Abstract: Continuous-wave phase-conjugate wavefront generation via real-time holography in Bi12 SiO20 crystals is presented. The efficiency of the device is analyzed in terms of wavefront reflectivity. Electro-optic configurations allowing gain in the reflected wave intensity are considered. Applications include real-time imaging through phase-disturbing media, optical processing, and interferometry.

Abstract: Three widely-used nodal resequencing algorithms were tested and compared for their ability to reduce matrix profile and root-mean-square (rms) wavefront, the latter being the most critical parameter in determining matrix decomposition time in the NASTRAN finite element computer program. The three algorithms are Cuthill–McKee (CM), Gibbs–Poole–Stockmeyer (GPS), and Levy. Results are presented for a diversified collection of 30 test problems ranging in size from 59 to 2680 nodes. It is concluded that GPS is exceptionally fast, and, for the conditions under which the test was made, the algorithm best able to reduce profile and rms wavefront consistently well. An extensive bibliography of resequencing algorithms is included.

Abstract: An optical scanning system including a spinner containing at least one plane linear diffraction grating. As the spinner is rotated, a plane reconstruction wave of wavelength λ r is directed onto the grating creating a diffracted wavefront which can be focused onto an image plane. The grating is constructed so that the ratio of the reconstruction wavelength λ r to the grating period d is a value lying between the range of 1 and 1.618. The angles of incidence and diffraction of the reconstruction wavefront in a preferred embodiment, approximate 45°.

Abstract: A study was made of wavefront reversal, accompanying stimulated Brillouin scattering in various media, and of the way it was affected by the geometrical, temporal, and polarization characteristics of the exciting radiation. In an oscillator-amplifier system, practically complete compensation was achieved for phase distortions of the oscillator signal introduced by the amplifier components. The output energy of the light beam was then 3 J, its diameter was 4 mm, and its divergence (diffraction limited) was 0.3 mrad. The results of the experiments indicated a practical possibility of applying the wavefront reversal phenomenon in high-power multichannel lasers.

Abstract: There is disclosed an integrated optical design of head-up displays suitable for use in aircraft cockpits and the like. The display system is comprised of a holographic optical element (11) used as the combiner for presenting a direct view of the exterior on which are superimposed image signals generated by a source device (51) such as a cathode ray tube (12) and transmitted to the combiner through an optical system (10) including a relay lens containing tilted and decentered optical elements to compensate for the aberration present in the holographic optical element (11). There are further disclosed four relay lens design forms particularly suited for use in the design of such holographic head-up displays. The disclosure includes integrated designs in which (a) the holographic element (11) may or may not be constructed with aberrated wavefront and (b) a beam splitter is incorporated for insertion of a stand-by sight, possibly-also being tilted for the correction of aberrations.

Abstract: A method is proposed and implemented for small-signal wavefront reversal during stimulated Brillouin scattering in an optical waveguide. This method may find applications in the wavefront reversal of nanosecond pulses.

Abstract: This paper presents theoretical and experimental descriptions of a novel application of the dispersion-free point associated with a pair of adjacent doublet transitions in atomic and molecular systems. At this point it is possible to observe enormous pulse amplification of a phase-conjugated wavefront and intense visible oscillation without mirror feedback in the degenerate four-wave parametric mixing in sodium vapor doublet at the characteristic wavelength of 5894 A. At the dispersion-free point one also observes an ac Stark-free condition which permits the generation of a new type of coherent optical radiation called "cooperative phased-array radiation" (COPAR) from a phased-array system of coherently excited atoms in the medium at the wavelength.

Abstract: The design of an aplanatic optical system with two aspheric surfaces according to a method developed by Vaskas is treated in more detail. The shape of each aspheric surface is determined by a differential equation. It is shown that the ray trajectories through the optical surfaces, located between the two aspheres, are found by solving a system of N linear equations where N is the number of intermediate surfaces. An example of an aspherized aplanatic system is given.

Abstract: An analysis is made of the mode structure of a plane-parallel resonator with wavefront-reversing mirrors. An integral equation is derived for the oscillation modes of the resonator. It is shown that these modes are identical with those in a confocal resonator of the same length.

