Single-element diffractive optical system for real-time processing of synthetic aperture radar data

I present an optical system for the polar formatting of data in a spotlight-mode synthetic aperture radar. This system is implemented with only one diffractive optical element (DOE). Previously such a DOE could not be produced because the phase of the required transmission function of the DOE does not obey the continuity condition, which is a prerequisite for the conventional implementation of such optical transforms. Here I show how a DOE can be produced to perform the complete polar-formatting transform by incorporating branch-point phase singularities in the transmission function of the DOE. The computation of the transmission function is shown, and numerically computed diffraction patterns obtained from this DOE are also shown.     

Optical Hough-transform processor with a two-dimensional array of computer-generated holograms

An optical implementation of the Hough transform that uses a two-dimensional array of computergenerated holograms based on a direct-binary-search algorithm is investigated. A Hough-transform filter consisting of 16 × 16 Fourier-transform direct-binary-search computer-generated holograms is examined. A novel matrix format, which uses the parameter domain in the Hough transform instead of a conventional orthogonal coordinate system, enables highly flexible fabrication of a Hough-transform filter by reducing constraints for reconstructed sample points of a computer-generated hologram. A completed Hough-transform filter has excellent performance both in the quality of the reconstructed image and in diffraction efficiency.     

Optical wavelet processor by holographic bipolar encoding and joint-transform correlation

A novel optical wavelet processor based on the techniques of the joint-transform correlator and computer-generated holograms is proposed. A coding technique that is a simplified version of Lee's hologram [Appl. Opt. 9, 639 (1970)] is used to represent positive and negative values for the object signal and wavelet functions. We experimentally demonstrate that wavelet transforms of two different daughter wavelet functions can be simultaneously obtained by the appropriate arrangement of the daughter wavelet functions and the object signal on the input plane.     

Computer-generated holograms on a metal ion-doped polymer system: contact copying

Dichromated poly(acrylic acid) films with dimethyl formamide have been used as a real-time recording medium for volume transmission holograms. In this study a simple computer-generated holographic grating with a sinusoidal amplitude profile is copied onto this recording material by the contact-copying technique. The experimental setup for the contact copying of a computer-generated hologram (CGH) is explained, and the phase modulation is observed for a different exposure time. Theoretical and experimental diffraction efficiency values for the CGH copy are also evaluated. Photographs of the original and copy of the CGH on the photopolymer film are presented.     

Object recognition using three-dimensional optical quasi-correlation

A novel method of three-dimensional (3-D) object recognition is proposed. Several projections of a 3-D target are recorded under white-light illumination and fused into a single complex two-dimensional function. After proper filtering, the resulting function is coded into a computer-generated hologram. When this hologram is coherently illuminated, a correlation space is reconstructed such that light peaks indicate the existence and locations of true targets in the observed 3-D scene. Experimental results and comparisons with results of another 3-D object recognition technique are presented.     

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.     

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.     

氖原子束计算全息编码成像模拟研究

将计算全息技术、原子光学及微细加工技术相结合，得出一种氛原子束计算全息编码成像技术，它弥补了利用激光梯度场控制原子堆积只能制作单一量子点、线等周期性图形的不足。对该技术进行了模拟研究，结果表明，可以制作所需的任意超微细结构图形，特征线宽可达纳米量级。     

Computer-generated holograms of three-dimensional realistic objects recorded without wave interference

We propose a method of synthesizing computer-generated holograms of real-life three-dimensional (3-D) objects. An ordinary digital camera illuminated by incoherent white light records several projections of the 3-D object from different points of view. The recorded data are numerically processed to yield a two-dimensional complex function, which is then encoded as a computer-generated hologram. When this hologram is illuminated by a plane wave, a 3-D real image of the object is reconstructed.     

One-dimensional collimation of laser array outputs

We consider a computer-generated hologram for the one-dimensional collimation in x of the output from a linear laser-diode array in y. Our concern is to produce one-dimensional pencil beams from each laser diode with small cross talk between the output from the separate laser diodes. Such outputs can be used in matrix-vector, neural net, and interconnection applications. The efficiency and the design of the computer-generated hologram are detailed, and initial optical laboratory results with an electron-beam recorded computer-generated hologram are presented.     

