30 ym with

appropriate selection of gratings. The grating presently in use is a plane grating 102 imi by 102 mm having 150 grooves per mm and is blazed at 500 nm. With this grating, the mono- chromator has a linear dispersion of 6.66 m/m.

The monochromator utilizes off-axis parabolic mirrors to collimate the beam on the

grating and to focus the dispersed beam on the exit aperture. The entrance and exit apertures

of the monochromator are located on rotational devices with four stop positions to allow

selection of apertures of 0.300 ran, 0.750 nrni, 1.500 mn, and 3.000 nm straight slits corre- sponding to bandpasses of 2 nm, 5 nm, 10 nm, and 20 nm respectively. The height of the slit

can be adjusted from zero to 10 hm. (A larger lamp filament or different source optics

would be required for 20 nm band operation.)

The wavelength setting of the monochromator 1s precise to 0.01 nm. The initial setting

of the wavelength scale in an experiment is accomplished by turning the wavelength drive by

hand and observing a vernier dial. A stepping motor is used to change the wavelength settings

during the experiment. The computer control program is designed to avoid errors due to backlash In the wavelength drive gear train, and at the end of each experiment the wavelength

scale is returned to the initial position to allow a check for mechanical slippage.

2. Calibrations and Tests

a. Wavelength calibration — For measurements in which wavelength is

critical, such as the measurement of highly chromatic color samples,

the wavelength calibration will be done using stable line emission

sources. The general procedure, which has been employed in broadband measurements made with the IBS reference spectrophotometer for

transmittance [4], is to scan the monochromator past a source line

wavelength and, at regular wavelength intervals, to take readings

proportional to the flux transmitted by the monochromator. From

these readings, the centrcid wavelength scale setting corresponding

to the line wavelength can be determined. Since no wavelengthcritical measurements have been performed to date with the instrument being described in this Technical Note, it has not been

calibrated with line sources. With the monochromator set at 10 nm bandpass, an NBS Standard

didymium glass, calibrated with 10 nm spectral width [5], was employed to check the wavelength scale. The didymium glass was placed in a pneumatically driven slider which was mounted on the

optical bench before the predisperser. The slider acconmodates one didymium glass plus a clear space, so that the spectral transmittance

of the didymium glass can be measured. The measured wavelength of

minimum transmittance are listed below with the assigned wavelengths

of minimum transmittance for the NBS Standard didymium glass.

Assigned

Wavelength

(nm)

Overall

Uncertainty

in Assigned Wavelength

(nm)

Measured

Wavelength

(nm)

441.0

475.5

528.7

585.0

684.8

743.5

±1.0

±1.0

±1.0

±1.0

±1.0

5

440.6

475.8

529.1

585.2

685.0

744.0

B-10
The differences between the measured and the assigned wavelengths

of minimum transmittance are all within the uncertainty in the

assigned values. Therefore it can be assumed from this test that

the wavelength scale is accurate at least to within ±1.0 nm.

b. Stray radiant energy — Stray radiant energy was checked by means

of two test methods. The same apertures (1.5 x 1.5 mm) were used

for these tests as are used for reflectance measurements with 10 nm bandpass

.

The first method is to measure the transmittance of glass

filters at the wavelengths for which their transmittance is low.

When the value of transmittance does not change when an additional

thickness of glass filter is palced in the light beam, then this

apparent transmittance is due to the stray radiant energy passed

by the filters at other wavelengths where their transmittance is high. The first filter check was made with two selenium orange

glasses [6] measured at 400 and 500 nm. The results are as follows:

Wavelength Transmittance of Transmittance of

(nm) One Glass Two Glasses

400 6.1 X 10-6 4.1 X 10"6

500 2.9 X 10"'+ 2.4 X lO-"*

Since the transmittance of one filter is approximately 0.9 at wavelengths above 600 nm and nearly zero below 550 nm it follows

that with the monochromator set at 400 nm the total stray radiant

energy at wavelengths above 600 nm contributes 5 x lO"^ of the

detector output due to the total incident radiation. With the

wavelength set at 500 nm, the contribution to the detector output

by radiation at wavelengths above 600 nm is 3 x 10"'*.

The second filter check was made with four cobalt blue

filters [6]. The transmittance measured for three and four

filters was found to be:

Wavelength Transmittance of Transmittance of

(nm) Three Glasses Four Glasses

600 4.6 X 10"5 4,6 X 10"5

Each of these filters transmits approximately 0.8 in the wavelength

region from 350 nm to 450 nm and approximately 0.9 above 700 nm. The total stray radiant energy in those wavelength ranges contributes approximately 1 x 10"'* of the detector output due to the total

incident radiation.

The second type of stray radiation test made use of a heliumneon laser (632.8 nm) as the source of input radiation. Readings

of the detector output were made at various wavelength settings

of the monochromator. The normalized detector outputs were as follows:

Wavelength Setting

(nm)

Normal ized

Detector Output

400

500

600

632.8

650

700

750

0.5 X 10"6

3.0 X 10"6

84.0 X 10"6

1 (peak)

84.0 X 10"6

16.0 X 10"6

1.0 X 10"6

B-11
If it Is assumed that a similar performance would occur for incident monochromatic radiation at all other wavelengths, one can calculate that roughly 4 x io"5 of the radiation passed by the

monochromator will be at wavelengths outside the nominal passband.

This is in order of magnitude agreement with the values observed

with filter glasses.

E. Exit Slit Optics

The exit slit of the monochromator is attached to a light tight diaphragm in a wall so that the emerging radiation enters a 3 by 3 meter dark chamber. A unique feature of the

instrument is an optical system located at the exit aperture of the monochromator which is

designed to collimate the beam, switch the beam from one of two paths to the other, and

provide for directing the beams to the positions required for the various experimental apparatus in the dark chamber. This system is located in the dark chamber, but is supported

by a rigid extension of the frame supporting the monochromator surface plate so that its

optical alignment remains stable with respect to the monochromator. It is illustrated in

figures 2 and 3. (See also appendix G.)

The entire system can be positioned vertically and horizontally by three precision

screw driven slides to facilitate its alignment with respect to the monochromator exit slit.

The key optical component in this system is a 15° off-axis parabolic mirror 52 mm In diameter.

The exit aperture of the monochromator is located near the focal point of the parabola. The

parabolis mirror is mounted on a pneumatic device which can rotate the mirror 180° clockwise

or counterclockwise In approximately 1/4' second. This enables the collimated beam to be

switched from one path to the otier. This rotation assembly Is mounted on a precision slide

for Independent vertical alignment. Located just above and below the exit aperture are sets

of two flat mirrors that Intercept the collimated beam from the parabolic mirror. Each flat

mirror closest to the parabolic mirror 1s adjusted to direct the beam to a second flat mirror,

located directly above it. The second flat mirror Is mounted on precision slides which

provide for up and down displacement of the beams. A rotation adjustment about a horizontal

axis on each of these mirrors allows for setting the up and down angular direction of each

beam. In addition, three spring washer loaded screws are provided for horizontal alignment

of the beam. The emerging beam is approximately 10 mm wide for a 10-nm bandpass and the

height is adjustable at the monochromator exit slit.

The accurate 180° rotation of the parabolic mirror is assured by means of a gravity

dependent system In which a steel ball on the end of an arm attached to the mirror mounting

disk Is caused to fall against a stop when the pneumatic piston Is triggered to rotate the

mirror. When the steel ball is at rest on one stop the beam Is directed to the upper mirror;

when It Is at rest on the second stop, the beam is directed to the lower mirrors. The piston

Intercepts an arm attached to the axis on which the mirror rotates and lifts the steel ball,

flipping the ball over the center of gravity, at which point, gravity causes it to come to rest on the stop. The action of the piston is reversible and it Is operated by the experiment

control system.

All the mirrors in the exit aperture optics. Including the off-axis parabolic mirror are made of Cer-V1t [1] glass having negligible thermal expansion. These mirrors are mounted on invar steel to further reduce mirror distortion due to variation In thermal expansion between

the mirror and its mounting.

Also Incorporated in the exit aperture system is a shutter consisting of two light traps,

attached to the shaft of a pneumatic piston, which can be adjusted to intercept the beam as it leaves the exit aperture mirror system by either path. This shutter, which is used to trap

the beam when making background signal measurements, can be moved In and out of the beam by

actuating the piston through the experiment control system.

III. MEASUREMEhfT ACCESSORY SYSTEMS

Because of the modular design of the Instrument, the optical system as it exists beyond

the exit aperture optics depends upon the measurement being made. For each type of measurement, there is a measurement accessory system which may incorporate sample mounts, radiation

gathering devices, and detectors. These are mounted on a platform which can be positioned

7

3-12
Figure 3. Exit aperture optics and beam switch.

B-13
vertically with a lift table and horizontally In both directions by means of ball bushing

slides. Stepping motors can be attached to provide automated horizontal positioning as required. In the following sections, several of the measurement accessory systems are described as they now exist or as they are proposed.

A. 6«ngral Purpost Integrating Sph<r<8

1. Description

Two integrating spheres which are used for measuring directional -hemispherical reflectance are shown in figures 4 and 5. The two spheres are the same except for a variation in

the angle at which the beam is incident upon the sample. In one sphere the beam is incident

on the sample nonnal to its surface so that the surface reflection from a high gloss sample

returns along the same path in which it entered the sphere and is excluded from the measurement. The other sphere includes most of the surface reflection because the beam is incident

on the sample at 6° from normal.

The spheres are approximately 30 cm in diameter. The sample and reference beams enter

through the same port, thus reducing the number of openings in the sphere to three: the

entrance port, which is 38 mm in diameter; the sample port, which is 50.8 mm; and the

detector port, which is approximately 48 mm. The spheres are constructed of two aluminum

hemispheres with a white coating of a tetraf1 uroethyl ene powder [7,8] called Halon [1].

This coating is applied so as to completely eliminate the seam between the hemispheres, when

they are assembled.

The two spheres are mounted '.ogether on a pier designed to allow measurements to be

made with the specular component included or excluded by rotating either sphere into the

position where the sample and reference beams are directed to enter the sphere. The support

pier is designed with interchangeable sphere yokes that allow the system to measure samples

by mounting them on the sample port in the vertical or horizontal plane. The provision for

horizontal mounting of the specimen is to allow for measuring loose powders and liquids.

An additional mirror is required to direct the sample and reference beams to the horizontally

mounted samples.

The sample port is designed so that the sample surface to be measured is slightly

inside the tangent to the curvature of the internal surface of the sphere. The edge of the

sample port is only approximately 0.6 tm thick where the inside curvature of the sphere

meets the plane of the sample to allow as much of the diffusely reflected radiation as possible to be included in the measurement. The sample beam illuminates an area of the

sample approximately 10 mm by 18 mm in the center of the 50.8 mm diameter port. This allows

for the complete return of the reflected signal from within most nearly opaque samples without losses caused by the port edge being too close to the area of illumination.

The relationship of the detector port to the entrance and sample ports is shown in

figure 6. The detector port is located 90° from the other ports. Direct reflections from

the sample port to the detector are prevented by a collar at the detector port. This collar

is coated inside and out with the same white material as the sphere wall. A pneumatically

operated shutter is located between the white lined collar and the photocathode surface to protect the detector when the room lights are turned on.

The reference beam strikes an area of the sphere near the sample port. The coating

on this area is slightly built up so that direct reflection of radiation from this spot to the sample port is prevented. This is required to reduce a slight non-linearity as described in Appendix A.

2. Definition of the Measurement

These accessory spheres are used to determine the ratio of the spectral directional

hemispherical reflectances and py of two flat diffusely reflecting samples x and y. The

spectral directional-hemispherical reflectance can be defined generally as

(1)

9

B-14
B-15
u

B-16
UJ

ocUJX

Q.

CO

UJOz

iSo

UJ

-I

u. o

UJ z

"5

UJ

(O o 3 UJ

U. I- o

liJ

bJ

_l3

0)

Q 2 I I < S q: z u ^ o P ^ I (!) U. ffl w o

Q.

S-o+Jo

0)

+-> 0) o

s0)oc

<o

!-> O

CD

<U

B-17
where Sx(P.U;p,u,x) , the generalized scattering function for sample x, is the radiance

emerging in a di recti oij u from point p on the sample surface resulting from a unit flux

incident in direction U at point P on the sample. These spheres are to be used only for

non-fluorescing samples for which Sx is a function only of one wavelength x. The integral

of the reflected radiance is taken with respect to area a over the entire sample surface

and with respect to solid angle oi over the entire hemisphere of directions of emergence.

(A complete discussion of this approach to defining measurements appears in an earlier

Technical Note. [9])

The measurement which is actually made involves the ratio Qx of two signals, Nx which

is obtained from the detector when the incident radiation falls on sample x, and which

is obtained when the incident radiation falls on the sphere wall.

In terms of the defining notation of reference [9],

mL S U'dXdnu'dadojdX

^ ^ (3)

dAdfiu*dadu)dX

where Lg = Ls(U,P,x) is the radiance in the sample beam at wavelength x which strikes the

sample at point ? in direction IJ, Lw is a simi^lar expression for the radiance in the

reference beam striking the sphere wall, Rsx(p.u,x) is a function describing the instrument's

response to the radiation reflected from the sample, and Ry^x ""S a similar expression for the

instrument's response to reference beam radiation reflected from the sphere wall. Note that

since the sample x is part of the sphere wall, both Rgx and R^x depend upon the reflectance

of the sample. The measurement assumption is that

P Q

^x ^x

The extent to which the approximation in eq. (4) approaches true equality depends upon a number of factors, some of which will be discussed later in part III. A. 4. In some cases, corrections for Qy/Qx can be determined which will cause the approximation in eq. (4) to be more reliably near equality. These corrected expressions are given in eqs. (8) and (9).

3. Reflectance Measurement Procedure

Measurements of spectral reflectance are made with these spheres by comparing first,

the reflected signal from the sample to the reference beam signal, and then making the same comparison with a reflectance standard in place of the sample.

With the measuring sphere in position and sample x in the sample port, the relative

directional -hemispherical reflectance of sample x to the sphere wall is ordinarily determined by the following procedure. The data are recorded for Z, N^. Ny/, N^, Z and corresponding time ti, t2, t3, t^, ts where is the detector output signal when the sample

beam strikes x; Nw is the signal when the reference beam strikes the sphere wall; and Z is

the dark current reading taken with the background shutters blocking both beams. The

measurement sequence above is repeated two more times. Since the parabolic mirror and the

shutter in the exit slit optical system are controlled remotely, this sequence of measurements is achieved easily. For each signal, the count from the current-to-frequency converter

is integrated over a ten second interval. A waiting period of 10 seconds is allowed after

changing the light level before the count is measured in order to allow any effects of

electrical transients to subside. A computer program was written to reduce the data in the

following manner. If the detection system is found to be non-linear as described in part

III. A. 4. a, the values of Nx and Nw are corrected accordingly. The signals of Z and Nj^ are

then linearly interpolated with respect to time to obtain a value for each at time t^. The

13

B-13
relative reflectance of the sample x is then computed

N;(t3) - Z(t3)

Q„ = (5)

^ N;(t3) - Z(t3)

The same computing procedure is repeated for the other two measurements. The average

of the three relative reflectance Q^, is computed and the standard error is determined.

= (1/3) EQ^ (6)

For highly reflecting sample, a typical value for a is found to be 2 x lO"** and is less for

a sample with low reflectance. This has been verified by repeated measurements. The values

for Qx are used in eq. (4) to calculate the measured ratio of reflectances pJp^-

4. Evaluation

a. Detector linearity

The linearity of the detector and electronic system was determined by using the lightaddition method with a double-aperture apparatus [4,10], that is, the output of the detector

system when irradiated by two light beams simultaneously is compared to the sum of the outputs obtained when the detector is irradiated by each light beam separately. Measurements

were also made of the signal as a function of time. Two typical cases are shown in figure 7. In both cases, the drift was approximately linear in time over a 30 minute time interval

which is sufficient for the requirements of the linearity test. (The slope of the drift-intime curve was not always negative.)

The non-linearity is less than 0.01 percent of the full-scale reading. The results are presented below together with the standard deviation of the non-linearity determination.

% AN SD(aN)

0.1 6.5 X 10"5 1.2 X 10"5

0.2 9.3 X 10"5 2.1 X 10"5

0.3 9.4 X 10"5 2.9 X 10"5

0.4 7.5 X 10"5 3.7 X 10"5

0.5 4.5 X 10"5 4.5 X 10"5

0.6 1.1 X 10"5 5.0 X 10"5

0.7 1.9 X 10"5 5.0 X 10"5

0.8 3.6 X 10"5 4.3 X 10"5

0.9 3.2 X 10"5 2.7 X 10"5

1 0 0

Nm = the measured signal normalized to 1 at a photomultiplier current of 3 x lO"'^ A. aN = the amount of the linearity correction on the same scale required to make N proportional to the flux striking the detector. N = Nm + AN. SD(aN) = the standard deviation of AN.

B-19
TIME (MINUTES)

Figure 7. System drift as a function of time.

15

B-20
b. Samp I G- induced nonlinearity

The magnitude of the responses Rgx ^nd R^jx in eq. (3) must have the same dependence

on Sx if eq. (4) is to approach equality. The departure from this ideal condition will be

called sample-induced nonlinearity, and some of its causes are discussed in appendix A. The

general purpose measuring sphere with 6° incident angle (specular component included) was tested for sample-induced nonlinearity as described in appendix B. In this appendix, eq. (4) as modified to take sample-induced nonlinearity into account takes on the form:

P Q'

^^-^-[1 + a(Q' - Q')) (8)

^x ^x ^

where is the relative reflectance of the sample x as measured and a is a correction

coefficient. (See final paragraph of appendix B.)

