Transport-of-intensity differential phase contrast imaging: defying weak object approximation and matched-illumination condition

Quantitative phase imaging (QPI) has emerged as a promising label-free imaging technique with growing importance in biomedical research, optical metrology, materials science, and other fields. Partially coherent illumination provides resolution twice that of the coherent diffraction limit, along with improved robustness and signal-to-noise ratio, making it an increasingly significant area of study in QPI. Partially coherent QPI, represented by differential phase contrast (DPC), linearizes the phase-to-intensity transfer process under the weak object approximation (WOA). However, the nonlinear errors caused by WOA in DPC can lead to phase underestimation. Additionally, DPC requires strict matching of the illumination numerical aperture (NA) to ensure the complete transmission of low-frequency information. This necessitates precise alignment of the optical system and limits the flexible use of objective and illumination. In this study, the applicability of the WOA under different coherence parameters is explored, and a method to defy WOA by reducing the illumination NA is proposed. The proposed method uses the transport-of-intensity equation through an additional defocused intensity image to recover the lost low-frequency information due to illumination mismatch, without requiring any iterative procedure. This method overcomes the limitations of DPC being unable to recover large phase objects and does not require the strict illumination matching conditions. The accurate quantitative morphological characterization of customized artifact and microlens arrays that do not satisfy WOA under non-matched-illumination conditions demonstrated the precise quantitative capability of the proposed method and its excellent performance in the field of measurement. Meanwhile, the phase retrieval of tongue slices and oral epithelial cells demonstrated its application potential in the biomedical field. The ability to accurately recover phase under a concise and implementable optical setup makes it a promising solution for widespread application in various label-free imaging domains.