Mathematical foundations of 2-dimensional diffraction: a biquaternionic approach

This paper presents what we believe to be a novel theoretical framework for analyzing two-dimensional (2D) diffraction phenomena using biquaternions. We introduce a rigorous mathematical development of the 2D integral theorem of Helmholtz and Kirchhoff, the 2D biquaternionic Fresnel-Kirchhoff diffraction formula, and the 2D biquaternionic Rayleigh-Sommerfeld diffraction formula. The proposed approach offers several advantages over traditional methods, including a more concise and elegant representation of the diffraction process.