The initial measurements were made with no baffle between the sample port and the point

at which the reference beam strikes the wall. In this case, the experimentally determined

value of ct was found to be -0.0076. In appendix E, it is shown that the value of the con- tribution to a caused by the sample's being flat is -0.0077. This suggests that the contribution to a due to other causes such as retrorefl ectance of the sphere wall was either

negligible or not detected by the test. When a baffle was introduced between the sample and

the incident point for the reference beam, the experimentally determined value of a was found

to be 0.002. In this case, the nonlinearity caused by the sample's being flat should have

been eliminated, but reflections from the baffle are estimated to contribute .001 to a. The

difference between the estimated and measured values of a may be due to the approximate nature

of the theory involved in estimating the nonlinearity caused by the baffle reflection or there

may be another contributing factor to sample-induced nonlinearity which has not been taken

into account. Since there is no reason at present to doubt the results of the nonlinearity

test, and since independent tests of the wall retroreflectance have indicated that its con- tribution to a is an order of magnitude smaller than that of reflections from the baffle,

the results of the test will be assumed correct and ratios of reflectance values will be

determined using 0.002 for a in eq. (8).

c. Polarization effects

The detection system was tested for sensitivity to polarization of the reflected

radiation and was found to be independent of polarization to within the measurement uncer- tainty of 0.05%. These tests are described in appendix D. The ratio of the signal for source radiation polarized with the electric vector parallel to the monochromator plane

to the signal for the same amount of source radiation polarized perpendicular to the

monochromator plane was 1.4 at 450 nm and 1.6 at 700 nm. This indicates that the monochromator partially polarizes the radiation it transmits, as would be expected in a grating

instrument.

d. Anfiular dependence of response

The response Rgx depends upon the direction of emergence u of radiation reflected from

the sample. The closer Rsx is to being constant, the more eq. (4) can be relied upon to approach equality. In the general purpose measuring spheres, there are two main departures

from constant Rsx- The first of these is that Rgx is zero within the solid angle subtended

at the sample by the entrance port. The second results from the structure of the sample port.

In order to taper the sphere wall to the sample port, the portion of the sphere wall bounding

the sample port is made of aluminum painted white, rather than being Halon.[l] Therefore,

the response in the solid angle subtended by this ring is lower thaa the response of other

directions by the ratio of the reflectance pp of the paint to the reflectance ph of the Hal on, both reflectances being for grazing incidence.

If both Sx and Sy depend upon u in the same way, no error will be introduced by the

nonuniformit^ of Rgv- However, if this is not the case, the detailed dependence of both Sx

and Sy upon u must be used to calculate the error for a given pair of samples. In such a case, a more reliable approximation than eq. (4) to the reflectance ratio could be written as

B-21
(9)

where

U'dadu (10)

P

where the integral with respect to solid angle u is taken only over the solid angle subtended

at the sample by the entrance port, and

where the integral with respect to solid angle oj is taken over the solid angle subtended at the sample by the painted ring surrounding the sample port. The projected solid angle subtended at the sample by the entrance port is .013 sr, the projected solid angle subtended

by the painted ring is .055 sr, and the ratio Pn/PH ^'^ approximately .85 for these measuring

spheres. A discussion of some common causes for measurement errors of this type is given

in appendix F and ways to estimate values for ep and are given for each cause. The

magnitude of ep and is usually quite small, except when samples of different surface

textures are compared using the 0° incidence sphere, in which case ep can be quite large.

For this reason the 6° incidence sphere will usually be used for directional-hemispherical

measurements with this instrument.

The general purpose measuring sphere with 6° incident angle (specular component included)

was tested for sample plane to port plane distance effect on the relative reflectance measurement. A BaS0i+ sample was measured from 400 nm to 750 nm with four sample locations: the

sample plane 0.9 mm into the measuring sphere from the normal location, at the normal location,

and 0.9 mm and 1.8 mn out of the measuring sphere from its normal location. The differences

of the relative reflectance from that in the normal position were 0.0009, 0, -0.0019, and

-0.0054 respectively. Since the sample surface can be prepared and mounted within 0.1 mm

to the port, the uncertainty in the relative reflectance measurement will be less than

0.0002.

B. Integrating Sphere for Measuring Relative Directiona l-HemisPherical Reflectance as a Function of Angle of Incidence

1. Description

The integrating sphere used in the measurement of relative directional-hemispherical

reflectance as a function of angle of incidence is illustrated in figure 8. This 45 cm diameter sphere is mounted on a kinematic support system for ease of alignment when this

device is to be used with the spectrophotometer system. The sphere is designed so that a sample can be suspended in the center of the sphere where it intercepts the sample beam.

The sample surface is at the sphere center and the sample can be rotated 360° about the

sphere center by means of a stepping motor controlled turntable at the top of the sphere.

The turntable and the support rod on which the sample is mounted can be removed as a unit

for changing samples. The beam goes through a cylindrical lens with its focal line at the

center of the sphere and then enters the sphere through an aperture just large enough to allow its entry. A removable plug opposite the sample beam entry port, is opened to initially align the beam through the center of the sphere. To determine the correct position

of the turntable for intercepting the beam at normal to the sample, a mirror is suspended in

the center of the sphere and rotated until the beam reflects back out the entr?nce port. The

mirror is then replaced with the sample to be measured. The stepping motor is programmed to turn the sample to any desired angle of incidence in the clockwise and counterclockwise

direction.

The multiplier phototude detector is located in the bottom of the sphere. The diffuse

radiation from the sphere must pass through the side of a transparent plastic rod projecting

17

(11)

e. Sample Plane to port Plane displacement effect

B-22
B-23
Into the sphere above the detector, 1n order to be measured. The top of this rod 1s capped

by an opaque white coating and the lower portion of the rod Is enclosed In the same white

material as the sphere coating. These two coatings act as baffles to prevent direct reflections from the sample to the detector. The plastic rod acts as a light pipe In transmitting

the signal to the detector and also acts as a rotatlonally symmetric support for the upper

baffle. A shutter is provided to protect the detector when the room lights are turned on. The sphere coating Is tetrafluorethylene powder, which completely seals the seam where the

two hemispheres are joined during assembly.

2. Measurement Procedure

With the sample mounted In the center of the sphere and with only the sample beam in use the relative directional-hemispherical reflectance of the sample at angle of incidence

of 9 to that at normal Incidence was determined using the following procedure. We choose to record data in the order of Z, Nq, N+g, N.q, N.g, N+q, Nq, Z and corresponding times ti, t2.

ta, ti», tg, tjt te, tg. The time which occurred about half way between two N.g's was also

recorded as ts. Nq is the signal at normal incidence; N+q and N.q are signals with angle of

incidence of e at opposite sides of the normal; and Z is the dark current reading. A com- puter program was written to analyze the data in the following manner. The signals of Z,

No, N+p, and N.g are first linearly interpolated in time to obtain a value for each at time

ts. Tne ratio Qq of the uncorrected relative directional hemispherical reflectance of the

sample at angle of incidence of e to that at normal incidence is then confuted as

Qg/h [N+fl(t5) - Z(t5)] + [N (tg) - Z(t5)]

%'7r^=— (12)

^ %/h 2CNo(t5) - Z(t5)]

The procedure above is carried out for polarizations parallel and perpendicular to the plane

of Incidence and the results are averaged.

Computer programs for the control system have been written which scan the wavelength to obtain the spectral relative directional -hemispherical reflectance of the sample at one angl

of incidence and which scan the angle of incidence at any desired interval at a fixed wavelength to obtain the goniometric relative directional-hemispherical reflectance of the sampl

at one wavelength.

3. The Entrance Port Correction

Some of the radiation reflected from the sample is lost out the entrance port. The

amount of radiation lost depends upon the angle of incidence because of the cosine law and

it may be affected further by non-Lambertian angular distribution of the reflected radiance.

To make the principal correction for this, we assume that the sample is a Lambertian reflector. The fraction, f, of the reflected flux which escapes through the entrance port from

the sample when it is at normal incidence is

A/R^

(13)

where A is the effective non-reflecting area of the entrance port, R is the inner radius of

the integrating sphere, and ir is the projected solid angle of the entire hemisphere. For other angles of incidence e, the fraction of the reflected flux which escapes through the

entrance port from the sample is f cose.

The ratio Qq, can be expressed by the true directional-hemispherical reflectance pq^^

at angle e and pg/h at normal as

Solving for the ratio of p^^^ to p^^^ , we have

19

B-24
I - fcose (15)

C. Auxiliary Spheres for Determination of the Absolute Reflectance Scale

The general purpose integrating sphere illustrated in figure 5, is equipped with a sampl.e flange for mounting an auxiliary sphere as shown in figure 9. The theory of the use of this type of sphere to determine the absolute reflectance of a material has been described in earlier papers [10,11]. Three of these auxiliary spheres have been constructed

having diameters of 30 cm, 20 cm, and 15 cm. The sphere illustrated in figure 9 is the

30 cm diameter auxiliary sphere, which is the same diameter as the detector sphere. These

spheres are used to determine the absolute reflectance of white coatings applied to the

auxiliary sphere. They have removable target plates that can be attached directly to the

detector sphere. These spheres have entrance apertures 2.54 cm in diameter and the removable

target is a section of the. sphere of 5.08 cm diameter. The spheres are designed to allow

the inside curvature of the white coating to meet the center of the entrance port. The

edge of the entrance port is beveled about 30° on the side facing the detector sphere, thus

providing a clean knife edge for the port. The sample beam enters the auxiliary sphere and

is incident on the target at 6° from normal to allow any specular component to be included

in the integration of the signal in this sphere. The coatings are applied to the two hemispheres which can be attached to each other so as to completely seal the seam between

the hemispheres.

Details of the use of these auxiliary spheres to determine directional-hemispherical

reflectance factor are to be given in a separate publication.

D. Bidirectional Diffuse Reflectance and Transmittance Factor Accessory System

A system has been constructed for utilizing the diffuse reflectance spectrophotometer

in measuring bidirectional reflectance factor, particularly for 45°-0°. With this accessory

set up for 45°-0° as shown in figure 10, the colli mated sample beam from the spectrophotometer

is incident on a sample at 45° from normal and the reflected signal at normal to the sample

is collected and measured. The multiplier phototube detector is equipped with a signal

averaging sphere. The detector and averaging sphere are attached to a stepping motor con- trolled vertical slide for alignment and scanning purposes. The averaging sphere has a limiting aperture facing the sample. The solid angle of collection is determined by the

size of the limiting aperture and its distance from the sample. In this system the sample

is mounted on a stepping motor controlled turntable, and the detector assembly is on an arm attached to another independently controlled turntable having the same axis of rotation as the sample turntable.

The sample is mounted on a two position slide that moves 12.5 cm between positions and

is pneumatically driven. In one position the sample intercepts the beam, in the second

position a polished black glass standard intercepts the beam. The polished black glass is

mounted so that it intercepts the beam at 22.5° from its normal and the specular reflection,

amounting to approximately 4%, is reflected into the detector averaging sphere. This black

glass acts as a standard reflector. It has a specular signal level of about 40 times the

magnitude of the diffuse signals that will be measured. Alignment is accomplished with the

alignment laser built into the spectrophotometer. The stepping motors are controlled by

computer to allow for scanning the detector position or changing the incident angle on the

sample or viewing angle from the sample. This device has not been tested at the date of

this publication.

IV. SUMMARY

Because of the modular nature of this instrument, it will probably never be completed

in the sense that no more accessories will be constructed. Therefore it was decided to publish this technical note to document the development and testing of the NBS Reference

Spectrophotometer for Diffuse Transmittance and Reflectance from its inception to the

present (May 1976). The principal use of the instrument to date has been to investigate

problems connected with realizing a scale of directional -hemispherical reflectance factor.

The results of this investigation are to be published separately.

B-25
21

B-26

At
B-27
APPENDIX A

SaniPle-Induced Non linearity

The type of nonlinearity to be discussed here is not the result of detector or electronic nonlinearity, but is the result of slight differences in the efficiency with which

the radiation reflected from the sample and the radiation from the reference beam, reflected

from the wall, reaches the detector. Since the sample when presented at the sample port

becomes part of the sphere wall, it affects the efficiency of the sphere in transmitting

the radiation from the initial reflection of the sample beam or of the reference beam to the

detector. In an ideal situation in which the sample is curved to fit the contour of the

sphere wall and all reflections are Lambertian, the efficiency for transmitting radiation

from the initial reflection from either beam will be the same, so that

where is the relative reflectance as defined in eq. (2), (ji^ is the flux incident upon the

sample, Px is the directional-hemispherical reflectance of the sample x, <^2 is the flux

incident upon the sphere wall, and py^ is the directional-hemispherical reflectance of the

sphere wall. However, real spheres seldom operate under such ideal conditions, so that a more complex and non-linear relationship exists between and px- Because this departure

from linearity is small, it can usually be adequately represented by adding a small quadratic

term in p^ to the right side of eq. (Al).

Three cases of such nonlinearity will be discussed in the remainder of this appendix.

In each case, the following approach will be taken in the analysis. The reflected flux from

the initial reflection of each beam will be described in terms of two or more parts. The

principal part of each flux will be that part which can reasonably be expected to reach the

detector with the same efficiency from both beams. The remaining parts of the flux will be

transferred with different efficiencies and will be the cause of the non-linearity. Since

the component which receives the same treatment will be by far the largest, the contribution

of the detected flux from each reflection of the other fluxes can be written in terms of a rapidly converging geometric series. The sum of such a series can be evaluated and even- tually written in an approximate simple quadratic form.

1. Wall Retro-Ref lectance NonI inearity

If the sphere wall coating retro-reflects , a simple model of the reflection from the

sphere wall is one in which a fraction fo of the incident radiation is returned in precisely

the opposite direction to the direction of incidence and the remaining fraction (1-fo) is reflected diffusely with a Lambertian distribution and will be transmitted to the detector

through the sphere with an efficiency nx* The retroreflected portion will be returned to the sample, where it will again be reflected with a reflectance p^. (In discussing the

reflectance from the sample, the sample will be treated as being non-retroreflecting, since

the initial retroreflective component, if any, will be lost out the entrance port and the

remaining contribution will produce only a small change in an already small correction term.)

Thus, the signal* from the first reflection from the sphere wall will be:

where is the flux in the beam of radiation incident on the sample. Let f be the fraction

of the reflected radiation which strikes the sphere wall as opposed, for example, to going

out the ports. It is assumed here that the sphere contains a baffle which prevents radiation

reflected from the sample from going directly to the detector. The retroreflected fraction

*In these appendices, the signal being discussed is the signal above background. In terms

of the notation in section III. A. 2, N^^ = - Z where is corrected for any detection

system nonlinearity.

B-28
returns to the sample and is reflected again. Of the re-reflected radiation, a fraction

(1-fn) makes a second contribution to the signal;

\2 = h'xW^^' - V \- (A3)

where Px is the reflectance of the sample for (hemispherical ly incident radiation. Similar

expressions can be written for the remaining contributions. The contributions form a geometric series in which the initial term is N^i and the ratio of successive terms is the

factor in brackets in eq. (A3). The entire signal is, then, the sum of the series, or:

N

= _0 _0 X

1 - Vx^'

When the signal from the reference beam is treated in the_same way, a simila^r expression,

in which is replaced by py^, (t)j is replaced by ^""^ Px replaced by p^^ will result.

The ratio of these two signals will be Q^, so that

5i = ^¥i^ W

where

= (1 - G^pJ

and

and terms in higher powers of G2Px have been dropped. It can be seen th^at (A5) has the

form of (Al) with a corrective term which depends upon the reflectance py of the sample.

In reality, the retro- reflected radiation is not returned from the wall in exactly the

direction it arrives, but is spread out typically in a distribution with a half-height

width of a degree or two. However, in the usual case in which the initial radiation is

reflected from the center of the sample, most of the retroreflected radiation is returned

to some point on the sample, so that fg probably represents most of the radiation in the

retro reflective peak along with a less easily defined contribution (either positive or negative) due to the fact that the level of the underlying diffuse radiation in the retro

direction may be above or below the average of the distribution. Because of this difficulty

in defining fg precisely, it is best evaluated using experiments such as are described

in appendix B.

2. Flat-Sample Non linearity

As is indicated in the literature [12], if the sample is flat, the comparison between

sample and reference may not be exact. The nonlinearity in this case arises because the

sample does not reflect directly onto itself, whereas if the sphere design is such that the

reference beam strikes the sphere at a point on the curved wall, some of the radiation from

the first reflection does strike the sample. The signal due to the radiation reflected from

the sample is given by

= *iP^n, (A5)

where nx is the average efficiency of transfer to the detector for radiation striking the

sphere wall anywhere outside the sample port. If the sample port receives a fraction fj of

the radiation from the initial reflection of the reference beam, the signal from the

reference beam is given approximately by

B-29
\ ' ^Z-'wCd - fj) * V;] (A7)

where pi 1s the reflectance of the sample for radiation incident on it from the direction of the point

of incidence of the reference beam. In this case, the ratio becomes

where

and

Aj = 1/(1 - fj)

= -fj/(l - fj)

Note that in this case, the nonlinearity term is of the opposite sign from the retroreflecti ve term so that the two contributions will tend to cancel.

3. Baffle-Induced Monlinearlty

In principle, the flat-sample nonlinearity just discussed can be avoided by placing the sample port

and the surface struck by the reference beam in the same plane in the way that was done by Hardy [13].

However, this distorts the sphere considerably, so we chose to reduce the flat sample nonlinearity by

introducing a small baffle between the sample port and the point of incidence of the reference beam. A sphere with baffle is shown in cross section in figure 11. Because of the presence of the baffle, the analysis becomes quite complex and depends upon the design of the baffle and the choice of the point of

incidence of the reference beam. This analysis will be carried out in detail in appendix E to evaluate

the specific sphere design we used. However, the procedure for carrying out the analysis and the nature

of the results can be discussed in general. The reflecting areas in the sphere are divided up into six

regions: region 1, the sample port; region 2, the portion of the sphere wall struck directly by the radiation reflected from the sample but not struck by the radiation reflected directly from the area irradiated by the reference beam; region 3, the side of the baffle toward the sample port; region 4, the

side of the baffle away from the sample port; region 5, the portion of the sphere wall which is struck

by the radiation from the Initial reflection of the reference beam, but which is not struck by radiation

reflected from the sample; and region 6, the remaining portion of the sphere. In a good sphere design

of this type, region 6 is by far the largest region and it contains the detector port. In the analysis,

once the radiation reaches region 6, it is assumed to be transferred to the detector with an efficiency

Hx which is independent of the beam from which the radiation originated.

