Theory of the amplitude-phase retrieval in any linear-transform system and its applications

Guozhen Yang; Ben-Yuan Gu; Bi-Zhen Dong

doi:10.1117/12.139042

29 December 1992 Theory of the amplitude-phase retrieval in any linear-transform system and its applications

Guozhen Yang, Ben-Yuan Gu, Bi-Zhen Dong

Proceedings Volume 1767, Inverse Problems in Scattering and Imaging; (1992) https://doi.org/10.1117/12.139042
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

This paper is a summary of the theory of the amplitude-phase retrieval problem in any linear transform system and its applications based on our previous works in the past decade. 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 distribution in terms of the rigorous mathematical derivation. We then show that, by using these equations and an iterative algorithm, a variety of amplitude-phase problems can be successfully handled. We carry out the systematic investigations and comprehensive numerical calculations to demonstrate the utilization of this new algorithm in various transform systems. For instance, we have achieved the phase retrieval from two intensity measurements in an imaging system with diffraction loss (non-unitary transform), both theoretically and experimentally, and the recovery of model real image from its Hartley-transform modulus only in one and two dimensional cases. We discuss the achievement of the phase retrieval problem from a single intensity only based on the sampling theorem and our algorithm. We also apply this algorithm to provide an optimal design of the phase-adjusted plate for a phase-adjustment focusing laser accelerator and a design approach of single phase-only element for implementing optical interconnect. In order to closely simulate the really measured data, we examine the reconstruction of image from its spectral modulus corrupted by a random noise in detail. The results show that the convergent solution can always be obtained and the quality of the recovered image is satisfactory. We also indicated the relationship and distinction between our algorithm and the original Gerchberg- Saxton algorithm. From these studies, we conclude that our algorithm shows great capability to deal with the comprehensive phase-retrieval problems in the imaging system and the inverse problem in solid state physics. It may open a new way to solve important inverse source problems extensively appearing in physics.

Citation Download Citation

Guozhen Yang, Ben-Yuan Gu, and Bi-Zhen Dong "Theory of the amplitude-phase retrieval in any linear-transform system and its applications", Proc. SPIE 1767, Inverse Problems in Scattering and Imaging, (29 December 1992); https://doi.org/10.1117/12.139042

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