Showing papers on "Wavefront published in 1975"

Use of an ac heterodyne lateral shear interferometer with real-time wavefront correction systems.

Abstract: An analysis is performed to determine the accuracy with which an ac heterodyne lateral shear interferometer can measure wavefront aberrations if a white light extended source is used with the interferometer, and shot noise is the predominate noise source. The analysis shows that for uniform circular or square sources larger than a derived minimum size, the wavefront measurement accuracy depends only upon the radiance of the source and not upon the angular subtense of the source. For a 1-msec integration time, a 25-cm(2) collecting area, and a source radiance of 10 W/m(2)-sr the rms wavefront error is approximately 1/30 wave, assuming the signal is shot noise limited. It is shown that for both uniform circular and square sources an optimum shear distance is approximately (1/2) the aperture diameter required to resolve the light source. Comments are made on the optimum shear for nonuniform radiance distributions.

Interferometric measurements of the nonlinear refractive-index coefficient relative to CS 2 in laser-system-related materials

Abstract: Using time-resolved interferometry, we have compared the nonlinear wavefront distortion induced by the simultaneous propagation of an intense light beam in pertinent sample materials relative to the known reference material. Utilizing several normalization techniques, these measurements have led to precise values for the nonlinear coefficient n 2 good to 10 percent.

Evaluation of large aberrations using a lateral-shear interferometer having variable shear.

Abstract: A variable shear lateral shearing interferometer consisting of two holographically produced crossed diffraction gratings is used to test nonrotationally symmetric wavefronts having aberrations greater than 100 wavelengths and slope variations of more than 400 wavelengths/diameter. Comparisons are made with results of Twyman-Green interferometric tests for wavefront aberrations of up to thirty wavelengths. The results indicate that small wavefront aberrations can be measured as accurately with the lateral-shear interferometer as with the Twyman-Green interferometer and that aberrations that cannot be measured at all with a Twyman-Green interferometer can be measured to about 1% accuracy or better.

Amplitudes of seismic waves; a quick look

Abstract: A form of Kirchhoff’s wave equation is presented which is useful to the geophysicist doing an amplitude interpretation of seismic reflection data. A simple rearrangement of Kirchhoff’s retarded potential equation allows the reflection process to be evaluated as a convolution of the derivative of the source wavelet with a term called the “wavefront sweep velocity”. The wavefront sweep velocity is a measure of the rate at which the incident wavefront covers the reflecting boundary. By comparing wavefront sweep velocities for geologic models with different curvature, one obtains an intuitive feeling for the relation of diffraction and reflection amplitudes to boundary curvature. Also, from this convolutional form of the wave equation, the geometrical optics solution for the reflection amplitude is easily obtained. But more important, from the wavefront sweep velocity approach, a graphical method evolves which allows the geophysicist to use compass and ruler to estimate the effects of curvature and diffractio...

Wavefront-error evaluation by mathematical analysis of experimental Foucault-test data.

Abstract: The diffraction theory of the Foucault test provides an integral formula expressing the complex amplitude and irradiance distribution in the Foucault pattern of a test mirror (lens) as a function of wavefront error. Recent literature presents methods of inverting this formula to express wavefront error in terms of irradiance in the Foucault pattern. The present paper describes a study in which the inversion formulation was applied to photometric Foucault-test measurements on a nearly diffraction-limited mirror to determine wavefront errors for direct comparison with ones determined from scatter-plate interferometer measurements. The results affirm the practicability of the Foucault test for quantitative wavefront analysis of very small errors, and they reveal the fallacy of the prevalent belief that the test is limited to qualitative use only. Implications of the results with regard to optical testing and the potential use of the Foucault test for wavefront analysis in orbital space telescopes are discussed.

