Source

Condenser 

 lens

Collimating

 lens

Averaging 

Sphere

Focusing

 lens

Receiver

aperture

Depolarizer

Source 

aperture

Filter

Sample Sample table

Detector

Optical Technology Division Sample normal

Iris

Iris

Specular Gloss

Maria E. Nadal

Edward A. Early*

E. Ambler Thompson

NIST Special Publication SP250-70
ii
iii

NIST Special Publication SP250-70

Specular Gloss

Maria E. Nadal 

Edward A. Early* 

Optical Technology Division 

Physics Laboratory 

National Institute of Standards and Technology 

Gaithersburg, MD 20899-0001 

E. Ambler Thompson 

Weights and Measures 

Technology Services Laboratory 

National Institute of Standard and Technology 

Gaithersburg, MD 20899-001 

August 2006 

U.S. Department of Commerce 

Carlos M. Gutierrez, Secretary 

Technology Administration 

Robert Cresanti, Under Secretary for Technology

National Institute of Standards and Technology 

William Jeffrey, Director 
iv

PREFACE 

*AFRL/HEDO, 2650 Loiuse Bauer Drive, Brooks City-Base, TX 78235 

Certain commercial entities, equipment, or materials may be identified in this 

document in order to describe an experimental procedure or concept adequately. Such 

identification is not intended to imply recommendation or endorsement by the 

National Institute of Standards and Technology, nor is it intended to imply that the 

entities, materials, or equipment are necessarily the best available for the purpose.

National Institute of Standards and Technology Special Publication SP250-70 

Natl. Inst. Stand. Technol. Spec. Publ. 250-70, 72 pages (August 2006) 

CODEN: NSPUE2 
v

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

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

instrument in achieving the highest possible levels of accuracy, quality, and productivity. NIST 

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 NIST. These services are offered to the public and private 

organizations alike. They are described in NIST Special Publication (SP) 250, NIST Calibration 

Services Users Guide. 

The User Guide is supplemented by a number of Special Publications (designated as the “SP250 

Series”) that provide detailed descriptions of the important features of specific NIST calibration 

services. These documents provide a description of the (1) specifications for the services; (2) 

design philosophy and theory; (3) NIST measurement services; (4) NIST operational procedures; 

(5) assessment of the measurement uncertainty including random and systematic errors and an 

error budget; and (6) internal quality control procedures used by NIST. These documents will 

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

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

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

This document, SP250-70 (2006), NIST Measurement Services: Specular Gloss, describes the 

instrumentation, standards, and techniques used to measure the specular gloss of materials at 20°, 

60°, and 85° geometries. A description of Special Test 38090S is also presented. Inquires 

concerning the technical content of this document or the specifications for these services should 

be directed to the authors or to one of the technical contacts cited in SP 250. 

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

Suggestions are also welcome concerning the need for new calibration services, special tests, and 

measurement assurance programs. 

Belinda L. Collins Katharine B. Gebbie 

Director Director 

Technology Services Physics Laboratory 
vi

ABSTRACT 

 

 This document describes the instrumentation, standards, and measurement techniques 

used at the National Institute of Standards and Technology (NIST) to measure specular gloss. 

The organization of this document is as follow. Section 1 describes the motivation for 

establishing a reference goniophotometer and primary standards for specular gloss and 

associated calibration services that are available. Section 2 presents the theory and measurement 

equations relevant to the measurements described in this document. The NIST reference 

goniophotometer including the illuminator, goniometer, receiver, and the characterization and 

uncertainty analysis of the instrument are described in Sec. 3. In Sec. 4 the new primary specular 

gloss standard and its characterization are presented. A sample calibration report and references 

containing details of the instrument and primary standard are reproduced in the appendices. 

Key words: appearance attributes; gloss standard; glossmeter; goniophotometer; luminous 

reflectance; specular gloss 
vii

TABLE OF CONTENTS 

Abstract ..........................................................................................................................................v 

1. Introduction ..............................................................................................................................1 

2. Theory ......................................................................................................................................2 

 2.1. Definitions .......................................................................................................................2 

 2.2 Measurement Equations ..................................................................................................3

3. Reference Goniophotometer ....................................................................................................7 

 3.1 Description ......................................................................................................................7 

 3.1.1 Illuminator ...........................................................................................................8 

 3.1.2 Goniometer .........................................................................................................9 

 3.1.3 Receiver ..............................................................................................................9 

 3.2 Characterization ..............................................................................................................9 

 3.2.1 Illuminator .........................................................................................................10 

 3.2.2 Goniometer .......................................................................................................11 

 3.2.3 Receiver ............................................................................................................11 

 3.3 Operation .......................................................................................................................14 

 3.4 Uncertainty Analysis .....................................................................................................14 

 3.4.1 Basic Definitions ...............................................................................................14 

 3.4.2 Specular Gloss ..................................................................................................15 

4. Primary Gloss Standard .........................................................................................................18 

 4.1 Description ....................................................................................................................18 

 4.2 Characterization ............................................................................................................19 

 4.2.1 Index of Refraction ...........................................................................................20 

 4.2.2 Luminous Reflectance ......................................................................................21 

 4.3 Comparison of Specular Gloss Standards .....................................................................22 

Acknowledgments ........................................................................................................................23 

References ....................................................................................................................................24 

Appendix A: Sample of Report of Calibration for Specular Gloss at 20°, 60°, and 85° 

geometries 

Appendix B: NIST Reference Goniophotometer for Geometrical Appearance Measurements 

(copy of Ref. 9) 

Appendix C: New Primary Standard for Specular Gloss Measurements (copy of Ref. 

21) 
viii

LIST OF TABLES 

Table 2.1 Geometries for specular gloss measurements and applications ................................2 

Table 2.2 Specular reflectance ρ0(θ, λD) of the theoretical gloss standard for each 

illumination angle of the standard geometries at wavelength λD = 589.3 nm ..........5 

Table 3.1 ASTM specifications and the NIST measured values for illuminator and 

receiver apertures with tolerances and uncertainties ................................................9 

Table 3.2 Average gain ratio and relative standard deviation for successive amplifier 

gain ratios ................................................................................................................12

Table 3.3 Correction factors for deviations from the standard conditions for a black 

glass calibrated with the primary specular gloss standard ......................................16 

Table 3.4 a. Components of uncertainty that depend on the scattering properties of the 

materials and the resulting relative standard uncertainties. The values are 

based on a BaK50 primary gloss standard and a highly polished black glass 

test sample ...............................................................................................................17 

 b. Components of uncertainty that are independent of the scattering 

properties of the materials and the resulting relative standard uncertainties............17 

Table 3.5 Relative expanded uncertainties of specular gloss measured by the NIST 

reference goniophotometer (k = 2) for the 20°, 60°, and 85° geometries ...............18 

Table 4.1 Index of refraction n of BaK50 glass as a function of wavelength .........................20 

Table 4.2 Calculated specular reflectance ρs(θ, λD) and specular gloss value Gs(θ) of 

the new primary standard at λD = 589.3 nm for each standard geometry ...............21 

Table 4.3 Average luminous reflectance ρv,s(θ) and specular gloss value Gs(θ) for the 

new primary standard for each standard geometry and method of calculation 

or measurement .......................................................................................................21 
ix

LIST OF FIGURES 

Figure 3.1 Schematic of the NIST reference goniophotometer ..................................................8 

Figure 3.2 Spectral flux distribution of the CIE standard illuminant C and the CIE 

spectral luminous efficiency function .....................................................................11 

Figure 3.3 Relative responsivity (ratio of the measured signal to the actual flux) of the 

photodiode-amplifier combination as a function of current for the listed gain 

settings ....................................................................................................................13 

Figure 3.4 Actual and ideal spectral products of the illuminator and receiver ........................13 

Figure 4.1 Schematic diagram of the new NIST primary standard showing the 

incoming and reflected beam at a specular geometry .............................................19 

Figure 4.2 Fitted refractive index, n(λ), for BaK50 glass as a function of wavelength ...........20 

Figure 4.3 Fitted refractive index, n(λ), for average black glass working standards, 

NIST old standard (Carrara black glass), BaK50, and quartz as a function of 

wavelength ..............................................................................................................23 

Figure 4.4 Normalized refractive index for BaK50, average of black glass working 

standards, and quartz as a function of wavelength ..................................................23 
1

1. Introduction 

This document describes the NIST reference goniophotometer and primary standards, as 

they existed at the time of publication, for the calibration of specular gloss at the 20°, 60°, and 

85° standard geometries. Updated information about calibration services is published 

periodically in the NIST Calibration Services Users Guide [1]. 

Specular gloss is the perception by an observer of the mirror-like appearance of a surface 

[2]. The measurement of specular gloss consists of comparing the luminous reflectance from a 

test sample to that from a calibrated gloss standard, under the same experimental conditions. 

Therefore, gloss is a dimensionless and psychophysical quantity whose accurate determination 

depends on the characteristics of the measuring instrument and on the gloss standard. Several 

documentary standards describe the proper measurement conditions to determine specular gloss 

for specific surfaces. In particular, the International Organization for Standards ISO 2813 [3] 

and the American Society for Testing Materials ASTM D523 [4] describe the measurement 

procedure for specular gloss of nonmetallic samples. These documentary standards specify the 

spectral and geometrical conditions of measurement. The spectral flux distribution of the 

illuminator is CIE standard illuminant C and the spectral responsivity of the receiver is the CIE 

spectral luminous efficiency function [5]. There are three standard geometries, corresponding to 

illumination angles of 20°, 60°, and 85°, each with specifications on the angular extent of the 

rays within the influx and efflux. 

The NIST reference goniophotometer was originally developed at NIST in the 1970’s. In 

1999, this instrument was updated, automated, and characterized to ensure proper operation and 

to verify agreement with the ISO and ASTM standards for specular gloss of nonmetallic 

samples. 

The accuracy of specular gloss measurements depends not only on the properties of the 

instrument but also to a considerable extent on the primary gloss standard. A new primary gloss 

standard using BaK50 barium crown glass has been developed at NIST. It possesses high 

chemical and mechanical durability and an index of refraction at the sodium D line of nD = 

1.5677. Different calibration procedures are detailed, and the new standard is compared with 

other primary standards. The new gloss standard and the NIST reference goniophotometer 

provide an accurate calibration facility for specular gloss. Note that the primary standard 

referenced in the documentary standards is referred to here as the theoretical standard, while the 

realization of the theoretical standard is referred to here as the primary standard. 

The NIST Calibration Services Program offers Service ID Number 38090S, Special Test 

of Specular Gloss, as listed in the Optical Properties of Materials section of the Optical Radiation 

Measurements Chapter of the NIST Calibration Services Users Guide [1]. The measurement 

service quality system is based on the ISO 17025 standard. 
2

2. Theory 

This section details the basic definitions and the relevant measurement equations to 

determine specular gloss. The approach used in this paper is based upon the concepts presented 

in Refs. [6-9]. 

2.1 Definitions 

Gloss is the perception by an observer of the shiny appearance of a surface. This 

perception changes whenever there is a change in the relative position or spectral distribution of 

the source, the sample, or the observer. Different geometries are used to determine the specular 

gloss of materials, as shown in Table 2.1. These geometries were selected based on their ability 

to produce optimum discrimination between samples and to correlate with visual rankings. 

Several documentary standards specify the geometrical and spectral conditions of measurement 

to determine specular gloss for specific surfaces. 

Table 2.1. Geometries for specular gloss measurements and applications 

Illumination angle Applications 

20° High gloss of plastic film, appliance and 

automotive finishes 

30° High gloss of image-reflecting surfaces 

45° Porcelain enamels and plastics 

60° All ranges of gloss for paint and plastics 

75° Coated waxes and paper 

85° Low gloss of flat matte paints and 

camouflage coatings 

The measurement of specular gloss compares the specular luminous reflectance from a 

test specimen to that from a standard surface under the same experimental conditions. The 

illumination beam is collimated with a spectral flux distribution approximating that of CIE 

standard illuminant C. The luminous flux in the reflected beam is measured with a receiver 

having a spectral responsivity that approximates the CIE spectral luminous efficiency function 

Vλ. The theoretical standard for specular gloss measurements is a highly polished plane black 

glass with a refractive index for the sodium D line of nD = 1.567. To set the specular gloss scale, 

the specular gloss of this theoretical standard has an assigned value of 100 for each of the three 

standard specular geometries of 20°, 60°, and 85°. For primary standards with a refractive index 

different from nD = 1.567, the specular gloss is computed from the refractive index and the 

Fresnel equations. 
3

2.2 Measurement Equations 

 The NIST reference goniophotometer measures luminous flux Φv [lm], defined by 

∫ Φv = K M ⋅ Φ(λ)⋅Vλ (λ)⋅ dλ , (2.1) 

where KM = 683 lm/W is the maximum spectral luminous efficacy for photopic vision, λ [nm] is 

the wavelength, Φ(λ) [W/nm] is the spectral flux, and Vλ(λ) is the spectral luminous efficiency 

function. For specular gloss measurements, the documentary standards specify that Φ(λ) have 

the spectral flux distribution of CIE standard illuminant C, so that the spectral flux is ΦC(λ). The 

goniophotometer has a spectral flux Φ(λ) and responsivity V(λ) that closely approximate the 

specified ΦC(λ) and Vλ(λ), respectively. 

 The specular luminous reflectance ρv(θ0) of an object at the standard illumination angle 

θ0 (20°, 60°, or 85°) is given by 

v,i

v,r 0

v 0

( ) ( ) ΦΦ= θ

ρ θ , (2.2) 

where Φv,r(θ0) and Φv,i are the reflected and incident luminous fluxes, respectively. In terms of 

the geometrical and spectral properties of the instrument and object, the luminous fluxes are 

given by 

∫ ∫ Φ ( ) = ⋅Φ ( , )⋅ ( , )⋅ ( ) v,r θ 0 dθ dλ C,i θ λ ρ θ λ Vλ λ and (2.3) 

∫ Φ = ⋅Φ ( )⋅ ( ) v,i dλ C,i λ Vλ λ , (2.4) 

where ρ(θ, λ) is the specular spectral reflectance of the object. The angles θ are the angles 

around θ0 resulting from the finite size of the source aperture. There is no angular dependence 

for Φv,i since the entire incident beam is collected by the receiver. 

 The current I [A] from the detector of the receiver is given by 

v

M

( ) ( ) ( )

( ) ( )

≅ ⋅Φ

= Φ ⋅ ⋅ ⋅ ⋅

= Φ ⋅ ⋅

∫

∫

K

R

R V r d

I R d

λ λ λ λ

λ λ λ

λ , (2.5) 

where R [A/W] is the responsivity of the detector and r(λ) is the difference between the spectral 

luminous efficiency function and the actual spectral responsivity of the detector. The current is 

converted to a voltage N [V], given by 

N = I ⋅ A , (2.6) 
4

where A [V/A] is the amplifier gain. Solving Eq. (2.5) for the luminous flux and substituting into 

Eq. (2.2) yields 

r

i

i

r

0 ( ) A

A

N

N v ρ θ = ⋅ , (2.7) 

where the subscripts i and r refer to measurements made of the incident and reflected luminous 

fluxes, respectively. 

 The specular gloss of a test sample at illumination angle θ0, Gt(θ0), is given by 

 

( )

( ) ( ) ( ) 

v,s 0

v,t 0

t 0 s 0

ρ θ

ρ θ

G θ = G θ ⋅ , (2.8) 

where Gs(θ0) is the specular gloss of the primary standard and ρv,t(θ0) and ρv,s(θ0) are the 

specular luminous reflectances of the test sample and primary standard, respectively. 

Substituting Eq. (2.7) for the luminous reflectances of the test sample and primary standard into 

Eq. (2.8) yields 

r,t

r,s

r,s

r,t

t 0 s 0 ( ) ( ) A

A

N

N

G θ = G θ ⋅ ⋅ , (2.9) 

which relates the specular gloss of the test sample to the specular gloss of the primary standard 

and the measured signals from the reflected luminous fluxes from the test sample and primary 

standard. The specular gloss of the primary standard is given by 

( , ) ( ) ( )

0 0 D

s

s 0 0 0

ρ θ λ

ρ G θ = G θ ⋅ , (2.10) 

where G0(θ0) is the specular gloss of the theoretical standard, ρ0(θ0, λD) is the specular 

reflectance of the theoretical standard at a wavelength λD = 589.3 nm, and ρs is the specular 

reflectance of the primary standard. For each angle of illumination, the specular gloss of the 

theoretical standard is defined as G0(θ) = 100. 

