Showing papers on "Wavefront published in 1970"

Nonorthogonal optical waveguides and resonators

Abstract: The modes of propagation in optical systems which do not possess meridional planes of symmetry (nonorthogonal systems) are investigated in the case where the effect of apertures and losses can be neglected. The fundamental mode of propagation is obtained with the help of a complex ray pencil concept. An integral transformation of the field, based on a quasi-geometrical optics approximation and a first-order expansion of the point characteristic of the optical system, is given; it shows that the complex (three-dimensional) wavefront of the fundamental mode is transformed according to a generalized “ABCD law.” A simple expression is also obtained for the phase-shift experienced by the beam. The higher order modes of propagation are obtained from a power series expansion of the fundamental mode. These higher order modes are expressed, in oblique coordinates, as the product of the fundamental solution and finite series of Hermite polynomials with real arguments. In the special case of systems with rotational symmetry, these series reduce to the well-known generalized Laguerre polynomials. The theory is applicable to media such as helical gas lenses and optical waveguides suffering from slowly varying deformations in three dimensions. Nonorthogonal resonant systems are also investigated. An expression for the resonant frequencies, applicable to any three-dimensional resonator, is derived. Numerical results are given for the resonant frequencies and the resonant field of a twisted path cavity which exhibits interesting properties: the usual polarization degeneracy is lifted and the intensity pattern of all of the modes possesses a rotational symmetry.

Diffraction-Limited Scalar Image Formation with Holograms of Arbitrary Shape

Abstract: A theory of image formation is presented for a large-angle, point reference hologram, whose recording arrangement consists of a surface of arbitrary shape, a point reference source, and the object. The hologram is illuminated by a spherical wave during reconstruction. The resulting image field is similar to that of a Fourier-transform hologram. An exact, integral formulation of monochromatic, scalar diffraction theory is used to find the image field. The hologram is modeled by surface sources determined from the irradiance of the recorded field. The image field produced by the holographic system approximates the field produced by the ideal system, which forms the image of a point object by launching a converging, spherical wave.

Image Reconstruction from Phase Information Only

Abstract: A quantitative analysis of the effect on image reconstruction of discarding the amplitude information contained in a wavefront reflected by a diffusely reflecting, coherently illuminated surface is given. The image reconstruction from a phase record alone is analyzed for the perfect and imperfect phase-matching cases.

Analysis of Perturbed Lens Systems

Abstract: In tolerancing a lens system, it is necessary to know the effects of fabrication and alignment errors on the image quality. In this report, the wavefront aberration due to a small parameter perturbation is derived. This may be calculated from ray tracing through the nominal system only, and its linearity is extremely useful for tolerancing. The results are applied to the calculation of the variance, or rms, of the wavefront as a tolerancing criterion.

Observation of Waves Radiated from Circular Cylinders Caused by an Incident Pulse

Abstract: Schlieren visualization and hydrophone measurements are used to observe the radiated wavefronts which result when an acoustic pulse is incident on a metal cylinder in water. The range of size parameter ka from 138 to 1419 is considered. The wavefront positions are traced by the refraction, internal reflection, and radiation of shear and compressional waves. In the case of solid cylinders, many wavefronts display an apparent circumferential property derived from the incidence of energy from the normal to the appropriate critical angle. Identification of one of these wavefronts as resulting from previously identified “Rayleigh‐type” wave propagation and a single incident angle is denied, although the circumferential property is verified. A previously identified faster circumferential wave is attributed to a composite wavefront resulting from direct compressional transmission and an increasing number of its internal reflections. Other wavefronts depending on mode conversions are also identified. A mechanism ...

Comments on "High-resolution frequency-wavenumber spectrum analysis"

Abstract: Capon has described an estimator that can be used to discriminate between wavefronts incident upon an array of sensors from different directions. It is shown here that for a received field consisting of a single "signal" wavefront and an uncorrelated "noise" component, Capon's estimator displays less angular resolution than the conventional estimator when the amplitudes and the delays of the received wavefront are not known within a given tolerance.

Holographic apparatus with automatic control system for maintaining constant phase relation between reference and object beams

Abstract: Apparatus for making holograms is disclosed which includes an arrangement for maintaining a constant phase relationship between the object and reference beams so that the fringe pattern remains stationary during the recording period. The apparatus includes means for detecting spurious motion of the object or elements of the apparatus by means responsive to the intensity of a portion of the wavefront interference pattern. The detection signal which is taken as being indicative of a phase shift between the reference and object waves is applied to an automatic control system including amplifying means and a transducer disposed in one of the beam paths for producing a corrective phase shift thereof relative to the other beam. The quiescent operating point for the automatic control system is established by an automatic bias system which includes means for producing a signal corresponding to the average value of the intensity of the wavefront interference pattern. In one preferred embodiment a bias signal corresponding to the average value of intensity is developed by a detector with means forming a portion of the interference pattern thereon with the fringe lines being spaced such that the detector responds to an area including both constructive and destructive regions of the interference pattern.

