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Showing papers on "Light field published in 1998"


Patent
01 Apr 1998
TL;DR: In this paper, a simple and robust method and system for generating new views from arbitrary camera positions without depth information or feature matching, simply by combining and resampling the available images.
Abstract: Described is a simple and robust method and system for generating new views from arbitrary camera positions without depth information or feature matching, simply by combining and resampling the available images. This technique interprets input images as two-dimensional slices of a four dimensional function--the light field. This function completely characterizes the flow of light through unobstructed space in a static scene with fixed illumination. A sampled representation for light fields allows for both efficient creation and display of inward and outward looking views. Light fields may be created from large arrays of both rendered and digitized image. The latter are acquired with a video camera mounted on a computer-controlled gantry. Once a light field has been created, new views may be constructed in real time by extracting slices in appropriate directions. Also described is a compression system that is able to compress generated light fields by more than a factor of 100:1 with very little loss of fidelity. Issues of antialiasing during creation and resampling during slice extraction are also addressed.

294 citations


Book
23 Jan 1998
TL;DR: In this article, the theory of field-induced atomic transitions was introduced and discussed in an inhomogeneous light field free-electron laser laser acceleration of electrons wave packets above-threshold ionization stabilization of atoms in a strong ionizing field.
Abstract: Introduction to the theory of field-induced atomic transitions multiphoton stimulated bremsstrahlung multiphoton Compton scattering and ponderomotive forces in an inhomogeneous light field free-electron lasers laser acceleration of electrons wave packets above-threshold ionization stabilization of atoms in a strong ionizing field.

182 citations


Book ChapterDOI
29 Jun 1998
TL;DR: A lazy decompression scheme is presented which allows for high-quality compression by making use of block-coding techniques and takes advantage of spatial coherence within the light field to aid compression.
Abstract: This paper describes a series of algorithms that allow the unconstrained walkthrough of static scenes shaded with the results of precomputed global illumination. The global illumination includes specular as well as diffuse terms, and intermediate results are cached as surface light fields. The compression of such light fields is examined, and a lazy decompression scheme is presented which allows for high-quality compression by making use of block-coding techniques. This scheme takes advantage of spatial coherence within the light field to aid compression, and also makes use of temporal coherence to accelerate decompression. Finally the techniques are extended to a certain type of dynamic scene.

176 citations


Journal ArticleDOI
TL;DR: In this article, the phase behavior of a charged two-dimensional colloidal system in the presence of a periodic light field composed of two interfering laser beams was studied and the first direct experimental observation of this reentrance phenomenon was reported.
Abstract: We study the phase behavior of a charged two-dimensional colloidal system in the presence of a periodic light field composed of two interfering laser beams. Above a certain light intensity, the light field initiates a liquid-solid transition. This effect is known as light-induced freezing. When the light field is increased above a critical value, however, the induced crystal is predicted to melt into a modulated liquid again. In this paper we report the first direct experimental observation of this reentrance phenomenon.

132 citations


Book ChapterDOI
01 Aug 1998
TL;DR: A new techniques for efficiently acquiring, storing, and reconstructing light fields in a (nearly) uniform fashion and allows a uniform sampling of all five dimensions of the light field.
Abstract: Image-based or light field rendering has received much recent attention as an alternative to traditional geometric methods for modeling and rendering complex objects. A light field represents the radiance flowing through all the points in a scene in all possible directions. We explore two new techniques for efficiently acquiring, storing, and reconstructing light fields in a (nearly) uniform fashion. Both techniques sample the light field by sampling the set of lines that intersect a sphere tightly fit around a given object. Our first approach relies on uniformly subdividing the sphere and representing this subdivision in a compact data structure which allows efficient mapping of image pixels or rays to sphere points and then to subdivision elements. We sample a light field by joining pairs of subdivision elements and store the resulting samples in a multi-resolution, highly compressed fashion that allows efficient rendering. Our second method allows a uniform sampling of all five dimensions of the light field, using hierarchical subdivision for directional space and uniform grid sampling for positional space. Light field models are acquired using parallel projections along a set of uniform directions. Depth information can also be stored for high-quality image rendering. The system can provide bounds on key sources of error in the representation and can be generalized to arbitrary scenes comprising multiple complex objects.