 The specular reflectance ρ from the surface of a dielectric sample depends on the incident 

angle θ defined relative to the normal of the sample, the wavelength λ, and the polarization σ (p 

or s) of the incident radiant flux. The specular reflectance as a function of these variables is 

given by the Fresnel equations, 

2

2 2 2

2 2 2

( ) cos ( ) sin

( ) cos ( ) sin

( , ,p) 















⋅ + −

⋅ − − =

λ θ λ θ

λ θ λ θ

ρ θ λ

n n

n n and (2.11) 
5

2

2 2

2 2

cos ( ) sin

cos ( ) sin ( , ,s) 















+ −

− − =

θ λ θ

θ λ θ

ρ θ λ

n

n , (2.12) 

where n is the index of refraction. The specular reflectance for unpolarized incident radiant flux 

is calculated from 

[ ] ( , , ) ( , , ) 2

1

ρ(θ,λ) = ρ θ λ p + ρ θ λ s . (2.13) 

From the documentary standards, the index of refraction of the theoretical standard at 

wavelength λD is n(λD) = 1.567. The specular reflectances at the standard angles of illumination 

for unpolarized radiant flux for the theoretical standard, ρ0(θ0, λD), are calculated from Eqs. 

(2.11) to (2.13) and are listed in Table 2.2 

 Table 2.2. Specular reflectance ρ0(θ, λD) of the theoretical gloss standard for each 

standard illumination angle at wavelength λD = 589.3 nm 

Illumination angle ρ0(θ, λD) 

20° 0.049078 

60° 0.100056 

85° 0.619148 

 The specular gloss of the primary standard depends, from Eq. (2.10), on its reflectance ρs. 

However, the documentary standards are ambiguous concerning the definition of this reflectance. 

One approach is to use the calculated ρs(θ0, λD) of the primary standard for its index of refraction 

at λD = 589.3 nm. 

An alternative approach, and the one taken for measurements with the reference 

goniophotometer, is to measure the luminous reflectance ρv,s(θ0) of the primary standard. This 

approach has the advantages of taking the dispersion characteristics of the standard into account 

and being a measurable quantity on the goniophotometer In terms of the geometrical and 

spectral conditions of measurement, the luminous reflectance is obtained from Eqs. (2.2) to (2.4) 

as 

∫

∫ ∫ ⋅Φ ⋅

⋅Φ ⋅ ⋅ = d ( , ) ( )

d d ( , ) ( , ) ( ) ( )

C,i λ

C,i s λ

v,s 0

λ θ λ λ

θ λ θ λ ρ θ λ λ

ρ θ

V

V

 , (2.14) 

while in terms of the measured signals the luminous reflectance is obtained from Eq. (2.7) as 

r,s

i

i

r,s

v,s 0 ( ) A

A

N

N

ρ θ = ⋅ . (2.15) 
6

Using the luminous reflectance of the primary standard and Eq. (2.10), Eq. (2.9) becomes 

r,t

r,s

r,s

r,t

0 0

v,s 0

t 0 ( , )

( ) ( ) 100

A

A

N

N

G

D

= ⋅ ⋅ ⋅ ρ θ λ

ρ θ

θ , (2.16) 

where ρ0(θ0, λD) is calculated and given in Table 2.2, ρv,s(θ0) is measured and given by Eq. 

(2.15), and the signals Nr,t and Nr,s are the measured signals from the test sample and primary 

standard, respectively, at amplifier gains of Ar,t and Ar,s. Equation (2.16) is the measurement 

equation for specular gloss in terms of measured and calculated quantities. 

 In terms of the spectral and geometrical quantities, using the appropriate modification of 

Eq. (2.14) in Eqs. (2.8) and (2.10), the specular gloss of a test samples is given by 

∫ ∫

∫ ∫ ⋅Φ ⋅ ⋅

⋅Φ ⋅ ⋅ = ⋅ ⋅ d d ( , ) ( , ) ( )

d d ( , ) ( , ) ( )

( , )

( ) ( ) 100

i s

i t

0 0 D

v,s 0

t 0

θ λ θ λ ρ θ λ λ

θ λ θ λ ρ θ λ λ

ρ θ λ

ρ θ

θ

V

V

G , (2.17) 

where Φi(θ, λ) and V(λ) are the incident spectral flux and responsivity of the reference 

instrument, respectively. In terms of the ideal case given in the documentary standards, the 

specular gloss Gt,id is given by 

∫ ∫

∫ ∫ ⋅Φ ⋅ ⋅

⋅Φ ⋅ ⋅ = ⋅ ⋅ d d ( , ) ( , ) ( )

d d ( , ) ( , ) ( )

( , )

( ) ( ) 100

C,i s

C,i t

0 0 D

v,s 0

t,id 0

θ λ θ λ ρ θ λ λ

θ λ θ λ ρ θ λ λ

ρ θ λ

ρ θ

θ

λ

λ

V

V

G , (2.18) 

 Deviations of the reference instrument from the ideal case include deviations from the 

specified spectral flux distribution of the illuminator, spectral responsivity of the receiver, 

unpolarized and collimated illumination beam with specified angular ranges, and illumination 

angle. The correction factors for the specular gloss of the sample under test as determined with 

the reference instrument are obtained using Eqs. (2.17) and (2.18). The correction factors are the 

ratio of the specular gloss for the ideal case to the specular gloss for the reference instrument, 

( )

( )

t 0

t,id 0

θ

θ

G

G

C = . (2.19) 

The correction factor for deviations from the ideal spectral flux distribution of the illuminator 

and spectral responsivity of the receiver is given by 

∫

∫

∫

∫ ⋅Φ ⋅ ⋅

⋅Φ ⋅ ⋅ ⋅ ⋅Φ ⋅ ⋅

⋅Φ ⋅ ⋅ = d ( ) ( , ) ( )

d ( ) ( , ) ( )

d ( ) ( , ) ( )

d ( ) ( , ) ( )

i t 0

i s 0

C,i s 0 λ

C,i t 0 λ

s

λ λ ρ θ λ λ

λ λ ρ θ λ λ

λ λ ρ θ λ λ

λ λ ρ θ λ λ

V

V

V

V

C . (2.20) 

The correction factor for deviations from an unpolarized illumination beam is given by 
7

∫

∫

∫

∫ ⋅Φ ⋅ ⋅

⋅Φ ⋅ ⋅ ⋅ ⋅Φ ⋅ ⋅

⋅Φ ⋅ ⋅ = d ( ) ( , , ) ( )

d ( ) ( , , ) ( )

d ( ) ( , ) ( )

d ( ) ( , ) ( )

C,i t 0

C,i s 0

C,i s 0 λ

C,i t 0 λ

p

λ λ ρ θ λ σ λ

λ λ ρ θ λ σ λ

λ λ ρ θ λ λ

λ λ ρ θ λ λ

λ

λ

V

V

V

V

C . (2.21) 

The correction factor for deviations from the angular ranges of the illumination beam is given by 

∫ ∫

∫ ∫

∫ ∫

∫ ∫ ⋅Φ ⋅ ⋅

⋅Φ ⋅ ⋅ ⋅ ⋅Φ ⋅ ⋅

⋅Φ ⋅ ⋅ = d d ( , ) ( , ) ( )

d d ( , ) ( , ) ( )

d d ( , ) ( , ) ( )

d d ( , ) ( , ) ( )

C,i t

C,i s

id C,i s λ

id C,i t λ

d

θ λ θ λ ρ θ λ λ

θ λ θ λ ρ θ λ λ

θ λ θ λ ρ θ λ λ

θ λ θ λ ρ θ λ λ

λ

λ

V

V

V

V

C 

 (2.22) 

The correction factor for deviations from the standard illumination angle is given by 

∫

∫

∫

∫ ⋅Φ ⋅ ⋅

⋅Φ ⋅ ⋅ ⋅ ⋅Φ ⋅ ⋅

⋅Φ ⋅ ⋅ = d ( ) ( , ) ( )

d ( ) ( , ) ( )

d ( ) ( , ) ( )

d ( ) ( , ) ( )

C,i t

C,i s

C,i s 0 λ

C,i t 0 λ

a

λ λ ρ θ λ λ

λ λ ρ θ λ λ

λ λ ρ θ λ λ

λ λ ρ θ λ λ

λ

λ

V

V

V

V

C . (2.23) 

Therefore, the specular gloss for the ideal case in terms of the correction factors is given by 

t,id 0 t s p d a G (θ ) = G ⋅C ⋅C ⋅C ⋅C . (2.24) 

 

 The final measurement equation, including the correction factors and the experimentally 

measured quantities, is given by 

s p d a

t

s

s

t

0 0 D

v,s 0

t,id 0 ( , )

( ) ( ) 100 C C C C

A

A

N

N G = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ρ θ λ

ρ θ

θ . (2.25) 

3. Reference Goniophotometer 

3.1 Description 

Interest in specular gloss measurements at NIST (formerly NBS) dates back to the 1930’s 

[10-12]. The goniophotometer described in this paper was originally developed at NBS [6] in 

the 1970’s by scientists active in the development of the ASTM standard test method, and has 

recently been updated, automated, and characterized. This instrument is a monoplane gonioinstrument with a fixed illuminator and a rotating sample Table and receiver arm. The sample 

Table and the receiver arm can be rotated independently of each other in the plane of incidence. 

A schematic diagram of the goniophotometer in reflectance mode is shown in Fig. 3.1 and a 

detailed description of the instrument is given below. This instrument complies with the 

geometrical and spectral conditions specified by the ASTM D523 and ISO 2813 documentary 

standards for the measurement of specular gloss of non-metallic surfaces at fixed specular 

geometries of 20°, 60°, and 85°. 
8

Source

Condenser 

 lens

Collimating

 lens

Averaging 

Sphere

Focusing

 lens

Receiver

aperture

Depolarizer

Source 

aperture

Filter

Sample Sample table

Detector

Optical Technology Division Sample normal

Iris

Iris

Figure 3.1. Schematic of the NIST Reference Goniophotometer 

3.1.1 Illuminator The illuminator supplies the influx onto the sample. It consists of a light 

source, a set of condenser lenses, a source aperture, a collimating lens, a depolarizer, a color 

filter, and an iris. The light source is a quartz-tungsten-halogen incandescent lamp rated at 

100 W. A constant dc current of 6.3 A is run through the lamp from a computer-controlled 

power supply. This current was chosen so that the spectral flux distribution from the lamp 

approximates CIE standard illuminant A. An image of the lamp filament is formed at the source 

aperture with the achromatic condenser lens system. This source aperture is the field stop of the 

illuminator. The recommended and actual dimensions of the source aperture are given in 

Table 3.1. The source aperture is at the focus of an achromatic lens with a focal length of 

192 mm, which collimates the beam. The polarization of the beam is determined using either a 

glass-laminated polarizer to provide linearly polarized light, or a scrambler to provide 

unpolarized light. The scrambler is used for most measurements. A color filter BG-34, 2.7 mm 

thick, converts the spectral flux distribution to CIE standard illuminant C. Finally, an iris 

diaphragm serves as the aperture stop of the illuminator. For most measurements the beam 

diameter is about 3 cm.
9

Table 3.1. ASTM specifications and the NIST measured values for full angles of 

the illuminator and receiver apertures with tolerances and uncertainties 

Apertures 

Parallel to the plane of 

incidence 

Perpendicular to the plane of 

incidence 

 ASTM spec. NIST apertures ASTM spec. NIST apertures 

Source 0.75° ± 0.25° 0.71° ± 0.01° 2.5° ± 0.5° 3.0° ± 0.01° 

20° receiver 1.8° ± 0.05° 1.82° ± 0.01° 3.6° ± 0.1° 3.64° ± 0.02° 

60° receiver 4.4° ± 0.1° 4.44° ± 0.02° 11.7° ± 0.2° 11.72° ± 0.01° 

85° receiver 4.0° ± 0.3° 4.03° ± 0.01° 6.0° ± 0.3° 6.02° ± 0.01° 

3.1.2 Goniometer The goniometer positions the sample and receiver for bi-directional 

luminous reflectance or transmittance measurements. It consists of two computer-controlled 

rotation stages. The sample stage has a diameter of 48 cm and the sample holder can 

accommodate rectangular samples with dimensions up to 10 cm high by 20 cm wide by 25 mm 

thick. In addition, a sample holder with vacuum suction can be mounted on the sample stage for 

use with non-rigid samples such as paper. The sample holder positions the front surface of the 

sample on the axis of rotation of the stage. The receiver is attached to a rotation stage whose 

axis of rotation is collinear with the rotation stage for the sample. 

3.1.3 Receiver The receiver collects and measures the efflux from the sample. It consists of 

an iris, a focusing lens, a receiver aperture, an averaging sphere, and a detector. The iris, lens, 

and aperture are enclosed in a light-tight tube with baffles to reduce scattered light. The iris has 

a clear diameter of 7.4 cm and is the aperture stop of the receiver. A lens with a focal length of 

508 mm immediately behind the iris focuses the light at the receiver aperture. The specified 

dimensions of the receiver aperture, with tolerances, and the measured dimensions of the 

receiver aperture are given in Table 3.1. The receiver aperture is located at the entrance port of 

the averaging sphere, and is the field stop of the receiver. The averaging sphere has a diameter 

of 30.5 cm and is packed with pressed polytetrafluoroethylene (PTFE). A photopic detector is 

located at the detector port of the averaging sphere and consists of a silicon photodiode and a 

filter that in combination approximates the spectral luminous efficiency function Vλ. The 

detector is temperature controlled with a thermoelectric heater and has an integral current-tovoltage amplifier. The voltage output from the detector is measured by a 6 1⁄2 digit voltmeter and 

sent to a computer. 

3.2 Characterization 

This instrument has been carefully characterized and calibrated to ensure proper 

operation and to verify agreement with the documentary standards for specular gloss 

measurements - ASTM D523 and ISO 2813. These documentary standards specify the geometry 

of the illumination beam, the specular angles, the dimensions of the source and receiver 

apertures, the spectral flux distribution of the illuminator, and the spectral responsivity of the 

receiver. Details of the characterization of the instrument are given below. 
10

3.2.1 Illuminator The lamp is burned in at 100 W for 24 hours and then at the operational 

current of 6.3 A for an additional 48 h prior to performing measurements. The stability of the 

source was investigated by measuring the flux incident on a Si photodiode at the sample location 

for a period of 30 min. A typical relative standard deviation of the signal over ten minutes is 

0.01 %.

The degree of polarization of the illuminator with no polarizing components was 

measured by rotating a polarizer in the beam and measuring the maximum and minimum 

transmitted signals. The difference of the signals was divided by the sum to obtain the degree of 

polarization of the source, approximately 9 %. Because the illuminator is not completely 

unpolarized, either a glass-laminated polarizer or a scrambler are used in the beam path just 

before the sample. The averaging sphere on the receiver arm in front of the photopic detector 

randomizes any additional polarization imparted by the sample. The leakage of the glasslaminated polarizer for luminous flux that is polarized perpendicular to the intended direction of 

polarization of the illuminator is 1.4 %. The degree of polarization of the source-scrambler 

combination is 0.02 %, providing an unpolarized illumination beam. 

The standard spectral conditions for specular gloss measurements are for the illuminator 

to approximate the spectral flux distribution of CIE standard illuminant C and for the receiver 

spectral responsivity to approximate the CIE spectral luminous efficiency function, both shown 

in Fig. 3.2. The spectral flux distribution of the illuminator, with no filter, for the spectral range 

of 380 nm to 1070 nm was measured using a calibrated scanning spectroradiometer [13]. A 

freshly pressed polytetrafluoroethylene (PTFE) sample [14] was placed in the sample holder at 

an illumination angle of 45° and a viewing angle of approximately 0°. The spectral reflectance 

of PTFE is non-selective in the visible region. The lamp current was set to 6.3 A to achieve a 

Correlated Color Temperature (CCT) of 2856 K ± 10 K with a coverage factor k = 2. A colortemperature conversion filter was placed in the illuminator to achieve the spectral flux 

distribution of CIE standard illuminant C (CCT = 6774 K). The spectral flux distribution of the 

illuminator was measured as before, and a CCT of 6740 K ± 30 K with a coverage factor k = 2 

was calculated. 

The dimensions of the source and receiver apertures are predetermined by the specular 

geometry, focal length of the collimator lens in the system, test material, and the correlation with 

visual ranking. Table 3.1 lists the standard aperture sizes and accepTable tolerances, and the 

measured values for the NIST apertures. The linear dimensions of the apertures were measured 

and the angular dimensions were calculated. All of the apertures are within the ASTM 

tolerances. The angle of incidence θ for any ray within the illumination beam with illumination 

angle θ0 is given by 

2 2 1/ 2

0 0

(1 tan tan )

cos sin tan

cos

α β

θ θ α θ

+ +

+ ⋅ = , (3.1) 

where α and β are the angles from the illuminator axis parallel and perpendicular to the plane of 

incidence, respectively. 
11

0

20

40

60

80

100

120

140

300 400 500 600 700 800

Wavelength [nm]

Flux distribution

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Luminous efficiency 

function

 

Figure 3.2. Spectral distributions of CIE standard illuminant C (dashed line) and 

the CIE spectral luminous efficiency function (solid line) 

3.2.2 Goniometer The angular scales of the sample Table and receiver were checked for 

accuracy and repeatability from 0° to ± 85°. The illumination angles on the sample Table were 

calibrated using a set of isosceles prisms made by the NIST Optical Shop. These prisms have 

nominal base angles of 20°, 60°, and 85° with maximum deviations of 0.05°, corresponding to 

the standard geometries. The prisms were calibrated by the Manufacturing Engineering 

Laboratory at NIST using a precision electronic autocollimator with an expanded uncertainty 

(k=2) of 0.005° [15]. For the calibration of the illumination angles, one of the calibrated prisms 

was mounted in the sample holder. The sample Table was then rotated to achieve retroreflection. 