A Holographic Technique for Recording a Hypervelocity Projectile with Front Surface Resolution

Abstract: Any motion of the scene during the exposure of a hologram results in a spatial modulation of the recorded fringe contrast. On reconstruction, this produces a spatial amplitude modulation of the reconstructed wavefront, which results in a blurring of the image, not unlike that of a conventional photograph. For motion of the scene sufficient to change the path length of the signal arm by a half wavelength, this blurring is generally prohibitive. This paper describes a proposed holographic technique which offers promise for front light resolution of targets moving at high speeds, heretofore unobtainable by conventional methods.

Dependence of Spatial and Temporal Correlation of Forward‐Scattered Underwater Sound on the Surface Statistics. II. Experiment

Abstract: The correlation of underwater sound forward scattered from a time‐varying statistically rough surface has been studied for the low‐roughness case. The surface was illuminated by a divergent sound beam. Directionality of the source and receivers was included in a surface‐illumination function. As an alternative to solving the Fresnel integral, the illuminated area was divided into subareas, for which the plane‐wave Helmholtz‐Kirchhoff treatment was valid. We used the criterion that the wavefront should be within λ/8 of the plane tangent to the wavefront over the subarea. The sound signals reflected and scattered at each subarea were separated into coherent and incoherent components, and the coherent components from the subareas were added coherently. The covariance of signals observed at a pair of receivers was computed with the aid of the bivariate Gaussian distribution function. Computations of the sound scattered by a traveling roughness, such as a gravity wave, showed that the covariance of the signals...

Holographically produced image arrays for photolithography

Abstract: This disclosure describes the generation of multiple identical images holographically. Wavefronts from a unit pattern and a pinhole array separately illuminated by branched, spatially filtered and collimated laser beams are Fourier-transformed and focused in front of a holographic medium. Illumination of the developed hologram with a laser beam conjugate to the wavefront from one of the pinholes produces a spaced array of real images of the unit pattern. The process is useful in photomask making, or as a way to directly expose photoresist in silicon device manufacture.

Electro-optical memory

Abstract: Information is optically written onto the electrically charged surface of a transparent storage medium by directing light modulated with this information at this surface. The light partially discharges the charge and creates an electrical charge pattern which remains stored for long periods. The light either may be scanned across the surface to achieve sequential information storage or may be employed to write a large amount of information in parallel, for example in the form of a hologram. The stored information may be optically recovered by directing polarized light at the storage medium and employing a suitably oriented analyzer or, in the case of hologram storage, by wavefront reconstruction.

Method of hologram recording

Abstract: METHOD OF HOLOGRAPHIC PHOTOPOLYMER RECORDING BY AN OPTICAL SYSTEM OF THE INTERFERENCE PATTERN BETWEEN WAVEFRONTS EMANATING FROM AN OBJECT ILLUMINATED WITH LASER RADIATION AND A COHERENT REFERENCE WAVEFRONT.

Response of an Elastic Cylindrical Shell to a Transverse Acoustic Shock Wave in a Light Fluid Medium

Abstract: A plane acoustic step‐wave traveling through a light fluid medium impinges upon an infinite, elastic, circular cylindrical shell whose axis is parallel to the wavefront of the incident wave. Approximate analytical expressions are given for the post‐envelopment response of the first three modes of the shell appropriate to both a rigorous treatment of the fluid‐shell interaction and a treatment that disregards the effects of the scattered wave. These analytical expressions, plus numerical computations of modal pressures and of displacement and strain responses for an aluminum shell in air, show why neglect of the scattered wave is a poor approximation.

Optimal control problems that test for envelope contacts

Abstract: Systems are studied whose state vector x is governed by the usual set of first-order differential equations. When the extremals x(t) that originate at a fixed point inn-dimensional state-variable space are stopped at a fixed final time, the locus of their endpoints defines a hypersurface called the wavefront. The well-known adjoint vector is normal to the wavefront. The principal point of this paper is that a second wavefront normal can be constructed from the δx(t) vectors that are available if the test for Jacobi conjugate points is performed. Verifying that the two normals are almost collinear shows that the errors due to computer truncation and numerical integration are negligible. This check is particularly useful when using the finite-difference approximation δx(t) ≃xi(t) − xj(t), where xi(t) and xj(t) are close but nonneighboring extremals. This approximation can simplify considerably the analysis and computation required for a conjugate-point test, particularly if the extremals have corners.

