Two-dimensional, three-dimensional, and gray-scale images reconstructed from computer-generated holograms designed by use of a direct-search method

A direct-search method for the computer design of holograms is demonstrated. Two-dimensional, three-dimensional, and containing holograms with different levels of intensity (gray scales) were designed, fabricated, and optically reconstructed. The number of effective gray levels and the image-intensity noise and contrast are discussed. A modification of the state-variables cost function used in the direct-search algorithm that permits reliable control of gray scales is presented. Optical reconstructions of two-dimensional, three-dimensional, and gray-scale binary phase computer-generated holograms are presented.     

Laser soldering with light-intensity patterns reconstructed from computer-generated holograms

We describe a laser soldering technology with diffractive optics. This technology provides efficient one-step laser illumination for components to be soldered. A phase-only computer-generated hologram set in a variable-focal-length optical configuration generates a diffraction pattern with the dimensions required for processing solder. We verified the effectiveness of the proposed scheme by sealing a ceramic package such that it could house a quartz device. The factors for successful soldering include alignment of the diffraction pattern to the work piece, the thermal properties of the materials involved, and the wavelength of the laser used to process the solder. The beam intensity across the diffraction pattern influences the process, and the 0th-order intensity should be minimized to prevent damage to the work piece.     

Computer-generated holograms of images reconstructed on curved surfaces

When one illuminates a computer-generated hologram by a plane wave, the obtained two-dimensional image is usually displayed on a planar plane. Other possibilities for reconstructing images on arbitrary curved surfaces are discussed herein. As an example, the reconstruction of an image on a virtual spherical surface is demonstrated.     

Design and fabrication of computer-generated beam-shaping holograms

For the design of computer-generated holograms reconstructing certain intensity patterns with phase freedom, we use an object-oriented approach. The given intensity pattern is decomposed into elementary objects for which appropriate phase-only hologram functions can be constructed. The total hologram function is found by the subsequent superposition of its constituents, with a relative amplitude and phase weighting for each of them. Thus, the degrees of freedom are dramatically reduced compared with those of sampling approaches. The design algorithm allows us to compensate on the one hand for the intensity and phase distribution of the impinging laser beam and on the other hand for the shape of the hologram aperture. We report on the computer-aided design of such holograms, as well as their fabrication through the use of laser lithography and reactive ion etching. Optical reconstructions are shown.     

Modifications of detour phase computer-generated holograms

The detour phase method for the design of computer-generated holograms can be modified to achieve multichannel reconstruction along various diffraction orders. It is shown how a single hologram can be used to display two patterns of different intensities along two diffraction orders. This is achieved by the release of any requirement on the phase distributions of these patterns, thus leaving them as free parameters. Various algorithms are suggested to make possible nonidentical reconstructions along two different off-axis diffraction orders. The two reconstruction orders can be chosen arbitrarily. The case of four-channel reconstructions for generating four different images is discussed as well. Computer simulations and optical experiments were carried out to demonstrate the capabilities of the proposed approaches.     

Design of computer-generated beam-shaping holograms by iterative finite-element mesh adaption

Computer-generated phase-only holograms can be used for laser beam shaping, i.e., for focusing a given aperture with intensity and phase distributions into a pregiven intensity pattern in their focal planes. A numerical approach based on iterative finite-element mesh adaption permits the design of appropriate phase functions for the task of focusing into two-dimensional reconstruction patterns. Both the hologram aperture and the reconstruction pattern are covered by mesh mappings. An iterative procedure delivers meshes with intensities equally distributed over the constituting elements. This design algorithm adds new elementary focuser functions to what we call object-oriented hologram design. Some design examples are discussed.     

Multiplexed computer-generated holograms with polygonal-aperture layouts optimized by genetic algorithm

Using a novel genetic algorithm (GA) with a Lamarckian search we optimize the polygonal layout of a new type of multiplexed computer-generated hologram (MCGH) with polygonal apertures. A period ofthe MCGH is divided into cells, and the cell is further divided into polygonal apertures according to a polygonal layout, which is to be optimized. Among an ensemble of 1.21 x 10(24) possible polygonal layouts, we take a population of 102 solutions, which are coded as chromosomes of bits, and find the optimal solution with our GA. We introduce rank-based selection with cumulative normal distribution fitness, double crossover, exponentially decreasing mutation probability and Lamarckian downhill search with a small number of offspring chromosomes into our GA, which shows a rapid convergence to the global minimum of the cost function. In a second step of optimization the phase distributions over the subholograms in the MCGH are determined with our iterative subhologram design algorithm. Our MCGH designs show large-sie reconstructed images with high diffraction efficiency and low reconstruction error.     

