Showing papers on "Wavefront published in 1991"

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Abstract: A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Principles of Adaptive Optics

Abstract: History and Background: Introduction. History. Physical Optics: Propagation with Aberrations. Imaging with Aberrations. Representing the Wavefront. Interference. Adaptive Optics Terms. Sources of Aberrations: Atmospheric Turbulence: Descriptions of Atmospheric Turbulence. Refractive Index Structure Constant. Turbulence Effects. Turbulence MTF. Thermal Blooming: Blooming Strength and Critical Power. Turbulence, Jitter, and Thermal Blooming. Non-atmospheric Sources: Optical Misalignments and Jitter. Thermally Induced Distortions of Optics. Manufacturing and Microerrors. Other Sources of Aberrations. Adaptive Optics Compensation: Phase Conjugation. Limitations of Phase Conjugation: Turbulence Spatial Error. Turbulence Temporal Error. Sensor Noise Limitations. Thermal Blooming Compensation. Artificial Guide Stars. Combining the Limitations. Linear Analysis of Random Wavefronts. Linear Analysis of Deterministic Wavefronts: Partial Phase Conjugation. Adaptive Optics Systems: Adaptive Optics Imaging Systems. Beam Propagation Systems: Local Loop Beam Cleanup Systems. Alternative Concepts. Pros and Cons of the Various Approaches. Unconventional Adaptive Optics: Nonlinear Optics. Elastic Photon Scattering, DFWM. Inelastic Photon Scattering. System Engineering. Wavefront Sensing: Directly Measuring Phase: The Non-uniqueness of the Diffraction Pattern. Determining Phase Information from Intensity. Modal and Zonal Sensing. Direct Wavefront Sensing--Modal: Importance of Wavefront Tilt. Measurement of Tilt. Focus Sensing. Modal Sensing of Higher-Order Aberrations. Direct Wavefront Sensing--Zonal: Interferometiric Wavefront Sensing. Hartman Wavefront Sensors. Curvature Sensing. Selecting a Method. Indirect Wavefront Sensing Methods: Multidither Adaptive Optics. Image Sharpening. Wavefront Sampling: Beamsplitters. Hole Gratings. Temporal Duplexing. Reflective Wedges. Diffraction Gratings. Hybrids. Sensitivities of Sampler Concepts. Detectors and Noise. WavefrontCorrection: Modal Tilt Correction. Modal Higher-Order Correction. Segmented Mirrors. Deformable Mirrors: Actuation Techniques. Actuator Influence Functions. Bimorph Corrector Mirrors. Membrane and Micromachine Mirrors. Edge Actuated Mirrors. Large Correcting Optics. Special Correction Devices: Liquid Crystal Phase Modulators. Spatial Light Modulators. Charged-large-array-mirrors. Reconstruction and Controls: Introduction. Single-Channel Linear Control: Fundamental Control Tools. Transfer Functions. Proportional Control. First- and Second-Order Lag. Feedback. Frequency Response of Control Systems. Digital Controls. Multivariate Adaptive Optics Controls: Solution of Linear Equations. Direct Wavefront Reconstruction: Phase from Wavefront Slopes. Modes from Wavefront Slopes. Phase from Wavefront Modes. Modes from Wavefront Modes. Zonal Corrector from Continuous Phase. Modal Corrector from Continuous Phase. Zonal Corrector from Modal Phase. Modal Correctors from Modal Phase. Indirect Reconstructions.Modal Corrector from Wavefront Modes. Zonal Corrector from Wavefront Slopes. Spatiotemporal Considerations. Subject Index.

Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star

Abstract: THE possibility of using an artificial 'guide-star' to measure optical wavefront distortion caused by atmospheric turbulence has been discussed for some time1–4, but few experimental data are available5. Here we report experimental results demonstrating that atmospheric wavefront distortion can be measured by taking fast 'snapshots' of a guide-star formed by light scattered from a laser beam focused in the upper atmosphere. These results agree with a theoretical prediction6 that the mean-square wavefront error created by using an artificial guide-star at a finite distance rather than a real (infinitely distant) star is proportional to the five-thirds power of the telescope aperture. Using this understanding of the physics, we have demonstrated continuous, real-time atmospheric compensation of a 1.5-m telescope using a high-pulse-rate laser, pulse-synchronized wavefront sensor and deformable mirror, and have been able to resolve the 1.3-arcsecond binary star 53 ξ Ursa Majoris in an exposure time of only one second.

Comparison of finite-difference and Fourier-transform solutions of the parabolic wave equation with emphasis on integrated-optics applications

Abstract: The solution of the scalar wave equation in the parabolic approximation is considered through the finite-difference and the Fourier-transform (i.e., beam propagation method) techniques. Examples are taken from the field of integrated optics and include propagation in straight, tapered, Y-branched, and coupled waveguides. A comparison of numerical results obtained by the two methods is presented, and a comparison with other analytical or numerical methods is also given. In the numerous cases studied it is shown that the finite-difference method yields a large, order-of-magnitude range improvement in accuracy or computational speed when compared with the Fourier-transform method.

