Use of Holographic Optical Elements (HOEs) in optical systems requires the ability to model the impact of HOEs on the system performance. Optical Research Associates' comprehensive optical design program CODE V accommodates this need by providing means for modeling a variety of HOE types. The HOE capability is a standard feature of CODE V and can be used in conjunction with conventional refracting and reflecting elements, tilts and decentrations, aspherics, etc. All analysis, optimization and tolerancing options include the effects of HOEs. A number of holographic systems including laser scanners, monochromators, and Head Up and Helmet Mounted displays have been designed with CODE V and successfully built, verifying the correctness of the program calculations of image quality and diffraction efficiency. Both transmission and reflection HOEs can be modeled. The HOE is specified in the end use system by the diffracted order, construction wavelength, and the location of the two construction sources. Aspheric construction wavefronts can be modeled by specifying a phase polynomial on the HOE surface. The construction parameters can be varied in the optimization option. Diffraction efficiency for volume HOEs can be calculated using the Kogelnik coupled wave formulation. The variation of efficiency can be displayed for each wavelength over aperture and field.

Diffraction by two-dimensional surface-relief dielectric gratings are analyzed using rigorous three-dimensional vector coupled-wave approach. The method applies to arbitrary plane wave angle of incidence, wavelength, and polarization. In the resulting conical diffraction, the input TE and TM polarization are coupled and the diffracted orders are, in general, elliptically polarized. Diffraction characteristics of two-dimensional binary gratings are presented. Ultrahigh spatial-frequency gratings (grating period less light wavelength) are shown to exhibit polarization independent antireflection behavior (zero-reflectivity).

When used with monochromatic light, holographic helmet displays have distinct advantages when compared to conventional helmet displays. Unfortunately, the holographic elements needed for such displays must perform over a large field of view, and generally suffer from severe aberrations. To overcome these aberrations it is necessary to holographically record complex wavefronts, which can not be obtained with standard optical components. A recursive design technique for obtaining the desired complex wavefronts from relatively simple intermediate holograms is developed. It is based on changing the geometries and the wavelength between the recording and readout of the intermediate holograms. The design technique is illustrated for a single holographic helmet display element having resolution of less then one miliradian over a field of view of 16°x16°.

We have prepared an extensive optimization program for holographic optical systems. The program employs damped least squares algorithm to simultaneously optimize the phase functions of several planar, curved, tilted or decentered holograms. We study the convergence of the damped least squares algorithm in the context of holographic systems, and compare the results to those obtained by the simpler wavefront matching technique. We also discuss the merits of different types of phase functions and demonstrate some limits to which holographic elements can improve system performance. As an example of an optical system containing an optimized holographic element, we consider a tilted spherical mirror used in conjunction with an aberration-correction hologram. Finally, we present a possible fabrication method of the hologram.

A wide field of view head-up display is described along with the construction optics required to produce its holographic combiner. Advantages of holography are outlined along with methods used in designing the combiner.

One of the first Holographic Head Up Display (HHUD) systems developed at Flight Dynamics, Inc. (FDI) was for the Boeing 727 class commercial transport. It has been certified by the FAA for landing operations under Category IIIa conditions and for windshear detection and recovery guidance. The combiner of a prototype exhibited a phenomenon called flare. Flare is most apparent when viewing bright objects in a dark surround, e.g. landing lights at night. It is caused by using Holographic Optical Elements (HOEs) with diffractive power and by HOE construction setups in which the formation of parasitic holograms is not controlled. The problem was solved by using a conformal reflection HOE constructed in a single beam configuration (U.S. Patent 4,582,389). Other HHUD systems have been developed by Flight Dynamics, Inc. for fighter cockpit geometries. Because no structure can protrude past the ejection line, the optical path must be folded forward to clear this area. Since the combiner element must work at substantial (>55°) off-axis angles which introduce large aberrations, a holographic fold element formed using aspheric wavefronts is used to introduce partially compensating aberrations (U.S. Patent 4,669,810). Large aspheric wavefront deformations can be achieved on a component which is manufactured by a replication process, thereby reducing costs.

