At present, ptychography seems to be the most natural and efficient method for approaching the diffraction-limited optical resolution. The general setup of a ptychoscope does not contain refracting or focusing elements and includes a coherent illumination source, a translation stage for displacement of a macroscopic object, and a detector for recording transmitted or reflected radiation from the object, which is connected to a computer for processing diffractograms. In classical optics, the main problem with achieving high spatial resolution is the correction and elimination of aberrations in optical systems, whereas the spatial resolution in ptychography mainly depends on the reliability of recording and computer processing diffractograms with large numerical apertures. After a brief introduction to the history and current state of ptychography, the wave-packet method for calculating the wave field on a detector in the far field and for a large numerical aperture is considered in detail. This gives a relation between fields on the object and on the detector, which underlies the ePIE (extended Ptychography Iterative Engine) algorithms for recovering images used in practice. The realization of algorithms involves operations with functions defined in certain domains (coordinate networks) of the direct space and Fourier space related to the object and detector. The size of and steps involved in such networks are strictly related to the object size, its distance from the detector, and the numerical aperture. The programs developed in this paper are used to refine the limits of applicability of the paraxial approximation (Fresnel integrals) in calculations of the field on the detector. Simulations of images obtained by the ptychography method are presented.

目前，ptychography 似乎是接近衍射极限光学分辨率的最自然和最有效的方法。ptychoscope 的一般设置不包含折射或聚焦元件，并且包括相干照明源、用于位移宏观物体的平移台和用于记录来自物体的透射或反射辐射的检测器，该检测器连接到计算机用于处理衍射图。在经典光学中，实现高空间分辨率的主要问题是光学系统中像差的校正和消除，而 ptychography 中的空间分辨率主要取决于记录和计算机处理具有大数值孔径的衍射图的可靠性。在简单介绍了ptychography的历史和现状后，详细研究了计算远场探测器上波场和大数值孔径的波包方法。这给出了对象和检测器上的场之间的关系，这是 ePIE（扩展 Ptychography 迭代引擎）算法的基础，用于恢复实际使用的图像。算法的实现涉及在与物体和检测器相关的直接空间和傅里叶空间的某些域（坐标网络）中定义的函数的操作。此类网络中涉及的大小和步长与对象大小、其与检测器的距离以及数值孔径密切相关。本文开发的程序用于细化近轴近似（菲涅耳积分）在探测器场计算中的适用范围。.