Abstract
We propose an algorithm to remove a parabolic wavefront from a convergent or divergent beam in the Wigner function. Using this approach we numerically collimate the beam. This avoids a dense sampling in phase space to describe a convergent wavefront. Thereby we reduce the required computer memory, but maintain computational accuracy and physical effects. Furthermore, we compare two algorithms, shearing and Radon transform, to propagate the Wigner function in free space. We use the fast Fourier transform to accurately perform shearing. However, zero-padding is necessary to circumvent aliasing. We prove that the Radon transform is a more efficient approach for a long propagated distance.
Highlights
The Wigner function is a helpful tool to analyze optical signals in phase space [1, 2]
In Shearing and Radon transform we describe another algorithm based on the Radon transform with a better computational efficiency
Our methods contribute to a fast implementation to paraxially propagate beams in phase space, for partially coherent light
Summary
The Wigner function is a helpful tool to analyze optical signals in phase space [1, 2]. It includes information about ray optics and wave optics [3]. In particular for partially coherent light, the Wigner function visualizes the coherence effects in a straightforward manner [4]. The computation of the Wigner function has certain difficulties. We require a two-dimensional Wigner function to describe light field with one transverse dimension. For a field with two transverse dimensions, the Wigner function spans four dimensions. The main goal of this work is to propagate light by using Wigner functions, while saving computer memory and keeping computational accuracy
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