Fast calculation method for spherical computer-generated holograms

The synthesis of spherical computer-generated holograms is investigated. To deal with the staggering calculation times required to synthesize the hologram, a fast calculation method for approximating the hologram distribution is proposed. In this method, the diffraction integral is approximated as a convolution integral, allowing computation using the fast-Fourier-transform algorithm. The principles of the fast calculation method, the error in the approximation, and results from simulations are presented.     

Calculation method for computer-generated holograms with cylindrical basic object light by using a graphics processing unit

It takes an enormous amount of time to calculate a computer-generated hologram (CGH). A fast calculation method for a CGH using precalculated object light has been proposed in which the light waves of an arbitrary object are calculated using transform calculations of the precalculated object light. However, this method requires a huge amount of memory. This paper proposes the use of a method that uses a cylindrical basic object light to reduce the memory requirement. Furthermore, it is accelerated by using a graphics processing unit (GPU). Experimental results show that the calculation speed on a GPU is about 65 times faster than that on a CPU.     

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.     

Double-multiplexed computer-generated holograms

One of the detour-phase computer-generated-hologram encoding methods was improved for obtaining two objects simultaneously without increasing the plotter resolution. The encoded patterns were reconstructed along two orthogonal diffraction directions. Such a hologram could be useful for two-channel coherent or incoherent optical correlation. Laboratory experiments demonstrate the suggested technique.     

Optical phase step method for absolute ranging interferometry using computer-generated holograms

One main problem of an interferometric measurement is to evaluate the object distance from the interference function. One of the known methods that delivers the object phase is the phase step method. Here we introduce computer-generated holograms to realize parallel phase steps without phase modulation of the reference path.     

Calculation method of reflectance distributions for computer-generated holograms using the finite-difference time-domain method

The research on reflectance distributions in computer-generated holograms (CGHs) is particularly sparse, and the textures of materials are not expressed. Thus, we propose a method for calculating reflectance distributions in CGHs that uses the finite-difference time-domain method. In this method, reflected light from an uneven surface made on a computer is analyzed by finite-difference time-domain simulation, and the reflected light distribution is applied to the CGH as an object light. We report the relations between the surface roughness of the objects and the reflectance distributions, and show that the reflectance distributions are given to CGHs by imaging simulation.     

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.     

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.     

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.     

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.     

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.     

Interferometric testing for off-axis aspherical mirrors with computer-generated holograms

The interferometers with computer generated holograms (CGHs) have been used to measure off-axis aspherical mirrors. However, the conventional CGH interferometer could not produce a high lateral resolution because of the blur and the distortion of the interferogram of the test mirror caused by the nonzero order diffraction of the CGH. We further develop the application of CGHs concerning interferometers in order to improve the lateral resolution of the interferogram. In particular, we change the application of the CGH in such a way that the returned test beam passes through the CGH with zeroth order diffraction and demonstrates the performance of the CGH interferometer when used for the measurement of the primary mirror of the Okayama Astrophysical Observatory 3.8 m telescope project. As a result, our CGH interferometer produces a good interferogram with high resolution of 2.8 mm for the off-axis aspherical mirror with a size of 1.2 m. With improved usage of the CGH, we successfully demonstrated a high lateral resolution interferometer.     

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.     

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.     

Polarization-controlled multistage switch based on polarization-selective computer-generated holograms

We describe a polarization-controlled free-space optical multistage interconnection network based on polarization-selective computer-generated holograms: optical elements that are capable of imposing arbitrary, independent phase functions on horizontally and vertically polarized monochromatic light. We investigate the design of a novel nonblocking space-division photonic switch architecture. The multistage-switch architecture uses a fan-out stage, a single stage of 2 x 2 switching elements, and a fan-in stage. The architecture is compatible with several control strategies that use 1 x 2 and 2 x 2 polarization-controlled switches to route the input light beams. One application of the switch is in a passive optical network in which data is optically transmitted through the switch with a time-of-flight delay but without optical-to-electrical conversions at each stage. We have built and characterized a proof-of-principle 4 x 4 free-space switching network using three cascaded stages of arrayed birefringent computer-generated holographic elements. Data modulated at 20 MHz/channel were transmitted through the network to demonstrate transparent operation.     

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.     

Calculation method for computer-generated holograms considering various reflectance distributions based on microfacets with various surface roughnesses

Computer-generated holograms are generated by three-dimensional technology, and they can be used to reconstruct natural and virtual objects by simulating light waves based on holography. This research was an improvement on previous work that took into consideration reflectance distributions from the various roughnesses of objects. The previous work generated roughness by using a simple model, so that only simple roughness was generated. The proposed method generated more complex roughness than that in the previous work, and the influence of roughness on the reflectance distributions was investigated. Computer simulations, which were compared with the reflectance distributions from the various roughnesses, were carried out. Moreover, computational and optical reconstructions were carried out as examples of reconstructions. As a result of the experiments, we confirmed that the various roughnesses actually influenced the reflectance distributions.     

Double-ion-exchange process in glass for the fabrication of computer-generated waveguide holograms

We experimentally optimize double-ion-exchange process parameters to achieve a designed phase modulation for a wave front passing through a computer-generated waveguide hologram and numerically analyze the effects of fabrication errors. We also demonstrate a gradient-thickness waveguide hologram for ? beam splitting.     

Analytical design for computer-generated Fourier holograms of shaded multi-polygonal three-dimensional objects

We report here on design and computer simulation of computer-generated holograms for three dimensional (3D) imaging and display. Angular spectrum of general polygon patches was calculated in closed analytical form that includes angular dependence of the intensity and linear gradient of phase at each polygon. Special attention was paid to reduction of the dynamic range in the amplitude transmittance of the hologram by proper random choices of slopes and initial phases of each polygon. Numerical computer simulation results proved that our polygon-patched design demonstrates halftones of object shades and shows expected sharp focusing of different parts of the reconstructed 3D images in their different cross-sections.