m

MattaWi Hi*'

IrS

mm

.v*--**"

i

EUHMw I

I *VJ( >7J I >a,* I owm

I —

KtnHM

tKjBJ
4^ °F Co.

'"'CM 0< * NBS TECHNICAL NOTE 594"10

U.S. DEPARTMENT OF COMMERCE/ National Bureau of Standards

—i
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology,

the Institute for Computer Sciences and Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United

States of a complete and consistent system of physical measurement; coordinates that system

with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry, and commerce. The Institute consists of a Center for Radiation Research, an Office of Measurement Services and the following divisions: Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics — Nuclear

Sciences 2 — Applied Radiation " — Quantum Electronics * — Electromagnetics 3 — Time

and Frequency " — Laboratory Astrophysics n — Cryogenics *. THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to improved methods of measurement, standards, and data on the properties of well-characterized

materials needed by industry, commerce, educational institutions, and Government; provides

advisory and research services to other Government agencies; and develops, produces, and

distributes standard reference materials. The Institute consists of the Office of Standard

Reference Materials and the following divisions: Analytical Chemistry — Polymers — Metallurgy — Inorganic Materials — Reactor

Radiation — Physical Chemistry.

THE INSTITUTE FOR APPLIED TECHNOLOGY provides technical services to promote

the use of available technology and to facilitate technological innovation in industry and

Government; cooperates with public and private organizations leading to the development of

technological standards (including mandatory safety standards), codes and methods of test; and provides technical advice and services to Government agencies upon request. The Institute consists of a Center for Building Technology and the following divisions and offices: Engineering and Product Standards — Weights and Measures — Invention and Innovation — Product Evaluation Technology — Electronic Technology — Technical Analysis — Measurement Engineering — Structures, Materials, and Life Safety * — Building

Environment * — Technical Evaluation and Application 4 — Fire Technology.

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research and provides technical services designed to aid Government agencies in improving cost effec- tiveness in the conduct of their programs through the selection, acquisition, and effective

utilization of automatic data processing equipment; and serves as the principal focus within

the executive branch for the development of Federal standards for automatic data processing

equipment, techniques, and computer languages. The Institute consists of the following

divisions: Computer Services — Systems and Software — Computer Systems Engineering — Information Technology.

THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and

accessibility of scientific information generated within NBS and other agencies of the Federal Government; promotes the development of the National Standard Reference Data System and

a system of information analysis centers dealing with the broader aspects of the National Measurement System; provides appropriate services to ensure that the NBS staff has optimum

accessibility to the scientific information of the world. The Office consists of the following

organizational units: Office of Standard Reference Data — Office of Information Activities — Office of Technical

Publications — Library — Office of International Relations.

1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234.

3 Part of the Center for Radiation Research.

a Located at Boulder, Colorado 80302.

* Part of the Center for Building Technology.
Optical Radiation Measurements:

The NBS 20-, 60-, and 85- Degree Specular

Gloss Scales

Jack J. Hsia

Heat Division

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

,** °F %

**eAu o*

U.S. DEPARTMENT OF COMMERCE, Rogers C. B. Morton, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director

Issued July 1975
National Bureau of Standards Technical Note 594-10

Nat. Bur. Stand. (U.S.), Tech. Note 594-10, 32 pages (July 1975) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1975

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. C13.46:594-10). Price 85 cents (Add 25 percent additional for other than U.S. mailing).
Preface

This is the tenth 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 radiometry, photometry, and spectrophotometry in the Optical Radiation Section of the Heat 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 radiometry 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 a nonspecialist to understand the gist of the argument if not the details.

At times, certain commercial 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

111
TABLE OF CONTENTS

Page

1. Introduction „ 1

2. Definition of Specular Gloss 1

3. Calibration Equations for Specular Gloss 2

3.1 Defining Measurement 2

3.2 Partially polarized source 5

k. Refractive Index Determination of the Primary Working Standard 6

5. Instrument 7

5.1 Light Source 7

5.2 Specimen Mount 7

5.3 Receiver 7

5.*+ Data Acquisition and Data Processing .".... 7

5.5 Equipment 7

6. Procedure of Measurement 9

7. Calibration of Instrument and Error Analyses 9

7.1 Spectral Condition 9

7.2 Polarization Condition 12

7.3 Receiver Solid Angle „ 15

7.1+ Specular Angle . 17

7.5 Linearity 19

7.6 Random Error 19

8. Summary 20

9. Appendices 21

A. Equipment 21

B. Calculation of Gloss Value with Known Index Refraction of a Smooth

Dielectric Surface 22

C. Details of Mathematical Derivations of Errors Caused by Size

Difference and Misalignment of Source and Receiver Apertures 22

D. The Error in Gloss Unit Based on the Allowed Tolerance of the

Receiver Aperture and the General Equations Derived in Appendix C . . . 26

10. References „ „ 26

IV
LIST OF TABLES

Page

1. Characterization of Receiver Apertures 18

2. The Error in Gloss Unit Caused "by Deviation From the ASTM

Specification of the Receiver Apertures 18

3. Linearity Determination of Detector and Electronic System 20

LIST OF FIGURES

1. A Diagram Describing the Coordinates of the Source and Receiver

Apertures 3

2. NBS Goniophotometer 8

3. Comparison Between the Spectral Condition Specified by the ASTM Method

and That of the NBS Instrument 13

k. Comparison of the Relative Reflectance Near the Specular Angle and the

Normal Distribution Function l6

The NBS 20-, 60-, and 85- Degree Specular Gloss Scales

Jack J. Hsia

The 20-, 60- , and 85- degree specular gloss scales are established at NBS with an accuracy of about one half gloss unit. This

is one of many programs of the spectrophotometry group of the Optical Radiation Section of NBS directed toward improving the accuracy

and assurance of spectrophotometric measurements made throughout the

scientific and industrial community.

The specular gloss scales are established through an unique

technique employing polarized light flux both parallel and perpendicular to the plane of incidence. General calibration equations

are derived. NBS instrumentation and measurement procedures are discribed. Instrument calibration and error analyses are performed.

Some of the analyses can also be applied to reflectance measurements

in general.

Key Words: Accuracy; appearance; error analysis; gloss; photometry;

reflectance; scattering; spectrophotometry; specular gloss.

1. Introduction

The fundamental purpose of the spectrophotometry group of the Optical Radiation Section of NBS is to improve the accuracy and usefulness of spectrophotometric measurements.

The purpose of this Technical Note is to present the technique and instruments employed at NBS to maintain the 20-, 60-, and 85- degree specular gloss scales according to the ASTM

method. This technique and some of the analyses will be used in our future work on specular gloss and reflectance measurements in general.

Specular gloss is just one of many aspects of appearance of material surfaces [l, 2] , but it is not within the scope of this Technical Note to discuss the physiological and

psychological aspects concerning our sensations of gloss. We will treat gloss as a special

type of reflectance*. Sections 2 and 3 provide the definition and calibration equations.

Section k deals with the refractive index determination of the primary working standard.

Details of the NBS instrument and the measurement procedures are given in section 5 and 6. Calibrations of instrument and error analyses based on theory and calibration results are given in detail in section 7. Finally, in the summary the error budget is presented to

give the estimated uncertainty of measurements for different geometries.