This procedure was repeated for the three prisms, resulting in a maximum uncertainty for the 

angular scale of the sample Table of 0.05°. The repeatability of the angular scale for the sample 

Table is 0.05°. To calibrate the receiver angular scale, a front surface mirror replaced the prism 

and the reflection was centered in the receiver aperture by rotating the receiver arm. The 

maximum uncertainty for the receiver arm angular scale is 0.05° and the repeatability is 0.05°. 

3.2.3 Receiver The photopic receiver consists of a temperature controlled silicon photodiode 

with a photopic filter and a computer controlled variable gain current-to-voltage amplifier. The 

gain setting of the amplifier is the power of ten by which the current is multiplied to convert it to 

voltage. For low gloss samples, the measured luminous flux is much lower than the luminous 

flux from the high specular gloss primary standard. In this case, several amplifier gain settings 

are required to cover the dynamic range. From eq (2.25), the ratio of the amplifier gains is the 

required quantity. The gain settings of the amplifier were calibrated using a reference constant 

current source as the input of the amplifier and a voltmeter was used to measure the output 

signal. At each gain setting, the current was set to obtain a range of voltages from 10 V to 0.1 V 

in twenty equally spaced steps and the output signal was measured at each current. This protocol 

yielded current settings that were common to successive gain settings. The average value of the 
12

gain ratio and relative standard deviation of these overlapping settings for successive gains are 

listed in Table 3.2. The gain ratios are not exactly equal to 10, and it is best to measure signals 

between the ranges of 0.5 V to 12 V.

Table 3.2. Average gain ratio and relative standard deviation for successive 

amplifier gain ratios 

Gain ratio Average value Relative standard deviation [%] 

A6/A5 9.999 0.002

A7/A6 9.998 0.002

A8/A7 9.997 0.002

A9/A8 10.017 0.003

A10/A9 9.952 0.003

The linearity of the photodiode-amplifier combination was measured using the NIST 

automated beam conjoiner [16]. This facility uses the beam addition method with a set of filters 

in the path of the two branches of the beam to vary the radiant flux at the receiver by three 

decades. The linearity of the photodiode-amplifier combination was checked at gain settings 

from 5 to 9. The maximum radiant flux at the receiver is controlled by a set of neutral-density 

filters in front of the receiver. Figure 3.3 shows a plot of the relative responsivity (ratio of the 

measured signal to the actual flux) as a function of current for the gain settings listed in the 

legend. The measured relative responsivity of the photodiode-amplifier combination is linear to 

within 0.2 % for gain settings of 5 to 8. Larger deviations are observed at gain 9 due to the small 

current at this setting. 

The absolute spectral responsivity of the filter and receiver package was measured in the 

NIST Spectral Comparator Facility [17], and approximates that of the CIE spectral luminous 

efficiency function. The measured spectral distribution was normalized to one at 560 nm to 

compare with the theoretical distribution. The responsivity spatial uniformity of the detector was 

not determined since an averaging sphere is used in front of the detector. Figure 3.4 shows a 

comparison of the spectral products of the illuminator and receiver and of the CIE standard 

illuminant C spectral flux distribution and the spectral luminous efficiency function. 
13

0.980

0.985

0.990

0.995

1.000

1.005

1.010

1.015

1.020

0.00001 0.001 0.1 10 1000 100000

Current [nA]

Relative Responsivity

5 7

8 9

Figure 3.3. Relative responsivity (ratio of the measured signal to the actual flux) 

of the photodiode-amplifier combination as a function of current for 

the listed gain settings 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

300 400 500 600 700 800

Wavelength [nm]

Relative spectral product

Actual

Ideal

Figure 3.4. Actual and ideal spectral products of the illuminator and receiver 
14

3.3 Operation 

The lamp current is adjusted to 6.3 A and allowed to warm up for at least an hour. An 

image of the lamp filament is formed at the receiver aperture by adjusting the positions of the 

lamp and collimating lens. The zero position of the sample Table is set by placing a mirror in the 

sample holder and adjusting the rotation stage so that the illumination beam is retroreflected back 

onto the illuminator iris. The zero position of the receiver arm is adjusted by centering the 

illumination beam on the front of the receiver aperture. These positions are recorded by the 

computer program to set the rotation stages to zero. The sample holder is designed so that the 

front surface of the sample is on the axis of rotation of the sample Table. The sample is 

manually centered in the horizontal and vertical directions. 

From Eq. (2.8), measurements of the specular gloss of a test sample require 

measurements of the reflected luminous fluxes from the test sample and the standard under the 

same experimental conditions. Measurements of the sample under test are bracketed with the 

primary standard measurements to correct for any instrumental drift. The specular gloss of the 

test sample is then calculated from the ratio of the measured luminous flux reflected from the 

sample to the average of the measured luminous fluxes reflected from the primary standard. If a 

polarizer is used, measurements are performed with parallel and perpendicular polarization with 

respect to the plane of incidence and the average of these two measurements yields the specular 

gloss value for unpolarized light. The dark signal is measured with the source blocked at the 

same geometry for the measurements, and the dark signal is subtracted from the measured signal 

from the standard and sample under test. The final gloss values are given by the average of at 

least three independent scans. 

 The specular gloss scale is checked before all calibrations by measuring check standards 

with gloss values similar to that of the sample under test. The check standards are black glass 

tiles with different gloss values. 

3.4 Uncertainty Analysis 

 

 This section describes the components of uncertainty, their evaluation, and the resulting 

uncertainty for specular gloss measurements. Throughout this document, uncertainty statements 

follow the NIST policy given by Taylor and Kuyatt [18], which recommends the use of an 

expanded uncertainty with a coverage factor k = 2 for the uncertainties of all NIST calibrations. 

The NIST reference goniophotometer was designed so that the various sources of uncertainty 

were minimized. The residual uncertainties were characterized to produce specular gloss with a 

minimum relative expanded uncertainty (k = 2) of 0.3 %. 

3.4.1 Basic Definitions The specular gloss of a test sample is not measured directly but is 

determined from reflected luminous fluxes through the measurement equation. In general, the 

value of a measurand, y, is obtained from n other quantities xi through a functional relation, f, 

given by 

 

( , , , , , ) 1 2 i n y = f x x ⋅⋅⋅ x ⋅⋅⋅ x . (3.2) 

The standard uncertainty of an input quantity is the estimated standard deviation associated with 

this quantity and is denoted by u(xi). The standard uncertainties may be obtained using either a 
15

Type A evaluation of uncertainty, which is based on statistical analysis, or a Type B evaluation 

of uncertainty, which is based on other means. The relative standard uncertainty is given by 

u(xi)/xi. The relative combined standard uncertainty uc(y)/y is given by the root-sum-square of 

the standard uncertainties associated with each quantity xi, assuming that these uncertainties are 

uncorrelated. The mathematical expression for the relative combined standard uncertainty is 

( ), 1 ( )/ 2

2

1

2 2

i

n

i i

c u x

x

f

y

u y y ∑= 















∂

∂ = (3.3) 

where (1/y)(∂f/∂xi) is the relative sensitivity coefficient. The expanded uncertainty U is given by 

k⋅uc(y), where k is the coverage factor and is chosen on the basis of the desired level of 

confidence to be associated with the interval defined by U. 

3.4.2 Specular Gloss The components of uncertainty associated with gloss measurements are 

divided into those arising from experimentally measured quantities and those arising from 

deviations from standard recommendations. The experimentally measured quantities include the 

source stability, responsivity of the detector, photodiode linearity, accuracy of the digital 

voltmeter, amplifier gain ratio, and signal noise. Deviations of the reference instrument from the 

standard conditions include deviations from the specified spectral flux distribution of the 

illuminator, spectral responsivity of the receiver, unpolarized influx, illumination angle, and 

angular distribution of the influx. The resulting uncertainty from deviations from the standard 

conditions depends on the nature of the sample under test and the primary standard. 

The appropriate measurement equation for the first set of uncertainties is eq (2.16) and 

for the second set, Eqs. (2.20) to (2.23). This uncertainty analysis was applied to representative 

measurements using a highly polished black glass as the test sample and a highly polished wedge 

of BaK50 glass as the primary standard. 

The components of uncertainty arising from the illuminator are uncertainties from the 

stability, polarization, and angular distribution of the influx. The relative standard uncertainty in 

source stability is caused by random effects and is 0.01 % from a Type A evaluation. The 

uncertainty arising from the polarization of the illuminator is caused by a systematic effect with a 

Type B evaluation and depends on the reflecting properties of the sample. The correction factors 

for deviations from an unpolarized illumination beam were calculated from Eq. (2.21) using the 

degrees of polarization determined in the previous section and are listed in Table 3.3 for the three 

standard geometries. The uncertainty arising from the angular distribution of the influx is caused 

by a systematic effect with a Type B evaluation and depends on the reflecting properties of the 

sample. The correction factor for deviations from the specified angular distribution of the influx 

in Table 3.1 was calculated from eqs (2.22) and (3.1). The correction factors for the three 

standard geometries are listed in Table 3.3. 

The uncertainties arising from the goniometer are the uncertainties in the angular 

positioning of the sample and receiver arm. These uncertainties are caused by a systematic effect 

with a Type B evaluation and depend on the reflecting properties of the sample. The angular 

setting uncertainty of 0.05° is smaller than the accuracy of 0.1° specified by ASTM D523. The 

correction factors for deviations of the illumination angle from eq (2.23) for the three standard 

geometries are listed in Table 3.3. 
16

The components of uncertainty arising from the receiver are uncertainties from the digital 

voltmeter (DVM), signal noise, amplifier gain ratio, and photodiode linearity. The uncertainty 

from the DVM is caused by a systematic effect with a Type B evaluation, assuming a normal 

probability distribution. Using the manufacturer’s specifications, the relative uncertainty 

resulting from the DVM is 0.002 %. Signal noise of the instrument results in an uncertainty 

caused by a random effect with a Type A evaluation. A typical relative standard deviation for a 

gloss measurement is 0.01 %. The uncertainties arising from the photodiode linearity and the 

amplifier gain ratio are caused by systematic effects with a Type A evaluation. The maximum 

relative standard deviation from linearity of the photodiode, for signals in the range of 0.1 V to 

12 V, is 0.1 %. The relative standard deviations for successive gain settings are listed in Table 

3.2. The maximum relative standard deviation is 0.003 %. The same gain is used when the 

standard and sample have similar gloss values; otherwise the gain ratios are applied in the 

calculations. 

The repeatability of the sample positioning results in an uncertainty caused by a random 

effect with a Type B evaluation. Assuming a rectangular probability distribution with a 

maximum deviation of 0.2 gloss units, the relative standard uncertainty is 0.1 %. 

Deviations from the spectral condition are important for low-gloss samples with spectral 

features. The spectral conditions of the illuminator and receiver are in close agreement with the 

recommended CIE standard illuminant C and CIE spectral luminous efficiency function. The 

difference between the instrument and the standard conditions results in an uncertainty caused by 

a systematic effect with a Type B evaluation. The correction factors for deviations from the 

standard recommendations for the three standard geometries, from eq (2.20), are listed in 

Table 3.3. 

Table 3.3. Correction factors for deviations from the standard conditions for a 

black glass calibrated with the primary specular gloss standard 

Correction factors 

Standard geometry 

Deviation 20° 60° 85° 

Polarizer, Cp 0.999890 1.000137 1.000222 

Depolarizer, Cp 0.999999 1.000001 0.999995 

Angular distribution, Cd 0.999999 0.999975 0.999993 

Illumination angle, Ca 0.999996 0.999875 0.999940 

Spectral product, Cs 1.000012 1.000006 0.999997 

Since all of the correction factors listed in Table 3.3 are nearly unity, no correction factor 

is applied and the variations from unity are considered to be uncertainties. The relative standard 

uncertainty from each component of uncertainty is listed in Tables 3.4a and 3.4b for sampledependent and sample–independent components, respectively. The relative expanded 

uncertainties given in Table 3.5 are calculated from the root-sum-square of the uncertainties 
17

listed in Tables 3.4a and 3.4b. The ISO 2813 standard specifies that gloss should be reported to 

the nearest full gloss unit. Therefore, the calibration of the reference instrument and primary 

standard should have an uncertainty of less than one gloss unit. The NIST reference 

goniophotometer has an expanded (k = 2) relative uncertainty of 0.3 % for calibrating a highly 

polished black glass. 

Table 3.4a. Components of uncertainty which depend on the scattering 

properties of the materials, and the resulting relative standard 

uncertainties. The values are based on a BaK50 primary gloss 

standard and a highly polished black glass test sample 

Relative standard uncertainty [%] 

Standard geometry Component of 

uncertainty Effect Type

20° 60° 85° 

Polarizer S B 0.01 0.01 0.02 

Depolarizer S B 0.0001 0.0001 0.0005 

Angular distribution S B 0.0001 0.003 0.0007 

Illumination angle S B 0.0004 0.005 0.006 

Spectral product S B 0.001 0.0006 0.0003 

Table 3.4b. Components of uncertainty which are independent of the scattering 

properties of the materials, and the resulting relative standard 

uncertainties 

Relative standard uncertainty [%] 

Component of uncertainty Effect Type Standard geometry 

20° 60° 85° 

Primary gloss standard S B 0.1 0.06 0.005 

Source stability R A 0.01 

DVM S B 0.002 

Signal noise R A 0.01 

Photodiode linearity S A 0.1 

Amplifier gain ratio S A 0.003 

Repeatability R A 0.1 
18

Table 3.5. Relative expanded uncertainties of specular gloss measured by the 

NIST reference goniophotometer (k = 2) for the 20°, 60°, and 85° 

standard geometries. 

Standard geometry Relative expanded uncertainty [%] 

20° 0.35 

60° 0.31 

85° 0.29 

4. Primary Gloss Standard 

The selection criteria for the new NIST primary specular gloss standard are described, 

along with the index of refraction, specular gloss, and luminous reflectance properties of the 

standard. Finally, the new primary standard is compared to other gloss standards. 

4.1 Description 

The theoretical standard for specular gloss measurements is specified to be a highly 

polished plane black glass with an index of refraction at the wavelength of the sodium D line, 

589.3 nm, of nD = 1.567 and is assigned a specular gloss value of 100 for each of the three 

standard geometries. The specular reflectances of unpolarized light for this index of refraction 

are calculated using the Fresnel equations and are listed in Table 2.2. Since there is no black 

glass with exactly nD = 1.567, other materials are used as primary standards and their gloss 

values are computed from the Fresnel reflectances. The primary specular gloss standard 

previously used at NIST in the 1970’s was a commercial Carrara black glass with nD = 1.527 [6]. 

A recent evaluation of this type of glass and its constituents was performed, and no match to any 

commercially available optical glass could be determined. 

In general, there are a number of disadvantages to using black glass as a primary specular 

gloss standard. The surface of black glass is inhomogeneous, ages poorly, and is easily 

damaged, and thus requires frequent repolishing and recalibration. Polished black glass has been 

reported to be unsTable due to surface chemical contamination, resulting in variations of 0.3 % 

to 0.5 % in the index of refraction over a period of three to four years [19]. These variations 

correspond to changes of about 2 % and 1 % in the specular gloss values for the 20° and 60° 

standard geometries, respectively. Optical polishing with cerium oxide can restore the original 

gloss value. The uniformity of the index of refraction has been investigated [20], and varies 

across the surface by approximately 0.5 %. 

The ISO 2813 documentary standard suggests an alternative to black glass – a clear glass 

with roughened edges and back surface, with the back surface painted black to absorb any 

transmitted light. A difficulty with such a primary standard is finding a black paint that provides 

a good match to the index of refraction of the clear glass. Otherwise, some scattered light from 

the back surface will enter the receiver and cause an error in the measured luminous flux. An 

alternative to the black paint is to cut the clear glass at an angle so that back reflections are not 
19

incident on the receiver, but this option is not feasible for small, porTable instruments commonly 

used in industry. 

The disadvantages of the previous primary standards for specular gloss described above 

motivated a search for a new primary standard at NIST [21]. The following selection criteria 

were used: First, the standard should be a commercially available, high-purity optical glass with 

high chemical and mechanical durability. Second, the index of refraction nD should be as close 

to 1.567 as possible to conform to the documentary standards. Third, the material should be 

homogenous and have dispersion characteristics similar to black glass. An optical quality 

barium crown glass BaK50 was selected as the new NIST primary standard since it possesses 

high chemical and mechanical durability and nD = 1.5677. In addition, the index of refraction 

homogeneity of this glass is within 5 x 10-6 over an area of 70 mm2

, which is better than the 

black glass. Three pieces of BaK50 with dimensions of 98 mm by 98 mm by 20 mm were 

purchased, and the NIST Optical Shop fabricated sa0mples with a 6° wedge at the back surface. 

