An Analytical Study of the Diffraction of Light by a Circular Aperture Using Spherical Harmonics for n≤1

Abstract

Based on the importance of spherical harmonics and their applicability in many physical problems, this research aimed to study the diffraction pattern of light by a circular aperture starting from the first Rayleigh–Sommerfeld diffraction equation and to expand the polar radius of a point on the surface of the circular aperture based on spherical harmonics. We depended on this theoretical framework in our paper. We calculated the optical intensity compounds C00,C10,C11,C1−1 for n=0,1,m=−1,0,1. We studied the intensity distributions in three special cases (along the optical axis, at the geometrical focal plane, and along the boundary of the geometrical shadow). We presented numerical comparative examples to illustrate the variation of the intensity versus a ratio (Z/A is the ratio of the distance between the circular aperture and the observation plane to a radius of the circular aperture), and we used Maple program to represent these results. We noticed that the expansion we made using spherical harmonic analysis led to an increase in the number of fringes bright enough to be visible to the naked eye. We then concluded with a brief discussion of the results.