Although the solution of the problem of the transfer of the radiation from the point of incidence

of the sample beam to region 6 is difficult, the form of the result can be anticipated.

\ - h^^^ ''^x

where a^ and b^^ are independent of the sample and depend only on the sphere geometry and the wall and

baffle reflectances. The constant a^ is nearly 1 and represents the portion of the radiation which

reaches region 6 without additional reflections from the sample, bx represents the portion of the radiation which is reflected again by the sample before reaching region 6, and is the effective

reflectance of the sample for irradiation from regions 2, 3 and 5. A similar expression can be written

for the reference beam ^ = 2''w(^w * w \ (^1°)

where i^, also nearly 1, represents the portion of the radiation transferred to region 6 without

renecting from the sample and b^^ represents the portion reaching region 6 by reflecting from the

sample. The signal ratio Qi takes the same form as in eq. (A8), except in this case

and

(All)

25

B-30
o> c C 4) C O •«-> c

f—

I/)

"T— E

(U 10 • o

10

V o.

I- <U E

0) (/) • V o) r— 0) ^

<0 E

•r- « >, 5 I— (o 2!T

91 <U lA j: 4-> •!- Q. (O

«/) E ^o

0) I— •!- ^ r- x:

4-> <0 2

«•- * <u O O) I—

I- «4-

C 0) 't- O jC fO

•r-

•->

W

(O 0) +J ^ J=

i= •-> 4J

S) 5

0)

O

t. Q.

Q. 3 —

(U

—

I. 4J te

•tS 3 0)

•»-> O) c O -D O

•I- OJ Q.

UJ o

I- a.

UJo

B-31
Because of the baffle's shielding effect, bx > by, so that in this case Gj is positive and the baffleinduced nonlinearity tends to be of the same sign as the wall retro- reflectance nonlinearity.

4. Combinations of Sample-Induced Non linearities

If the sample-induced nonlinearities are small, the wall retro-reflective nonlinearity term can simply be added to the appropriate geometrically-related nonlinearity term to yield an expression of the

form:

where Gj is given either by ea. (A8) or eq. (All), depending upon the absence or presence of a baffle,

and where G2 is given by eq. (A5). Because of the sample-induced nonlinearities, it follows that the ratio of the actual reflectances of two samples y and x can be obtained from correcting the ratio of

the corresponding measured values Qy and Qx- This correction can be determined from eq. (A12) to be:

(A12)

(A13)

27

B-32
APPENDIX B

Method of Evaluating Sample-Induced Nonlinearity

The sample- induced nonlinearity can be evaluated by using two thin masks, each of which has a hole

in it. The masks are identical in size, but one is painted black and the other is painted white. The

hole in the mask is made smaller than the sample port, but larger than the irradiated area on the sample. Two measurements are made on a given sample, one with each mask in place between the sample and the sphere port. In both of these measurements, the relative reflectance must be corrected for scattered

radiation surrounding the main incident beam as discussed in appendix C. For each measurement, the mask is aligned so that the incident beam passes through the hole. In this way, the average reflectance

of what appears in the sample port can be changed without changing the surface which is initially struck

by the incoming beam of radiation. Equation (A13) can be modified to give the measured relative reflec- tance with the white mask in place as:

where is the ratio of the area of the mask to the area of the sample port, Fo represents the fraction

of the retroreflected radiation which spills over from the irradiated area of the sample onto the mask,

during the interreflections_, is the reflectance of the_white mask at the same angle of incidence at which Px is evaluated and pa bears a similar relation to p^. (See discussion proceeding eq. (A8) and following eq. (A3) in appendix A.) It is expected that F2 will be smaller than Fp

A similar equation can be written for the black mask to obtain a relative reflectance Q^b- Taking

the ratio Q^b to Q^^ one obtains

where use is made of the assumption that << 1 and G2 << 1. Since the correction coefficients Gi and

G2 are small, there will be a large uncertainty in determining them. Therefore, the approximations used

to determine the correction term in eq. (8) will be made conservatively, i.e., in such a way as to make

the correction small in order to avoid overcorrection. The relative reflectance and Qg of the mask

materials can be measured. Since 411 ^2 ^""^ Pw — ^» these measur.ed values can be used in place of p/\ and py\ in the first term of eq. (B2j and also in place of p^ and pg in the second term of eq. (B2).

With this assumption, eq. (B2) can be written

^xB^^xA ^ 3 ^ Q - ^ (53)

Fi(Q^-Q^)

Under the same assumption, eq. (A13) can be written as

P

Q' = ^ [1 + (G, + G2)(Q' - Q')] (B4)

p Q'

1 ^ X y

^x ^x

Since F2 < Fp it follows that

hi < |Gj + (B5)

when G]^ and G2 have the same sign. Therefore, in the case of the sphere with baffle, eq. (8) provides

a conservative correction when a is determined using eq. (B3).

28

B-33
APPENDIX C

Corrsctini for Scattered Radiation in Incident 3eam

The beam of radiation incident on the sample can be considered to be made up of three fluxes: (^j, which falls inside a given central circle and contains most of the Incident radiation, which falls

between the central circle and the boundary of the sample port, and which falls outside the boundary

of the sample port. These three make up the total incident flux ^^j^, i.e.

'^xmw ^b ^c

where (j>i » and >> is the case in a good instrument. An expression for the uncorrected rela- tive reflectance QZ as read from the instrument is

where px is the reflectance of the sample in the central area, is the reflectance of the sample in the area struck by 4ih, Fi and F2 are defined after eq. (B2) and, products of two small terms are neglected, and k is AiA2/<ti2Pw- (See discussion in last paragraphs of appendix A.) One would like to correct Qy to obtain the contribution due just to the light reflected from the central area, i.e.

q; = k^jp^d . G^Cd - F^) p; . F^p;] . ^i^i - f^) p^ * f^p^]} (c3)

To make this correction, four additional measurements are made. First a value of Qx is obtained with the

sample port empty. This is called and Is given by:

Q; = k,^p„ (C4)

Second the value of QJ^ is obtained with a white card In the area struck by and the central area empty (a hole in the card). This is called Q^w and is given by:

'^cw = ^(^b-'c ' *c^w) (")

where p^ is the reflectance of the card. Third a value of QJJ is obtained with a white card of the same material filling the entire port. This is called Q^cw ''s given by:

•^ccw = "^h^c^l * Vc * Vc) * ^Vc ^ "^Vw

For measurements in which the area struck by is to be occupied by a mask of reflectance p^i a measure- ment of Qx with only the mask in place can be made. This is called and Is given by:

Q" = kf^i. p + 41 p ) (C7) ^mw ^^b^m ^c^w' ^

'

when a mask is used, a correction of the general measurement can be made as:

led with

q; =

q;; - q;^ ics)

This expression is used to obtain and Q'g in appendix B. When the entire sample port is fil the same material (p^, = Px) • one can correct QJJ to give Qx as shown in eq. (C3) by using

(Q" - Q" ) Q. = (Q" . Q") _CCW CW_

(j.gj x X w _ Q,.. ^^ccw ^w'

This expression is used when comparing a sample without mask to a sample with mask for which eq. (C8)

applies. This circumstance occurs In the use of the auxiliary sphere attachment described in III.C.

When two samples are to be con^ared, each of which fills the entire entrance port, a simpler

correction is applicable. In this case, the mask area and, therefore ^b, is considered to be zero

and the corrected relative reflectance is:

29
q; = Mjp^d + G^p; + G^p^) (CIO)

This can be obtained from the uncorrected values as:

Q' = Q" - Q" (Cll)

APPENDIX D

Test for Polarization Effects

The incident radiation can be polarized using a polarizer in the input optics as indicated in figure 2. The monochromator will not depolarize the radiation if the plane of

polarization is either perpendicular to or parallel to the plane of the monochromator. For the polarization tests, the instrument is used in a single-beam mode, and the measurements

are made in a time-symmetrical sequence to allow correction for linear drift of the source

and detector in time.

To determine whether the reflectance measurement on a sample is polarization dejiendent,

the ratio of the fluxes and i,^ with the beam in the two polarizations is determined by

using a second integrating sphere as a target. This sphere acts as a polarization insensitive target which effectively reflects depolarized radiation. The ratio of the signals,

equal to the ratio of the incident fluxes in this case, is

If a highly polarizing diffusing reflector is measured with ())/^ incident and then rotated 90"^ and measured with incident, the ratio q[j is determined.

% - ^ <°^'

where and nj_ ai^^ the sample beam efficiencies of the sphere for the given polarization.

The polarizing diffuse reflector is made by cementing an absorbing polarizing film on a piece of white opal glass and using it in the orientation for maximum reflectance of the

polarized light. If q^ and q^^ are equal, the measuring sphere is polarization independent.

Finally, the polarization dependence of a sample can be evaluated by obtaining signals

for each polarization to determine the ratio q^-.

P// ^// "t*// q = V II It (D3)

P_L <tij_

where p and Pj_ are the sample reflectances for the two polarizations with the given orientation ^of the sample. If q|-, = q^, the sample reflectance is polarization independent.

B-35
APPENDIX E

Estimation of Samp I e-Dcpendent Nonl incarity

In this appendix, an approximate evaluation of the constants Gj defined in appendix A

will be made for the general purpose integrating sphere. The measured dimensions of the

spheres will be used as a basis for the estimation. The radius of the interior wall of the

sphere is R = 14.6 cm and the sample port takes the form of a circle of radius r = 2.54 cm

on this surface.

1. Sphere Without Baffle

From elementary geometry and the assumption of Lambertian reflection from the sphere

wall, the fraction fj of the radiation reflected from the reference beam into the sample is

Thus one can evaluate for this sphere from eq. (A3) as

= 0.0077

2. Sphere With Baffle

The treatment of a sphere with a baffle is considerably more complicated and a method of

detailed flux balance will be used here to obtain an estimate of Gj as given in eq. (AH).

The flux i^jpfi, transferred from region n to region m can be obtained from evaluating an expression of the following form:

where Lp is the radiance leaving dA^, dAi is an element of area on surface i, (i = m or n),

D is the length of the line connecting dAp to dA^, and e-j is the angle between the connecting line and the normal to dA^ . In the present estimate, this expression will be approximated as

where the quantities Vp^i aif"e given by

The assumption here is that Lp is uniform at some average value over the entire region n. Except for the case when regions n and m are both on the sphere and in clear view of each

other, it is difficult to evaluate V^^ exactly. For the general purpose integrating

sphere described in section ill and pictured in figure 11, rough estimates were made of

the areas A^ of each region and the non-zero Vp^i- (A Vnm would be zero if no part of

region m is visible from region n.) The areas Ap were first determined, and then approximate Vpni not involving area 6 were obtained from the geometry of the sphere and baffle. The sum of all the V^^ involving region n must be

(El)

(E2)

(E4)

6

n (E5)

31

B-36
From which V„c is calculated as

m=l

This, with the fact that Vp^ = Vn,^, assures that the set of V^n, and are consistent, even

if only approximate. These values are presented below with the numbering of the regions the same as described in the first paragraph of part 3 in appendix A and as illustrated in

figure 11.

A„ (cm^) n

Aj = 20.3 A4 = 3.9

A2 = 299 A5 = 3.5

A3 = 3.9 Ag = 2350

steradian)

^26

=

^13 - 0-28

^16

= "45

=

= 105

V23 = 5.3 V55 ' 0.014

V25 = 0.7 ^6 = S.6

Figure 12 is a schematic illustration of the radiation transfer in the sphere. If the

radiation is considered to be detected once it reaches the "common ground", region 6, then

the fact that it is afterwards reflected and re-reflected need not be considered further and

flux balancing equations can be set up which deal with only the photons which have never

reached region 6. If L«p is the radiance Lp leaving the surface of region n when the

sample x is irradiated by the incoming beam, the following set of flux balance equations can

be set up with the aid of figure 12.

ttAA

^^2^2

rxl ^rx ^'12"x2 •I3"x3'

^12^x1 ' ^22^x2 ' h3^.3 ' "zS^.S^ %

(E7)

(E8)

^^L,3 = (Vi3L,i + V23^2)

^w

(E9)

(ElO)

(Ell)

Using the Ap and the Vpp, from the foregoing list, the radiances L^p can be determined by

simultaneous solution of these equations in terms of t^i px p^ and py^. From these, the

signal corresponding to the sample beam can be calculated as:

B-37
33

B-38
Nx = Z\e^xu - h^x\(0-9989 + 0.0011 p^) (E12)

where it has been assumed that =1. In a similar fashion the flux balance equations can

be calculated for the case in which the incoming beam of radiation strikes region 4.

'^AlLwl = (Viz^wZ Vi3L^3) (E13)

^'^zLwZ = (^12^1 + V22L^2 ' hz^v^S ' ^25^5^ "w (^1^)

^^^3^3 = (^3Lwl ^ ^23^2^ (E15)

^^L,5 = (^25^2 ^451,4 - V^^L^^) p^ (E17)

From the L^^p determined by simultaneous solution of these equations, the signal N^^ corresponding to the reference beam can be calculated as \ - \ E V.gL^ = *2Pw\(0-99997 . O.OOOOSp;) (E18)

where it has been assumed that after initial reflection p,^ = 1. Comparing eqs. (E12) and

(E18) with eqs. (A9) and (AlO) respectively, it can be determined from eq. (All) that

Aj = .9989 and = .0011 (E19)

From the crudeness of the approximations used, this value for may be in error by as much as a factor of two.

B-39
1

APPEHDIX F

Estimatlntf Error Dut to Angular DtP<nd<nc« of Response

The amount of error introduced by the entrance port and the painted ring around the

sample port as discussed in section III. A. 4. d depends upon the details of the specific

scattering functions and Sy of the san^Jles x and y being compared. However, general

cases can be treated in a way which will permit the magnitude of the errors introduced

by the entrance port and the painted ring to be estimated. The scattering function Sx

can be regarded as being the sum of two parts, Sjx which describes the Fresnel surface

reflection and Sbx which describes the body reflection due to scattering which takes place

beneath the surface. These two components are quite naturally distinguished in the case of

polished surfaces, but the choice of the separate functions becomes more arbitrary in the case of san?)les with rough surfaces. However, even a rather arbitrary division can be useful, and no first order error will be introduced as long as

1. Surface Reflection

The surface reflected component is not strongly chromatic but depends strongly on the

texture of the surface. A function representative of the commonly occurring angular dependence of Sjx is:

S^^iu) = P^^r{y)e'^^^ (F2)

where pjx is the total surface reflectanc^ at the given angle of incidence and e is the

angle between the direction of emergence u and the direction of specular reflection which

would occur if the sample were replaced by a plane mirror. The constant r(k) is a normalization constant which will be chosen so that

r{k)e"'^^^ du) = 1 (F3)

when the integral is taken over the entire hemisphere. Since this is only a generalized

model, since the angle of incidence is nearly normal, and since the response is polarization

insensitive, it was felt to be unnecessary to include the details of polarization effects

in the model for the purpose of estimating the measurement errors which are introduced by

differences between Sjx foi^ different samples. With this model for Ssx» the fraction of

the total surface reflected radiation which is lost out the port can be calculated as

where the integral is taken over the entrance port, and the fraction of the total surface

reflected radiation which strikes the painted ring is

where the integral is taken over the painted ring. The argument G is the percent of the

total surface reflected flux which falls within a 11.7** by 4.4° rectangular solid angle

centered on the specular direction. (The solid angle defining G is arbitrarily chosen the same as that in a glossmeter measuring ASTM 60° gloss [14]. Thus, for dark colored

dielectric materials, G is approximately the ASTM 60° gloss [14].) Fp(G) and Fr(6) are

35

B-40
shown in figure 13. Fr(G) is approximately the same for both of the spheres, but Fp(G)

differs markedly between the 0° and 6° incidence spheres. From the surface component of

reflection, the contribution e to e as defined in eq. (10) is

= ^ F (G ) - ^ F (G ) (F6)

From the surface component of reflection, the contribution e to e as defined in eq. (11)

IS

e,, = 0.15

sr ^ F (G ) - ^ F (G ) Py y' r^ x^ (F7)

To obtain an estimate of the magnitude of errors which can result, the case in which py < p^

will be considered. With non-metallic materials for which pgy 2i psx — -05, it follows that

the maximum possible is 1.3 x 10"'*/py, which would occur when y was perfectly diffuse

(Gy = 0.49) and Gx > 1. For the 6° incidence sphere, the largest possible value of esp is

2 X 10~2/py which would occur when a low gloss sample y for which Gy 10 is being compared

to a higher gloss sample x(Gx > 60). In either case, when py is reasonably large, a cor- rection based on using measured gloss values for Gx and Gy would reduce the errors to insignificance. On the other hand, egp can be as great as 5 x lO'^/py for the 0° incidence

sphere, and the uncertainty in egn pei^ gloss unit is approximately 5 x 10~'*/py. For this reason the 0° incidence sphere will generally be restricted to use with samples with flat

highly polished surfaces (G > 95). Since the Fp curves are almost the same for both the 0° and 6° incidence spheres only for G < 2, a very matte sample will be used to calibrate the

0° sphere measurements using a standard which has been evaluated on the 6° sphere, or a very

high gloss standard (G > 95) for which the surface reflectance pg is known will be used.

