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Abstract-Diffraction and holography are fertile areas for application of signal theory and processing. Recent work on 3DTV displays has posed particularly challenging signal processing problems. Various procedures to compute Rayleigh-Sommerfeld, Fresnel and Fraunhofer diffraction exist in the literature. Diffraction between parallel planes and tilted planes can be efficiently computed. Discretization and quantization of diffraction fields yield interesting theoretical and practical results, and allow efficient schemes compared to commonly used Nyquist sampling. The literature on computer-generated holography provides a good resource for holographic 3DTV related issues. Fast algorithms to compute Fourier, Walsh-Hadamard, fractional Fourier, linear canonical, Fresnel, and wavelet transforms, as well as optimization-based techniques such as best orthogonal basis, matching pursuit, basis pursuit etc., are especially relevant signal processing techniques for wave propagation, diffraction, holography, and related problems. Atomic decompositions, multiresolution techniques, Gabor functions, and Wigner distributions are among the signal processing techniques which have or may be applied to problems in optics. Research aimed at solving such problems at the intersection of wave optics and signal processing promises not only to facilitate the development of 3DTV systems, but also to contribute to fundamental advances in optics and signal processing theory.

Holography is usually considered as the ultimate way to visually reproduce a three-dimensional scene. Computer-generated holography constitutes an important branch of holography, which enables visualization of artificially generated scenes as well as real three-dimensional scenes recorded under white-light illumination. In this article, we present a comprehensive survey of methods for synthesis of computer-generated holograms, classifying them into two broad categories: wavefront-based methods and ray-based methods. We examine their modern implementations in terms of the quality of reconstruction and computational efficiency. As it is an integral part of computer-generated holography, we devote a special section to speckle suppression, which is also discussed under two categories following the classification of underlying computer-generated hologram methods.

The holographic wavefront printer decodes the wavefront coming from a three-dimensional object from a computer generated hologram displayed on a spatial light modulator. By recording this wavefront as an analog volume hologram this printing method is highly suitable for realistic color 3D imaging. We propose in the paper spatial partitioning of the spatial light modulator to perform mosaic delivery of exposures at primary colors for seamless reconstruction of a white light viewable color hologram. The method is verified for a 3 × 3 color partitioning scheme by a wavefront printer with demagnification of the light beam diffracted from the modulator.

Zero-order and twin images are a serious obstacle in achieving a high-quality output in in-line digital holography (DH). They decrease the useful bandwidth of the off-axis DH. Over the years the twin image removal problem was approached both by instrumental and numerical means. The paper provides an extended survey of the proposed solutions with their pros and cons as a guide for further advance in this field. Processing of a single spatial carrier fringe pattern involves spatial filtering in the frequency domain, spatial phase-shifting (PS) or wavelet transform. A point source digital holographic microscopy (DHM), introduction of calibration measurements or various modifications of PS technique are instrumental solutions to the twin image problem for in-line DH. Numerical solutions to the same problem include iterative and non-iterative approaches, diffraction-based and inverse problem solutions, reconstruction of purely real or phase objects and of complex objects, reconstruction of plane and volume objects. Elimination only of the zero-order image relies on non-linear filtering or additional calibration measurements.

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A new phase-added stereogram algorithm for accelerated computation of holograms from a point cloud model is proposed. The algorithm relies on the hologram segmentation, sampling of directional information, and usage of the fast Fourier transform with a finer grid in the spatial frequency domain than is provided by the segment size. The algorithm gives improved quality of reconstruction due to new phase compensation introduced in the segment fringe patterns. The result is finer beam steering leading to high peak intensity and a large peak signal-to-noise ratio in reconstruction. The feasibility of the algorithm is checked by the generation of 3D contents for a color wavefront printer.

The performance of direct and unwrapped phase retrieval, which combines digital holography with the transport of intensity, is examined in detail in this paper. In this technique, digital holography is used to numerically reconstruct the intensities at different planes around the image plane, and phase retrieval is achieved by the transport of intensity. Digital holography with transport of intensity is examined for inline and off-axis geometries. The effect of twin images in the inline case is evaluated. Phase-shifting digital holography with transport of intensity is introduced. The performance of digital holography with transport of intensity is compared with traditional off-axis single- and dual-wavelength techniques, which employ standard phase unwrapping algorithms. Simulations and experiments are performed to determine and compare the accuracy of phase retrieval through a mean-squared-error figure of merit as well as the computational speeds of the various methods.