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## Complete Rayleigh Sommerfeld model (Version 2)

version 1.0.0 (3.2 KB) by
Calculates the near field diffraction pattern of circular apperture with complete Rayleigh Sommerfeld; refer G. D. Gillen et al AJP, 2004

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Updated 16 Apr 2020

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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

### Cite As

Wendwesen Gebremichael (2021). Complete Rayleigh Sommerfeld model (Version 2) (https://www.mathworks.com/matlabcentral/fileexchange/75049-complete-rayleigh-sommerfeld-model-version-2), MATLAB Central File Exchange. Retrieved .

### Comments and Ratings (2)

Guanghao Chen

What's the purpose of these sums?
integral_2D = h*h/4*(f_xy(1,1)+f_xy(1,N)+f_xy(N,1)+f_xy(N,N)+4*sum(sum(f_xy))+...
2*(sum(f_xy(1,:)+f_xy(N,:))+sum(f_xy(:,1)+f_xy(:,N))-2*f_xy(1,1)...
-f_xy(1,N)-f_xy(N,1)));

Guanghao Chen

Thank you!

##### MATLAB Release Compatibility
Created with R2013a
Compatible with any release
##### Platform Compatibility
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