The optical properties of holographic kinoforms are described. It is shown that paraxial designs are not adequate for f-numbers less than approximately F/10. A non-paraxial design is introduced which retains the high diffraction efficiency of the paraxial designs, yet also produces a non-aberrated diffracted wavefront for the design wavelength. Aberration calculations and computer calculations, based on the Huygens-Fresnel principle, of the point spread functions for these elements show the necessity of using the non-paraxial design.

An achromatic Fourier processor is presented that is capable of Fourier transforming and imaging spatial frequencies up to 30 lines per millimeter within a 200 nm. spectral bandwidth. A procedure is outlined for optimization using a computer lens design program.

Multilayer thin film theory for a quarterwave stack of thin films is compared with the coupled wave analysis of unslanted reflection volume holograms. The thin film analysis is then extended to simulate holograms in which the average index, index modulation amplitude, and index modulation wavelength are a function of depth in the hologram. Specific examples are shwon which correspond to the spectral shape of actual holographic notch filters. Phenomenological mechanisms are postulated to explain the line shape based on the theoretical analysis.

Our goal was to determine the feasability of replacing a refractive collimation lens with a diffractive collimation HOE. Two aspects of the design were especially critical to feasability. The first was dispersion and compensation for dispersion, the second was blocking the zero order in an on axis configuration. Other details to be studied were aberrations and the means by which they could be controlled and corrected. The work that was performed included fabrication of several prototype single and sandwich HOE devices in sizes from 3.8 cm to 20 cm diameter. Angular bandwidth and effeciency both had to be as high as possible while meeting recording conditions that would minimize both aberrations and Bragg plane distortions. Results of our fabrication efforts were in close agreement with prior work except that we did acheive higher efficiencies at broader angular bandwidths than were previously shown. The sandwich efficiencies were high enough to effectively block out the zero order light in an on axis configuration. No light control film or air space was needed to acheive good viewability. The prototype shows bad blurring for 50 nm bandwidths but almost none for 15 nm bandwidths. The various prototypes each had some imperfections in design or fabrication but they demonstrate that efficiencies and field of view are acheivable to make a useful HUD collimator. The horizontal field of view can easily exceed 25 degrees with a near 10 degree vertical field and efficiencies approached 98% with some areas blocking 99% of the zero order light in both polarizations.

This paper presents a review of high-efficiency Bragg holography at Physical Optics Corporation (POC). Various commercial and space applications of high-efficiency Bragg holographyTmare presented including IR mirrors (or holowindows for solar control), VLSI Holoplanar interconnects (in near IR region), holographic notch filters (IR, Visible and UV), UV/Visible/IR Lippmann holographic mirrors and HOEs, and XUV holographic mirrors and HOEs for soft X-ray laser optics.

Scanning electron micrographs of volume phase, reflection holograms recorded in DMP-128 reveal microstructure that is responsible for holographic efficiency. Solid and porous payers alternate with a spacing commensurate with the recorded fringe pattern. The difference in material density between the solid and porous regions accounts for the refractive index modulation and therefore the holographic activity of DMP-128 holograms. The pores of the hologram are interconnected and are filled with many low and moderate viscosity liquids upon immersion. Important optical properties of the holograms are profoundly and predictably affected by filling of the hologram pores.

The fundamental holographic properties of Polaroid's DMP-128 have been measured. Diffraction efficiencies over 90% have been obtained with an index modulation of 0.033. It was found that the diffraction efficiency could be reduced from 90% to less than 10% by the use of an index matching fluid. When the index matching fluid was allowed to evaporate, the diffraction efficiency returned to its original value. This observation suggests that the index modulation produced in the photopolymer is due to tiny cracks or voids formed in the polymer.

Silver halide (sensitized) gelatin has the sensitometric response of silver halide emulsions and the holographic characteristics found in dichromated gelatin. We have demonstrated high diffraction efficiencies with low emulsion scatter noise using commercially available emulsions and standard photographic processing. Like DCG this process suffers from emulsion thickness variations which are related to sensitizer concentration and processing conditions. We describe chemical methods which permanently modify the gelatin binder to minimize thickness variations in gelatin emulsions. The technique also can be used to stabilize the processed hologram to adverse environmental effects.