As a final observation on the effects of the distribution of the surface reflected flux

uoon measurements, a curve is shown in figure 13 giving the fractional error in measuring

Ps using a 0°/45° bidirectional reflectometer. As long as G > 5, the fractional error in

measuring pg is -1, i.e. the surface component of reflection is effectively excluded from

all measurements of samples having G > 5. Relative measurements of the reflectance of such

samples can be made in this mode with negligible effects due to surface reflection. However,

this mode of measurement will not be used with samples in the transition range 5 > G > 1,

and it should not be used for dark colored samples when G < 5.

2. Body Reflection

A second contribution to ep the reflection of samples x and y

Sbx can be described as:

and zy is due to differences between the body component of

For normal incidence, the generalized scattering function

(F8)

where the Z-j(Y) are a complete orthonormal set of functions such that

f (0; ir'j

/Z.(y) lAi) COSY sinY dY = ( J ^ ' (l; i=j

(F9)

and Y is the angle of emergence measured from the normal to the sample surface. Such a set

can be written in terms of functions resembling spherical harmonics in 2y. and since most

of the detailed structure of the total radiance distribution can be attributed to surface

reflectance, the angular variation of the body reflection can be represented in most cases

by the first three terms of eq. (F8) where

Zo(y) (FIG)

B-41
B-42
ZjCy) = ^3/7 cos2y

Z2(y) = V5/47T (3 cos^(2y) - 1)

(Fll)

(F12)

With the entrance port subtending 0.013 sr at y 1 0, one obtains E^p, the body reflection

portion of ep, from eq. (10) as

with the painted ring of reflectance 0.85 subtending 0.055 sr at y 2i '^/^t one obtains ebr»

the body reflection part of er» ^i^oi^ ^q. (11) as

The magnitude of these contributions depend upon ajx* a2x» ^'ly ^2y' which can be determined from bidirectional reflectance measurements made at the angles of viewing at which

Zi(y) and Z2(y) go to zero. If reflecting surfaces x and y have the same goniometric

distribution of reflected radiation.

llx = !l:^ and !2x.!2^

and that both ebp and e^^ will be zero. One rather common occurrence in highly absorbing

diffuse reflector's is for the body reflected radiation to be concentrated toward the surface

normal, thereby resulting in a relatively large positive Zi(y) component. Although ebp and

tend to cancel under these circumstances, the cancellation is not complete and such

measurements must be treated with special caution.

B-A3
APPENDIX 6

Focusini! tht Exit Slit Optics

Because the width (up to 3 inn) of the exit silt Is significant compared to the focal

length (178 ran) of the off-ax1s parabolic mirror In the exit slit optics. It Is not practical

to colUmate the exit beam 1n the usual sense 1n which the exit slit Is placed at the focus

of the off-ax1s parabolic mirror. If this were done, the beam of radiation would diverge

strongly* nearly doubling In Its dimensions In going from the off-axis parabolic mirror to

the experiment location. Instead, an Image of the exit sl1t Is formed at such a distance

that the dimensions of the Image and the dimensions of the illuminated area of the off-axis

parabolic mirror are approximately the same. A simplified schematic optical diagram of this

arrangement is shown in figure 14, where, for clarity the off-axis parabolic mirror is represented schematically as a lens and the beam-deflecting plane mirrors have been omitted. It can be seen from the figure that over the entire distance D, the radiation is confined to approximately a constant cross section, although the distribution of the radiation across

the cross section differs at different locations along this path. With the instrument set

for a 10 nm half-height bandpass (1.5 nin slit width) and adjusted for the conditions shown

in figure 14, the distance D is approximately 1.4 meters and the distance d is approximately

.4 meters.

The plane P in which the image of the monochromator exit mirror lies is of particular

interest. At this location, the beam cross section is sharply defined and, in the ideal case of perfect optics, the spectral irradiance is independent of location within the cross section. At the location of the image of the exit slit, the spectral irradiance distribution is shifted by one half-height bandwidth from one side of the exit slit image to the

other. For most of the experiments which are conducted with this instrument, it would be

ideal if the sample could be located in plane P. However, because of the size of the

accessory apparatus, in most of the measurements the sample is located at or just a little

beyond the image of the exit slit. For this reason, when a sample is measured for which

the uniformity of the spectral reflectance across the surface is suspect, the sample will be

measured, rotated 180°, and remeasured in order to ascertain the effect of the coupling

between the shift in spectral irradiance distribution across the beam and the non-uniformity

in sample reflectance across the beam.

39

B-44
B-45
V, REFERENCES

1. Certain conmercial materials are identified in this Technical Note in order to specify

adequately the procedure. In no case does such identification imply endorsement or evaluation by the National Bureau of Standards.

2. Popenoe, C.H. and Campbell, M.C., "MIDAS Modular Interactive Data Acquisition System -

Description and Specification", NBS Tech. Note No. 790 (August 1973).

3. Tests performed by Dr. John M. Jerke, Optics and Micrometrology Section, Optical Physics

Division, National Bureau of Standards.

4. Mielenz, K.D. and Eckerle, K.L., "Design, Construction, and Testing of a New High Accuracy

Spectrophotometer", NBS Tech. Note No. 729 (June 1972).

5. Keegan, H.J. and Gibson, K.S., "On the Use of Working Standards of Didymium and Vitrolite Glasses for Spectrophotometric Measurements", J. Opt. Soc. Am. 34 (12), 770 (1944).

6. Keegan, H.J., Schleter, J.C., and Judd, D.B., "Glass Filters for Checking Performance

of Spectrophotometer - Integrator System of Color Measurement", J. Res. NBS. 66A (3),

203 (June 1962).

7. Eckerle, K.L., Venable, W.H., Jr., and Weidner, V.R., "Averaging Sphere for Ultraviolet,

Visible, and Near Infrared Wavelengths: A Highly Effective Design:, Appl . Opt. 15 (3),

703 (March 1976).

8c, Grum, F. and Saltzman, M. , "New White Standard of Reflectance", presented at the 18th

session of CIE, London, England in September 1975.

9. Venable, William H., Jr., and Hsia, Jack J., "Optical Radiation Measurements: Describing

Spectrophotometric Measurements", NBS Tech. Note No. 594-9 (November 1974).

10. Mielenz, K.D. and Eckerle, K.L., "Spectrophotometer Linearity Testing Using the DoubleAperture Method", Appl. Opt. 11 (10), 2294 (1972).

11. Goebel , D.G., Caldwell, B.P., Hammond, H.K. Ill, "Use of an Auxiliary Sphere with a Spectroreflectometer to Obtain Absolute Reflectance", J. Opt. Soc. Am. 56^ (6), 783

(June 1966).

12. Van den Akker, J. A., Dearth, L.R. , and Shillcox, W.M., "Evaluation of Absolute Reflectance for Standardization Purposes", J. Opt. Soc. Am. 56. (2), 250 (February 1966).

13. Jacquez, J. A. and Kuppenheim, H.F., "Theory of the Integrating Sphere", J. Opt. Soc. Am. 45 (6), 460 (1955).

14. ASTM Designation: 0523-67(1972), Standard Method of Test for Specular Gloss, Annual

Book of ASTM Standards Part 27 (1974).

41

B-46
APPENDIX C

Reprinted from Applied Optics, Vol. 19, page 1268, April, 1980 Copyright © 1980 by the Optical Society of America and reprinted by permission of the copyright owner.

NBS specular reflectometer-spectrophotometer

Victor R. Weidner and Jack J. Hsia

A specular reflectometer has been constructed and tested for calibrating the reflectance of mirror standards

over the 250-2500-nm spectral range. This instrument is a measurement accessory to a reference spectro- photometer, which is also used for diffuse hemispherical spectral reflectance and 45°/0° spectral reflectance. The specular reflectometer is designed to measure mirror reflectances at angles of incidence between 5 and

80° using both vertically and horizontally polarized radiation. Absolute reflectance measurements are ob- tained by an optical system, which provides for direct measurement of the incident beam and for the sample

mirror reflectance using the same beam. This is accomplished by means of a beam tracking system through

which the beam is directed into a signal averaging sphere. The sphere rotates with the beam tracking optics, and the stationary detector views the interior of the sphere. Control of the beam tracking optical system

is accomplished by a computer-controlled stepping-motor-driven precision turntable. Uncertainties of the

reflectance measurements obtained with this system are estimated to be ±0.2% of the measured value.

I. Introduction

The increasing requirements for standard specular

reflectors, such as mirrors for reference measurements

in activities associated with the solar energy utilization program, have also increased the need for instrumentation development to provide the required standard

mirrors. The spectrophotometry group of the Radiometric Physics Division at NBS has developed a specular reflectometer for this purpose. It is designed to measure the specular reflectance of mirrors over the

250-2500-nm wavelength range. The instrument can be used to measure the specular reflectance of mirrors

at angles of incidence between ~5 and 80°. The spec- trophotometer provides a collimated beam, which can be polarized in either the vertical or horizontal plane.

The spectral bandpass is usually set at 5 or 10 nm. The specular reflectometer will be used primarily to calibrate mirrors for the NBS Standard Reference

Materials program. Several types of mirrors will be

available through the NBS Office of Standard Refer- ence Materials when work is completed on the calibration of several master standards, and this reflectance

scale can be transferred to the SRM mirrors. The

mirrors being prepared for calibration include (a) glass

substrates with either aluminum or rhodium front- surface coatings and (b) second-surface aluminum

coatings sealed between quartz. A portion of this

mirror preparation and calibration work is funded by

the Department of Energy.

Calibrating a mirror for specular reflectance as a function of wavelength, polarization, and angle of in- cidence requires many individual measurements.

These calibrations are impractical without automation.

As an example, measurement of the specular reflectance of a single mirror at fifty wavelengths, for five angles of

incidence and two polarizations requires 500 determinations. Moreover, this number is doubled if the angle

of incidence is measured to both the left and right of the

normal and then averaged. Since at each angle of in- cidence three measurements are made and other cali- bration data also have to be recorded, the total number

of data may reach 13,000 individual numbers to be ac- cumulated and processed. Even with automation it would be time-consuming and expensive to calibrate

many mirrors at this many wavelengths and angles of

incidence. For this reason most mirrors are calibrated

at near normal incidence for 50- or 100-nm intervals and

at only a few wavelengths for other angles of inci- dence.

The authors are with U.S. National Bureau of Standards, Washington, D.C. 20234. Received 29 October 1979.

II. NBS Reference Spectrophotometer

The specular reflectometer is an accessory to the NBS

reference spectrophotometer for reflectance. ^ The

monochromator, light source, and associated equipment

are located in a system control room. The exit-slit housing of the monochromator is attached to a lighttight diaphragm in a wall, which allows the exit beam

1268 APPLIED OPTICS / Vol. 19, No. 8 / 15 April 1980 C-1
or sample beam to enter a second room where the vari- ous reflectance-measuring devices, such as integrating

spheres or the specular reflectometer, are installed. The advantages of this arrangement are that the second room can be used as an experimental dark chamber,

while the electronics, light sources, 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. The beamwidth is determined by the

selected bandpass. For a 10-nm bandpass, the beam

is ~12 X 18 mm at the sample plane.

To measure spectral reflectance over the full wavelength range of the monochromator, the system employs

a xenon source for measurements in the UV spectrum,

a tungsten strip lamp for the visible spectrum, and a tungsten IR source for the IR spectrum. A photomultiplier detector is used for the UV and visible spectrum

and a lead sulfide detector for the IR spectrum. A

complete description of the spectrophotometer is given

in an earlier publication,^ with the exception of the IR

detection and signal-processing system, which was

completed at a later date.

III. Construction of the Specular Reflectometer

The concept around which the specular reflectometer

is designed allows for detecting the incident beam either

directly or after it is reflected from a mirror sample at some selected wavelength' and angle of incidence. To

accomplish this it is necessary to employ two turntables—one for positioning the sample mirror at a desired

angle of incidence with respect to the sample beam and

another for directing the reflected sample beam to reach

the detector. The instrument is illustrated in Figs. 1-3.

It is undesirable to irradiate the detector directly with

the beam to be measured because the detector area lacks

the necessary uniformity of sensitivity required for a system involving the movement of optical elements that

direct the beam to the detector. Therefore, reproducibility of the measurements is not adequate for highaccuracy determinations. Since photomultiplier detectors tend to be affected by magnetic fields, which

vary from one location to another, the instrument was

designed with the detector located in a fixed position.

To overcome the problems of detector nonuniformity,

the specular reflectometer is designed so that the sample

beam enters a 15-cm diam averaging sphere; output

variations caused by nonuniformity of the beam or by

nonuniformity of the detector sensitivity to this beam

are effectively reduced when the beam is first diffusely

mixed by multiple reflections within the averaging

sphere. The sphere coating is a fluorocarbon powder,

which is a nearly perfect diffuser of very high reflectivity

throughout the 250-2500-nm spectral range. The detector views the interior of the averaging sphere and is irradiated by the diffused flux. The incoming sample

beam is incident on the sphere wall at a location outside

the field of view of the detector to avoid direct viewing

of this bright spot on first reflection. The problem of magnetic fields affecting the detector

performance required a design for the reflectometer that

would keep the detector in a fixed position for all measurements regardless of the angle of incidence selected

for the specular-reflectance measurements. To do this a mirror was attached to an arm suspended from a turntable located above the sample turntable. This

mirror, referred to as the tracking mirror, can orbit the

sample, intercepting the reflected sample beam at any

angle of reflectance (= angle of incidence) between ~5

and 80° . The tracking mirror also intercepts the direct

beam when the sample mirror is moved out of the beam

by the slider on which it is mounted.

The tracking mirror is tilted upward at an angle of 20°

with respect to the incident beam and reflects the beam

up through a baffle tube and into the averaging sphere,

which rotates with the tracking mirror and baffle tube.

The axis of rotation of the averaging sphere is collinear

with the axis of rotation of the sample turntable. The

detector is mounted on a stationary platform above the

averaging sphere and does not rotate with the sphere.

A diaphragm allows the top of the sphere to rotate just

below the detector aperture and maintains a radiation

seal between the stationary and rotating parts. A

51-mm diam port on the top of the sphere allows the

signal to pass into the detector. A shutter between the

sphere and the detector can be opened or closed automatically or as required.

The baffle tube is attached to the averaging sphere

and extends from the 32-mm diam entrance aperture

of the sphere to near the 51-mm diam tracking mirror.

The baffle tube limits the field of view of the averaging-sphere entrance aperture to the direction of the

tracking mirror. The entrance aperture to the sphere

is the limiting aperture in the optical system.

The tracking mirror orbits the sample at a radius of

25 cm. The axis of rotation of the sample and the axis

of rotation of the tracking mirror must be collinear if the

tracking mirror is to intercept accurately the reflected

beam at all angles of incidence and reflection and

redirect the beam into the averaging sphere.

The sample-mirror turntable and tracking-mirror

turntable are driven by identical 240-tooth precision

worm gears. Two hundred steps are required to turn

the stepping-motor drive shaft through 360°. This

translates through the worm gear into 48,000 steps to

rotate the turntables 360°. The angular resolution for the turntable rotation is ~27 sec of arc/step of the

stepping motor. The problem of backlash in the gear

drive is avoided by always approaching the desired

position from the same direction. This is done through

the computer routines that control the direction of

movement in approaching the desired angular settings

for specular-reflectance measurements.

The IR measurements required the addition of a chopper at the light source, a preamplifier for the lead

sulfide detector, and a lock-in amplifier that locks in the

chopped signal and provides a suitable input to the data

processing electronics. Figure 4 is a schematic diagram

of the IR-system electronics and the signal-generation

and detection system.

The signal processing of the output from the detector

utilizes a current-to-frequency converter that can in15 April 1980 / Vol. 19, No. 8 / APPLIED OPTICS 1269
PHOTOMULTIPLIER DETECTOR -

(STATIONARY)

AVERAGING SPHERE AND

TRACKING MIRROR TURNTABLE

POSITION OF

TRACKING MIRROR

FOR INTERCEPTION OF SPECULAR SAMPLE BEAM

COLLIMATED

INCIDENT BEAM

POSITION OF

TRACKING MIRROR FOR INTERCEPTION OF INCIDENT BEAM

Fig. 1. General scheme of the NBS specular reflectometer showing the relationship of the sample turntable and beam-tracking turntable and detector systems.

TRACKING MIRROR

INTERCEPTING SAMPLE BEAM

TRACKING MIRROR

-INTERCEPTING

INCIDENT BEAM

COLLIMATED

INCIDENT BEAM

Fig. 2. Horizontal x section through the plane of the sample beam,

specular sample, and the tracking mirror that orbits the sample.

PHOTOMULTIPLIER DETECTOR

AREA VIEWED

BY DETECTOR

(BELOW DASHED LINE

COMMON AXIS OF

ROTATION FOR SAMPLE

AND TRACKING MIRROR

SHUTTER

AVERAGING -SPHERE

Fig. 3. A vertical x section through the plane of the sample beam,

specular sample, tracking mirror, averaging sphere, and detector.

1270 APPLIED OPTICS / Vol. 19, No. 8 ,' 15 April 1980 C-3
INFRARED SOURCE I 1

I OPTICAL I

LEAD SULFIDE DETECTOR

I SYSTEM I

I I CHOPPER

DETECTOR

SIGNAL

DETECTOR

BIAS

CIRCUIT

PREAMPLIFIER

LOCK-IN

AMPLIFIER

3.3MA

RESISTOR

CURRENT

TO

FREQUENCY CONVERTER

) COUNTER -) COMPUTER

Fig. 4. Schematic of the IR signal processing system for the NBS

specular reflectometer-spectrophotometer system.

tegrate the detector output over a selected time interval. The integration time may be as short as 1 sec or as long

as 9 sec. This integrated signal is accumulated on a

digital counter. The digital results in the counter are transferred to a computer for analysis. The results of

the computer analysis are stored for future reference

and printed out on a teletype printer.

