Abstract: A Memory-Linked Wavefront Array Processor (MWAM) which computes a broad range of signal processing, scientific and engineering problems at ultra-high speed. The memory-linked wavefront array processor is an array of identical programmable processing elements (34) linked together by dual-port memory elements (32) that contain a set of special purpose control flags (126). All communication in the network is done asynchronously via the linking memory elements (32), thus providing asynchronous global communication with the processing array. The architecture allows coefficients, intermediate calculations and data used in computations to be stored in the linking elements between processing stages (34). The novel architecture also allows coefficients, intermediate calculations and data to be passed between the processing elements (34) in any desired order not restricted by the order data is to be used by the receiving processing element (34). Further, each processing element (34) is capable of simultaneous arithmetic computation, multi-direction communication, logic discussions, and program control modifications.

Abstract: A holographic multiplexer and holographic demultiplexer, which has a diffraction grating formed of a hologram with an interference pattern produced by interference of two wave fronts, of which at least one wave front is of an aspherical wave and the other is of, for example, a spherical wave, and its manufacturing method are disclosed. The aspherical wave is used for correction of aberration and provided by obtaining the phase function φ G of the aspherical wave using a computer generated hologram and through an optical method or an electron-beam direct drawing method. The hologram serving as the diffraction grating for the holographic multiplexer/demultiplexer is produced by a two-beam interference method of an electron-beam direct drawing method. As the result, a holographic multiplexer/demultiplexer having a high degree of multiplexing, which is compact in size, and exhibiting low loss of light can be provided.

Abstract: A wavefront sensor for detecting distortion in light wavefronts is described in which the wavefront is divided into a plurality of subapertures and light amplified or intensified and imaged as spots of light from each subaperture onto a filter mask. The filter mask encodes a predetermined function of the spot intensity distributor onto the light intensity of the spot transmitted through the filter. For spot centroid calculation, the function is linearly variable. Mask embodiments include linearly varying alternate opaque and transparent chevrons, electronically variable chevrons, and quadratically varying chevrons.

Abstract: We determine the Fraunhofer and Fresnel diffraction patterns produced by a thin linear axicon when it is illuminated by a plane wavefront. An interferometric method of recording zone plates using linear axicons is presented.

Abstract: We review theories and experimental demonstrations of oscillation with photorefractive gain. The unidirectional ring resonator; the linear passive phase conjugate mirror, a phase conjugate resonator (the semilinear passive phase conjugate mirror), and the double phase conjugate resonator are treated, the applications in path-length-to-frequency converting interferometers and one-way wavefront converters are described.

Abstract: Plane-wave spectral and induced source representations of directly excited and (or) scattered fields constitute alternative approaches for analyzing wave propagation. Although the plane-wave spectra, on the one hand, and the source distributions, on the other, generally require continuous superpositions that lead to integral formulations in the spatial-spectral and the physical configuration domains, respectively, phenomena of constructive and destructive interference at high frequencies permit contraction of these distributed constituents around interference maxima represented by stationary points, end points, or other critical points in the integration interval. This leads to a representation of the high-frequency field in terms of physically meaningful compact spectral objects generated by local portions of the source distribution that radiate energy from the (actual or induced) source region to the observer by local plane waves traversing the ray trajectories of the geometrical theory of diffraction. If the critical points in the integrals are real, the compact representation identifies nonevanescent wave bundles emitted by source patches at a real physical location. However, for many wave phenomena involving beam-type initial source fields, concave and convex boundaries, leaky waveguides, etc., as well as damped resonances in the time domain, the spectral contraction occurs around damped complex constituents identifying bundles of evanescent plane waves that travel along complex ray trajectories. Thus the initial source configuration and propagation space must be extended by analytic continuation to complex values. Insisting on real spectral and configurational domains expresses in a smeared-out unnatural manner what is compact and natural in the complex domain. These concepts are illustrated here in various examples, with emphasis on the physical importance of compact representations.

