THEORY OF THE AMPLITUDE-PHASE RETRIEVAL IN ANY LINEAR TRANSFORM SYSTEM AND ITS APPLICATIONS

This paper is based on our previous works in the past decade and is a summary of the theory of the amplitude-phase retrieval problem in any linear transform system and its applications. We describe the general statement on the amplitude-phase retrieval problem in an imaging system and derive a set of equations governing the amplitude-phase distributions in terms of the rigorous mathematical derivation. By using these equations and an iterative algorithm, a variety of amplitude-phase problems can be successfully handled. We carry out systematical investigations and comprehensive numerical calculations to demonstrate the utilization of this new algorithm in various transform systems. We also indicated the relationship and distinction between our algorithm and the original Gerchberg-Saxton algorithm. This new algorithm possesses considerable capability to deal with the various phase-retrieval problems in the arbitrary linear transform system and some inverse problems in solid state physics.