IV. Alignment of the Reflectometer

Alignment of the specular reflectometer involves the

spatial relationship of three basic elements in the sys- tem. These are the sample beam, the sample, and the

tracking mirror. The sample beam is initially adjusted

so that it is in a horizontal plane and passes over the

sample turntable with the axis of rotation bisecting the

beam. The reflectometer is mounted on a lift table for convenience in selecting the desired vertical position for the instrument. This lift table rides on bearings so that

the instrument can be moved into or out of the sample

beam at right angles to the beam. When these vertical and horizontal adjustments are correct for the rela- tionship of the sample turntable with respect to the

sample beam the system is locked to prevent further

movement.

The upper portion of the specular reflectometer,

consisting of the tracking-mirror turntable and the

stationary detector platform, is independent of the

sample turntable. This assembly is supported by three

columns located at 120° intervals with respect to the

axis of rotation of the turntables. Each of these col- umns is designed to provide a kinematic alignment of

the detector and tracking-mirror assembly. The three

legs of the tracking-mirror turntable assembly rest on

the kinematic supports at the top of the three columns.

The legs are fitted with steel-ball-tipped feet that fit into the kinematic supports consisting of a flat for one

ball tip, a V-groove for the second ball tip, and a conical

cavity for the third. The ball tips of the legs are on

finely threaded bolts that screw into the legs and pro- vide a means for adjusting the height and leveling the

tracking mirror to the plane of the incident beam and

sample mirror.

The alignment procedure involves a number of adjustments of the sample mirror and tracking mirror.

These procedures involve a number of mechanical fix- tures and optical techniques that will not be described

in detail. As a final check of the overall alignment of

the reflectometer system, the baffle tube is temporarily

removed from the tracking mirror arm, and the sample

turntable and tracking mirror turntable are pro- grammed to move to several angles of incidence and

interception, respectively. At these locations the

sample beam must pass through the center of the en- trance aperture to the averaging sphere. If this condition is not satisfactorily arrived at, the alignment

procedures are rechecked and refined until they meet

the required conditions.

A laser is used to monitor the system alignment for possible trouble during continued lengthy measure- ments in which the system is being driven by computer-controlled stepping motors. The laser is fixed

to a stationary pier. The laser beam reflects off the

sample mirror and strikes a target scale, which is used

to initiate a measurement cycle. At the end of each

measurement cycle the turntables return to this position

if the stepping motors and computer have not malfunctioned and no mechanical misalignment has oc- curred. This laser alignment-checking procedure is especially useful when the measurements of specular

reflectance are being made at wavelengths where the

sample beam cannot be visually observed. However,

the initial alignment is usually made with a samplebeam wavelength of 550 nm. Should a computer malfunction occur while working at IR or UV wavelengths,

the laser is turned on, and the turntables are manually

reset to the starting angles. Any large malfunction

involving the positioning of the turntables is usually

readily detected because the sample beam under these

conditions ordinarily misses the detector system completely, a condition easily recognized in the data output.

The laser alignment check alerts the operator to small

misalignment problems that might not be apparent in the data output. The laser is used primarily to check

the sample-turntable alignment. The tracking-mirror

starting point can be accurately set by a scale mark on

the 60-cm diam track and a similar scale mark on the

tracking-mirror holder, which moves around this track. This initial sample-turntable position must be established by optical techniques to achieve the required

accuracy in programming the angles of incidence for specular-reflectance measurements.

V. Measuring Specular Reflectance

Measurements of specular reflectance on the NBS

specular reflectometer involve the following series of

measurements repeated for each selected wavelength,

polarization, and angle of incidence: B, Si, S2, Sy, B,

Si, S2, Si, B, Si, So, Si, B, where B is the background

signal, Si is the measured signal of the incident beam,

and So is the measured signal of the beam after reflec- tion from the sample mirror. The average B, average

Si, and average S2 are used in the data reduction. The

background is subtracted from Si and S2. A correction

15 April 1980 / Vol. 19, No. 8 / APPLIED OPTICS 1271

C-4
is also made for those effects associated with the rotation of the averaging sphere as determined in the /3-Hght

mapping procedure, which will be described in a later section.

The sample mirror reflectance R is calculated asR =

S2/S1. The average value of specular reflectance for the vertically and horizontally polarized incident beam

is usually reported. The usual practice is to determine

the specular reflectance of a mirror at a specified angle

of incidence by measuring the reflectance with the plane

of the mirror rotated to the left with respect to the in- cident beam and again for the same angle of incidence

with the mirror plane rotated to the right. These two

determinations are then averaged. The specular re- flectometer is programmed to perform these measurements, and the data are processed at the completion of

each measurement cycle. A complete measurement

cycle includes the specified wavelength and angles of

incidence.

VI. Performance

It is beyond the intent of this paper to describe in detail the various checks that were made on the per- formance of the monochromator and other components

of the spectrophotometer, except to mention briefly the

magnitudes of errors associated with this portion of the

system, since they do influence the accuracy of measurements of specular reflectance. Information re- garding some of these investigations is presented in Ref.

1. Involved in checking the performance of the instrument are wavelength scale uncertainties, stray light

levels, detector linearity, and variations in detector re- sponse associated with movement of the specular re- flectometer optical components.

The wavelength scale of the monochromator is periodically checked by measuring the emission lines of

several line-source lamps, the transmission of a di- dymium glass wavelength standard, polystyrene absorption bands, and the absorption bands of 1-2-4 tri- chlorobenzene.2 Uncertainty in the wavelength scale

is 1 nm or less. 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 recent extension of the instrument to cover the

IR spectral range to 2.5 fim involved checking for stray

light in this spectral range. The amount of information on stray radiation in the IR range is limited somewhat

by the lack of suitable filters for this purpose in the

2-2.5-fxm wavelength range. Several IR cutoff selenium

glass filters, silicon filters, and chloroform were used to check for stray radiation in the 0.8-1. 7-/Lim wavelength

range.^ The selenium glass filters have sharp cutoffs

between 0.7 and 0.9 iim, and the silicon filter cuts off at ~1.0 jum. The filters block the UV and visible wavelengths and transmit the IR. The chloroform absorbs

strongly^ at 1.69 yum. The stray radiation levels for the

wavelengths checked with these filters were found to be

less than 0.1%. This is below the signal level for an

optical density of 3, which is about as low a level as can

be measured with a lead sulfide detector of the type

used for these measurements.

The linearity of the lead sulfide detector was measured by the light addition method with a double aperture apparatus."* The results of these linearity measurements indicate that the detector is linear to better

than ±0.1% at all photometric levels between 10 and

100%, which is the photometric range of interest for most of the reflectance measurements of mirrors.

Radiation scattered off the optical components such

as mirrors between the exit slit of the monochromator

and the limiting aperture of the detector system is undesirable in a specular reflectometer. The room containing the reflectometer is lined with a black felt material to absorb scattered radiation. The level of scat- tered radiation in this room is low enough to be undetectable above the dark current signal of the detector

with the sample beam trapped by the background

shutter at the exit slit of the monochromator. Since the

baffle tube limits the field of view of the limiting aper- ture to the area of the tracking mirror, very little scat- tered radiation can enter the averaging sphere. Most

of the scattered radiation is associated with the scat- tering in the optical path of the sample beam. It is important that all the mirrors in this system be kept

reasonably clean and free of dust. One problem associated with a measurement of re- flectance in which optical components are moved between the source and the detector to change the inci- dence and viewing angles is that of determining the

magnitude of errors introduced by these movements.

In this system the number of components that require

movement has been reduced to the' beam-tracking

mirror and the averaging sphere. The detector remains

stationary and views the interior of the sphere through

a 51-mm diam port, which rotates with minimum

translation in the field of view of the detector. The flux received by the detector is diffuse in nature since the

interior of the sphere is a nearly perfect diffuser. To

test the sensitivity of the detector response to changes

in the angular positioning of the beam-tracking mirror, a 18 light was attached to the baffle tube entrance. The

13 light is radioactive tritium gas, which emits visible

light when the /3 radiation excites a phosphorous target.

This stable light source is also enclosed in a magnetic

shield. Light from this source illuminates the averaging

sphere at the other end of the baffle tube. Variations

in the intensity of the signal from the 13 light as the

tracking system turntable rotates may then be attributed to some change in the signal intensity at the detector, which is related to the turning of the averaging

sphere and not to the instability of the light source. The maximum variation in signal intensity observed by

this techninue was ~±0.2%. It was thought that this

variation might be caused by the fact that the entrance

port of the averaging sphere, which appears as a black

spot in the detector field of view, is changing position

as the averaging sphere rotates. However, when a white

1272 APPLIED OPTICS / Vol. 19, No. 8 / 15 April 1980 C-5
baffle was installed in the sphere to prevent the detector

from seeing this black spot, the variation in signal in- tensity for the l3 light test still existed and was actually

larger than that observed without the baffle. The

variation in signal intensity can be mapped as a function

of the turntable position with respect to the incident

beam, and corrections can be derived for this error. The (3 light mapping check is a regular part of the cali- bration procedure.

An analysis of the various sources of error that may

be expected to affect the accuracy of specular reflec- tance measurements on the NBS specular reflectometer

indicates that the final uncertainty in these measure- ments will be on the order of ±0.2% of the measured

value.

as stray radiation levels, detector linearity, wavelength

scale uncertainties, and spatial sensitivity of the detector system. Uncertainty in the measurements of

specular reflectance will be on the order of ±0.2% of the

measured value. The instrument will be used to pro- vide calibrated mirrors, which will become available

through the NBS Office of Standard Reference Materials.

The authors are indebted to William H. Venable, Jr., formerly of NBS and presently employed by Hunter

Associates, Inc., for his contributions to the design and

development of the specular reflectometer and refer- ence spectrophotometer.

VII. Summary

A specular reflectometer spectrophotometer was

constructed for calibrating the reflectance of mirrors

over the 250-2500-nm spectral range. The instrument

is automated and computer controlled. The measurements are made as a function of wavelength and

angle of incidence with a polarized light beam. The

system performance was examined for such parameters

References

1. W. H. Venable, Jr., J. J. Hsia, and V. R. Weidner. Development

of an NBS Reference Spectrophotometer for Diffuse Transmittance and Reflectance, Nat. Bur. Stand. Tech. Note U.S. 594-11 (October 1976).

2. E. K. Plyer and C. W. Peters, J. Res. Nat. Bur. Stand. 45, 462 (December 1950).

3. W. Kaye, Appl. Opt. 14, 1977 (1975).

4. K. D. Mielenz and K. L. Eckerle, Appl. Opt. 11, 2294 (1972).

15 April 1980 / Vol. 19, No. 8 / APPLIED OPTICS 1273
APPENDIX D

Metrologia 17. 97-102 (1981) , metrologia

© by Springer Verlag |981

NBS 45°/Normal Refleclometer 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 gonioreflectometer 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 I'Eclairage — CIE) re- commended that starting in 1969, in colorimetric

measurements of opaque materials, the perfect diftuser was to be taken as the primary reference standard. There

is no existing material ha\iiig diffuse reflection properties corresponding to the perfect diffuscr with sufficient approximation. Therefore, the characteristics of all physical standards actually employed in comparison

measurements must be established by techniques

tlirough wliicii iheir absolute rcfloctance factors can be determined. Tlic measurements involve not only the determination of the ratio of radiometric quantities but

also the determination of lineardimensions.

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 gi%'en 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 2:: steradians, the reflectance factor approaches radiance

factor or reflectance, respectively.

The reflectance factor of sample x, R^, can be ex- pressed as

f^LiU,X)SJU4i,X)r(u,X) U-dA dP.u da dcj dA

i^L{U,k) riu,)) U dA dP. u 6a dcj dA (1)

where L is the incident radiance; 5^ and 5y are the

scattering functions of the sample and of tiic ideal sur- face, r is the relative responsivity of the receiver; t'and u arc the direction vectors of travel of the incident and

emergent radiation; dil and dcj are elements of solid angle oriented in the direction 6^ and u\ d.4 and da arc elements of area through which the energy pusses on to the sample and emerges t'rom the sample; d A is the ele- ment of wavelength; and the symbol /" indicates intcD-1

0026-1 394/8 1 /OO 1 7/0097/$O 1 . 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 C(A) and

luminous efficiency function V{^.), Eq. (1) can be

written as

KA) (2)

[/^Z.(fO S^(U,u,X) r{u) U-M. dfl u da dw] dA

[S^J^L{U) r{u) f/-A4 dH u-6a dcj] dA

^ m) K^)Rx(A)dA

(3)

The spectral reflectance factor Rx(A) is expressed as

S^'LiU) S^{U,u,\) Km) U-dA dn u da do; W

S^^SL{U) r(u) U-dA d^ u da dw

For a receiver system with uniform responsivity

within the cone,

r{u) = r within oj and r{u) = 0 outside of cj. The scattering function of a perfect diffuser could be

written as Si^=8(P-p)/n (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

77 ^JX) (7)

R^(A) = — " CO, <D,(A) where cOp = p wda doj is the projected solid angle of

the cone onto the surface to be measured.

<I>x = f"" L{U) S^(U,u,X) U-dA d^u-dadco is the reflect- ed radiant flux for the sample that enters the Umiting re- ceiver aperture, and

*i = f L{U) 8{P - p) U-dA dO. is the incident radiant

flux.In radiation heat transfer [12, 13], oj^/tt (orfi-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 fracfion 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

1 *,(A)

fl-2 H^)

(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 dovm' the in- cident flux, the reflectance factor of sample x can be

calculated as

1 ^''^^^^ fTT 5^ ''' (9)

where <I>s and pg 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 AAl, 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:

J/K]/2,

where J = 1 + -

(10)

2\2 il/2 K = [GH2G"(1-B^) + (1+B^)2]

B=D/2d

G = c/d

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

f>-2=fA^l-^2=[l+4rfVi)']-' (11)

and when the illuminated area is finite, the view factor is

fl Al

r _ AAl y f A2

(12)

(13)

if AA 1 is selected to be sufficiently small.

' Procedure described in Sect. 5

98
3. NBS Reference Spectrophotometer

The 45°/norinal reflcctonieter is an accessory to the NBS reference spectropliotometer for reflectance (15].

Tlie light source, nionochromator, electronics and other

associated equipment arc located in a system control room. Tiie e.xit slit housing of the monochromator is attached to a light-tight diaphragm in a wall, wliich allows the exit light beani or sample beam to enter a second room where the various reflectance-measuring

devices, such as the specular reflectometer or the 45°/

normal reHectometer, 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-nin bandpass, the Ught 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 published [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. 4S*'/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''/norma! Reflecto- meter. a Top view with top sphere not shown, for clari- ty. S: Sample, LA: Limiting: Aperture. DA: Detector

assembly, SA: Aperture between spheres; b l-roiit view

of the two-splicre Receiver Assembly. AS: Averaging

Sphere, Sll: Shutter, D: Detector, LA: l.imitmg

Aperture, SA: Aperture between spheres

the sample surface and, in turn, 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.

Tne photomultiplier is mounted horizontally on the upper .sphere. TTie spheres are attached to a steppingmotor-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 lir.nting 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-controUed turntable. The detector assembly is on an arm attached to another

independently-controlled turntable having the same axis of rotation as that of the sample turntable. 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

tlie reflected light beam wliich is 45 from the incident

light beam. A tliin mirror, with the reflecting surface

facing the Hmiting aperture, is held against the Umiting

aperture. The hmiting 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 light beam 45° from the incident beam.

The diameters of the limiting aperture were measured 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. Tlic average diameter is 38.238 mm. The distance bc99

D-3
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 Hmiting 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. Perfontiance

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 hnearity of the receiver system was measured by

the bght 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 utiHzes 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 hmiting 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(45°/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°/d)

using the following expression:

/ R(O°/0) COS0 sine 2nde

R(07h)=

/ cosd sind 2ndd

Divided by R(0°/45°), Eq. (14) can be written as:

(14)

R(0°

R(0°

=2 y R(0>) singcosgdg (15)

°/45°) i R(0°/45°)

In terms of measurable quantities, (15) can be rewritten

as:

n/2

where

^^=2 f

B(O°/0)sin0cos0d0 (16)

R(0 /45 ) ^

^ ' ^ <I<0°/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

D-4
made with light polarized parallel and perpendicular to

tlie plane of incidence. B(0°/9)'s were calculated for each polarization and the averages obtained.

Average hiO^/Oys 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 V' (18)

i = 0

Inserting (18) into (16), we have

R(0» -

1^(0745")

where

Ii=/?/2fli sine cose dd (20)

8. Summary

A 4S°/normal refiectometer 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 uniformjiy,

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.

The values [1] of the integrals I, 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(07h)/R(07

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(457o'') is equal to R(0745°)

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 uiuty.

Table 1. Comparison of R(45°/0°) and R(6''/h)* (at 550 nm)

Sample

Measured Value

R(45°/0°)R(6°/h)*

(b) (a)

R(45°/0°)/R(6°/h)

(b)/(a) Integrated**

BaS04 0.987 0.982 1.005 1.002 Fluorocarbon 1.009 0.994 1.015 l.Oll

Vitrolite 0.922 0.884 1.043 1.044 Enamel 0.8751 0.839 1.043 1.040

* Specular component excluded

** Integration using normalized goniorellectance data

References

1. W.H. Venable Jr, J.J. Hsia, V.R. Weidner: Establish- ing a scale of directional-hemispherical reflectance

factor. I: The Van den Akker method. National Bu-

. reau 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..VI.B. Sparrock, F.A. Gargorth: Research on absolute reflectance stand- ards 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- 1 86 ( 1 97 1

)

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 lor the standard plates of the Institute ot Metrology.