2. Definition of Specular Gloss

According to the ASTM Method [3], specular gloss is defined as the ratio of the luminous flux reflected from, to that incident on, a specimen at the specular direction for

specified solid angles and system spectral response. To set the specular gloss scale,

polished black glass with a refractive index of 1.5&7 is assigned a value of 100 for each

of the three geometries, 20, 60, and 85 degree [3].

+Figures in brackets indicate the literature reference at end of this technical note.

*Earlier works on gloss by former and present members of the NBS staff such as Dr. D.B. Judd, Mr. R.S. Hunter, Mr. H.K. Hammond, III, and Mr. I. Nimeroff, have led to the establishment of 'the present ASTM method [3].
3. Calibration Equations for Specular Gloss

General Equations will be derived for the gloss and luminous flux ratio using an un- polarized light source according to the definition. If the light source is not completely

unpolarized, separate measurements should be made with the light source polarized parallel

and perpendicular to the plane of incidence. A calibration equation for the luminous flux

ratio is derived to permit converting the measured quantities with polarized components to

gloss for an unpolarized light source.

3.1 Defining Measurement

The method and mathematical notations of NBS Technical Note 59^+—9 [h] will be used in

the development of calibration equations. In this method, each point in the space is as- signed to either the instrument space, the sample space, or the boundary surface between

the two spaces, and the measurement is defined on the boundary surface along.

According to paragraph 6 of the ASTM Test Method [3], the sample surface should have

good planarity. Therefore, it is sensible to designate the boundary surface as a plane

parallel to the average surface and tangent to it at its farthest point toward the instrument space. The gloss value of sample x, g can be written as

Sx

= F

xs

gs (3.D

where g is the gloss value of the standard. F is the luminuous flux ratio which is ex-

°s xs pressed as

f LS E U'dit dfi u«da du dA

F = -*— 2 _ (3.2) xs .5

/ L S R U'dA dfi u«da du> dX " s

where L is the radiance input; S and S are the scattering functions of the sample and of

the standard; R is the relative responsivity of the receiver; U and u are the direction

vectors of travel of the incident and emergent radiation; dfi and do) are elements of solid

angle oriented in the directions U and u; dA and da are elements of area through which the

energy passes onto the sample and emerges from the sample; and dX is the element of wavelength.

Paragraph k.k of the ASTM method provides that the spectral characteristics of the

source-filter-photoreceiver combination shall yield the CIE source C weighted for CIE luminous efficiency function. The spectral characteristic of the radiance input L is represented by the source C relative weighting function C^ and the relative responsivity R with the luminous response V^. Since the ASTM method makes no mention of the distribution

of L and R with respect to points on the boundary plane, it is logical to assume an ideal,

namely that L is non-zero over a finite area and that R is uniform over the entire boundary. The specimen area to be measured is not specified, but this creates no problem if

the gloss of the sample is uniform.

Figure 1 shows a schematic^diagram of the source and receiver apertures. BOb forms

the plane of incidence. + dA, da are normal to the sample surface and are in the plane of

incidence. Plane XY is perpendicular to OB and plane xy is perpendicular to Ob and the

*the symbol f indicates integration with respect to n variables.

+Plane of measurement.
Fig. 1 A diagram describing the coordinates of the source and receiver apertures
points B and Id are the origins (0,0) in (X,Y) and (x,y), respectively. The X and x axes

lie in the plane of incidence. (X,Y) and (x,y) are scaled so that 0B=1 and Ob=l, respectively. The geometric characteristics of L and R are indicated by the name "specular

gloss" with specular angle y . The angular limitations described in paragraph 1+.2 and

table 1 of the ASTM method require that L=0 outside of the source aperture and that R=0

outside of the receiver aperture.

Thus

L=C, for y -AT., < tan X < y + AT in the plane of incidence

A o J. o _L

and o <| tan" y| < Ar from the plane of incidence

over a finite area

and zero elsewhere where T is the angle of incidence, and

R=V

X over the entire boundary

-1

for y -Ay.. < tan x < y + Ay, in the plane of incidence

-1

and o<| tan y| < Ay from the plane of incidence

and is zero at other angles. Where y is the angle of viewing.

Equation (3.2) can be rewritten as

fc, D V, dX „ J A X A XS

Where D

fC, D V, dX

J

X S A

x or s -/'x or s U«dA u«da dfi dw

(3.5)

(3.6)

Equation (3.6) can further be expressed as

D = /J S x or s x or s cosT dA cosy da dft da>

where

cosr = (cosy + X siny )(l + X + Y

)" o o

dfi = dXdY(l+X2 + Y

2 )" 3 ' 2

cosy = (cosy + x siny )(l + x^ + y^)"

o o

du = dxdy(l + x

2 + y2 )~

Equation (3.5) implies the following assumptions for a defined measurement:

(3.7)

(3.8)

(3.9)

(3.10)

(3.11)

a. The experimental conditions are the same for both the sample and primary standard, that is, no change in source, filters, aperture sizes, angles of incidence

and viewing, detector and gains.

b. The detector system response is linear.

c. The source is unpolarized.

k
3.2 Partially Polarized Source

Since the measured gloss is sensitive to source polarization, when a partially polarized light source is used, separate measurements should be made with light polarized parallel and perpendicular to the plane of incidence. The gloss value is then computed in

such a way that fulfills the requirement that the light source is completely unpolarized.

An unpolarized light can be assumed to consist of two equal components: a component,

C... , polarized parallel to the plane of incidence, and a component, C^., polarized perpendicular to the plane of incidence. For a detection system insensitive to polarization,

equation(3.5)can be rewritten as

_ /

C A1

Dxl V

X dX+ /

C X2 Lx2-.V, dX

/

C Al D

sl

V

X dX+

/

C X2 L

s2 'A

(3.12)

V, dX

Since C. = C^ , equation (3.12) can be simplified to

F

xs

" (5xl

+ S

x2

)/(Ssl

+ V (3.13)

where D = /C

X D V.dX

fc, v, dx (3.H0

'X "X

For a partially polarized source, C!*, the receiver signals, I, for sample and standard measured with light polarized parallel and perpendicular to the plane of incidence,

are:

*xl- K[/

C

X*l Dxl VX dA

Jx2 = K/

C X2 Dx2 V

X dX

X sl " K/C X1 D

sl

V

X dA

J s2

= K/

C X2 D

s2

V

X dA

(3.15)

(3.16)

(3.17)

(3.18)

where K is the instrument constant. But C' # CT* , since the light source is partially

polarized. C. and C* can be expressed in terms of C^ and C,

C X1 " l C X1 (3.19)

and

C X2 = m C X2 (3.20)

where I and m are proportionality constant that have been measured and found to be roughly

independent of wavelength.

The ratio of the V. weighted irradiance of parallel-polarized light to that of perpendicular-polarized light is called the polarization ratio, a, /

C X1 v

> " /

C X2

V

>

dX

"dX (3.21)
Inserting equations (3.19) and (3.20) into equation (3.21) and using the relation

C = C, , the expression for a reduces to

AX kd

a = l/m or I = a m (3.22)

Using relations (3.19), (3.20), (3.22) and (3.1*0 in equations (3.15) to (3.18), we

have

5

xl

= V^ a m/

C Xl

V

A dX > (3.23)

5

x2

= Ix2 /(Km/

C A2V

A dA) (3.2U)

5

sl

= I sl /(Kam/

C ^^ dA) (3 * 25)

5

s2

= I s2 /(K m/

C A2V

A dA) (3.26)

where C, = C, . AX kc.

