Representation-related errors in binary digital holograms: a unified analysis

Complementary computer generated holography for aesthetic watermarking

We present herein an original solution for the watermarking of holograms in binary graphic arts without unaesthetic diffractive effect. It is based on the Babinet principle of complementary diffractive structures adapted to Lohmann-type computer generated holograms. We introduce the concept and demonstrate its interest for anti-counterfeiting applications with the decoding of a hidden data matrix. A process of thermal lithography is used for the manufacturing of binary graphic arts containing complementary computer generated holograms.

Synthesis of three-dimensional light fields with binary spatial light modulators

Computation of a binary spatial light modulator (SLM) pattern that generates a desired light field is a challenging quantization problem for which several algorithms have been proposed, mainly for far-field or Fourier plane reconstructions. We study this problem assuming that the desired light field is synthesized within a volumetric region in the non-far-field range after free space propagation from the SLM plane. We use Fresnel and Rayleigh-Sommerfeld scalar diffraction theories for propagation of light. We show that, when the desired field is confined to a sufficiently narrow region of space, the ideal gray-level complex-valued SLM pattern generating it becomes sufficiently low pass (oversampled) so it can be successfully halftoned into a binary SLM pattern by solving two decoupled real-valued constrained halftoning problems. Our simulation results indicate that, when the synthesis region is considered, the binary SLM is indistinguishable from a lower resolution full complex gray-level SLM. In our approach, free space propagation related computations are done only once at the beginning, and the rest of the computation time is spent on carrying out standard image halftoning.

Selective mode excitation in graded-index multimode fiber by a computer-generated optical mask

We report on the generation of optical masks that permit the spatial shaping of a laser beam so that one can selectively excite single modes of a multimode parabolic graded-index optical fiber. The amplitude masks are determined by the analytical radial function of the fiber mode in the weakly guiding approximation. Phase reversal is encoded on the transparency through a shifted-grating technique. Effective injection and propagation of a single mode in a largely multimode fiber are shown as examples.

Optical binary phase-only filters for circular harmonic correlations

In our previous paper we proposed using successively binary cosine and sine filters and combining the correlation intensities for rotation-invariant phase-only circular harmonic correlation. This paper presents an alternative method that uses a single filter. We present theory and optical and computer experimental results to show that, with a spatial frequency carrier, the binary phase-only filter [1, -1] and the binary filter [1, 0] yield the impulse response of a continuous phase-only filter. Compared with conventional computer-generated holographic filters, the binary phase-only filter and the binary filter have no representation-related error, require a minimum space-bandwidth product, and may be implemented in a spatial light modulator.

Optical correlation CGHs with modulated error diffusion

Error diffusion presents a very attractive method for manufacturing computer-generated holograms. However, it has certain defects that make it unsuitable for various optical processing applications, such as correlation. We present an extension of error diffusion which makes it suitable for the implementation of correlation filters.

Parallel holographic generation of multiple Hough transform slices

Many uses for the Hough transform (HT) require only several theta slices, not the entire 2-D Hough space. A new holographic optical architecture is advanced to achieve this in parallel. The computer-generated holograms and holographic optical elements used are discussed, and laboratory results are provided. As a case study, we consider determining printing skew and other defects on cigarette packs. We also discuss how these holograms can produce the entire 2-D HT space.

Computer-generated holograms with error compensation

We analyze computer-generated holograms (CGH) of Lohmann types I and III and discuss their overall errors employing the following modifications, listed in order of increasing importance: phase-only correction (Ptype), virtual increase of the cell number, optimized use of the available plotting area, expansion of the amplitude dynamic range (D-type), circular overflow correction (OFC), and iterative overall error compensation. We compare the computing and plotting times for the listed CGH variants and their accuracy. As an application, we show the reconstruction of very complicated fields which may excite multimode and singlemode optical fibers, and a line grating with an in-between phase shift of 180 degrees ; the latter structure is useful in producing lambda/4-shifted semiconductor DFB lasers. Finally, we comment on some advanced techniques employing a desk-top computer and laser printer for producing hologram masks.

Comparison of binary encoding schemes for electron-beam fabrication of computer generated holograms

The suitability of various binary encoding methods for electron-beam recording of computer generated holograms is systematically evaluated. Subjected to the limitations of computing resources, a set of criteria is established according to which these encoding schemes are evaluated and compared. This comparison can be used to determine the optimum encoding method for desired wavefront properties.

Synthesis of digital holograms by direct binary search

A new approach to the design of computer-generated holograms makes optimal use of the available device resolution. An iterative search algorithm minimizes an error criterion by directly manipulating the binary hologram and observing the effect on the desired reconstruction. Several measures of error and efficiency useful in assessing the optimality of digital holograms are defined. Methods for designing digital holograms that are based on projections and error diffusion are presented as established techniques for comparison to direct binary search.

Reducing quantization error in Hsueh-Sawchuk holograms

Expressions for the quantization error in Hsueh-Sawchuk holograms are presented. These expressions suggest that the Hsueh-Sawchuk algorithm may be improved using a technique called prequantization. We demonstrate that the addition of prequantization reduces the quantization error in Hsueh-Sawchuk holograms by ~25%.