Improved reconstruction with Butterworth-weighted transfer function for Fourier ptychographic microscopy

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Fourier ptychographic microscopy (FPM) is an effective computational imaging method that incorporates many advantages such as large field of view, high resolution, label-free, and quantitative phase-contrast imaging. Typically, an LED array is used as the illumination source. Due to the small size and narrow spectral width of the LED unit, FPM is usually treated as a coherent imaging system. However, practically, each LED unit is a spatially-extended light source with a certain emitting area, rather than an ideal point source. The ideal point source approximation will decrease the quality of the reconstructed image, to a certain extent. In this paper, the spatial coherence characteristics of FPM system based on LED illumination is analyzed, and it is found that the optical field on the object plane is partially coherent. Thus, the artifacts exist when the coherent transfer function is used as the frequency domain constraint. To address this problem, a Butterworth-weighted transfer function is proposed as the frequency domain constraint in the iterative reconstruction process. The simulation and experimental results demonstrate that this new constraint approach can not only reduce the ringing effect in low-resolution images, but also improve the reconstruction quality due to its following better the actual physical mechanism inherent in FPM. In addition, it may reduce the requirement of the spatial coherence of the illumination source, which has great significance for promoting the application of FPM.