Showing papers on "Wavefront published in 1969"

The kinoform: a new wavefront reconstruction device

Abstract: A new, computer-generated, optical element called a kinoform is described. This device operates only on the phase of an incident wave and forms a single image by wavefront reconstruction without the unwanted diffraction orders characteristic of holograms. The kinoform is also more efficient in the use of spatial frequency potential and reconstruction energy and can be synthesized in considerably less computer time than the digital hologram.

Gaussian light beams with general astigmatism.

Abstract: This paper considers the propagation and diffraction of coherent light beams through nonorthogonal optical systems such as sequences of astigmatic lenses oriented at oblique angles to each other. The fundamental (gaussian) mode has elliptical light spots in each beam cross section and ellipsoidal (or hyperboloidal) wavefronts near the axis. It is found that the orientation of the light spot differs from that of the wavefront, and changes continuously by as much as pi radians as the beam propagates through free space. A theory of these general astigmatic beams is given and simple experimental observations are described. The coupling factor between two such beams is also given.

Probing of Acoustic Surface Perturbations by Coherent Light

Abstract: The need for sensitive methods of detection and visualization of acoustic surface perturbations has grown with the increasing interest in such fields as acoustic holography, ultrasonic surface wave devices, and acoustic trapped energy resonators. One very sensitive detection method utilizes a coherent light beam as a probe for locally measuring phase and amplitude of the acoustic field. Several variants of this technique are possible, based on measuring phase, deflection, wave front curvature, and spatial frequency content of the reflected beam. Each one of these variants may be combined with a scanning motion of the beam in order to visualize the entire sound field. This paper will attempt to survey the present state of the art and compare the different techniques on the basis of their sensitivity and applicability to specific requirements.

Transient Excitation of an Elastic Half Space by a Point Load Traveling on the Surface

Abstract: The propagation of transient waves in an elastic half-space excited by a traveling normal point load is investigated. The load is suddenly applied and then it moves rectilinearly at a constant speed along the free surface. The displacements are computed for all points of the half-space as well as for all load speeds. The disturbance is analyzed by using multi-integral transforms and an inversion scheme based on the well-known Cagniard technique. This reduces the displacements to single integral and algebraic contributions, each of which is identified as the disturbance behind a specific wave front. The same solution is valid for all load speeds, even though the wave front geometry varies greatly, depending on the speed of the load relative to the body wave speeds. Moreover, the surface displacements are obtained from the interior ones, but only after the Rayleigh waves are computed by a separate calculation. Then, by taking advantage of the form of the exact solution, wave front expansions and Rayleigh wave approximations are computed for all load speeds. Several other analytical results are obtained for restricted values of the load speed. In particular, when it exceeds both of the body wave speeds the steady-state displacement field is separated from the transient one and reduced to algebraic form. Also, for the limit case of zero load speed a new representation of the interior displacements for Lamb's point load problem is displayed in terms of single integrals.

Astigmatic Gaussian beams produced by axially asymmetric laser cavities

Abstract: Gaussian beams generated within astigmatic resonators are themselves astigmatic, having wavefront curvatures and spot sizes that are different when measured in two orthogonal directions. Expressions are derived for the confocal parameters, spot sizes, waist positions, and stability conditions of beams formed within spherical mirror resonators that contain one or more inclined plates (or Brewster-ended laser rods). An expression is also derived for the resonant frequencies of the TEM mn mode in such a resonator. It is shown that the frequency degeneracy between modes of the same m + n is lifted and the frequency splittings are calculated. The astigmatism produced by prisms used for dispersion is also considered and precautions are described for avoiding serious astigmatism in resonators containing such prisms.

Reflection and Refraction of Gaussian Light Beams at Tilted Ellipsoidal Surfaces

Abstract: This paper deals with the reflection and refraction of a gaussian laser beam at a curved interface between media of different refractive indices. The analysis extends beyond the usual case of normal incidence at spherical surfaces to include arbitrary angles of incidence and interfaces of ellipsoidal shape. By matching the transverse variations of optical phase at the interface, equations for the spot sizes and wavefront radii of the beams are obtained. These results have been converted to ray matrix form, which is particularly convenient for analyzing thick lenses or systems of several elements. With these matrices, one can readily design and evaluate optical systems containing such astigmatic elements as tilted spherical or cylindrical lenses and mirrors.

Efficient solution of load-deflection equations.

Abstract: Load deflection equation solution based on row operations, involving three passes of coefficient matrix, using wavefront processing and modified Gauss algorithm

Resolution in holography.

