The Rayleigh scattering distribution may be applied to any non-sequential volume object using a user defined DLL (RAYLEIGH.DLL) that has been provided with the ZEMAX installation (\ZEMAX\Objects\DLL\BulkScatter\). Tests have been conducted to investigate both the distribution of power and the angular distribution of the scattering model in ZEMAX, and they confirm that the Rayleigh model has been properly implemented. These tests are identical to those described in the Knowledge Base article “Using the Henyey-Greenstein Distribution to Model Bulk Scattering”.

A test has also been conducted to validate the wavelength dependence of the scattering model. The test file (Rayleigh_WaveTest.ZMX) is provided in the .ZIP file located at the end of this article.

The test design consists of a source launching rays at normal incidence to a rectangular volume in which the Rayleigh scattering model has been applied. Inputs to the DLL are the reference wavelength and the transmission:



The reference wavelength (l₀) is specified in microns; it is the wavelength associated with the input value of scattering mean free path (M), as provided in the “Mean Path” input of the dialog box. Thus, in the example shown above the scattering mean free path is 1.0 mm (M is always specified in lens units) at a wavelength of 0.55 mm. The mean free path varies with wavelength as:

M(l) = M(l₀)*(l/l₀)⁴

The transmission parameter describes how much of the input power is attenuated during scattering.

Rays that pass through the rectangular volume are then recorded on a Detector Rectangle object. For arbitrary values of the mean free path (M) and the length of the volume (L), some rays may pass through the volume without undergoing bulk scattering. The fraction of “unscattered” rays can be determined from the fact that rays which travel a distance x within the volume have an integrated probability of having been scattered given by:

p(x) = 1.0 - e^-x/M

as described in the chapter of the ZEMAX manual entitled “Non-Sequential Components”. Thus, the integrated probability of a ray traveling a distance x within the volume and not undergoing scattering is given by 1 - p(x) = e^-x/M. Setting x = L, we find that the probability of a ray traveling through the full volume and not being scattered is e^-L/M.

In our example, L = 1.0 mm and M = 1.0 mm at a reference wavelength of 0.55 mm, which is also the wavelength of the source rays. For this case, the fraction of unscattered rays is simply e^-1.0/1.0 = e^-1 = 0.368.