Abstract: The origins and the dynamics of optical nonlinearities in nematic liquid crystal films, namely, laser-induced molecular reorientational and thermal refractive index changes, are analyzed in the context of optical wave mixings. Theoretical expressions for the basic non-linearities, the rise and decay time, diffraction efficiencies, and other pertinent parameters involved in the dynamic grating formation are derived. Experimental results obtained with visible and infrared laser pulses are analyzed. Some newly observed novel nonlinear processes are also reported.

Abstract: Imaging techniques offer attractive alternatives to small-angle Thomson scattering for scale lengths of density fluctuations causing diffraction in the Raman-Nath regime. This is the case for fluctuations with wavelengths above about 3 mm for Tokamak sized plasmas, when a CO2 laser probe beam is used. Four methods ('phase scintillation', phase contrast, wavefront shearing and interferometry) are compared, on the basis of their transfer properties. They offer new means of studying density fluctuations of magnitude up to the dimensions of the plasma, such as those associated with turbulence, magnetic islands, convective cells or driven waves. The long wavelength limitations are discussed in detail and are related to those encountered for far-field techniques. An experimental comparison of 'phase scintillation' and phase contrast is given, and the criteria relative to the depth of field of imaging instruments in this context are considered.

Abstract: Canonical operator theory of paraxial optics is generalized to address the case of misaligned optics. The formal group structure is extended from the aligned case in terms of Heisenberg–Weil and inhomogeneous canonical transforms and the associated 3 × 3 augmented ray matrices. Certain misalignment phase shifts that are often mistreated and ignored have been derived and incorporated into the theory.

Abstract: A general algorithm is presented for reconstructing a two-dimensional wavefront optical path difference (OPD) map from noisy slope or difference measurements by means of a least squares fit using complex exponentials. This form of modal estimation can be described as a filtering operation in the spatial frequency domain. Thus fast Fourier transform (FFT) algorithms can be used for rapid reconstruction. The reconstruction is unbiased also in the case of finite data arrays. The error propagation from the noisy measurement data to the integrated wavefront is minimal in a least squares sense. It is believed that this reconstruction algorithm can be implemented in an adaptive optical system by using commercially available array processor hardware, thus reducing the total system cost and the need for specialized hardware.

Abstract: This paper presents a method for designing optimal holographic optical elements. The method is based on the minimization of the mean-squared difference between the desired and the actual output waves. The minimization yields an integral equation for the grating function of the designed optical element. The integral equation is converted into a set of linear equations that can be easily solved. The resulting coefficients form the final solution as a sum of polynomials. This procedure yields a well-behaved grating function that defines a holographic optical element that can be realized with the help of computer-generated holograms. The method is illustrated with a design of an imaging lens. The performance of this lens is then compared, both theoretically and experimentally, with that of a spherical holographic lens. The results show that the newly designed lens is clearly superior to the spherical lens.

Abstract: An eroding or growing solid surface is treated as an advancing nonlinear wavefront and characteristic methods are used to describe its progress, when the normal velocity of erosion is a well-defined function of spatial position, and time and surface orientation Facets, points and edges can develop as the surface evolves and the formation of these are described in terms of the theory Some interesting examples are computed that have important application in microfabric­ation, surface analysis and ion beam processing

Abstract: Wavefronts and resonances form alternative descriptions for transient scattering by targets, with the former most effective at early observation times and the latter most effective at later times. Wavefronts can be employed to synthesize resonances, and both constituents can be combined self-consistently within a hybrid format that seeks to exploit the best features of each. These aspects are illustrated here for the special case of impulsive plane wave scattering by a perfectly conducting flat strip. Since the multiple diffracted wavefront fields are found by geometrical theory of diffraction (GTD) asymptotics, the example also highlights the detrimental effects caused by approximations confined essentially to the high frequencies in the incident signal spectrum. Despite these inadequacies (present for impulsive signals but not for those with low frequency cutoff), the analysis and numerical comparisons confirm the wavefront-resonance equivalence, with inclusion of the branch cut integral due to the two-dimensional geometry of the scatterer; the role of the "entire function" in, and the poor convergence of, the resonance expansion at early times, the improved convergence achieved by delayed resonance series turn-on in a hybrid format; and the internal consistency of that format. Moreover, the GTD approximations are adequate for accurate synthesis of the resonance frequencies.

