Computational algorithm from the Huygens-Fresnel’s diffraction integral for two-dimensional holographic reconstruction

Abstract

While most common holographic methods of digital reconstruction are based on the convolution theory, for the ease in the mathematical approach, here we present an algorithm by a discretization of the Huygens-Fresnel integral from a Taylor series expansion to produce a bidimensional Fourier transform. Compared to the digital convolution method, the algorithm presented here is more concise and generates a reduction in processing time, since the Fourier transform appears only once in the discretization. Another advantage is associated with the production of results in the frequency domain, allowing the optical information to be obtained directly.