Svetsteknika I, 16-19 (1966); also available as translation NRC TT-1 265

8. Commission Internationale dc I'^clairage: Absolute

methods for reflection measurements. CIE Publica- tion Nos. 44 a nd 46 ( 1 979)

9. Commission internafionale de IVclairage: Colori- metry, official CIE recommendations. CIE Publication No 1 5 ( 1 97 1

)

10. F.E. Nicodenius. J.C. Richmond, J.J. Hsia, J.W.

Ginsberg, T. Limperis: Geometrical considerations

and nomenclature for reflectance. Nat. Bur. Stand. (US). Monogr. 100(1977)

ir. W.H. Venable. Jr, J.J. Hsia: Describing spcctrophotometric measurements. Nat. Bur. Stand. (L'S). Tech. Note 594-9(1976)

D-5

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. U 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, 1 597- 1605 (1 969)

18. V.R. Weidner, J.J. Hsia: NBS specular reflecto- meter-spectrophotometer. Appl. Opt. 19, 1 268-

1273 (1980)

19. C.E. Hodgman (ed.): Handbook of Chemistry and

Physics, 44th. edn, pp. 2892, 2931 , 2961.

The Chemical Rubber Publishing Co. 1962-1963

20. K.D. Mielenz, K.L. Eckerle: Design, construction,

and testing of a new high accuracy spectrophotometer. Nat. Bur. Stand. (US). Tech. Note 729(1972)

21. K.D. Mielenz, K.L. Eckerle: 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

D-6
APPENDIX F

JOURNAL OF RESEARCH of the National Bureau of Standards Volume 82, No. 1, July-August 1977

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 Akker or "auxiliary sphere" method of determining a scale of directional-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 196.5 are in agreement to within the uncertainty 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 resuhs

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 finishes.

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

Figures in brackets indicate the literature references on page 49.

29

L-1
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,

ANSI, and TAPPI for possible incorporation in standard

procedures. When the international discrepancies have been

eliminated, we will be working with NRC, PTB, and possibly

other laboratories as standardizing laboratories for ISO re- flectance measurements.

I. Introduction

Directional-hemispherical [dlh] 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

dlh 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°)-hemispherical 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

E-2
Table II

Data from an intercomparison between NRC and PTB of reflectance measurements on a pressed BaS04 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 FTB 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 djh 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 djh reflec- tance, p (U, P, A.) 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 S as:

p (U, P, X) = // 5 (U, P; u, p, X) u-da doi (1)

where S(U, P; u, p, X) 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 X. The

integral with respect to the solid angle, (o, 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

whi('h 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, X), 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 &>' which in magnitude is on the order of 10~^ steradians. None

of the flux falling into U)' 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, k) for collection over the entire solid angle except for O)'. That is to say, the

retroreflected flux is excluded from the measurement. To a

very good approximation,

P(Y = ff'SlU, P; P, Xju-dado)

' //'[8(P -p)/7r]u-^/a^tu ^ '

where the prime on the integral indicates integration over the

entire hemisphere except for to' and S(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, A.) and F(F, k). The primary rr^easurement 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

pj(k). A flux is introduced into the sphere by reflecting a

collimated beam of radiation from the back of the sphere.

31

E-3
REFLECTOMETER

SPHERE ^

REFLECTOMETER

SAMPLE PORT

RADIUS -

HEMISPHERE ASSEMBLY FLANGE REMOVEABLE

TARGET

SECTION

POLISHED BEVELLED PORT

EDGE

STAINLESS STEEL

PORT PLATE

( .6 mm THICK)

ALUMINUM SPHERE SHELL

Figure 1. Sphere used for measuring Van den Akker rejlectaru e.

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, Lj,

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 9 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 djh 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{^)

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 Pj,^ is determined. A flux (/)o (A.) is introduced into the sphere in a collimated beam which strikes the target area of reflectance

pt (F, A.), providing a nearly Lambertian source of radiation which emits a flux (^oPt- 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 p^, the average reflectance of the sphere wall, excluding the port. This flux, the strength of which is given

by <f>oPt (1 ~~ f)p'v, 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{A.) striking the sphere boundary. A fraction / of Xj passes out through the

port, and a fraction (1 — p'v) 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 0i 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:

<AoP^l -f)P'v = <f>i\f+ (!-/)(!- p'v)]. (3)

If the flux (/)o is the sample beam flux from a dual beam

reflectometer, a signal Q is obtained with the sphere in the sample position:

Qs = -/') + 0oP,/(i -/")] (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 Q^k) is obtained:

Q, = ^0oP,(l -/'). (5)

It is arranged that the angle of incidence F at which

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 of Qt, Qsiff and /".

Pv

k^here

1 - {fQ,/Qs)ii/ii - «))

1 -/

fif' - /") Qt

(1 -/) Qs

(6)

(6a)

If a were 0, this would be the usual form cited for the Van

den Akker reflectance. The factor 1/(1 — oc) 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.

^ To keep (he writing uncluttered, the functional dependence of each quantity is show

it is introduced and at key points in the development.

only whe

E-4
An additional modification must be made in the original

Van den Akker etiiiation to take into aceounl the effec t on

of the retroreflectanee of the sphere wall. This modification,

which results in only a small adjustment but which greatly

complicates the form of eq (6), is discussed in detail in appendix A. Since (1 ~ J){1 ~ Pv) in eq (3) represents the portion of (f)i which is lost everywhere but out of the port, it follows that the reflectance Pj,' is the average reflectance over the sphere area excluding the port. To relate p^ 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 p^ must be suitably corrected in order

to obtain the Van den Akker reflectance p„ of the sphere

coating.

B. Adjustment from Van den Akker Reflectance Pt,(X) to d/h Reflectance p(r, k)

In order that the need for the next steps be more readily

understood, Pi, will be interpreted in terms of the directional- hemispherical reflectance, p, as defined in eq (1).

7r/2

Pv

2tt \ Ls{T) p{T) cos(r) sin(r) dY

277 I LsiT) cos(r) sin(r) dT

(7)

where Ls(r) is the radiance associated with <j>i at the incident angle F and explicit indication of the dependence on wavelength has been omitted for clarity. As we have indicated, p„

is just the weighted average over all directions of incidence T

of the d/h reflectance. The weighting function Ls(T) cosF

sinT is proportional to the irradiance of the sphere wall per

unit angle at the angle T. If the d/h reflectance were inde- pendent of angle of incidence, one can see from equation (7) that p„ and p(T) would be identical. However, in any real sphere coating, p(T) is not quite constant and this variation must be taken into account if d/h reflectance is to be deter- mined from p„. The flux, (^i, 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 Lg could be determined by solving the

integral equation

' Lir)S{r, y) cosT sinT dT.

n (8)

Because the irradiance of the sphere wall is uniform, the self radiance distribution, Lg, can be determined to within a constant by measuring the radiance, Ls(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 Ls(y) as

(9)

where ki is a constant of [)ro[)()rtioiiiilily

.

To complete the adjustment, information ahoiil llic lortii of p(r, \) is obtained. A flat sample o( the sphere wall coaling

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(r. X) = k^ik) !Vg(T, X). (10)

The constant can be expressed in terms of measured

quantities by simultaneous solution of eqs (7), (9), and (10).

^2(X) =

p.(X)jA^„(r, X) sinr</r _ p„(x)

/A^cCr, X) Ngir, X) sinF dT ~ A'g(X)

(11)

where A'g is the weighted average of A'G(r, X) with weighting

function A'j,(r, X) sinT. 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 for p{T , X)

which takes the form of a small adjustment of the Van den

Akker reflectance. By substituting the expression for k2 from

eq (11) into eq (10) and using some algebraic manipulation, one can put eq (10) into the form

p(r, X) = p„(X) [1 + C(r, X)]

c(r,x) = ^-i.

(12)

C. From d/h Reflectance p(r, X) to d/h Reflectance

FactorF(r, X)

If the generalized scattering function S for directions of incidence and reflectance both falling within the reflectometer entrance port (retroreflectance at entrance angle D were

equal to the average of S over all directions of viewing, then

the reflectance p(r, X) and the reflectance factor F(r, X) will be equal. However, for the usual type of sphere coating, 5 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 a>' surrounding the incident direction U and the relationship

between F(r, X) and p(r, X) determined from eqs (1) and (2)

p(r, X) — — f P(U, u)cosy d(i) F{T, X) = (13)

^1 — — O)' cosy^

where the integral in (o is taken over a>'. (Note that F(U, u)

TT / 5 (U, u) rfa.

)

33
D. Determining the Directional-Hemispherical Reflec- tance Factor of Standards and Other Samples

The djh reflectance factor FiT, A.) as determined in the preceding four steps is the djh 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 F(.(r, \) of the standard is calculated from the previously determined djh reflectance factor F(r, K) of the sphere

wall as

F,(r, X) = nr, X)

^^^^

(i4)

2 QAT, k)

1=1

where Q(. is the reflectometer signal for the standard and Qi is the reflectometer signal for the j'th one of the n samples which

are taken to represent the sphere wall. In day-to-day use, the djh reflectance factor Fj.(r, \) of a sample can be measured

by comparison to the stable standard.

F^(r, A) = F,(r, X) ^4^^ (15)

QciT, X)

where the reflectometer readings Qj. and 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 Pv{^)

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/? results which has no crack at the plane where the hemispheres join.

Figure 2. Apparatus used io produce the sphere coating.

1 . Determining the Uncorrected Van den Akker Reflectance p'v

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., /=(!-(!- {r/Rf)"-')/2. (16)

Associated with each determinaton off there is an estimated

random error, as defined in appendix B. A random error dR

arises from our inability to pack the sphere to the same radius

E-6
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 df which is given by:

2(1 - {r/R)^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

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°//^ 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 Q'g 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'g 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 Qfin the reflectometer is approximately the reflectance of the sample relative to the sphere wall which in turn has a reflectance nearly 1, Qf v/as 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 + 2Qf)/i. 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 &>e, an expression for the corrected sphere reflectance Qg can be written as

POLISHED BEVELED PORT EDGE

(STAINLESS STEEL)

Figure 3. Cross section detail of polished beveled port ed^e.

Associated with this determination of Qg, there is a random

error arising from the random errors in measuring Q'f> Qp, and Qf. Because of the smallness of co^, the denominator in eq (19) is approximately 1 and the small random error

in Qf has little effect on the total random error. Therefore

(20)

Also associated with the determination of Qg is a systematic

error A^j which arises from the uncertainty in (Og 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

^Qs - <?. 2(1 - Qf)

377

1/2 (21]

The reflectance of the removable target was measured

using the same instrument. In this case a value Q'l 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 Qp 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 Q, is obtained

(22)

An expression for the random error associated with this determination of ^( is determined in a straightforward fashion and resembles eq (20).

8Q, = [dQ',-' + 8QI]

211/2 (23)

The values of/, Qs, and obtained above were used in eq

(6) (more specifically, eq (A7)) to calculate values of pI,(A.),

35

E-7
the Van den Akker reflectance of the sphere wall in its entirety. The random error in py is obtained from eq (6) as

sp; = [((1 - QtiQsVii -y)W

+ ((//<?.)/( 1 -f)f m

+ mtiQ%m -f)f S(?i]"^

The systematic error in pj, is given similarly by:

Ap; = [((1 - QJQsVil -fff^f

+ ((/<? «/(?!)/( 1 -f)?^QVi"^

(24)

(25)

where A(?s is only that portion of the systematic uncertainty,

in Qs given by eq (21). Note that the contribution to the systematic error m Q g 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 QtJQ g is taken in determining p^, from eq (6). Therefore there is no t term in eq (25).

2. From Uncorrected Van den Akker Reflectance p[, to Corrected Van

den Akker Reflectance Pi,

The quantity p[, as determined in the preceding section is the average Van den Akker reflectance of the sphere wall. In order to obtain the Van den Akker reflectance of a thick coating of the sphere wall material, it is necessary to correct

p[, for the effect of the crack around the removable target section and for translucency in the sphere wall coating.

a. Th* Gap Around th* Targat

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 Pj, of the wall

coating, the loss in the gap must be accounted for:

Pv

Pv

(26)

where is the radius of the target, W is the width of the gap, r

is the radius of the entrance port, and kf 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

Apt, = Pv Ap;y ^

/M,\2 ^

/ nW

p'J \ kj Ur^ -

(27)

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, Poo [22]. Therefore, for these

coatings kt = 1. 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 A:; was obtained by a calculation having the follow- ing form:

Pio

/ dA

(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 Poo), 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

1—

r

8

A

1

8

o

\- A A nm HALON X nm 1 BaS04

400 o 400 •

550 n 550

700 A 700 1_1 12 4 6 8 10 THICKNESS (mm)

Figure 4. Reflectance of wall coalings a.s funi tion of thickness.

(Normalized In give a reflectanee of approximalely . for thick samples.)

b. Translucency of the Wall Coaling

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 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 8k t of this correction. An expression for

E-8
the random error in as given by eq (26) is Tabi.k III

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 kf — PJPio^ and estimating the systematic error as (k't — A>)/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 kt, 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°/h 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 Pv 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.

Comparison of the Van den Akker r< different size spheres eoated with BaS(X

flectance of p„

[16j.

of the walls of two

Wavelength Sphere rad ius R

(nm) Difference in p„

14.6 cm 9.5 cm

400

42.5 450

475

0.9744

.9771 .9789

.9802

0.9744

.9769

.9788

.9801

0

0.0002 .wm

.0001

500

525 550

575

.9813 .9823 .9829*

.9834

.9812

.9821 .9828

.0001 .0002

.0001

600

625 650

675

.9836

.9838

.9838

.9837

.9835

.9836

.9836 .9836

.0001 .0002

.0002

.0001

700

725

7.50

.9836

.9835

.9832

.9835

.9833

.9831

.0001 .0002

.0001

* For this value, €p„ = 2. 1 X 10-^

Table IV

First Determination BaS04 [14] Wavelength

(nm) Van den Akker

Reflectance p„

P(6°, \) F{6°. Kj

400

425

450

475

500

525

550 575 600

625

650

675

700

725 750

0.9661 ^ .9688

.9721 .9744

.9767

.9788 .9806t

.9823 .9835

.9845

.9852 .9858

.9864 .9869

.9873

0.9606

.9638 .9675

.9703 .9728

.9752

.9774*

.9793 .9807

.9818 .9826

.9834

.9840 .9846

.98.50

0.9.599 .9631 .9668

.9696

.9721 .9745 .9767@

.9786

.9800

.9811 .9819

.9827

.9833 .9839

.9843

t €p„ is 2.3 X lO--* (8p„ = 2.1 X 10"^ and Ap„ = 1.1 x lO"").

* ep is 9.8 x 10-^ (8p = 9.5 X lO"" and Ap = 2.3 x lO""). @e6 is 1.01 X 10-3 {SF = 9.5 x 10" and AF = 3.3 x 10"^).

Table V

Second Determination Halon [1,5]

Wavelength

(nm) Van den Akker

Reflectance p„

P(6°, \) F{6°. \)

400 0.9961 0.99,30 0.9927 425 .9961 .9932 .9929 450 .9961 .9933 .9930 475 .9960 .9934 .9931 500 .9959 .9935 .9932 525 .9958 .9935 .9932 550 .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 .9933 .9930 725 .9949 .9932 .9929 750 .9948 .9931 .9928 t€p„is9.0X 10-''(Sp„= 7.3 x 10

* ep is 9.6 X 10-''(8p = 7.9 x 10 -* (®6F is 9.7 X 10"" {SF = 7.9 x 10"

and Apt, and Ap =

" and AF =

= 5.1 5.5 X

5.6 X

X U)-"). 10- ). 10-').

37

E-9
I

Table VI

Third Determination BaS04 [16]

1.00

Wavelength

(nm) Van den Akker

Reflectance P;, P(6 , A.) F(6 , A.)

400 0.9744 U.SHjVo 0.9688 425 .9771 .9732 .9725 450 .9789 .9757 .9750 475 .9802 .9775 .9768 500 .9813 .9791 .9784

52i5 .9823 .9804 .9797 550 .98291 .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 ep„ is 2.3 X lO"" (8p„ = 2.1 x 10"^ and Ap„ = 1.1 X 10"").

* ep„ is 2.1 X 10"^ (5p = 2.1 X 10"^ and Ap = 2.3 X 10"^). @eF is 2.1 X 10-3 (5F = 2.1 X 10"^ and AF = 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 Qi 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 uncerxxxxxxxxxxx

.99

X X X )i 1

o o o o

400 500 600 700 750

WAVELENGTH (nm)

Figure 5. Van den Akker reflectance of three coatings.

(The heighl of the symbols X represent the total uncertainty. Height of the symbols 0 and A

represents approximately 4 times the total uncertainty.) The associated solid curves show p(6°, X) for each coating.

tainty would not exist if the Halon coating were twice as

thick.

B. Adjustment from Van den Akker Reflectance Pi>(X) to 6°lh Reflectance p(6°, X)

The second main step is the transition from Pu(X) to p(6°,

A.). 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 and p is small. For this reason, we will refer to the transition step from Pp 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 p^ (X = 550 nm) for BaS04 [14]. Sym bol 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) f, (16) 1.90 X 10-' calculated using r and R above.

(d) Qs (19) 8.731 X 10-2 measured reflectance of auxiliary sphere.

(e) Qp (19) 1.24 X 10"' measured with stainless port open to dark room.

(0 Qf (19) 7.0 X 10-' measured reflectance of stainless steel port plate.

(g) (19) 3.78 X 10-2 calculated from dimensions of port structure [17], radians

(h) (19) 8.630 X 10-2 calculated using Q'g, Qp, Qf. and big above.

(i| Q'c (21) 9.832 X 10-' measured reflectance of target. U) 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 Qg above.

(1) Pv (6) and (A7) 9.805 X 10-' calculated using/, Qg and Qi from lines (c), (h) and (k) above respectively. (m) ri (26) 25.4 mm measured with micrometer caliper.

(n) W (26) 0.17 mm measured with traveling microscope.

(o) k, (26) 1 BaS04

(0.9974) (Halon determination only).

(P) Pv (26) 9.806 X 10-' calculated using p„, r,, W, and k, above.

38

E- 10
Table VIII

Calculation of the Random Error in the Van den Akker Reflectance Symbol Reference Et^udtion Comments

(a) SR (17) .8 mm Uncertainty in packing sphere coating to constant ra- dius.

(b) ^ (17) 2 X 10-^ Calculated from SR above.