Abstract: A device for steering a wavefront of electromagnetic radiation comprising a pumping means for coherently pumping a plurality of phase conjugate mirrors with a monochromatic coherent beam having a wavelength substantially the same as the wavelength of the wavefront. The device further comprises an array of phase conjugate mirrors wherein the acceptance of each phase conjugate mirror, for conjugate reflection of the wavefront, is pointing in substantially the same direction, and the phase conjugate mirrors are composed of material responsive to the beam wavelength. The device further comprises a Fourier transform lens, a control reflector positioned such that the reflected beam from the reflector back to the lens is within the acceptance angle of the ray, and a beam splitter positioned between the array and the control reflector for extracting a steered beam. Each phase conjugate mirror may provide amplification of the wavefront, or amplifying lasers may be used. The phase conjugate mirrors may be positioned close to each other, or telescopes may be used in conjunction with each phase conjugate mirror to expand each beam.

Abstract: Apparatus is disclosed for correcting wavefront errors in adaptive optics systems. A modified liquid crystal light valve is used as an integrated wavefront sensing and wavefront control system. A remote reference aberrated wavefront 10 first reflects off the liquid crystal substrate 20 and is then transferred by beam-splitters 14 and 15a, b and reflector 19 to the rear surface ofo the liquid crystal light valve 12. A one-to-one imaging system composed of lenses 70a, b and spatial filter 72 provide a new diffraction-limited optical transfer system which allows full use of the extremely high resolution capabilities of the liquid crystal light valve 12. The wavefront 10, after being imaged by the optical transfer system, is combined with a local reference plane 16, the interference pattern from which strikes the rear surface photoconductor 26. The photoconductor electrons liberated serve to alter the voltage across the liquid crystal at those points where the interference pattern has right maxima. Using a tunable birefringent liquid crystal layer 20, a voltage change causes a commensurate refractive index change in the liquid crystal substrate. These refractive index changes alter the optical path length of particular portions of the aberrated wavefront and the device's inherent negative feedback drives these phase errors to zero, at which point the wavefront 18 is completely corrected. A second laser beam 11 may be sent out of the device, reflecting off the corrective liquid crystal layer and predistorting it in order to correct for atmospheric path disturbances. The present invention provides an adaptive optics correction system possessing extraordinarily high spatial resolution.

Abstract: Manufacture of the 2.4-meter diffraction-limited hyperboloidal primary mirror for the Hubble Space Telescope encompassed several state-of-the-art processes. These included computer-controlled polishing and interferometric test and evaluation. To advance the manufacturing processes to the 0.008μm rms surface figure level achieved on the primary mirror, full-aperture and sub-aperture interferometric test configurations were developed in conjunction with a precision interferogram analysis facility. Full-aperture interferometric testing of the uncoated mirror took place in air with the test chamber providing the necessary thermal and vibrational stability. A remotely-controlled, six-degree-of-freedom table was used to orient and position the mirror with respect to the fixed geometry metrology unit consisting of a Co-axial Reference Interferometer (CORI) and a reflective null corrector. The CORI generated a high quality spherical wavefront which, in turn, was converted to a hyperboloidal wavefront characteristic of the desired mirror surface by the reflective null corrector. Interferograms in the form of photographic negatives recorded the departures from the highly corrected null condition to provide surface contour and aberration data. The high spatial frequency surface defects, so important to the ultraviolet (UV) performance of the Space Telescope, were measured via sub-aperture interferometry. A laser interferoscope and precision test plates with reference surface radii appropriate to several zones on the primary mirror were employed to produce high fidelity measurements of "mid-frequency" defects at the 0.002μm rms level.