Composite wavefront decomposition via multidimensional digital filtering of array data

Abstract: A solution is obtained to the problem of estimating the number, vector velocity, and waveshape of overlapping planewaves in the presence of interfering planewaves and channel noise, where previous solutions have assumed one or more of these quantities as known. A general optimum solution is not found; instead, a heuristic solution is presented along with a complete working implementation program for large scale computers. For the case where the number of waves and the vector velocities are known, the solution is optimum. The detection of waves and the estimation of their bearing, velocity, and waveshape is accomplished via digital filtering of the frequencywavenumber power spectrum, which is computed via an efficient estimator, of the array sensed data. A new approach to the multiwave estimation problem is to reduce it to a succession of single wave problems using especially developed frequency-wavenumber filters. Special attention is given throughout the study to computationally efficient approaches. The results of the paper are placed in perspective by showing how the historically important approaches to the processing of array data such as delay and sum, weighted delay and sum, array prewhitening, beam forming, inverse filtering, least mean-square estimation, and maximum likelihood estimation are related via the spatio-temporal filtering of the frequency-wavenumber spectrum. The spectral estimation, digital filtering, and the multiwave maximum likelihood estimator developments are demonstrated by the processing of a set of simulated planewaves of various bearings, velocities, and frequencies, as well as by processing electroencephalographic (brain wave) data monitored via an array of scalp electrodes.

First order statistics of speckle produced by weak scattering media

Abstract: A weak scattering medium produces random phases in a transmitted or reflected wavefront distributed over less than 2π. The far-field speckle pattern has a central maximum. The statistics of intensity in this maximum are calculated and the applications of the results to surface roughness measurement are indicated.

Spherical Aberration Measurement with Shearing Interferometer Using Fourier Imaging and Moiré Method

Abstract: The experimental and quantitative study of the measurement of the lateral spherical aberration with the shearing interferometer using Fourier imaging and the moire method is given. When the aberration of a camera lens with small f/number(1.7) is measured with an optical arrangement employing the spherical wavefront as a reference at the observation plane, the distortion correction of the obtained fringes is necessary. However, the fringe pattern directly illustrating the lateral spherical aberration can be obtained by the proposed optical arrangement using the plane reference wavefront, without correcting the fringe distortion.

A recording and display system for hologram interferometry with low resolution imaging devices

Abstract: The optical configuration comprises an imaging lens with the reference point source on the optical axis in the centre of the exit pupil of the lens. The spatial frequency band is determined by the aperture and is independent of object size. In spite of the similarity to inline image plane holograms, image and intermodulation wavefront terms are separated by means of slit apertures in the recording step and matched spatial filters in the reconstruction step. Reconstruction is performed with thermal light, the interferograms can be displayed or printed directly on photographic paper.

Conversion of stripe-geometry junction laser emission to a spherical wavefront

Abstract: In a micrographics system of the type in which holes are machined in a thin film by means of a laser (see, for example, reissue U.S. Pat. No. 28,375 of D. Maydan, M. I. Cohen and R. E. Kerwin, granted Mar. 25, 1975), it is advantageous that the laser be a solid-state unit of the stripe-geometry double-heterostructure type. But the optical output beam of such a laser typically exhibits astigmatism and an elliptical cross-section. To assure high-quality machining of the film, it is important that the astigmatic nature of the beam be corrected and, in addition, that the beam be converted to one having a circular cross-section. As described herein, this is accomplished by means of an inexpensive and easily adjustable compact array of optical components that are relatively insensitive to beam-steering and to certain filamentation effects that may occur in the laser.

Holographic interferometer to test optical surfaces.

Abstract: A new interferometric method for testing optical surfaces is given. It is related to Murty's Fresnel zone plate interferometer and suggests the fruitful applications of holography to this branch of optics. In this paper a theoretical model that explains both interferometers is developed. Experimental results and pertinent comments are included.

