# Imaging problem

1. Feb 26, 2015

### ibonasa

Dear all,

I have pretty simple problem in terms of understanding but I can't write an analytical solution.

Consider you have a laser beam (without divergence, single wavelength). You can see the intensity distribution on the screen perpendicular to the beam. Then you insert a thin glass layer which from side has some roughness at scales above (or much above than) wavelength: photons are simply scattered with certain angle. You can imagine this piece of glass as a distribution function of angles in space (we neglect even refraction).
Problem: I need a function which shows me the intensity distribution at any distance after the glass layer.
Problem 2: solve reverse case - we don't know angle distribution, but distributions (or just one distribution) after deflection rays by the glass layer.

What equation should I write?
Boltzmann probably doesn't fit as soon as integral over transversal space must be constant in time (number of particle with certain angular speed doesn't change over the propagation distance).
And I can't solve continuity equation because velocity field is changed during the propagation...

Thank you in advance!

2. Feb 27, 2015

### Simon Bridge

1. you need to describe the scattering from the glass ... that tells you the intensity distribution.
i.e. if the scattering is equally likely into any angle, then the resulting photon flux is going to be a superpositon of spherecial distributions from each area element inside the beam.

2. unclear - don't know what you mean. If you have an intensity pattern on, say, a screen, then, without any informations, there is no way to reconstruct the original beam.

Usually these problems are handles by working out the transfer matrix for the glass thingy that did the scattering.
The forward function is a matter of applying the transfer matrix to the incoming wave while the reverse is a matter of applying the inverse of the transfer matrix.
But you do need the transfer matrix.

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