Image enhancement technique is utilized to emphasize the overall or local characteristics of pictures and widely used in aerospace, and machine vision application. However, most of these techniques are mathematical algorithms based on captured pictures instead of the imaging process. Fourier ptychographic microscopy (FPM) is a recently developed computational imaging approach which stitches together low-resolution images acquired under different angles of illumination with the same intensity in Fourier space to produce a wide-field, high-resolution complex sample image. In this article, a theoretical model about the illumination intensity is proposed. The effect of uneven illumination intensity can be reduced significantly based on our model. Furthermore, the quality of the reconstructed image can be enhanced by adjusting the intensity of the illumination light corresponding to the high frequency components of the original spectrum.
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.
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