Scattering of spherical pressure pulses by a hard cylinder

Abstract: The transient scattering of spherical pressure pulses by an infinitely long acoustically hard circular cylinder is analyzed. The pressure in the neighborhood of the reflected wavefront is calculated by the method of series expansion in conjunction with the transport equations. From the wave equation, a simple integral formula is derived by means of which the solution to the present three‐dimensional problem can be effectively constructed from the two‐dimensional line source solution. Thus, the pressure in the neighborhood of the diffracted wavefront is computed based upon Friedlander’s diffraction formulas pertaining to the scatttering of a cylindrical pulse by a hard cylinder. Outside the neighborhood of the scattered wavefronts, the solution is obtained by the Fourier series and integral transform techniques and is accurately computed by this formula. By combining the various solutions, the true time histories of the scattered pressure are inferred for various locations on the cylinder. Some features of...

Image scanning through the acousto−optical effect produced by acoustic surface waves

Abstract: The scanning of a transparency is done by letting a collimated light wave front illuminate it and be diffracted by very short pulses of ultrasonic surface waves. Detection of diffracted light follows a time dependence that equals the transparency brightness along each line that is successively scanned. 94−MHz wave trains, about 10 wavelengths long, give a potential number of resolved spots per second almost equal to 107. Interaction geometry by back−surface reflection has been used, which greatly enhances the diffraction efficiency and yet retains the large acousto−optical bandwidth proper to surface waves.

Diffraction-limited imaging with astronomical telescopes

Abstract: This thesis is a theoretical investigation of a digital processing technique that can be used to obtain diffraction-limited images of stellar objects from large, ground-based astronomical telescopes. The input to this processing scheme consists of a set of short-exposure photographs taken of an object over a short period of time. An averaging process is used which suppresses the atmospheric noise and thereby removes the blurring caused by the atmospheric seeing. A related processing method, developed by Labeyrie, has already been used to recover diffraction-limited information about several double stars on the 200-inch Hale telescope. The output of Labeyrie's technique is in the form of the autocorrelation of the object. This information is quite sufficient for studying an object such as a double star but it is not very useful for viewing an arbitrarily shaped object. The extra knowledge that is needed is the phase of the Fourier transform of the object. The processing method presented in this thesis averages the short-exposure images in a different manner, which retains this phase information. When the phase is combined with the modulus of the object Fourier transform, as determined by Labeyrie's technique, it is then possible to reconstruct a diffraction-limited image of the object. As a result, this method should be particularly useful for the study of extended objects whose surface details are presently masked by the atmospheric turbulence. The properties of the technique are analyzed theoretically using a gaussian phase model to describe the atmospheric seeing. The calculations show that a detailed knowledge of the atmospheric conditions at the time of observation is not necessary for the technique to work. The only condition on the atmosphere, required by the technique, is that the r.m.s. value of the wavefront distortions across the aperture of the telescope be large, i.e. greater than one wavelength of light. The effects of telescope aberrations on the technique are also considered. It is shown that the technique is very insensitive to any aberrations which may be introduced by the optical system. In other words, the resolution of the processed images corresponds to the resolution that would be obtained with a telescope of the same size that had no aberrations. An extensive analysis has also been made on the effects of noise on the quality of the reconstructed images. It is shown that the reconstructions are most sensitive to errors made in determining the phase of the object Fourier transform. In general, the fluctuations in the processed images vary inversely with the square root of the number of photographs used in the averaging procedure. To further investigate the technique, a one-dimensional computer simulation was performed. The parameters of the simulation were chosen to correspond to a 200-inch telescope with 2 arc seconds seeing. The resolution obtained by processing a set of computer generated "blurred" images corresponded…

Optical-wave near field specified from far-field data

Abstract: An optical-wave field is represented in the positive half-space by (1) evanescent plus uniform plane waves and (2) nonuniform plane waves that propagate in all positive directions. A method is given to determine the spectrum of the latter from the spatial distribution of magnitude and phase of the far field.

Device and method for testing high reflectivity autostigmatic optical elements and systems

Abstract: An optical device and method for testing high reflectivity autostigmatic optical elements and systems is disclosed. A thin, partially transmissive optical element, e.g., a pellicle with an optical coating having a transmission factor determined by the nominal reflectivity of the test article, is placed in the measurement leg of a spherical wavefront Fizeau interferometer so that high contrast, two-beam interference fringes can be obtained from a high reflectivity autostigmatic optical element or system.

