Browsing by Subject "Diffraction fields"

Now showing 1 - 6 of 6

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
Effect of sample locations on computation of the exact scalar diffraction field (in English)
(IEEE, 2012) Esmer, G. B.; Özaktaş, Haldun M.; Onural, Levent
Computer generated holography is one of common methods to obtain three-dimensional visualization. It can be explained by behavior of propagating waves and interference. To calculate the scalar diffraction pattern on a hologram, there are myriad of algorithms in the literature. Some of them employ several approximations, so the calculated fields may not be the exact scalar diffraction field. However, there are algorithms to compute the exact scalar diffraction field with some limitations on the distribution of the given samples over the space. These algorithms are based on "field model" approach. The performance of an algorithm, based on field model, is investigated according to the distribution of given samples over the space. From the simulations, it was observed that the cumulative information provided by the given samples has to be enough to solve the inverse scalar diffraction field. The cumulative information can be increased by having more samples, but there are some scenarios that differential information obtained from the given samples can be infinitesimal, thus the exact diffraction field may not be computed. © 2012 IEEE.
Open Access
Exact diffraction calculation from fields specified over arbitrary curved surfaces
(Elsevier, 2011-07-30) Esmer, G. B.; Onural, L.; Özaktaş, Haldun M.
Calculation of the scalar diffraction field over the entire space from a given field over a surface is an important problem in computer generated holography. A straightforward approach to compute the diffraction field from field samples given on a surface is to superpose the emanated fields from each such sample. In this approach, possible mutual interactions between the fields at these samples are omitted and the calculated field may be significantly in error. In the proposed diffraction calculation algorithm, mutual interactions are taken into consideration, and thus the exact diffraction field can be calculated. The algorithm is based on posing the problem as the inverse of a problem whose formulation is straightforward. The problem is then solved by a signal decomposition approach. The computational cost of the proposed method is high, but it yields the exact scalar diffraction field over the entire space from the data on a surface.
Open Access
Scalar diffraction field calculation from curved surfaces via Gaussian beam decomposition
(Optical Society of America, 2012-06-29) Şahin, E.; Onural, L.
We introduce a local signal decomposition method for the analysis of three-dimensional (3D) diffraction fields involving curved surfaces. We decompose a given field on a two-dimensional curved surface into a sum of properly shifted and modulated Gaussian-shaped elementary signals. Then we write the 3D diffraction field as a sum of Gaussian beams, each of which corresponds to a modulated Gaussian window function on the curved surface. The Gaussian beams are propagated according to a derived approximate expression that is based on the Rayleigh-Sommerfeld diffraction model. We assume that the given curved surface is smooth enough that the Gaussian window functions on it can be treated as written on planar patches. For the surfaces that satisfy this assumption, the simulation results show that the proposed method produces quite accurate 3D field solutions.
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
Thereconstruction quality improvement of holographic stereograms via variable size segmentation
(IEEE, 2010) Şahin, Erdem; Onural, Levent; Kang, Hoonjong
As computer generated holograms becomes more common, the fast computation of holographic interference patterns in digital environment becomes a necessity. Since the computation time of holograms via Fresnel (or Rayleigh-Sommerfeld) diffraction models makes real time applications impossible, the holographic stereograms are developed to be a solution for this problem. Holographic stereograms divide the hologram plane into segments. In phase added stereograms the coordinates of 3D source points are used while calculating the diffraction field. And that enables to calculate the diffraction field with appropriate sized FFTs. Although the phase added stereograms are advantageous in terms of computation time, the quality of the reconstructed three dimensional images may not be satisfactory. The main reason is that the diffraction field of a given point source is approximated as a pure complex sinusuoid in each segment. To increase the reconstruction quality, we propose a method that uses variable sized segments, as opposed to previously developed holographic stereograms that use fixed sized segments. While approximating the diffraction field of a point source, higher frequency regions are covered with smaller segments and lower frequency regions with larger segments. As a result of this, we keep the total number of oscillations of pure sinusoidal waves constant in each segment. The simulations that we carried out for a point source show that we are able to obtain better quality reconstruction with our method. ©2010 IEEE.