Combining equations (3.13), (3.23), (3.2U)-, (3.25) and (3.26), the luminous flux

ratio can be expressed by the measured quantities I , . I ^, I ,, t c^a TM. xl x2 si S 2'

Xxl

+ a Jx2

F

xs I ' + a I I (3.27)

si s2

Thus the gloss value of sample x can be written as

I . + a I _ xl x2

1 -, + a I o si s2

where g is the gloss value of the standard,

s

!3.28;

k. Refractive Index Determination of the Primary Working Standard

The primary working standard is a highly polished, plane, black glass. Its refractive index for sodium light at 589 nm was determined by means of the Abbe total- reflectometer which has a glass hemisphere with a refractive index of 1.7971 for sodium light.

The method consists of directly measuring the angle of total reflection at the plane surface of the hemisphere, on which the black glass is laid. Intervening is a thin liquid

film of refractive index higher than that of the black glass, in order to avoid any chance

of total reflection before the black glass surface is reached. A sodium light was used to

illuminate from the hemispherical side, and a telescope attached to a rotatabl.e arm with

an angular index was used to view the bright and dark fields and determine the critical

angle, <jt> . The refractive index of the black glass is equal to 1.7971 sin £ .

The total-reflectometer was first calibrated using NBS #38 refractive index standard

with a value of 1.522727 at 25°C. This standard is in the shape of a triangular prism

with one surface highly polished. Its refractive, index measured on the total-reflectometer at 25°C is 1.5228. Thus the accuracy of the total-reflectometer in measuring refractive index around 1.52 is 0.0001.

The refractive index of the black glass standard (NBS NO. 600315-B) is determined to

be I.5269 ± 0.0001. The primary working standard is assigned, according to the ASTM

method [3], gloss values of 89.2, 93.6, and 99. k for the 20, 60 and 85 degree geometries,

respectively, (See Appendix B).
The uncertainty of ± 0.0001 in refractive index will contribute a systematic error in

the measurement of a high gloss sample of no more than 0.027, 0.016, and 0.002 gloss unit

for specular angles of 20, 60, and 85 degrees, respectively. The luminous flux ratio F

is smaller for a low gloss sample. Thus, according to equation (3.1), an even smaller error would result in the low gloss sample "by this uncertainty in the primary working stan- dard.

5. Instrument

The NBS goniophotometer is used for our gloss measurements „ The design geometry is

that of a monoplane goniophotometer with a fixed source unit, and with specimen and re- ceiver units each rotatable about an axis normal to the plane of incidence. A schematic

drawing of the goniophotometer is shown in Figure 2.

5.1 Light Source

The source contains a 100-watt incandescent lamp (rated for 6.6a) with a singlycoiled tungsten filament. The current in the tungsten lamp is regulated by a power supply

using external sensing (0.01$ regulation).

The lamp filament is imaged onto a precision source aperture through an achromatic

condenser lens. With another achromatic lens (f.l. 192 mm), the flux that leaves the source aperture is collimated into a 50-mm diameter beam. Either an iris diaphragm or an adjustable rectangular diaphragm is used to limit the size and the shape of the collimated

beam. Filters can be used to change the spectral distribution. A rotatable, glass-laminated plastic polarizer is used to provide linearly polarized light. A shutter is mounted

after the polarizer.

5.2 Specimen Mount

The specimen mount is on a large rotatable table ( i+80 mm in diameter) engraved with

«an angle scale. It will hold specimens that range in size up to 100 mm by 200 mm rectan*» gular and up to 10 mm thick. The table can be rotated manually or by using a stepping

motor.

5.3 Receiver

The receiver optical components are enclosed in a light-tight baffle tube, at the

front of which is placed an iris diaphragm. The acromatic collector lens (f.l. 508 mm),

70 mm diameter, is placed behind the iris diaphragm. Receiver apertures of different

sizes may be mounted at the focal point of the collector lens to restrict the solid angle

within which the flux from the specimen is collected.

A thirty-cm diameter sphere coated with BaSO, powder is placed directly behind the

receiver aperture. The detector, mounted in a housing attached to the sphere, is an 11-

stage, end-on photomultiplier with an S-20 response. The high voltage power supply is

voltage regulated to 0.001$ and the anode current is measured by using a preamplifier and

a picoammeter, with the voltage output from the picoammeter measured by a digital voltmeter.

5.1+ Data Acquisition and Data Processing

Data are obtained with a data acquisition and control system which consists of a teletypewriter, logic circuits, and a timer. The control system has start and stop codes,

codes for recording data, and codes for sequentially actuating the electrical switches.

The angles of incidence and viewing and the shutter can be programmed with a punched paper

tape, or a minicomputer, allowing data to be taken automatically.

5.5 Equipment

Appendix A[5] contains more detailed information of apparatus employed and gives manufacturer and model number.
UJ

u

<u •p1

-poao

•Hao

ei

to

•H
6. Procedure of Measurement

The polarization ratio, a, is defined in section 3.2 as the ratio of the V. weighted

irradiance of the light polarized parallel to that polarized perpendicular to the plane of

incidence. Polarization ratios of the light source are determined before and after each

set of measurements.

To illustrate how a set of data are obtained, the procedure for three sample measurements will be discussed which will demonstrate how measurements are made on from one to

three samples. A set of measurements consisting of 35 readings, with 25-second intervals,

is recorded on a punched paper tape according to the sequence:

0,10,0,11,0,12,0,13, 1

0,10,0,13,0,12,0,11,0,10 2

0,11,0,12,0,13,0,10,0, 2

13,0,12,0,11,0,10,0 1

All readings in lines marked '1* are obtained with the source polarized parallel to the

plane of incidence, and in lines marked '2* with the source polarized perpendicular to the

plane of incidence. ! 0' is a dark-current reading. '10', 'II 1 , '12', and '13' are the

readings obtained when the black glass standard, sample 1, sample 2, or sample 3 respectively are in the sample holder. These data are then processed by computer as follows:

(a) The dark currents on both sides of each 10, II, 12, and 13 are averaged and subtracted from these readings, yielding a sequence of 17 adjusted signal currents.

1(0), 1(1), 1(2), 1(3), 1

1(0), 1(3), 1(2), 1(1), 1(0), 1(1), 1(2), 1(3), 1(0) 2

1(3), 1(2), 1(1), 1(0) 1

) , 1(1) ,1(2) , I(3)

1

, 1(0) , I(D 2

, I(2)

2

, and l(3)

2 together

it ion ratio, a are then used to compute the gloss value of the

(b) The averages 1(0).

with the polarizat

samples, g(i), by the following equation according to equation (3.28):

:d =

I(i)

x + al(i)

2 I(0)

1

+ al(0)

2 g(0) (6.1)

where i = 1, 2, & 3 and g(0) is the assigned gloss value of the black glass,

primary working standard at the measured angle.

7. Calibration of Instrument and Error Analyses

In this section instrument calibration and error analyses will be performed for spectral condition, polarization, receiver solid angle, specular angle, linearity, and random

error. Under each subsection the following format is used: 1. deriving mathematics of error analysis to find, out what parameter we need to know, 2. describing measurements of

parameters, that is calibration of instrument components, and 3. indicating results and

contribution to error budget.

