A Fourier-based Solving Approach for the Transport of Intensity Equation without Typical Restrictions

TL;DR

This paper introduces a Fourier-based method for solving the Transport-of-Intensity Equation (TIE) that removes common assumptions like non-zero intensity and uniformity, broadening its practical applicability.

Contribution

The proposed approach eliminates typical restrictions in Fourier-based TIE solutions, enabling phase retrieval without assumptions of intensity uniformity or collinearity.

Findings

Allows phase retrieval without intensity restrictions

Extends TIE application domain

Maintains computational efficiency

Abstract

The Transport-of-Intensity equation (TIE) has been proven as a standard approach for phase retrieval. Some high efficiency solving methods for the TIE, extensively used in many works, are based on a Fourier-Transform (FT). However, to solve the TIE by these methods several assumptions have to be made. A common assumption is that there are no zero values for the intensity distribution allowed. The two most widespread Fourier-based approaches have further restrictions. One of these requires the uniformity of the intensity distribution and the other assumes the collinearity of the intensity and phase gradients. In this paper, we present an approach, which does not need any of these assumptions and consequently extends the application domain of the TIE.