A physical model has been proposed to explain the behavior of a thin oil film (~1 μm) on a glass substrate under the influence of IR irradiations; this model is formulated mathematically with a physicochemical hydrodynamics approach. Numerical solutions of the model are shown to fit very well with experimental results. Extrapolation of this model and the experimental method will be discussed as possible application in the study of thin films and very small thickness modulation.

A Mach-Zehnder interferometer is used to produce lateral shear between two infrared (10 μm) wave fronts. These two parallel sheared wave fronts, together with a tilted infra-red reference beam, are incident on a dynamic recording medium consisting of a thin oil film on a glass substrate: a phase hologram is obtained. Illumination of this hologram with a visible (HeNe) beam permits to visualize the characteristic shear interferogram in the direction of the +1 diffracted order. Practical realization of the Mach-Zehnder interferometer is easily carried out with long-wavelength interferometry, and experimental results include gaussian beam analysis, aluminum deposit thickness evaluation and afocal system inspection and adjustment. The properties of the recording medium are determined, in the context of infrared shearing interferometry, and shown to be satisfactory when compared to other recording media already reported.

In many applications, the correlation plane of an optical correlator must give not only the identity but also the location of a target of interest. In many cases, such as with robotic vision, the coordinate information must be given with considerable precision. This paper outlines a technique for calibrating a correlation plane relative to the input frame. Test results are given.

A universal hologram construction layout, which takes advantage of the resonant coherent modes of a laser, is described. A master transmission hologram made with this layout can be used to make transmission, reflection, or rainbow copies with a minimum amount of component movement between exposures of each type of hologram. This saves much of the set-up time normally involved between exposures, thus reducing the cost of each hologram. The theory of resonant axial coherence modes explains how different object and reference beam lengths can still result in bright, efficient holograms.

Broadband imaging systems that contain holographic lenses can be lightweight and have large apertures. We report a Fresnel diffraction analysis of an imaging system that consists of three lenses of arbitrary dispersion. A general solution is obtained for the wavelength dependence of the lenses to simultaneously correct the imaging system for both longitudinal and lateral paraxial chromatic aberration. As a special case, we describe an optical system that uses holographic lenses to produce a well-corrected image in broadband light. Experiments are reported that demonstrate system performance in both laser and broadband illumination.

Holographic optical elements of various types can be formed with light of reduced coherence, either spatial or temporal or both. Here we describe the synthesis of fringes of non-sinusoidal profile with either extended source monochromatic or extended source polychromatic light. Recording of such fringes yields blazed gratings.

Diffractive optical elements have the potential to improve the performance of infrared optical systems. An approach to constructing high quality diffractive elements has been developed using standard integrated circuit techniques. It is possible to implement arbitrary phase profiles since the elements are computer generated.

Holographic filters in spectacle lenses, helmet visors and other types of substrates have been proposed for eye protection against visible lasers. Dyes and filter glasses, commonly used as laser protection at visible wavelengths, typically suffer from poor visual transmittance. Holographic filters offer potentially high visual transmittance due to a narrow spectral notch, but the angular dependence of the spectral notch position dictates a tradeoff between eye protection and visual transmittance. The relative merits of various exposure and substrate configurations for laser-protective eyewear are compared. Emphasis is placed on single-beam exposure, surface-conformal fringe structures in which the local Bragg angle is determined by the fringe spacing as opposed to the fringe tilt. This type of hologram is readily made free from flare or multiple images in transmission. Performance is evaluated in terms of visual transmittance versus eye protection, including retinal area and eye rotation. The relationship between angular and spectral response of holographic laser filters determines the exposure source for optimum performance to be roughly coincident with the center of eye rotation, regardless of the substrate geometry. Performance may be improved by locating the filters a greater distance from the eye. A more dramatic improvement in performance may be achieved by increasing the curvature of the substrate so that it is concentric with the eye.