7.1 Spectral Condition

7.1.1 Derivation of Mathematics

From equations (3.1) and (3.5), the gloss value of sample x can be expressed as
s„ =_. AD V,dA x A «/V V.dA B

s

S A (T.l)

Let f(y) ( =c tT>) lDe ^e normalized CIE source C - luminous efficiency combination

function and y be the rescaled wavelength from to 1 for 1+00 to TOO nm. Equation (T.l) can thus be written as -4f(y) Dx

dy

f(y) D dy fe s s

and

£f(y) dy = 1

(T.2)

(T.3)

Systematic error would be introduced if the experimental spectral condition deviates

from the above. In such case, the gloss value obtained for sample x is

dy

f'(y) D

s dy * S,

and the systematic error introduced will be

Ag = g* - g„

(l.k)

(T.5)

As will be indicated in the next subsection, the difference between function f(y)

and f(y) of this experiment can well be expressed as a sine function

f'(y) = f(y) + h sin(2iry)

where h is the proportionality constant.

(1.6)

Assuming D and D are quadratic functions of y, where D and D in this case are the

reflectance functions, equation (1.2) and (l .h) can be rewritten as £ ' 2-

to f(y)[a"+ b"y + c"y ] dy

/* "] * o

/ f(y)[a + by + cy2

] dy

Jo

(T.T)

and

Jo [f (y) + h

Sx

= A \t(v) + h

sin 2iry][a'+ b'y + Cy2

] dy

f

1 [f(y) + h sin 2Try][a + by + cy2"] dy

Upon integration, equation (T.8) is simplified to

, X f( y )(a ' + b 'y + c >2) ^\-h {1°' +

(T.8)

/" 1

f(y)(a + by + cy

2

) dy] - ~ (b +

(1.9)

10
Inserting equations (7.7) and (7.9) into equation (7.5) » we have the systematic error Ag expressed by the following equation

Uv - Vu

V(V-v) * gs

where

V - /

1 f(y)(a + by + cy

2 )dy

u = h(b" + c*) /2ir

v = h(b + c) /2tt

(7.10)

(7.11)

(7.12)

(7.13)

(7.U0

7.1.2 Calibration of Instrument

In order to evaluate the spectral condition of the instrument, measurements are made of the color temperature of the source, the relative spectral response of the receiver, and the spectral transmittance of selected filters to obtain the composite

source-filter-receiver spectral condition.

a. Color temperature of the source unit.

The source unit consists of the tungsten lamp, the condenser lens, the collimation lens, and the polarizer. The lamp current is set at 6.50 amperes. A freshly

pressed MgO tablet is placed in the specimen mount oriented to yield a U5-degree

angle of incidence. A red to blue ratio photometer is used to determine the color

temperature [6] by sighting on the MgO tablet. The spectral reflectance of the

freshly pressed MgO is non-selective within 1% with respect to wavelengths in the

visible region. Thus the use of an MgO diffuser will have no significant effect on the measurement of color temperature. The color temperature of the unit was determined to be 2856 K ± 30 K.

b. The relative spectral response of the receiver.

The relative spectral transmittance of the collector lens and the twelve-inch

diameter sphere was measured by using a small sphere over the detector as the detection unit.

The relative spectral response of the detector alone was measured on a photodetector spectral response console. The console has a 3.5 nanometer spectral reso- lution and an uncertainty of ± 3 percent of the peak response. In this measurement,

the detector is irradiated diffusely by light reflected from a pressed MgO tablet.

The detector anode current is adjusted to about 1 x 10~'A, approximately the level

used when making gloss measurements. The relative spectral response of the detector

is determined by the ratio of its output to that of a spectrally non-selective thermopile at each wavelength. A reference thermopile is used in conjunction with an electronic servo system to maintain an approximately constant flux at the test port

of the instrument regardless of its wavelength. The test port flux is measured with

a large area standard thermopile at frequent intervals to check the calibration of

the instrument.

c. Source-filter-receiver spectral condition.

With the color temperature of the source unit and the response of the receiver

unit measured, a set of filters is then selected such that the spectral condition of

the source-filter-receiver combination closely resembles that of the CIE luminous

11
efficiency with CIE source C. The comparison is given in figure 3.

7.1.3 Contribution to Error Budget

The proportionality constant h, first introduced in equation (7.6), is determined to

he approximately 0.13 from figure 3« Fitting the measured 20-deg. specular spectral re- flectance values of the black glass and a ceramic tile having a 20- deg. gloss of 60 with

quadratic function in y as defined preceding equation (7.2), one has

a = 0.0^55, b = -0.001+7, c = 0.0022, and

a' = 0.0300, f = 0.0009, C = -0.0002.

For a first approximation, U and V in equations (7.11) and (7.12) can he reduced to a" and a respectively. Using a standard with gs = 89.2 and all the quadratic parameters to

calculate u and v, the systematic error Ag is computed to be -0.07 gloss unit. The error will be smaller for lower gloss specimens.

7.2 Polarization Condition

7.2.1 Derivation of Mathematics

Refer to equation (3.28). Let the polarization ratio, a, be the only variable.

Taking the derivative of gx , we have the error in gloss value caused by the uncertainty

in determining this ratio as follows

Agx

= gx

I "f^- >

:

I (7 L?)

where

and

Jx

= Xxl

+ aIx2 <7.16)

X

s = Z sl

+ aI

s2 <T.1T)

Uncertainty in the polarization ratio can be caused by the measurement imprecision

and imperfect polarization. Imprecision of measurement uncertainty is due to the noise

in the measurement system. The effect of an imperfect polarizer will be discussed below.

When the polarizer leaks in the direction normal to the intended direction of polarization, systematic error will be introduced in a. Define the transmittance ratio of the

polarizer, 3 S as the ratio of the transmittance of the polarizer in the direction normal

to the polarization direction to that in the polarization direction. $ is assumed to be

independent of wavelength. Under this condition, the signals obtained by the instrument

are

Zxl

r

x2

Kf

CXl D

xl YX dX+ K/

3 °X2

Dx2

dA (7 ' 18)

K/C X2 \2 Y

X dX + Kp°'xi Dxl

dA (7 - 19)

and similarly, for if and l" with x replaced by s in equations (7.l8) and (7.19). In terms of the expressions by equations (3.15) and (3.l6), the above two equations can be

simplified to

^xl

=I

xl

+3I

x2 (7 ' 20)

12
z

z>o

UJN

O

z

<

UJ

(r

<

3 -

2 -

400

1931 OBSERVER $

SOURCE C

THIS INSTRUMENT

500 600

X (nm) —

700

»T* y

y

Fig. 3 Comparison between the spectral condition specified by the ASTM method and that

of the NBS instrument

13
Xx2

=I

x2

+ eixl ^.21)

and similarly,

X sl

= J sl + 6I

s2 ^.22)

r

s2

Ib2 +W^ (T ' 23)

The luminous flux ratio obtained by using an imperfect polarizer will be calculated

as

. ^xl * aI

^x2

XS " ^sl + aI %2

(1.2k)

Combining equations (7.20), (7.21), (7.22), (7.23), and (7.2U), we have:

Jxl

+ a

'Zx2

F

x's - i* ; a-I ^.25 ) si s2

where

7.2.2 Calibration of instrument

The leakage of the polarizer, installed in the instrument, for radiation polarized

normal to the intended direction of polarization on the source unit was evaluated. Another polarizer made with the same material as that of the polarizer to be determined is

placed on the receiver unit. Signals with the polarizing directions . 6f the two polarizers parallel (P ) and crossed (P?