This angle is sufficient to reflect the light incident on the back surface out of the field of view of 

the receiver for all of the standard geometries, as shown in Fig. 4.1. The front and back surfaces 

were polished to a roughness of 0.6 nm to 1.0 nm. A black felt material was placed at the back 

and edges of the samples to eliminate reflections from the surrounding black anodized holder. 

BaK50 Wedge

Reflection from back surface

Illuminator Iris

Receiver Iris

Figure 4.1. Schematic diagram of the new NIST primary standard showing the 

incoming and reflected beam at aspecular geometry (not to scale) 

4.2 Characterization 

The specular gloss value of the primary standard is determined relative to the theoretical 

gloss standard from the ratio of the luminous reflectance to the Fresnel reflectance of the 

theoretical standard, as shown in eq (2.10). The luminous flux reflected from the primary 

standard is used to determine the specular gloss of the test sample, from eq (2.8). There are two 

methods for determining the luminous reflectance of the primary standard, one from 

measurements of the index of refraction over the visible wavelength range, the other from direct 

measurements of this reflectance. 
20

4.2.1 Index of Refraction The index of refraction of BaK50 was measured on a prism-shaped 

sample prepared from the same melt as the wedge samples. The minimum deviation technique 

[22] was used to determine the index of refraction at five different wavelengths, including 

589.3 nm, with a standard uncertainty of 4 x 10-5 (k = 2). The indexes of refraction as a function 

of wavelength are given in Table 4.1. The data was fitted with a cubic spline over the range of 

data and linearly extrapolated to give the dispersion curve for wavelengths from 380 nm to 780 

nm at 10 nm intervals, shown in Fig. 4.2. The calculated specular reflectances ρs(θ, λD) and 

specular gloss value Gs(θ) of the new NIST primary standard at λD = 589.3 nm are listed in 

Table 4.2 for the standard geometries.

Table 4.1. Index of refraction n of BaK50 glass as a function of wavelength 

Wavelength [nm] n 

435.8 1.5800 

480.0 1.5753 

546.1 1.5702 

589.3 1.5677 

643.9 1.5654 

Figure 4.2. Fitted refractive index, n(λ), for BaK50 glass as a function of 

wavelength 

1.550

1.560

1.570

1.580

1.590

1.600

300 400 500 600 700 800

Wavelength [nm]

Refractive Index
21

Table 4.2. Calculated specular reflectance ρs(θ,λD) and specular gloss value Gs(θ) 

of the new primary standard BaK50 at λD = 589.3 nm for each 

standard geometry 

Standard geometry ρs(θ, λD) Gs(θ) 

20° 0.049172 100.19 

60° 0.100167 100.11 

85° 0.619204 100.01 

4.2.2 Luminous Reflectance There are two methods to determine the luminous reflectance of 

the primary standard. The first calculates the luminous reflectance from the index of refraction 

as a function of wavelength, while the second measures the luminous reflectance directly. The 

luminous reflectances and specular gloss values from these two methods are listed in Table 4.3, 

with the details of the calculations and measurements given below.

Table 4.3. Average luminous reflectance ρv,s(θ) and specular gloss value Gs(θ) 

for the new primary standard BaK50 for each standard geometry and 

method of calculation or measurement 

 Standard geometry 

 20° 60° 85° 

Method ρv,s(θ) Gs(θ) ρv,s(θ) Gs(θ) ρv,s(θ) Gs(θ) 

Index of 

refraction 

0.049464 100.8 0.100510 100.5 0.619375 100.0 

Luminous 

reflectance 

0.049587 101.0 0.100743 100.7 

For the first method, the index of refraction as a function of wavelength, from Table 4.1 

and Fig. 4.2, is used in eqs (2.11) to (2.13) to calculate ρs(θ, λ) for each of the standard 

geometries from 380 nm to 780 nm every 10 nm. The luminous reflectance ρv,s(θ) is calculated 

from Eq. (2.14) using ρs(θ, λ), CIE standard illuminant C for S(λ), and the CIE spectral luminous 

efficiency function. Finally, the specular gloss value Gs(θ) for the primary standard is given by 

eq (2.10) but with ρv,s(θ) in place of ρs. 

The second method measures luminous reflectance by an absolute technique using the 

NIST reference goniophotometer. For a fixed specular geometry, the following steps are 

followed for absolute luminous reflectance measurements. The sample is manually removed 

from the path of the influx beam, the receiver is rotated into the beam path, and the net 

illumination signal is measured. The sample is then placed in the beam path, the sample Table 

and receiver arm are rotated to the desired geometry, and the net reflected signal is measured. 

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

illumination signal. The luminous reflectance is calculated from the ratio of the net reflected 
22

signal to the net illumination signal. From the measured luminous reflectance of the primary 

standard, the specular gloss value was calculated as described in the previous paragraph. The 

85° geometry was not measured due to limitations in the instrument. The relative expanded 

uncertainty (k=2) for the luminous reflectance of BaK50 at the specular geometries of 20o and 

60o is 0.22 %. The random effects, which include the source stability and detector noise, result 

in a relative expanded uncertainty (k=2) of 0.1 % for both geometries. The systematic effects, 

which include the DVM accuracy, amplifier gain, detector linearity, source polarization, angular 

scale and spectral product, result in a relative expanded uncertainty (k=2) of 0.2 % for both 

geometries. 

4.3 Comparison of Specular Gloss Standards 

The specular gloss values of the new primary standard are nearly 100 for all three 

standard geometries as a consequence of nD being close to the theoretical value of 1.567. 

Comparing Tables 4.2 and 4.3, the specular gloss values calculated from the luminous 

reflectance are greater than those calculated using only nD for the 20° and 60° standard 

geometries, and are approximately equal for the 85° standard geometry. Finally, the luminous 

reflectances and corresponding specular gloss values obtained from each of the two methods, 

from Table 4.3, agree well with each other, the maximum difference in Gs(θ) being only 0.2. 

The uncertainty analysis shows that the calculated gloss value following the two different 

luminous reflectance procedures agree within the uncertainties. 

The dispersion characteristics of BaK50 were compared to those of black glass and 

quartz gloss standards. Three different types of highly polished black glasses were investigated - 

the gloss standard previously used at NIST and two currently used in industry. Neither black 

glass nor quartz are a good match for nD = 1.567. The refractive indexes for the black glass 

samples were measured using an Abbe refractometer at three different wavelengths and fit with a 

cubic spline over the range of data and linearly extrapolated to give the dispersion curves, from 

380 nm to 780 nm at 10 nm intervals, shown in Fig. 4.3. The uncertainty of these measurements 

is 0.05 % (k=2). The refractive indexes for quartz listed in Ref. [23] was fitted using a cubic 

spline function over the range of the data and linearly extrapolated to give the dispersion curve 

for wavelengths from 380 nm to 780 nm at 10 nm interval shown in Fig. 4.3. The normalized 

dispersion curves of BaK50, black glass, and quartz standards are shown in Fig. 4.4. The index 

of refraction is normalized at a wavelength of 560 nm and plotted as a function of wavelength. 

The average of the dispersion curves for the black glass samples is plotted. The relative 

dispersion characteristic of BaK50 closely resembles that of the black glass samples, while 

quartz has a different characteristic. The international and national standards define the specular 

gloss value for the theoretical and working standards based upon a single refractive index, nD, 

but the instruments are specified for luminous reflectance measurements. This ambiguity leads 

to a situation where the gloss value of the sample under test depends on the dispersive 

characteristics of the secondary-working standard, such as black glass. This is particularly 

important for instruments whose spectral characteristics are in poor agreement with those 

specified by the documentary standards. Ideally, the calibration of a test sample should not be 

affected by the properties of the working standard. This ambiguity produces differences in 

practical gloss measurements of up to 0.5 % since this recommendation ignores the dispersion 

characteristic of the material represented by changes in refractive index as a function of 

wavelength. 
23

Figure 4.3. Fitted refractive index, n(λ), for average black glass working 

standards, NIST old standard (Carrara black glass), BaK50, and 

quartz as a function of wavelength 

0.990

0.995

1.000

1.005

1.010

1.015

300 400 500 600 700 800

Wavelength [nm]

Normalized Refractive Index

BaK50 Average of blk glass Quartz

Figure 4.4. Normalized refractive index for BaK50, average of black glass 

working standards, and quartz as a function of wavelength 

 

Acknowledgments 

 

The success of the measurement service for specular gloss was aided by the efforts of 

Albert Parr and Sally S. Bruce.

1.40

1.45

1.50

1.55

1.60

300 400 500 600 700 800

Wavelength [nm]

Refractive Index

Average Black Glass NIST Old Standard BaK50 Quartz
24

References 

[1] NIST Calibration Services Users Guide, NIST Special Publication 250. 

[2] R. S. Hunter and R. W. Harold, The Measurement of Appearance, 2nd Ed., John Wiley 

and Sons, Inc., New York (1987). 

[3] International Standard ISO 2813, Paint and Varnishes-Measurements of Specular Gloss 

of Nonmetallic Paint Films at 20°, 60°, and 85° (International Organization for 

Standardization 1978). 

[4] Standard Test Method for Specular Gloss, ASTM D523, American Society for Testing 

and Materials, West Conshohocken, PA (1995). 

[5] Commission International de l’Eclairage: International Lighting Vocabulary, 

Colorimetry, 2nd ed., Publ. No. 15.2 (1986). 

[6] J. J. Hsia, The NBS 20-, 60-, and 85- Degree Specular Gloss Scales, NIST Tech. Note 

594-10 (1975). 

[7] F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, and T. Limperis, 

Geometrical Considerations and Nomenclature for Reflectance, U.S. NBS Monograph 

160 (1977). 

[8] W. Budde, The Calibration of Gloss Reference Standards, Metrologia 16, 89-93 (1980). 

[9] M. E. Nadal and E. A. Thompson, NIST Reference Goniophotometer for Geometrical 

Appearance Measurements, Journal Coatings Technology, 73, 73-80 (2001). 

[10] R. S. Hunter, Gloss Investigations Using Reflected Images of a Target Patters, Journal of 

Research, 16, 359 (1936). 

[11] R. S. Hunter, Methods of Determining Gloss, NBS Research paper RP 958, Journal of 

Research, 18, No. 77, 281 (1937). 

[12] I. Nimeroff, Analysis of Goniophotometric Reflective Curves, Journal of Research, 48, 

No. 5, 441 (1952). 

[13] Y. Ohno, Photometric Calibrations, NIST SP 250-37 (1997). 

[14] P. Y. Barnes and J. J. Hsia, 45°/0° Reflectance Factor of Pressed Polytetrafluoroethylene 

(PTFE) Powder, NIST Technical Note 1413 (1995). 

[15] T. Doiron and J. Stoup, Uncertainty and Dimensional Calibrations, J. Res. Natl. Inst. 

Stand. Technol. 102, 647 (1997). 

[16] R. D. Saunders and J. B. Shumaker, Automated Radiometric Linearity Tester, Appl. Opt. 

23, 3504 (1984). 

[17] T. C. Larson, S. S. Bruce, and A. C. Parr, Spectroradiometric Detector Measurements, 

NIST SP 250-41 (1998). 

[18] B. N. Taylor and C. E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty 

of NIST Measurements Results, NIST Tech. Note 1297 (1994). 

[19] J. Zwinkels and M. Nöel, Specular Gloss Measurement Services at the National Research 

Council of Canada, Surface Coatings International 12, 512 (1995). 

[20] B. Wolfang and C. X. Dodd, Stability Problems in Gloss Measurements, Journal of 

Coating Tech. 552, 44-48, (1980). 

[21] M. E. Nadal and E. A. Thompson, New Primary Standard for Specular Gloss 

Measurements, Journal of Coatings Technology, 72, No. 911 (2000). 

[22] G. E. Fishter, Refractometry, Applied Optics and Optical Engineering, Vol. IV, 

Academic Press, New York (1967) p. 363-382. 

[23] I. H. Malitson, Interspecimen Comparison of the Refractive Index of Fused Silica, 

Journal of the Optical Society of America 55, 1205-1209 (1965). 
Calibration Date: Month Day, year 

NIST Test No.: Division number/Test Folder Number-Year Page 1 of 5 

Appendix A 

REPORT OF CALIBRATION 

38090S Specular Gloss 

for 

Specular Gloss Plates 

Submitted by: 

Any Company, Inc. 

Attn.: Ms. Jane Doe 

123 Calibration Street 

Measurement City, MD 20800-1234 

(See your Purchase Order No. 12345, dated month Day, Year) 

1. Description of Calibration Items 

Twelve specular gloss plates, 10.8 cm square, manufactured by Hunter Associates Laboratory, 

Inc., with serial numbers SG-01, SG-02, SG-03, SG-04, SG-05, SG-06, SG-07, SG-08, SG-09, 

SG-10, SG-11, and SG-12, submitted by Any Company, Inc. 

2. Description of Calibration 

Specular gloss is a measure of the specular luminous reflectance of an item under geometrical 

and spectral conditions specified by the American Society for Testing Materials (ASTM) D523 

[1] and the International Organization for Standardization (ISO) 2813 [2] documentary 

standards. 

The calibration items were measured using the NIST Reference Goniophotometer for Specular 

Gloss. This instrument was originally developed at NIST [3] in 1970 and recently updated, 

automated, and characterized [4] to comply with the requirements in the documentary standards. 

An achromatic condenser lens system images radiant flux from a quartz-tungsten-halogen 

incandescent lamp onto the source aperture. The beam emerging from the aperture is collimated 

by a lens, passes through a polarization scrambler, a color filter, and an iris with a clear diameter 

of 3 cm, and is incident upon the sample holder. The radiant flux reflected by the item in the 

sample holder is collected by the receiver iris and focused by a lens onto the receiver aperture at 

the port of an integrating sphere. The integrating sphere has a diameter of 30.5 cm and is packed 
REPORT OF CALIBRATION 

38090S Specular Gloss Specular Gloss Plates 

Any Company, Inc. Serial Nos.: SG-01, SG-02, SG-03, SG-04, 

 SG-05, SG-06, SG-07, SG-08, 

 SG-09, SG-10, SG-11, SG-12 

Calibration Date: Month Day, year 

NIST Test No.: Division number/Test Folder Number-Year Page 2of 5 

with pressed polytetrafluoroethylene (PTFE). A Si photodiode with a photopic filter is attached 

to the sphere and produces a signal proportional to the radiant flux in the sphere, and hence to the 

radiant flux reflected by the item in the sample holder. The sample holder and receiver are 

located on independent, aligned rotation stages used to select the angles of illumination and 

viewing. 

Measuring the specular gloss of a calibration item is a relative measurement and therefore 

requires comparison to a standard with a calibrated specular gloss. The standard is the NIST 

primary specular gloss standard [5], a wedged piece of BaK50 glass. 

The calibration items and primary gloss standard were cleaned with an air bulb and sequentially 

mounted in the sample holder so that their front surface was aligned with the axis of rotation of 

the rotation stage and the illumination beam was centered on the front surface. The calibration 

items were aligned in the direction of illumination, as indicated on the back of the sample. 

Measurements of the calibration items were bracketed with measurements of the primary 

specular gloss standard to correct for any instrumental drift. 

The documentary standards specify the geometrical conditions of measurement for three 

geometries, designated by illumination angles of 20o, 60o, and 85o. For all three geometries, the 

angle from the center of the collimating lens of the illuminator to the source aperture was 0.75o 

in the plane of illumination and 3o perpendicular to this plane. For the 20o geometry, the angle 

from the center of the converging lens of the receiver to the receiver aperture was 1.8o in the 

plane of illumination and 3.6o perpendicular to this plane. For the 60o and 85o geometries, these 

angles were 4.4o and 11.7o and 4o and 6o, respectively. The documentary standards also specify 

the spectral conditions. The spectral power distribution of the illuminator was that of CIE 

standard illuminant C and the spectral responsivity was that of the CIE spectral luminous 

efficiency function Vλ. Both the geometrical and spectral conditions of the NIST Reference 

Goniophotometer for Specular Gloss fell within the tolerances given in the documentary 

standards. 

3. Results of Calibration 

The specular gloss G is given by 

( )

0 0 D s

s,v 0

0 ( , )

( ) 100

I

I G = ⋅ ⋅ ρ θ λ

ρ θ

θ , (3.1) 

where θ0 is the angle of illumination (20o, 60o, or 85o), λD is the wavelength of the sodium D-line 

(589.3 nm), ρs is the reflectance of the NIST primary gloss standard, ρ0 is the reflectance of the 

theoretical standard (nD = 1.567), and I and Is are the currents from the receiver when measuring 

the calibration item and primary standard, respectively. 
REPORT OF CALIBRATION 

38090S Specular Gloss Specular Gloss Plates 

Any Company, Inc. Serial Nos.: SG-01, SG-02, SG-03, SG-04, 

 SG-05, SG-06, SG-07, SG-08, 

 SG-09, SG-10, SG-11, SG-12 

Calibration Date: Month Day, year 

NIST Test No.: Division number/Test Folder Number-Year Page 3of 5 

The final specular gloss is obtained by averaging the values from multiple measurements. The 

certified 20o, 60o, and 85ospecular gloss values for the calibration items are given in Tables 1 to 

3, respectively. 

