Sampled fourier transform hologram generated by computer

Contribution to the Improvement of the Correlation Filter Method for Modal Analysis with a Spatial Light Modulator

Modal decomposition of light is essential to study its propagation properties in waveguides and photonic devices. Modal analysis can be carried out by implementing a computer-generated hologram acting as a match filter in a spatial light modulator. In this work, a series of aspects to be taken into account in order to get the most out of this method are presented, aiming to provide useful operational procedures. First of all, a method for filter size adjustment based on the standard fiber LP-mode symmetry is presented. The influence of the mode normalization in the complex amplitude encoding-inherent noise is then investigated. Finally, a robust method to measure the phase difference between modes is proposed. These procedures are tested by wavefront reconstruction in a conventional few-mode fiber.

Pupil-aberration calibration with controlled illumination for quantitative phase imaging

Quantitative phase imaging (QPI) exploits sample-induced changes in the optical field to analyze biological specimens in a label-free manner. However, the quantitative nature of QPI makes it susceptible to optical aberrations. We propose a method for calibrating pupil aberrations by imaging a sample of interest. The proposed method recovers pupil information by utilizing the cross-spectral density between optical fields at different incident angles and allows both thin and weakly scattering three-dimensional samples for calibration. We experimentally validate the proposed method by imaging various samples, including a resolution target, breast tissue, and a polystyrene bead, and demonstrate aberration-free two- and three-dimensional QPI.

High spatial resolution pixel synthesis structure for full-complex amplitude modulation with twisted nematic LCD

Various optics applications require a low-cost twisted nematic LCD that can modulate phase and amplitude independently. We propose a high spatial resolution light-synthesis structure that achieves full-complex amplitude modulation with a twisted nematic LCD. The synthesis structure uses two sparse lateral-shift pixel arrays for the x direction and four sparse lateral-shift pixel arrays for the y direction. The structure recreates an image with two superpixels formed from pairs of adjacent pixels in both directions, and as a result, the spatial resolution is only halved in both directions, which yields an appropriate image quality for the synthesis technique. In experiments, we demonstrate the precise control of amplitude and phase using a twisted nematic LCD.

Holography with Photochromic Diarylethenes

Photochromic materials are attractive for the development of holograms for different reasons: they show a modulation of the complex refractive index, meaning they are suitable for both amplitude and phase holograms; they are self-developing materials, which do not require any chemical process after the light exposure to obtain the final hologram; the holograms are rewritable, making the system a convenient reconfigurable platform for these types of diffractive elements. In this paper, we will show the features of photochromic materials, in particular diarylethenes in terms of the modulation of a transparency and refractive index, which are mandatory for their use in holography. Moreover, we report on the strategies used to write binary and grayscale holograms and their achieved results. The outcomes are general, and they can be further applied to other classes of photochromic materials in order to optimize the system for achieving high efficiency and high fidelity holograms.

Measurement of a Temperature Field Generated by a Synthetic Jet Actuator using Digital Holographic Interferometry

This paper shows the possibility of the measurement of a temperature field generated by heated fluid from a synthetic jet (SJ) actuator. Digital holographic interferometry (DHI) was the main measuring method used for the experiments. A single-projection DHI was used for the visualization of the temperature field as an average temperature along the optical axis. The DHI results are compared with data obtained from constant current anemometry (CCA) experiments for the validation of the method. Principle of 3D temperature distribution using a tomographic approach is also described in this paper. A single SJ actuator, multiple continual nozzle, and the SJ actuator with two output orifices are used as a testing device for the presented experiments. The experimental configuration can measure high-frequency synthetic jets with the use of a single slow-frame-rate camera. Due to the periodic character of the SJ flow, synchronization between the digital camera, and the external trigger driving the phenomenon is performed. This approach can also distinguish between periodic and random parts of the flow.

Study of wide-spectrum and high-resolution diffraction optical elements by stacks of binary phase gratings

This work theoretically investigates wide-spectrum and high-resolution diffraction optical elements that are made of stacks of low-resolution binary phase gratings, whereby the two-dimensional grids in different grating layers are arranged with specified displacements. We remodel the common kinoform algorithm for this multi-scale architecture. Numerical computations show that, by increasing the number of stacking layers, the resolution of the far-field image can be improved and also that the optical elements are more insensitive to variations of incident wavelengths at the cost of part accuracy of the image reconstructions. Practical concern focuses on largely increasing the number of grating layers and efficiency of the optical designs in theory and on the manufacture of stacks of ultra-thin grating films.