123 citations


Book
01 Jan 1998
TL;DR: In this article, the authors describe phase in classical and nonlinear optics phase-space description of light field phase in quantum optics phasedependent measurements, including phase-dependent measurements of light fields.
Abstract: Phase in classical and nonlinear optics phase-space description of light field phase in quantum optics phase-dependent measurements.

72 citations


Journal ArticleDOI
TL;DR: In this paper, a unified approach to the problem of optical decomposition of coherent light fields in terms of orthogonal bases with rotor or angular harmonics is presented. And the results of computer simulation are discussed.
Abstract: We take a unified approach to the problem of an optical decomposition of coherent light fields in terms of orthogonal bases with rotor or angular harmonics. Examples of such bases are given: functions describing diffraction-free beam (Bessel functions), circular Zernike polynomials and modal Gauss–Laguerre functions. We consider an iterative algorithm for the design of phase diffractive optical elements serving to decompose the coherent light field in terms of the mentioned bases. The results of computer simulation are discussed.

67 citations


Journal ArticleDOI
01 Sep 1998
TL;DR: In this article, a mooring was deployed in the Sargasso Sea near Bermuda in September 1994 to collect time series of water pressure, spectral downwelling irradiance (Ed), and spectral upwelling radiance (Lu) at 412, 443, 490, 510, 555, 665, and 683 nm.
Abstract: Examples of short-term variations of the underwater light field associated with surface-wave focusing and cloud cover, and occurring at intermediate depths of the euphotic zone in the oligotrophic ocean are discussed. Time series of water pressure, spectral downwelling irradiance (Ed), and spectral upwelling radiance (Lu) at 412, 443, 490, 510, 555, 665, and 683 nm were acquired with moored instruments. The mooring was deployed in the Sargasso Sea near Bermuda in September 1994. The measurements were made at 15 and 35 m once every hour from 6 a.m. to 8 p.m. local time, with a 6 Hz sampling rate over time periods of 2 or 5 min duration. Time series of Ed, Lu, and water pressure were subject to spectral analysis. Under clear sky conditions, the power spectra of Ed at the blue/green wavelengths exhibited distinct maxima due to focusing of sunlight by surface waves. These maxima were located at a frequency higher than the dominant frequency in the power spectrum of water pressure variations. Similar maxima were present in the power spectra of Lu, but the position of the peak was dependent on light wavelength. The coefficient of variation for Ed and Lu depended on light wavelength and increased towards the red wavelengths. This coefficient was much smaller for Lu than for Ed, which reflects the fact that the upwelling light field is less affected by wave focusing than the downwelling light field. At depths of our measurements, the light fluctuations in the red can be attributed to variations in inelastically scattered radiation, that is, the fluorescence of phytoplankton cells and Raman scattering. This is because the fluoresced light and Raman scattered light in the red follow fluctuations that occur at shorter excitation wavelengths. When clouds covered the sky, we observed a decrease of the coefficient of variation for Ed and Lu. In this case, the fluctuations of light were well correlated with variations of water pressure associated with water surface displacement due to the wave motion.

55 citations


Journal ArticleDOI
TL;DR: In an optical lattice the interaction of an atomic gas with a spatially modulated light field is exploited to damp the atomic motion and then to trap the slowly moving atoms on a regular array of points associated with particular local states of the light field.
Abstract: In an optical lattice the interaction of an atomic gas with a spatially modulated light field is exploited to damp the atomic motion and then to trap the slowly moving atoms on a regular array of points associated with particular local states of the light field. The result of this process is the formation, from the initially cold but disordered gas, of a structure reminiscent of those found in solid-state crystalline materials. The study of these novel, optically-bound media necessitates the introduction to the description of the atom-light interaction of concepts more usually encountered in solid-state physics and promises to shed new light on the nature of atom-light interactions. Additionally, it provides a new means for the precise and highly parallel manipulation of atoms and a novel test-bed for some fundamental problems in physics.

