Wave packet in the phase problem in optics and ptychography

Abstract: Ptychography currently seems the most natural and effective method of approaching the diffraction limit of optical resolution. Schematic diagram of a ptychography microscope does not contain refractive or focusing elements. It includes a source of coherent illumination, a platform for (macroscopic) movement of the object, and a detector for recording transmitted or reflected radiation from the object. The detector is connected to a computer that processes diffraction patterns. In this paper, after a brief introduction to the history and current state of ptychography, we consider in detail the wave packet method for calculating the wave field at a detector in the far zone. It allows to establish the relationship between the fields on the object and the detector up to a numerical aperture of ~1. Theoretically substantiated formulas are proposed that determine the size and discretization step of a domain on an object, for given sizes of detector, pixel and object to detector distance. Based on these formulas, a comparison with the paraxial approximation for a point source is performed, as well as modeling of ptychography imaging by the PIE algorithm.