Abstract: We describe the general principles behind a polychromatic adaptive optics prograff astronomy which was started at NOAO recently. In this program the atmospheric wavef distortions are measured at visible wavelengths (700nm) using an astronomical object vicinity of the infrared object of interest. The resulting wavefront corrections ar applied to an infrared imaging system which utilizes a two-dimensional detector arra

Abstract: When a beam is focused into grating elements, it is diffracted and phase-shifted. These fundamental characteristics of gratings have been found very useful for converting conventional interferometers into real-time wavefront sensors for digital computer control and data analysis. The principle of phase-shifting interferometry has been combined with above characteristics of the gratings to produce instantaneous multichannel interferograms. Attempts have been made successfully to apply these principles to three well-known interferometers, (1) the point-diffraction interferometer, (2) the radial-shear interferometer, and (3) the double-frequency crossed-grating lateral-shear interferometer. The advantages of these new approaches are simplicity and versatility, in particular, these wavefront sensors can measure wavefronts from both continuous and pulsed sources. Optical principles and the laboratory results will be shown.

Abstract: Two light beams capable of interference with each other are applied to an area sensor while they are inclined to each other. The area sensor reads a pattern of interference fringes formed by the two light beams. The read interference fringe pattern is subjected to a Fourier transform, and then an inclination-related component is removed therefrom. Thereafter, an inverse Fourier transform is effected. The shape of the wavefront of light to be measured is determined on the basis of a phase difference between the two light beams which is known from the result of the inverse Fourier transform.

Abstract: When a vertical seismic profile (VSP) is recorded, the illuminated part of a reflector depends upon the shape and position of the reflector itself as well as on the seismic velocities and the positions of sources and receivers. A preferable arrangement for the investigation of structures of reflectors is to fix the receiver(s) at constant depth(s) in the well and move the source horizontally along a line at the Earth’s surface, usually called a “multioffset VSP” (MSP) or “walkaway VSP.” As a test of the resolution power of this survey geometry, synthetic records were generated from a subsurface model by inverse Kirchhoff migration. Three different methods were applied for the reconstruction. Wavefront construction leads to the correct shape of the reflectors, thus assuring the validity of the modeling method applied. Reflection‐point mapping delivered a near similarity to the model, but without focusing fault edges. Kirchhoff migration resulted in a detailed image of the reflectors with fault edges focuse...

Abstract: It is shown that point diffraction interferometry (PDI) can very conveniently be used for the study and analysis of transparent objects and for the detection of wave front distortion caused by a perturbation of refractive index in the testing path. A very simple method of fabricating these PDI plates is also described using mercury micro-balls.

Abstract: A method and device for imaging three dimensions with a single pulse of energy is described. An embodiment is disclosed which uses a single monopolar transmitted pulse which radiates through a wide solid angular volume. Echoes caused by objects in this volume are detected by a large diameter, sparse circular array of receiver elements. The time history of each element is stored in a digital memory. A reconstruction processor uses this stored time history to reconstruct an image of the reflecting objects. A simple time of flight algorithm, based on Huygens principle, is used in the reconstruction. The algorithm automatically takes into account transmitted wave front curvature and makes no approximations such as Frensnel or Fraunhofer in the reconstruction. A circular array of receiver elements can be used, which is axicon, and is focused throughout the imaged volume. A perspective processor controls the reconstruction processor such that the volumetric image may be viewed from various perspectives. Tomographic images may be selected from the imaged volume at various positions and orientations. The perspective processor controls the reconstruction process such that the reconstructed points may be accumulated, summed and thus integrated so that a three dimensional volume may be viewed on a two dimensional display.