(c) s^; (20) 7 X lO"'^ Uncertainty from .3 measurements.

(d) 8Q^ (20) 7 X 10-^ Roundoff uncertainly.

(e) 8^. (20) 1 X 10-" Calculated from SQ, and SQp as given above.

(0 8^; (23) 2 X lO-* See comment on (d) above.

(g) (23) 7 X 10-5 See comment on (d) above.

(h) SQ, (23) 2.1 X lO-" Calculated from SQ'i and SQ,, above.

(i) 8p; (25) 2.1 X 10-" Calculated from Sf, SQ„ and from (<), (g) and (j) above.

0) 8fc, (27) (7 X 10-")* Corresponds to an uncertainty in coating thickness of 0.5 mm.

(k) Sp„ (27) 2.1 X 10-"

(7.3 X 10-")* Calculated from 8p'„ and

Skt 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-^ rad

(d) A<?. (21) 1.1 X 10-" Calculated from AcOj above and from Qf, Ct>,, and Q, from entries (f), (g) and (h) in table VII.

(e) Ap; (25) 9.7 X 10-5 Calculated from A/and A^, from (b) and (d) above.

(f) Met (27) (5 X 10"")* Wavelength dependent error ::.0OO5 estimated from

fig. 4; uncertainty due to ttoered edges of coating ±0.0001.

(g) r,W (27) 5 X 10-5 Calculated using/?, r, r,, W from (a), (b), (m), and (n) in table VII.

(h) Apv (27) 1.1 X 10-"

(5.1 X 10-")* Calculated using Ap^, A/c(, and the gap uncertainty as given in (e), (f) and (g) above respectively.

* Halon coaling only.

1 . Determining the Relative Self-Radiance Ng{y)lcos y

For each type of sphere coating, the relative self-radiance ^g{y)/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 coUi- 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 nni high pass filter which resulted in a centroid spectral weighting at approxi39

E-11
COLLIMATED

RECEIVER

COLLIMATED BEAM

COLLIMATED SOURCE

Figure 6. Arrangement of knife-edge apparatus for measuring Ngiy)-

mately 700 nm. No distinction between the measurements

under different spectral weightings were observed, indicating

that Lj^y) depends principally on the geometrical nature of the surface. The relative magnitude of the obsei'ved flux divided by the cosine of the observation angle is sh5wn 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 A'g('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 measure- ments using the knife-edge indicate. Two possible sources for the difficulties at large y are reflections from the corner 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 A'g(y)/cos y results in only a small

uncertainty in determining C{T, K). A discussion of our

in i. o

o

z

uT

o

z

<

<

1.3

1.2

cno

UJy I.I

o 1.0

1

1

|St O BaS04

J 2n<l X HALON

A BaS04

+ HALON (telescope meas.)

X

X

X

A o-l

o

0 30 60 90

ANGLE OF VIEWING Y(DEG.)

Figure 8. Normalized self-radiaru e at 550 nm for each of three coating

materials.

choice of function to represent A'g(y) will be deferred to part IV. B. 3 in which C(r, A.) is calculated.

2. Determining the Relative Directional-Hemispherical Reflectance Nc(r)

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

E-12
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^F, \) shown in figure 10. These curves were

used to determine the adjustment function C(r, A.) 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.

DIRECTIONAL - HEMISPHERICAL REFLECTANCE

(4S CM OIA. SPHERE)

Figure 9. Integrating sphere for measuring relative directional-hemispherical reflectance as a function of angle of incidence.

3. Determining C(r, X)

For each type of coating, the function C was evaluated using in eq ( 13) the N y) and A'ci T, A.) 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 ior NJ,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(V, A.). We will do this by using a lower case y in N(J(y)/cos y to indicate the data obtained directly from

the measurements and by using an uppercase T in A'g(r)/cos r to indicate the processed data used as the relative radiance

distribution incident on the sphere wall when we calculate C{T, \). The first set of C(r, A.) was calculated assuming that

ANGLE OF INCIDENCE T (DEG.)

Figure 10. Relative directional- hemispherical reflectance Ng(r, K) as a

function of angle of incidence T for each of three coatings at three wavelengths.

N(J{y)/cos y is independent of y. This provides a lower limit on C. The second was calculated by using 1 for A'g(y)/cos y

between 0 and 45°. To obtain the NJ(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 A'g(y). (See fig. 11 for a diagram illustrating this procedure for the Halon data in fig. 8.) The set of/Vg(y) obtained in this way were consistent with

the more accurate data from the telescopic detector scan and

the C(r, A) calculated with these A^y) are used as the accepted values. Finally, as an upper limit, Cs are calculated using the unmodified knife-edge experiment data given

in figure 8. The functions CiT, A) corresponding to the accepted values, are plotted against F 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°. A) at 25 nm intervals over the wavelength range 400 nm < A < 750

nm, we need values of C(6°, A) at these wavelengths. Since

the large amount of data required would make impractical

determining all of these values of C(6°, A) in the way described above, we choose to determine C(6°, A) 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°, A) which comes from eq (12)

C(6°,A) = ^^^^^-1. (30)

41

E-13
1.5

1.4 -

1.3- <

<

1,2

o I.I

£ 1.0

straight lln ttirough first three points

Ng(r)/cosr lower limit J I 30 60 ANGLE OF VIEWING Y (DEG.) 90

Figure 11. An illustration of the three assumptions used in interpreting the Ng{y) data from the knife-edge determinations.

K .5

o 0

1 2nd RUN (HALON)1

450nm

550nm

1 1

750nm

30 60 ANGLE OF INCIDENCE P (DEG.)

Figure 12. CiT, K) as a function of r at three wavelengths for each of

three coalings.

Making use of this, we can write a correction factor C(6°, X) which is a rough approximation to C(6°, A.) as:

(32)

Since C and C are approximately equal, their ratio is a smoothly varying function of wavelength. Therefore, we de- termined J(k) as

such that

J{k)

C(6°, k)

C'(6°, k)

(33)

(34)

at the wavelengths 450 nm, 550 nm and 750 nm. We then determined C(6°, k) at other wavelengths as

C(6°, k) = J{k)C'{6°, k) (35)

where C'(6°, A.) is calculated from expression (32) using

values o{N(^6°, k) and A' 0(45°, A.) measured with the relative d/h reflectance instrument [12]. The values of C(6°, k) so determined are plotted in fig. 13.

-.001

-002

-.003

O „

-.004

-.005

-.006400 500 600

WAVELENGTH (nm) TOO 750

Figure 13. C(6°, K) as a function of wavelength for each of three coatings.

4. Results and Error Analysis

Since the weighing to determine A'g(A) is heaviest at 45°, it follows that

A'g(A) - /Vg(45°. k). (31)

The three sets of values forC(6°, k) determined above were

used in eq (12) to calculate p(6°. A) 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.

E-14
From eq (12) one can determine a propagation of error formula for the random error 8p(6°, k) as:

8p(6°. k) = [6pr(k)- + 8Ag(6°. kf + 8.\G(kfV''. (36)

In this form Py, A c and A^g^are each assumed to be 1, and

errors common to A'c and A'g 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 show n in appendix C. The principal random

uncertainty in A g is due to the noise in the d/h data. Since

the value of A g(6°, A.) 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 w'hich depended as little as possible on arbitran 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 Nq, two such fittings are involved, one to the original data as a function of angle and one to the C{k) data used in the

interpolation. A summan,- of the random error analysis for the

Piik] to p(6°, k) 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 A g due to the correction which is made for the entrance port of the reflectometer. This results in an uncertainty in C{T. k) of 2 X 10~^ independent of wavelength.

The total uncertainty in p(6°. A.) for a given determination

is obtained by adding 8p(6°, A.) and Ap(6°. k) in quadrature.

The additional uncertainty introduced in making the adjust- ment from pxJiki to p(6°, \) is of the same order of magnitude

as the uncertainty in pjk) 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 A'G(r, X) data from this surface.

C. Adjustment from d/h Reflectance p(6°, X) to dfh

Reflectance Factor F{6°, k)

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 Pr(X) to p(6°. \1 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) SA',(6°. X) 7 X 10-" 3 X 10-" 20 X 10-" Component due to fitting angular data

for A'c(r, X).

(d) 6 X lo-'' 3 X 10-" 5 X 10-" Component due to fitting wavelength

data to C'(X).

(e) 9.2 X 10-" 4.3 X 10-" 21 X 10-" Quadrature combination of (c) and (d) above.

(f) 8p(6°, X) . 9.5 X 10"" 7.9 X 10-" 21 X 10-" Quadrature combination of (a), (b) and

(c) above.

(g) App 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 with 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

E-15
To make the measurements, the receiver was placed in the sample position and a signal A' n proportional to the normal

illuminance I r 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 NAI^), which is in the same way proportional to the illuminance 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 FriP) can be determined from

Nn (P cos (D cos (r + 13}'

(38)

The value of F64/3) so determined as a function of observation

angle )8 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 Fe<{P) 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 iii eq (13) be- comes

F(U, u) cos y w = 2 Trcos6° J y^'Feili) 13 d p (39)

and oj' in (13) becomes= 2 7T To'"' 13 d(3 (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°, X) using eq (13). In general, the difference

p(6°, \) - F(6°, A.) 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°, \) 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°, X) 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 F^{6°, X) 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 Fc,j(6°, X) the reflectance factor for stan- dard c as obtained from the yth determination. Equation (14) takes the form: F = ^F.

or

(41)

where

Fj =Fj(6°, X) is the reflectance factor for the y'th wall

coating.

4 2 -

6"" ANGLE OF INCIDENCE

0 1st BgS04

X 2nd Halon

OBSERVATION ANGLE

Figure 15. Retroreflective bidirectional reflectance factor for 6° inci- dence as a function of obsemation angle.

(}(. is the measured relative reflectance of working stan- dard c, and

Qj \s the average of the measured relative reflectance for several representative samples of the 7th 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:

bFr

Qc +

1/2 (42)

The largest new contribution to the uncertainty which is introduced in this step is dQj. 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 Qj differ significantly a small

correction^ for instrument non-linearity must be made in the

ratio Qc/Qj- With this non-linearity is associated a small

contribution to the systematic uncertainty.

AFcj = Fc ( MQc/Qj]

A (Qc/Oi) +

^F^'•

Fj)

112 (43)

Three different working standards are currently used. These are identified and described in appendix D. The values

of Fc,} 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.

E-16
Table XI

Reflectancf Facliir of Working Standard 1 (Russian Opal Glass, Polished)

3vt^lpn^t h

( nm) FU2 ^1.3 400 0.9793 0.9734 0.97.38 0.97.59 0.97.53 425 0.9781 0.9739 0.9743 0.97.56 0.97.53 0.976.5 0.9/ /y 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 0.9821 0.9845 0.9836 0.9a38 550 0.9837 0.9813 0.9830 0.9823 0.9835 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 0.97.57 0.9760 650 0.9770 0.9745 0.9774 0.97.56 0.9761 675 0.9771 0.9751 0.9772 0.97,59 0.9763 700 0.9761 0.9736 0.9761 0.9747 0.97.50 725 0.9742 0.9718 0.9741 0.9728 0.97.32 750 0.9716 0.9687 0.9711 0.9699 0.9702

S 2.2 X 10-3 1.6 X 10-3 2.7 X 10-3 1.3 X 10-3 1.2 X 10-3 A 3.3 X lO"" 5.5 X 10-" 3.3 X lO-" 5.5 X 10-" 5.5 X 10-"

£ 2.2 X 10-3 1.7 X 10-3 2.7 X 10-3 1.4 X 10-3 1.3 X 10-3 W 4.5 6.0 3.7 W 10.5 14.2

Table XII

Reflectance Factor of Working Standard 2

(Vitrolite)

Wavelength

(nm) F2.r F2.2 F2,2

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

8 2.2 X 10-3 1.6 X 10-3 2.3 X 10-3 1.3 X 10-3 9.8 X 10-" A 3.2 X 10-" 5.3 X 10-" 3.2 X 10-" 5.3 X 10-" 5.3 X 10-"

e 2.2 X 10-3 1.7 X 10-3 2.4 X 10-3 1.4 X 10-3 1.1 X 10-3 w 4.5 5.9 4.2 W 10.4 14.6

The systematic uncertainty associated with the F 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 Ff-'s from a number of determinations. We maintain a running weighted average F

of the results of all determinations from 1 throughj by means

of the calculation

where the weighting factor Wc, j for the y'th determination of Fc is

Wc, j = 1/100 eFe. j (45)

where eFc, j is the total uncertainty in F^^j as is given in appendix B. The weighting factor Wcj for the average of the j

determinations is

i Wcj = 1 t^c.i • (46)

i=l

45

E-17
Table XIII

Reflectance Factor of Working Standard 3

(Porcelain Enamel 80-1)

Wavelength

F3.2 F3,3

- F3,2 F3.3

400 0.7615 0.7573 0.7571 0.7591 0.7585

'*Zd 7Q1 1 7Q1 ^ 7Q99 7Q9n 450 .8042 .8019 .8034 .8029 .8030 475 .8093 .8072 .8073 .8081 .8079 500 .8105 .8078 .8101 .8090 .8093 525 .8104 .8091 .8096 .8096 .8096 550 .8090 .8083 .8094 .8086 .8088 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

8 2.1 X 10-3 1.5 X 10-3 2.3 X 10-3 1.3 X 10-3 1.1 X 10-3 A 3.0 X 10-" 4.7 X 10"" 3.0 X 10-* 4.7 X 10-" 4.7 X 10-"

e 2.2 X 10-3 1.6 X 10'3 2.3 X 10-3 1.4 X 10-3 1.2 X 10-3 w 4.6 6.2 4.2 W 10.8 15.0

Table XIV

Calculation of the Uncertainties in the p(6°,X.) to F(6°,A.) and F(6°,\) to F c, j(6°, \) steps as determined for Working Standard No. 2.

Symbol BaS04 [14]

Value

Halon [15] BaS04 [16] Comments

6F(6°, \) 9.5 X 10-" 7.9 X 10-" 2.1 X 10-3 See table X, entry (f). (a) (=Sp(6°, k))

(b) Fj 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) 8Q, 2 X 10-3 1.2 X 10-3 1.2 X 10-3 From measurements on a number of samples.

(f) Qj 0.985022 1.00283 0.985982 Measured.

(g) F2.i .9245 0.9222 0.9243 Calculated from (b), (d) and (f) above in equation (41).

(h) 2.2 X 10-3 1.6 X 10-3 2.3 X 10-3 Calculated from equation (42) and (a) through

(g) above.

(i) -1 X 10-" -1 X 10-" -1 X 10-" From reference [17]. (—A(>;)

(J) AF, 3.3 X 10-" 5.6 X 10-" 3.3 X 10 " From tables IV, V, and VI.

(k) AF2. 3.2 X 10-" 5.3 X 10-" 3.2 X 10-" Calculate from equation (43) and (b), (d), (f).

(i) and (j) above.

(1) eF2. j 2.2 X 10-3 1.7 X 10-3 2.4 X 10-3 Quadrature combination of (i) and (k) above.

(m) Wc, i 4.5 5.9 4.2 Calculate from equation (45) using (1) above.

(n) 10.4 14.6 Calculate from equation (46) using (m) above.

(0) Fc.i 0.9232 0.9235 Calculate from equation (44) using (g) and (m) above.

(P) 8Fc.j 1.3 X 10-3 9.8 X 10-" Calculate from equation (47) using (g), (m).

(n), and (0) above.

iq) Afc.j 5.3 X 10-" 5.3 X 10-" Largest entry from (k) above.

(r) 1.4 X 10-3 1.1 X 10-3 Quadrature combination of (p) and (q) above.

E-18
The random uncertainty in the F^j is given by

^"cj jj^ V*')

The values of Fc,2 and Fc,3 appear in tables XI, XII, and XIII along with the F^j- 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 . Detennining the Van den Akker Reflectance PiX^)

In an experiment designed and carried out with reasonable

care, the Van den Akker reflectance Pn 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 J) 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 Qt in eq (6).

2. Adjustment from the Van den Akker Reflectance p„ 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(r,

X) can never be greater than 1, it follows that this adjustment

will be smaller for samples for which Pt, 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 < oatinj:; 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 agr< <-ment between their results, which are the basis of the earlier NBS

scale of F{6°, A.), 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 dir(;ction can result from assuming p„ and p to be equal, and an adjustment based on relative d/h reflectance measurements /Vc{r, K) shoulfl be

made if an uncertainly 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., Nfj{y, A.)/cos y is constant.

It should be pointed out that in every case p„ and p45'^/ft are very nearly equal, as can be determined from the CiV, k) 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°,

A.) 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 reflectan( e 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°, k)

The present NBS scale of spectral d/h reflectance factor is maintained by means of three carefully preserved working

standards which have been evaluated at 25 nm intei-\als. The

reflectance factor data for the first three determinations are given in tables XI, XII and XIII. Figure 16 provides a

47

E-19
-.1

-.2

-.3

WORKING STANDARD NO. I (RUSSIAN OPAL GLASS)

• |st RUN (80304)

X Z"** RUN (HALON)

O Sfd RUN (BaS04)

y.''>^^ AVERAGE ittSgndRUN • WORKING STANDARD NO. 2 (VITROLITE) * • *

400 500 600

WAVELENGTH (nm)

700 750

Figure 16. Rejlectam e factor differences for the measurement of three working standards in three reflectam e scale determinations.

graphical record of the establishment of the average value for 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 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 dih 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 0.0015.

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 196.5 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

X X

_ • RUSSIAN OPAL GLASS X VITROLITE "h ENAMEL eo-l — GE AVERAGE

NRC VALUE X

400 500 600 WAVELENGTH ( nm )

700 750

Figure 17. Comparison ofpresent NBS scale ofFs"-* (taken as zero line) to preidows NBS scale and to Results of an intercomparison 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

E-20
probably be attributed to the imprecision of the NBS GE

spectrophotometer.

