  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.