Uncertainties were calculated according to the procedures outlined in [6]. Sources of uncertainty 

due to random effects are source stability, detector noise, and item uniformity. The uncertainty 

contribution caused by these effects was evaluated from the standard deviation of repeat 

measurements of each item. 

Sources of uncertainty due to systematic effects included those that depend on the scattering 

properties of the calibration item (polarization, divergence and spectral power distribution of the 

illuminator, illumination angle, and spectral responsivity of the receiver) and those that are 

independent of the scattering properties (detector linearity, amplifier gain ratio, and voltmeter 

accuracy). The uncertainties from these effects were evaluated as part of the characterization of 

the NIST Reference Goniophotometer for Specular Gloss, taking into account the spectral 

reflectance properties of the calibration items. All uncertainty components were assumed to 

have normal probability distributions. 

The resulting uncertainty contributions to specular gloss values due to systematic and random 

effects are also given in Tables 1 to 3. The expanded uncertainty was obtained from the rootsum-square of the uncertainty contributions multiplied by a coverage factor k = 2. The expanded 

uncertainties in specular gloss are also given in Tables 1 to 3. 

 

4. General Information 

1) The calibration items were measured in the “as received” condition after cleaning using an 

air bulb. 

2) This calibration report may not be reproduced except in full without the written consent of 

this Laboratory. 

Prepared by: Approved by: 

Maria E. Nadal Gerald T. Fraser 

Optical Technology Division For the Director, 

Physics Laboratory National Institute of 

(301) 975-4632 Standards and Technology 

 (301) 975-3797 
REPORT OF CALIBRATION 

38090S Specular Gloss Specular Gloss Plates 

Any Company, Inc. Serial Nos.: SG-01, SG-02, SG-03, SG-04, 

 SG-05, SG-06, SG-07, SG-08, 

 SG-09, SG-10, SG-11, SG-12 

Calibration Date: Month Day, year 

NIST Test No.: Division number/Test Folder Number-Year Page 4of 5 

References: 

[1] “Standard Test Method for Specular Gloss, ASTM D523,” American Society for Testing 

and Materials, West Conshohocken, PA (1995). 

[2] International Standard ISO 2813, “Paint and Varnishes-Measurements of Specular Gloss of 

Nonmetallic Paint Films at 20°, 60°, and 85°” (International Organization for 

Standardization 1978). 

[3] Hsia, J. J., “The NBS 20-, 60-, and 85- Degree Specular Gloss Scales,” NIST Tech. Note 

594-10 (1975). 

[4] Nadal, M. E. and Thompson, E. A., "NIST Reference Goniophotometer for Reflection 

Gloss Measurements,” Journal Coatings Technology, vol. 73, 73-80, June 2001. 

[5] Nadal, M. E. and Thompson, E. A., “New Primary Standard for Specular Gloss 

Measurements,” Journal of Coatings Technology, Vol. 72, December 2000. 

[6] B. N. Taylor and C. E. Kuyatt, “Guidelines for Evaluating and Expressing the Uncertainty 

of NIST Measurement Results,” NIST Technical Note 1297 (1994). 
REPORT OF CALIBRATION 

38090S Specular Gloss Specular Gloss Plates 

Any Company, Inc. Serial Nos.: SG-01, SG-02, SG-03, SG-04, 

 SG-05, SG-06, SG-07, SG-08, 

 SG-09, SG-10, SG-11, SG-12 

Calibration Date: Month Day, year 

NIST Test No.: Division number/Test Folder Number-Year Page 5of 5 

Table 1. 20° specular gloss, uncertainty contributions, and expanded uncertainties (k = 2) for the 

calibration items. 

Uncertainty Contribution Item 

Serial 

Number 

Specular 

Gloss Random Systematic 

Expanded 

Uncertainty 

(k = 2) 

SG-01 9.00 0.35 0.13 0.75 

SG-02 12.00 0.18 0.13 0.44 

SG-03 42.12 0.13 0.13 0.37 

SG-04 64.35 0.29 0.13 0.64 

Table 2. 60° specular gloss, uncertainty contributions, and expanded uncertainties (k = 2) for the 

calibration items. 

Uncertainty Contribution Item 

Serial 

Number 

Specular 

Gloss Random Systematic 

Expanded 

Uncertainty 

(k = 2) 

SG-05 5.87 0.35 0.11 0.73 

SG-06 13.33 0.37 0.11 0.77 

SG-07 38.65 0.11 0.11 0.31 

SG-08 90.41 0.03 0.11 0.23 

Table 3. 85° specular gloss, uncertainty contributions, and expanded uncertainties (k = 2) for the 

calibration items. 

Uncertainty Contribution Item 

Serial 

Number 

Specular 

Gloss Random Systematic 

Expanded 

Uncertainty 

(k = 2) 

SG-09 8.47 0.55 0.10 1.12 

SG-10 43.26 0.48 0.10 0.98 

SG-11 58.32 0.25 0.10 0.54 

SG-12 85.41 0.30 0.10 0.63 
1

Appendix B 

NIST Reference Goniophotometer for Specular Gloss Measurements 

María E. Nadal and E. Ambler Thompson 

Optical Technology Division 

National Institute of Standard and Technology 

Gaithersburg, MD 20899-8442 

ABSTRACT 

A new reference goniophotometer for specular gloss measurements has been assembled and 

characterized, and will provide calibrations with an expanded uncertainty (k = 2) of 0.3 gloss 

units. 

Keywords: appearance attributes; gloss; gonio-apparent; goniophotometer; specular gloss; 

specular reflectance. 
2

I. Introduction 

The current global economy has increased international competition and the need to 

improve the quality of many manufactured products. Appearance measurements are used to 

determine the quality and acceptability of a variety of products from textiles to machine finishes. 

Since the manufacture and marketing of these products is international in scope, the methods, 

instruments, and standards for the measurement of appearance must be precise, reproducible, and 

internationally standardized as well. 

The appearance of an object is the result of a complex interaction of the light incident on 

the object, the optical characteristics of the object, and human perception. The scientific basis 

for the measurement of appearance attributes has been under investigation for the better part of a 

century and was standardized by the Commission Internationale de l’Eclairage (CIE) [1]. The 

visual response of human observers to wavelengths of light for the spectral region of 360 nm to 

830 nm is tabulated as the CIE standard observer. The CIE has defined a series of standard 

spectral distributions that are known as the CIE Standard Illuminants. 

Appearance attributes of an object are roughly divided into chromatic and geometric. 

The chromatic attributes are those that vary the spectral distribution of the reflected light (color). 

The geometric attributes are those that vary the spatial or angular distribution of the reflected 

light (gloss and haze). 

This paper describes the reference goniophotometer at the National Institute of Standard 

and Technology (NIST). This instrument complies with the geometrical and spectral conditions 

specified by the American Society for Testing Materials (ASTM) D523 [2] and the International 

Organization for Standardization (ISO) 2813 [3] documentary standards for the measurement of 

specular gloss of non-metallic surfaces at fixed specular geometries of 20°, 60°, and 85°. Gloss 

measurements for other industrial applications using different geometries can also be 

accommodated. This goniophotometer is also capable of characterizing the distribution of 

unabsorbed incident radiation by reflection or transmission from a material at incident angels 

from 0° to 85° in compliance with ASTM E167 [4]. Figure 1 shows a plot of the luminous 

reflectance as a function of the observation angle for a set of black glasses with different values 

of gloss. 

This goniophotometer was originally developed at NIST [5] in the 1970’s by scientists 

active in the development of the ASTM standard test method, and has recently been updated, 

automated, and characterized. The instrument was revived to meet industrial needs, such as the 

paint and automotive industries, for accurate gloss measurements and direct traceability to 

national standards. 

The outline of this paper is as follows. Section II presents the gloss definition and the 

measurement equations. The instrument design is presented in Sec. III and the characterization 

of this instrument is described in Sec. IV. The uncertainty analysis is discussed in Sec. V. 

Finally, the conclusions are detailed in Sec. VI. 

II. Gloss Definition and Measurement Equations 

This section details the basic definitions and the relevant measurement equations to 

determine specular gloss. The approach utilized in this paper is based upon the concepts 

presented in Refs. [5-7]. 

Gloss is the perception by an observer of the shiny appearance of a surface. This 

perception changes whenever there is a change in the relative position or spectral distribution of 

the source, the sample, and the observer. Different standard geometries are used to determine the 

specular gloss of materials. Table 1 lists examples of these geometries and their applications. 
3

These geometries were selected based on their ability to produce optimum discrimination 

between samples and to correlate with visual rankings. 

The measurement of specular gloss compares the specular luminous reflectance from a 

test specimen to that from a standard surface under the same experimental conditions. The 

incident beam is a collimated white light source that simulates CIE standard Illuminant C and the 

amount of radiation in the reflected beam is measured with a photopic receptor. The theoretical 

standard for specular gloss measurements is a highly polished plane black glass with a refractive 

index for the sodium D line nD = 1.567. To set the specular gloss scale, the specular gloss of this 

theoretical standard has an assigned value of 100 for each of the three standard specular 

geometries of 20°, 60°, and 85°. For primary standards with a refractive index different from nD

= 1.567, the specular gloss is computed from the refractive index and the Fresnel equations. 

Recommendations for specular gloss standards and a new NIST primary gloss standard are 

described in Ref. [8]. 

Measuring the specular gloss of a test sample involves the ratio of the luminous 

reflectances of the test sample and primary standard. The specular gloss of a test sample at a 

nominal angle θ0 is given by 

( )

( ) ( ) ( ) 

v,s 0

v,t 0

t 0 s 0

ρ θ

ρ θ

G θ = G θ ⋅ , (1) 

where Gs(θ0) is the specular gloss of the primary standard and ρv,t(θ0) and ρv,s(θ0) are the 

specular luminous reflectances of the test sample and primary standard, respectively. 

Furthermore, the specular gloss of the primary standard is given by 

( , )

( , ) ( ) ( )

0 0 D

s 0 D

s 0 0 0

ρ θ λ

ρ θ λ G θ = G θ ⋅ , (2) 

where G0(θ0) is the specular gloss of the theoretical standard and ρs(θ0, λD) and ρ0(θ0, λD) are the 

specular reflectances of the primary and theoretical standards, respectively, at a wavelength λD = 

589.3 nm. Combining Eqs. (1) and (2), the specular gloss of the sample under test is given by 

( )

( )

( , )

( , ) ( ) ( )

v,s 0

v,t 0

0 0 D

s 0 D

t 0 0 0

ρ θ

ρ θ

ρ θ λ

ρ θ λ G θ = G θ ⋅ ⋅ . (3) 

For each of the three standard geometries (20°, 60°, and 85°), the specular gloss of the 

theoretical standard is defined as G0(θ0) = 100. The specular reflectance ρ from the surface of a 

nonmetallic sample depends on the incident angle θ defined relative to the normal of the sample, 

the wavelength λ, and polarization σ (p or s) of the incident radiation. The specular reflectance 

as a function of these variables is given by the Fresnel equations, 

2

2 2 2

2 2 2

( ) cos ( ) sin

( ) cos ( ) sin ( , , p) 















⋅ + −

⋅ − − =

λ θ λ θ

λ θ λ θ

ρ θ λ

n n

n n and (4) 

2

2 2

2 2

cos ( ) sin

cos ( ) sin

( , ,s) 















+ −

− − =

θ λ θ

θ λ θ

ρ θ λ

n

n (5) 

The specular reflectance for unpolarized light is calculated from the average of Eqs. (4) and (5). 

The specular reflectances for unpolarized light for the theoretical standard ρ0(θ0, λD) with nD = 

1.567 are calculated from Eqs. (4) and (5) and are listed in Table 2. For the case of the new 

primary gloss standard [8], the specular reflectances are calculated from the measured nD = 

1.5677 ± 0.0004 and Eqs. (4) and (5). 
4

The experimentally measured quantity is the ratio of the luminous fluxes reflected from 

the test sample and primary standard, Φv,t,r and Φv, s, r respectively, 

t

s

s

t

t

s

v,t,i

v,s,i

v,s,r

v,t,r

v,t,i

v,s,i

v,s 0

v,t 0

( )

( )

A

A

N

N

R

R

⋅ ⋅ ⋅ Φ

Φ= Φ

Φ

⋅ Φ

Φ= ρ θ

ρ θ

 (6) 

where R is the responsivity of the receptor, N is the measured signal, A is the amplifier gain 

factor, and the subscripts s and t denote standard and test sample, respectively. Therefore, 

combining Eqs. (3) and (6), the specular gloss of a test sample in terms of the measured 

quantities reduces to 

( )

t

s

s

t

t

s

v,t,i

v,s,i

0 0 D

s 0 D

t 0 ( , )

( , ) 100

A

A

N

N

R

R G ⋅ ⋅ ⋅ Φ

Φ = ⋅ ⋅ ρ θ λ

ρ θ λ θ . (7) 

The stability of the incident flux and responsivity are determined from the characterization of the 

instrument. 

In terms of spectral and geometrical quantities, the luminous reflectance ρv of a sample at 

a nominal angle θ0 is given by 

∑∫ ∫

∑∫ ∫

⋅ ⋅

⋅ ⋅ ⋅

=

σ

σ

θ λ θ λ σ θ λ σ

θ λ θ λ σ ρ θ λ σ θ λ σ

ρ θ

d d ( , , ) ( , , )

d d ( , , ) ( , , ) ( , , )

( ) v 0

S V

S V

, (8) 

where S is the incident spectral flux distribution, V is the relative response function, and ρ is the 

reflectance of the sample. These variables depend on the angle of incidence θ, wavelength λ,

and polarization σ of the incident beam . In practice, the luminous reflectances of the standard 

and test sample are not measured separately. Rather, the ratio of these reflectances is measured 

and is given by 

∑∫ ∫

∑∫ ∫

⋅ ⋅ ⋅

⋅ ⋅ ⋅

=

σ

σ

θ λ θ λ σ ρ θ λ σ θ λ σ

θ λ θ λ σ ρ θ λ σ θ λ σ

ρ θ

ρ θ

d d ( , , ) ( , , ) ( , , )

d d ( , , ) ( , , ) ( , , )

( )

( )

s

t

v,s 0

v,t 0

S V

S V

 (9) 

Then, the specular gloss of a test sample is given by 

∑ ∫ ⋅ ⋅ ⋅ ∫

∑ ∫ ⋅ ⋅ ⋅ ∫

= ⋅ ⋅

σ

σ

θ λ θ λ σ ρ θ λ σ θ λ σ

θ λ θ λ σ ρ θ λ σ θ λ σ

ρ θ λ

ρ θ λ θ

d d ( , , ) ( , , ) ( , , )

d d ( , , ) ( , , ) ( , , )

( , )

( , ) ( ) 100

s

t

0 0 D

s 0 D

t 0 S V

S V

G (10) 

 Following the standard recommendations, the incident spectral flux distribution S(λ) is 

specified to be CIE standard Illuminant C SC(λ) and the relative response function V(λ) is 

specified to be the CIE 1931 2° observer spectral luminous efficiency function Vλ. In addition, 

the incident beam of light is specified to be collimated and unpolarized at a nominal incident 

angle θ0. The specular gloss of the sample under test for the ideal case is given by 

∫ ⋅ ⋅ ⋅

∫ ⋅ ⋅ ⋅ = ⋅ ⋅ d ( ) ( , ) ( )

d ( ) ( , ) ( )

( , )

( , ) ( ) 100

C s 0

C t 0

0 0 D

s 0 D

t,id 0 λ λ ρ θ λ λ

λ λ ρ θ λ λ

ρ θ λ

ρ θ λ θ

λ

λ

S V

S V G . (11) 

Deviations of the reference instrument from the ideal case include deviations from the 

specified spectral flux distribution of the source, spectral responsivity of the receptor, 

unpolarized and perfectly collimated incident beam, and nominal incident angle. The correction 

factors for the specular gloss of the sample under test as determined with the reference 

instrument are obtained using Eqs. (10) and (11). The correction factors are the ratio of the 

specular gloss for the ideal case to the specular gloss for the reference instrument 
5

( )

( )

t 0

t,id 0

θ

θ

G

G

C = . (12) 

The correction factor for deviations from the ideal spectral flux distribution is given by 

∫

∫

∫

∫ ⋅ ⋅ ⋅

⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅⋅ ⋅ ⋅ = d ( ) ( , ) ( )d ( ) ( , ) ( )

d ( ) ( , ) ( )

d ( ) ( , ) ( )

t 0

s 0

C s 0

C t 0

s

λ λ ρ θ λ λ

λ λ ρ θ λ λ

λ λ ρ θ λ λ

λ λ ρ θ λ λ

λ

λ

S V

S V

S V

S V

C . (13) 