Some Optical Communications Experiments

Abstract: Experiments performed to evaluate the possibilities and limitations of beams of coherent light as carriers of wideband information are described. These include transmission of television pictures, multiplexed voice-frequency channels, and other signals over enclosed paths by both phase and amplitude modulation of optical carriers. It is shown that long-distance transmission can be achieved without serious distortion of the beam wavefront. This is verified from determinations of heterodyne detection efficiency and by direct measurements of the optical phase distribution over wavefronts which have been transmitted for distances as great as 20 miles through beam waveguides.

A variable refractive null lens.

Abstract: Null lenses, for use with rotationally symmetric but nonspherical surfaces, are extremely useful for testing during production. In general, each different system to be tested requires a different null lens. A variable null lens is proposed which consists of two aspheric plates, each of which introduces approximately fourth- or sixth-order spherical aberration. When the plates are inserted in a diverging beam, the effect on the wavefront may be changed by varying the plate spacing. The system may be used to test parabolas and other nonspherical mirrors at center of curvature, aspheric plates in conjunction with spherical mirrors, and various other systems. Once the two plates have been produced and measured, the spacing of the plates used may be determined for each test. This would normally be done by computer, using any of the optimization techniques for lens design. Examples are shown, and an estimate of obtainable accuracy is given.

A Simple Interferometric Method for Workshop Testing of Optics

Abstract: A simple step-by-step method is given for deriving the shapes of wavefronts from data obtained with a wavefront shearing interferometer. No mathematics, other than arithmetic, is used. The result is the accurate deviation of the wavefront from a reference sphere that coincides with it at three chosen reference points. The method is intended primarily for the use of opticians in optical workshops, but is also quite practical for the final testing of optics for performance rating. A method is given by which an optician can evaluate an optical surface by comparing the interferogram produced by it and a known prism interferometer, with a drawing of the desired interferogram. This procedure is analogous to using test plates for visual inspection of optical surfaces.

Degenerate Optical Cavities. III: Effect of Aberrations

Abstract: The capability of degenerate optical cavities to transmit faithfully incident optical signals with arbitrary wavefronts is limited primarily by geometrical optics aberrations. This capability is expressed by an acceptance factor which is calculated for various types of cavities lacking first-order degeneracy, or suffering from primary aberrations. It is found that the acceptance factors of spherically symmetric cavities are larger, by orders of magnitude, than the acceptance factors of cavities possessing only rotational symmetry (such as the well-known confocal cavity). The correction of primary aberrations for both types of cavities is discussed. Acceptance factors of the order of 107 with finesses of the order of 100 can be obtained. The mechanical accuracy required is, however, a few orders of magnitude higher than in conventional optical instruments.

Diffraction of Light from a Filamentary Source by Parallel Acoustic Wave Fronts

Abstract: The scattering of light by sound has been examined in the past mostly in terms of a single incident plane wave and approximations have often been used that are overly restrictive for many practical cases. To gain a better understanding of the basic diffraction process associated with realistically bounded light sources, we employ a rigorous approach to examine the irradiance from a line source or scatterer embedded in a medium traversed by an acoustic disturbance. As usual, we assume that the acoustic wave modulates the dielectric properties of the medium and thus produces a periodic stratification that serves to scatter the radiant energy. After deriving a formal solution for the scattered radiant flux produced by an arbitrary periodic modulation, we show that the principal diffraction aspects can be found by examining the simpler case of sinusoidal stratification. Since this particular case may be regarded as a prototype for the more general problem, we restrict our detailed quantitative analysis to the basic sinusoidal acoustic modulation. We find that the resulting illumination exhibits regions characterized by different diffraction effects that are intimately related to the Bragg directions prescribed by the acoustic wave fronts. These directions serve to classify the various diffraction regions into three basic varieties: (1) a set of wide angular domains wherein the radiant flux density is explainable by simple geometric-optical arguments, (2) another set of wide angular domains wherein the predominant diffraction effect is described in terms of a Bragg wave mechanism, and (3) a set of narrow angular domains that serve as transition regions between the other diffraction domains. Each transition region contains a caustic that accounts for multiple peaks of radiant energy density in the neighborhood of the Bragg directions. Physical interpretations and quantitative estimates for each diffraction domain are presented by employing asymptotic results that are very accurate for the sound intensities that are usually available.

