Angular Distribution of BSDF

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Abstract:: This little Mathematica-program makes it possible to visualize the distribution of scattering on smooth surfaces as they appear according to the Generalized-Harvey-Shack (GHS) theory (Harvey et al., 2010). For defining the surface properties, the K-correlation model is used, whereas here a 1-D measured power-spectra-density (PSD) function is converted into a 2-D PSD function. As a matter of fact, this program thus needs the input of the 1-D PSD function as a list of parameters (ABC), describing the fitted 1-D PSD curve (Krywonos, PhD thesis, 2000; Harvey et al, 2012). Also combinations of two or more 1-D PSD functions are possible. The here given ABC-combinations are from measurements of the beam splitter used in KAGRA.
In the below given presentations it is assumed that a laser-beam (infinitesimal small) is (for angles of incidence that are not zero) approaching from the left and leave the area to the right. Hence, the illuminated circles and spheres in this presentation represent a hypothetical projection hemisphere where the scattered light is made visible through units of the bidirectional reflection distribution function (BRDF) or the bidirectional transmission distribution function (BTDF). The combination of both (as can be seen in the last section) becomes the bidirectional scattering distribution function (BSDF).

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