The correction factor for deviations from an unpolarized incident beam is given by 

∑∫

∑∫

∫

∫ ⋅ ⋅ ⋅

⋅ ⋅ ⋅

⋅ ⋅ ⋅ ⋅

⋅ ⋅ ⋅ =

σ

λ

σ

λ

λ

λ

λ λ σ ρ θ λ σ λ

λ λ σ ρ θ λ σ λ

λ λ ρ θ λ λ

λ λ ρ θ λ λ

d ( , ) ( , , ) ( )

d ( , ) ( , , ) ( )

d ( ) ( , ) ( )

d ( ) ( , ) ( )

C t 0

C s 0

C s 0

C t 0

p

S V

S V

S V

S V

C . (14) 

The correction factor for deviations from a perfectly collimated incident beam is given by 

∫ ∫

∫ ∫

∫

∫ ⋅ ⋅ ⋅

⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅⋅ ⋅ ⋅ = d d ( , ) ( , ) ( )

d d ( , ) ( , ) ( )

d ( ) ( , ) ( )

d ( ) ( , ) ( )

C t

C s

C s 0

C t 0

d

θ λ θ λ ρ θ λ λ

θ λ θ λ ρ θ λ λ

λ λ ρ θ λ λ

λ λ ρ θ λ λ

λ

λ

λ

λ

S V

S V

S V

S V

C . (15) 

The correction factor for deviations from the nominal incident angle is given by 

∫

∫

∫

∫ ⋅ ⋅ ⋅

⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅⋅ ⋅ ⋅ = d ( ) ( , ) ( )

d ( ) ( , ) ( )

d ( ) ( , ) ( )

d ( ) ( , ) ( )

C s

C t

C s 0

C t 0

a

λ λ ρ θ λ λ

λ λ ρ θ λ λ

λ λ ρ θ λ λ

λ λ ρ θ λ λ

λ

λ

λ

λ

S V

S V

S V

S V

C . (16) 

Therefore, the specular gloss for the ideal case in terms of the correction factors is given by 

t,id 0 t s p d a G (θ ) = G ⋅C ⋅C ⋅C ⋅C . (17) 

The final measurement equation, including the correction factors and the experimentally 

measured quantities, is given by 

s p d a

t

s

s

t

t

s

v,t,i

v,s,i

0 0 D

s 0 D

t,id 0 ( , )

( , ) ( ) 100 C C C C

A

A

N

N

R

R G ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ Φ

Φ = ⋅ ⋅ ρ θ λ

ρ θ λ θ . (18) 

III. Instrument Design 

The reference goniophotometer is a monoplane gonio-instrument with a fixed source arm 

and a rotating sample table and receptor arm. The sample table and the receptor arm can be 

rotated independently of each other in the plane of incidence. A schematic diagram of the 

goniophotometer in reflectance mode is shown in Fig. 2 and a detailed description of the 

instrument is given below. 

The source system consists of a lamp unit, a set of condenser lenses, a precision source 

aperture, a collimating lens, and a color filter. The light source is a quratz-tungsten-halogen 

lamp rated at 100 W. A constant dc current is run through the lamp from a computer controlled 

power supply. An image of the lamp filament is formed on the source aperture with the 

achromatic condenser lens system. This source aperture is the field stop for this optical system. 

The dimensions of the source aperture are within the tolerances of the documentary standard 

specifications as shown in Table 3. A second lens (focal length 192 mm) collimates the beam 

into an approximate 3 cm diameter beam at the sample holder. A color filter is used so that the 

spectral flux distribution of the source-filter combination closely resembles that of CIE Standard 

Illuminant C. A glass-laminated polarizer is used to provide linearly polarized light or a 

scrambler is used to provide unpolarized light in the incident beam. 

The goniometer positions the sample and receptor for bi-directional reflectance and 

transmittance measurements. This goniometer consists of two rotation stages, which are 

computer controlled. The sample table is 480 mm in diameter and holds rectangular samples 
6

with dimensions up to 110 mm by 200 mm and thickness up to 35 mm. In addition, a sampler 

holder with vacuum suction is used for non-rigid samples such as paper. The optical components 

for the receptor arm are enclosed in a light-tight baffle tube with an iris diaphragm at the 

entrance. The collector lens (focal length 508 mm) is behind this iris diaphragm and focuses the 

reflected beam at the receptor aperture. Table 3 lists the recommended dimensions of the 

receptor aperture with specified tolerances and the measured dimensions for the NIST apertures. 

This aperture is located at the entrance of the sphere to restrict the field of view of the receptor. 

The receptor package consists of a 30.5 cm diameter sphere packed with pressed 

polytetrafluoroethylene (PTFE) and a photopic receptor. The photopic receptor is a temperature 

controlled silicon photodiode and a filter with a computer controlled variable gain current to 

voltage amplifier. The photodiode-filter combination approximates Vλ. The amplified output 

from the receptor is measured by a 6 1/2-digit voltmeter and sent to a computer. 

Measurements of the sample under test are bracketed with primary specular gloss 

standard measurements in order to correct for any instrumental drift. The specular gloss of the 

test sample is then calculated from the ratio of the measured luminous flux reflected from the 

sample to the average of the measured luminous flux reflected from the primary gloss standard. 

If a polarizer is used, measurements are performed with parallel and perpendicular polarization 

with respect to the incident plane and the average of these two measurements yields the 

reflectance for unpolarized radiation. 

IV. Characterization of Instrument 

This instrument has been carefully characterized and calibrated to ensure proper 

operation and to verify agreement with the documentary standard specifications for specular 

gloss measurements - ASTM D523 and ISO 2813. These documentary standards specify the 

incident beam to be a collimated unpolarized beam, the specular angles, the source and receptor 

apertures, and the spectral flux distribution of the source and spectral response of the receptor. 

Details of the characterization of the instrument are given below. 

The lamp is burned in at 100 W for 24 h and then at the operational current of 6.3 A for 

an additional 48 h prior to performing measurements. The stability of the source was 

investigated by measuring the flux incident on a Si photodiode at the sample location for a period 

of 30 min. A typical relative standard deviation over ten minutes is 0.01 %. 

The degree of polarization of the source unit was measured by rotating a polarizer and 

measuring the maximum and minimum transmitted signals. The difference of the signals was 

divided by the sum to obtain the degree of polarization of the source. This ratio is approximately 

9 %. Because the light source is not completely unpolarized, a glass-laminated polarizer or 

scrambler is used in the beam path just before the sample. The averaging sphere on the receptor 

arm in front of the photopic receptor randomizes any additional polarization imparted by the 

sample. The leakage of the glass-laminated polarizer for radiation polarized perpendicular to the 

intended direction of polarization on the source unit is 1.4 %. The degree of polarization of the 

source-scrambler combination is 0.02 %, providing a good beam of unpolarized incident 

radiation. The divergence of the source was determined experimentally by measuring the source 

size at specific distances. In the plane of measurement, the half-angle divergence of the source is 

0.3°. 

The recommended spectral condition for specular gloss measurements is for the source to 

simulate the spectral distribution of CIE standard Illuminant C and for the receptor response to 

simulate the CIE 1931 2° luminous efficiency function. The spectral distributions of these 

standards are shown in Fig. 3. 
7

A color filter was designed so that the spectral flux distribution of the source-filter 

combination will closely resemble that of CIE Standard Illuminant C. The Correlated Color 

Temperature (CCT) and the spectral flux distribution of the source for the spectral range of 380 

nm to 1070 nm were measured using a calibrated scanning spectroradiometer [9]. A freshly 

pressed polytetrafluoreethylene (PTFE) sample [10] was placed in the sample holder at an 

incident angle of 45° and an observation angle of ~0°. The spectral reflectance of PTFE is nonselective in the visible region. Therefore, the PTFE sample has no significant effect on the 

measured CCT of the source. The lamp current is set at 6.3 A to achieve a CCT of 2856 K ± 10 

K with a coverage factor of k = 2. A color-temperature conversion filter was designed to 

simulate the spectral flux distribution of CIE standard Illuminant C (CCT = 6774 K), achieving a 

CCT of 6740 K ± 30 K with a coverage factor of k = 2. 

The absolute spectral responsivity of the filter and receptor package was measured in the 

NIST Receptor Comparator Facility [11], and approximates that of the CIE 1931 2° standard 

observer. The measured spectral distribution was normalized to one at 560 nm to compare with 

the theoretical distribution. The responsivity spatial uniformity of the receptor was not 

determined since an integrating sphere is used in front of the receptor. Figure 4 shows a 

comparison of the spectral products of the source and receptor and of the CIE standard 

Illuminant C and the 1931 2° luminous efficiency function. 

The angular scales of the sample table and receptor were checked for accuracy and 

repeatability from 0° to ± 85°. The incident angles on the sample table are calibrated using a set 

of isosceles prisms made by the NIST optical shop. These prisms have nominal base angles of 

20°, 60°, and 85° with maximum deviations of 0.05°. These angles correspond to the standard 

geometries for evaluation of the specular gloss of nonmetallic paint samples. The prisms were 

calibrated by the Manufacturing Engineering Laboratory at NIST using a precision electronic 

autocollimator with an expanded uncertainty (k = 2) of 0.005° [12]. For the calibration of the 

incident angles, one of the calibrated prisms was mounted in the sample holder. The sample 

table was then rotated so that the back reflection was retro-reflected. This procedure was 

repeated for the three prisms, the resulting maximum uncertainty for the angular scale of the 

sample table is 0.05°. The repeatability of the angular scale for the sample table is 0.005°. Then, 

to calibrate the receptor angular scale, a front surface mirror replaced the prism and the reflection 

was centered in the receptor aperture by rotating the receptor arm. The maximum uncertainty for 

the receptor arm angular scale is 0.05° and the repeatability is 0.001°. 

The dimensions of the source and receptor apertures are predetermined by the specular 

geometry, focal length of the collimator lens in the system, test material, and the correlation with 

visual ranking. Table 3 lists the standard recommended aperture sizes and acceptable tolerances 

and measured values for the NIST apertures. The linear dimensions of the apertures were 

measured and the angular dimensions were calculated. All of the apertures are within the ASTM 

tolerances. 

The photopic receptor consists of a temperature controlled silicon photodiode with a 

photopic filter and a computer controlled variable gain current to voltage amplifier. The gain 

setting of the amplifier is the power of ten by which the current is multiplied to convert it to 

voltage. For low gloss samples, the measured signal is much lower than the signal from the high 

specular gloss primary standard. In this case, several amplifier gain settings are required to 

cover the dynamic range. From Eq. (7), the ratio of the gain is the required quantity. The gain 

settings of the amplifier were calibrated using a reference constant current source as the input of 

the amplifier and a voltmeter was used to measure the output signal. At each gain setting, the 

current was set to obtain a range of voltages from 10 V to 0.1 V in twenty equally spaced steps 

and the output signal was measured at each current. This protocol yielded current settings that 
8

were common to successive gain settings. The average value of the gain ratio and relative 

standard deviation of these overlapping settings for successive gains are listed in Table 4. The 

gain ratios are not exactly equal to 10, and for better results, it is best to measure signals between 

the ranges of 0.5 V to 12 V. 

The linearity of the photodiode-amplifier combination was measured using the NIST 

automated beam conjoiner [13]. This facility uses the beam addition method with a set of filters 

in the path of the two branches of the beam to vary the radiant flux at the receptor by three 

decades. The linearity of the photodiode-amplifier combination was checked at gain settings 

from 5 to 9. The maximum radiant flux at the receptor is controlled by a set of neutral-density 

filters in front of the receptor. Figure 5 shows a plot of the relative responsivity (ratio of the 

measured signal to the actual flux) as a function of current for the gain settings listed in the 

legend. The measured relative responsivity of the photodiode-amplifier combination is linear 

within 0.2 % for gain settings of 5 to 8. Larger deviations are observed at gain 9 due to the small 

current at this setting. 

V. Uncertainty Analysis 

This section describes the components of uncertainty, their evaluation, and the resulting 

uncertainty for specular gloss measurements. The uncertainty analysis described below follows 

the guidelines given in Ref. [14]. The NIST reference goniophotometer was designed so that the 

various sources of uncertainty were minimized and the residual uncertainties were characterized 

to produce specular gloss with a minimum relative expanded uncertainty (k = 2) of 0.4 %. 

The specular gloss of a test sample is not measured directly. In fact, specular gloss is 

determined from quantities such as incident and reflected fluxes through the measurement 

equation. In general, the value of a measurand, y, is obtained from n other quantities xi through a 

functional relation, f, given by 

( , , , , , ) 1 2 i n y = f x x ⋅⋅⋅ x ⋅⋅⋅ x (19) 

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

associated with this quantity and is denoted by u(xi). The standard uncertainties are classified by 

the effect of their source and the method of evaluation. The effect is either random or 

systematic. The method of evaluation is either Type A, which is based on statistical analysis, or 

Type B, which is based on other means. The relative standard uncertainty is given by u(xi)/xi. 

The relative combined standard uncertainty uc(y) is given by the root-sum-square of the standard 

uncertainties associated with each quantity xi, assuming that these uncertainties are uncorrelated 

for multiplicative functional relationships. The mathematical expression for the relative 

combined standard uncertainty is 

( ), 1 ( )/ 2

2

1

2 2

i

n

i i

c u x

x

f

y

u y y ∑= 















∂

∂ = (20) 

where (1/y)(∂f/∂xi) is the relative sensitivity coefficient. The expanded uncertainty U is given by 

k⋅uc(y), where k is the coverage factor and is chosen on the basis of the desired level of 

confidence to be associated with the interval defined by U. For the purpose of this paper, k = 2 

will be used, which defines an interval with a level of confidence of 95 %. 

The components of uncertainty associated with gloss measurements are divided into 

those arising from experimentally measured quantities and those from deviations from standard 

recommendations. The appropriate measurement equation for the first case is Eq. (7) and for the 

latter case Eqs. (13) to (17) are applicable. The resulting uncertainty from deviations from the 

standard recommendations depends on the nature of the sample under test and the primary 

standard. This uncertainty analysis was applied to representative measurements of a highly 
9

polished black glass as the test sample and to a highly polished wedge of BaK50 as the primary 

standard. 

The component of uncertainty arising from the specular reflectance of the primary gloss 

standard is uncertainty in the refractive index measurements. The uncertainties from the 

refractive index measurements are a systematic effect with a Type B evaluation. The relative 

uncertainty resulting from the refractive index measurements is 0.1 %, 0.06 %, and 0.005 % for 

the 20°, 60°, and 85° geometries, respectively. 

 The components of uncertainty arising from the source are uncertainties from the stability, 

polarization, and divergence of the source. The source stability results in an uncertainty from a 

random effect with a Type A evaluation. The relative standard uncertainty due to instability of 

the source is 0.001 % for a measurement time of 10 min. The uncertainty arising from the 

polarization of the source is a systematic effect with a Type B evaluation and depends on the 

scattering properties of the material. The correction factor for deviations from an unpolarized 

incident beam were calculated from Eq. (14) using the degrees of polarization determined in the 

previous section. The correction factors for the three standard geometries are listed in Table 5. 

The uncertainty arising from divergence of the source is a systematic effect with a Type B 

evaluation and depends on the scattering properties of the material. The correction factor for 

deviations from a perfectly collimated incident beam were calculated from Eq. (15) using the 

divergence determined in the previous section. The correction factors for the three standard 

geometries are listed in Table 5. 

The uncertainties arising from the goniometer are the uncertainties of the angular scales. 

This uncertainty is a systematic effect with a Type B evaluation and depends on the scattering 

properties of the sample. The angular setting uncertainty of 0.05° is smaller than the 0.1° 

recommended accuracy by the ASTM D523. The correction factors from deviations of the 

nominal incident angle from Eq. (16) for the three standard geometries are listed in Table 5. 

The components of uncertainty arising from the detection system are uncertainties from 

the digital voltmeter (DVM), signal noise, amplifier gain ratio, and photodiode linearity. The 

uncertainty from the DVM is a systematic effect with a Type B evaluation, assuming a normal 

probability distribution. Using the manufacturer’s specifications, the relative uncertainty 

resulting from the DVM is 0.002 %. Signal noise of the instrument results in an uncertainty 

from a random effect with a Type A evaluation. A typical relative standard deviation for a gloss 

measurement is 0.01 %. The uncertainties arising from the photodiode linearity and the 

amplifier gain ratio are systematic effects with a Type A evaluation. The maximum relative 

standard deviation from linearity of the photodiode, for signals in the range of 0.1 V to 12 V, is 

0.09 %. The relative standard deviations for successive gain settings are listed in Table 4. The 

maximum relative standard deviation is 0.002 %. 

