A linear model is adopted herein that expresses the ptychographic iterative engine (PIE) as a system of linear equations between the object and probe in the frequency domain. And using this linear model, the unique solution of the complex object can be directly determined without the additional iterative calculation. Simultaneously, based on this linear model, the effect of the detector photoelectric parameters on PIE can be characterized by the existence of the unique solution. A series of investigative simulations have been implemented that discuss the effect of the reconstruction with different photoelectric parameters (such as target surface width and pixel size) for PIE. This mathematical model provides a direct method to obtain the underlying physics of PIE and can also be used to predict the accuracy and error in PIE applications with imperfect detector photoelectric parameters.
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