Reconstruction of Talbot self-image using Fourier ptychographic microscopy

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Fourier ptychographic microscopy (FPM) is used to merge a sequence of low-resolution Talbot images into a high-resolution image with a large field of view such that both integer and fractional Talbot lengths are clearly resolved. It is also revealed that the diffraction orders present in the dark field Fourier plane images reconstructed based on the Talbot effect i.e. the microscope’s back focal plane images are the ones responsible for rendering FPM amenable for the self-imaging phenomena. These diffraction spots have an arced-shaped diffraction patterns which are consistent with the Talbot image when illuminated with a parabolic wavefront. i.e. Gaussian sums only for the dark field images, and are crucial for FPM to successfully achieve a full complex image recovery. Herein, the Talbot image is treated as a phase-recovery problem, and further analyses are presented by comparing the performance of FPM when the periodic grating Talbot effect is imaged with other standard phase-recovery methods, namely the Fienup and Gercberg-Saxton algorithms.