Effects of Index Inhomogeneities on Optical Second‐Harmonic Generation

Abstract: Some nonlinear optical materials useful for optical second‐harmonic generation and parametric amplification are troubled with index inhomogeneities, one form of which is striae which are quasiperiodic variations in the indices of refraction. Propagation of a laser beam normal to the plane in which these variations occur results in servere distortion of the wavefront. Propagation along the direction of the striae minimizes the wavefront distortion but introduces variations in the propagation constant of a traveling wave. In optical second‐harmonic generation or parametric amplification this results in a quasiperiodic modulation of the momentum mismatch Δk. The effects of this modulation of the momentum mismatch on second‐harmonic generation (and hence parametric amplification) are evaluated for the idealized case of periodic index variations. It is found that the shape of the curve of harmonic generated versus average momentum mismatch (produced for example by varying the crystal temperature) has a number ...

Resolution testing of coherent optical systems by means of linear gratings.

Abstract: Testing of coherent optical data processing systems has shown a need for a method which measures resolution at all points in the image format. The use of multifrequency linear gratings as test objects satisfies this need. Quantitative data may be obtained if care is taken to calibrate and linearize the photographic process. However, the method’s principal application seems to be for qualitative testing. A comparison is made between calculated wavefront aberrations and experimental results obtained using linear gratings.

Gaussian beams in turbulent media.

Abstract: The propagation of a gaussian beam in a turbulent medium is investigated by the geometrical optics method. The correlation function as well as the structure function of the phase fluctuations at two points of an imperturbed wavefront are derived in a closed form in the two limiting cases when the points belong to two almost parallel rays or to two highly diverging rays. It is shown that the focused beams may permit a detailed investigation of the parameters of the turbulence, when the turbulence is inhomogeneous and its parameters are slowly varying functions of the coordinates.

Hologram copying for reconstruction of an aberration-free wavefront at a wavelength differing from the copying wavelength

Abstract: A first thick hologram of the wave front from an object is formed at a first wavelength to which a first hologram-recording medium is sensitive. A second hologram is recorded on a second recording medium sensitive to a second wavelength by placing the second recording medium adjacent the first and illuminating the first hologram with radiation at the second wavelength. This second hologram can then be illuminated with radiation of the first wavelength to reconstruct with minimum aberration the wave front associated with the object recorded on the first hologram.

An analysis of optical effects caused by thermally induced mirror deformations.

Abstract: This paper analyzes thermally induced mirror deformations and their resulting wavefront distortions which occur under the conditions of radially nonuniform mirror heating. The analysis is adaptable to heating produced by any radially nonuniform incident radiation. Specific examples of radiation distributions which are considered are the cosine squared and the gaussian and TEM(0, 1) laser distributions. Deformation effects are examined from two aspects, the first of which is the reflected wavefront radial phase distortion profile caused by the thermally induced surface irregularities at the mirror face. These phase distortion effects appear as aberrations in noncoherent optical applications and as the loss of spatial coherence in coherent applications. The second aspect is the gross wavefront bending due to mirror curvature effects. The analysis considers substrate material, geometry, and cooling in order to determine potential deformation controlling factors. Substrate materials are compared, and performance indicators are suggested to aid in selecting an optimum material for a given heating condition. Deformation examples are given for materials of interest and specific absorbed power levels.

Variable electro-optic element

Abstract: A variable optical device for varying the shape of a wavefront is disclosed including an electro-optic medium whose index of refraction varies as a function of the intensity of an applied electric field and means for applying to that medium an electric field whose intensity varies in a pattern representative of the spatial variation of the index of refraction of the medium required to vary the shape of a wavefront in some predetermined manner.

Method of and Apparatus for Testing the Angular Position of a Reflecting Surface

Abstract: 1,178,972. Optical testing apparatus. NATIONAL RESEARCH DEVELOPMENT CORP. Feb.8, 1967 [Feb. 10, 1966], No.5955/66. Heading G2J. In apparatus for testing the angular position of a reflecting surface R, white light from source S is passed through a wavefront inversion device I, reflected at surface R and returned through device I, the interference between light components which have suffered an odd number of wavefront inversions respectively in their outward and returns paths through device I being observed at E as an indication of the angular position of surface R. Device I comprises a cylindrical glass block with its longitudinal axis on OO' and having partially reflecting coated spherical end surfaces C, C' with a common focal plane within the block, and equal radii of curvature. Source S is at an external focal plane F of the device, and a beam splitting prism D diverts returning light to an image plane F' for observation. Images 1, and k are selected of which one is invented at surface R, whereby lateral misalignment of surface R from axis OO' may be corrected by bringing the images into coincidence. Tilting of the surface is corrected by observing the spacing of the straight fringes formed by interference between the rays forming images 1, h. Surface R is normal to axis OO' for infinite fringe spring. In a modification, a polariser is included in beam splitter D and a quarter-wave plate Q is placed between device I and surface R to eliminate unwanted reflections.