Huygens Wave Equations in the Field of 2D-CWT

TL;DR

This paper establishes a mathematical connection between Huygens' wave equations and the continuous wavelet transform, providing a new perspective on scalar diffraction and wave propagation analysis.

Contribution

It introduces wavelets that satisfy wave principles and links Huygens-Fresnel diffraction with the wavelet transform, bridging classical optics and modern signal processing.

Findings

Derived equations linking diffraction and wavelet transform

Demonstrated correspondence between Huygens-Fresnel and wavelet methods

Proposed wavelets meeting wave and wavelet principles

Abstract

In this paper it is shown the performing of an optical transform to state the scalar diffraction in the formulation of the wavelet transform and the 'wave equations'. From there, a bridge is build between equations of spherical waves presented in 1678 by Huygens and the continuous wavelet transform. For such a purpose, wavelets are introduced that meet the principles of waves and the properties of wavelets. The following equations are applied in solution to show a correspondence between the Huygens-Fresnel diffraction and the wavelet transform.