Experimental robustness of Fourier Ptychography phase retrieval algorithms

TL;DR

This paper evaluates the robustness of Fourier ptychography phase retrieval algorithms, highlighting the importance of cost function choice and proposing a robust, efficient Newton's method for improved reconstruction under noise and calibration errors.

Contribution

It systematically compares inverse algorithms for Fourier ptychography, emphasizing the role of cost functions and introducing a robust Newton's method for enhanced performance.

Findings

Amplitude-based cost functions outperform intensity-based ones.

Noise and model mis-match errors scale with image intensity.

The proposed Newton's method improves robustness and efficiency.

Abstract

Fourier ptychography is a new computational microscopy technique that provides gigapixel-scale intensity and phase images with both wide field-of-view and high resolution. By capturing a stack of low-resolution images under different illumination angles, a nonlinear inverse algorithm can be used to computationally reconstruct the high-resolution complex field. Here, we compare and classify multiple proposed inverse algorithms in terms of experimental robustness. We find that the main sources of error are noise, aberrations and mis-calibration (i.e. model mis-match). Using simulations and experiments, we demonstrate that the choice of cost function plays a critical role, with amplitude-based cost functions performing better than intensity-based ones. The reason for this is that Fourier ptychography datasets consist of images from both brightfield and darkfield illumination, representing a large range of measured intensities. Both noise (e.g. Poisson noise) and model mis-match errors are shown to scale with intensity. Hence, algorithms that use an appropriate cost function will be more tolerant to both noise and model mis-match. Given these insights, we propose a global Newton's method algorithm which is robust and computationally efficient. Finally, we discuss the impact of procedures for algorithmic correction of aberrations and mis-calibration.