
Using the RayleighSommerfeld diffraction theory it is possible to calculate the diffracted field at an arbitrary aperture. The 2D integral integral is transformed into a 1D integral (see figure at left). When a parallel wave front is diffracted by an aperture the diffracted waves obtained using the RayleighSommerfeld diffraction integrals take the general form [7] [8]:
The figure at left shows the model used for the simulations for 2 shells of circular apertures. The lattice constant is and each aperture has radius .
A C++ program using the GNU Scientific Library (GSL 1.3) was written to calculate the intensity and phase of the scalar field above the array.

Relative field intensity of the simulation for images of size 2020 . Lattice constant: 3176 . Radius of the aperture 250 and wavelength 488 . The images have been calculated using the RS diffraction integral of the first kind, using an array of circular apertures with 5 hexagonal shells and a total of 91 apertures. For each image is indicated the distance to the diffraction array .
Below are shown the relative intensities calculated for 3 axis
parallel to with coordinates
,
and
.