The repeatability of the sample positioning results in an uncertainty from a random effect 

with a Type B evaluation. Assuming a rectangular probability distribution with a maximum 

deviation of 0.2 gloss units, the relative standard uncertainty is 0.1 %. 

Deviations from the spectral condition are important for low-gloss materials with strong 

colors. The spectral conditions of the source and receptor are in close agreement with the 

recommended CIE Standard Illuminant C and CIE 1931 2° luminous efficiency function. The 

difference between the instrument and the standard recommendations results in a systematic 

effect with a Type B evaluation. The correction factors for deviations from the standard 

recommendations for the three standard geometries, from Eq. (13), are listed in Table 5. 

Since all of the correction factors listed in Table 5 are nearly unity, no correction factor is 

applied and the variations from unity are considered to be uncertainties. The relative standard 

uncertainty from each component of uncertainty is listed in Tables 6a and 6b for sample-
10

dependent and –independent components, respectively. The relative expanded uncertainties 

given in Table 7 are calculated from the root-sum-square of the uncertainties listed in Tables 6a 

and 6b. The ISO 2813 standard specifies that gloss should be reported to the nearest full gloss 

unit. Therefore, the calibration of the reference instrument and primary standard should have an 

uncertainty of less than 1 gloss unit. The NIST reference goniophotometer has an expanded (k = 

2) relative uncertainty of 0.3 % for calibrating a highly polished black glass. If the specular 

gloss of successive measurements on the same sample do not agree to within 0.3 %, the 

instrument is assumed to have failed during the measurements and the sample is measured again. 

VI. Conclusions 

The appearance attributes of surfaces indicate the acceptability and quality of a large 

number of manufactured products. Specular gloss is the second most utilized attribute, after 

color to evaluate products such as automotive coatings, textiles, and papers. The reference 

goniophotometer described in this paper complies with the standard recommendations for 

specular gloss at 20°, 60°, and 85° geometries for non-metallic paint samples from low to high 

gloss levels, as described in the ISO 2813 and ASTM D523 documentary standards. In addition, 

this reference instrument is capable of performing bi-directional reflectance and transmission 

measurements at angles from 0° to 85° for both incident and viewing angles in compliance with 

the ASTM E 167 documentary standard. This instrument has been carefully characterized and 

calibrated to ensure proper operation and to verify agreement with the standard 

recommendations. The relative expanded uncertainty (k = 2) of the NIST goniophotometer for 

specular gloss is 0.3 % at all three standard geometries. The accuracy of specular gloss 

measurements depends not only on the properties of the instrument but also to a considerable 

extent on those of the primary gloss standard. A new primary gloss standard was developed at 

NIST and details on this standard characterization are the subject of another paper [8]. The new 

gloss standard and the NIST reference goniophotometer provide an accurate calibration facility 

for specular gloss. 

Acknowledgements 

The authors wish to express special thanks to Edward Early for many useful discussions and the 

collaboration with the National Institute of Standards and Technology researchers who are 

working on the Measurement Science for Optical Reflectance and Scattering Project. 

References 

[1] Commission International de l’Eclairage: International Lighting Vocabulary, 

Colorimetry, 2nd ed., Publ. No. 15.2 (1986). 

[2] ASTM D523, “Standard Test Method for Specular Gloss,” in ASTM standards on Color 

and Appearance Measurement, 5th ed., (ASTM, Philadelphia, PA, 1996). 

[3] International Standard ISO 2813, “Paint and Varnishes-Measurements of Specular Gloss 

of Nonmetallic Paint Films at 20°, 60°, and 85°” (International Organization for 

Standardization 1978). 

[4] ASTM E167, “Standard Practice for Goniophotometry of Objects and Materials,” in 

ASTM standards on Color and Appearance Measurement, 5th ed., (ASTM, Philadelphia, 

PA, 1996). 
11

[5] Hsia, J. J., “The NBS 20-, 60-, and 85- Degree Specular Gloss Scales,” NIST Tech. Note 

594-10 (1975). 

[6] Nicodemus, F. E., Richmond, J. C., Hsia, J. J., Ginsburg, I. W., and Limperis, T., 

“Geometrical Considerations and Nomenclature for Reflectance,” U.S. NBS Monograph 

160 (1977). 

[7] Budde, W., “The Calibration of Gloss Reference Standards,” Metrologia 16, 89-93 

(1980). 

[8] Nadal, M. E. and Thompson, E. A., “New Primary Standard for Specular Gloss 

Measurements,” submitted to JCT. 

[9] Ohno, Y., “Photometric Calibrations,” NIST SP 250-37 (1997). 

[10] Barnes, P. Y. and Hsia, J. J., “45°/0° Reflectance Factor of Pressed 

Polytetrafluoroethylene (PTFE) Powder,” NIST Technical Note 1413 (1995). 

[11] Larson, T. C., Bruce, S. S., and Parr, A. C., “Spectroradiometric Receptor 

Measurements,” NIST SP 250-41 (1998). 

[12] Doiron, T. and Stoup, J., “Uncertainty and Dimensional Calibrations,” J. Res. Natl. Inst. 

Stand. Technol. 102, 647 (1997). 

[13] Saunders, R. D. and Shumaker, J. B., “Automated Radiometric Linearity Tester,” Appl. 

Opt. 23, 3504 (1984). 

[14] Taylor, B. N. and Kuyatt, C. E., “Guidelines for Evaluating and Expressing the 

Uncertainty of NIST Measurements Results,” NIST Tech. Note 1297 (1994). 
12

List of Figures 

1. Luminous reflectance as a function of the observation angles for a set of black glasses 

with different levels of gloss an indicated in the legend. 

2. A schematic diagram of the NIST reference goniophotometer. 

3. Spectral flux distribution of the CIE Standard Illuminant C and CIE 1931 2° luminous 

efficiency function. 

4. Actual and ideal spectral products of the source and receptor. 

5. Relative responsivity (ratio of the measured signal to the actual flux) of the photodiodeamplifier combination as a function of current for the listed gain settings. 
13

Figure 1 

0.00

0.10

0.20

0.30

0.40

50 55 60 65 70

Observation Angle [°]

Luminous Reflectance

30

50

70

95
14

Figure 2 

Source

Condenser 

 lens

Collimator

 lens

Averaging 

Sphere

Collector

 lens

Receptor

field stop

Depolarizer

Source 

field stop

Filter

Sample Sample table

Detector

Optical Technology Division Sample normal
15

Figure 3

0

20

40

60

80

100

120

140

300 400 500 600 700 800

Wavelength [nm]

Spectral flux distributio

n

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Luminous efficienc

y

function
16

Figure 4 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

300 400 500 600 700 800

Wavelength [nm]

Relative spectral 

product

Actual

Ideal
17

Figure 5 

0.980

0.985

0.990

0.995

1.000

1.005

1.010

1.015

1.020

0.00001 0.001 0.1 10 1000 100000

Current [nA]

Relative Responsivity

5 7

8 9
18

List of Tables 

1. Standard geometries for specular gloss measurements and their applications. 

2. Specular reflectance ρ0(θ, λD) of the theoretical gloss standard for each incident angle of 

the standard geometries at wavelength λD = 589.3 nm. 

3. ASTM specifications and the NIST measured values for source and receptor apertures, with 

tolerances and uncertainties, respectively. 

4. Average gain ratio and relative standard deviation for successive amplifier gain ratios. 

5. Correction factors for deviations from the standard recommendations of an unpolarized 

source, a perfectly collimated incident beam, nominal incident angle of 20°, 60°, and 85°, 

and spectral conditions. 

6. a. Components of uncertainty that depend on the scattering properties of the materials and 

the resulting relative standard uncertainties. The values are based on a BaK50 primary 

gloss standard and a highly polished black glass test sample. 

b. Components of uncertainty that are independent of the scattering properties of the 

materials and the resulting relative standard uncertainties. 

7. Relative expanded uncertainties of specular gloss measured by the NIST reference 

goniophotometer (k = 2) for the 20°, 60°, and 85° geometries. 
19

Table 1 

Specular Angle Applications 

20° High gloss of plastic film, appliance and 

automotive finishes 

30° High gloss of image-reflecting surfaces 

45° Porcelain enamels and plastics 

60° All ranges of gloss for paint and 

plastics 

75° Coated waxes and paper 

85° Low gloss of flat matte paints and 

camouflage coatings 

Table 2 

Incident Angle ρ0(θ, λD) 

20° 0.049078 

60° 0.100056 

85° 0.619148 

Table 3 

Apertures In plane (°) Perpendicular to the plane(°) 

ASTM Spec. NIST Apertures ASTM Spec. NIST Apertures 

Source 0.75 ± 0.25 0.75 ± 0.01 3.0(max.) ± 0.5 3.01 ± 0.01 

20° receptor 1.8 ± 0.05 1.82 ± 0.01 3.6 ± 0.1 3.64 ± 0.02 

60° receptor 4.4 ± 0.1 4.44 ± 0.02 11.7 ± 0.2 11.72 ± 0.01 

85° receptor 4.0 ± 0.3 4.03 ± 0.01 6.0 ± 0.3 6.02 ± 0.01 

Table 4 

Gain ratio Average value Relative standard deviation [%] 

G6/G5 9.999 0.002

G7/G6 9.998 0.002

G8/G7 9.997 0.002

G9/G8 10.017 0.003

G10/G9 9.952 0.003
20

Table 5 

 Correction factors Deviation 20° 60° 85° 

Source-polarizer, Cp 0.999890 1.000137 1.000222 

Source-depolarizer, 

Cp 

0.999999 1.000001 0.999995 

Divergence, Cd 0.999999 0.999806 0.999999 

Nominal angle, Ca 0.999996 0.999875 0.999940 

Spectral Condition, Cs 1.000012 1.000006 0.999997 

Table 6a 

Relative standard uncertainty 

[%] Component of 

Uncertainty 

Effe

ct Type

20° 60° 85° 

Source-polarizer S B 0.01 0.01 0.02 

Source-depolarizer S B 0.0001 0.0001 0.0005 

Source divergence S B 0.0001 0.02 0.0001 

Nominal angle S B 0.0004 0.01 0.006 

Spectral condition S B 0.001 0.0006 0.0003 

Table 6b 

Relative standard uncertainty [%] 

Component of Uncertainty Effect Type

20° 60° 85° 

Primary gloss standard S B 0.1 0.06 0.005 

Source stability R A 0.01 

DVM S B 0.002 

Signal noise R A 0.01 

Photodiode linearity S A 0.09 

Amplifier gain ratio S A 0.002 

Repeatability R B 0.1 

Table 7 

Geometry [°] Relative expanded uncertainty [%] 

20 0.34 

60 0.30 

85 0.27 
1

Appendix C 

New Primary Standard for Specular Gloss Measurements 

María E. Nadal and E. Ambler Thompson 

Optical Technology Division 

National Institute of Standard and Technology 

Gaithersburg, MD 20899 

ABSTRACT 

The measurement of specular gloss consists of comparing the luminous reflectance from a 

specimen to that from a calibrated gloss standard, under the same geometric conditions. The 

specifications for the gloss standard are discussed. A new primary gloss standard using BaK50 

barium crown glass has been developed. Different calibration procedures are detailed, and the 

new standard is compared with other primary standards. 

Keywords: specular gloss; gloss standard; glossmeter; goniophotometer. 
2

I. Introduction 

 Specular gloss is the perception by an observer of the mirror-like appearance of a surface. 

This appearance cannot be measured; only the specific reflectance characteristics of the surface 

are measured. Gloss is a commercially important attribute of many materials such as paints, 

papers, plastics, and textiles, and is affected by the production, storage and use of these materials 

products. Several documentary standards describe the proper measurement conditions to 

determine specular gloss for specific surfaces. Particularly, the International Organization for 

Standards ISO 2813 [1] and the American Society for Testing Materials ASTM D523 [2] 

describe the measurement procedure that best correlates with visual ranking of specular gloss for 

nonmetallic samples. These standards specify the geometrical and spectral conditions of 

measurement. The incident beam, either collimated or converging, has a spectral flux 

distribution of Commission International de l’Eclairage (CIE) [3] Illuminant C and incident 

angles of 20o, 60o, or 85o. These angles are referred to as the standard geometries. The reflected 

beam is measured with a detector having the CIE luminous efficiency function Vλ. [3] Figure 1 

shows a graphical representation of CIE illuminant C and the luminous efficiency function. The 

angular dimensions of the apertures for the source and detector are also specified for each 

incident angle. 

 For practical reasons, the specular gloss of a sample is measured relative to that of a primary 

standard, whose specular gloss is in turn determined relative to that of the theoretical standard 

[4]. This theoretical standard is specified to be a highly polished plane black glass with an index 

of refraction at the wavelength of the sodium D line, 589.3 nm, of nD = 1.567. The specular 

reflectance of unpolarized light for this index of refraction is calculated using the Fresnel 

equations, and assigned a specular gloss value of 100 for each of the three standard geometries. 

 Since there is no black glass with exactly nD = 1.567, national metrology institutes use 

primary standards to realize their scales of specular gloss. Two such primary standards have 

been in use, Carrara black glass [5] and quartz [6]. A new primary standard for specular gloss 

developed by the National Institute of Standards and Technology (NIST) using barium crown 

glass BaK50 [7] is reported here, which has several advantages over other primary standards. 

This new primary standard and the recently refurbished NIST reference goniophotometer [8] will 

provide accurate specular gloss measurements. The theory of specular gloss standards and 

measurements is presented first, followed by a discussion of other primary standard materials. 

The selection criteria for the new NIST primary standard are described, along with the index of 

refraction, specular gloss, and luminous reflectance properties of the standard. Finally, the new 

primary standard is compared to other standards. 

II. Theory 

 Determining the specular gloss of a test sample involves measuring the luminous reflectance 

of the sample and a primary standard and determining the specular gloss value of the primary 

standard relative to that of the theoretical standard. The equations describing these 

measurements are presented in this section. 

 For unpolarized light, the specular reflectance ρ from the surface of a dielectric sample 

depends on the incident angle θ relative to the normal of the sample and the wavelength λ. The 

specular reflectance as a function of these variables is given by the Fresnel equations, namely 





 





+ ′

− ′ +

+ ′

− ′ = tan ( )tan ( )

sin ( )

sin ( )

2

1 ( , ) 2

2

2

2

θ θ

θ θ

θ θ

θ θ

ρ θ λ , (1) 

where θ ́ is the angle of refraction given by 
3

θ ′ = arcsin( ) sin(θ )/ n(λ) . (2) 

 In general, the luminous flux Φv is given by 

∫ Φv = K m ⋅ S(λ)⋅Vλ (λ)⋅ dλ , (3) 

where Km = 683 lm/W is the maximum spectral luminous efficacy for photopic vision, S(λ) is the 

spectral flux distribution, and Vλ(λ) is the spectral luminous efficiency function. The luminous 

flux incident on a sample Φi is given by Eq. (3), while the luminous flux reflected by a sample 

Φr is given by 

∫ Φr = K m ⋅ S(λ)⋅ ρ(θ ,λ)⋅Vλ (λ)⋅ dλ . (4) 

Therefore, the luminous reflectance ρv(θ) of a sample is given by the ratio of Eq. (4) to Eq. (3), 

∫

∫ ⋅ ⋅

⋅ ⋅ ⋅ = λ λ λλ ρ θ λ λ λ

ρ θ

λ

λ

( ) ( ) d

( ) ( , ) ( ) d

( ) v

S V

S V

 . (5) 

 The specular gloss of a sample under test, Gt(θ), is given by 

( )

( ) ( ) ( )

v,s

v,t

t s ρ θ

ρ θ

G θ = G θ ⋅ , (6) 

where Gs(θ) is the specular gloss of the primary standard and ρv,t(θ) and ρv,s(θ) are the specular 

luminous reflectances of the test sample and primary standard, respectively. Furthermore, the 

specular gloss of the primary standard is given by 

( , )

( , ) ( ) ( )

0 D

s D

s 0

ρ θ λ

ρ θ λ G θ = G θ ⋅ , (7) 

where G0(θ) is the specular gloss of the theoretical standard and ρs(θ, λD) and ρ0(θ, λD) are the 

specular reflectances of the primary and theoretical standards, respectively, at wavelength 

λD=589.3 nm. Combining Eqs. (6) and (7), the specular gloss of the sample under test is given 

by 

( , )

( , )

( )

( ) ( ) ( )

0 D

s D

v,s

v,t

t 0

ρ θ λ

ρ θ λ

ρ θ

ρ θ

G θ = G θ ⋅ ⋅ . (8) 

 From the documentary standards, the index of refraction of the theoretical standard at 

wavelength λD is n(λD) = 1.567, from which the specular reflectance ρ0(θ, λD) is calculated using 

Eqs. (1) and (2). These specular reflectances are listed in Table 1 for the angles of incidence 

specified in the documentary standards. For each angle of incidence, the specular gloss of the 

theoretical standard is defined as G0(θ) = 100. Thus, for example, a specular reflectance ρ0(60°, 

λD) = 0.100056 corresponds to a specular gloss value of 100. Similarly, the specular reflectance 

of the primary standard ρs(θ, λD) is determined from its n(λD) using Eqs. (1) and (2). These 

values for the new primary standard are presented in Section IV. B. 

