Point Spread Function of Specular Reflection and Gonio-Reflectance Distribution

Abstract

In this article, the specular reflection phenomenon is analyzed by the concept of the point spread function (PSF). The conventional PSF, which is a sharpness criterion, is used for the transfer function in image science. In general, print (an ink image on paper) is observed as diffuse reflection light, and the light source image, i.e., gloss, is observed as specular reflection. We first introduce the point spread function of specular reflection (SR-PSF). A measurement principle for the SR-PSF is proposed, and a measurement apparatus for the SR-PSF is developed by using a collimator optical system. The experimental results show that the measured SR-PSF works as a transfer function for a specular reflection image. Each detected position is in agreement with the angle of reflected light. The apparatus works as a goniophotometer within a narrow solid angle. The relation between the SR-PSF and the specular reflection angle distribution is discussed in terms of surface geometry. It is concluded that the measured data are the SR-PSF and they have a gonio-reflectance distribution. The reflection angle is caused by the surface normal, and the surface normal distribution can be calculated from the gonio-reflectance distribution by using the mathematical model. We plan to apply our proposed principle to the development of an evaluation technique for the visual gloss. In addition, the high-resolution goniophotometer can be further developed by this measuring technique.