Following a general overview of applications and limitations of computer holography some comments on computer aided coding procedures and hologram geometries are given.

The light efficiency of computer generated Fourier holograms is compared for different amplitude distributions of the filter function. Then a tandem configuration with two separate phase filters is discussed. It allows a general wavefront modification with very high light efficiency.

The computation of binary Fourier transform holograms can be viewed as three sequential steps: 1) quantization of the object spectrum, 2) sampling of the object spectrum, and 3) binarization of the quantized, sampled spectrum to form the plottable hologram. The errors from each step in the computation are cumulative, and depend on the particular hologram encoding method used, as well as the parameter values associated with the process. A number of different methods for hologram synthesis are compared experimentally in terms of these errors. The results are related to an earlier analysis of images reconstructed from digital holograms. A procedure for optimally quantizing the object spectrum is also described.

A computer-generated hologram (CGH) for reconstructing independent NxN resolution points would actually require a hologram made up of NxN sampling cells. For dependent sampling points of Fourier transform CGHs, the required memory size for computation by using an interpolation technique for reconstructed image points can be reduced. We have made a mosaic hologram which consists of K x K subholograms with N x N sampling points multiplied by an appropriate weighting factor. It is shown that the mosaic hologram can reconstruct an image with NK x NK resolution points. The main advantage of the present algorithm is that a sufficiently large size hologram of NK x NK sample points is synthesized by K x K subholograms which are successively calculated from the data of N x N sample points and also successively plotted.

The results of a comparative experimental study of hologram coding methods using hybrid (opto-digital) techniques are presented. A series of Fresnel CGH (computer generated holograms) transparencies of a simple test object are produced using different binary and non-binary encoding schemes and the corresponding optically reconstructed images are compared and used to present and support the findings and conclusions of the study. A new binary hologram encoding method derived from the Lissajous pattern representation of amplitude and phase is also discussed and demonstrated. The method appears to furnish images with better quality than other binary encoding techniques because of better utilization of the degrees of freedom available for coding holographic data in each pixel of a purely amplitude modulating transparencies.

Various diagnostic procedures in medicine, industry and defense produce 3-Dimensional data bases adequate to calculate a hologram. In most cases the nearer to real time the hologram can be produced the more beneficial. Since a hologram is a superposition of Fresnel zone plate patterns from each point source in the object volume on to the image plane a cellular array processor is suggested which will produce a factor of a million reduction in the time to calculate a hologram.

Computer Generated holograms offer a wide variety of applications, specifically in the synthesis and processing of real and synthetic images. In this paper we examine and demonstrate the major aspects of recording these holograms using an ejectron beam exposure system (MEBES). Holographic patterns stored in memory can be recorded directly onto an electron sensitive resist with a IX format, thus requiring no reduction techniques. The MEBES system can record holograms as large as 12 cm. by 12 cm. square with a resolution of 500 cycles per mm. without significant distortions. The amount of information required to record such a hologram can far exceed 15 gigabytes. But by the method presented this process can be divided into manageable parcels (260k bytes) which are then combined to form a large scale hologram. The end effect of this project was to demonstrate that computer generated binary holograms can be recorded using an electron beam exposure system (MEBES). The results of this technique have been modest but more important, offer a promising future.

The E-beam pattern generators, developed for making masks for integrated circuits with submicron features, are extremely attractive for producing high quality computer generated holograms (CGH). The procedure for making the E-beam written CGH along with its properties will be described. Application of these CGH's to spatial frequency multiplexed optical processors for pattern recognition will be discussed.

We have produced highly efficient binary diffraction gratings -- 94% first order diffraction efficiency measured in the infrared (10.6 μm) on straight binary gratings and on binary holographic off-axis lenses. The observed point-spread functions of these lenses (F/10, f = 25 cm) were limited only by diffraction. To fabricate gratings we adapted IC production techniques. Our work brings together three independent developments: (1) theories on binary diffraction gratings operating in the EM domain, (2) large-scale integration (LSI) advances in pattern generation and substrate depositions, and (3) improvements in reactive ion-beam etching techniques.

In previous reports we described a way of writing very high accuracy binary computer holograms by CRT writing of interferometrically abutted cells. Because the amount of information which needs to be written is so great there is inadequate time for z modulation. We describe here a way of half toning in the CRT plane which can result in continuous tone on the hologram.

Optical filters which are capable of performing discrete two-dimensional coordinate transformations for space-variant image processing are described. Several examples of space variant image processing are given, including the application of conformal mapping to a problem in potential flow theory. With simple optical arrangements, both the forward and inverse transformations can be performed with the same filter. Production of these filters by a microcomputer controlled scanning Interferometric Pattern System is detailed.