Deep-learning-generated holography

We present a method for computer-generated holography based on deep learning. The inverse process of light propagation is regressed with a number of computationally generated speckle data sets. This method enables noniterative calculation of computer-generated holograms (CGHs). The proposed method was experimentally verified with a phase-only CGH.

Dynamic spatial filtering using a digital micromirror device for high-speed optical diffraction tomography

Optical diffraction tomography (ODT) is an emerging microscopy technique for three-dimensional (3D) refractive index (RI) mapping of transparent specimens. Recently, the digital micromirror device (DMD) based scheme for angle-controlled plane wave illumination has been proposed to improve the imaging speed and stability of ODT. However, undesired diffraction noise always exists in the reported DMD-based illumination scheme, which leads to a limited contrast ratio of the measurement fringe and hence inaccurate RI mapping. Here we present a novel spatial filtering method, based on a second DMD, to dynamically remove the diffraction noise. The reported results illustrate significantly enhanced image quality of the obtained interferograms and the subsequently derived phase maps. And moreover, with this method, we demonstrate mapping of 3D RI distribution of polystyrene beads as well as biological cells with high accuracy. Importantly, with the proper hardware configuration, our method does not compromise the 3D imaging speed advantage promised by the DMD-based illumination scheme. Specifically, we have been able to successfully obtain interferograms at over 1 kHz speed, which is critical for potential high-throughput label-free 3D image cytometry applications.

Multispectral metasurface hologram at millimeter wavelengths

We demonstrate a computer-generated metasurface hologram in which four distinct images are encoded at four different W-band (75-110 GHz) frequencies. The metasurface hologram consists of a planar array of resonant metamaterial elements excited by a collimated reference beam incident on the hologram at an oblique angle. Each of the images is encoded by a subset of metamaterial elements that are resonant at the specific excitation frequency and are spatially positioned to achieve a desired phase distribution in the plane in conjunction with the reference wave. The phase-only hologram is optimized using the Gerschberg-Saxton algorithm. The four well-defined images are produced at specific distances within the Fresnel zone of the aperture.

Transmission-Type 2-Bit Programmable Metasurface for Single-Sensor and Single-Frequency Microwave Imaging

The programmable and digital metamaterials or metasurfaces presented recently have huge potentials in designing real-time-controlled electromagnetic devices. Here, we propose the first transmission-type 2-bit programmable coding metasurface for single-sensor and single- frequency imaging in the microwave frequency. Compared with the existing single-sensor imagers composed of active spatial modulators with their units controlled independently, we introduce randomly programmable metasurface to transform the masks of modulators, in which their rows and columns are controlled simultaneously so that the complexity and cost of the imaging system can be reduced drastically. Different from the single-sensor approach using the frequency agility, the proposed imaging system makes use of variable modulators under single frequency, which can avoid the object dispersion. In order to realize the transmission-type 2-bit programmable metasurface, we propose a two-layer binary coding unit, which is convenient for changing the voltages in rows and columns to switch the diodes in the top and bottom layers, respectively. In our imaging measurements, we generate the random codes by computer to achieve different transmission patterns, which can support enough multiple modes to solve the inverse-scattering problem in the single-sensor imaging. Simple experimental results are presented in the microwave frequency, validating our new single-sensor and single-frequency imaging system.

Generation and characterization of a perfect vortex beam with a large topological charge through a digital micromirror device

Optical vortices are associated with a spatial phase singularity. Such a beam with a vortex is valuable in optical microscopy, hyper-entanglement, and optical levitation. In these applications, vortex beams with a perfect circle shape and a large topological charge are highly desirable. But the generation of perfect vortices with high topological charges is challenging. We present a novel method to create perfect vortex beams with large topological charges using a digital micromirror device (DMD) through binary amplitude modulation and a narrow Gaussian approximation. The DMD with binary holograms encoding both the spatial amplitude and the phase could generate fast switchable, reconfigurable optical vortex beams with significantly high quality and fidelity. With either the binary Lee hologram or the superpixel binary encoding technique, we were able to generate the corresponding hologram with high fidelity and create a perfect vortex with topological charge as large as 90. The physical properties of the perfect vortex beam produced were characterized through measurements of propagation dynamics and the focusing fields. The measurements show good consistency with the theoretical simulation. The perfect vortex beam produced satisfies high-demand utilization in optical manipulation and control, momentum transfer, quantum computing, and biophotonics.