44 citations


Patent
03 Apr 1998
TL;DR: In this paper, a method for particle size detection comprises passing particles in a fluid medium relative to a light source which generates a light field the optical axis of which is transverse to the direction of fluid movement relative to the said light source.
Abstract: A method for particle size detection comprises passing particles in a fluid medium relative to a light source which generates a light field the optical axis of which is transverse to the direction of fluid movement relative to the said light source and having a plurality of non-interferometrically formed variations in intensity spaced along the direction of movement of the particles relative to the light field, detecting variations in light intensity caused by the particles as they pass through the variations in the light field, and measuring the size of a detected particle substantially independently of the optical characteristics of the particle by plotting the mean peak signal as a function of the normalised peak-to-trough variation in the output pulses generated by the passages of the particle through the light field.

33 citations


Patent
03 Mar 1998
TL;DR: In this paper, an off-axis photon stimulation of a person's eye, provided by a light field which is either uniform or interactive depending on pupil position, provides for biological and/or psychological benefits.
Abstract: Off axis photon stimulation of a person's eye, provided by a light field which is either uniform or interactive depending on pupil position, provides for biological and/or psychological benefits. The photon stimulation is advantageously provided using eye wear with embedded or affixed light delivery elements such as fiber optic members.

Journal ArticleDOI
TL;DR: In this article, a standing wave formed by two counterpropagating beams is folded and brought into intersection with itself, and the values of the relative timephases are stable, a priori known, and can be altered arbitrarily by means of retardation plates.

Patent
04 Feb 1998
TL;DR: In this article, the arrangement has a rastered light field with a matrix of grouped light sources controllable individually, in groups or as a whole, and a lens system with a spatially defined light distribution.
Abstract: The arrangement has a rastered light field with a matrix of grouped light sources controllable individually, in groups or as a whole, esp. LEDs (14), on a printed board (10) and a lens system with a spatially defined light distribution. The lens system contains at least one scattering lens (12) extending over the entire light field and of externally flat profile and with internal parallel grooves (18) with at least partially asymmetrically curved surfaces (26). The plane region is slightly angled between the grooves. An Independent claim is also included for a method of monitoring the light intensity of the arrangement.

Patent
15 Jan 1998
TL;DR: In this article, a computer system to project and localize radiation treatment portals on patient skin without using a light field is disclosed, which includes a multimedia software program that interacts with a three-dimensional digitizer which acquires the coordinates of any point in space that is accessible by the probe.
Abstract: A computer system to project and localize radiation treatment portals, i.e., field center, field borders, on patient skin without using a light field is disclosed. The system includes a multimedia software program that interacts with a three-dimensional digitizer which acquires the coordinates of any point in space that is accessible by the digitizer probe. The system constructs and employs coordinate system transformations from digitizer coordinates to room coordinates to radiation beam coordinates. For any point digitized, the invention system calculates the position of this point relative to the radiation field, and displays or signals to the user whether the digitized point is in the radiation field, outside of the field or on the field border. This is accomplished through a screen display of the radiation beam's eye view, an audio signal and/or LED light indicators mounted on the digitizer probe.