Abstract: An experimental investigation was made of the use of liquid-crystal phase correctors of wavefronts. Prototype correctors were prepared with independent addressing of the elements and these were found capable of compensating distortions of wavefronts of radiation of wavelengths 0.5–6μ.

Abstract: A classically ruled diffraction grating consists of grooves which are equidistant, straight and parallel. Conversely the so-called "holographic" grating ( formed by the interfering waves of coherent visible light ) , although severely constrained by the recording wavelength and recording geometry, has grooves which are typically neither equidistant, straight nor parallel. In contrast a varied line-space (VLS) grating, in common nomenclature, is a design in which the groove positions are relatively unconstrained yet possess sufficient symmetry to permit mechanical ruling. Such seemingly exotic gratings are no longer only a theoretical curiosity, but have been ruled and used in a wide variety of applications. These include 1) aberration-corrected normal incidence concave gratings for Seya-Namioka monochromators and optical demultiplexers, 2) flat-field grazing incidence concave gratings for plasma diagnostics, 3) aberration-corrected grazing incidence plane gratings for space-borne spectrometers, 4) focusing grazing incidence plane grating for synchrotron radiation monochromators, and 5) wavefront generators for visible interferometry of optical surfaces (particularly aspheres). Future prospects of VLS gratings as dispersing elements, wavefront correctors and beamsplitters appear promising. I discuss the history of VLS gratings, their present applications and their potential in the future.

Abstract: Nonparaxial imaging by holograms on a spherical surface, with a limited circular cross section, is formulated mathematically. Starting from a point-shaped object, the image point (called the point of reference) is redefined such that the deviation in the positions of the actual image-forming wave front and a spherical wave front centered around this point contains no terms of the first order in the hologram coordinates. Furthermore, their second-order contribution, averaged over the hologram, vanishes. The remaining terms up to the fourth order describe the primary aberrations. Compared with earlier theories, this formulation yields a more accurate position for the holographic image. In addition, expressions are obtained for the primary aberrations, which not only consist of astigmatism, coma, and spherical aberration but also contain three additional contributions, which occurred as higher-order aberrations in previous literature. Experiments support our conclusions.

Abstract: An "unusual" optical surface is the plane symmetric equivalent of the general rotationally symmetric aspheric familiar to optical designers. This surface was introduced to facilitate the design of fast, unobstructed aperture, large field-of-view, reflecting telescopes, and has resulted in a number of successful designs of such systems. The fabrication of these systems is inhibited primarily by the difficulty of testing such surfaces, so in this paper we describe an appropriate test procedure. This is an interferometric method that makes use of a hybrid setup in the test arm where the geometry, test optics, and a computer-generated hologram are all used to attain zero aberration.

Abstract: Phase sensors that are most commonly used in the adaptive-optics area typically measure the gradient of the phase. A phase reconstructor is necessary to obtain the phase at the actuator positions of the deformable mirror. In the past reconstructors to obtain the optical phase from gradient measurements have been built using resistive nets. These nets simulate a least-squares reconstruction algorithm. There are other algorithms which can be used to mate wavefront sensors and deformable mirrors with different geometries or which can improve the noise performance by using the spatial correlation of the phase. These types of algorithms are difficult to implement and change using analog techniques. In addition, since the movement of an actuator can influence the position of adjacent actuators it is desirable to include this effect in the reconstructor. One may also want to remove the piston and the tip and tilt from the signal applied to the deformable mirror, and determine the values of the focus and tip and tilt terms in order to provide signals to auxiliary mirrors. A digital reconstructor can provide this capability. An approach to a digital reconstructor which can calculate an optical phase which is any linear function of the gradient measurements is described. This reconstructor is based on using a multiplier-accumulator circuit in each channel. A single phase value is calculated in each channel by summing the result of multiplying each gradient measurement by a stored matrix coefficient. Several sets of matrix coefficients are stored in memory to allow one to change the reconstruction algorithm quickly. The circuitry used and the time taken to perform the reconstruction will be described.