Overlap relation between free-space Laguerre Gaussian modes and step-index fiber modes

We investigated the overlap relation of the free-space Laguerre-Gaussian modes to the corresponding linearly polarized modes of a step-index fiber. To maximize the overlap for an efficient coupling of the free-space modes into a fiber, the scale-dependent overlap was theoretically and experimentally determined. The presented studies pave the way for further improvement of free-space to fiber optical connections.

Mode-resolved gain analysis and lasing in multi-supermode multi-core fiber laser

Multi-core fibers (MCFs) with coupled-cores are attractive large-mode area (LMA) specialty fiber designs that support the propagation of a few transverse modes often called supermodes (SMs). Compared to other LMA fibers, the uniqueness of MCF arises from the higher degrees of design space offered by a multitude of core-array geometries, resulting in extended flexibility to tailor SM properties. To date, the use of MCF as gain media has focused on lasers that operate in only one selected SM, typically the lowest order in-phase SM, which considerably limited the potential of these multi-core structures. Here, we expand the potential of MCF lasers by investigating multi-SM amplification and lasing schemes. Amplifier and laser systems using a 7 coupled-cores Yb-doped MCF as gain medium were successfully designed and assembled. Individual SM could be decomposed using the correlation filter technique mode analysis and the modal amplification factors (γi) were recorded. With access to amplification characteristics of individual transverse modes, a monolithic MCF laser was demonstrated that operates simultaneously on the two SMs carrying the highest optical gain.

GPC light shaper: static and dynamic experimental demonstrations

Generalized Phase Contrast (GPC) is an efficient method for generating speckle-free contiguous optical distributions useful in diverse applications such as static beam shaping, optical manipulation and, recently, for excitation in two-photon optogenetics. GPC allows efficient utilization of typical Gaussian lasers in such applications using binary-only phase modulation. In this work, we experimentally verify previously derived conditions for photon-efficient light shaping with GPC [Opt. Express22(5), 5299 (2014)]. We demonstrate a compact implementation of GPC for creating practical illumination shapes that can find use in light-efficient industrial or commercial applications. Using a dynamic spatial light modulator, we also show simple and efficient beam shaping of reconfigurable shapes geared towards materials processing, biophotonics research and other contemporary applications. Our experiments give ~80% efficiency, ~3x intensity gain, and ~90% energy savings which are in good agreement with previous theoretical estimations.

GPC light shaper for speckle-free one- and two-photon contiguous pattern excitation

Generalized Phase Contrast (GPC) is an efficient method for generating speckle-free contiguous optical distributions useful in diverse applications such as static beam shaping, optical manipulation and recently, for excitation in two-photon optogenetics. To fully utilize typical Gaussian lasers in such applications, we analytically derive conditions for photon efficient light shaping with GPC. When combined with the conditions for optimal contrast developed in previous works, our analysis further simplifies GPC's implementation. The results of our analysis are applied to practical illumination shapes, such as a circle and different rectangles commonly used in industrial or commercial applications. We also show simple and efficient beam shaping of arbitrary shapes geared towards biophotonics research and other contemporary applications. Optimized GPC configurations consistently give ~84% efficiency and ~3x intensity gain. Assessment of the energy savings when comparing to conventional amplitude masking show that ~93% of typical energy losses are saved with optimized GPC configurations.

Modal characterization of fiber-to-fiber coupling processes

We present a detailed experimental investigation of a fiber-to-fiber coupling process by characterizing the mode content at the output of the system. In our experiment a single-mode fiber is transversally scanned with respect to a multimode fiber, revealing position-dependent higher-order mode excitation. The outlined measurement system can be used for automated optimization of fundamental mode content and beam quality. Additionally, our approach characterizes the modal transmission properties of the multimode waveguide in its present state and is hence of high relevance for the conception of transport fibers and fiber laser systems.

Replication of Holograms with Corn Syrup by Rubbing

Corn syrup films are used to replicate holograms in order to fabricate micro-structural patterns without the toxins commonly found in photosensitive salts and dyes. We use amplitude and relief masks with lithographic techniques and rubbing techniques in order to transfer holographic information to corn syrup material. Holographic diffraction patterns from holographic gratings and computer Fourier holograms fabricated with corn syrup are shown. We measured the diffraction efficiency parameter in order to characterize the film. The versatility of this material for storage information is promising. Holographic gratings achieved a diffraction efficiency of around 8.4% with an amplitude mask and 36% for a relief mask technique. Preliminary results using corn syrup as an emulsion for replicating holograms are also shown in this work.