Transient electromagnetic properties of two, infinite, parallel wires

Abstract: An analysis is presented of the transient electromagnetic field around two parallel wires. It is shown that the field can be expressed in terms of a discrete spectrum and a continuous spectrum. The discrete part of the spectrum can be interpreted as modes whose properties are investigated. The time history of the current at different points on the wires is also calculated when each wire is excited by a slice generator with a step-voltage source. Two different modes of excitation are considered: 1) the two voltage generators have equal strength but opposite polarity, and 2) they have equal strength and same polarity. With the first type of excitation the induced current on the wires can be described accurately by the TEM mode alone provided that one transit time or so between the wires has elapsed after the passage of the wavefront.

Aberrations of a system of arbitrarily inclined planar surfaces placed in non-collimated light beam

Abstract: The refraction of spherical wavefronts through a system of arbitrarily inclined planar surfaces is theoretically considered and general expressions for evaluation of aberrations developed. The formulae developed are applied towards computing aberrations caused individually by a single inclined plane parallel plate, single wedge prism, and two separated wedge plates. The studies carried out are helpful in proper design of flat plates refraction system for either complete elimination of a particular aberration or their balancing for optimal performance or for compensation of residuals in a given optical system.

Effects of the troposphere on the propagation time of microwave signals

Abstract: Technological developments in the microwave spectrum have made possible highly accurate radio systems for position determination. Most of these systems depend upon measurements of the signal transit time or of the differential transit time for different portions of the received wavefront. In practice, the performance of such systems when operating in the Earth's atmosphere is usually limited by the random signal velocity. This effect is a consequence of the variable density and water vapor distribution throughout the normal troposphere. Theoretical and experimental work has provided a useful degree of understanding of these tropospheric effects and some progress has been made in reducing them in certain applications. (auth)

Holographic Storage of Acoustic Surface Waves with Schottky Diode Arrays

Abstract: : Silicon Schottky-diodes have been used to store images of surface acoustic waves propagating on lithium niobate. These images were subsequently employed to provide programmable matched filter or coherent integration fuctions. This technique could also be used to holographically store a large number of acoustic beams to provide a storage capacity as large as 100,000 bits of information. The basic storage element is a Schottky diode with an overlay of polysilicon. Many such diodes are arrayed on centers which are less than an acoustic wavelength apart. When the acoustic signal is in position beneath the diode array, the diodes are forward-biased for several nsec, which causes charge to flow to the diode contact in response to the piezoelectric field of the surface wave. These charges diffuse into the polysilicon in several microseconds, after which a succeeding signal can be overlayed in the array. These charges, which are an image of the acoustic signal are retained in the polysilicon for as long as 100 ms. The stored image is proportional to the acoustic signal in every respect, including the amplitude, phase and wavefront details. This procedure could be repeated for many acoustic beams, and a subsequent signal along a given stored beam causes an electrical signal to appear across the silicon-lithium noibate composite which is proportional to the cross-correlation of the signal with all stored images. This gives rise to the desired output signal, plus undesirable cross-talk signals. Also the desired signal is relatively weak, and its signal-to-noise ratio needs to be increased with a coded interrogating signal and a matched filter. (Author)

Apparatus and method for the imaging of the internal structure of a three-dimensional solid and/or liquid object

Abstract: A system employing ultrasound for the reconstruction of the absorptivity and refractivity properties of ultrasonic radiation internal to a solid, liquid or partly solid and liquid object, air vacuoles being excluded, in the vase that this radiation is highly scattered (reflected or refracted). The reconstruction consists of a three-dimensional simulation of these acoustic properties in a powder mixture which allows access to absorptivity and refractivity information without disturbance either to itself or to the object which it simulates. The reconstruction method is a multi-stage process in which the absorptivity and refractivity of the object are sampled layer-by-layer and recorded in mirror-image layers in the reconstruction. At each stage of the process, the previously constructed image layers are used as "corrective optics" to decode the highly distorted information from the object into the exact wave front geometry and wave form at the given layer that this wave had in the corresponding, mirror-image layer in the object, except for being inverted with respect to one spatial dimension as a mirror image. The necessary sonic data processing is done with a powder mixture, each particle of which is a microscopic mechanism capable of amplifying, recording, erasing and recalling the acoustic impedance information by means of mechanical flexions and other movements.