Abstract: The utility of holography for many applications will depend upon the quality and resolution of the images reconstructed from the hologram. In this paper some of the practical limitations encountered in the'attainment of high resolution images from holograms are investigated on a theoretical and experimental basis. The ultimate resolution of a holographic system depends upon the numerical aperture of the system, but it is found that the aberrations introduced by practical tolerances will generally limit the resolution to something less than the optimum value. The limiting factor found in this study was the angular alignment of the reconstruction wavefront.

Reconstruction of Objects from Their Sound‐Diffraction Patterns

Abstract: A method is presented for reconstructing the shape of an object from a measurement of the diffraction pattern of the object when placed in the path of a monochromatic sound wave. It is shown that measurements of amplitude and phase in a plane at a distance from the object enable reconstruction of the wavefront everywhere. It is further shown that measurements at only a discrete set of points (a square lattice of suitable dimensions) suffice. The results of computer simulation, as well as of an experiment conducted in an anechoic chamber, are presented.

Holographic polarization recording with an encoded reference beam

Abstract: Complete wavefront reconstruction, including polarization, is accomplished with an encoded reference beam, generated by using a single depolarizing diffuser as the reference beam source. The orthogonal polarization components of the object wave are encoded by different random wavefronts because of the scattering properties of the depolarizing diffuser.

Improvements in feedback apparatus for stabilizing holograms

Abstract: Method and apparatus for stabilizing the wave fronts at the recording plane of a hologram during hologram manufacture or while viewing a stored-beam interferogram. The disclosed system alleviates vibration isolation restrictions normally encountered with holographic work. A negative feedback system is utilized to monitor the change in intensity of a reconstructed optical wave front of light transmitted through or reflected from the hologram, relate such change to a known change in phase, and to phase modulate either the reference or signal beam accordingly. The intensity is monitored in either the signal beam or reference beam portion of the transmitted or reflected light. The wave fronts are controlled by adjusting the phase of either beam in accordance with a control signal. The negative feedback system includes a photodetector, a band-pass amplifier, a phase detector, a signal generator, a summing amplifier, a high voltage amplifier and an electro-optic phase modulator. Special purpose embodiments suitable for sampling local density fluctuation in a flowing gas are disclosed. Optional embodiments employing AC or DC stabilization circuits are presented.

Information Processing with Coherent Light

Abstract: In any plane of an optical tract coherent light is fully described by the complex amplitude, that is to say by a two-valued function. Nevertheless, it can be also described by a one-valued or real function, such as photographic density plus a known, coherent reference wave. This is the basis of wavefront reconstruction or holography. The history of holography is presented, and some of its applications, such as holographic interferometry, contour mapping and three-dimensional pictures in monochrome or in natural colours are discussed. Some prospective applications are holographic panoramas and three-dimensional projection of moving pictures. Information coding and storage are very promising applications, but held up by the phenomenon of ‘laser speckle’. Finally it is pointed out that holographic coding, which is a very complicated and multi-dimensional type of coding, has greater potentiality than expected on the basis of Shannon's communication theory. With a code of blocks consisting of N data only N dat...

The Performance of Optical Systems with Quasi-Monochromatic Partially Coherent Illumination

Abstract: The design and the prediction of the imagery of an optical system that is used with partially coherent illumination are complicated by the nonlinearities of this operation. The performance of the optical system is affected by both the nature of the illumination and the characteristics of the object, as well as by the aberrations of the system. A program for computing the energy distribution in the images of a class of standard objects as a function of the illumination and the pupil function of the optical system has been written. The theoretical approach is similar to that described by H. H. Hopkins in 1957.

Radiation translation by rotary transducer scanning

Abstract: A METHOD AND APPARATUS FOR SCANNING A RADIATION FIELD CARRYING INFORMATION OF AN OBJECT WITH ONE OR MORE POINT TRANSDUCERS ATTACHED TO A CIRCULAR DISK WHICH IS ROTATED FOR THE TRANSDUCER OR TRANSDUCERS TO SCAN OUT A DESIRED SURFACE OF THE RADIATION FIELD. THE SPECIFIC SYSTEMS DISCLOSED TRANSLATE ACOUSTIC ENERGY INTO LIGHT ENERGY HAVING A CORRESPONDING WAVEFRONT, THEREBY TO GIVE A VISUAL IMAGE OF THE ULTRASONIC WAVEFRONT SCANNED. BOTH HOLOGRAPHIC AND NON-HOLOGRAPHIC IMAGING SYSTEMS UTILIZING VARIOUS FORMS OF THE ROTARY POINT TRANSDUCER SCANNER ARE DISCLOSED. A TECHNIQUE FOR HOLOGRAPHIC IMAGING OF A MOVING OBJECT BY SCANNING A POINT RECEIVER ALONG A LINE IS ALSO DISCLOSED.