Computational reconstruction of images from holograms

The equations to reconstruct an image plane from a hologram are developed. This development is carried out for planes parallel to the hologram, which allows fast computation through the use of fast Fourier transforms. Algorithms for a digital computer are developed so images can be reconstructed, both with and without the Fresnel approximation, from a digitized hologram without the need for three-dimensional optical reconstruction equipment. Examples of holographically recorded images of marine micro-organisms are shown. A computational method for counting the number of micro-organisms in the holographically recorded volume is developed, and an example is provided.     

Three types of computer-generated hologram synthesized from multiple angular viewpoints of a three-dimensional scene

We describe various techniques to synthesize three types of computer-generated hologram (CGH): the Fresnel-Fourier CGH, the Fresnel CGH, and the image CGH. These holograms are synthesized by fusing multiple perspective views of a computer-generated scene. An initial hologram is generated in the computer as a Fourier hologram. Then it can be converted to either a Fresnel or an image hologram by computing the desired wave propagation and imitating an interference process of optical holography. By illuminating the CGH, a 3D image of the objects is constructed. Computer simulations and experimental results underline the performance of the suggested techniques.     

Frequency and phase swept holograms in spectral hole-burning materials

A new hologram type in spectral hole-burning systems is presented. During exposure, the frequency of narrow-band laser light is swept over a spectral range that corresponds to a few homogeneous linewidths of the spectrally selective recording material. Simultaneously the phase of the hologram is adjusted as a function of frequency-the phase sweep function. Because of the phase-reconstructing properties of holography, this recording technique programs the sample as a spectral amplitude and phase filter. We call this hologram type frequency and phase swept (FPS) holograms. Their properties and applications are summarized, and a straightforward theory is presented that describes all the diffraction phenomena observed to date. Thin FPS holograms show strongly asymmetric diffraction into conjugated diffraction orders, which is an unusual behavior for thin transmission holograms. Investigations demonstrate the advantages of FPS holograms with respect to conventional cw recording techniques in freq ncymultiplexed data storage. By choosing appropriate phase sweep functions, various features of holographic data storage can be optimized. Examples for cross-talk reduction, highest diffraction efficiency, and maximal readout stability are demonstrated. The properties of these FPS hologram types are deduced from theoretical considerations and confirmed by experiments.     

Computing the Electric and Magnetic Green’s Functions in General Electrically Gyrotropic Media

A method for an approximate computation of the electric and magnetic Green’s functions for the time-harmonic Maxwell’s equations in the general electrically gyrotropic materials is proposed. This method is based on the Fourier transform meta-approach: the equations for electric and magnetic fields are written in terms of images of the Fourier transform with respect to space variables and as a result of it the linear algebraic systems for finding Fourier images of the columns of the Green’s functions are obtained. The explicit formulas for the solutions of the obtained systems have been found. Finally, elements of the Green’s functions are determined by the inverse Fourier transform in the space of tempered distributions. The approximate computation of the inverse Fourier transform has been implemented by MATLAB tools. The computational experiments confirm the robustness of the method.     

Exact complex-wave reconstruction in digital holography

We address the problem of exact complex-wave reconstruction in digital holography. We show that, by confining the object-wave modulation to one quadrant of the frequency domain, and by maintaining a reference-wave intensity higher than that of the object, one can achieve exact complex-wave reconstruction in the absence of noise. A feature of the proposed technique is that the zero-order artifact, which is commonly encountered in hologram reconstruction, can be completely suppressed in the absence of noise. The technique is noniterative and nonlinear. We also establish a connection between the reconstruction technique and homomorphic signal processing, which enables an interpretation of the technique from the perspective of deconvolution. Another key contribution of this paper is a direct link between the reconstruction technique and the two-dimensional Hilbert transform formalism proposed by Hahn. We show that this connection leads to explicit Hilbert transform relations between the magnitude and phase of the complex wave encoded in the hologram. We also provide results on simulated as well as experimental data to validate the accuracy of the reconstruction technique.     

