Transport of intensity equation-based computational phase retrieval for robust quantitative phase imaging

A computational phase retrieval method is presented that utilizes the transport of intensity equation (TIE) and its solution as a physics-based prior in an iterative reconstruction process. TIE is a non-interferometric quantitative phase imaging (QPI) method that is experimentally simple to implement, needing a minimum of two through focus intensity measurements. However, the accuracy of TIE is severely affected by certain theoretical and practical limitations such as the requirement of uniform intensity, prior knowledge of boundary conditions. Moreover, the finite-difference approximation for intensity derivatives produces blurring for large defocus distances. We propose an iterative phase recovery algorithm that updates the required phase by minimizing the difference of axial intensity derivatives obtained using experiments and expected from angular spectrum propagation theory while integrating a TIE phase-compensation solution in the iterative steps for a fast and accurate phase recovery. We show the validity of the proposed algorithm with simulations for different cases of non-uniform intensity, noise, boundary conditions, and defocus distance. We experimentally verify the working of the proposed method for large defocus distances and compare the results with standard TIE solutions and algorithms to verify its robustness.