Effect of detector photoelectric parameters on ptychographic iterative engine

Abstract

An analytical solution model for ptychographic iterative engine (PIE) is proposed. In this model, PIE can be described as a system of linear equations between the sample and the illumination in the frequency domain. This system of linear equations (<i> <b>AX</b> </i> = <i> <b>B</b> </i>) is derived with the spectrum of the illumination as the coefficient (<i> <b>A</b> </i>), the spectrum of the sample as the unknown (<i> <b>X</b> </i>), and the intensity of the diffraction pattern as the vector (<i> <b>B</b> </i>). Hence, the sample can be recovered by solving this linear system. In PIE, the detector (such as Pike F-100, AVT) has a large resolution, meaning that 1000 × 1000 linear equations can be generated by recording a single pattern. It is still the case, however, that the number of obtained equations is smaller than the number of unknowns, leading to the inability to obtain a unique solution about the sample. Relative motions of sample and illumination, can generate more diffraction patterns to construct a sufficient number of linear independent equations. For coefficient (<i> <b>A</b> </i>), since the initial illumination is known, the illumination after shifting can still be obtained by recording its shifting distance. Hence the unique solution for the sample can be directly obtained by solving this linear independent system of equations. Simultaneously, the photoelectric parameters of the detector have a significant influence on the imaging quality of PIE. Using this linear system, the photoelectric parameters of the detector can be characterized by the number of linear equations and unknowns in each equation. According to the conditions that there is a unique solution in the system of equations and the requirements of the photoelectric parameters (such as pixel sampling interval, width of target surface, pixel size, sensitivity and dynamic range), the influence of the reconstruction for PIE is quantified theoretically. Obviously, the numerical simulation results based on this theory not only verify the correctness of the theoretical analysis and predictions, but also reveal the physical mechanism of recovering high-quality results in imperfect photoelectric parameters of detector, which can contribute to improving the quality of their reconstruction and optimizing the experimental setup.