Showing papers on "Wavefront published in 1992"

Basic Wavefront Aberration Theory for Optical Metrology

Abstract: VIII. IX. X. XI. XII. Sign Conventions Aberration-Free Image Spherical Wavefront, Defocus, and Lateral Shift Angular, Transverse, and Longitudinal Aberration Seidel Aberrations A. Spherical Aberration B. Coma C. Astigmatism D. Field Curvature E. Distortion Zernike Polynomials Relationship between Zernike Polynomials and Third-Order Aberrations Peak-to-Valley and RMS Wavefront Aberration Strehl Ratio Chromatic Aberrations Aberrations Introduced by Plane Parallel Plates Aberrations of Simple Thin Lenses 2 4 9 12 15 18 22 24 26 28 28

Time-reversal of ultrasonic fields. III. Theory of the closed time-reversal cavity

Abstract: For pt.II see ibid., vol.39, no.5, p.567-78 (1992). A theoretical model for time-reversal cavities to optimize focusing in homogeneous and inhomogeneous media is described. The concept of the cavity can be understood as the most realistic approximation to an exact three-dimensional (3-D) time-reversal of ultrasonic fields; it is also a generalization of the time-reversal mirrors realized experimentally in the laboratory. The proposed method is based on an approach in the transient regime that is more general than the monochromatic formalism used in optics to analyze the phase conjugation mirrors efficiency. This method uses impulse diffraction theory to obtain the impulse response of the cavity in any inhomogeneous medium. An original interpretation of the limitations due to diffraction observed in wave field propagation in terms of the different waves generated inside the cavity is also proposed. The time-reversal focusing process using a closed cavity in a weakly inhomogeneous medium is compared with more classical techniques to compensate wavefront distortions, thus illustrating the focusing improvement due to the time-reversal method. >

Screw Dislocations in Light Wavefronts

Abstract: We discuss screw dislocations of a phase surface as the one type of wavefront of a monochromatic wave. The simple method for construction of the optical wavefronts with an isolated screw dislocation is reported. Laser beams with the dislocations of different orders were experimentally achieved by using diffraction on computer-synthesized gratings.

Wave-front reconstruction using a Shack-Hartmann sensor

Abstract: An analysis of the problem of wave-front reconstruction from Shack–Hartmann measurements is presented. The wave-front aberration is assumed to result from passage of the wave front through Kolmogorov turbulence. Limitations of using Zernike polynomials as an orthogonal basis for wave-front reconstruction are highlighted, and the advantage of using the Karhunen–Loeve functions for computing the higher-order modes of the wave front is shown.

Measurement of ocular local wavefront distortion with a spatially resolved refractometer

Abstract: Local wavefront distortion by the total refractive system of the eye is measured by a variant of the Scheiner principle at some thirty loci of 1 mm diameter. At each locus we find the normal to the wavefront that could form a point focus. A simple visual display is used to review the data, and a steepest descents fit of the wavefronts with a power series enables comparison with more traditional measures of refractive error.

Atmospheric structure function measurements with a Shack-Hartmann wave-front sensor

Abstract: The phase structure function has been used as a convenient way to characterize aberrations introduced on optical propagation by the atmosphere. It forms the theoretical basis for the calculation of such things as the long- and short-exposure atmospheric transfer function. The structure function is difficult to measure directly and is usually assumed to follow Kolmogorov statistics. We present here a technique for direct measurement of the structure function through the use of a Shack–Hartmann wave-front sensor. Experiments confirm that the atmosphere behaves according to Kolmogorov theory most of the time. However, some instances of non-Kolmogorov behavior have been noted.

Illumination from curved reflectors

Abstract: A technique is presented to compute the refkted illumination from curved mirror surfaces onto other surfaces. In accordance with Fermat’s principle, this is equivalent to fiiding extremal paths from the light source to the visible surface via the mirrors. Once pathways of illumination are found, h-radiance is computed from the Gaussian curvature of the geometrical wavefront. Techniques from optics, differential geometry and interval analysis are applied to this problem in global illumination. CR Categories and Subject Descriptions: 1.3.3 [ Computer Graphics ]: Picture/Image Generation; 1.3.7 [ Computer Graphics ]: Three-Dimensional Graphics and Realism

Beam-jitter measurements of turbulent aero-optical path differences.

Abstract: We have developed new a technique for measuring aero-optical aberrations in flowing turbulent fluids. The rms optical path difference power spectral density is obtained from angular beam-jitter measurements. We tested the technique in an airflow in which there was a temperature discontinuity at a turbulent interface. It was validated by comparison with the data from a pulsed interferometer.

