The iterative alternating projections onto constraint sets (POCS) algorithm is applied to the design of computer-generated holograms (CGH's). The performance of the resulting CGH's is compared to those designed by the non-iterative error diffusion algorithm and direct binary search (DBS), which is another iterative technique. Both iterative methods are distinguished from earlier iterative methods for CGH design by their ability to simultaneously control the amplitude and phase of the reconstructed wavefront.

Generating a hologram by computer is essentially plotting a Fourier transform. Many of the hologram's properties are manifestations of simple Fourier mathematical relations. Although the relations are simple, finding the proper relation to explain an effect sometimes is not. The origin of this work was actually a question put to me some years ago about Fourier transforms in the context of image processing for scanning electron microscopy. The question: Why does a strong cross structure sometimes appear in an image's Fourier transform when we know that no corresponding structures exist in the object? The answer is well known, but let us delay discussing it until the next section where we explain the question's relevance to the computer generated hologram (CGH).

Computer codes for design of holograms have been developed by Teledyne Brown Engineering. Techniques have been incorporated to evaluate performance of holographic systems and to optimize the hologram design. This paper documents the hologram production methods and describes the performance evaluation and optimization techniques. This unique approach should accelerate the use of general purpose diffractive optics in numerous application areas.

Computer algorithms for the encoding of electron-beam written holographic optical elements (HOEs), previously developed on a large main-frame computer, have been ported to a desktop computer and upgraded to use a more prevalent a-beam lithography system. Hardware requirements, encoding methods, and space-bandwidth limitations are discussed. Inasmuch as the inefficiency of the a-beam pattern description language in describing non-repetitive, non-rectilinear hologram patterns remains the prime limiter of hologram space-bandwidth product, the transition to a desktop computer has been accomplished without penalty.

An algorithm is presented for the computation of large size FFTs for computer generated holograms. The algorithm is useful when the recording device has a very large space-bandwidth product, while the computation is under memory restrictions. The number of complex operations required using this algorithm is only slightly increased over the number of operations necessary using the FFT algorithm.

Computer Aided Design (CAD) systems that have been developed for electrical and mechanical design tasks are also effective tools for the process of designing Computer Generated Holograms (CGH), particularly when those holograms are to be fabricated using Electron Beam Lithography. CAD stations provide efficient and convenient means of computing, storing, displaying, and reformatting features that are common to many CGH encodings. CGH's have been designed on a CAD workstation using eight encoding methods. Though existing CAD workstations have many of the features that CGH design requires, suggestions are made so that future workstations may further accommodate the CGH design process.

Computer-generated holograms (CGHs) are used in a number of important optical technology application areas such as holographic optical elements, optical processing and computing, optical testing, image and information display, beam forming, and beam scanning. Many different CGH fabrication devices (e.g., laser beam scanners, electron beam writers) and facilities have been developed and are in use. However, none of these devices ideally suit the requirements (e.g., resolution, space-bandwidth product, recording material) of many CGH applications. Furthermore, the access of many researchers to these facilities is limited and the technical support available is often poor. New facilities specifically designed for CGH fab-rication would better serve the needs of the CGH research and development community. The requirements for a successful CGH fabrication facility including appropriate technical support for users are established.

This paper presents the use of a standard electron-beam lithography for the fabrication of computer-generated holograms (CGH).

This paper describes a procedure which utilizes a focused laser beam to record computer generated holograms. The potential for gray-scaling using this recording scheme is also investigated.

A computerized optical system has been constructed for the design and the generation of space-variant holographic filters. Special considerations on the computerized design of the space-variant filters and the operation and performances of the system are addressed and discussed. The system was experimentally employed to generate holographic optical filters for the optical implementations of Hough Transform, coordinate transformations, etc. Experimental performances of the generated space-variant filters are evaluated and discussed.

Computer generated holograms (CGHs) are an important tool in the realization of optical processing systems. One of the reasons why CGHs are receiving attention is that there are high resolution recording devices available. High quality CGHs can be made and can now be utilized in optical data processing systems and algorithms. Many different CGH coding schemes exist, and much research is being done to compare and find their characteristics. This report presents a laboratory comparison of eight different types of CGHs. The method of making the CGHs and the recorder used are discussed. The experimental results are then compared with the non-experimental results derived previously.

