# Phase retrieval problem for laser profile

Good morning,
Before all, I also posted a question to maths forum, but I am convienced that this is the forum I was more like looking for.

Firstly, hello to this forum, secondly I want to apologize if this is not a place I would like to post a question like that, maybe in another thread ?; ) Anyways, I am a student and I am having problems with phase retrieval. I want to get a phase profile from a single measurement of a laser beam profile. I measured the intensity and I would like to extract a phase. The intensity is a 124x124 pixel grid from a sensor.

To do that I implemented a Gerchberg-Saxton algorithm which is an error reduction algorithm (I find it best to look at the paper from J.R. Fineup: Phase retrieval algorithms: a comparison) and well it gives me some results but the algorithm says that after some steps I should satisfy function's and fourier's constraints but I have no idea what that means. From the text I can't make a clear answer for that question so maybe anybody knows here ? It says that the values must be non-negative, but the values of modulus, imaginary part of the estimate of the phase ? I have no idea.

Maybe you have another ideas how to tackle problem of the phase retrieval?

Thank you very much : ) If something is not clear, ask and I will try to make my question clearer.

## Answers and Replies

Good morning,
Anyways, I am a student and I am having problems with phase retrieval. I want to get a phase profile from a single measurement of a laser beam profile. I measured the intensity and I would like to extract a phase. The intensity is a 124x124 pixel grid from a sensor.

To do that I implemented a Gerchberg-Saxton algorithm which is an error reduction algorithm (I find it best to look at the paper from J.R. Fineup: Phase retrieval algorithms: a comparison) and well it gives me some results but the algorithm says that after some steps I should satisfy function's and fourier's constraints but I have no idea what that means. From the text I can't make a clear answer for that question so maybe anybody knows here ? It says that the values must be non-negative, but the values of modulus, imaginary part of the estimate of the phase ? I have no idea.

Maybe you have another ideas how to tackle problem of the phase retrieval?

Thank you very much : ) If something is not clear, ask and I will try to make my question clearer.

this question would be better on either the math section or better yet the engineering section. Who specialize in fourier transforms. hopefully a MOD will move this thread there.

Its been too long since I learned Fourier analysis or laptase transforms for that matter but this may help

http://www.iro.umontreal.ca/~pift6080/H09/documents/eck_fft.pdf

The non-negativity constraint applies to the intensity values in the detector plane.

You should also check out this reference, it may serve as a better introduction to phase retrieval for a beginner:
http://www.optics.rochester.edu/workgroups/fienup/PUBLICATIONS/AO93_PRComplicated.pdf

I'm a bit worried that Gerchberg-Saxton may not be applicable to your current experimental setup. The algorithm assumes that you're estimating the electric field in the pupil plane of an optical system with a known aperture and a measured point-spread-function in the image plane. The pupil plane field and the image plane field are related by a Fraunhofer diffraction integral, which is computed with a Fourier transform - hence the FFT's. From your description of the problem, it's not clear which plane you're trying to estimate the phase in, or that there is a Fourier transform relation between that plane and the plane where you have measured intensity.

I can't edit my previous post, but after thinking about it some more I realized that the non-negativity constraint isn't actually related to the measured intensity in the detector plane. Instead it's a constraint that in some cases can be applied to the plane where you don't have measured intensity, but do know that the phase should be constant across the surface of the object you're estimating. This happens in x-ray crystallography and some other applications, but I don't think it applies to your problem. Sorry for the error.

Thank you all for replies. I've been travelling a bit, so sorry for a long delay.

Anyway, I am now getting through that thick paper you suggested... really hard stuff in there for me. But I am trying :)

Also, if I understand correctly, Gerchberg Saxton should work if I also involve some information about propagation of my beam ?

The set up is roughly like this : there is laser's aperture, then bunch of optics among which is the place I want to get the information about the phase. After this bunch of optics there is a lens that gives me the image of the profile I want the phase from. Then I want to extract the information about another place in the system and compare the changes in the phase to get the information about what kind of processes happen with the phase through some distance (actually the beam goes through a crystal and I want to know what is going on inside).

I also looked at the wave propagation spectrum and eh, I can't get a grasp of it. If you have any helpful links, I'll be grateful. I'm tired of papers that are packed with tons of equations and no real practical explanations in : )