3D Fourier Ptychographic Microscopy Based on the Beam Propagation Method and Time-Reversal Scheme

3D Fourier ptychographic microscopy can recover objects with high resolution across large volumes, which is very challenging in 3D imaging particularly because multiple scattering may occur within the sample. In this paper, we assume the thick sample is composed of a number of thin slices, and employ the beam propagation method (BPM) to model the propagation process of the light wave among successive slices capturing multiple scattering effects. 3D imaging is then accomplished by utilizing the gradient descent method to minimize the difference between the estimated intensity images by BPM and the captured measurements with angle-varied illuminations. We adopt a time-reversal scheme to obtain the gradient of the transmitted light intensity with respect to the complex refractive index of the volumetric sample and use the error backpropagation method to update the 3D sample iteratively. To further preserve the sharpness of the edges, we introduce a sparsity regularization term into the optimization process. Our method can achieve higher performance of 3D reconstruction compared to the original multi-slice approach, demonstrated in both simulation and experiment.