Hologram Schlieren and Phase-Contrast Methods

Abstract: Holography was applied to the schlieren and phase-contrast methods and enabled the visualization of a minute phase change occurring in an object which scattered light. One makes a hologram first with the phase object in position and afterwards illuminates it by the object illuminating beam with the object out of the path. Then the phase change due to the object is made to add to the reconstructed reference wavefront and is rendered visible by spatial-filtering the point image formed by the wavefront. First experiment was carried out of a striation of liquid in a cell which was illuminated diffusely from behind. This principle is also applicable to the removal of aberrations of a conventional arrangement for transparent objects. The second experiment was performed of a hot soldering iron placed in a pipe of glass and a sensitivity competitive to that realized by using an aberration-free arrangement was obtained. An accuracy necessary to locate the hologram plate to its original position and the effect of the emulsion shrinkage were also discussed.

Shearing interferometry by wavefront reconstruction using a single exposure

Abstract: Wavefront reconstruction techniques are used to produce a shearing interferogram of an object. The desired shear of the object is produced by birefringent elements which make it possible to record simultaneously two holograms on a photographic plate. This avoids the errors due to the instability of the recording apparatus which are usually present when two exposures are made successively. The method is applicable to stationary phenomena and to those transient phenomena which change inappreciably during the time of exposure.

Multiple-Beam Interferometry by Wavefront Reconstruction

Abstract: A method is presented for producing multiple-beam interferograms by using holographic techniques. A conventional image hologram of the object under test is processed in such a way that nonlinearities are introduced. Then, in the reconstruction process, several reconstructed images of the object with successively amplified phase will arise from the consecutive diffraction orders. These images are made to superpose and form the multiple-beam interferogram by illuminating the hologram with an appropriate set of illuminating beams. The method is useful for testing optical surfaces and systems as well as in studies of refractive-index variations in transparent objects. One of the advantages of the method is that multiple-beam Fizeau fringes can be obtained from a non-reflecting object with a single light passage through the object.

Long‐Wavelength Acoustic Holography

Abstract: To date, acoustic holography has been used as a means of acoustically imaging objects. Since faithful imaging requires short wavelengths, interest has centered on ultrasonic holography. The idea of this paper is to show that acoustic holography using long wavelengths (several centimeters or more) is a valuable tool for studying acoustic phenomena. In the experiment described, the acoustic wavefront radiating from a thin plate vibrating in air is reconstructed optically. At the test frequency of 9800 Hz, the plate is vibrating below coincidence frequency, i e., the bending wavelength in the plate is shorter than the wavelength in air. The holographically produced real optical image of the plate shows that the edge of the plate and the point of excitation are the principal contributors to the farfield sound pattern. This image is the first direct experimental evidence of the “edge‐effect” and “force‐distortion” radiation previously predicted theoretically. Other specific applications of long‐wavelength acou...

Holographic data reduction with periodic dispersive mediums and method of orthoscopic image reconstruction

Abstract: A method of holography in which the object wavefront is dispersed before reaching the hologram detector for recordation thereon and an image-carrying diffracted wavefront reconstructed from the hologram detector is dispersed in a manner related to the dispersion of the object wave front during the hologram''s construction. Several specific techniques are disclosed for reconstructing an orthoscopic (actual) image of the object. A preferred technique for reconstructing an orthoscopic image includes making from such a hologram a second hologram without dispersion of the wave front recorded on the second hologram. Dispersion techniques for reducing the space-spatial frequency product of the information holographically recorded are also disclosed wherein a periodically phase-varying diffusion plate etched on one side thereof is utilized for wave front dispersion.

Method for detecting an aberration-compensated image

Abstract: This invention relates to a method for sharply detecting an image which comprises, preparing a hologram with an aberrationfree wave front and an aberration wave front, illuminating the hologram with a wave front produced as a result of removing only the change in light path length caused by a phenomenon to be measured or of adding newly the change in the light path length from or to the aberration front, and effecting filtering such as the schlieren method or phase difference method at the focus of the aberration-free wave front against the change in the wave front caused by the phenomenon and superimposed on the aberration-free wave front.

The use of an improved diffraction grating interferometer.

Abstract: A conventional schlieren system was converted into a Kraushaar interferometer by the addition of matched diffraction gratings as the beam splitting and recombination elements. Optical quality of the added features of this installation were shown to be not a limiting factor, but the optical platform must be isolated well for good results. Basic optical theory applicable to this device is summarized. Several aspects are indicated which enhance the fringe or image quality. This device has been used to find the surface pressures and flow field structure around some simple two-dimensional airfoil shapes. Comparison of these results with calculations indicates good agreement between the diffraction grating interferometer data and analytical data.

