## Abstract

The gloss of a sample is determined as the ratio of the specular reflectance of the sample to that of a black-glass reference standard for angles of incidence of 20°, 60°, or 85°. The angle of 60° is close to the Brewster angle of the black glass, and it must be expected that the natural polarization of the incident radiation in the gloss meter affects the gloss measurements. Calculations for unpolarized and for partially polarized incident radiation show that in general the gloss value of the black glass changes drastically with increasing degree of polarization but that the gloss value of a sample, determined from the ratio mentioned above, is affected very little, particularly if the refractive index of the sample is close to that of the reference.

© 1979 Optical Society of America

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### Equations (23)

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(1)
$${G}_{s}={G}_{r}\times {\rho}_{s}/{\rho}_{r},$$
(2)
$${G}_{s}(m)={G}_{r}(u)\times {\rho}_{s}(m)/{\rho}_{r}(m),$$
(3)
$$\rho (u)=({\rho}_{p}+{\rho}_{s})/2,$$
(4)
$${\rho}_{p}=\left[\frac{{n}^{2}\hspace{0.17em}\text{cos}\alpha -{({n}^{2}-{\text{sin}}^{2}\alpha )}^{1/2}}{{n}^{2}\hspace{0.17em}\text{cos}\alpha +{({n}^{2}-{\text{sin}}^{2}\alpha )}^{1/2}}\right],$$
(5)
$${\rho}_{s}={\left[\frac{{({n}^{2}-{\text{sin}}^{2}\alpha )}^{1/2}-\text{cos}\alpha}{{({n}^{2}-{\text{sin}}^{2}\alpha )}^{1/2}+\text{cos}\alpha}\right]}^{2},$$
(6)
$$\rho (l)={\rho}_{p}\hspace{0.17em}{\text{cos}}^{2}\beta +{\rho}_{s}\hspace{0.17em}{\text{sin}}^{2}\beta .$$
(7)
$${\varphi}_{0}={\varphi}_{l}+{\varphi}_{u},$$
(8)
$${\varphi}_{l}=k{\varphi}_{0}\hspace{0.17em}\text{and}\hspace{0.17em}{\varphi}_{u}=(1-k){\varphi}_{0},$$
(9)
$$\rho (m)=k\rho (l)+(1-k)\rho (u),$$
(10)
$$P=({I}_{\text{max}}-{I}_{\text{min}})/({I}_{\text{max}}+{I}_{\text{min}}),$$
(11)
$${I}_{\text{max}}=c({\varphi}_{l}+{\varphi}_{u}),$$
(12)
$${I}_{\text{min}}=c{\varphi}_{u},$$
(15)
$${G}_{s}(u)={G}_{r}(u)\xb7{\rho}_{s}(u)/{\rho}_{r}(u),$$
(16)
$${G}_{r}(u)=100\xb7{\rho}_{r}(\alpha ,{n}_{r})/{\rho}_{0}(\alpha ,{n}_{0}),$$
(17)
$${G}_{r}(u)=F(\alpha ){\rho}_{r}(\alpha ,{n}_{r})$$
(18)
$${G}_{s}(u)=F(\alpha ){\rho}_{s}(\alpha ,{n}_{s})$$
(19)
$${G}_{r}(m)=100{\rho}_{r}(m,\alpha ,{n}_{r})/{\rho}_{0}(u,\alpha ,{n}_{0}).$$
(20)
$${G}_{s}(m)={G}_{r}(m){\rho}_{s}(m)/{\rho}_{r}(m),$$
(21)
$${G}_{s}(m)=100{\rho}_{s}(m)/{\rho}_{0}(u,{n}_{0})=F(\alpha ){\rho}_{s}(m).$$
(22)
$${G}_{s}(m)={G}_{r}(u){\rho}_{s}(m)/{\rho}_{s}(u).$$
(23)
$$E=\frac{{G}_{s}(m)}{{G}_{s}(u)}=\frac{{\rho}_{s}(m)}{{\rho}_{s}(u)}\times \frac{{\rho}_{r}(u)}{{\rho}_{r}(m)}.$$