) to each other are measured:

P

1

= T

2 + a2

Tjl 2 (7.27)

and

P

2 = (1 + a) TT£ (7.28)

where for each polarizer, T and T^ are the transmittance in the polarization direction

and in the direction normal to it, respectively. Solving equations (7.27) and (7.28),

the transmittance ratio of the polarizer can be calculated as

B

. !t. (p

i * np2 )

h

-y± - nP

2 1

t a^P1+ nPs^^P^nP^J

Where n = 2a/ (l + a). Since P

2«PlS equation (7.29) can be reduced to

(7.29)

6 TT^y \

<*•»>

lit
The transmittance ratio of the polarizer, g was determined to be -0.0035.

The polarization ratio a of the source unit is approximately 0.9 with an uncertainty

of about OoOOl due to the noise of the measurement system.

7.2.3 Contribution to error budget

From equation (7.26), using the values of a and g, a" = 1.00007 a is obtained. Thus

the total uncertainty, due to both the imperfect polarizer and measurement noise, of the

polarization ratio a is 0.00107. The systematic error in the gloss value caused by this

uncertainty, using equation (7.15), is computed to be much less than 0.01 gloss unit for

both low and high gloss samples.

7.3 Receiver Solid Angle

7.3.1 Derivation of mathematics

Referring to equation (7.1), the gloss value of sample x is expressed as ./C, D V, dA

A x A yv> V, dA

S A

s

s (7.31)

For simplicity, assuming D and D are independent of A, one has

Dx

Sx

" D ' Ss s

From equation (3.7) » the above equation can be expressed as

•uS cosT dA cosy da dto dft

(7.32)

Sx f\ S cosT dA cosy da dto dft

' S

s (7.33)

When the solid angles subtended by the source and detector are small, cosT and cosy are nearly constant. Assuming. the light is uniformly distributed on the sample and the sample

surface is homogeneous, equation (7.33) can further be reduced to

*2 .1S dto dfi x /

S dto dfi s (7.310

The scattering function from the polished black glass is represented by S . Since the re- flected beam size is much smaller than that of the receiver aperture, a small deviation

in the receiver aperture dimension from that specified by the ASTM method will not change

the integration in the denominator. Equation (7.3*0 can therefore be expressed as,

g^ = K / 2 S^ dco dft (7.35) fThe characteristic surface scattering function of a sample can generally be ex- pressed by a normal distribution function. The empirical evidence is shown in figure h. The normalized reflectances of a roughened black glass are given, as a function of angles

of viewing with 1.2 deg. circular receiver aperture. The angle of incidence is fixed at

60 degrees from normal. Some theoretical considerations of scattering and reflecting

properties of surfaces are given in reference [9].

In Appendix C, a general equation is set up for estimating the uncertainties in

gloss caused by deviation from the specification of the aperture sizes and misalignment.

15
EXPERIMENTAL DATA

NORMAL DISTRIBUTION

FUNCTION

(0.2° OFF- SPECULAR )

o

z

oc

1.0

.8

.6

N 4 J—

_l

<

o

Z

.2 1-

-5 -4 -3 -2 -I

(0-60°)

Fig. U Comparison of the relative reflectance near the specular angle and the normal

distribution function

16
Finite sizes of source and receiver apertures are considered. Also included in the

general equation is the displacement of the angular peak location of the reflectance

curve designated as the off-specular peak in reference [10].

7.3-2 Calibration of instrument

Due to the monoplane design, the goniophotometer was only used to measure 9 , the

angular dimensions of receiver apertures in the plane of incidence. The widths of the

receiver apertures in and perpendicular to the plane of incidence were measured with a micrometer. The angular dimensions of the receiver apertures perpendicular to the plane

of incidence were calculated.

For the determination of 9jj, a source aperture subtending 0.75 degree in the plane of

incidence was used. The light beam was adjusted to a width of 5 mm in the plane of incidence. The receiver aperture was scanned to determine the angle between the points at which the signal dropped to half its center value. This is defined as the angular width

of the receiver aperture. For example, to calibrate the receiver aperture with k.k

degree nominal dimension, first the receiver unit is lined up with the light source. This

sets the receiver position at degree. The high voltage power supply was then adjusted

to 2.600 volts DC on the digital voltmeter. The receiver was scanned around +2.2 degree

and -2.2 degree, and the reading recorded. With an interpolation method, the two angular

positions yielding 1<,300 volts DC were determined. The sum of the absolute values of the

two angular positions is the angular width of this receiver aperture in the plane of incidence.

The respective widths of the receiver aperture x,y in and perpendicular to the plane

of incidence were measured by using an optical scanning device. The angular dimensions

of the receiver aperture perpendicular to the plane of incidence, , was then calculated

using the following equation

-lr

©, = 2 tan -[(£) tan (~) ] [rad], (7.36)

The results of the calibration of the receiver aperture used for 20, 60, and 85 degree gloss measurements are presented in Table 1. Table 1 also contains the ASTM specified values and allowable tolerances, the measured values and uncertainties, and the deviation of the measured value from the specified value.

7»3.3 Contribution to error budget

Using the general equations derived in Appendix C and measured data of receiver apertures in table 2, the error in gloss value caused by the deviation of the receiver apertures of this instrument from that specified by the ASTM method is shown in table 2 which

also includes off-specular angle designating the displacement of the angular peak location

of the reflectance curve from the specular angle.

7.*+ Specular Angle

7.^.1 Derivation of mathematics

In section 7.3.1 and Appendix C, a general equation is set up for estimating the uncertainties in gloss caused by misalignment of the source and detector, that is, the deviations of the angles of incidence and viewing from that specified by the ASTM method.

Also included in the general equation is the displacement of the angular peak location of

the reflectance curve designated as the off-specular peak in reference [10].

l.k.2 Calibration of instrument

The source and receiver units as well as specimen mount are first aligned. The optical axis of the receiver unit is in line with the optical axis of the source unit.

When both units are set at zero degree across the turntable, the common axis ajoins, but

17
Table 1. Characterization of Receiver Apertures

In plane of measurement

(Full Angle)

Perpendi cular to plane of measurement

(Full Angle)

ASTM

Spec.

NBS

Measured Uncertainty

ASTM

Spec.

NBS

Measured Uncertainty

20- deg.

Receptor

1.8° 1.81° ±0.01° 3.6° 3.613° ±0.01°

tolerance ±0.05 c ±0.1°

Deviation

from ASTM

0.01°

0.013°

60- deg.

Receptor

k.k° i+.i+3° ±0o01° 11.7° 11.703° ±0.01°

tolerance ±0.1° ±0.2°

Deviation

from ASTM

0.03° 0.003°

85- deg.

Receptor

k.0° U.oi° ±0.01° 6.0° 6.000° ±0.01°

tolerance ±0.3° ±0.3°

Deviation

from ASTM

0c01° 0.000°

Table 2. The error in gloss unit caused by deviation

from the ASTM Specification of the receiver apertures

NBS Goniophotometer

deviation from ASTM Spec.

Gloss

Degree

OffSpecular

angle (deg.)

Aa

(deg.)

Ab

(deg.) 30 50 70 i

20 0.01 0.013 0.07 0.07 0.06 1

60

60 0.5

0.03

0.03

0.003

0.003

0.10

0.11

0.11

0.12

0.11

0.12

85

85

85

0.5

1

0.01

0.01

0.01

0.0U

0.01+

0.0U

0.0*1

0.0U

0.05

0.0U

0.0*1

0.05

18
is perpendicular to, the axis of rotation of the turntable.