Fast M2 measurement for fiber beams based on modal analysis

We report on a fast and experimentally easy technique for measuring the beam propagation ratio M(2) of light guided by optical fibers. A holographic filter enables us to determine amplitudes and phases of the excited fiber eigenmodes. The coherent superposition of modes allows the reconstruction of the optical field. With this information at hand, we are able to simulate the free-space propagation of the beam and to perform a virtual caustic measurement. Associated beam propagation ratios M(2) accurately agree with ISO-standard measurements.

Effects of aliasing on the fidelity of a two dimensional array of foci generated with a kinoform

This paper investigates, through simulation and experiment, the behavior of two dimensional foci arrays generated via phase-only holography where an iterative algorithm was used to produce the kinoforms. Specifically, we studied how aliasing of the signal on a spatial light modulator affects the quality of the foci array as the density and size of the array are varied. This study provides a reference for applications where it is important to understand how the fidelity and overall quality of the foci array changes as the number of foci increases and as the spacing between foci decreases.

Improvement of grayscale representation of the horizontally scanning holographic display

The horizontally scanning holographic display has increased viewing angle and display screen size as compared to conventional holographic displays. Elementary holograms, which are generated by a high-speed SLM and projected by an anamorphic imaging system, are aligned horizontally by a galvano mirror. When the frame rate of the SLM is high, the width of the elementary holograms becomes several times as large as their horizontal display pitch so that several sets of elementary holograms can be displayed. A laser is modulated to illuminate different elementary hologram sets by different laser powers. The grayscale representation of reconstructed images is improved by properly designing the elementary hologram sets and the illumination laser powers.

Complete modal decomposition for optical fibers using CGH-based correlation filters

The description of optical fields in terms of their eigenmodes is an intuitive approach for beam characterization. However, there is a lack of unambiguous, pure experimental methods in contrast to numerical phase-retrieval routines, mainly because of the difficulty to characterize the phase structure properly, e.g. if it contains singularities. This paper presents novel results for the complete modal decomposition of optical fields by using computer-generated holographic filters. The suitability of this method is proven by reconstructing various fields emerging from a weakly multi-mode fiber (V approximately 5) with arbitrary mode contents. Advantages of this approach are its mathematical uniqueness and its experimental simplicity. The method constitutes a promising technique for real-time beam characterization, even for singular beam profiles.

Rapid hologram updates for real-time volumetric information displays

We have demonstrated that holograms incorporating changes in three-dimensional (3D) scenes can be recalculated in real time to present dynamic updates on information displays. This approach displays 3D information in a compatible format for fast and reliable interpretation of changes in the 3D scenes. The rapid-update algorithm has been demonstrated by real-time computation and transcription of the holograms to our digital micromirror device hologram projection system for visual validation of the reconstruction. The reported algorithm enables full parallax 1024 x 768 pixel holograms of 3D scenes to be updated at a rate of 0.8 s with a 1.8 GHz personal computer. Volumetric information displays that can enhance reliable data assimilation and decrease reaction times for applications such as air-traffic control, cockpit heads-up displays, mission crew stations, and undersea navigation can benefit from this research.

Phase-shifting with computer-generated holograms written on a spatial light modulator

We propose a new computer-controlled phase-shifting method based on computer-generated holograms (CGHs) displayed on a spatial light modulator (SLM). In this method the accurate phase shifts required in phase-shifting digital holography or interferometry are induced by a suitable transformation of the encoding patterns of the CGH displayed on a SLM. Both the theoretical analysis and the experimental results demonstrate the feasibility of this approach. We also discuss possible applications of this method in the field of interferometric null testing of aspheres.

Encoding amplitude and phase information onto a binary phase-only spatial light modulator

We report what to our knowledge is a new technique for encoding both amplitude and phase information onto a single binary-valued spatial light modulator. In our approach, we spatially modulate the diffraction efficiency of the filter. Light that is not diffracted into the first order is sent into the zero order, effectively allowing amplitude modulation of either the first-order or zero-order diffracted light. This technique has applications in both optical pattern recognition and image processing. Experimental results are included.

