## Abstract

To study the optical properties of materials, one needs a complete
set of the angular distribution functions of surface scattering from
the materials. Here we present a convenient method for collecting a
large set of bidirectional reflectance distribution function (BRDF)
samples in the hemispherical scattering space. Material samples are
wrapped around a right-circular cylinder and irradiated by a parallel
light source, and the scattered radiance is collected by a digital
camera. We tilted the cylinder around its center to collect the
BRDF samples outside the plane of incidence. This method can be
used with materials that have isotropic and anisotropic scattering
properties. We demonstrate this method in a detailed investigation
of shot fabrics. The warps and the fillings of shot fabrics are
dyed different colors so that the fabric appears to change color at
different viewing angles. These color-changing characteristics are
found to be related to the physical and geometrical structure of shot
fabric. Our study reveals that the color-changing property of shot
fabrics is due mainly to an occlusion effect.

© 2000 Optical Society of America

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### Equations (11)

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(1)
$$cos{\mathrm{\theta}}_{i}=cos\mathrm{\alpha}cos\mathrm{\beta}sin\mathrm{\gamma}-\mathrm{sin}\mathrm{\beta}\mathrm{cos}\mathrm{\gamma},$$
(2)
$$cos{\mathrm{\varphi}}_{i}=\frac{cos\mathrm{\alpha}cos\mathrm{\beta}cos\mathrm{\gamma}+sin\mathrm{\beta}sin\mathrm{\gamma}}{sin{\mathrm{\theta}}_{i}},sin{\mathrm{\varphi}}_{i}=\frac{cos\mathrm{\beta}sin\mathrm{\alpha}}{sin{\mathrm{\theta}}_{i}},$$
(3)
$$cos{\mathrm{\theta}}_{r}=\mathrm{cos}\mathrm{\alpha}\mathrm{sin}\mathrm{\gamma},$$
(4)
$$cos{\mathrm{\varphi}}_{r}=\frac{cos\mathrm{\alpha}cos\mathrm{\gamma}}{{\left(1-{cos}^{2}\mathrm{\alpha}{sin}^{2}\mathrm{\gamma}\right)}^{1/2}},sin{\mathrm{\varphi}}_{r}=-\frac{sin\mathrm{\alpha}}{{\left(1-{cos}^{2}\mathrm{\alpha}{sin}^{2}\mathrm{\gamma}\right)}^{1/2}}.$$
(5)
$${v}_{j}=\frac{{\displaystyle \sum _{i=1}^{n}}{v}_{i}\left({d}_{j}/{\mathit{ad}}_{j}+{r}_{i}\right)}{{\displaystyle \sum _{i=1}^{n}}\left({d}_{j}/{\mathit{ad}}_{j}+{r}_{i}\right)},$$
(6)
$$p\left(y,a\right)=\left\{0,y,asiny\right\}.$$
(7)
$$t\left(y,a\right)=\left\{0,\frac{1}{{\left[{\left(1+{a}^{2}{cos}^{2}y\right)}^{2}\right]}^{1/2}},\frac{acosy}{{\left[{\left(1+{a}^{2}{cos}^{2}y\right)}^{2}\right]}^{1/2}}\right\}.$$
(8)
$${e}_{1}=\left\{1,0,0\right\},$$
(9)
$${e}_{2}=\left\{0,-\frac{acosy}{{\left[{\left(1+{a}^{2}{cos}^{2}y\right)}^{2}\right]}^{1/2}},\frac{1}{{\left[{\left(1+{a}^{2}{cos}^{2}y\right)}^{2}\right]}^{1/2}}\right\}.$$
(10)
$$i\left(\mathrm{\theta}\right)=\left\{0,sin\mathrm{\theta},cos\mathrm{\theta}\right\}.$$
(11)
$$r\left(y,a,\mathrm{\theta}\right)=-\left[t\left(y,a\right)i\left(\mathrm{\theta}\right)\right]t\left(y,a\right)+{\left\{1-{\left[t\left(y,a\right)i\left(\mathrm{\theta}\right)\right]}^{2}\right\}}^{1/2}\times \left({e}_{1}cos\mathrm{\varphi}+{e}_{2}sin\mathrm{\varphi}\right),$$