Absolute interferometric test of aspheres by use of twin computer-generated holograms

A complete absolute interferometric test of axially symmetric aspheres is presented. The method is based on a specially designed computer-generated hologram (CGH) that reconstructs an aspherical wave as well as a spherical auxiliary wave. Since both phase functions have the same symmetry and their pattern is simultaneously encoded, we call this type of multiplex hologram a Twin-CGH. The spherical wave is used for calibration. The aberrations of the spherical auxiliary wave are measured absolutely with either a spherical mirror or an absolute test for Fresnel zone plates. Thus the two types of aberration inherent in the CGH can be identified and separated from each other. The errors of the spherical wave can be transferred to those of the aspherical wave. Two different methods thatuse Twin-CGHs for absolute testing of aspheric surfaces are described. Test procedures are explained, equations are derived, and experimental results are presented. A mutual comparison of the two results and a comparison with the established N-position rotation test are given.     

Analysis of phase sensitivity for binary computer-generated holograms

A binary diffraction model is introduced to study the sensitivity of the wavefront phase of binary computer-generated holograms on groove depth and duty-cycle variations. Analytical solutions to diffraction efficiency, diffracted wavefront phase functions, and wavefront sensitivity functions are derived. The derivation of these relationships is obtained by using the Fourier method. Results from experimental data confirm the analysis. Several phase anomalies were discovered, and a simple graphical model of the complex fields is applied to explain these phenomena.     

Fast numerical generation and encryption of computer-generated Fresnel holograms

In the past two decades, generation and encryption of holographic images have been identified as two important areas of investigation in digital holography. The integration of these two technologies has enabled images to be encrypted with more dimensions of freedom on top of simply employing the encryption keys. Despite the moderate success attained to date, and the rapid advancement of computing technology in recent years, the heavy computation load involved in these two processes remains a major bottleneck in the evolution of the digital holography technology. To alleviate this problem, we have proposed a fast and economical solution which is capable of generating, and at the same time encrypting, holograms with numerical means. In our method, the hologram formation mechanism is decomposed into a pair of one-dimensional (1D) processes. In the first stage, a given three-dimensional (3D) scene is partitioned into a stack of uniformed spaced horizontal planes and converted into a set of hologram sublines. Next, the sublines are expanded to a hologram by convolving it with a 1D reference signal. To encrypt the hologram, the reference signal is first convolved with a key function in the form of a maximum length sequence (also known as MLS, or M-sequence). The use of a MLS has two advantages. First, an MLS is spectrally flat so that it will not jeopardize the frequency spectrum of the hologram. Second, the autocorrelation function of an MLS is close to a train of Kronecker delta function. As a result, the encrypted hologram can be decoded by correlating it with the same key that is adopted in the encoding process. Experimental results reveal that the proposed method can be applied to generate and encrypt holograms with a small number of computations. In addition, the encrypted hologram can be decoded and reconstructed to the original 3D scene with good fidelity.     

Dual-wave-front computer-generated holograms for quasi-absolute testing of aspherics

Testing of aspherics by means of computer-generated holograms (CGHs) is well known. To perform a quasi-absolute test of rotationally symmetric aspheric surfaces, two wave fronts must be encoded in the CGH. Both the null lens and a spherical lens have to be stored. This enables successive measurements of the aspheric and of a cat's-eye position without changing the object arm of the interferometer. Two possibilities for encoding both wave fronts have been investigated. A first-order approximation for estimating the influence of disturbing diffraction orders is given.     

Rendering of specular surfaces in polygon-based computer-generated holograms

A technique is presented for realistic rendering in polygon-based computer-generated holograms (CGHs). In this technique, the spatial spectrum of the reflected light is modified to imitate specular reflection. The spectral envelopes of the reflected light are fitted to a spectral shape based on the Phong reflection model used in computer graphics. The technique features fast computation of the field of objects, composed of many specular polygons, and is applicable to creating high-definition CGHs with several billions of pixels. An actual high-definition CGH is created using the proposed technique and is demonstrated for verification of the optical reconstruction of specular surfaces.     

Multicriteria optimality for iterative encoding of computer-generated holograms

We propose a new multicriteria method for the determination of computer-generated holograms (CGH's). For this purpose, the direct binary search (DBS) algorithm for computing CGH's has been modified to converge on a new error function that defines the optimal trade-off among different criteria. This approach allows us to control the trade-off between the amplitude error and the diffraction efficiency and to provide a rigorous figure of merit. Comparisons among different encoding methods show that the best results are obtained with a modified version of the DBS method combined with the iterative Fourier transform algorithm.     