Journal ArticleDOI
V. Gomer1, F. Strauch1, B. Ueberholz1, Svenja Knappe1, Dieter Meschede1 
TL;DR: In this paper, a single-atom trap was used to study a single trapped atom in a magneto-optical trap, which is loaded from a cesium background vapor, and the intensity correlation function defined classically in terms of the fluorescence intensity was given by
Abstract: Fluorescence emitted by laser-cooled atoms provides valuable information for a noninvasive study of the atomic dynamics in laser fields. If many atoms are observed, their fluorescence can fluctuate due to beating of the Dopplershifted light from different atoms. This idea was used to study atomic transport in a standing laser field on the scale of the optical wavelength @1# and for spectral analysis of scattered light from atoms in optical molasses @2# by analyzing intensity correlations. Another application of the intensity correlation technique is the observation of nonclassical behavior in the resonance fluorescence, e.g., photon antibunching @3#. In such experiments intensity fluctuations are caused by a one-atom effect, by time dependence of the atomic excitation in the light field ~Rabi oscillations!. The presence of several atoms or, even worse, fluctuations of the atom number in the observation region leads to a smearing out of the correlation signal. This makes a single trapped ion the best experimental choice @3#. Trapping of individual ions was accomplished a long time ago @4#, but only recently has it been for neutral atoms @5#. Using a standard magneto-optical trap ~MOT !@ 6 #, which is loaded from a cesium background vapor, we study fluorescence fluctuations from a single trapped atom. We will show here that single-atom trapping causes atomic dynamics to manifest itself in fluorescence fluctuations at all relevant time scales. At the shortest time scale ~nanoseconds! we have found intensity correlations in the form of Rabi oscillations. The Rabi frequency is a measure of the interaction strength of the local electric field and the atomic dipole and gives direct access to the internal dynamics of the atom. At a microsecond time scale additional intensity fluctuations ~and also polarization fluctuations observed in @1#! become visible. These are induced by atomic motion through the standing light fields. At even larger times, atomic transport up to macroscopic ~trap size! scales can be studied, provided that photon detection is spatially resolved @7#. Thus a single simple method allows us to analyze both qualitatively and quantatively the details of the atom-field interaction in a self-consistent manner. The intensity correlation function defined classically in terms of the fluorescence intensity I(t) is given by

Journal ArticleDOI
TL;DR: In this article, an analytic classical relativistic derivation for a general expression of the harmonic power generated per unit laboratory solid angle due to Compton scattering of plane wave, linearly polarized light of arbitrary intensity from free electrons moving initially with arbitrary velocity.
Abstract: We present an analytic classical relativistic derivation for a general expression of the harmonic power generated per unit laboratory solid angle due to Compton scattering of plane wave, linearly polarized light of arbitrary intensity from free electrons moving initially with arbitrary velocity. We show graphically the generated frequency as a function of the coordinates of the observation point for several initial electron kinetic energies and light field intensities.

Journal ArticleDOI
01 Jul 1998-EPL
TL;DR: In this article, a dielectric sphere was attached to the AFM cantilever and placed into the evanescent light field of the Ar-laser beam illuminating a sapphire prism surface at an angle larger than the critical.
Abstract: We present the first direct measurement of the radiation pressure force acting on a sphere in the evanescent field of a totally reflected light beam using the atomic force microscope (AFM). A dielectric sphere was attached to the AFM cantilever and placed into the evanescent light field of the Ar-laser beam illuminating a sapphire prism surface at an angle larger than the critical. A repulsive force due to the evanescent field was observed. The force decreases exponentially with the characteristic length of (45 ± 20) nm as the distance between the sphere and the total reflection surface increases. The measured magnitude of the force close to the surface is (3 ± 1.5) 10−10 N. Both the magnitude and the decay length are in good agreement with the calculated values.

Proceedings ArticleDOI
19 Aug 1998
TL;DR: In this article, a phase Zernike filter was designed to decompose the coherent wavefront into a set of diffraction orders with amplitudes proportional to the circular Zernikes polynomials.
Abstract: Aberration of the coherent wavefront are analyzed using a phase Zernike filter. Developed iterative methods allow us to design a filter that decomposes the analyzed light field into a set of diffraction orders with amplitudes proportional to the circular Zernike polynomials. Operation of a 25-channel filter is simulated.

Journal ArticleDOI
TL;DR: In this article, the light force on slow atoms in a light field with an arbitrary polarization distribution is explicitly evaluated in the case of an atomic transition J→J with half-integer J values.

Proceedings ArticleDOI
01 Sep 1998
TL;DR: This paper applies light field reconstruction and rendering of object views to the problem of automatic generation of training material for a statistical object recognition system and shows how the recognition rate of the classifier trained by the light field depends on its resolution.
Abstract: In this paper we apply light field reconstruction and rendering of object views to the problem of automatic generation of training material for a statistical object recognition system. The advantages of using a light field instead of real images are shown. We evaluate with respect to the error rate of the classifier, whether the reconstructed light field can be applied to the training step. We also show how the recognition rate of the classifier trained by the light field depends on its resolution.

