The performance of an optical imaging system is typically characterized by the intensity Point Spread Function (PSF) or Optical Transfer Function (OTF). But the Coherent Transfer Function (CTF) is better for describing the coherent optical imaging system. Though the CTF characterizes the complex amplitude transfer properties of the light field, it is hard to measure compared with PSF. Fourier Ptychographic Microscopy (FPM) is a promising computational technique that can obtain both complex amplitude information of an object and the CTF of coherent imaging system, which provides a way to retrieve the CTF. FPM, combining the concept of aperture synthesis and phase retrieval, is a recently developed imaging technique that allows the reconstruction of high-resolution complex images with an extended field of view. By acquiring a series of low-resolution brightfield and darkfield images under inclined illumination and stitching them together in the Fourier domain, FPM can break through the frequency limit of the employed objective determined by its numerical aperture. Consequently, the space-bandwidth product of the optical imaging system can be effectively increased without precise mechanical scanning. The flexibility with low-cost hardware requirements makes FPM a powerful tool particularly potential for imaging biomedical samples in the field of digital pathology. Although many advanced FPM techniques have been proposed to achieve higher data acquisition efficiency and recovery accuracy in the past few years, little is known about the precision, stability, and requirements of the CTF, especially when there are inevitable system errors. If FPM can retrieve high-precision CTF, it will provide a new means for CTF calibration. Therefore, this thesis mainly studies the acquisition of CTF with high precision, stability and efficiency via FPM. In this paper, we investigate the reconstruction quality of the CTF under different system errors with different targeted algorithms and find that the reconstructions of CTF is more robust than the reconstructions of object. In addition, under the condition of good recovery of object function, different objective algorithms can also recover basically the same CTF. Therefore, the CTF recovered by FPM algorithm can be used to quantitatively characterize coherent optical systems. Based on this, we report a sub-region translation method named ST-FPM, which is used in Fourier ptychographic microscopy imaging. Based on the basic assumption that the aberration of adjacent local fields is basically unchanged, asymmetric spatial information is introduced to eliminate the grid noise caused by periodic illumination, which improves the recovery accuracy of CTF and accelerates the convergence speed of CTF reconstruction in limited images. The recovered CTF is deconvolved with incoherent images. And the contrast is additionally improved compared with the traditional FPM. In addition, this method can realize image refocusing without the prior information of defocus. In addition, we study the spatial and frequency domain data redundancy of Fourier ptychographic microscopy to recover the coherent transfer function, and find that at least about 40% spectral overlap rate is needed to accurately reconstruct the coherent transfer function, which is 10% higher than that without aberration. And at least 25 original low-resolution images are needed for the stability of coherent transfer function. Finally, we discuss the necessary conditions for stable CTF reconstruction, and verify the conclusion in simulation and experiment.
