Linear algorithms for phase retrieval in the Fresnel region

Linear methods for solving the problem of optical phase retrieval from intensity measurements have the advantage of being deterministic and computationally more efficient compared to most alternative non-linear techniques. In the present work the relationship between two popular linear phase retrieval methods based on the Transport of Intensity equation and the first Born approximation, respectively, is clarified using a unified theoretical approach. It is also shown that a new phase retrieval method combining the two techniques has a broader validity range, higher accuracy and stability compared to the same techniques used separately. The new method is tested on simulated images and is demonstrated to be efficient for phase retrieval in the "near-Fresnel" region. (C) 2003 Elsevier B.V. All rights reserved.