Traveltime and amplitude estimation using wavefront construction

Abstract: We have developed and implemented a new method for estimation of first and later arrival traveltimes and amplitudes in a general 2D model. The basic idea of this wavefront (WF) construction approach is to use ray tracing to estimate a new WF Erom the old one. The calculation goes along the WFs rather than along the rays.

Reading device for multi-layered optical information carrier

Abstract: A device for reading data stored in a high density multi-layered optical information carrier. Data which is stored in a carrier having a plurality of partially reflective data layers is read by wavefront shearing interferometry with low interlayer crosstalk. This allows data layers to be more closely spaced than previously possible thereby reducing spherical aberration and increasing the data density.

Laser Resonators and the Beam Divergence Problem

Abstract: FOREWORD BY A.E. SIEGMAN INTRODUCTION Briefly on the history and essence of the problem THE LAWS OF LIGHT-BEAM PROPAGATION Fundamentals of the theory of multielement optical systems Laws of propagation for major types of light beams Angular divergence of radiation IDEAL RESONATORS General information on open resonators Classification of open optical resonators and the condition of their equivalence Stable resonators Plane resonators Unstable resonator BASIC CONCEPTS CONCERNING THE PROPERTIES OF REAL RESONATORS AND THE PROCESSES OCCURRING IN THEM Some experimental data and their discussion Principal kinds of perturbations and parasitic effects Large-scale aberrations and light scattering Mode competition in the onset of lasing and in steady-state operation Pump energy conversion efficiency in laser resonators RESONATOR APPLICATIONS AND SPECIAL CONFIGURATIONS Basic resonator types Methods of the angular selection of radiation Resonators of lasers with controlled spectral and temporal characteristics Specific resonator configurations THE SIMPLEST CAUSES OF ABERRATIONS AND METHODS OF WAVEFRONT CORRECTION Thermal deformations of resonators Optico-mechanical and holographic methods of wavefront correction-stimulated scattering-based lasers Wavefront conjugation APPENDIX REFERENCES INDEX

Custom laser resonators using graded-phase mirrors

Abstract: The authors derive a simple algorithm for designing a stable graded-phase-mirror resonator. First, the desired output beam profile of the fundamental mode is propagated into the laser medium. The wavefront is then extracted and serves to determine the appropriate phase profile of the mirror. The diffractional analysis of the resonator using this graded-phase mirror indicates a very low loss for the fundamental mode with a very large discrimination of higher modes. Practical design parameters such as the geometric factor, the Fresnel numbers, and phase profile perturbations are discussed. The authors conclude that this type of resonator can increase significantly the mode volume and favor the single-mode operation of laser systems relying on a stable resonator geometry. >

Improved imaging rate through simultaneous transmission of several ultrasound beams

Abstract: The main requirement of pulsed-echo ultrasound applications such as cardiac imaging, 3-D imaging, or blood flow imaging can be identified as frame rate. Currently, frame rate is limited by the imaging depth range and the number of ultrasonic fires. For example, a 15 cm imaging range gives rise to 200 microsecond(s) lines or to a 2 s acquisition time for 100 planes of 100 lines in 3-D medical applications. The only way to increase frame rate is parallel beam formation in the receive mode. Simultaneous parallel beam forming allows us to divide the acquisition time by a factor proportional to the number of beam formed lines. In the technique developed by S. W. Smith, an increase frame rate of 16 is achieved. However, this technique is limited by a loss in lateral resolution due to the requirement for a wide illumination beam of the explored medium in the transmit mode. We propose an alternate illumination scheme that minimizes the loss in resolution in the transmit mode. In this technique, ultrasonic energy is transmitted simultaneously in several narrow beams. This technique works in pulsed mode and we have built the hardware needed for the simultaneous production of several beams. Each transducer is connected to a transmitter able to generate a sequence of excitation pulses. If n beams are to be transmitted, the excitation signal is the sum of n cylindrical wave fronts. For those, among elements where the n wave fronts are disjoint, the excitation signal is thus the succession of n pulses with specific time positions with respect to the system synchronization. For the others, the excitation signal is more complex since it consists in a (n - 1) level signal (0, 1, 2, ... n - 1 times the basic excitation signal). We show the performances of such a parallel transmit scheme based on beam plots as well as on tissue phantom images. This leads to an evaluation of the maximal number of beams compatible with current medical imaging quality standards. It is shown that a gain of 16 in the acquisition time can be achieved without any loss in lateral resolution.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Wavefront sensor having a lenslet array as a null corrector

