Theoretical analysis of diffraction imaging in Fourier ptychography microscopy

Fourier ptychography microscopy (FPM) is a recently developed computational imaging approach which surpasses the resolution barrier of a low numerical aperture (NA) imaging system. It is a powerful tool due to its ability to achieve super resolution of complex sample function, pupil aberration, LED misalignment, and beyond. However, recent studies have focused more on the optimization algorithms and set-ups instead of its theoretical background. Although some imaging laws about FPM have already been set forth, the formulas and laws are not fully defined, and the connection between diffraction theory and Fourier optics has a gap. Therefore, there exist a need for comprehensive research on physical and mathematical basis of FPM for future applications. Keeping this goal in mind, this manuscript utilizes scalar field diffraction theory to rigorously study the relationship between wavelength, the propagation mode, illumination direction of the incident wave, sample structure information and the direction of the output wave. The theoretical analysis of diffraction imaging in FPM provides a clear physical basis for not only the FPM systems, but also for the ptychography iterative engine (PIE) and any other coherent diffraction imaging techniques and systems. It can help to find the source of noise and therefore improve image quality in FPM technique and systems.