Browsing by Author "Uzunov, V."

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Open Access
Bessel functions-based reconstruction of non-uniformly sampled diffraction fields
(IEEE, 2007) Uzunov, V.; Esmer, G. Bora; Gotchev, A.; Onural, Levent; Özaktaş, Haldun M.
A discrete computational model for the diffraction process is essential in forward problems related to holographic TV. The model must be as general as possible, since the shape of the displayed objects does not bear any restrictions. We derive a discrete diffraction model which suits the problem of reconstruction of diffraction fields from a set of non-uniformly distributed samples. The only restriction of the model is the wave nature of the field. The derivation takes advantage of changing the spatial and frequency coordinates to polar form and ends up with a model stated in terms of Bessel functions. The model proves to be a separable orthogonal basis. It shows rapid convergence when evaluated in the framework of the non-uniform sampling problem.
Open Access
Diffraction field computation from arbitrarily distributed data points in space
(Elsevier BV, 2007-02) Esmer, G. B.; Uzunov, V.; Onural, L.; Özaktaş, Haldun M.; Gotchev, A.
Computation of the diffraction field from a given set of arbitrarily distributed data points in space is an important signal processing problem arising in digital holographic 3D displays. The field arising from such distributed data points has to be solved simultaneously by considering all mutual couplings to get correct results. In our approach, the discrete form of the plane wave decomposition is used to calculate the diffraction field. Two approaches, based on matrix inversion and on projections on to convex sets (POCS), are studied. Both approaches are able to obtain the desired field when the number of given data points is larger than the number of data points on a transverse cross-section of the space. The POCS-based algorithm outperforms the matrix-inversion-based algorithm when the number of known data points is large.
Open Access
Performance assessment of a diffraction field computation method based on source model
(IEEE, 2008-05) Esmer, G. Bora; Onural, Levent; Özaktaş, Haldun M.; Uzunov, V.; Gotchev, A.
Efficient computation of scalar optical diffraction field due to an object is an essential issue in holographic 3D television systems. The first step in the computation process is to construct an object. As a solution for this step, we assume that an object can be represented by a set of distributed data points over a space. The second step is to determine which algorithm provides better performance. The source model whose performance is investigated is based on superposition of the diffraction fields emanated from the hypothetical light sources located at the given sample points. Its performance is evaluated according to visual quality of the reconstructed field and its algorithmic complexity. Source model provides acceptable reconstructed patterns when the region in which the samples are given has a narrow depth along the longitudinal direction and a wide extent along the transversal directions. Also, the source model gives good results when the cumulative field at the location of each point due to all other sources tends to be independent of that location. ©2008 IEEE.
Open Access
Reconstruction of scalar diffraction field from distributed data points over 3D space
(IEEE, 2007) Esmer, G. Bora; Uzunov, V.; Onural, Levent; Gotchev, A.; Özaktaş, Haldun M.
Diffraction field computation is an important task in the signal conversion stage of the holographic 3DTV. We consider an abstract setting, where the diffraction field of the desired 3D scene to be displayed is given by discrete samples distributed over 3D space. Based on these samples, a model of the diffraction field should be built to allow the field computation at any desired point. In our previous works, we have proved our concepts for the simplistic 2D case. In this paper, we generalize the earlier proposed techniques, namely the projection onto convex sets and conjugate gradient based techniques and test them for their computational efficiency and memory requirements for a specific 3D case.
Open Access
Signal processing problems and algorithms in display side of 3DTV
(IEEE, 2006-10) Ulusoy, E.; Esmer, Gökhan Bora; Özaktaş, Haldun M.; Onural, Levent; Gotchev, A.; Uzunov, V.
Two important signal processing problems in the display side of a holographic 3DTV are the computation of the diffraction field of a 3D object from its abstract representation, and determination of the best display configuration to synthesize some intended light distribution. To solve the former problem, we worked on the computation of ID diffraction patterns from discrete data distributed over 2D space. The problem is solved using matrix pseudo-inversion which dominates the computational complexity. Then, the light field synthesis problem by a deflectable mirror array device (DMAD) is posed as a constrained linear optimization problem. The formulation makes direct application of common optimization algorithms quite easy. The simulations indicate that developed methods are promising. ©2006 IEEE.
Open Access
Three-dimensional monochromatic light field synthesis with a deflectable mirror array device
(SPIE, 2006) Ulusoy, Erdem; Uzunov, V.; Onural, Levent; Özaktaş, Haldun M.; Gotchev, A.
We investigated the problem of complex scalar monochromatic light field synthesis with a deflectable mirror array device (DMAD). First, an analysis of the diffraction field produced by the device upon certain configurations is given assuming Fresnel diffraction. Specifically, we derived expressions for the diffraction field given the parameters of the illumination wave and the tilt angles of the mirrors. The results of the analysis are used in later stages of the work to compute the samples of light fields produced by mirrors at certain points in space. Second, the light field synthesis problem is formulated as a linear constrained optimization problem assuming that mirrors of the DMAD can be tilted among a finite number of different tilt angles. The formulation is initially developed in the analog domain. Transformation to digital domain is carried out assuming that desired fields are originating from spatially bounded objects. In particular, we arrived at a Dp = b type of problem with some constraints on p, where D and b are known, and p will be solved for and will determine the configuration of the device. This final form is directly amenable to digital processing. Finally, we adapt and apply matching pursuit and simulated annealing algorithms to this digital problem. Simulations are carried out to illustrate the results. Simulated annealing performs successful synthesis when supplied with good initial conditions. However, we should come up with systematic approaches for providing good initial conditions to the algorithm. We do not have an appropriate strategy currently. Our results also suggest that simulated annealing achieves better results than MP. However, if only a part of the mirrors can be used, and the rest can be turned off, the performance of MP is acceptable and it turns out to be stable for different types of fields.