Abstract: A wavefront sensor (10) includes a radiation sensor (2) and an array (12) of lenslets (12A) that are optically coupled to the radiation sensor. The array of lenslets has a radiation receiving surface for receiving an incident wavefront and for focussing the wavefront at a plurality of focal positions upon the radiation sensor. Each of the lenslets comprises a diffractive optical element having an optical center that is located at a predetermined point for inducing an equal and opposite tilt to a portion of the wavefront incident on the lenslet. As a result, an aberration within that portion of the wavefront is cancelled. The predetermined point is determined to be equal to and opposite a focal spot shift of the lenslet.

Holographic deformation measurements by Fourier transform technique with automatic phase unwrapping

Abstract: A carrier fringe technique for measuring surface deformation is described and verified by experiments. In contrast to conventional holography and fringe analysis, this holographic system is based on fiber optics and automatic spatial carrier fringe pattern analysis techniques. Single-mode optical fibers are used to transfer both the object and reference beams. Carrier fringes are generated by simply translating the object beam between two exposures. The fast Fourier transform method is used to process the interferograms. The experiment gives an example of the tile-level minimum spanning tree phase unwrapping technique and introduces a new pixel-level noise immune unwrapping strategy also based on minimum spanning trees. The test object is a centrally loaded disk. An excellent correlation between the theoretical deformation profile and that suggested by the technique is given.

Time-Reversal of Ultrasonic Fields-Part 111: Theory of the Closed Time-Reversal Cavitv J

Abstract: Abstruct- A theoretical model for time-reversal cavities to optimize focusing in homogeneous and inhomogeneous media is described.The concept of the cavity can be understood as the most realistic approximation to an exact three-dimensional (3-D) time-reversal of ultrasonic fields; it is also a generalization of the time-reversal mirrors realized experimentally in our laboratory. The proposed method is based onan approach in the transient regime, that is more general than the monochromatic formalism used in optics to analyze the phase conjugation mirrors efficiency. This method uses impulse diffraction theory to obtain the impulse response of the cavity in any inhomogeneous medium. It is also proposed an original interpretation of the limitations due to diffraction observed in wave field propagation in terms of the different waves generated inside the cavity. The time-reversal focusing process using a closed cavity in a weakly inhomogeneous medium is finally compared with more classical techniques to compensate wavefront distortions, thus illustrating the focusing improvement due to the time-reversal method.

Simple adaptive optical system

Abstract: A system for correcting wavefront distortion includes an eight channel deformable mirror 11 attached to a two-axis, tip/tilt mount 12. The deformable mirror 11 reflects an incoming telescopic wavefront 10 onto a beamsplitter 14. The beamsplitter 14 divides the reflected telescopic wavefront 13 into two separate beams 15, 20. The beam 20 reflected by the beamsplitter 14 may be used for experimentation and measurement. The beam 15 transmitted by the beamsplitter 14 is directed toward a modified Hartmann-Shack wavefront sensor 16. The modified Hartmann-Shack sensor 16 detects the slope of the wavefront at several locations across this transmitted beam 15 and provides analog signals 17 representing these slopes to a series of actuator drive circuits 18. The actuator drive circuits 18 provide excitation signals 19 to actuators 22, 30 on the deformable mirror 11 and the two-axis, tip/tilt mount 12. These actuators 22, 30 facilitate the reforming and repositioning of the deformable mirror 11 so as to correct any incoming wavefront 10 distortion.

Microlens arrays for Shack-Hartmann wavefront sensors

Abstract: Microlens arrays are a component of atmospheric wavefront sensors used recently with success by ground-based astronomers to obtain diffraction-limited images of stars in spite of wavefront disturbances introduced by the earth's atmosphere. Typical requirements for individual lenses are a size measured in tenths of millimeters, a sag measured in micrometers, and no room left between lenses, i.e., square or hexagonal lenses rather than circular lenses. Actual monolithic square microlens arrays up to 20 x 20 mm in size for 0.18- to 1.5-mm individual contiguous lenses of 0.0035-mm maximum sag are engraved in photoresist coatings by a two-axes rastering process. These arrays have been used for diurnal and nocturnal atmospheric wavefront measurements.

