A systematic analysis for the quantitative comparison of phase retrieval methods based on alternating projections

We present a numerical and experimental scheme for the systematic analysis and comparison of phase retrieval techniques based on alternating projection numerical methods. This comparison allows us to evaluate the most common and recently introduced phase retrieval methods. The proposed scheme gives a quantitative comparison that helps to elucidate the differences between them and develop proper technical implementations of phase retrieval. The comparison is made by means of a numerical and experimental scheme that allows us to evaluate phase retrieval experiments. In this work, the drawbacks of using arbitrary random initial seeds to support the phase retrieval numerical algorithms are also analyzed and discussed. Moreover, we show the convenience of using a rough object phase estimation, which is obtained by means of a simple holographic technique, as the initial seed. This seed dramatically reduces the computational load of the algorithms by decreasing the successive iterations from hundreds to less than twenty. The experimental object under study is a random phase object within a micro-channel. As a proof of concept, this micro-channel combined with a millimeter size semicircular hole, which provides a reference wave, conforms a primitive sensor. The performance of the algorithms is not only measured by the usual convergence error, but also by means of a quality index that requires a direct comparison against the generally unknown original phase object. Thus, in order to evaluate the experimental performance of the phase retrieval techniques, we implement an interferometric optical setup that allows us to compare the results obtained by both techniques. The experiment proposed is a valuable tool for quantitative experimental evaluation of phase retrieval techniques in the optical domain.