Calculation of scalar optical diffraction field from its distributed samples over the space

Abstract

As a three-dimensional viewing technique, holography provides successful threedimensional perceptions. The technique is based on duplication of the information carrying optical waves which come from an object. Therefore, calculation of the diffraction field due to the object is an important process in digital holography. To have the exact reconstruction of the object, the exact diffraction field created by the object has to be calculated. In the literature, one of the commonly used approach in calculation of the diffraction field due to an object is to superpose the fields created by the elementary building blocks of the object; such procedures may be called as the “source model” approach and such a computed field can be different from the exact field over the entire space. In this work, we propose four algorithms to calculate the exact diffraction field due to an object. These proposed algorithms may be called as the “field model” approach. In the first algorithm, the diffraction field given over the manifold, which defines the surface of the object, is decomposed onto a function set derived from propagating plane waves. Second algorithm is based on pseudo inversion of the systemmatrix which gives the relation between the given field samples and the field over a transversal plane. Third and fourth algorithms are iterative methods. In the third algorithm, diffraction field is calculated by a projection method onto convex sets. In the fourth algorithm, pseudo inversion of the system matrix is computed by conjugate gradient method. Depending on the number and the locations of the given samples, the proposed algorithms provide the exact field solution over the entire space. To compute the exact field, the number of given samples has to be larger than the number of plane waves that forms the diffraction field over the entire space. The solution is affected by the dependencies between the given samples. To decrease the dependencies between the given samples, the samples over the manifold may be taken randomly. Iterative algorithms outperforms the rest of them in terms of computational complexity when the number of given samples are larger than 1.4 times the number of plane waves forming the diffraction field over the entire space.