Fabrication error analysis and experimental demonstration for computer-generated holograms

Aspheric optical surfaces are often tested using computer-generated holograms (CGHs). For precise measurement, the wavefront errors caused by the CGH must be known and characterized. A parametric model relating the wavefront errors to the CGH fabrication errors is introduced. Methods are discussed for measuring the fabrication errors in the CGH substrate, duty cycle, etching depth, and effect of surface roughness. An example analysis of the wavefront errors from fabrication nonuniformities for a phase CGH is given. The calibration of these effects for a CGH null corrector is demonstrated to cause measurement error less than 1 nm.     

Rotation of nanowires with radially higher-order Laguerre-Gaussian beams produced by computer-generated holograms

In this paper, the influence of radially higher index p of Laguerre-Gaussian (LG) beams on the rotation of nanowires is studied. Radially higher-order LG beams are produced by computer-generated holograms, which are displayed on a spatial light modulator. A series of experiments on manipulating ZnO nanowires was performed on our holographic optical tweezers platform. The experiments demonstrated that radially higher-order LG beams could effectively rotate nanowires along the innermost bright ring of themselves. Compared with radially low-order LG beams, they have larger torques exerted on nanowires and can make nanowires rotate more quickly.     

Space-variant optical interconnection through the use of computer-generated holograms

A space-variant optical interconnection through the use of computer-generated holograms is proposed, and specific configurations to increase the number of parallel channels are analyzed. To this end, the well-known method based on a matrix composed of subholograms is applied. The field diffracted by each channel (assumed to be square apertures) is calculated through the angular-spectrum technique, and the resulting fields are suitably superimposed to obtain a hologram matrix with a reduced bandwidth. Results show that a compact transmissive planar configuration can be handled; in particular, the small interconnect distance between the array planes and the hologram yields a limited system volume.     

Polarization-selective computer-generated holograms: design, fabrication, and applications

We constructed polarization-selective computer-generated holograms that apply an independent phase profile during readout by horizontal and vertical light polarizations. These elements are composed of two surface-relief-etched birefringent substrates joined face to face. We describe the design methodology for arbitrary birefringent substrate and gap materials. We show how these holograms are fabricated with standard microelectronics technology and discuss the effects of etching and alignment errors on performance. We demonstrated a diffraction efficiency of 60% with a polarization contrast ratio of >100:1 using a multilevel phase hologram made from two birefringent lithium niobate substrates. We also showed that a single-layer SiO(2) thin-film antireflection coating on all surfaces can reduce reflections from the high-index substrates without significant effect on hologram performance. We also consider some possible applications of this technology and demonstrate experimentally a dual focal-length lens and a self-interconnecting binary 2 × 2 polarization switch.     

Three-dimensional shape recognition using computer-generated holograms and temporal light-in-flight technique

Visualization of light propagation and light in flight are general names for viewing a pulse of light traveling through an optical system. Abramson suggested [Appl. Opt. 30, 1242 (1991)] the use of light-in-flight techniques for holographic comparison of different objects. His system is based on sending picosecond pulses in such a sequence that, if the object has the desired shape, all the scattered light arrives simultaneously at an ultrafast detector. The result is that the shortness of the detected pulses is a measure of the similarity between a holographically recorded master object and the test object. The reference hologram is recorded from a master surface, which is not always available. This method suffers from low-contrast results. A computer-generated-hologram technique is suggested and mathematically analyzed. This technique overcomes the low-contrast problem, and a master object is not needed.     

Coupling of surface roughness to the performance of computer-generated holograms

Computer-generated holograms (CGHs), such as those used in optical testing, are created by etching patterns into an optical substrate. Imperfections in the etching can cause small scale surface roughness that varies across the pattern. The variation in this roughness affects the phase and amplitude of the wavefronts in the various diffraction orders. A simplified model is developed and validated that treats the scattering loss from the roughness as an amplitude effect. We demonstrate the use of this model for engineering analysis and provide a graphical method for understanding the application. Furthermore, we investigate the magnitude of this effect for the application of optical testing and show that the effect on measurement accuracy is limited to 1 nm for typical CGHs.     

Optimal annular computer-generated holograms for the generation of optical vortices

We analyze a method for efficiently generating optical vortices by use of annular computer-generated holograms and a spatial light modulator. We found that there exists an optimal annular width by which the reconstructed vortex ring in the focal plane has the steepest gradient and the worthless subbright rings can be largely suppressed. We fitted a general formula for determining the value of this optimal annular width and propose a method for designing a multiring structure of optical vortices and specialized interferometric vortex patterns. Finally, we discuss the situation of a Gaussian beam as illuminated light and find that there exists an optimal beam waist that results in the best energy efficiency.