Complete Rayleigh Sommerfeld model (Version 2)

Calculates the near field diffraction pattern of circular apperture with complete Rayleigh Sommerfeld; refer G. D. Gillen et al AJP, 2004

The following functions illustrates the on-axis calculated intensities of the complete Rayleigh–Sommerfeld model presented in: "Modeling and propagation of near-field diffraction patterns: A more complete approach" by Glen D. Gillen and Shekhar Guha; American Journal of Physics 72:9, 1195-1201. (https://doi.org/10.1119/1.1767102). This model presents a diffraction formula which has no limitations on the maximum size of either the aperture or observation region.
In the first part in relation to Fig. 2, a detector is placed at position (0,0,z), where z is on the order of 1000a, or 1000 aperture radii, and observe the central intensity as we reduce z. The code below calculates the intensity as a function of position along the z-axis with x_1 & y _1 = 0 for incident plane waves with a wavelength of 10 µm and a round aperture with a radius (a) of 100 µm in the aperture plane. The amplitude of the electric field of the incident light is assumed to be unity.
In parallel to Fig. 2.a, Fig. 4 is an image plot as a function of the distance from the aperture, z, and the radial distance from the z-axis, using the complete Rayleigh–Sommerfeld model and the same aperture and laser field as in Fig. 2.
Version 2 - presents Fresnel-Kirchoff and Fresnel Near Field approximations as a comparison