A diffractive microlens array was used to collimate a one-dimensional array of gain-guided AlGaAs lasers. The astigmatism of the lasers was removed by using anamorphic microlenses. The Strehl ratio of the resulting wavefront was 0.98. The microlens array was placed in an external cavity to produce a single coherent diffraction-limited beam from the AlGaAs laser array.

In recent years there has been a resurgent of research activities in the area of computer-generated holograms. The results of these activities have been the development of tools and methodologies for making the computer-generated holograms. The tools for making computer-generated holograms have progressed from the CRT displays, computer plotters and computer printers used in the 60's and 70's to more sophisticated systems such as laser scanners and E-beam graphic output devices. Many techniques for encoding the wavefront information into the holograms have been investigated 4. Moreover, the limitations imposed on the performance of the computer-generated holograms by the resolutions of the output systems have also been fully explored. It has also been recognized that computer-generated holograms are more versatile and are more compact than conventional lenses. However, the replacement of lenses by computer-generated holograms has not yet taken place due to difficulties both in material processing and fabrication in achieving high light diffraction efficiency in the holographic optics. It is interesting to note that computer-generated holograms belong to the class of diffractive optical elements. With this point of view, one discovers that computer-generated holograms have already been employed in many practical optical applications. For example, multiple beam gratings generated by computer or other means are used currently in compact disc audio players. More recently, computer-generated holograms are further utilized in compact audio disc players and optical disk drives to replace many of the conventional optical components. In this paper we will discuss a number of different computer-generated holograms which have been used in optical data storage systems. The fabrication process of each of these optical elements are also briefly reviewed.

Electron beam lithography is applicable to the fabrication of binary optics. Practical aspects of generating binary masks for zone plates and diffraction gratings using the Manu-facturing Electron Beam Exposure System (MEBES III) at Perkin-Elmer are discussed.

Binary optics is an emerging technology whereby light is directed, combined, or distributed by the surface of an optical material that has a binary, or "stepped," phase or transmission microstructure. Binary optical elements can be fabricated under computer control to behave as thin lenses, prisms, gratings, holograms, or phase plates, as the need arises. Their useful properties have been demonstrated in several applications at Perkin-Elmer.

A new concave semi-cylindrical reflection holographic stereogram, called the "reflection alcove hologram," offers computer-generated 3-D real images that project within the alcove space and offer a very wide angle of view. The hologram is viewed with a white light source, and is extendable to full-color imaging.

Reflective computer-generated holographic elements are used in a quasi-optical fashion to modify both the phase and polarization of a high-power coherent microwave beam. The design code currently allows any two-element, ofd axis configuration.

This paper describes fabrication of miniature holographic lenses to collimate the output beams from small-aperture systems such as optical fibers and diode lasers. Special attention is given to arrays of such elements. The lenses are created as computer generated holograms by two methods and then copied to form hybrid holograms.

Interest in holographic, or diffractive, optics has been rekindled in the last few years with demonstrated advances in three areas: computer-aided design (CAD) tools, VLSI lithographic and dry etching processes, and mathematical modeling of diffractive elements.1 The availability of CAD tools and electron-beam lithography led first to the emergence of computer-generated holography (CGH). CGH work at Honeywell was started and brought to maturity by Arnold2 in 1980-1983. However, because of the inherently low diffraction efficiency (-10%), lithographic CGHs have found a place in only a relatively few practical applications, such as testing diamond turned aspherics, and thus CGHs have not been widely accepted within industry. The first step in changing this situation came in the 1970s with numerical approaches to rigorously solve the vector field equations for diffraction from blazed gratings.3 The extensive numerical results from these models not only showed that high diffraction efficiencies are possible with etched surface profiles, but also indicated the sensitivity to various profile configurations and design parameters. Veldkamp et al.1,4'-'61 at MIT Lincoln Laboratories have taken the final step necessary to establish the practical feasibility of diffractive optics by using reactive ion etching techniques to produce the surface profiles prescribed by the numerical models and delineated by CGH lithographic masks. With this combined approach, they have demonstrated the feasibility of high-efficiency diffractive elements for a variety of diverse applications, such as the CO2 laser radar telescope,4 coherent beam addition of laser diode arrays,5 and on-axis, broadband, aspheric lens elements for infrared imagers.6 These elements are fabricated using well-established VLSI lithographic and dry etching techniques. Moreover, the ability to replicate each diffractive element provides the potential for high-volume, low-cost producibility. With this precedent, Honeywell has become convinced that the emerging diffractive optics technology may be practical for some of its products. To assess the technology and determine its utility, a major initiative program has been established at Honeywell Systems and Research Center to set up a complete design and prototype fabrication facility for diffractive optics. This paper summarizes the results of this activity.

