Pattern-illuminated Fourier ptychography microscopy with a pattern-estimation algorithm

In this paper we proposed a new method that combines random pattern illumination, the pattern-estimation algorithm, and the Fourier ptychography (FP) algorithm to recover a super-resolution image. We shifted one multispot pattern to different positions to capture images, and estimated these illumination patterns using a gradient descent algorithm that shares the same root with blind structured illumination microscopy (SIM). Based on the captured images and estimated patterns, the FP algorithm is then applied to recover a super-resolution image. Our method, termed as pattern-estimated Fourier ptychography (PEFP) microscopy, does not need the prior information about the scanning position, and is thus insensitive to rotational errors and shift errors. The performance of PEFP has been demonstrated both in simulations and experiments, and PEFP achieves better resolution than the pattern-illuminated FP method when shift errors appear in our simulations. Moreover, PEFP shows strong resistance towards aberrations and works fine when there is noise in the captured image. Compared with a newly proposed blind-SIM method, PEFP also shows better resolution enhancement both in our simulations and experiments. Our method also provides the possibility to extend the application of pattern-illuminated FP to any illumination pattern because we estimated every illumination pattern separately, as blind-SIM does.