A simple low-order adaptive optics system for near-infrared applications

Abstract: It is shown that low-order wavefront compensation can significantly improve astronomical images over most of the sky. A novel approach to wavefront sensing and compensation is described. It is optimized for low-order correction and high efficiency. Computer-simulation results show it can achieve the desired performance, and preliminary laboratory tests demonstrate its feasibility.

Optical resonators using graded-phase mirrors

Abstract: Optical resonators using graded-phase mirrors are analyzed with the help of the generalized ABCD propagation law for a real optical beam. This analysis gives the second-order moment gross characteristics of the eigenmode and indicates a design procedure. An example of a super-Gaussian output beam shows that this type of optical resonator might have large transverse-mode discrimination that could provide operation in a large fundamental-mode beamwidth.

Wavefront aberration of the eye: a review.

Abstract: The concept of monochromatic wavefront aberration is discussed in relation to ray aberration, and methods for its measurement in the case of the eye are described. Examples are given of the measured aberration in individual eyes: in general the aberration falls within the Rayleigh quarter-wavelength criterion for pupil diameters less than 2 to 3 mm but significantly degrades image quality for larger pupils. The use of wavefront data to explore both the modulation and phase transfer functions of the eye as a function of pupil diameter and focus is described, together with typical results. Potential applications to clinical problems such as the effects of contact lenses, intraocular implants, refractive surgery, and pathology on the optical quality of the eye are outlined.

A wavefront shearing interferometer

Abstract: A new type of interferometer is described by means of which the asphericity of an optical wavefront can be measured, by testing it against itself with lateral displacement or shear. Continuous control of the amount of this shear, and of the meridional or sagittal fringes is obtained in white light.

Effects of high-numerical-aperture focusing on the state of polarization in optical and magneto-optic data storage systems.

Abstract: Using vector diffraction theory and an exact method for computing reflection coefficients for multilayer structures, we analyze the effects of high-numerical-aperture focusing on the state of polarization in optical data storage systems. The focused incident beam is decomposed into a spectrum of plane waves, and the reflected beam is obtained by the superposition of these plane waves after they are independently reflected from the multilayer. Plots of polarization rotation angle and ellipticity for several disk structures are presented.

Adaptive optics on a 3.6-m telescope : results and performance

Abstract: The results of the first observations made on a large (3.6-m) telescope with the adaptive optics prototype, named COME-ON, conceived to explore the application of this technique for the European Very Large Telescope, are presented. The wavefront is studied, after its correction by the servo-system, using a Zernike polynomial expansion. The analysis of uncorrected and corrected images in the near infrared (≤5 μm) leads to a detailed evaluation of the system performance in terms of improvement of angular resolution, reaching nearly the ideal diffraction profiles down to 2.2 μm, and Strehl ratio, approaching 0.6 to 0.8 at 3.8 μm

Radial shearing interferometer

Abstract: A new type of wave front shearing interferometer is described in which two images of the wave front under test which are of different sizes are made to interfere. When the centres of the two images coincide, this results effectively in shear along the radial direction. It is shown that the interpretation of the resulting interferogram is comparatively easy. In addition, the instrument is extremely convenient to handle, since all the adjustments can be made with a white light source.

A 3-D raytracer for teleseismic body-wave arrival times

Abstract: In this article, we present a method for determining the minimum time ray path from a planar wavefront at depth to a fixed point at the surface through a 3-D heterogeneous velocity structure. The program is based on the two point raytracer of Prothero et al. (1988), with a modification to use odd quarter-cycles of sinusoids to distort the rays. These functions produce zero displacement at the fixed receiver but non zero displacement at the wavefront. This allows the raytracer to explore a wide variety of ray paths starting at different points on the wavefront, while the rays leaving the wavefront remain normal to it. To find the minimum time path, amplitudes of these functions are systematically perturbed using the simplex algorithm. The approach is analogous to using a Fourier series to fit a curve with specific properties at each end. Development of this raytracer was motivated by the desire to model our observations of large perturbations in the bearings and phase velocities of teleseismic P waves recorded in Long Valley caldera, California. These observations clearly show the inadequacy of 1-D raytracing in regions having complex, three-dimensionally varying velocity structure. This raytracer provides a basic tool with which to study the effects of ray bending on tomographic results from these kinds of environments.

Huygens's wave propagation principle corrected.

