Uzayda dağılmış örneklerden skalar optik kırınım alanı hesaplanması

As a three-dimensional viewing technique, holographyprovides successful three-dimensional perceptions. The technique isbased on duplication of the information carrying optical waves whichcome from an object. Therefore, calculation of the diffraction fielddue to the object is an important process in digital holography. Tohave the exact reconstruction of the object, the exact diffractionfield created by the object has to be calculated. In the literature,one of the commonly used approach in calculation of the diffractionfield due to an object is to superpose the fields created by theelementary building blocks of the object; such procedures may becalled as the ``source model" approach and such a computed field canbe different from the exact field over the entire space. In thiswork, we propose four algorithms to calculate the exact diffractionfield due to an object. These proposed algorithms may be called asthe ``field model" approach. In the first algorithm, the diffractionfield given over the manifold, which defines the surface of theobject, is decomposed onto a function set derived from propagatingplane waves. Second algorithm is based on pseudo inversion of thesystem matrix which gives the relation between the given fieldsamples and the field over a transversal plane. Third and fourthalgorithms are iterative methods. In the third algorithm,diffraction field is calculated by a projection method onto convexsets. In the fourth algorithm, pseudo inversion of the system matrixis computed by conjugate gradient method. Depending on the numberand the locations of the given samples, the proposed algorithmsprovide the exact field solution over the entire space. To computethe exact field, the number of given samples has to be larger thanthe number of plane waves that forms the diffraction field over theentire space. The solution is affected by the dependencies betweenthe given samples. To decrease the dependencies between the givensamples, the samples over the manifold may be taken randomly.Iterative algorithms outperforms the rest of them in terms ofcomputational complexity when the number of given samples are largerthan 1.4 times the number of plane waves forming the diffractionfield over the entire space.