Mapping the Earth with Elastic Wave Holography

Abstract: Remote sensing of the earth has been carried on for many years by the use of transient elastic waves, as in the seismic method. With the advent of optical holography and the development of high-power sonic sources and electromechanical vibrators, it is now possible to map the subsurface structure of the earth with steady-state coherent waves. This is the process of earth holography, which provides a three-dimensional optical view of the earth's interior. The basic principles of wavefront reconstruction in optics are reviewed and their application to sonic and seismic wave holography discussed. The problems of scaling and field sampling are discussed in connection with the resolution of elastic wave systems. It is shown that the sampling density required is within practical field limits for adequate resolution. Experiments were carried out with a small water tank model using frequencies in the low MHz range and small metal objects. Data were recorded on magnetic tape and subsequently displayed. The resulting holograms and photographs of the reconstructed images are shown. Synthetic holograms and reconstructions are shown and the problems of recording and display are discussed. Possible extensions of this work to large area, deep mapping of the oceans and the earth are outlined.

Design of a wavefront shearing interferometer useful for testing large aperture optical systems

Abstract: The construction of a Drew type variable shear wavefront shearing interferometer, useful for testing optical systems of large aperture and short focal length, is described. The mechanical arangement, used for adjustment of the mirrors and the dividing plate, and a novel arrangement to achieve white light compensation easily, are described. Sheared interferograms of some lenses are shown.

Electro-optical decorrelation of wavefront distortion due to atmospheric scintillation

Abstract: A device for determining the angular position of a light source wherein light from the source is received by a lens, split into two paths, and detected by quadrant detectors placed before the focal point of the first path and after the focal point of the second path. The out-of-focus image (blur circle) received by one detector is inverted with respect to the image received by the other detector. The blur circles received by the detectors contain variations in intensity due to atmospheric scintillation. By comparing the light intensity received by the quadrants of each detector, the effects due to atmospheric scintillation are canceled, and the true angular position of the light source with respect to the axis of the detectors may be determined.

Waves on a Spherical Shell

Abstract: Within the framework of classical linear elasticity theory, the dynamic equations governing the motion of a spherical shell are given. These include the effects of transverse shear and rotatory inertia, and can be derived on the basis of three assumptions additional to those of linear elasticity. The response of an incomplete spherical shell subject to a suddenly applied, constant moment Mθ is studied. The wavefront behavior of the solution is found by taking the Laplace transform of the equations, and then making an asymptotic expansion for large values of p, the Laplace variable. The solution is given in the form of a traveling wave, which is followed into the focus point and on its reflection from there. The applied discontinuity at the wavefront grows as θ → π; it gives a square‐root singularity at θ = π, and a logarithmic singularity on the reflected wavefront. These results are synthesized by an elliptic function.

Light intensity redistribution

Abstract: 1,144,182 Optical systems PERKIN-ELMER CORP May 26, 1966, No 23677/66 Heading G2J A beam of coherent light having a predetermined intensity distribution and a predetermined equiphase surface is produced by passing a beam of coherent light having a different intensity distribution along optical paths in an optical system having an optical surface which redistributes the rays to alter the intensity distribution and at least one optical surface spaced from the first surface which redirects the redistributed rays to their original direction Light source 10, eg a gas type laser emits a continuous beam of light having a planar wavefront The optical system has lens 12, 13 spaced along optical axis 14 The surface 17 redistributes the rays 11 into a beam of substantially uniform intensity while the surface 18 forms the planar wavefront Data and formulae are given for calculation of the radii of the surfaces 17, 18

Propagation of Shear‐Stress Waves in an Infinite Nonhomogeneous Elastic Medium with Cylindrical Cavity

Abstract: The problem of the radial propagation of shear waves in a nonhomogeneous elastic medium with a cylindrical cavity is solved by the theory of propagating surfaces of discontinuity. Thus, numerical integration that is required in using method of characteristics is avoided. An analytical solution, in the form of a Taylor series expanded about the time of arrival of the wavefront, is obtained. Two numerical examples, which are shown to agree with previous results, are also presented.

Wavefront sampling in holography

Abstract: Image formation from sampled wavefronts is shown to be a special case of Monte Carlo integral evaluation. Simulation of the sampling-degraded image by a spatial filtering technique demonstrates the great superiority of Monte Carlo importance sampling to the usual uniformly spaced sampling.