# Light scattering vs roughness

I've been searching for an answer to this question in professional circles for a while; now I'd like to ask here, to find out why the answer is not there :)

In my optical modelling (computer simulation), I would like to take scattering on rough surfaces into account. Professional software (like Zemax) can do it, provided that I know the scattering model (e.g. in terms of Gaussian scattering). However I cannot find the model parameters anywhere. It is possible to derive the model parameters if one knows the BSDF of the surface, which in turn can be measured. But I cannot find any standard values, like for example scattering by aluminium surface with a roughness of Rz=5. Photopia seems to include the measured values for some surfaces, but the range is very limited, and it's the only such database I could find. Others, such as Disney's BRDF Explorer, seem to be less accurate and are probably not applicable for design optimization. At the same time, refractive indices of dozens of glasses are readily available.

Specialists gave me reasons why such information cannot be provided: one has to assume ergodicity of the manufacturing processes, which is not necessarily there. Then I wonder: from the general point of view, does an aluminium surface with a defined roughness really look very different depending on who made it?

Any comments or additional data on the topic would be highly appreciated. I was actually asked to suggest an optimal shape of some element for an experiment, and it turns out it should be scattering. However, while I can optimize scattering in simulation, I will not be able to convert it to roughness, i.e. tell the guys: "sand-blast it to Rz=x". This is what I am missing, and I cannot understand why the situation is as it is.

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"from the general point of view, does an aluminium surface with a defined roughness really look very different depending on who made it? " I know from experience that well defined grades of stainless steel can have varying optical properties depending on their manufacture and finishing (meaning how they were treated while making them "clean" for low background experiments, not stuff painted on). No references or ability to quantify it. –  dmckee Jun 5 '13 at 15:49

Surface roughness is dependant on the mode of manufacturing. A finish by sandblasting or rolled aluminium sheets differs in

• surface roughness
• homogenity (long or short periodic defects)
• isotropy (production in one line)
• abrasion of finishing tool

Regarding the latter the production stability and repeatability of different batches should be kept in mind when using in an optical device.

from the general point of view, does an aluminium surface with a defined roughness really look very different depending on who made it?

Yes, abrasion of your surface finishing tool and chemical components may alter your surface. A mechanical engineer in my company stated that there also may be different surface patterns, due to the fact, that most non-optical surface finishes are made by a turning head of different size. The ultimate accuracy will be archived by a nickel clad steel block, which is finished by a fresh ultra precission diamond turning head: Diamond turning. This is the process of manufacturing the injection molding tool for modern optics.

There is a german industry norm connecting manufacturing processes to surface roughness. The finest known uses Ultra-fine, abrasive polishing paste. So far for the experimental/industry part.

Depicted is the surface roughness average $R_a$, which is mostly used. It is averaged over measurements from the center line of the surface. A completely regular roughness with a single frequency as depicted does not exist in real world.

But I cannot find any standard values, like for example scattering by aluminium surface with a roughness of $R_z=5\mu m$.

As you mentioned there are models based on Gaussian or Monte-carlo models. However reality differs. Therefore I recommend using measured BSDF data or a worst case approximation by a lambertian scatterer. I also didn't find fit parameters for these models. I suspect because of the former mentioned differences and it's angle dependance. In a question about roughness of glass I linked measurement data of rough glas.

For theory there are typical values depending on surface roughess $R_a$. However this aluMatter does not name qualified industry partners. Therefore excessive tests in a BSDF measurement lab have to be performed to get the data bases of your simulation.

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The simulation you linked to is a nice illustration. However it is unclear where they get the results from. It would be nice to see the code producing those curves. –  texnic May 2 '14 at 11:39
I agree. However I don't have deeper knowledge on that. –  Stefan Bischof May 2 '14 at 23:32
@texnic Paramters of rough glas can be found in table 1 of the second publication - see link to the question about roughness of glas. –  Stefan Bischof May 4 '14 at 10:54