The transport-of-intensity equation (TIE) enables quantitative phase imaging (QPI) under partially coherent illumination by measuring the through-focus intensities combined with a linearized inverse reconstruction algorithm. However, overcoming its sensitivity to imaging settings remains a challenging problem because of the difficulty in tuning the optical parameters of the imaging system accurately and because of the instability to long-time measurements. To address these limitations, we propose and experimentally validate a solution called neural-field-assisted transport-of-intensity phase microscopy (NFTPM) by introducing a tunable defocus parameter into neural field. Without weak object approximation, NFTPM incorporates the physical prior of partially coherent image formation to constrain the neural field and learns the continuous representation of phase object without the need for training. Simulation and experimental results of HeLa cells demonstrate that NFTPM can achieve accurate, partially coherent QPI under unknown defocus distances, providing new possibilities for extending applications in live cell biology.

We propose a high-accuracy artifacts-free single-frame digital holographic phase demodulation scheme for relatively low-carrier frequency holograms—deep learning assisted variational Hilbert quantitative phase imaging (DL-VHQPI). The method, incorporating a conventional deep neural network into a complete physical model utilizing the idea of residual compensation, reliably and robustly recovers the quantitative phase information of the test objects. It can significantly alleviate spectrum-overlapping-caused phase artifacts under the slightly off-axis digital holographic system. Compared to the conventional end-to-end networks (without a physical model), the proposed method can reduce the dataset size dramatically while maintaining the imaging quality and model generalization. The DL-VHQPI is quantitatively studied by numerical simulation. The live-cell experiment is designed to demonstrate the method's practicality in biological research. The proposed idea of the deep learning-assisted physical model might be extended to diverse computational imaging techniques.