An improved version of the relative entropy minimization approach for the phase retrieval problem

Abstract This paper presents an investigation on the reliability of an iterative phase retrieval (PR) approach from intensity-only measurements on multiple planes. PR tends to converge, regardless of the particular method chosen, in the ideal case where intensity is negligible outside the scan plane field-of-view. However, convergence may be adversely affected when the intensity distribution extends beyond the field-of-view. In this paper, a remedy is proposed for data truncation, and is tested on a recently introduced PR method [R.W. Deming, Phase retrieval from intensity-only data by relative entropy minimization, J Opt Soc Am A 24 (2007) 3666–3679]. This remedy incorporates a priori knowledge about the extent of the source under test by way of constraints in the plane-wave spectrum (PWS) of the unknown complex wave field. In addition, the adopted representation permits control of the path to convergence using a gradual increase in the number of unknown model parameters during the PR iterations. Reconstruction results show the feasibility and reliability of the proposed solution strategy.

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