Abstract: A theoretical analysis is made of wavefront reversal of depolarized light in the four-photon interaction. Methods for implementing full spatial-polarization reversal are suggested.

Abstract: Summary. An improved finite difference scheme is applied to simulate wave propagation in the vicinity of a slot normal to the surface of an elastic half space. It provides visualization of the scattered wave pattern at a sequence of time steps, and also the components of displacement as functions of time at a series of observation points. After being hit by a normally incident plane P pulse, the slot oscillates with two main cycles and two shear-compressional pairs of diffracted waves, and also Rayleigh pulses, are scattered from it. The resulting wavefronts are parallel to the vertical surfaces of the slot and curve in semicircular arcs around the bottom of the slot. Experimental tests of the theory were performed, using 0.5-6 MHz ultrasonic pulses on duralumin cylinders with surface-breaking slots ranging from 0.5-2 mm in width and from 2-6 mm in depth. The numerical results were confirmed by these experiments.

Abstract: A simple interferometric method capable of displaying quantitatively the wave front aberration of any image-forming optical system is described. Its application for testing and aligning grazing incidence reflection optics at the same conjugates as those of short-wavelength use is demonstrated. The image-forming wave front from the system being tested is compared with a true spherical wave front generated within the interferometer from a point at the intended focus. The differences are displayed as a fringe pattern superimposed on an image of the exit pupil. Each fringe corresponds to one wavelength of separation between the actual image-forming wave front and the Gaussian reference sphere. The principle originates from a paper by W. P. Linnik published in Russian and German in 1933. A translation is included as an appendix. Four variations on Linnik’s design are discussed, one of which avoids the use of transmitting optics and normal incidence reflections altogether and could therefore be used at ultraviolet or soft x-ray wavelengths.

Abstract: A simple closed-loop system for estimating optical phase, called an interference phase loop, is presented. In this system the output intensity from an elementary interferometric phase sensor (e.g., Zernike phase contrast, homodyne, heterodyne, polarization, or shearing interferometer) is detected and used to drive a phase modulator in the path of the wavefront being measured. It is shown theoretically and experimentally that with large gain this configuration ignores amplitude fluctuations and unambiguously estimates phase at high speed over a dynamic range of multiple-pi radians. When self-interference (e.g., Zernike phase contrast) is employed, monochromatic light is not required.

Abstract: The transmission of ultrasonic wavefronts through a medium and the reflection of these wavefronts from an object or interface depend upon the bulk mechanical properties of the medium or object. Measuring or visualizing the wavefront yields important information about various transmission media and objects under study and has found application in nondestructive evaluation, medical diagnosis, underwater imaging, and acoustic microscopy. This paper reviews the various methods by which ultrasonic wavefronts are detected, measured, and visualized. Special emphasis is placed on optical diffraction by ultrasound and optical interferometric detection of acoustic particle displacement. Shorter summaries are given of chemical, thermal, liquid crystal, electromechanical, and mechanical methods. The distinction between these methods are not always clear. For example, the displacement of an air/water interface by radiation force is a mechanical method even though the displacement may be recorded optically. Therefore, an attempt is made to distinguish between the physical effect of the wavefronts on the medium or measurement device as opposed to the process used to record that effect.

Abstract: This paper describes a shearing interferometer capable of the direct measurement of the slopes and curvatures of reflecting plates. The wavefront shear is produced by a double-frequency grating which is simply a grating containing two closely spaced frequencies. The first-order waves associated with each frequency form the interferogram, the contours of which are related to the model's slope or curvature depending upon system arrangement and recording procedure.

Abstract: A holographic scanning system includes a reflective type holographic spinner having a plurality of diffraction gratings on its surface. A reconstruction wavefront incident on a non-grating surface of the spinner is reflected into a corrective optical element which displaces and redirects the wavefront so that it is incident at the grating at an angle corrected for the effects of spinner wobble.

Abstract: The fundamental measurement required for proof of quality of an optical system is the shape of its transmitted wavefront. A knowledge of wavefront error and the transmission characteristics of an optical system allow calculation (at the measurement wavelength) of all commonly used quality factors such as optical transfer function, point spread function, Strehi ratio, etc. This paper describes a recently developed shearing interferometer that is designed for general purpose laboratory use. Included is a description of the instrument characteristics and principle of operation as well as a comparison of measured and theoretical accuracy limits.

