Computation of holographic patterns between tilted planes

Computation of the diffraction pattern that gives the desired reconstruction of an object upon proper illumination is an important process in computer generated holography. A fast computational method, based on the plane wave decomposition of 3D field in free-space, is presented to find the desired diffraction pattern. The computational burden includes two FFT algorithms in addition to a shuffling of the frequency components that needs an interpolation in the frequency domain. The algorithm is based on the exact diffraction formulation; there is no need for Fresnel or Fraunhofer approximations. The developed model is utilized to calculate the scalar optical diffraction between tilted planes for monochromatic light. The performance of the presented algorithm is satisfactory for tilt angles up to 60°

Simulation of scalar optical diffraction between arbitrarily oriented planes

Scalar optical diffraction between arbitrarily oriented planes for monochromatic waves is analyzed and a simulator based on a discrete model is developed. The model is based directly on the Rayleigh-Sommerfeld diffraction integral; there is no need for Fresnel and Fraunhofer approximations. Furthermore, the model permits to use of the FFT algorithm. The simulator results are satisfactory

Bessel functions - Based reconstruction of non-uniformly sampled diffraction fields

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

Performance assessment of a diffraction field computation method based on source model

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

Reconstruction of scalar diffraction field from distributed data points over 3D space

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

Signal processing problems and algorithms in display side of 3DTV

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

Reconstruction of computer generated holograms by spatial light modulators

Computer generated holograms generated by using three different numerical techniques are reconstructed optically by spatial light modulators. Liquid crystal spatial light modulators (SLM) on transmission and on reflection modes with different resolutions were investigated. A good match between numerical simulation and optically reconstructed holograms on both SLMs was observed. The resolution of the optically reconstructed images was comparable to the resolution of the SLMs. © Springer-Verlag Berlin Heidelberg 2006