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.
A variable aperture-based ptychographical iterative engine (vaPIE) is demonstrated both numerically and experimentally to reconstruct the sample phase and amplitude rapidly. By adjusting the size of a tiny aperture under the illumination of a parallel light beam to change the illumination on the sample step by step and recording the corresponding diffraction patterns sequentially, both the sample phase and amplitude can be faithfully reconstructed with a modified ptychographical iterative engine (PIE) algorithm. Since many fewer diffraction patterns are required than in common PIE and the shape, the size, and the position of the aperture need not to be known exactly, this proposed vaPIE method remarkably reduces the data acquisition time and makes PIE less dependent on the mechanical accuracy of the translation stage; therefore, the proposed technique can be potentially applied for various scientific researches.
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