Optical-wave field determined over a hemispherical boundary surface

Abstract: Magnitude and phase of an optical-wave field are determined over a hemispherical boundary surface under far-field conditions from data obtained by interferometry with three reference waves.

Synthetic Holography for Optical Testing

Abstract: —Computer Generated Holograms (CGH’s) have been used for the testing of aspherical surfaces. The CGH acts as a reference element in an interferometric configuration. The CGH’s may be generated either by coding both amplitude and phase or by coding only the phase of the wavefront. It may be safely assumed that the wavefronts encountered during testing are of uniform amplitude and hence the methods using only phase coding for the generation of the hologram are of more relevance to testing. We have modified the procedure by Birch et al for generating CGH. This modified procedure along with the concept of aberration balancing extends the capability of the CGH; even steep aspherics can be tested. The CGH’s have been generated for the wavefront from a plano-convex lens both for its axial and off-axial positions. The results of the experiments indicate that the CGH and provide a reference wavefront to an accuracy better than λ/10. An analysis of the errors introduced during fabrication and use of the CGH has been presented.

Ultrasonovision: An Interferometric Means For Measurement And Visualization Of Ultrasonic Wavefront Interactions With Biologic Tissue

Abstract: Ultrasonovision is a system for the measurement and visualization of ultrasonic fields which operates by interferometrically measuring the displacement amplitude of the acoustic wave. Its unique features include: high sensitivity, large dynamic range, wide angular response, good resolution, broad frequency range, and the capability for reflective or transmissive imaging. We shall describe the operation of the system and several areas of application, including the imaging and measurement of biological tissue.© (1975) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Composite wavefront decomposition via multidimensional digital filtering of array data

Abstract: A solution is obtained to the problem of estimating the number, vector velocity, and waveshape of overlapping planewaves in the presence of interfering planewaves and channel noise, where previous solutions have assumed one or more of these quantities as known. A general optimum solution is not found; instead, a heuristic solution is presented along with a complete working implementation program for large scale computers. For the case where the number of waves and the vector velocities are known, the solution is optimum. The detection of waves and the estimation of their bearing, velocity, and waveshape is accomplished via digital filtering of the frequencywavenumber power spectrum, which is computed via an efficient estimator, of the array sensed data. A new approach to the multiwave estimation problem is to reduce it to a succession of single wave problems using especially developed frequency-wavenumber filters. Special attention is given throughout the study to computationally efficient approaches. The results of the paper are placed in perspective by showing how the historically important approaches to the processing of array data such as delay and sum, weighted delay and sum, array prewhitening, beam forming, inverse filtering, least mean-square estimation, and maximum likelihood estimation are related via the spatio-temporal filtering of the frequency-wavenumber spectrum. The spectral estimation, digital filtering, and the multiwave maximum likelihood estimator developments are demonstrated by the processing of a set of simulated planewaves of various bearings, velocities, and frequencies, as well as by processing electroencephalographic (brain wave) data monitored via an array of scalp electrodes.

Wave propagation in a viscoelastic rod with temperature‐dependent properties

Abstract: In this paper the unidirectional wave propagation in a rod made of viscoelastic material of the Maxwell type is considered. The rod is subjected to nonuniform temperature gradients and its mechanical properties are assumed to be temperature‐dependent. A perturbation technique incorporated with the usual Laplace transform method is employed to obtain the analytical solution in series form. The strong temperature‐history effect on the attenuation of the wavefront is demonstrated in simple examples for the case where a stress discontinuity due to constant velocity impact propagates along the rod.Subject Classification: 40.22; 35.50.