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1、This article illustrates use of the Rayleigh distribution to model bulk scattering.Authored By: Sanjay Gangadhara Published On: May 2, 2008IntroductionThe Rayleigh model describes scattering of light by particles whose size is much smaller than the wavelength of the light. This scatter model is appl
2、icable to many situations, the most common of which is scattering of sun light in the Earths atmosphere.In the Rayleigh model, the distribution of scattered light for an input beam which is unpolarized is given by:p(q,l) = 0.375*(1 + cos2q)/l4wherel is the wavelength and q is the angle of the scatte
3、red ray with respect to the specular ray;q = 0 degrees refers to scattering along the specular ray in the forward direction, andq = 180 refers to scattering along the specular ray in the backward direction. (The coefficient of 0.375 is needed to ensure that the Total Integrated Scatter (TIS = p(q,l)
4、 sinq dq, with the limits of integration from0 to p) is equal to unity.)Modeling Rayleigh scattering in ZemaxThe Rayleigh scattering distribution may be applied to any non-sequential volume object usinga user defined DLL (RAYLEIGH.DLL) that has been provided with the Zemax installation (ZemaxObjects
5、DLLBulkScatter). 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 “
6、Using the Henyey-Greenstein Distribution to Model Bulk Scattering#8221;.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 so
7、urce 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
8、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)4The trans
9、mission 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 volu
10、me 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/Mas described in the chapter of the Zemax manual entitled
11、“Non-Sequential Components”. Thus, the integrated probability of a ray traveling a distance x within the volume and not undergoing scattering is given by1 -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 exa
12、mple, 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.Validating the wavelength dependence of the Rayleigh modelA ray trace may be performed, in which th
13、e results are saved to a ray database file:This file is used to filter the ray data that is obtained from the Detector Viewer. Specifically, we are only interested in those rays which do not undergo bulk scattering. The filter string “!B2” can be used to isolate such rays:The total number of rays wh
14、ich do not undergo scattering and hit the detector is about 36800 (the actual number will vary for any given ray trace):(When the filter is applied, all of the associated rays only strike the center pixel of the detector, which is why emission is not seen elsewhere). According to the equations given
15、 in the previous section, when the length of the volume equals the input mean free path and the source wavelength is the same as the reference wavelength as they are in this case the fraction of unscattered rays is 0.368. In this test 100,000 rays were launched towards the volume, so we would expect 0.368*100,000 = 36800 rays to pass through the volume without undergoing scattering. This is indeed the case!Since the mean-free
