Projection-Slice Theorem as a Tool for Mathematical Representation of Diffraction

Cataloged from PDF version of article.Although the impulse (Dirac delta) function has been widely used as a tool in signal processing, its more complicated counterpart, the impulse function over higher dimensional manifolds in R-N, did not get such a widespread utilization. Based on carefully made definitions of such functions, it is shown that many higher dimensional signal processing problems can be better formulated, yielding more insight and flexibility, using these tools. The well-known projection-slice theorem is revisited using these impulse functions. As a demonstration of the utility of the projection-slice formulation using impulse functions over hyperplanes, the scalar optical diffraction is reformulated in a more general context

Sampling of the diffraction field

Cataloged from PDF version of article.When optical signals, like diffraction patterns, are processed by digital means the choice of sampling density and geometry is important during analog-to-digital conversion. Continuous band-limited signals can be sampled and recovered from their samples in accord with the Nyquist sampling criteria. The specific form of the convolution kernel that describes the Fresnel diffraction allows another, alternative, full-reconstruction procedure of an object from the samples of its diffraction pattern when the object is space limited. This alternative procedure is applicable and yields full reconstruction even when the diffraction pattern is undersampled and the Nyquist criteria are severely violated. Application of the new procedure to practical diffraction-related phenomena, like in-line holography, improves the processing efficiency without creating any associated artifacts on the reconstructed-object pattern. (C) 2000 Optical Society of America. OCIS codes: 050.1940, 070.6020, 090.1760, 100.2000

Exact solution for scalar diffraction between tilted and translated planes using impulse functions over a surface

Cataloged from PDF version of article.The diffraction relation between a plane and another plane that is both tilted and translated with respect to the first one is revisited. The derivation of the result becomes easier when the impulse function over a surface is used as a tool. Such an approach converts the original 2D problem to an intermediate 3D problem and thus allows utilization of easy-to-interpret Fourier transform properties due to rotation and translation. An exact solution for the scalar monochromatic propagating waves case when the propagation direction is restricted to be in the forward direction is presented. (C) 2011 Optical Society of America

Television in 3-D: What are the prospects?

Cataloged from PDF version of article.Examines the possibilities being explored for three-dimensional television

Diffraction from a wavelet point of view

Cataloged from PDF version of article.The system impulse response representing the Fresnel diffraction is shown to form a wavelet family of functions. The scale parameter of the wavelet family represents the depth (distance). This observation relates the diffraction-holography-related studies and the wavelet theory. The results may be used in various optical applications such as designing robust volume optical elements for optical signal processing and finding new formulations for optical inverse problems. The results also extend the wavelet concept to the nonbandpass family of functions with the implication of new applications in signal processing. The presented wavelet structure, for example, is a tool for space-depth analysis

Utilization of the recursive shortest spanning tree algorithm for video-object segmentation by 2-D affine motion modeling

Cataloged from PDF version of article.A novel video-object segmentation algorithm is proposed, which takes the previously estimated 2-D dense motion vector field as input and uses the generalized recursive shortest spanning tree method to approximate each component of the motion vector field as a piecewise planar function. The algorithm is successful in capturing 3-D planar objects in the scene correctly, with acceptable accuracy at the boundaries. The proposed algorithm is fast and requires no initial guess about the segmentation mask. Moreover, it is a hierarchical scheme which gives finest to coarsest segmentation results. The only external parameter needed by the algorithm is the number of segmented regions that essentially control the level at which the coarseness the algorithm would stop. The proposed algorithm improves the “analysis model” developed in the European COST211 framework

Scalar diffraction field calculation from curved surfaces via Gaussian beam decomposition

Cataloged from PDF version of article.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. (C) 2012 Optical Society of Americ

Introduction to the Special Section on 3DTV

Cataloged from PDF version of article.The set of six papers that we invited to this part of the Special Section present extensive reviews of the state-of-the-art in functional building blocks of 3DTV systems

Real-time phase-only color holographic video display system using LED illumination

Cataloged from PDF version of article.A real-time full-color phase-only holographic display system generates holograms of 3D objects. The system includes a 3D object formed by voxels, an internet-based transmission capability that transmits the object information to the server, a real-time hologram generation unit, and a holographic display unit with incoherent illumination. The server calculates three phase holograms for RGB components using multiple GPUs. The resultant phase holograms are saved into an RGB bitmap image and loaded to the phase-only spatial light modulators (SLMs). SLMs are illuminated uniformly by LEDs, and reconstructed waves are aligned and overlapped by using high precision optics and stages. Experimental results are satisfactory. © 2009 Optical Society of America

Graphics processing unit accelerated computation of digital holograms

Cataloged from PDF version of article.An approximation for fast digital hologram generation is implemented on a central processing unit (CPU), a graphics processing unit (GPU), and a multi-GPU computational platform. The computational performance of the method on each platform is measured and compared. The computational speed on the GPU platform is much faster than on a CPU, and the algorithm could be further accelerated on a multi-GPU platform. In addition, the accuracy of the algorithm for single-and double-precision arithmetic is evaluated. The quality of the reconstruction from the algorithm using single-precision arithmetic is comparable with the quality from the double-precision arithmetic, and thus the implementation using single-precision arithmetic on a multi-GPU platform can be used for holographic video displays. (C) 2009 Optical Society of America