Fast calculation method for computer-generated cylindrical holograms

Since a general flat hologram has a limited viewable area, we usually cannot see the other side of a reconstructed object. There are some holograms that can solve this problem. A cylindrical hologram is well known to be viewable in 360 deg. Most cylindrical holograms are optical holograms, but there are few reports of computer-generated cylindrical holograms. The lack of computer-generated cylindrical holograms is because the spatial resolution of output devices is not great enough; therefore, we have to make a large hologram or use a small object to fulfill the sampling theorem. In addition, in calculating the large fringe, the calculation amount increases in proportion to the hologram size. Therefore, we propose what we believe to be a new calculation method for fast calculation. Then, we print these fringes with our prototype fringe printer. As a result, we obtain a good reconstructed image from a computer-generated cylindrical hologram.     

Hardware architecture of high-performance digital hologram generator on the basis of a pixel-by-pixel calculation scheme

In this paper we propose a hardware architecture for high-speed computer-generated hologram generation that significantly reduces the number of memory access times to avoid the bottleneck in the memory access operation. For this, we use three main schemes. The first is pixel-by-pixel calculation, rather than light source-by-source calculation. The second is a parallel calculation scheme extracted by modifying the previous recursive calculation scheme. The last scheme is a fully pipelined calculation scheme and exactly structured timing scheduling, achieved by adjusting the hardware. The proposed hardware is structured to calculate a row of a computer-generated hologram in parallel and each hologram pixel in a row is calculated independently. It consists of and input interface, an initial parameter calculator, hologram pixel calculators, a line buffer, and a memory controller. The implemented hardware to calculate a row of a 1920×1080 computer-generated hologram in parallel uses 168,960 lookup tables, 153,944 registers, and 19,212 digital signal processing blocks in an Altera field programmable gate array environment. It can stably operate at 198 MHz. Because of three schemes, external memory bandwidth is reduced to approximately 1/20,000 of the previous ones at the same calculation speed.     

Dual Computer-generated Holograms for Testing Aspherical Surfaces

The use of a dual computer-generated hologram for performing interferometric testing of aspherical surfaces is described. The dual hologram consists of apertures whose positions are modulated along two different directions. The dual hologram allows the simultaneous generation of two different wavefronts whose sum and difference can be obtained with appropriate spatial filtering. This has been proved theoretically and verified experimentally. Finally, the dual hologram is utilized to test steep aspherics, and some practical advances of the dual hologram are mentioned.     

64-channel correlator implementing a Kohonen-like neural network for handwritten-digit recognition

We present an optical implementation of an improved version of the Kohonen map neural network applied to the recognition of handwritten digits taken from a postal code database. Improvements result from the introduction of supervision during the learning stage, a technique that also simplifies the map layer labeling. The experimental implementation is based on a frequency-multiplexed raster computer-generated hologram used to realize the required N(4) interconnection. The setup is shown to be equivalent to a 64-channel correlator. Computer simulations are used to study various detection and classification procedures. The results of the optical experiments, obtained with binary phase computer-generated holograms, are presented and shown to be in excellent agreement with the simulations.     

Suppression of undesired diffraction orders of binary phase holograms

A method to remove undesired diffraction orders of computer-generated binary phase holograms is demonstrated. Normally, the reconstruction of binary Fourier holograms, made from just two phase levels, results in an undesired inverted image from the minus first diffraction order, which is superposed with the desired one. This can be avoided by reconstructing the hologram with a diffuse light field with a pseudorandom, but known, phase distribution, which is taken into account for the hologram computation. As a consequence, only the desired image is reconstructed, whereas all residual light is dispersed, propagating as a diffuse background wave. The method may be advantageous to employ ferroelectric spatial light modulators as holographic display devices, which can display only binary phase holograms, but which have the advantage of fast switching rates.