Question

Diffuser with Gaussian scattering model

  • 10 November 2023
  • 3 replies
  • 107 views
J
Userlevel 2

I have implemented a simple system composed of:

  1. Diode Source with 2deg divergence in x and y;
  2. Diffuser implemnted with cylinder volume with a single scaterring surface following a gaussian model with sigma = 0.27
  3. Polar detector to monitor the angular distribution of energy after the diffuser in the range -90, +90 deg;

 

After exporting the detector data using the ”Detector Viewer", I have fitted the data points with the gaussian model described in the Help documentation: BSDF = A*exp(-x**2 / sigma ** 2):

The value of the fitted sigma (sigma_i = 23.194) has nothing to do with the specified sigma of the diffuser (sigma = 0.27), which tells me that my interpretation of the scattering model is wrong. Where does the discrepancy come from? 

3 replies

R
Userlevel 4
Badge

Hi Jonasz,

Unfortunately, the documentation for the Gaussian scattering model is deficient (to say the least), and none of the online articles I have seen help. Hopefully someone from Zemax see this thread and update the documentation (if my explanation below is correct, that could be just a matter of adding 1 or 2 sentences).

Most diffusers communicate their scattering angle in degree (sometimes FWHM, sometimes 1/e, ...), however Zemax’ Gaussian scattering model is not a Gaussian distribution in angle (unlike LightTools for example). The scattering formula is applied in cosine directors space (that is closer to the physics). As a result, the scattered cone becomes elliptic when the incidence is not normal. However, the value at normal incidence is the one you want to use for the definition.

So the sigma in Zemax is most likely following the sine of the angle, which for 0.27° would be 0.0047 (sigma is dimensionless according to the documentation, so that looks consistent. There may be some factor 2 or sqrt(2) to account for.

Of course, that is contradictory with the documented value of 5 for Lambertian (a sine of 5 is not really defined for an angle). A long time ago, I ended up computing tabulating values from 0 to 5 and their resulting sigma in ° in Excel and interpolating the value. The sine formula matched this tabulated way within 1% up to 10°, 5% to 25°, 10% to 40°.

 

J
Userlevel 2

Dear Ray,

Indeed, the manual entries on scatering models is lacking.

I´ve tried to fit the formula using the cosine directors but still did not manage to find an agreement between the nomimal sigma and the fitted sigma. In the end I followed the black box approach, similar to the your tabulated data approach.

Kind regards,

 

R
Userlevel 4
Badge

Hi Jonasz,

Did you get a value close to 0.0047 to work for your 0.27° ?

Best regards,

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