Showing papers on "Wavefront published in 1986"

Reverse-time migration of offset vertical seismic profiling data using the excitation-time imaging condition

Abstract: To apply reverse-time migration to prestack, finite-offset data from variable-velocity media, the standard (time zero) imaging condition must be generalized because each point in the image space has a different image time (or times). This generalization is the excitation-time imaging condition, in which each point is imaged at the one-way traveltime from the source to that point.Reverse-time migration with the excitation-time imaging condition consists of three elements: (1) computation of the imaging condition; (2) extrapolation of the recorder wave field; and (3) application of the imaging condition. Computation of the imaging condition for each point in the image is done by ray tracing from the source point; this is equivalent to extrapolation of the source wave field through the medium. Extrapolation of the recorded wave field is done by an acoustic finite-difference algorithm. Imaging is performed at each step of the finite-difference extrapolation by extracting, from the propagating wave field, the amplitude at each mesh point that is imaged at that time and adding these into the image space at the same spatial locations. The locus of all points imaged at one time step is a wavefront [a constant time (or phase) trajectory]. This prestack migration algorithm is very general. The excitation-time imaging condition is applicable to all source-receiver geometries and variable-velocity media and reduces exactly to the usual time-zero imaging condition when used with zero-offset surface data. The algorithm is illustrated by application to both synthetic and real VSP data. The most interesting and potentially useful result in the processing of the synthetic data is imaging of the horizontal fluid interfaces within a reservoir even when the surrounding reservoir boundaries are not well imaged.

An algorithm for profile and wavefront reduction of sparse matrices

Abstract: SUMMARY An algorithm for reducing the profile and wavefront of a sparse matrix is described. The scheme is applicable to any sparse matrix which has a symmetric pattern of zeros and may be used to generate efficient labellings for finite element grids. In particular, it is suitable for generating efficient labellings for profile and frontal solution schemes. Empirical evidence, obtained from analysis of the 30 test problems collected by Everstine, suggests that the new algorithm is superior to existing methods for profile and wavefront reduction. It is fast, requires only a small amount of memory, and is simple to program.

Memory-linked wavefront array processor.

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.

Modal estimation of a wave front from difference measurements using the discrete Fourier transform

Abstract: It is shown that a wave front, or in general any scalar two-dimensional function, can be reconstructed from its discrete differences by a simple multiplicative filtering operation in the spatial-frequency domain by using complex exponentials as basis functions in a modal expansion. Various difference-sampling geometries are analyzed. The difference data are assumed to be corrupted by random, additive noise of zero mean. The derived algorithms yield unbiased reconstructions for finite data arrays. The error propagation from the noise on the difference data to the reconstructed wave fronts is minimal in a least-squares sense. The spatial distribution of the reconstruction error over the array and the dependence of the mean reconstruction error on the array size are determined. The algorithms are computationally efficient, noniterative, and suitable for large arrays since the required number of mathematical operations for a reconstruction is approximately proportional to the number of data points if fast-Fourier-transform algorithms are employed.

Holographic multiplexer/demultiplexer and its manufacturing method

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.

Optical wavefront sensing system

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.

Combining beams from separated telescopes.

Abstract: In the present paper, work is discussed which arose in the context of optical design studies for the proposed space-based COSMIC (Coherent Optical System of Modular Interferometric Collectors) telescope. The operation of COSMIC involves the combination of a number of parallel beams with a central beam-combining telescope which forms an image of the sky. The paper is mainly concerned with the aspects of beam combination. The paraxial constraint condition is considered along with tolerances regarding the individual optical elements, and imaging as a nonshearing recombination. A first-order requirement for achieving a finite field of view is discussed, taking into account specifically the case of a coherent imaging optical system.

Diffraction Patterns and Zone Plates Produced by Thin Linear Axicons

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.

Oscillation with photorefractive gain

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.

Real spectra, complex spectra, compact spectra

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.

Dynamic gratings and the associated self diffractions and wavefront conjugation processes in nematic liquid crystals

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.

Imaging Methods for the Observation of Plasma-Density Fluctuations

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.

Misaligned first-order optics: canonical operator theory

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.

Wavefront Reconstruction from Noisy Slope or Difference Data Using the Discrete Fourier Transform

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.

Optimized holographic optical elements

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.

National Optical Astronomy Observatories (NOAO) Infrared Adaptive Optics Program II: Modeling Atmospheric Effects In Adaptive Optics Systems For Astronomical Telescopes

Abstract: However pertect an adaptive optical system can he, it win never tuiiy correct tne image We discuss here the effects of amplitude errors due to stellar scintillation, the effects of chromatic errors due to both refraction and diffraction in a two-wavelength system, and the effects of non-isoplanicity All these errors are directly related to the height of turbulence layers An expression is derived for the scale height of turbulence which should be considered as an important parameter in selecting new sites for astronomica observations The performances of adaptive optical systems are usually described in terms of Strehl ratios We present here the results of computations of the whole transfer function for lon exposure compensated images It is shown that the point-spread function for a partially compensated image generally consists of an Airy disk surrounded with a halo The ratio of the energy in the Airy disk over the energy in the halo is independent of the telescope aperture and provides a better measure of the quality of the compensation

Wavefront and resonance analysis of scattering by a perfectly conducting flat strip

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.

Laser beam steering apparatus

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.

Method for improvidng the spatial resolution in an integrated adaptive optics apparatus

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.

The Theory of Surface Erosion by Ion Bombardment

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

National Optical Astronomy Observatories (NOAO) Infrared Adaptive Optics Program I: General Description

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

Multichannel Grating Phase-Shift Interferometers

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.

Test And Evaluation Of The Hubble Space Telescope 2.4-meter Primary Mirror

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.

Method of and apparatus for measuring the shape of a wavefront

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.

Reconstruction of reflecting structures from vertical seismic profiles with a moving source

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...

Further applications of point diffraction interferometer

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.

Single pulse imaging device using huygens wavelet reconstruction

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.

Varied Line-Space Gratings: Past, Present And Future

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.