A New Approach to Two-dimensional Phase Retrieval

Phase retrieval in imaging

The phase problem (PP) in imaging is reviewed in this paper, i.e., retrieving the phase of the image field from the recorded image irradiance distribution. The PP in one spatial lateral dimension (perpendicular to the optic axis) is treated from analytical (uniqueness) and numerical points of view (algorithms). A heuristic discussion of the 2-D PP is given based on the approach by Bruck and Sodin.

Improvement in evaluating the logarithmic Hilbert transform in phase retrieval

The logarithmic Hilbert transform in one dimension can be used for two-dimensional phase retrieval. I present an effective algorithm of numerical evaluation of the convolution integral in the logarithmic Hilbert transform. The usefulness of the method is shown in computer-simulation studies of the reconstruction of the two-dimensional real and positive objects.