We investigate how the distance between probe positions and the resolution of measured diffraction patterns affects iterative ptychographic reconstruction. The ptychographic phase retrieval problem where both the object and probe are reconstructed is analyzed theoretically, by introducing a 4D object to describe the 4D ptychopgraphical data set. This is similar to introducing the 3D Ewald sphere to describe the field in a 3D focal volume. Conclusions drawn on the basis of the theoretical analysis are verified using simulations with a simplified 2D ptychographic problem where the probe and object are 1D. Though the 2D problem is a simplification compared to the typical 4D ptychography problem of lensless imaging, it still has practical applications for pulse reconstruction.

中文翻译：

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关于 ptychography 的采样要求

我们研究探针位置之间的距离和测量的衍射图案的分辨率如何影响迭代 ptychographic 重建。通过引入4D对象来描述4D ptychopgraphical数据集，从理论上分析了重建对象和探针的ptychographic相位检索问题。这类似于引入 3D Ewald 球体来描述 3D 焦点体积中的场。在理论分析的基础上得出的结论通过模拟验证了一个简化的 2D ptychographic 问题，其中探针和对象是 1D。尽管与无透镜成像的典型 4D ptychography 问题相比，2D 问题是一种简化，但它仍然具有脉冲重建的实际应用。