Journal ArticleDOI
TL;DR: In this article, a theory for photo-induced phase transition in a Peierls system being irradiated by light with a finite width of the optical spectrum and a central frequency close to the upper van Hove singularity is presented.
Abstract: A theory is constructed that explains photoinduced phase transitions in a Peierls system being irradiated by light with a finite width of the optical spectrum and a central frequency close to the upper van Hove singularity of the first kind in the combined density of electron states. The electron spectrum and the matrix elements of the dipole-moment operator are calculated by Bogolyubov’s method of canonical transformations. The interaction with the light is described by the Liouville equation for the density matrix of the electron subsystem in the dipole approximation. The light field is considered a quasimonochromatic time-independent random process with a Lorentzian spectrum. The derived equations are analyzed for two limits: (1) when the width of the optical spectrum tends to zero (a monochromatic light field), and (2) when the width of the optical spectrum is close to the upper limit (a bifurcation point) at which a photoinduced phase transition can still be observed. An existence criterion for such a transition is obtained, and the main parameters of the transition (the critical points and the size of the hysteresis loop) are calculated. The broadening of the optical spectrum of the incident light is shown to narrow the range of values of the central frequency of the light field and to reduce the size of the hysteresis loop. Finally, near the phase transition point, cavityless optical bistability sets in in the system, with light absorption increasing in the process.

Journal ArticleDOI
TL;DR: In this article, the authors developed a systematic scheme to treat binary collisions between ultracold atoms in the presence of a strong laser field, tuned to the red of the trapping transition, where the Rabi frequency is much less than the spacing between adjacent bound-state resonances.
Abstract: We develop a systematic scheme to treat binary collisions between ultracold atoms in the presence of a strong laser field, tuned to the red of the trapping transition. We assume that the Rabi frequency is much less than the spacing between adjacent bound-state resonances. In this approach we neglect fine and hyperfine structures, but consider fully the three-dimensional aspects of the scattering process, up to the partial d wave. We apply the scheme to calculate the S matrix elements up to the second order in the ratio between the Rabi frequency and the laser detuning. We also obtain, for this simplified multichannel model, the asymmetric line shapes of photoassociation spectroscopy, and the modification of the scattering length due to the light field at low, but finite, entrance kinetic energy. We emphasize that the present calculations can be generalized to treat more realistic models, and suggest how to carry out a thorough numerical comparison to this semianalytic theory. @S1050-2947~98!04902-6#

Journal ArticleDOI
TL;DR: In this article, the physical origin of the peculiar spatio-temporal instability observed in liquid crystals subject to the influence of a light wave of ordinary polarization is revealed, and the results allow evaluation of the threshold intensity and the range of the light incidence angles where the longitudinal instability is possible.

Journal ArticleDOI
TL;DR: In this paper, a laser beam is transmitted through a vapour cell without external feedback or with feedback by a single mirror, and a lateral separation of the light field into domains of orthogonal circular polarization is found.
Abstract: The occurrence of polarization instabilities in alkaline vapours and their coupling with spatial degrees of freedom are considered. We discuss experiments in which a laser beam is transmitted through a vapour cell without external feedback or with feedback by a single mirror. In both cases a lateral separation of the light field into domains of orthogonal circular polarization is found. Without feedback, relatively simple structures like rings or two spots are obtained. With feedback, more complicated polarization patterns result from spontaneous symmetry breaking. We emphasize the crucial role of the polarization ellipticity of the input beam. Changing this control parameter we observe a transition from positive to negative hexagons in one of the circular polarization components, while simultaneously the opposite transition occurs in the other one. The transition is mediated by square patterns occurring for linear input polarization. This metamorphosis is governed by symmetry principles and therefore provides an example of the ease of influencing the symmetry properties of systems consisting of multilevel atoms interacting with a vector light field.