Abstract: A technique is described which converts in real time the fringe pattern resulting from two interfering beams into a wavefront map. The interferometer incorporates, as part of a servo system, a piezoelectrically driven mirror that is capable of applying both a known optical phase offset and a periodic optical phase modulation to one beam. The ac signal detected by a single photodiode is processed to generate an error signal for the servo system and a signal proportional to the optical phase difference between the two beams. Three instruments built on this principle will be discussed. The instruments are capable of detecting phase differences with a precision approaching A/100 and may be used for measuring surface topography (roughness, irregularity) or transparent phase objects such as biological samples, microballoons and gradient index materials.

Abstract: A system of three ordinary non-linear first order differential equations is proposed for the computation of the geometrical spreading of the wave front of a seismic body wave in a three-dimensional medium. The variables of the system are the parameters which provide a second order approximation of the wave front.

Abstract: A system to achieve heterodyne detection of optical (i.e., infrared, visible and ultraviolet) signal wavefront is disclosed. The system employs a holographic phase grating that, when illuminated by laser radiation, will generate a plurality of wavefronts each of which has a predetermined spatial distribution of amplitude and phase. The grating is part of an optical local oscillator that includes a laser that illuminates the holographic phase grating. The system further includes a mechanism to receive an optical-signal wavefronts and combine this wavefront with a plurality of local-oscillator wavefronts to provide combined optical wave fields that are applied as input to an array of discrete detector elements; each detector of the array optimally mixes the one local-oscillator wavefront directed to it with the optical-signal wavefront and generates therefrom an electrical output with optimum detection efficiency and with optimum amplitude and fixed phase relationships to the outputs of the other detectors of the array. The optical heterodyne array detection system produces detection of a plurality of optical-signal, spatial-resolution elements simultaneously.

Abstract: An analysis is made of the problem of determination of the oscillation modes in a plane-parallel resonator with one wavefront-reversing mirror. No restrictions are imposed on the dimensions of the mirrors forming the resonator. Expressions are obtained for the fields of the oscillation modes on the mirrors. It is shown that these fields are in the form of Gaussian-Hermitian beams with parameters depending on the ratio of the transverse dimensions of the mirrors.

Abstract: We aim to shed some new light on the concept of wavefront dislocations by using ideas from catastrophe theory. Wavefront dislocations were originally defined as phase singularities in a complex wavefunction, which provides a very convenient way to analyse their properties. The reason why wavefront dislocations are common features of wavefields is explained by considering some typical global behaviour of wavefronts. Catastrophe theory tells us that in two dimensions we should consider the wavefronts around a cusp caustic. Consideration of the way dislocations are likely to be observed experimentally suggests that they may be regarded as wavefront catastrophes of a real wavefunction. We can theref.

Abstract: Reflective holographic elements replayed at the 10.6 μm wavelength of the CO 2 laser can generate wavefronts that cannot be obtained using conventional optical elements. One proposed application is to use the projected holographic real image for laser materials processing, such as cutting or soldering. Three methods are discussed for producing the required holograms: computer generation, direct recording at 10.6 μm, and indirect recording in the visible. Results are presented on image intensity roll-off and aberrations introduced in image reconstruction.

Abstract: A simple null lens is described that is moved back and forth relative to a point source to provide large amounts of variable wave front aberration. This device can be used to test a wide variety of optical components and systems.

Abstract: The basic principles of operation of the point-diffraction interferometer are briefly discussed. Properties of this interferometer such as formation of the reference wavefront at the image (allowing its use in a single-pass mode) and relative insensitivity to vibration make it especially convenient for testing large complex optical systems in situ. Examples of such kinds of tests are described.© (1979) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Abstract: Measurements of the energy spectra of infra-red images of stellar point sources were made at the Coude focus of the 3·8 m telescope at Kitt Peak National Observatory, U.S.A. A scanning slit was used to record the irradiance distribution in the image plane. Experimental results are compared with theoretical models, assuming either a circular gaussian or a log-normal statistic for the perturbation of the complex amplitude of the incoming wavefront. In both cases the telescope central obscuration is taken into account. A good fit is obtained with the log-normal model for the highest scanning rate.