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

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.