Digital-phase gratings are synthetic optical elements operating in-line as direct-vision components. They are called digital because only a few discrete values are allowed for the phase-structure within each grating period. Digital-phase gratings can be used for different applications. Three examples are described: star-couplers using binary-phase gratings for generating a central block of diffraction orders with equal intensity; color-splitters using gratings with more than two phase-levels; alterable gratings the blaze of which can be switched between the 3 central diffraction orders. Surface-relief digital-phase gratings are made by reactive ion etching in glass, and cheap plastic copies are obtained by a simple replication technique.

The concept of a computer-generated polarization hologram (CPH) is based on the anisotropic interaction of light with photodichroic crystals. The most unique feature of this technique lies in the realization of phase information recording without the application of the detour phase or the optical path difference effect as used in the conventional technique. Basic principle of information writing and reading scheme using M-centers in alkali halide crystals such as sodium flouride ( NaF ) are descrived, and several technical merits and problems associated with this method are presented. This technique provides a real-time holographic system where accurate recordability and high storage capacity are attainable due to its possibility of recording a calcurated complex amplitude of wavefront only by means of controlling the polarization direction of illuminating beam. We also report on our trially developed automatic hologram making and reading system with the results of its operation experiment, and on discussions concerning the quality of the reconstructed image. We succeeded in completing a full automatic system which is able to make holograms automatically in a short time and in observing a reconstructed image of good quality in real-time.

A conceptually simple method for producing a hologram of a computer-specified object is to illuminate the photosensitive recording plate with a reference wave and trace out the object distribution with a point of light moved by a computer-controlled scanning system. The principal drawback is the poor signal-to-noise ratio (SNR) of the reconstructed object, because of bias buildup in the recording process. Two methods for improving reconstruction SNR are discussed in this paper: (1) maximizing the contrast of each fringe or zone-plate pattern exposing the hologram, and (2) recording intermediate holograms of portions of the object, which are then reconstructed for use in recording a final hologram of higher signal-to-bias ratio.

Displays have only one function: the conveying of information to human beings. To do this well, the display must be well suited to the human viewing-comprehending system. Evolving in a three-dimensional (3D) world, humans have an exquisitely tuned system for seeing in 3D. A display capable of providing information in 3D would have a significant advantages over its more common 2D competitors: television, the printed page, etc. The fact that 3D displays are not in common use can only mean that the existing 3D displays have major drawbacks. Indeed that is the case.

Theory and experiments in the area of computer-generated holograms for geometric transformations are presented. Geometric transform holograms are divided into two categories: (1) those which have a continuous fringe structure and (2) those which consist of a set of discrete subholograms. Criteria for the realizability of a continuous geometric transform hologram are described. Examples of both types of holograms are developed to map rings of different radii to a linear sequence of points. They allow the replacement of a ring detector by a linear detector array without loss of signal energy and can be applied to optical spectrum analysis and angle-wavelength multiplexing for data transmission through optical fibers.

Interest in optical logic systems has been revived recently for several reasons. One major reason is that optics provides a means for overcoming the communication bottlenecks which are beginning to limit the development of electronic systems both at the chip level and at higher levels. This stems from the fact that an optical system in effect processes a large number of independent parallel channels. However, in attempting to implement optical interconnection networks, one is quickly faced with the need to realize space-variant interconnections. In this paper we describe various means of achieving space-variant interconnections for optical logic systems. All of the techniques use computer-generated holograms (CGH) as combination beam-splitting and beam directing elements. The space-variance can be obtained with either a direct approach where a separate CGH element forms the interconnections for each logic element, or with a basis set approach which provides significant reductions in the CGH storage requirements. Examples of the different approaches are discussed.

We have recently proposed a new, simple method capable of optically implementing logic gates in parallel. This method requires image encoding for an input binary object. Introducing the concept of computer generated holographic filtering, two encoding methods for input binary objects have been presented. One is the method to obtain a 1-D coded image for an input binary object. The other is that to get a 2-D coded image for two input binary objects at a time.

Optical computing will have to meet the challenge of the tremendous progress actually made in the numerical field. We present prospective ideas towards the implementation of purely optical fast parallel Arithmetic and Logic Units (ALU). We first describe what could be envisionned as an electro-optical ALU system which would use a large adressable holographic memory. The corresponding (hypothetical) performance is shown to be not sufficient. The main idea which is proposed consists in trying to build processing units which can be "optically" connected together, without using any special propagating medium, or any special transducing property. As in instance, we describe an Elementary Optical Processing Unit (E.O.P.U.) based on a two-step diffraction principle. Then, a system is examined, in the aim of realizing a Purely Optical Parralel Processor (P.O.P.). Its principle would be based on a filtering process - FOUT filter - which is extended to the processing of 2 D. binary patterns, with a possible feedback implementation. The configuration of the system is studied in order to conceive the arithmetical and logical operations. It is also shown that such processors can present some associative performance. For the implementation, C.G.H. methods can be used. However, the real implementation of the filter leads to a singular problem which we have not been able to solve in general. In the last two sections, we finally propose simple logical operators based on Snell's law, and optical registers based on the propagation of very short light pulses in simple optical set-ups. The main characteristics of the proposed methods are due to the fundamental advantages of optics: speed, parallelism processing capabilities, connexion possibilities. However, severe limitations have been encountered all along the study, mostly due to the lack of non-linear possibilities. In general, these ideas will have to be tested in practice, regarding the available techniques, and particularly the possible development of integrated optical technologies.

