Let’s take a look at a simple example using real BSDF data measured by the IS-SA instrument at Radiant Imaging. The data are for an automotive dashboard vinyl material named Brown Vinyl. The BSDF data for this material are provided in the ASCII file BrownVinyl.BSDF, which is provided with the ZEMAX installation (located in the directory \ZEMAX\Objects\DLL\SurfaceScatter\). This file contains monochromatic BSDF data, and data are defined for 13 incident angles, 19 azimuthal angles, and 11 radial angles:

#Data Generated by Radiant Imaging's 'Imaging Sphere'
#3/11/2008 9:37:42 AM
Source  Measured
Symmetry  PlaneSymmetrical
SpectralContent  Monochrome
ScatterType  BRDF
SampleRotation  1
0
AngleOfIncidence  13
15    20    25    30    35    40    45    50    ...
ScatterAzimuth 19
0    10    20    30    40    50    60    70    ... 
ScatterRadial 11
0    5    10    15    20    30    40    50    ....

We use this data to define the scattering distribution on a Rectangle object in non-sequential mode:



Since the data are monochromatic, the Tristimulus parameter is set to 0. We also specify that 100% of the input ray energy goes into scattering (Scatter Fraction = 1) – so there will be no specular output ray – and that each input ray is split into 5 scattered rays (Number of Rays = 5).

A Source Ray object is then used to launch rays towards the Rectangle at an angle of incidence of 30 degrees, and a Detector Rectangle object is placed in front the Rectangle to view emission that results from scattering in reflection:



The Detector Rectangle object is rotated 180 degrees with respect to the Rectangle object, and the “Front Only” flag is set to 1, so that only the reflected rays are recorded by the detector. This simple setup is provided in a lens design file (Tabular BSDF scattering surface.zmx) which is provided with the ZEMAX installation (located in the directory \ZEMAX\Samples\Non-sequential\Scattering\).

When 1 million analysis rays are launched from the source, the incoherent irradiance distribution on the detector is observed to be:



and the Radiant Intensity distribution is:



Artifacts in the radiant intensity distribution can be seen near the edges of the plot, i.e. the “staircase” structure near the bottom of the plot. This structure arises from the coarseness of the input data, which are provided with a resolution of 10 degrees in the azimuthal direction and over most of the radial direction. To eliminate these artifacts, the angular resolution of the input data needs to be increased. Nonetheless, the results indicate that the resolution is sufficient over most of the field-of-view. Since the BSDF file format allows for non-uniform spacing of data in angle space, it would be sufficient to increase the resolution of the data only in the region where the artifacts appear. This keeps the file size compact while providing a high level of accuracy to the ray trace results.