High-Accurate Quantitative Phase Imaging Based on the Transport of Intensity Equation and Wavelet Transform

We propose a high-accurate quantitative phase imaging (QPI) method by using transport of intensity equation (TIE) and wavelet transform (WT). TIE provides a simple and fast method for QPI, but its accuracy is always limited due to the nonlinear error and noise problems caused by the defocus distance. To improve the accuracy of the phase recovered by TIE, WT is introduced to combine with TIE under several defocus distances. With the help of the multiresolution characteristics of the WT, effective information can be extracted from the phases retrieved with TIE at different defocus distances. As a result, a more accurate phase can be obtained by fusing this effective information. Moreover, to extend the applicability of our method, the problems of phase discrepancy and phase singularity in TIE are discussed and solved with an iterative WT-TIE algorithm. Numerical simulations and experiments with various types of phase maps are presented to comprehensively demonstrate the accuracy and effectiveness of our method.