On-axis computer-generated holograms based on centrosymmetric partitioning of the pixel

A novel, to our knowledge, configuration for the design and fabrication of zero-order computer-generated holograms in which each pixel is split into two centrosymmetric equal-sized regions is proposed and tested. In a manner similar to other approaches this configuration also permits the encoding and the reconstruction of a complex function that exhibits phase as well as amplitude variations by use of a phase-only filter. A detailed mathematical analysis is followed by evaluation of the error of the encoding approach, which is calculated and compared with the error exhibited by other approaches. Computer simulations as well as optical experiments demonstrate the capabilities of this novel configuration.

Two-pixel computer-generated hologram with a zero-twist nematic liquid-crystal spatial light modulator

We present a method of producing a computer-generated hologram by use of a zero-twist linear nematic liquid-crystal spatial light modulator. A 2x1 macro pixel method is used; one pixel represents the real data, and one, the imaginary. A method is shown that produces both positive and negative analog amplitude modulation.

Gray-level computer-generated hologram filters for multiple-object correlation

Synthesis of gray-level computer-generated holograms allows for an increase of the information storage capability that is usually achieved with conventional binary filters. This is mainly because more degrees of freedom are available. We propose to profit from this feature by synthesizing complex filters formed by many superimposed holograms, each with a different carrier frequency. We apply these gray-level filters to perform multichannel correlation and in this way enhance the capability of optical correlators to process the information in parallel and simultaneously. First, we analyze the behavior of some performance criteria on the impulse response and on the correlation as a function of the number of holograms that are multiplexed. Then we show the results of two experiments: In the first a composed phase-only filter is used in a multiple-object recognition process. In the second a composed synthetic discriminant function filter is used to implement an object classification by means of a binary code.

Filter implementation technique for multicriteria characterization of coding domains in the joint transform correlator

An improved method for implementing correlation filters in the joint transform correlator architecture is proposed. We derived the method from computer-generated holography techniques. It allows us to use any correlation filters, especially ones that provide an optimal trade-off between noise robustness, peak sharpness, and optical efficiency, with any spatial light modulator (SLM). This method also allows for an objective comparison of the performance of the coding domains of various SLM's.

Computer-generated holograms to produce high-density intensity patterns

A computer-generated hologram consisting of N x N resolution cells produces a reconstructed image consisting of N x N sampling points. Since the width of the primary peaks in the point-spread function is twice the pitch of the sampling points, the intensity at intermediate points between the sampling points depends on the interference between the sampling points. Carefully controlling the complex amplitudes of the sampling points makes it possible to control the intensity not only at the sampling points but also at the intermediate points; the intensity of the reconstructed image can be controlled at 2N x 2N points. Preliminary experiments demonstrating the generation of high-density intensity patterns were performed.

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.

Encoding technique for design of zero-order (on-axis) Fraunhofer computer-generated holograms

Diffractive optical elements able to generate zero-order (on-axis) distributions with phase as well as amplitude distributions are described. The proposed elements are surface relief plates, i.e., phase-only elements, that are based on the concept of computer-generated masks followed by common etching processes. The encoding method assumes fixed spatial partitioning of the cell and a phase-only value allocated to each subelement. The reconstructed amplitude and phase distributions contain imperfections (noise) resulting from the encoding process. Methods of error reduction and improvements are provided.

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.

Nonlinear filtering in object and Fourier space in a joint transform optical correlator: comparison and experimental realization

The use of different kinds of nonlinear filtering in a joint transform correlator are studied and compared. The study is divided into two parts, one corresponding to object space and the second to the Fourier domain of the joint power spectrum. In the first part, phase and inverse filters are computed; their inverse Fourier transforms are also computed, thereby becoming the reference in the object space. In the Fourier space, the binarization of the power spectrum is realized and compared with a new procedure for removing the spatial envelope. All cases are simulated and experimentally implemented by a compact joint transform correlator.

Application of position encoding to a complex joint transform correlator

Because a joint transform correlator can be used as a general optical signal processor, complex-impulse-response implementations in the spatial domain are often requested. We introduce a position-encoding technique with which complex-valued references for the joint transform correlator can be obtained with an amplitude-modulated spatial light modulator. A proof-of-concept experiment is also provided.

Computer-generated multiple-object discriminant correlation filters: design by simulated annealing

The computer generation of multiple-object discriminant correlation filters is studied. The quantization of filter functions influences the correlation response. This may cause misdetection or incorrect classification of patterns and is especially serious in the case of multiple-object discriminant filters. We propose synthesizing the matched-filter functions by the simulated-annealing algorithm. The recording of Lohmann-type computer-generated holograms is considered. By this method the filter functions can be encoded with a reduction in the quantization levels of amplitude and phase. Acomputer simulation is performed, and the expected correlation responses are obtained.