Journal Article
01 Dec 1998-Optik
TL;DR: In this article, an analysis of the light field and intensity distribution within a double-layer thin-film stack coated on a prism is presented, and the effect of the thickness and the refractive index of a sample is investigated in order to use the double layer structure in near-field microscopy.

Proceedings ArticleDOI
08 May 1998
TL;DR: The optical second-harmonic polarization of a magnetic medium is described by a third-rank polar tensor for the crystallographic contribution and a fourth-rank magnetization-induced part of the incoming light field and the magnetization of the medium as discussed by the authors.
Abstract: The optical second-harmonic polarization of a magnetic medium is generally described by a third-rank polar tensor for the crystallographic contribution and a fourth-rank polar tensor for the magnetization-induced part of the incoming light field and the magnetization of the medium. In centrosymmetric materials, both tensors are only nonzero at surfaces and interfaces, where the inversion symmetry is broken.

Journal Article
TL;DR: The idea to decompose the light field into sub-light-fields that do not change as scene changes is raised, which expands the advantage of light field rendering to dynamic scenes where the position and orientation of objects, lights and viewpoint can be modified arbitrarily.
Abstract: Image based rendering has displayed advantage in speed over traditional geometry based rendering algorithms. With the four dimensional light field descriptions, static scene can be generated with interactive rate on ordinary computer. The limitation of the scheme is that it can only handle static scene and fixed illumination. This paper raises the idea to decompose the light field into sub-light-fields that do not change as scene changes. It expands the advantage of light field rendering to dynamic scenes where the position and orientation of objects, lights and viewpoint can be modified arbitrarily. The sub-light-fields include: ambient light field and spot light field. The latter is actually an eight- dimensional space. Because diffuse reflection is independent on view direction, this paper presents a four- dimensional representation of spot light field. Considering the linearity of diffuse reflection to different spot lights, the spot light fields of an object can be represented by the reflection light field to a pure-color light with unit intensity, to decrease storage and preprocessing. Owing to the coherency in their data structures, data of the corresponding point in the ambient light field, diffuse light field and depth field are combined into a 5- dimensional vector which can be compressed efficiently with vector quantization. The algorithm given in this paper accurately computes typical characteristics of dynamic scene such as changes in surface color and shadow.

Proceedings ArticleDOI
11 Nov 1998
TL;DR: In this paper, a theoretical model for the near field of light diffracted by ultrasound in an isotropic medium which becomes birefringent in the presence of an acoustic wave was presented.
Abstract: A theoretical model is presented for the study of the near field of light diffracted by ultrasound in an isotropic medium which becomes birefringent in the presence of an acoustic wave. Due to the interference with the sound wave, the diffracted light wave in its near field is seen to act as a quasi-monochromatic light wave which is partially polarized. Thedegree of coherence is seen to coincide with the degree of polarization and can be controlled acoustically. Hence coherentlaser light can be transformed into incoherent light by sending it through an isotropic material with acoustically inducedbirefringence. In the experimental part of the work, the non-diagonal elements of the diffracted light beam coherencymatrix were measured and a good agreement with the theoretical model was obtained.Keywords: Ultrasonic light diffraction, acousto-optic interaction, acoustically induced birefringence, optical near field,degree ofpolarization, degree of coherence 1. INTRODUCTION In ultrasonic light diffraction (ULD), one can distinguish between the far field (Fraunhofer region) and the near field(Fresnel region) of the diffracted light. In the former, a lens is usually required to isolate the various diffraction orders,especially if the diffraction angles are small. Without a lens, it is possible to observe an interference pattern on a screenplaced on any plane where the diffraction orders are not yet separated in space. These planes are situated in the opticalnear field of the diffracted light. In that region, one can observe a modulation of the intensity of the diffracted light field,which is extremely sensitive to variations ofthe ultrasonic amplitude15. Moreover, from the patterrn of this modulation, itis possible to reconstruct the time waveform ofthe diffracting ultrasonic beam'.Thus far, the near field of light diffracted by ultrasound has been studied in isotropic media. In anisotropic media,like transparant birefringent materials, additional effects occur. As known, when light passes through a UniaXial crystal, itis decomposed into two mutually perpendicular and linearly polarized light beams, an ordinary and extraordinary ray.Due to the birefringency, the two beams meet different refractive indices, which results into an accumulated phase shift.In general, the final result is an elliptically polarized light beam. This phenomenon does not occur in isotropic media likewater or in cubic crystals like fused silica. However, if the birefringence is induced acoustically, the effects are multipleand very interesting, even in some liquids8. In addition to the accumulated phase shift, both orthogonal light componentsare diffracted by the sound grating, the diffraction effects being different for both rays because of the birefringence. Thecombination of all these effects results into a whole scale of polarization effects in all diffraction orders. Moreover, as theeffects are produced by the sound wave, the state of polarization (ellipticity and azimuth angle) can be controlled to a highdegree by varying the acoustic parameters9'2.

