Edge effect removal in Fourier ptychographic microscopy via periodic plus smooth image decomposition

TL;DR

This paper introduces two algorithms, DCT and PFT, to effectively remove edge artifacts in Fourier ptychographic microscopy, significantly enhancing phase measurement accuracy and addressing a previously overlooked artifact caused by FFT extension.

Contribution

The paper proposes and systematically compares DCT and PFT algorithms for edge effect removal in FPM, with PFT achieving comparable efficiency and substantially improved phase accuracy.

Findings

PFT reduces phase error standard deviation by a factor of 4.

Both DCT and PFT effectively remove Fourier space artifacts.

PFT maintains efficiency similar to FFT while improving accuracy.

Abstract

Fourier ptychographic microscopy (FPM) is a promising computational imaging technique with high resolution, wide field-of-view (FOV) and quantitative phase recovery. So far, a series of system errors that may corrupt the image quality of FPM has been reported. However, an imperceptible artifact caused by edge effect caught our attention and may also degrade the precision of phase imaging in FPM with a cross-shape artifact in the Fourier space. We found that the precision of reconstructed phase at the same subregion depends on the different sizes of block processing as a result of different edge conditions, which limits the quantitative phase measurements via FPM. And this artifact is caused by the aperiodic image extension of fast Fourier transform (FFT). Herein, to remove the edge effect and improve the accuracy, two classes of opposite algorithms termed discrete cosine transform (DCT) and perfect Fourier transform (PFT) were reported respectively and discussed systematically. Although both approaches can remove the artifacts in FPM and may be extended to other Fourier analysis techniques, PFT has a comparable efficiency to conventional FFT. The PFT algorithm improves the standard deviation of phase accuracy as a factor of 4 from 0.08 radians to 0.02 radians. Finally, we summarized and discussed all the reported system errors of FPM within a generalized model.