Autocorrelation, Wigner and Ambiguity Transforms on Polygons for Coherent Radiation Rendering

TL;DR

This paper introduces a method to compute the Wigner transform of arbitrary polygons using geometric and Fourier transforms, enabling more accurate radar illumination simulations that incorporate wave effects in scene rendering.

Contribution

It presents a novel approach to generate the Wigner transform of polygons, facilitating coherence ray-tracing in radar and wave-based rendering.

Findings

Wigner transform of polygons can be computed via geometric and Fourier transforms.

The method improves radar illumination simulation accuracy.

Application to Monte-Carlo rendering demonstrates practical utility.

Abstract

Simulating the radar illumination of large scenes generally relies on a geometric model of light transport which largely ignores prominent wave effects. This can be remedied through coherence ray-tracing, but this requires the Wigner transform of the aperture. This diffraction function has been historically difficult to generate, and is relevant in the fields of optics, holography, synchrotron-radiation, quantum systems and radar. In this paper we provide the Wigner transform of arbitrary polygons through geometric transforms and the Stokes Fourier transform; and display its use in Monte-Carlo rendering.