A roughness number does not tell what the shape of your surface structures is, and as a consequence, what the scattering is going to be. It only work in the other direction. You can have totally different surfaces with the same Ra (or Rq, or Sa, or Sq, ...).


See an illustrations on these pages


https://www.comcoinc.com/surface-finish-specs/basic-cmyk-3/


https://www.researchgate.net/publication/310861650_Optical_Characterization_of_Nanostructured_Surfaces/figures?lo=1


https://www.cnccookbook.com/surface-finish-chart-symbols-measure-calculators/


And this is for a 1D example. You may have a circular pattern, a linear pattern, or whatever anisotropic pattern so it is even more disconnected.


In addition, most of the time, people will give a single number while Ra (and friends) are functions of the spatial frequency of the structure (computed after applying 2-3 filters).





What such parameter can be used to is to define an acceptable limit for a given machine & process: You generate many samples and measure their roughness and their scattering, then determine what scattering is acceptable and you can set a limit to the roughness. As long as the same machine is used (e.g. SPDT generating a circular roughness pattern), that criterion is quite fine to set the acceptance.





Of course, if your Ra is 0, the surface is smooth and you have no scattering. That is the only case where you can know the scattering from the roughness: optically polished surfaces. In such cases Rq and Rdq (not Ra) can be useful (There used to be an article on Zemax knowledge base on the topic). But VDI data, from what I can see, is not for polished profiles (at best 100nm Ra).

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Here is an image from one of the links (the original post was considered "too long" with it)





 

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Got it. Thanks for a response!


Suppose that we have a set of samples with different roughness finish. Could you advice what scattering model is better to be used? Does it necessarily requires BSDF data? 





 

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Determining scattering profile from a roughness measurement is a very involved process.  If you are serious about this I would recommend Stover's book (https://spie.org/Publications/Book/975276?SSO=1).





The process is basically:

1. Get a roughness measurement.



2. Determine the surface power spectral density (PSD) from this measurement (not straight forward)



3. From the PSD you get generate the BSDF (not straight forward)



4. The BSDF data can be imported into Zemax.

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My experience is that the only way to get accurate BSDF data on rough surfaces is by optically measuring the BSDF of the surface.  Trying to calculate the BSDF from physical measurements is prone to massive errors.  If you can get within a factor of 2 of the predicted scattering using calculations of the BSDF from physical measurements you should consider that a very good result and don't be surprised if it is a factor of 5 out at large angles.





Andrew

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Thanks everybody very much for sharing the information! 

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Andrew,


Have you had measurements done on smooth surfaces (like 1nm rms)?  I have found what I think are reliable BSDF measurements done on rough surfaces but suspicious results on smooth surfaces, eg integrating the BSDF giving very high TIS.  I have seen "signature" BSDF values of the measurement tool having a bump and seeing this bump in the scatter data. I'm not convinced the scatter from the measurement tool can easily be removed from the measured data if the measured data is from smooth surfaces.





I'd be interested to know your experience on this.





Ian

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