The angular displacement scale of the turntable is checked for accuracy from 0° to ± 85°. A standard angle block accurate to ±5 seconds is used together with an auxiliary

collimator and a sighting telescope. A standard angle block with two mirror-like sur- faces is secured on the specimen mount. The angle between these two surfaces is 95 degrees (compliment of 85 degrees). With the turntable set at 0°, the auxiliary collimator

is adjusted in order to view the reflected light from the angle block through the telescope cross hair and the reading recorded. The turntable is then set at 85 degrees. The

above sighting procedure is repeated. The difference between these two readings is the

deviation from the 85 degree setting. The angular setting accuracy thus determined is

within 0.02 degree.

7.1*. 3 Contribution to error budget

For 85-degree gloss measurement, a 0.02 degree misalignment in incident angle and

viewing angle will each yield a change of about 0.1 gloss unit and less than 0.03 gloss

unit for 20- and 60- degree gloss measurements.

7.5 Linearity

7.5.1 Derivation of mathematics

Refer to equation (3.28).

in gloss value determination.

Non-linearity in the measurement system will cause error

The error can be evaluated by the following equation:

Ag = g x x

AI . + aAI _ xl x2

I + al

L xl x2

AI . + aAI

" si s2

I , + ol _ si s2

(7.37)

where AI , AI , AI , and AI are non-linearity errors.

jCjL JLc. SJ_ 'd> c

7.5.2 Calibration of instrument

The linearity of the detector and electronic system is measured by using the lightaddition method with a double-aperture apparatus [7], 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. The non- linearity is less than 0.05 percent of the full-scale reading. The results are presented

in table 3 together with the standard deviation of the non-linearity determination.

7.5.3 Contribution to error budget

Departure from a true non-linear response is corrected in determination of gloss

values by using the values in table 3. Note that the standard deviation of the linearity

correction is less than 0.008% thus making a negligible contribution to the random error

in gloss measurement.

7.6 Random Error

The measurement procedure described in section 6 is used to minimize the effect of

linear drift.

The random error dg of the measured gloss g is given by

dg = x €*-#)

2 -fW**-fHT 17.38)

19
where 1^ = 1^.+ al

x2

and I

g = I gl + otl^. dl^, dl^, dl

gl , and dl

s2 are evaluated from

measurements. Random error amounts to O.lU, 0.10, and 0.06 gloss unit for samples with

gloss values of 70, 50, and 30, respectively.

Table 3. Linearity determination of detector and electronic system

I (%) M(%) SD(AI) %

10

20

30

Uo

50

60

70

80

90

100

-.0303 .0022

-.01+76 .0033

-.051+1 .0039

-.0521+ .001+7

-.okk6 .0059

-.0333 .0069

-.0208 .0073

-.0095 ,0066

-.0018 .001+1+

0. 0.

where

I is the measured radiant flux in percent of maximum

aAI is the amount of the linearity correction required to obtain the true radiant

flux in percent of maximum, 1=1 + AI

EL SD(AI) is the standard deviation of AI.

8 . Summary

In this technical note the NBS procedure for measuring gloss according to ASTM D523

has been analyzed to determine the accuracy with which the measurements can be made.

All the components of errors discussed above are summarized below:

Component of error Range of error

(Gloss Unit ) 1. Spectral condition 0.01+ - 0.08

2. Polarization condition <0.01

3. Receiver solid angle 0.07 - 0.12

1+. Specular angle 0.03 - 0.20

5. Linearity <0.01

6. Random error 0.06 - 0.11+

20
The overall uncertainties of the 20-, 60-, and 85- degree gloss measurement geometries

are computed as the sum of the component errors.

Uncertainty at Selected Gloss Levels

(Gloss Unit)

70 5P_ 30

0.5 0.5 O.k

0.5 0.5 0.3

0.7 0.6 0.5

Geometry (deg. )

20

60

85

The NBS procedure utilizes a light source polarized parallel and perpendicular to

the plane of incidence. Calibration equations are derived to convert the measured data to

gloss unit according to the definition. The refractive index of the primary working stan- dard has been determined. Instrument components are described and calibration results are presented. A detailed error analysis has been performed.

Using the ASTM allowed tolerance for receiver apertures and the general equations

derived in Appendix C, the equivalent allowed tolerance in gloss is about one and half

units for 85- degree gloss measurements, or an allowed range of three gloss unit which is

rather large (see Appendix D). Perhaps this ASTM allowed tolerance for 85- degree gloss

measurement should be given further studies. The development of intermediate gloss standards with good planarity and gloss uniformity is also one of the continuous efforts in

NBS directed toward improving the accuracy and measurement assurance of gloss measurement

in the industry. Progress in this and other efforts by NBS to improve gloss measurements

in the field will be reported in future technical notes.

The author thanks Dr. William H. Venable, Jr. for many stimulating discussions con- cerning this Technical Note. Mr. Wiley A. Hall determined the color temperature of the

source unit and Mr. Robert J. Bruening measured the relative spectral response of the detector. The angular setting of the turntable was calibrated by Mr. Burnice N. Norden.

The author acknowledges Mr. Kenneth L. Eckerle's assistance in the Linearity determination

using double-aperture method. Appreciation is extended to Mr. Irving Malitson for the

loan of a refractive index standard and help in refractive index determination of the

primary gloss working standard, and to Mr. William B. Fussell for helpful consultation on the mathematical analyses in Appendix C.

9. Appendices

A. Equipment*

SOURCE UNIT

KEPC0 regulated DC power supply

model KS I8-5OM-6956, Ser. c-33685

Leeds & Northrup shunts 0.1 ohm, 15 amp; 0.5 ohm, 10 amp,

DIGITEC (United System Corp. ) DC voltmeters

model 202N, ser. 8l0Uc

model 251, ser. 1553

"Certain commercial instruments or materials are identified here in order to specify ad- equately the procedure. In no case does such identification imply endorsement or evaluation by the National Bureau of Standards.

21
DETBCTOR UNIT

John Fluke MFG. Co. Inc. high voltage DC power supply

model 1+13D, ser. 157.

DATA ACQUISITION UNIT

Keithley Instruments high speed picoammeter

model Ul7, ser. 33339 with model 1+170 input head,

using 10"' V scale.

DANA digital voltmeter model 5^03, ser. 5^2131A

accessory module 020. using DC mode, 10 V range.

COMPUMETRICS control data acquisition system.

Industrial Timer Corp. timer (model Cu-A).

Teletype teletypewriter.

B. Calculation of gloss value with known index of

refraction of a smooth dielectric surface

According to the ASTM method [3], the gloss value of the primary working standard

at specular angle y , g [y ), can be obtained as follows with known refractive index nn

.

p(yo

. n=n ) gS

( V

=

P ( V n=i: 5 67 )' 10° (Ba)

Where p(y »n) is the specular reflectance determined by the Fresnel's equation:

p(y ,n) = h

sin (y - Y ) tan (y - Y ) o o

,2 /„ . „*s + P + y") tan^ (y„ + y') (B.2)

and y" = sinrl (!ili) \

1 (B.3)

C. Details of mathematical derivations of errors caused by size

difference and misalignment of source and receiver apertures

Refering to equation (7.32), the gloss value of sample x is expressed as DD

B

s

s (7.32)

The error in gloss value caused either by incorrect dimensions or misalignments of

source and receiver apertures, can be determined from the derivative of equation (7.32):

dg dD dD x x s , c

» g D

" D ^- 1; X X s

Refer to equation (3.7). For small subtended solid angles of source and receiver apertures, uniform illumination, and a homogeneous sample surface, D and D can be ex- pressed as

D =// S dojdfi (C.2)

s f s

22
D =/ S x J

x

doodft (C.3)

Where S and S are the scattering functions of the primary standard and the sample, re- spectively.