Two-mirror unobscured optical system for reshaping the irradiance distribution of a laser beam

Abstract: The design of a two-mirror optical system for reshaping the irradiance distribution of a laser beam is presented. The second mirror is decentered relative to the first to eliminate the obscuration inherent in an axially symmetric design. A geometric-optics approach is used to derive a set of equations that describe the surface figures of each of the mirrors. (In general, the mirror surfaces are not rotationally symmetric.) The special case of a system to convert a Gaussian input beam into a uniform output distribution is considered. The expressions for the surface figures are evaluated numerically for several specific systems to provide illustrative examples. It is observed that in some cases rotationally symmetric aspheres may be used to construct the beam-shaping system.

Two independent spatial variable degree of freedom wavefront modulator

Abstract: To provide electrical isolation to piezoelectric parallel shear mode elements in wavefront phase modulators arrays, the functionality of the mounting configuration is increased. The mounting configuration involves embedding a respective interface electrode affixed to a second face of each piezoelectric element of the array in an insulating ridge. This allows the ridge to provide electrical isolation to interface electrodes affixed to adjacent elements. A first surface of every element is electrically connected to a common potential source by a suitable means. Electrically connecting the first surface of every adjacent element in the array to a common potential source avoids electrical interference between adjacent elements. By increasing the functionality of the ridges and making judicious use of common potential interconnects between adjacent elements, extraneous components, such as electrical insulators can be eliminated. This facilitates implementation of piezoelectric wavefront phase modulator arrays.

New contra old wavefront measurement concepts for interferometric optical testing

Abstract: Three new and modified wavefront analysis concepts for interferometric optical testing are presented, specifically a moire fringes version of a temporal phase-shifting method and spatial-carrier phase-shifting and Fourier transform methods. All of these techniques require working with a finite fringe observation field in the interferometer, therefore additional analysis of the imaging optics is necessary. The impact of the interferometer construction and the method of analysis on the measurement error is discussed. A detailed experimental and theoretical comparison of the techniques is presented to fulfill a wide range of user requirements.

Corneal topography system including single-direction shearing of holograph grating in orthogonal directions

Abstract: A system for producing a three-dimensional image of a surface, such as a surface of a cornea, includes a laser beam that passes through a beamsplitter and an objective lens to produce a spherical wavefront that impinges on the cornea and is reflected by the cornea as a return beam back through the objective lens. The return beam is reflected by the beamsplitter through an imaging lens that focuses the return beam onto an imaging screen, through a dual phase plate, and onto a photosensitive array. The dual phase plate includes two sets of spaced periodic refractive features spaced along orthogonal directions. The phase plate is modulated by incrementing it at a 45 degree angle relative to the first and second directions, thereby simultaneously producing phase shear along the two orthogonal directions. The resulting intensities at each pixel of a CCD camera are digitized and used to compute an optical phase difference (OPD) map consisting of the relative deviation of the cornea surface from the impinging spherical wavefront at each pixel. The OPD map then is summed with a "spherical map" of the impinging spherical wavefront, which has height coordinates measured relative to a limbus plane under the cornea, to obtain a complete three-dimensional image of the cornea. Various d-spacings of the dual phase plate patterns, in conjunction with corresponding capture intervals or shifts produced by the incrementing, allow scaling of the sensitivity of the system to allow "close up" viewing of the cornea.

Testing spherical surfaces: a fast, quasi-absolute technique.

Abstract: A technique for measuring the quality of spherical surfaces that provides a quasi-absolute result is presented. It requires only two measurement positions rather than the traditional method of absolute sphere measurement that requires three measurement positions. A measurement is taken with a mirror at the focus of the interferometer diverger lens and is subtracted from a measurement of the sphere tested at its center of curvature. This test assumes that the test sphere does not contain any aberrations with odd symmetry so that these aberrations can be subtracted to provide a fast, quasi-absolute measurement. We describe the new technique and compare measurement results from testing a λ/12 peak-to-valley sphere (numerical aperture = 0.4) by using a phase-measuring Fizeau interferometer with results from the three-position absolute sphere measurement technique. The repeatability of this measurement technique is ±0.01 waves peak to valley.

Active multi-stage cavity sensor

Abstract: In accordance with the present invention, an optical sensing device and method are provided for processing with extremely low energy requirements. Spontaneous emissions from an excited optical gain medium generate a propagating waveform. Either a spatial modulator or the pattern under investigation modulates the optical wavefront generated by the fluorescing gain medium to impose a first spatial pattern thereon. When the first spatial pattern imposed on the wavefront has duality with another spatial pattern imposed by the other of the pattern under investigation or the SLM, light is directed back along pathways through a cavity defined by the gain medium, a reflector, the SLM, and the object under investigation to induce stimulated emission and eventually resonance in the cavity.

