Neural-field-assisted transport-of-intensity phase microscopy: partially coherent quantitative phase imaging under unknown defocus distance

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 He La cells demonstrate that NFTPM can achieve accurate, partially coherent QPI under unknown defocus distances, providing new possibilities for extending applications in live cell biology.