The scattering function S of the primary standard is almost a delta function. A

small deviation of the receiver aperture size from that specified, or misalignment of

source and receiver aperture, will not change the value of D except due to index of re- fraction.

The characteristic scattering function of a sample can generally be expressed by a normal distribution function of angular displacement from the specular angle. (See

figure k and reference 9)« Consider the rectangular source aperture (2A, 2B) and re- ceiver aperture (2a, 2b). For small subtended solid angles of source and receiver apertures 2A and 2a are approximately equal to the angular dimensions in radian in the plane

of incidence while 2B and 2b are angular dimensions perpendicular to the plane of incidence and 1 + x2 + y2 - 1 and 1 + X

2 + Y

2 - 1. From equations (3.9) and (3.11),

equation (C.3) can be written as

/• B >• A y.b f

a

= / / / / S c **-B J-A J-b J-a. Dx

~ / / / / SjlxdydXdY (C.U)

Where S = exp{-l/2[ (x-X-d)

2 +'>(y-Y)

2

]} (C.Ua)

and d is the off-specular angle in the plane of incidence.

Four different cases will be considered:

(i) Size error in receiver aperture: the dimension of the receiver aperture is

(2a + 2Aa, 2b + 2Ab) and the receiver aperture is centered on the mirror image of

the source axis.

/• B r A f

b+Ab /*a+Aa -III I

s dxdydXdY

J-B J-A J-\>-&> •'-a-Aa x

D = X jU

dD = X D'-D

X X

dD =

s

(C5)

(C6)

(C7)

(ii) Size error in source aperture: the dimension of the source aperture is

(2A + 2AA,2B+2AB) and the source aperture is centered on the specular angle.

/B+AB rA+AA /* b /• a

/ II s dxdydXdY (C.8)

•B-AB J-A-AA J-b J-a X

dDXXX = D* - D (C.9)

For a uniform illumination D is proportional to the solid angle subtended by the

source aperture. Thus

dD (2A + 2AA)(2B + 2AB) - (2A)(2B) AA AB AA« AB ~eT

= (2A)(2B)

= ~A

+ B~+ A«B (CIO)

s

23
(iii) The receiver aperture is misaligned Aa and Ab.

Dx /B fk /*b+Ab /*a+Aa

/ / / S dxdydXdY (C.ll)

B J-A y-b-Ab -/-a+Aa

dDXXX = D' - D (C12)

..

dD

s = (C.13)

(iv) The source aperture is misaligned AA and AB.

/B+AB rA+AA /• b fa.

\ II s dx<aydXdY

B+AB J -A+AA J-b J-a. X (ClU)

dDXXX = D' - D (C.15)

dD = (C.16)

s

Using the definition of error function and equations (C.l) and (C.Ua), the error in

gloss value caused by the above four cases can be evaluated considering both first and

second orders.

(i) Receiver aperture (size error)

dgx

1 r 12 (Aa) 2I 1 r [2 (Ab) 2

-j m^ |_V Aa +S ^

' ea t—J

+ \ L2R

c* Ab + 2 h Ec t—J

+ m^ [VVAa' Ab

] - (ciT)

(ii) Source apertiire (size error)

dg

x _ 1 [\, .. . ./5\. (AA) 2

1 .1 r„ .« . _ fg, (AB)'

(iii) Receiver aperture (misalignment)

dg

v

! T f

2

" (Aa)

2

"| 1 [ f2 (Ab)

2 " "| M^[RB Aa+V7 EA—J+ ^

[

2 V7 Ec-2—J (C - 19)

(iv) Source aperture (misalignment)

\2t , , rr /a-d"* 2 . isx

i r

x 1

[2 (AA)^l 1 T [2 (ABr-,

\7 EA—J

+ ^

[

2 i

E

c -r-J

(c - 20)

21*
gs w andg =— jM^

s

(C.21:

where

M

l

= Vf EA

+ (U + A)R

l"

(U " A)R

2 + (V + A)R

3 "

(v " A)R

1+

M

2 = 2 Vf E

C + 2(b + B)R

5 " 2(b " B)R

6

RA

= R

l + R2 + R

3 + R

U

RB

= R

l " R

2 " R

3 + \

\

= \- E

2 + *3-*k

R

G = R

5 "

R

*

*D " R

5 + R

6

R

2 = erf

R = erf

R, = erf

k

R = erf[

R

6 = erf| u = a - d

EA

= E

l " E2 + E

3 " ^

E

C = E

5 " E

6

E = exp -%(u + A) 2

E

2 = exp

E_ = exp

E^ = exp

E = exp

-%(u - A)

__J5( V + A)

2J

[-h(v - A) 2]

\-h{\> + B)

2]

Eg = exp [-^(b - B)

2

J v = a + d

For each geometry, "a" value is determined to give a maximum error in gloss value

when gx

is 50 gloss unit. Using equation (C.21), the ratio of gs /D

s is also determined.

For simulation of higher or lower gloss sample, the limit of integration "a" (also b, A,

and B) is scaled which is equivalent to changing the characteristic scattering function.

According to the ASTM method b/a, A/a, and B/a are 2.0000, 0.1*167, and 0.8333 re- spectively for 20° gloss measurement; 2.6667, 0.1705, and 0.6818 respectively for 60°

gloss measurement; and 1.5000, 0.1875 > and 0.7500 respectively for 85° gloss measurement,

Thus b, A, and B are determined once "a" is selected.

25
D. The error in gloss unit based on the allowed tolerance

of the receiver aperture and the general equations

derived in Appendix C

ASTM allowed tolerance

of receiver Aperture

Gloss Unit

Degree

OffSpecular

Angle (deg.)

Aa

(deg.)

Ah

(deg.) 30 50 70

20 0.05 0.10 0.1+1 0.1+2 0.38

60

60 0.5

0.10

0.10

0.20

0.20

0.35

0.35

0.38

0.39

0.31+

0.37

85

85

85

J

0.5

1

0.30

0.30

0.30

0.30

0.30

0.30

1.39

1.1+2 1

1.51

1.1+6

1.53

1,1k

1.29

1.1+1

1.79

.I

10. References

[l] Harrison, V.G.W. , Definition and Measurement of Gloss , W. Heffer & Sons Ltd.,

Cambridge, England, Dec. 191+5

•

[2] Hunter, R.S. , The Measurement of Appearance , Hunter Associates Laboratory, Inc., 1973.

[3] ASTM Designation: D523-67 (1972), Standard Method of Test for Specular Gloss,

Annual Book of ASTM Standards Part 27(197!+).

[1+] Venable, W.H. , Jr. and Hsia, J. J. , Describing Spectrophotometric Measurements,

Natl. Bur. Stand. (U.S.), Tech. Note 591+-9, November I97I+.

[5] Certain commercial instruments or 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.

[6] Burns, V.I., and McSparron, D.A. , Photometric Calibration Procedures, Natl. Bur. Stand. (U.S.), Tech. Note 591+-3, November 1972.

[7] Mielenz, K.D. and Eckerle, K.L., Spectrophotometer Linearity Testing Using DoubleAperture Method, Appl. Opt. 11(10), 2291+ (Oct. 1972).

