Angular distribution of diffusely scattered light

[Daniiel]

Hey,

I recently did a pretty simple experiment to model the angular distribution of diffusely scatter light. I had four different surfaces, two were obviously smooth and two were obviously rough. I use an apparatus shown in the below picture where I used horizontally polarised light.

[PLAIN]http://img97.imageshack.us/img97/6615/aparatus.jpg

The surface was placed in position of the "triangle" (it wasn't actually a triangle the apparatus is actually from a previous section of the experiment where I used a prism) such that the angle of incidence was 70deg. I then rotated a detector around the surface between a range of angles to measure the intensity reflected light. I plotted the detectors angle against the intensity. The graph is below.

[PLAIN]http://img694.imageshack.us/img694/8955/asdzu.jpg

What I found was the two smooth surfaces (S1,S3) gave results that were expected, the peaks were centred when the angle of incidence = angle of reflection (the plateau of each peak is because the detector plate was large). However with the rough surfaces the peaks were not centred at the expected angle, they shifted up by around 4degrees. The only explanation I can think of is that the rough surfaces resemble a disc or a "dirty" diffraction grating.

Does anyone have any ideas why the peaks have shifted? We ran the experiment three times and received the same result with the rough surfaces

 

[Andy Resnick]

Nice measurement. You are measuring something called the BRDF (bidirectional reflectance distribution function), which is a complex relationship between surface properties, illumination angle, and scattering angle.

http://www-modis.bu.edu/brdf/brdfexpl.html

http://en.wikipedia.org/wiki/Bidirectional_reflectance_distribution_function

http://math.nist.gov/~FHunt/appearance/brdf.html

 

[Daniiel]

Oh thanks a lot,

So if I were to apply this function to the experiment it would tell me that the angle of reflection is great then the angle of incidence?

So really its just that the properties of these particular rough surfaces reflect the light at a larger angle?

 

[JeffKoch]

Does anyone have any ideas why the peaks have shifted? We ran the experiment three times and received the same result with the rough surfaces

How well do you know the zero of the angular scale, and is it the same for every surface? Mounting a random piece of material on the stage, you don't know where the surface normal points unless you zero it by back-reflecting, and then count degrees of rotation from that orientation. Also, surfaces have variations in normal vectors depending on how much of the surface you are averaging over, and how flat the surface is over different spatial scales (obviously over very small scales, a rough surface is not flat at all). Also, to be precise you would need to rotate the object about the illumination point on the surface, and to take care to set up the experiment that way. So, errors can creep in from various places, and ~ few-degree offsets wouldn't be surprising unless you are very careful to look out for these sources of error.

 

[Andy Resnick]

Oh thanks a lot,

So if I were to apply this function to the experiment it would tell me that the angle of reflection is great then the angle of incidence?

So really its just that the properties of these particular rough surfaces reflect the light at a larger angle?

I don't know of any BRDF that can be calculated (except for idealized surfaces like Lambertian)- they are all measured. There are some modeling approaches (Kubelka-Munk, Torrance-Sparrow, Oren-Nayar, etc.), but the surface roughness properties must be quantitatively specified in some way.

There's also polarization dependence and wavelength dependence, I forgot to mention that earlier.

The behavior can be extremely complex- many rough surfaces, even 'black' ones, will specularly reflect at grazing angles of incidence.