Frequency-domain filtering for feature enhancement using recursive transport of intensity and phase equations

Quantitative phase imaging enables label-free visualization of transparent and weakly absorbing cells with the transport of intensity equation, derived from the paraxial wave equation widely used for its simple and non-interferometric approach. However, it struggles with noise and high-frequency details, which are strongly influenced by the choice of defocus distance. In this study, we enhance the feature of retrieved phase through the recursive transport of intensity and phase equations using frequency-domain filtering. The filter identifies the frequency range where the phase transfer functions of transport of intensity and the contrast transfer function converge, enabling accurate and feature-enhanced phase reconstruction while mitigating diffraction and noise artifacts. The study establishes the upper limit of allowable frequency information in the phase image, with particular relevance to weak-phase samples. The proposed concept has been verified through numerical simulations, considering the initial (ground-truth) phase as a weak-phase sample. For experimental validation, the method is first tested using a resolution chart and subsequently applied to onion peels.