The performance of computer-generated binary holograms recorded on a 128x128 pixel supports was studied experimentally, with the objective of recording holograms on spatial light modulators such as the Semetex SIGHT-MOD for rotation-invariant pattern recognition. Since the performance was unsatisfactory, a new method of diagonal coding was introduced. This method yields much better results, as it allows a more accurate phase quantization. Experimental results of computer simulations show that high-speed rotation-invariant recognition of simple shapes is possible with such holograms.

Conventional techniques of designing distortion-invariant filters for optical correlators presuppose the use of complex-valued filters. Synthetic-discriminant-functions (SDFs)," lock-and-tumble filters," and circular harmonic filters5 are examples of these methods. However, since programmable, complex-valued spatial-light-modulators (SLMs) do not exist and appear difficult to fabricate, the utility of these techniques for actual implementation are severely limited. On the other hand, programmable SLMs limited to quantized levels of amplitude and/or phase are presently available. Jared and Ennis6 recently proposed a modification to the conventional SDF approach which includes the filter modulation in the filter synthesis called filter-SDF (fSDF). They demonstrated that it is possible to construct a filter limited to binary modulation or phase modulation that will achieve a specified peak-correlation for a set of training images. The development of the fSDF approach was driven by the practical concern to make present-day SLMs with limited modulation capabilities functional for distortion-invariant pattern recognition. However, initial work on fSDFs did not examine the peak-correlation response for images in the distortion-range that were not members of the training set. This paper considers the performance of fSDF binary-phase-only-filters (BPOFs) for images in the distortion-range that were not members of the training set. This evaluation is essential towards understanding the number of training images necessary to span a distortion-range. As the extent of the distortion-range increases, the number of training images necessary to effectively cover the distortion-range increases. Since filters of limited modulation have an implicit information capacity, a trade-off occurs between the extent of the distortion-range and the performance of the correlator. This paper considers the nature of this trade-off for fSDF-BPOFs, and the likely constraints this trade-off will impose on a realized optical correlator. A brief review of the fSDF method is presented in Section 2. Aspects of the simulation are discussed in Section 3. The results of correlating fSDF-BPOFs with images not in the training set and the effect of increasing the distortion-range are presented in Section 4 for in-plane-rotation and out-of-plane-rotation. A discussion of these results and the conclusions reached are found in Sections 5 and 6, respectively.

We introduce the notion of the Optimal Phase-Only Filters (OPOF) which yield higher Signal-to-Noise Ratios (SNR) compared to the conventional phase-only filters. We illustrate this improvement in SNR resulting from the use of OPOF's with the help of simulation results.

Major limitations to the successful application of optical pattern recognition systems have usually been the memory requirements necessary for realistic tasks and the implementation of such optical memory techniques. Here, we have con-sidered the possibility of generating the NXN array of filters by using real-time computer generated holography where the Fourier transforms of the NXN reference image are produced in the computer. The NXN array of Fourier transform holograms are converted to phase-only encoded filters by utilizing the phase function of the Fourier transform elements of the array. The phase-only encoded NXN array is written onto a spatial light modulator for pattern recognition applications. Thus, a phase-only encoded correlator with high storage capacity is produced. An importamt feature of the proposed technique is the ability to update or change each element of the NXN filter array in real-time independent of the other members of the filter set. This feature does not exist in the previous large memory correlation techniques since the filters were stored on film and to change a member of the array required a new synthesis of the entire array. We shall study the performance of the proposed binary capacity correlator by determining the peak to sidelobe ratio and the bandwidth of the resulting correlation signals. The effects of phase-encoding and the finite space-bandwidth pro-duct of each element of the array will be studied. The effects of overlapping terms at the filter plane contributing to cross talk will also be investigated. Both binary phase-only encoding and continuous phase-only encoding are investigated and the results are compared to the multiplexed classical matched filters.