Wave packet in the phase problem in optics and ptychography

TL;DR

This paper explores the wave packet method for calculating the wave field in ptychography, providing formulas for domain discretization and comparing it with traditional approximations, enhancing optical resolution analysis.

Contribution

It introduces a wave packet approach to model the wave field in ptychography, offering theoretical formulas for domain discretization and validating them through modeling.

Findings

Wave packet method accurately models the wave field in ptychography.

Formulas for domain size and discretization are theoretically validated.

Comparison shows advantages over paraxial approximation for certain conditions.

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.