Phase Retrieval – an alternative theoretical analysis

Damien P. Kelly

Metrology Department

The Institute for Laser Technologies in Medicine and Metrology at the University of Ulm (ILM)

Phase retrieval is a coherent optical technique for estimating the phase of an optical field from a set of intensity distribution measurements. A classical algorithm for recovering the phase, the Gerchberg-Saxton algorithm, uses the intensity distribution in the image and Fourier planes and an initial guess at the phase distribution as the inputs to the algorithm. An iterative procedure is then set in motion and the initial estimate of the phase is continually adjusted until a defined error (or quality) metric is improved beyond some desired limit. One issue that arises with these iterative algorithms is stagnation, where the phase estimate converges to a result that is not optimal and does not improve further. Here, we re-examine the phase retrieval problem and outline how a deterministic algorithm can in principal be developed. We show that for low numbers of contributing point sources, our algorithm can deterministically find the correct solution and many other solutions that are unphysical. Limitations and applications of our approach are discussed.