An ameliorated fast phase retrieval iterative algorithm based on the angular spectrum theory

Abstract

For designing the light beam shaper in the optical transmitting antenna in inter-satellite optical communication system, the essential problem is, according to the input optical field and ideal output light field, to determine the shaper of phase distribution, in which its core is in phase recovery. Based on the traditional Gerchberg-Saxton (G-S) iterative algorithm, using the angular spectrum propagation theory, a kind of amplitude gradient addition iterative algorithm is proposed, and the detailed algorithm process and analysis are given. Compared with G-S algorithm, the new one using iterative process, constructs the light field amplitude feedback loop, and searches out the optimal iteration path using the gradient; their joint action accelerates the convergence process. Numerical simulation shows that the iterative error-drop speed caused by unit iterations in the new algorithm is 1.7 times that of the G-S algorithm, its convergence rate is obviously superior to the G-S algorithm; for different random initial phase, the new algorithm can effectively carry out iteration, show the advantages of the strong adaptability and the good convergent consistency. Amplitude gradient addition iterative algorithm gives a new effective way of recovering the complex optical field phase, and provides technical support for designing all kinds of diffraction optical element.

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“…refer to the amplitude of the object plane and image plane, respectively. According to the theory of angular spectrum propagation, the relationship between ( ) U x y , 1 and ( ) U x y , 2 can be expressed as follows [27]:…”