Phase discrepancy analysis and compensation for fast Fourier transform based solution of the transport of intensity equation

The transport of intensity equation (TIE) has long been recognized as a quantitative method for phase retrieval and phase contrast imaging. However, it is shown that the most widely accepted fast Fourier transform (FFT) based solutions do not provide an exact solution to the TIE in general. The root of the problem lies in the so-called “Teague’s assumption” that the transverse flux is considered to be a conservative field, which cannot be satisfied for a general object. In this work, we present the theoretical analysis of the phase discrepancy owing to the Teague’s assumption, and derive the necessary and sufficient conditions for the FFT-based solution to coincide with the exact phase. An iterative algorithm is then proposed aiming to compensate such phase discrepancy in a simple yet effective manner.Published versio