 At this point, three of the five quantities on the right-hand-side of Eq. (8) are known. The 

other two quantities are the luminous reflectances of the primary standard and test sample, which 

are generally not measured separately. Rather, the ratio of these reflectances is measured, given 

by the ratio of the luminous fluxes reflected from the test sample and primary standard, Φr,t and 

Φr,s, respectively. Therefore, 

∫ ⋅ ⋅ ⋅

∫ ⋅ ⋅ ⋅ = Φ

Φ = λ ρ θ λ λ λ

λ ρ θ λ λ λ

θ

θ

ρ θ

ρ θ

λ

λ

( ) ( , ) ( ) d

( ) ( , ) ( ) d

( )

( )

( )

( )

s

t

r,s

r,t

v,s

v,t

S V

S V . (9) 

Using the definition for G0(θ) and Eq. (9), Eq. (8) becomes 
4

( , )

( , )

( )

( ) ( ) 100

0 D

s D

r,s

r,t

t ρ θ λ

ρ θ λ

θ

θ

θ ⋅ Φ

Φ

G = ⋅ . (10) 

This equation expresses the gloss value of the test sample as a function of the measured reflected 

luminous fluxes for the test sample and primary standard and the specular reflectances of the 

primary and theoretical standards. 

From the discussion above, the specular gloss value of the primary standard is determined 

using monochromatic radiant flux, from Eqs. (1), (2), and (7), while the luminous flux reflected 

from the primary standard is used to calibrate the specular gloss of the test sample, from Eq. 

(10). This ambiguity produces differences in practical gloss measurements of up to 0.5 % since 

this recommendation ignores the dispersion characteristic of the material represented by changes 

in refractive index as a function of wavelength. It has been suggested in Ref [9] that this 

ambiguity be removed by defining the specular gloss of the primary standard from its luminous 

reflectance, given by Eq. (5). There are two methods for determining the luminous reflectance of 

the primary standard, one from measurements of the index of refraction over the wavelength 

range of visible light, the other from direct measurements of this reflectance. Results from both 

methods are presented below. 

III. Other Primary Standards 

 The primary specular gloss standard previously used at NIST was a commercial Carrara black 

glass with nD = 1.527 [5]. A recent evaluation of this type of glass and its constituents was 

performed, and no match to any commercially available optical glass could be determined. The 

National Research Council (NRC) of Canada investigated the stability of highly polished black 

glasses used as specular gloss standards [10]. They found that surface chemical contamination 

of these standards results in variations of 0.3 % to 0.5 % in the index of refraction over a time 

period of three to four years. These variations correspond to changes of about 2 % and 1 % in 

the specular gloss values for the 20° and 60° standard geometries, respectively. Repolishing the 

surface with cerium oxide recovered the original specular gloss values of these standards. They 

also investigated the uniformity of the index of refraction, which varied across the surface by 

approximately 0.5 %, and concluded that these variations were a result of inhomogeneities in the 

glass. 

In general, there are a number of disadvantages to using black glass as a primary specular 

gloss standard, primarily inhomogeneity and aging of the glass, as well as easy damage to the 

front surface, requiring frequent repolishing and recalibration. The ISO 2813 suggests an 

alternative to black glass – a clear glass with roughened edges and back surface, with the back 

surface painted black to absorb any transmitted light. A difficulty with such a primary standard 

is finding a black paint that provides a good match to the index of refraction of the clear glass. 

Otherwise, some scattered light from the back surface will enter the detector and cause an error 

in the measured flux. An alternative to the black paint is to cut the clear glass at an angle so that 

back reflections are not incident on the detector, but this option is not feasible for small, portable 

instruments commonly used in industry. In 1980, NRC developed wedged quartz samples as 

their primary standards. Quartz was selected because of its high optical quality, stability, and 

durability. However, it does not have the same dispersion characteristics as the crown black 

glass standards used previously at NIST and commonly in industry. 

IV. New Primary Standard 

 A. Description 

 The disadvantages of the previous primary standards for specular gloss described above 

motivated a search for a new primary standard. A good standard should be smooth, stable, 
5

cleanable, durable, uniform, and homogeneous with known optical properties. The selection 

criteria for the new primary standard were threefold. First, the standard would be a 

commercially available, high-purity optical glass with high chemical and mechanical durability. 

Second, the index of refraction nD should be as close to 1.567 as possible to conform to the 

documentary standards. Third, the material should be homogenous and have dispersion 

characteristics similar to black glass. 

An optical quality barium crown glass BaK50 was selected as the new NIST primary 

standard since it possesses high chemical and mechanical durability and nD = 1.5677. In 

addition, this glass has a better homogeneity of the index of refraction than does black glass. 

The manufacturer’s specifications are as follows: no bubbles, index of refraction homogeneity 

within 5 x 10-6 over an area of 70 mm2

. Three pieces of BaK50 with dimensions of 98 mm by 98 

mm by 20 mm were purchased, and the NIST optical shop fabricated these pieces into samples 

with a 6° wedge at the back surface. This angle is sufficient to reflect the light incident on the 

back surface out of the field of view of the detector for all of the standard geometries, as shown 

in Figure 2. The front and back surfaces were polished to a roughness of 0.6 nm to 1.0 nm and 

the edges were roughened. A black felt material was placed at the back and edges of the samples 

to eliminate reflections from the surrounding black anodized holder. 

B. Properties 

1. Index of Refraction 

According to the documentary standards, primary standards for specular gloss are calibrated 

from measurements of the index of refraction. The index of refraction of BaK50 was measured 

on a prism-shaped sample prepared from the same melt as the wedge samples. The minimum 

deviation technique [11] was used to determine the index of refraction at five different 

wavelengths with a standard uncertainty of 4 x 10-5. The index of refraction as a function of 

wavelength is given in Table 2. The data was inter/extrapolated using a cubic spline to give the 

dispersion curve for wavelengths from 380 nm to 780 nm at 10 nm interval shown in Figure 3. 

2. Specular Reflectance 

Specular gloss values for the primary standard were determined from the index of 

refraction nD, as specified in the documentary standards. From Table 2, nD = 1.5677 at 

wavelength λ= 589.3 nm, and using Eq. (1) the specular reflectance for each standard geometry 

was calculated. These reflectances and their corresponding gloss values, from Eq. (7) and Table 

1, are listed in Table 3. 

3. Luminous Reflectance 

The discussion at the end of Section II suggested that the specular gloss value of the 

primary standard be defined from its luminous reflectance, and noted that there are two methods 

for determining this reflectance. The first calculates the luminous reflectance from the index of 

refraction as a function of wavelength, while the second measures the luminous reflectance 

directly. The luminous reflectances and specular gloss values from these different methods are 

listed in Table 4, with the details of the calculations and measurements given below. 

For the first method, the index of refraction as a function of wavelength, from Table 2 

and Fig. 3, is used in Eqs. (1) and (2) to calculate ρs(θ, λ) for each of the standard geometries 

from 380 nm to 780 nm every 10 nm. The luminous reflectance ρv,s(θ) is calculated from Eq. (5) 

using ρs(θ, λ), CIE Illuminant C for S(λ), and the CIE 1931 2° Observer for Vλ(λ). Finally, the 

specular gloss value Gs(θ) for the primary standard is given by Eq. (7) but with ρv,s(θ) in place of 

ρs(θ, λD). The relative expanded uncertainty (k=2) for the luminous reflectance is <0.002 %. 

 The second method measures luminous reflectance by an absolute technique using the NIST 

reference goniophotometer [8]. For a fixed specular geometry, the following steps are followed 

for absolute luminous reflectance measurements. The sample is manually removed from the path 
6

of the incident beam, the detector is rotated into the beam path, and the net incident signal is 

measured. The sample is then placed into the beam path, the sample table and detector arm are 

rotated to the desired geometry, and the net reflected signal is measured. The net incident signal 

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

luminous reflectance is calculated from the ratio of the net reflected signal to the net incident 

signal. From the measured luminous reflectance of the primary standard, the specular gloss 

value was calculated as described in the previous paragraph and these quantities are listed in 

Table 4. The listed values represent the average values for two NIST BaK50 samples. The third 

sample requires additional polishing. The 85° geometry was not measured due to limitations in 

the source aperture and the signal to noise level. The relative expanded uncertainty (k=2) for the 

luminous reflectance of BaK50 at the specular geometries of 20o and 60o is 0.22 %. The random 

effects, which include the source stability and detector noise, result in a relative expanded 

uncertainty (k=2) of 0.1 % for both geometries. The systematic effects, which include the DVM 

accuracy, amplifier gain, detector linearity, source polarization, angular scale and spectral 

product, result in a relative expanded uncertainty (k=2) of 0.2 % for both geometries. 

 Several important conclusions can be drawn from the results presented in Tables 3 and 4. The 

specular gloss value of this standard is nearly 100 for all three standard geometries, as shown in 

Table 3, a consequence of nD of the new primary standard being close to the theoretical value of 

1.567. Comparing Tables 3 and 4, the specular gloss values calculated from the luminous 

reflectance are greater than those calculated using only nD for the 20° and 60° standard 

geometries, and are approximately equal for the 85° standard geometry. Finally, the luminous 

reflectances and corresponding specular gloss values obtained from each of the two methods, 

from Table 4, agree well with each other, the maximum difference in Gs(θ) being only 0.2. The 

uncertainty analysis shows that the calculated gloss value following the two different procedures 

agree within the uncertainties. 

V. Comparisons of Specular Gloss Standards 

The dispersion characteristics of BaK50 were compared to those of black glass and quartz 

gloss standards. Three different types of highly polished black glasses were investigated - the 

gloss standard previously used at NIST and two currently used in industry. Neither black glass or 

quartz are a good match for nD = 1.567. The refractive indexes for the black glass samples were 

measured using an Abbe refractometer at three different wavelengths and fit with a cubic spline 

function to give the dispersion curves, from 380 nm to 780 nm at 10 nm intervals, shown in Fig. 

4. The uncertainty of these measurements is 0.0005. The refractive indexes for quartz listed in 

Ref. [12] was inter/extrapolated using a cubic spline to give the dispersion curve for wavelengths 

from 380 nm to 780 nm at 10 nm interval shown in Figure 4. 

The normalized dispersion curves of BaK50, black glass, and quartz standards are shown in 

Figure 5. The index of refraction is normalized at a wavelength of 560 nm and plotted as a 

function of wavelength. The average of the dispersion curves for the black glass samples is 

plotted. The relative dispersion characteristic of BaK50 closely resembles that of the black glass 

samples studied in this paper, while quartz has a different characteristic. The international and 

national standards define the specular gloss value for the theoretical and working standards based 

upon a single refractive index, nD, but the instruments are specified for polychromatic radiation 

and broad spectral range detectors. This ambiguity leads to a situation where the gloss value of 

the sample under test depends on the dispersive characteristics of the secondary-working 

standard, such as black glass. This is particularly important for instruments whose spectral 

characteristics are in poor agreement with those specified by the documentary standards. Ideally, 

the calibration of a test sample should not be affected by the properties of the working standard. 
7

VI. Conclusions 

The new NIST primary standard for specular gloss has three important advantages over 

other materials used as primary standards. First, BaK50 is a commercially available high-purity 

glass with good homogeneity. Second, since nD of BaK50 is close to the value of 1.567 specified 

for the theoretical standard, the specular gloss values for this glass differ from 100 by less than 

0.2 for all three standard geometries. Third, the relative dispersion of BaK50 is similar to that of 

black glass, which is important for calibrating samples with instruments whose spectral 

characteristics are not in good agreement with those specified by the documentary standards. 

This new standard and the NIST reference goniophotometer provide a facility for specular gloss 

measurements of the best possible accuracy. 

Acknowledgments 

The authors wish to express special thanks to Edward Early for many useful discussions and the 

collaboration with the National Institute of Standards and Technology researchers who are 

working on the measurement science for optical reflectance and scattering project.
8

References 

[1] International Standard ISO 2813, “Paint and Varnishes-Measurements of Specular Gloss 

of Nonmetallic Paint Films at 20°, 60°, and 85°” (International Organization for 

Standardization 1978). 

[2] “Standard Test Method for Specular Gloss, ASTM D532,” American Society for Testing 

and Materials, West Conshohocken, PA (1995). 

[3] Commission International de l’Eclairage: International Lighting Vocabulary, CIE Publ. 

No. 15.2 (1987). 

[4] R. S. Hunter and R. W. Harold, The Measurement of Appearance, 2nd Ed., John Wiley & 

Sons, New York, N. Y. (1987). 

[5] J. J. Hsia, “The NBS 20-, 60-, and 85- Degree Specular Gloss Scales,” NIST Tech. Note 

594-10 (1975). 

[6] J. Zwinkels and M. Nöel, “Specular Gloss Measurement Services at the National 

Research Council of Canada,” Surface Coatings International 12, 512 (1995). 

[7] Certain commercial equipment, instruments or materials are identified in this paper to 

specify adequately the experimental procedure. Such identification does not imply 

recommendation or endorsement by the National Institute of Standards and Technology, 

nor does it imply that the materials or equipment identified are necessarily the best 

available for the purpose. 

[8] M. Nadal and A. Thompson, “NIST Reference Goniophotometer for Geometrical 

Appearance Measurements,” submitted to the Journal of Coatings Technology. 

[9] B. Wolfang and C.X. Dodd, “Stability Problems in Gloss Measurements,” Journal of 

Coating Tech. 552, 44-48, (1980). 

[10] W. Budde, “The Calibration of Gloss Reference Standards,” Metrologia 16, 89–93 

(1980). 

[11] G. E. Fishter, “Refractometry,” in the Applied Optics and Optical Engineering, Vol. IV, 

edited by R. Kingslake (Academic Press, New York, 1967), p. 363-382. 

[12] I. H. Malitson, “Interspecimen Comparison of the Refractive Index of Fused Silica,” 

Journal of the Optical Society of America 55, 1205-1209 (1965). 
9

List of Tables 

Table 1 Specular reflectance ρ0(θ, λD) of the theoretical gloss standard for each standard 

geometry 

Table 2 Index of refraction n of BaK50 glass as a function of wavelength 

Table 3 Calculated specular reflectance ρs(θ, λD) and specular gloss value Gs(θ) of the 

new primary standard at λD = 589.3 nm for each standard geometry 

Table 4 Average luminous reflectance ρv,s(θ) and specular gloss value Gs(θ) for the New 

Primary Standard for each standard geometry and method of calculation or 

measurement. 
10

Table 1 

Standard Geometry ρ0(θ, λD) 

20° 0.049078 

60° 0.100056 

85° 0.619148 

Table 2 

Wavelength [nm] n 

435.8 1.5800 

480.0 1.5753 

546.1 1.5702 

589.3 1.5677 

643.9 1.5654 

Table 3 

Standard Geometry ρs(θ, λD) Gs(θ) 

20° 0.049172 100.19 

60° 0.100167 100.11 

85° 0.619204 100.01 

Table 4 

 Standard Geometry 

 20° 60° 85° 

Method ρv,s(θ) Gs(θ) ρv,s(θ) Gs(θ) ρv,s(θ) Gs(θ) 

Index of 

refraction 

0.049464 100.8 0.100510 100.5 0.619375 100.0 

Luminous 

reflectance 

0.049587 101.0 0.100743 100.7 
11

List of Figures 

Figure 1 Graphical representation of the spectral power distribution of the CIE Illuminant 

C and the luminous efficiency function. 

Figure 4.1 Schematic diagram of the new NIST primary standard showing the incoming and 

reflected beam at 60° specular geometry. The wedge deflects the reflection from 

the back surface away from the detector. 

Figure 3 Fitted refractive index, n(λ), for new primary standard as a function of 

wavelength 

Figure 4 Fitted refractive index, n(λ), for Carrara black glass, quartz, and black glass 

working standards as a function of wavelength. 

Figure 5 Normalized index of refraction as a function of wavelength for the samples 

indicated in the legend. 
12

Figure 1 

Figure 2 

BaK50 Wedge

Reflection from back surfac

Source Detector

0

20

40

60

80

100

120

140

300 400 500 600 700 800

Wavelength [nm]

Spectral power 

distribution Illuminant C

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Luminous efficiency 

function
13

Figure 3 

Figure 4 

1.550

1.560

1.570

1.580

1.590

1.600

300 400 500 600 700 800

Wavelength [nm]

Refractive Index

1.40

1.42

1.44

1.46

1.48

1.50

1.52

1.54

1.56

1.58

1.60

300 400 500 600 700 800

Wavelength [nm]

Refractive Index

Average Black Glass NIST Old Standard BaK50 Quartz
14

Figure 5 

0.990

0.995

1.000

1.005

1.010

1.015

300 400 500 600 700 800

Wavelength [nm]

Normalized Refractive Inde

x

BaK50 Average of blk glass Quartz