Proceedings ArticleDOI
03 Aug 1998
TL;DR: One-dimensional light field synthesis is carried out by means of two one-dimensional phase elements located at some distances along the beam propagation as discussed by the authors, and the masks were realized experimentally on dichromated gelatin layers which were made by sensibilization of standard holographic photoplates.
Abstract: In reference 1 it was shown that beams containing phase singularities have enough various intensity distributions, in particular, the distribution looked like an arbitrary planar curve. In this work we present a method of synthesis of these beams by means of one-dimensional phase elements. The basis of the method is the result stated in reference 1 that Fourier transform with an additional astigmatic phase converts such beams into light fields with one-dimensional structure. Thus, the synthesis of a singular beam can be reduced to formation of one-dimensional light fields with subsequent astigmatic Fourier transform of them. One-dimensional light field synthesis is carried out by means of two one-dimensional phase elements located at some distances along the beam propagation. One-dimensional phase masks were realized experimentally on dichromated gelatin layers which were made by sensibilization of standard holographic photoplates. The masks were recorded through an exposure of layers by an argon ion laser operating at the wavelength of 0.488 mkm. The laser beam was transformed into a narrow line of 10 mkm width. The recording was made by moving a layer in its own plane step-by-step with the help of an electric motor controlled by a computer. (The step size was 5 mkm.) After the exposure these layers were developed by water vapors according to a technique described in reference 2. Experimental results of synthesis of a beam whose intensity looks like a boundary of a regular triangle are presented.

01 Jan 1998
TL;DR: In this article, the authors considered the diffraction of a coherent, stationary, beam of atoms from a standing wave of light, and treated it within the framework of a set of differential difference equations due to Raman and Nath.
Abstract: The diffraction of a coherent, stationary, beam of atoms from a standing wave of light is considered. Particular attention is paid to long interaction times for which the motion of the atoms inside the light field must be taken into account. This is the regime of dynamical diffraction, and is treated within the framework of a set of differential difference equations due to Raman and Nath. The popular Raman-Nath approximation, in which the kinetic energy imparted to the atoms by the light wave is ignored, is no longer valid and the full equations must be solved. When the interaction between the atoms and the light is very weak then few beams are produced. To describe spontaneous emission from the atom one can invoke a complex potential as a model for dissipation. If the atom beam is obliquely incident one finds anomalously high transmission close to the Bragg angles which is the physical manifestation of degeneracies in non-Hermitian matrices. The classical limit is approached when the atom-light interaction is strong, producing many beams. The classical dynamics (geometrical rays) reveal that the farfield intensity pattern is dominated by caustics. These proliferate with increasing interaction distance. Two methods are presented for analytically treating the semiclassical limit of the wave mechanics. The first begins with W.K.B. solutions to the continuised Raman-Nath equations. Mapping onto parabolic cylinder functions removes the spurious divergences of the W.K.B. solutions, giving eigenvectors which are uniformly valid for all scattering angles and may be summed to give the wavefunction. The second method transforms the original W.K.B. eigensum, using the Poisson summation formula, giving a new sum, each term of which has classical significance. This method shows that wave theory decorates the classical caustics with an Airy function intensity profile, as predicted by catastrophe theory.