Phase discrepancy analysis and compensation for fast Fourier transform based solution of the transport of intensity equation
Date of Issue2014
School of Mechanical and Aerospace Engineering
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.
© 2014 Optical Society of America. This paper was published in Optics Express and is made available as an electronic reprint (preprint) with permission of Optical Society of America. The paper can be found at the following official DOI: http://dx.doi.org/10.1364/OE.22.017172. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.