In this paper we describe the use of a multifacet holographic optical element which utilizes nearly all the energy in an incident Gaussian laser beam to form a gray tone output pattern or image.

The hybrid optical implementation of a real formalism of discrete fourier transform in terms of circular correlations is discussed. This approach makes possible to develop new architectures which are fully parallel both for the electronic and the optical parts of the system. As applications of the proposed system, correlation of 2 signals and multidimensional DFT's are considered.

A microwave kinoform that modifies both the phase and polarization of an incident wavefront has been designed. This kinoform for the TMX-U magnetic fusion experiment has been fabricated and tested. The design procedure, method of fabrication, and experimental test results are discussed.

In high energy physics experiments, pattern recognition in digital or analog data, is a current technical problem. Considerable effort is expended in these experiments in the development of real time and high speed decision making logic which is used as a rapid filter to enrich data samples with events of desired character. Optical processing techniques are a novel approach to this problem. It offers the advantage of parallel data treatment with a decision speed within 100 ns depending on the optoelectronic devices. A Prototype device was constructed in conjunction with a high energy physics experiment at Brookhaven National Laboratory in which the input data are transformed into an optical pattern through an array of LED's. The device is an incoherent correlator with a kinoform filter; The results are presented and discussed. Other applications are possible in which a computer generated hologram, like a kinoform, acts as an optical element which transforms points on a curve into parameters of that curve. This can solve a major problem in particle physics which is to recognize straight lines in parallel plate detectors. The recent progress and development of Ring Imaging Cerenkov Detectors need to detect a pattern on which the photons are disposed on a circle. It does appear that a great deal in the high energy physics will involve the production of jets. By driving light sources whose intensity is proportional to particle energy and by using a filter which contains geometrical informations, it is possible to calculate variables relating directly to jets, in real time.

An optical correlator combining most of the features required by a practical automatic control system has been built and used to control small series of work pieces. With the holographic matched filtering technique the optimization of the spatial filter leads to a well-defined response curve which is used to calibrate the output of the optical correlator in terms of shape error. It is shown, that the techniques of computer holograms offer the widest possibilities to perform this optimization. Simple examples show the capability of detecting shape errors of a few microns.

We have generated bidirectionnal spatial differentiation optical operators as synthetic holograms following the method of Lohmann. We use these filter holograms to perform mathematical operations: - the first and second order bidirectionnal spatial differentiation as Gradient and Laplacian operators, - the Exponential and Gaussian operators, High-pass and Low-pass filters. We have tried to apply these generated holograms to extract information from radar and aerial imaging for the enhancement and the restitution of contours of the images in the hope of improving qualitative and quantitative information. The holographic image processing can be done with extreme rapidity and is convenient when we have sets of several images to process. Furthermore we present some results in the domain of spatial light modulators able to record and read either images or convolution operators (to avoid photography).

In recent years, we and others have developed a type of reflective tomography based on coherent processing of Doppler frequency shifted echoes from rotating objects. The objects are placed in the Fraunhofer region and irradiated with microwave as they rotate. The returned signals are coherently processed by optical means and highly-resolved, two-dimentional cross-sectional images can be reconstructed. Holographic character is apparent in the processed data. The holograms can have either a rectangular or a polar format. We have completed the experiments using both simulated objects and measured data. To produce images we first make the holograms as data film using computer, and then irradiate the computer-generated holographic data film with He-Ne laser in our optical processor. Thus, the images of the simulated objects can be obtained. We have made both binary holograms and grey holograms with 64 grey scales using computer.

Binary holographic diffraction gratings were developed to shape Gaussian laser-beam profiles into flattop profiles and to multiplex local oscillator wavefronts for use in active infrared laser radar systems. The use of detector arrays in such systems requires amplitude and phase matching of multi-beam local oscillators to signal wavefronts in order to maximize the system's signal-to-noise ratio and resolution and to minimize the heat generated on the focal plane. In addition, a beam shaper in the transmit beam of the laser radar must shape the centro-symmetric Gaussian profile of the laser beam into a stretched profile that efficiently and uniformly illuminates the far-field footprint of the detector array. Other potential applications include synthetic optical elements, laser beam samplers, and uses in laser annealing and optical communication.