Deformable mirrors: design fundamentals, key performance specifications, and parametric trades

Abstract: A wide variety of deformable mirror structures have been studied for wavefront correction since the advent of adaptive optics nearly two decades ago. These structures generally fall into two categories: (1) segmented facesheet and (2) continuous facesheet. The segmented mirror technology features independently activated mirror elements controlled in the piston, tip, and tilt modes. The continuous facesheet designs use discrete electroceramic or electrostatic displacement actuators arranged in either an axial or bimorph position to bend the continuous facesheet. In addition there are two methods of correction: (1) zonal control and (2) modal control. The basic mirror types are discussed and analyzed in terms of wavefront correction capabilities. Curve fitting characteristics are explained in terms of the optical influence function and mirror meshing functions. The continuous facesheet deformable mirror is used as a model to develop basic design equations which are used for parametric trades.

Mechanics of polarization ray tracing

Abstract: Polarization ray tracing, which consists of several extensions to geometrical ray tracing, calculates the evolution ofpolarization states along ray paths and determines the intrinsic polarization properties, such as diattenuation andretardance, associated with ray paths. This paper compares the suitability of the Jones, Mueller, and a three dimensionalpolarization ray tracing calculi, examining the issues of local vs. global coordinates, amplitude vs. phase representations,inclusion of the wavefront aberration function, partially polarized light, measurements of images by polarimeters, anddiffraction image formation by low and high numerical aperture beams. 1. INTRODUCTION Polarization ray tracing is an established technique which supplements the phase information from geometrical ray tracingwith information on the ray's amplitude and polarization.1-5 Polarization ray tracing is normally applied to "polarizationcritical systems", those optical systems where the polarization properties are important to the correct operation of thesystem, and where there may be some difficulty to design or fabricate a system with suitable polarization behavior.The goal of this paper is to consider how to represent the polarization ray trace, both internally in the computer program,and externally when presenting the results to an optical designer or a broader audience. Algorithms for polarization raytracing of interfaces and birefringent media have been given elsewhere and are not repeated here.110 Threerepresentations of polarized light or polarization calculii are available for use in polarization ray tracing, and each is bestsuited for different tasks. There is no single definitive best representation which is optimum for all purposes, but I willcritically compare the methods and present my opinions on this matter. The basic issues to be debated are whether to workwith amplitude or intensity calculus, and whether to work in local or global coordinates. I will argue for working in globalcoordinates with an amplitude calculus within the program, but translating the results into both amplitude and intensitycalculii for certain output calculations and for presenting the output of the ray trace to the designer.First, the basic calculation in a ray tracing program is the propagation of a ray through an optical system. A particular ray isspecified by its object coordinate h , pupilcoordinate p ,

Diffraction of converging electromagnetic waves

Abstract: Using the electromagnetic equivalent of the Kirchhoff diffraction integral, we investigate the effect of spherical aberration and defocus on the diffraction of Gaussian, uniform, and centrally obscured beams. We find, among other things, that in high-angular-aperture systems suffering from either spherical aberration or defocus the axial intensity distribution is no longer symmetric. Equations are derived for the axial intensity near focus for different beam profiles. Intensity contours in focal and meridional planes are depicted for both ideal and aberrated lenses. It is shown that, contrary to certain previous theories, our theory is valid for both high and low angular aperture systems.

Refractor imaging using an automated wavefront reconstruction method

Abstract: The classical wavefront method for interpreting seismic refraction arrival times is implemented on a digital computer, Modern finite-difference propagation algorithms are used to downward continue recorded refraction arrival times through a near-surface hetero­ geneousvelocity structure. Two such subsurface trav­ eltime fields need to be reconstructed from the arrivals observed on a forward and reverse geophone spread. The locus of a shallow refracting horizon is then defined by a simple imaging condition involving the reciprocal time (the traveltime between source posi­ tions at either end of the spread). Refractor velocity is estimated in a subsequent step by calculating the directional derivative of the reconstructed subsurface wavefronts along the imaged interface. The principle limitation of the technique arises from imprecise knowledge of the overburden velocity distribution. This velocity information must be obtained from up­ hole times, direct and reflected arrivals, shallow re­ fractions, and borehole data. Analysis of synthetic data examples indicates that the technique can accurately image both synclinal and anticlinal structures. Finally, the method is tested, apparently successfully, on a shallow refraction data­ set acquired at an archeological site in western Crete.