Size reductions of reflex type sights and head-up displays (HUDs) can be achieved with holographic components. For the reflex type sight, the image formed by a high-quality optical system is recorded in a holographic plate with an edge-illuminated reference beam. This hologram reconstructs the original image and duplicates its original quality. The system is compact, consisting of a hologram on a flat glass plate and a compact laser beam expansion optics. The illuminating beam enters the hologram plate through its edge. The laser is remotely located with light guided through a fiber optics cable to the sight. HUDs can also be made more compact by using a pair of gratings attached to a flat glass plate. The plate guides the display to a position in front of the pilot and occupies a small volume.

An important application of holographic optical elements (HOE) is coordinate transformations (or mappings) to put data into a format that can be operated on by an optical processor. In optical coordinate transformation, a specific one-to-one mapping of pixel locations in the input plane to pixel locations in the output plane is produced. For some desired transformations, the data redistribution cannot be realized with a single continuous-phase hologram, and in these cases a multiple hologram system must be considered. The processing of spotlight synthetic aperture radar (SSAR) data is used as a sample application to illustrate the concept. The design and fabrication of the holograms for SSAR data processing is discussed and experimental results are given.

In the next year embossed holograms will be produced and applied to more products than in the last five years combined. The primary reason for this increased productivity is improved methods of applying holograms to products.

Focusing grating couplers can be constructed using holographic techniques. As a result of wavelength scaling between the construction of the focusing grating coupler and its final end-use operation, aberrations exist in the final spot. A design is demonstrated, using geometrical optics and a commercially available ray-trace code, that uses conventional optics to correct the aberrations of a holographic optical element resulting from the wavelength scaling.

The principle of operation of an achromatic modulator or phase shifter is presented. Specific triangular configurations are described that consist of two base gratings and a vertex element which may be either a transmission-type hologram or an acousto-optic modulator. The application of this concept is illustrated by a generalized white light interferometer with very fine differential phase control and two separated, collinear output paths. The achromatic phase shifter is also shown to make an important improvement to the white light cosinusoidal transform hybrid. Two different configurations are presented.

While page oriented holographic memories are extremely valuable, they can take a great amount of lateral space. We show here how to stack a number of holograms in such a way that we can select one layer to be "active." As a result, the lateral area needed to store a given number of holograms is reduced by L, the

We have developed a compact, high-readability POS scanner which uses a new type of holographic technology. We call this technology the "holo-window". The holo-window is capable of changing the scan direction and collecting the signal light. While compaction of current scanners would decrease their readability, these features enable the optical system of a scanner featuring the holo-window be made compact while maintaining high readability. Using the holo-window, we have developed a new scanner which has a letter-size footprint and is only 8 cm high.

Holographic Optical Elements (HOE's) of space-variant impulse response have been designed and generated using a computerized optical system. HOE's made of dichromated gelatin have been produced and used for spatial light modulator defect removal and for optical interconnects. Experimental performance and characteristics are presented.

A two holographic-optical-element system is described for converting a round-shaped Gaussian-profile laser beam into a square-shaped beam that is uniform in amplitude and phase. The goal is to develop a compact, high-quality and efficient system for this conversion. Theoretical analysis, design considerations, and experimental results are presented.

Theoretical and experimental data will be presented that show how the bow in a scan-line generated by a hologon deflector can be minimized by incorporating either a prism or grating element into the deflector geometry. In addition to minimizing scan-line bow, these dispersive optical elements permit lower wavelength to grating periodic values to be used for the hologon which results in improved cross-scan and radiometric system performance.

In this paper we discuss the design and construction of holographic optical elements (HOEs) and their applications in conjunction with thermally induced refractive nonlinear logic devices in the demonstration of the first generation of all-optical logic circuits. The diffraction efficiencies for these HOEs are > 90% whilst switch energy of < 25 pJ for pixellated, micrometer-dimension logic elements are predicted.

The application of holographic associative memories to binary addition based on symbolic substitution is described. Experimental results of parallel half-addition are presented. The use of a liquid crystal television (LCTV) as a computer-programmable spatial light modulator in the hybrid binary adder is also discussed.