Accurate quantitative phase imaging by the transport of intensity equation: a mixed-transfer-function approach

As a well-established deterministic phase retrieval approach, the transport of intensity equation (TIE) is able to recover the quantitative phase of a sample under coherent or partially coherent illumination with its through-focus intensity measurements. Nevertheless, the inherent paraxial approximation limits its validity to low-numerical-aperture imaging and slowly varying objects, precluding its application to high-resolution quantitative phase imaging (QPI). Alternatively, QPI can be achieved by phase deconvolution approaches based on the coherent contrast transfer function or partially coherent weak object transfer function (WOTF) without invoking paraxial approximation. But these methods are generally appropriate for "weakly scattering" samples in which the total phase delay induced by the object should be small. Consequently, high-resolution high-accuracy QPI of "nonweak" phase objects with fine details and large phase excursions remains a great challenge. In this Letter, we propose a mixed-transfer-function (MTF) approach to address the dilemma between measurement accuracy and imaging resolution. By effectively merging the phases reconstructed by TIE and WOTF in the frequency domain, the high-accuracy low-frequency phase "global" profile can be secured, and high-resolution high-frequency features can be well preserved simultaneously. Simulations and experimental results on a microlens array and unstained biological cells demonstrate the effectiveness of MTF.