Mirror hologram recording with a phase-change medium

We propose mirror hologram recording with a phase-change material, which has a large refractive-index difference between its amorphous and crystalline states. It offers excellent diffraction efficiency and is erasable and nonvolatile. We designed an optimum multilayer structure for high diffraction efficiency by simulating the effect of each film thickness on diffraction efficiency. Experiments with a germanium tellurium alloy as the phase-change material show a high diffraction efficiency close to the calculated value. This medium can also be used for directly drawing computer-generated holograms. Lee-type computer-generated holograms were drawn on this medium with optical-disk technology.

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.

Design and analysis of fixed planar holographic interconnects for optical neural networks

A neural-network architecture of multifaceted planar interconnection holograms and optoelectronic neurons is analyzed. Various computer-generated hologram techniques are analyzed and tested for their ability to produce an interconnection hologram with high-accuracy interconnects and high diffraction efficiency. A new technique is developed by using the Gerchberg-Saxton algorithm, followed by a random-search error minimization that produces the highest interconnect accuracy and the highest diffraction efficiency of the techniques tested. Analysis of the system shows that the hologram has the capacity to connect 5000 neuron outputs to 5000 neuron inputs with bipolar synapses and that the encoded synaptic weights have an accuracy of ~5 bits. A simple feedback system is constructed and demonstrated.

Optical multiscale morphological processor using a complex-valued kernel

Morphological transformations are typically performed on binary images by convolution with a binary kernel, which is followed by a threshold. We present an alternate approach that uses a complex-valued kernel with odd symmetry to perform these morphological operations. The complex-valued kernel increases the information-processing ability of the processor with no increase in system complexity. One advantage is that the processor operates on all constant regions of a gray-level image in parallel. A scale-space representation of this processor is obtained by varying the size of the kernel continuously through a range of scales. By using redundant information in the scale representation, this system is found to be robust in the presence of noise and spatial nonuniformities in the image. An optical system to perform morphological filtering based on this system is presented.

Pattern recognition with quantized computer-generated filters

The influence of the quantization levels used in the computer-generated filter on the correlation is studied. Two types of objects, binary characters and gray-tone objects, are used in the scene and in the test. The filters are codified by the method proposed by Burckhardt. Three different filters (a classical matched filter, a high-frequency-enhanced filter, and an amplitude-encoded phase-only filter) are generated, and the influence of the quantization levels in such cases is studied. Numerical and experimental results are obtained.

Cyclic matrix representation for sequential multiplication of complex matrices

A cyclic matrix representation for complex numbers is proposed for sequential multiplication of complex matrices. The related optical implementation is discussed.

Hybrid acousto-optic and digital equalization for microwave digital radio channels

Digital radio transmission systems use complex modulation schemes that require powerful signal-processing techniques to correct channel distortions and to minimize bit error rates. We propose combining the computation power of acousto-optic processing and the accuracy of digital processing to produce a hybrid channel equalizer that exceeds the performance of digital equalization alone. Analysis shows that a hybrid equalizer for 256-level quadrature amplitude modulation (QAM) performs better than a digital equalizer for 64-level QAM.

Experiments on annealed binary phase only filters fabricated with electron beam lithography

A binary phase only filter is encoded using a simulated annealing algorithm to distinguish two similar characters. Characters that cannot be distinguished with conventional filter encoding methods are clearly distinguished with the annealed binary phase only filter in a computer simulation. Two binary phase only filters have been fabricated by use of electron beam lithography and chemical etching. One is an annealed binary phase only filter, and the other is a binary phase only filter encoded with a conventional method. Optical pattern recognition experiments using the filters agree well with computer simulation results.

Efficient electron beam pattern data format for the production of binary computer generated holograms

Current pattern data formats for electron beam lithography are specifically designed to meet the needs of the VLSI industry. As a result, pattern data file size is often the limiting factor in the production of a binary computer generated hologram and not the spatial bandwidth product. This paper explores one alternate pattern data format that facilitates the full utilization of the e-beam machine's spatial bandwidth product without introducing prohibitive amounts of pattern data. The pattern data format uses two well-established data compression techniques specifically tailored to remove the redundancies present in holographic fringe patterns.