Simplifying the Experimental Detection of the Vortex Topological Charge Based on the Simultaneous Astigmatic Transformation of Several Types and Levels in the Same Focal Plane

It is known that the astigmatic transformation can be used to analyze the topological charge of a vortex beam, which can be implemented by using various optical methods. In this case, in order to form an astigmatic beam pattern suitable for the clear detection of a topological charge, an optical adjustment is often required (changing the lens tilt and/or the detection distance). In this article, we propose to use multi-channel diffractive optical elements (DOEs) for the simultaneous implementation of the astigmatic transformations of various types and levels. Such multi-channel DOEs make it possible to insert several types of astigmatic aberrations of different levels into the analyzed vortex beam simultaneously, and to form a set of aberration-transformed beam patterns in different diffraction orders in one detection plane. The proposed approach greatly simplifies the analysis of the characteristics of a vortex beam based on measurements in the single plane without additional adjustments. In this article, a detailed study of the effect of various types of astigmatic aberrations based on a numerical simulation and experiments was carried out, which confirmed the effectiveness of the proposed approach.