The dashed line at approximately —0.004 indicates the combined error for this comparison. Since the NRG 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 NRG 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 dih

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°, A.) 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 oid/h 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, 783 (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).

[II] 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., Retroreflectance measurements of photometric standards and coatings. Applied Optics 15, 1845

(1976).

[14] BaS04 manufactured by Mallin( rodt Chemical Works (Reagent powder

for X-ray diagnosis) #.S808. (3j [15] Halon tetrafluoroethylene powder manufa< tured 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- 101 1) (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 White, H. K., Fundamentals of Optics, 3rd edition (McGraw-Hill, N. Y., 1957) pg. .521, figure 25M.

[20] Jakob, Max, Heat Transfer, Volume 11, p. 14 (John Wiley and Sons, N.

Y., 1963), {ojjTT = 1 -/,.,). [21] See section III. A. 4 of reference [8] above.

[22] Kubelka, Paul, New contributions lo the Optics (jf liiletisciy Light- Scattering Materials. Part 1, J- Opl- Soc. Amer. 38, 448 (1948).

[23] Grum, F. and Saltzman, M.; P-75-77 New Whit.- 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 I.E.S. 15, 802 (1920).

[26] Budde, Wolfgang, and Dodd, C. X., Absolute reflectance measure- ments in the D/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

Retroreflectance 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 </)j(X) (see III. A.) striking the sphere boundan

can be seen by going one step backwards in determining the source of </)i. 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

(f)i can be deteriTiined 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

<t>i, is made up of two parts

</)i = 0r + <l>i (Al)

49

E-21
where 0^ is the retroreflected fraction of the reflected flux

4>r^fr<f>i (A2)

and (f)i is the diffusely reflected fraction

(f>l = (1 - fr)<t>i- (A3)

With this model, the power balance equation, equation (3) of

part III. A., takes on the following form.

p;( 1 +/rp;)(l - /)/)r0o (A4) = 4>[f+[{i + - p;)

where pt 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

Q, = k\_i^'if{\ -70 + M + frPv)ptAi - /')]' (A5)

and the relative reflectance of the target is, as before

Qt = kc}>oPt{l -/'). (A6)

Equations (A2), (A3), (A4), (A5), and (A6) can be solved to obtain an expression for p„ in the following form:

Pv = l-f(l-fr)^

Vs

1 -/(I -fr) 1 - a

(A7)

^ f/(l + P'vfr)lf' -/"] ^ m-frPv') \Qt "

1 (1-/) 1 -P^[l -/(I -/r)]J<?.

(A7a)

Comparing (A7) with (6), it is seen that /in the dominant first term is replaced by /(I — 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 the value obtained from (A7) with a —

0. Taking the retrorefleclance into account has a very small

effect on the calculated value of p'y. 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 />„ by

approximately 10"^. Note that p'„ must be the total reflec- tance, including retrorefleclance, since 1 — p'„ represents

loss of radiation by absorption.

2. Models for Retroreflec tive 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 retrorefleclance which

they observed from barium sulfate paint and other highly

reflective white coatings. Other possible mechanisms for producing retrorefleclance include cube comer reflectors formed from broken cubic crystals and retrorefleclance by

focussing, as occurs in glass beaded retroreflecling 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 !»nk: round 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

F(U, u)

7rL(u)

(A8)

where ^(U) is collimated irradiance incident in the direction U and L(u) is the reflected radiance in the direction u, both averaged over a sufficiently large area of the sample. In the case of retrorefleclance, we set the unit vectors U and u

equal. The average reflected radiance is given by definition as

L{xx) =

^{(o. A)

(«(u)Acos'y

(A9)

where cu(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 ^(cu. A) is the flux reflected from

area S into solid angle ft). 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 <u is defined in terms of a small arbitrary area a on the sphere

4a

(AlO)

The flux reflected from this area into (i) is given by

4> = pEa/cosy (All)

E-22
where p is the reflectance of the sphere surface. (Note that since we cire treating retroreflectance, a is chosen so that it is centered on a radius in the direction oiE, and therefore the

direction of incidence is normal to a.) The area A occupied by

this sphere in a hexagonal close-packed array is

A =

6r2 V5

(AI2)

Using expressions (A9), (AlO), (All), and (A12) above in (A8) one obtains under conditions of retroreflectance:

F (U, u) = —^p/ cos^7 24

0.227p/cos2y. (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

pt = p?(l - pzf (A14)

where pi is the reflectance of the cube faces and p2 is the reflectance of the entrance surface. For a perfect internal comer pi is 1 and p2 is roughly 0.05, so that p, is roughly

0.9. For an external comer (cube comer "hole"), P2 ~ 0 and

Pi is roughly 0.05 so that pt is roughly 1.25 X 10"^ in that case. The reflected radiance is distributed in the diffraction pattem associated with the reflecting faces treated as apertures. For this order of magnitude calculation, we will assume

the pattern to be that of a circular aperture of effective radius

r = a/— where A is the area of the entrance surface. The

radiance in such a pattem would be given by [28].

EA

(A15)

where

X = 2Trr sin (/3)/A.,

from which it follows that the reflectance factor is given by

ttA X

Pi- (A 16)

The data in figure 1.5 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 al x =

3.8. For an effective wavelength of approximately 5.50 nm, it follows that the particle size would have to be such that r —

20 p,m. Thus, the reflectance factor at /3 1° would be

roughly

F()3) - lOV,. (A17j

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 (1 in fig. 18<-.) 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 p.m. 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

C.

REFLECTING

SURFACE

Figure 18. Diagrams for estimating magnitude oj retroreflectanre 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 (A 12)

and (A16) that a closely packed array of such spheres would

have a reflectance factor for )8 1 of

Fift) 6 X lO^p, (A18)

for a specular reflector of reflectance Pt located at I and

F{f3) - 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 corner 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 corner 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 patterns 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

F{P) = 1 + exp(a + bfi') (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 F(/3) for BaS04 over the range 0 < fi < 0.5° is 1.42 which is in good agreement with the data of Egan and Hilgeman [13]. The difference values for p(6°. A.) — ^"(6°, A.) 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

(|/3| < 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^f BaS04 using a beam splitter yielded p(6°, k) - F{6°, k) = 0.0006 which is in good agreement with the value of 0.0007 obtained from the data in figure 15.

VIII. 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 (jf 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 Tess 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

E-24
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, A.)

The integrals in (11) are evaluated in closed form after

fitting the experimental data for A^^ and Nq.

1. Fitting Ng(T, \)

The data for A'g were fitted by an expression of the form:

yVcCr, X) = a^ik) + ai(X)P + a2(X)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{Y, k)

Since the experimental data for A'g(y, X)/cos (y) were found

to be nearly independent of wavelength, only one function

A'a(r) is needed for each type of coating. However, since

there was such a large uncertainty in the A'g(r) data, three

sets of A'g(r) were fitted as described in part IV. B. 3. in the main text. The form used for the fitting the data was:

yv,(r)/cosr = i biV. (C2)

i=0

Table CI

Coefficients for the expansion of A/gfT, \) in even powers of the angle of incidence F in radians at three different wavelengths for three sphere wall coatings.

Coating Wavelength oo X 10^ a2* X 10* 450 0.999942 5.99 0.438 BaS04 (14] 550 .99978 4.40 0.159 750 1.00011 3.27 -0.00814

4.50 0.999875 3.97 -0.172

Halon [15] 550 1.00004 4.17 -0.985

750 1.00027 3.68 -1.20

450 0.999829 4.08 0.405 BaS04 [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 <jf the

coefficients, as obtained by least s(juares fitting, are given in table CII as describing thf> "upper limit" curve. In the

original data, the least uncertainty was associated with the r = 0 reading. Therefore, all data were normalized to the Y = 0 reading and was taken to be 1 when the data were

fitted. Because of the symmetry in azimuth, />, aru) 63 are taken to be zero. In the accepted data, A'j,(r)/cos Y was taken as I u\> lo Y =

7r/4. To obtain the remaining part of this curve we obtained

Ng(y) according to the expression

yV„(7)/cosy = 1 + Ci7. (C3)

The difference data Ng(y) — N'g(y) using the data for the angles 7r/3 (60°), .S7r/12(7.5°) and 177r/36(8.5°j were fitted using the form

Ng{y)/{^os y)=\ + b'iY-j)' + b,{Y- j)\ (C4)

4 4

After 61 and 62 were determined, these were used to obtain

the bi in the expression (C2).

3. Calculating C(Y , k)

With the expressions (CI) for A'G(r. A.) and (C2) for Ag(r.

k) substituted into eq (11), the integrals in that equation can be evaluated in closed form in terms of integrals of the form

h = Jo'T* cosT sinF^^r (C.5)

for the upper and lower limit functions, and = So'* cos r sin YdY (C6)

and

i|' = r* cos r sin YdY (c?)

for the accepted value functions. The values of thesejntegrals

are given in table CIII, and the resulting values of A'g(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 Vg in all cases. Therefore only the accepted value of A'g will be used in each case to calculate C(r, A.). 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 b\

measuring Ng.

X. Appendix D. The Three Working Standards

The properties which standards for reflectaiu e fai'tor 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 inslnmient. Based on this definition, the best standard for calibrating an

53

E-2G
Table CII

Coefficient for the expansion of A/gl rj/cosF in powers of the angle of incidence T in radians for three different sphere coatings and three different assumptions concerning the self-radiance distribution.

Coating Curve Type bo bi X 100 62 X 100 63 X 100 64 X 100

upper limit 1 0 7.0 0 -1.1

/ accepted^ D„cr\ ri/ii c>ac)U4 [l^J < 1 -^77/^ 0 \j 0

1.03 -1.240 1 0 /I 10. / -5.33

lower limit 0 f\v u 0

upper limit I 0 5.3 0 6.1

/ accepted; Halon [15] ) r<7r/4 0 0 0 0 \ r>7r/4 1.45 -219 405 -339 107

lower limit 0 0 0 0

upper limit 0 3.8 0 1.6

/ accepted; BaS04 [16] J r<7r/4 0 0 0 0

\ r>77/4 1.17 -120 271 -248 79

lower limit 0 0 0 0

Table CIII Values of the integrals in equations (C5). (C6), and (C7) for nine values of

1.

i li" 0 0.50000 0.25000 0.25000

1 .39270 .12.500 .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 Nc(A.) for each of three coatings for three wavelengths and three different assumptions concerning the self-radiance

distribution.

Determination number

Wavelength A Upper limit Accepted

value Lower limit

BaS04 [14] 4.50 1.00486 1.00479 1.00476

5.50 1.00343 1.00338 1.00.336

7.50 1.00244 1.00240 1.00239

Halon [1.5] 450 1.00294 1.00282 1.00277

5.50 1.00233 1.00225 1.00223

7.50 1.00175 1.00170 1.00169

BaS04 [16] 4.50 1.00343 1.00335 1.00333

5.50 1.00173 1.00168 1.00167

7.50 1.002.53 1.00247 1.00247

instrument to measure reflectance factor would be a totally reflecting Lambertian 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 pL, 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 vei7 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 4360.5

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

E-26

1

1
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 ihe

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 instmment 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

E-27

856 J. Opt. Soc. Am./Vol. 71. No. 7/July 1981 V. R. Weidner and J. J. Hsia

Reflection properties of pressed

polytetrafluoroethylene powder

Victor R. Weidner and }ack 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. Techniqufes 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 rt flection 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 g'ass 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. 77, 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 > o

UJ «2 0.995

uj -o u! S 0.990f

o

c 0.985yb

0.980

PTFE POWDER

• 300 to 1800 nm . (average of 10 wavelengths) \~

2000 nm \ (average 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/citi^) 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 glcxv? 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 )/Rp, where

Rm is proportional to the reflectance of the PTF'E 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

F-3
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

5.50 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 g/cm^ 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

g/cm-^. 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 1,500 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.

F-4
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 750 nm

6° 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 lO" 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 i.UUDD i.UUoo i.UvZD 1l.UUl'i nm 4 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 CD

1.015

UJ ^

ij_ <

UJ -Ia:

I.OlO

1.005

1.000

DIRECTIONAL/HEMISPHERICAL

REFLECTANCE OF

PTFE

POWDER

/250

/(NM)

^300"

^^350

450

750

-lid^^ L i-L go 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 +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.

F-5
V. R. Weidner andJ. 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 Viewing300 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 OAO 20 U.95Z 1.001 1.022 l.UOZ 1.003 1.027 i.Ub / A CkQd u.yoD 1.012 1.018 1 ACA i.UbU 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

o >

UJ liJ

0-

PTFE

POWDER

(600 NM)

ANGLE OF INCIDENCE!

-10° -30» -50° -70°

5.0

-80° -40° 0" 40°

ANGLE OF VIEWING

Fig. 5. The bidirectional reflectance factor at 600 nm of pressed

PTFE powder having a rough surface finish.

4.0-

UJ

i:^>3.o

UJ 5

^UJ

9 °^ m

. -10°

-30°

I- -50°

-70°

2.0

.0

BARIUM SULFATE

POWDER

(600 NM)

ANGLE OF INCIDENCE:

ROUGH

J L J L

-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 G

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 Gnmi 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 resultinc; data provided some insight into the problems associa^

The authors are with U.S. National Bureau of Standards, Radio- metric 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 range. For the

15 July 1985 / Vol. 24. No. 14 / APPLIED OPTICS 2225

G-1
Table I. Round-Robin 1; Spectral Reflectance of Pressed PTFE Powder Wavelength

(nm) 1 1 2 2 Laboratory

2 2 2 3 3

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 240U U.9bU (J. 960 u.yoy

A ACQ 0.923 0.926 u.yob A A£M u.ybi A n/?A 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/cm^)

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 0.9S1 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
TabI* IL Round Robin 2; Spectral R«fl«ctanc« o( PrM«M«l PTFE Powdcf Wavelength Laboratory

(nm) 1 1 2 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.%9 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 n Qfii 0.981 0.980 0.980 0.980 0.979 U.J / *t (\ Q7ft u.y i 0 2100 0.970 0.965 0^970 0.967 0.971 0.969 0.969 0.963 0.%7 0.963 2200 0.976 0.973 0.981 0.976 0.982 0.974 0.977 0.968 0.971 0.976 2300 0.970 0.973 0.971 0.967 0.970 0.967 0.%7 0.961 0.%7 0.%8

2400 0.968 0.962 0.962 0.964 0.964 0.962 0.960 2500 0.964 0.960 0.960 0.960 0.960 0.%2 0.961 0.946 0.955

(0 905) (0 990) (0.835) (0.920) (0.800) (1.025) (1.025)

Wavelength Laboratory Average Standard (mm) 6 7 7 8 8 9 9 of 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 V.J ( 0 ( 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) 1(0.895) (g/cm3)

B. Round-Robin Experiment 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 ± O.OS-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, £md 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 bsised 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

G-3
Some of the variation in reflectance for the PTFE

specimens Usted 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

I00<

300 n m

95

^ I00< o

z

- 550 nm ?o

UJ 95

u.

LlJ

\ooi

1800 nm ^^^"X)^

95

1 1 1 1

1 1 1 1 1 1 1 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
Tabto III. DttfATMCM In Spectral R«fl«ctanc« of PTFE Obtained from

MaiHifacturara A and B W&v6l6n^n ITXC00 CUICll %f (nm) differences uncertainty

+0.004 ±0.005

AtV\ 4UU +0.003 ±0.005 ow +0.002 ±0.005

+0.002 ±0.005

700 +0.001 ±0.005

QAA +0.001 ±0.005

ono +0.001 ±0.005

lUUU 0.000 ±0.005

1 inn 0.000 ±0.005

1200 +0.001 ±0.005

xouu —0.002 ±0.005

l*«Uv +0.001 ±0.005

1 W) -0.002 ±0.005

—0.001 ±0.005

1700 -0.001 ±0.005

-0.002 ±0.005

u.uuu 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

TabI* iV. Standard Davlailon for Thra* Indapandant Daiarmlnailons of Mm 6''/Ham(spharical Raflactance Factor of Praatad PTFE Powdar t>y tha Doubla-Sphara Tachrtlqua for Maaauring Abaoluta Raflactanca

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

PLEXICLAS PLUNGER

POWDER

STAINLESS 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 sUndards. 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

pwwder 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

6-5
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, Kollmorgen

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

G-6
FORM NBS-1 14A (REV, 11 -84)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. MBS/SP-250/8

2. Performing Organ. Report No 3. Publication Date

Juiv iqpj

4. TITLE AND SUBTITLE

NBS Measurement Services

Spectral Reflectance

5. AUTHOR(S)

Victor R. Weidner and Jack J. Hsia

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

U.S. DEPARTMENT OF COMMERCE

GAITHERSBURG, MD 20899

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Final

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Same as item 6.

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 87-619843

I I Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information . If document includes a si gnificant

bi bl iogratihy or literature survey, mention it here) This documentation describes the instrumental ion, -standards, and techniques used in the measurement of spectral reflectance ove*- the ultraviolet,

visible, and near infrared spectral ranges. The documentation is diviaec

into three parts. Part I describes the guiding philosophy for maintaining

reference and transfer spectrophotometers for spectral reflectance measurements, and standards and services that are available. Part II describes the

NBS high accuracy reference spectrophotometer including specially developed

accessory ref lectometers. This instrument provides the basis for the

development of absolute NBS standards of diffuse and specular reflectance.

Part III describes the NBS transfer spectrophotometer, a high precision

commercial spectrophotometer used for calibrating Standard Reference

Materials (SRMs) •such as diffuse reflectance and specular reflectance

standards. The transfer instrument relies on master standards that are periodically calibrated on the high accuracy reference spectrophotometer

described in Part II. The transfer instrument is also used for performing

special measurements on samples submitted by other laboratories in industry

and government. References containing details and equations are reproduced

in the appendices.

12. KEY WORDS fS/x to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s)

diffuse reflectance; spectrophotometers; spectrophotometry; spectral reflectance;

specular reflectance

13. AVAILABILITY

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