Real-time complex amplitude retrieval in Fourier ptychographic microscopy using dual-channel input GAN

Fourier Ptychographic Microscopy (FPM) is a well-established imaging modality to access wide area imaging with large space-bandwidth product. Typically, in FPM a low NA microscope objective is employed to access wide field of view. Specimens are probed under different illumination directions to collect subsets of their spatial frequencies. A significant portion of spatial frequencies would fall outside the limited NA of the optical system and are collected in dark-field conditions. Stitching the spectra of the collected intensity images allows synthesizing a larger NA to gather superresolved images. A complex-amplitude retrieval process is carried out using iterative engines (e.g. the EPRY algorithm). Thus, although FPM would be ideal to image stain-free tissue slides, the time-consuming iterative estimation process impairs the transfer of FPM to clinical practice. Here we show the use of Generative Adversarial Networks (GANs) to emulate the complex-amplitude retrieval process of FPM. The network is trained by inserting as input the real and imaginary part of the complex field obtained after the first iteration of the EPRY algorithm. The network guess is compared with the ground-truth (i.e. the result of the iterative engine after convergence) using a loss function that considers both channels. Quantitative evaluation of the results shows the very accurate generation of FPM complex amplitudes of biological tissues. We benchmark the network capabilities using brain and kidney tissue slides. Expert nephrologists were enrolled to judge the GAN result against the EPRY algorithm output. Results show a very accurate reconstruction of the high-resolution complex-amplitude.