%0 Journal Article
%T On the Stability of Reconstruction of Irregularly Sampled Diffraction Fields
%A Vladislav Uzunov
%A Atanas Gotchev
%A Karen Egiazarian
%J Advances in Optical Technologies
%D 2010
%I Hindawi Publishing Corporation
%R 10.1155/2010/138024
%X This paper addresses the problem of reconstruction of a monochromatic light field from data points, irregularly distributed within a volume of interest. Such setting is relevant for a wide range of three-dimensional display and beam shaping applications, which deal with physically inconsistent data. Two finite-dimensional models of monochromatic light fields are used to state the reconstruction problem as regularized matrix inversion. The Tikhonov method, implemented by the iterative algorithm of conjugate gradients, is used for regularization. Estimates of the model dimensionality are related to the number of degrees of freedom of the light field as to show how to control the data redundancy. Experiments demonstrate that various data point distributions lead to ill-poseness and that regularized inversion is able to compensate for the data point inconsistencies with good numerical performance. 1. Introduction Many optical applications require a generation and control of light fields. Digital processing by computers is an attractive way of implementing such operations as it overcomes possible physical limitations of analog devices. However, signal processing has to be suitably coupled with the otherwise naturally continuous optical signals. This coupling requires effective discrete representation of the continuous functions, associated with the light fields. From one point of view, the discrete representation of a light field should preserve the degrees of freedom of the continuous model which describes the physical properties of the field. From another point of view, the discrete representation should admit the requirements on the light field which are imposed by the application. Three-dimensional (3D) imaging deals with the reconstruction of captured optical signals by digital means as CCD arrays and recreation of synthetic or computer generated, 3D data by holographic means [1]. Light beam shaping requires the reconstruction or synthesis of light beams which maintain certain properties along their propagation [2]. This paper addresses the problem of monochromatic light field reconstruction from ensemble of data samples with free positions, distributed within a volumetric region of interest. Setting the light field specification at a nonuniform irregular grid of points is rather general and can be utilized in a wide range of applications. For example, computer generated holography [3] reconstructs a light field to approximate a synthetic or a captured object, given its 3D abstract model¡ªa point cloud, mesh, NURBS, and so forth [4]. The data provided by
%U http://www.hindawi.com/journals/aot/2010/138024/