[8] Jokob, M. , Heat Transfer , Vol. II, p. 18, John Wiley & Sons (1963).

[9] Davis, H. , The Reflection of Electromagnetic Waves From a Rough Surface,

Proc. IEE 101 , 209(1951+).

.10] Torrance, K.E. and Sparrow, E.M. , Theory for Off-Specular Reflection from Roughened

Surfaces, J. Opt. Soc. Am. 57(9), 1105(1967).

26
NBS.1MA (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS TN-59U-102. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE 5. Publication Date OPTICAL RADIATION MEASUREMENTS:

The NBS 20-, 60-, and 85-Degree Specular Gloss Scales

July 1975

6. Performing Organization Code

7. AUTHORM

Jack Jo Hsia

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as No. 9

13. Type of Report & Period Covered Final

14. Sponsoring Agency Code

SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less (actual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here.)

The 20-, 60- , and 85- degree specular gloss scales are established at NBS

with an accuracy of about one half gloss unit. This is one of many programs of

the spectrophotometry group of the Optical Radiation Section of NBS directed

toward improving the accuracy and assurance of spectrophotometric measurements

made throughout the scientific and industrial community.

The specular gloss scales are established through an unique technique

employing polarized light flux both parallel and perpendicular to the plane of

incidence. General calibration equations are derived. NBS instrumentation and

measurement procedures are described. Instrument calibration and error analyses

are performed. Some of the analyses can also be applied to reflectance measurements in general.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Accuracy; appearance; error analysis; gloss; photometry; reflectance; scattering;

spectrophotometry; specular gloss.

18. AVAILABILITY [j£ Unlimited

i n For Official Distribution. Do Not Release to NTIS

|"Xl Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. C13. 46:594-10

I | Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

32

22. Pr

85*

USCOMM.DC 29042-P74



NBS TECHNICAL PUBLICATIONS

PERIODICALS JOURNAL OF RESEARCH reports National Bureau

of Standards research and development in physics,

mathematics, and chemistry. It is published in two sections, available separately:

• Physics and Chemistry (Section A)

Papers of interest primarily to scientists working in these fields. This section covers a broad range of physical and chemical research, with major emphasis on

standards of physical measurement, fundamental constants, and properties of matter. Issued six times a

year. Annual subscription: Domestic, $17.00; Foreign,

$21.25.

• Mathematical Sciences (Section B)

Studies and compilations designed mainly for the mathematician and theoretical physicist. Topics in mathematical statistics, theory of experiment design, numerical analysis, theoretical physics and chemistry, logical design and programming of computers and computer

systems. Short numerical tables. Issued quarterly. Annual subscription: Domestic, $9.00; Foreign, $11.25. DIMENSIONS/NBS (formerly Technical News Bulletin) —This monthly magazine is published to inform

scientists, engineers, businessmen, industry, teachers,

students, and consumers of the latest advances in science and technology, with primary emphasis on the work at NBS. The magazine highlights and reviews such

issues as energy research, fire protection, building tech- nology, metric conversion, pollution abatement, health and safety, and consumer product performance. In addition, it reports the results of Bureau programs in measurement standards and techniques, properties of matter and materials, engineering standards and services, instrumentation, and automatic data processing. Annual subscription: Domestic, $9.45; Foreign, $11.85.

N0NPERI00ICALS Monographs—Major contributions to the technical liter- ature on various subjects related to the Bureau's scientific and technical activities. Handbooks—Recommended codes of engineering and

industrial practice (including safety codes) developed

in cooperation with interested industries, professional

organizations, and regulatory bodies.

Special Publications—Include proceedings of confer- ences sponsored by NBS, NBS annual reports, and other

special publications appropriate to this grouping such

as wall charts, pocket cards, and bibliographies.

Applied Mathematics Series—Mathematical tables, manuals, and studies of special interest to physicists, engineers, chemists, biologists, mathematicians, computer programmers, and others engaged in scientific and technical work.

National Standard Reference Data Series—Provides

quantitative data on the physical and chemical properties of materials, compiled from the world's literature and critically evaluated. Developed under a world-wide

program coordinated by NBS. Program under authority

of National Standard Data Act (Public Law 90-396). NOTE: At present the principal publication outlet for these data is the Journal of Physical and Chemical

Reference Data (JPCRD) published quarterly for NBS

by the American Chemical Society (ACS) and the American Institute of Physics (AIP). Subscriptions, reprints, and supplements available from ACS, 1155 Sixteenth

St. N. W., Wash. D. C. 20056.

Building Science Series—Disseminates technical infor- mation developed at the Bureau on building materials, components, systems, and whole structures. The series presents research results, test methods, and performance criteria related to the structural and environmental functions and the durability and safety characteristics of building elements and systems.

Technical Notes—Studies or reports which are complete

in themselves but restrictive in their treatment of a

subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of the subject area. Often serve as a vehicle for final reports of work performed at NBS under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under pro- cedures published by the Department of Commerce in Part 10, Title 15, of the Code of Federal Regulations. The purpose of the standards is to establish nationally

recognized requirements for products, and to provide

all concerned interests with a basis for common under- standing of the characteristics of the products. NBS

administers this program as a supplement to the activities of the private sector standardizing organizations. Federal Information Processing Standards Publications (FIPS PUBS)—Publications in this series collectively constitute the Federal Information Processing Standards Register. Register serves as the official source of information in the Federal Government regarding stand- ards issued by NBS pursuant to the Federal Property and Administrative Services Act of 1949 as amended,

Public Law 89-306 (79 Stat. 1127), and as implemented

by Executive Order 11717 (38 FR 12315, dated May 11, 1973) and Part 6 of Title 15 CFR (Code of Federal

Regulations). Consumer Information Series—Practical information, based on NBS research and experience, covering areas

of interest to the consumer. Easily understandable language and illustrations provide useful background

knowledge for shopping in today's technological

marketplace.

NBS Interagency Reports (NBSIR)—A special series of interim or final reports on work performed by NBS for outside sponsors (both government and non-government). In general, initial distribution is handled by the sponsor; public distribution is by the National Technical Information Service (Springfield, Va. 22161) in paper

copy or microfiche form.

Order NBS publications (except NBSIR's and Biblio- graphic Subscription Services) from: Superintendent of Documents, Government Printing Office, Washington,

D.C. 20402. BIBLIOGRAPHIC SUBSCRIPTION SERVICES

The following current-awareness and literature-survey

bibliographies are issued periodically by the Bureau:

Cryogenic Data Center Current Awareness Service A literature survey issued biweekly. Annual subscription: Domestic, $20.00; foreign, $25.00.

Liquefied Natural Gas. A literature survey issued quarterly. Annual subscription: $20.00. Superconducting Devices and Materials. A literature

survey issued quarterly. Annual subscription: $20.00. Send subscription orders and remittances for the pre- ceding bibliographic services to National Technical Information Service, Springfield, Va. 22161.

Electromagnetic Metrology Current Awareness Service Issued monthly. Annual subscription: $100.00 (Special rates for multi-subscriptions). Send subscription order and remittance to Electromagnetics Division, National Bureau of Standards, Boulder, Colo. 80302.
U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Washington, D.C. 20234

OFFICIAL BUSINESS

Penalty for Private Use, $300

POSTAGE ANO FEES PAID

U.S. DEPARTMENT OF COMMERCE COM-21 5

r -

U.S.MJ

SPECIAL FOURTH-CLASS RATE BOOK

^ovunov