Some computational aspects of using Huygens-Fresnel-Kirchoff diffraction theory

TL;DR

This paper discusses computational challenges of the Huygens-Fresnel-Kirchoff diffraction theory and applies it to three-dimensional objects, highlighting ongoing issues in classical diffraction calculations.

Contribution

It introduces computational aspects of the Huygens-Fresnel-Kirchoff method and extends its application to 3D objects, addressing unresolved issues in classical diffraction modeling.

Findings

Identified computational challenges in diffraction calculations

Extended the Huygens-Fresnel-Kirchoff method to 3D objects

Provided insights into classical diffraction phenomena

Abstract

Diffraction is a phenomenon, discussed for centuries from various points of view. The very simple principle, proposed by Huygens [1] and then modified by Fresnel[2], Stokes [3] and Kirchoff [4], allows us to make calculations, substituting an incident wave by the multitude of waves, radiated by the number of secondary sources with regard for interference. Besides mentioned scientists, many others have contributed to this theory. A reasonable historical review can reveal a challenging history of the research of this phenomenon with many names and this story is not still ended. A good historical re-view can be seen in [5]. Classical cases of the diffraction by a hole and a disk are included in many text-books for scholars. Nevertheless, there is still some place for discussions. This paper is an attempt to discuss some computational issues, based on the original Huygens-Fresnel-Kirchoff method and apply it to 3D objects.