![]() ![]() With the “maximum intensity assumption,” we first simplify TIE as a standard Poisson equation to get an initial guess of the solution. In this Letter, we propose a universal solution to TIE with the advantages of high accuracy, convergence guarantee, applicability to arbitrarily shaped regions, and simplified implementation and computation. Nevertheless, the accuracy and validity of state-of-the-art TIE solvers depend on restrictive pre-knowledge or assumptions, including appropriate boundary conditions, a well-defined closed region, and quasi-uniform in-focus intensity distribution, which, however, cannot be strictly satisfied simultaneously under practical experimental conditions. It directly recovers the quantitative phase distribution of an optical field by through-focus intensity measurements in a non-interferometric, deterministic manner. The transport-of-intensity equation (TIE) is one of the most well-known approaches for phase retrieval and quantitative phase imaging.
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