Study of Behavior of Geometric Symmetries of 3D Objects with Digital Fresnel–Kirchhoff Holograms, Using Non-Redundant Calculations

Techniques for producing fast Huygens–Fresnel–Kirchhoff digital holograms using kernel symmetry are studied. This study demonstrates non-linear behavior in computing time, as the sampled area changes with respect to the propagated diffracted area. Given the large amount of data involved in 3D object formation, symmetries are crucial in reducing the computational time. The evaluation of diffraction patterns is implemented to avoid redundant calculations while preserving the precision of the results. This algorithm decreases the required computing time depending on the symmetry of the axes, compared to direct calculation. Interestingly, the reduction in computing time relative to the number of symmetries is not linear. Computing time curves are presented. Some redundant computations are determined by the initial conditions of the object matrix, whether even or odd, along its x and y axes. Diagonal symmetries possess intrinsic redundancy along their axes. The rotation of the image must align with the rotation of the geometric coordinates in each section to ensure accurate calculations.