As all know surface roughness is one of the way to reduce light refection. But is there any mathematical relation between from where I can justify my results.
Not even roughness but uniformity in structures is also a major concern to decrease surface reflectance. I experienced these facts but lacking with the correct reference.
I have heard this question many times. I would be interested if there is a clear mathematical relation between surface roughness and reflectance.
For some companies we have done test and sometimes we found that the Rdq or Sdq (average slope of roughness) as a correlation to reflectance.
for definition of Sdq take a look into ISO 25178-2
Dear Franz Helmli, thank you so much for your response. It was very helpful for me.
dear Igael Azoulay,
you can go through this ISO 25178-2 for some information .
Lambertian reflectance is proportional to albedo, which is a function of surface roughness. There are many microstructural theories of reflectance that you can research.
There are several effects:
1. the (complex) refractive index of the material; a flat gold surface reflects different than a flat silver surface or a flat glass surface.
2. roughness on a subwavelenth scale may act as an anti-reflection coating to a surface, the reflectance will still be specular
3. roughness on a larger scale, typically where roughness parameters are measured, may cause diffuse reflectance. If the diffuse component is rather small, there are equations that relate the diffuse fraction to the Rq parameter.
4. for a larger or dominant diffuse component the situation is most complex. The Sdq parameter, as Helmli mentioned, is a logic correlating parameter as it indicates the squared averaged angle, so a higher Sdq might indicate a more diffuse reflecting specimen. However this also depends on the lateral roughness scale.
You raise some interesting points with your question. First and foremost must be the nature of the material in question. The obtain a viable answer it may be necessary to apply comparative constraints to establish a nominal form condition. there by isolating and constraining as many form and condition factors as possible.
I would suggest a 25mm x 25mm flat square sample with a defined thickness and flatness spec. This then leeds to the focus on Surface Texture vs Reflectivity (with a defined light source/type).
Dear Arti,
Reflectance and roughness are both connected by local areal surface gradients according to the scheme:
Reflectance -> Surface gradients -> Surface roughness (texture)
An integration stage is required to convert local surface gradients to local surface roughness. Local surface gradients and local surface normals are straightfully related. For theoretical details, follow:
- Coleman et al., "Obtaining 3-Dimensional Shape of Textured and Specular Surfaces Using Four-Source Photometry", 1982 - http://booksc.org/book/2603832/52a830
In addition, as a concrete case study, check out:
- Janko et al., " Colour Dynamic Photometric Stereo for Textured Surfaces ", 2010 - https://hal.inria.fr/inria-00525869/document
- Hernandez et al., " Non-rigid Photometric Stereo with Colored Lights ", 2007 - http://mi.eng.cam.ac.uk/~cipolla/publications/inproceedings/2007-ICCV-colour-photometric-video.pdf
Regards
Dear Arti
I may help through surface emittance, since for opaque samples: Reflectivity = 1- Emissivity (at the same wavelength).
The length scale also plays a major role in definding both the roughness itself and the roughness to optical wavelength ratio.
in case the ratio Rq/lambda
Yes Rdq will always correlate with optical scattering. The math for understanding the correlation require Fourier space analysis.
Take a look at very good introduction to the topic
SPIE PRESS BOOK
Optical Scattering: Measurement and Analysis, Third Edition uthor(s): John C. Stover
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