Abstract: Huygens's principle that each point on a wave front represents a source of spherical waves is conceptually useful but is incomplete; the backward parts of the wavelets have to be neglected ad hoc, otherwise backward waves are generated. The problem is solved mathematically by Kirchhoff's rigorous integration of the wave equation, but the intuitive appeal of Huygens's simple principle is lost. I show that, by using spatiotemporal dipoles instead of spherical point sources, one can recover a simple principle of scalar wave propagation that is correct whenever the concept of a wave front is meaningful.

Broadband optical detection of transient motion from a scattering surface by two-wave mixing in a photorefractive crystal

Abstract: A method and apparatus for optically detecting transient motion from a scattering surface. A laser beam having a predetermined frequency is directed onto such a surface to thereby scatter the laser beam and produce a scattered laser beam defining an optical wavefront and having an optical spectrum with a central peak at the laser frequency and a sideband on either side of the central peak. The scattered laser beam is caused to interfere inside a photorefractive crystal with a pump beam derived from the laser beam so as to form an index of refraction grating diffracting the pump beam into a reference beam having an optical wavefront substantially matching the wavefront of the scattered laser beam and an optical spectrum with a single peak at the laser frequency and no sidebands, whereby to produce at an exit face of the photorefractive crystal a transmitted scattered laser beam and a diffracted reference beam interfering with one another. The interfering beams at the exit face of the photorefractive crystal, or polarization components thereof, are at least temporarily out of phase, thereby obtaining an optical signal sensitive to phase perturbations produced by the transient motion, which optical signal is detected and converted into an electrical signal representative of the transient motion. The invention is particularly useful for detecting small surface formations or displacement of a material subjected to ultrasonic energy, enabling displacements ranging from a fraction of 1Å to a few hundred Å to be detected with a large etendue or light gathering efficiency and a broad frequency bandwidth extending from frequencies as low as 1 KHz, and even below.

Novel phased array optical scanning device implemented using GaAs/AlGaAs technology

Abstract: A novel type of optical beam scanning device based on the same principle as a phased array radar has been made and demonstrated. This phased array optical scanning device consisted of a uniformly illuminated array of ten closely spaced, single mode GaAs/AlGaAs electrooptic waveguides, each of which was individually addressed to give more than 2π radians of optical phase control. This gave a line of ten point sources of light on a 3 μm pitch at the output face of the array. By independently phase shifting these light sources the output wavefront was controlled to scan a 2° wide beam through 20° in the far field.

Adaptive optics: a progress review

Abstract: Active and adaptive optics technology has emerged from the laboratory and is being applied to improve the performance of optical imaging and laser systems. In the last few years, development of both systems and components has accelerated. Many new concepts and devices have appeared, among which are high-performance deformable mirrors, new types of wavefront sensors, and more sophisticated wavefront processing algorithms. Equally important, a better understanding of the system design aspects of adaptive optics has been reached, particularly of the need for optimizing each system according to its application. For example, the dominant requirement in laser systems is to achieve a high Strehl ratio, whereas for ground-based astronomy the availability of guide stars is a major concern. Current developments in adaptive optics for ground-based astronomy include the use of IR wavelengths, partial wavefront compensation using natural guide stars, and the use of laser guide stars to allow all-sky coverage with full compensation at visible wavelengths. While progress to date has been impressive, much work remains to bring this technology into general use.

Reaction-diffusion fronts in periodically layered media

Abstract: We compute the effective wavefront speeds of reaction-diffusion equations in periodically layered media with coefficients that have small-amplitude oscillations around a uniform mean state. We compare them with the corresponding wavefront speeds in the uniform state. We analyze a one-dimensional model where wave propagation is along the layering direction of the medium and a two-dimensional shear flow model where wave propagation is othogonal to the layering direction. We find that the effective wave speed is smaller in the one-dimensional model and is larger in the two-dimensional model for both bistable cubic and quadratic nonlinearities of the Kolmogorov-Petrovskii-Piskunov form. We derive approximate expressions for the wave speeds in the bistable case.

Spherical aberration and the electromagnetic field in high-aperture systems

Abstract: We present a model for investigating the effect of spherical aberration on the electromagnetic field and the Poynting vector in the focal region of a high-aperture lens. The fields are obtained by integrating the vector equivalent of Kirchhoff’s boundary integral over the aberrated wave front. We have studied both diffraction patterns and transfer functions. Our results differ significantly from those obtained by classical focusing theory. For example, the intensity peak is narrower. Also the intensiy distribution is no longer symmetric on the optical axis. A similar asymmetry has recently been measured.

Method and apparatus for imaging a physical parameter in turbid media using diffuse waves

Abstract: Imaging of a turbid object utilizes interference among the modulation wavefronts of a plurality of modulated light rays propagating through the object by diffusion and having predetermined phases relative to one another. A computer controlled phase and amplitude selecting device, such as a zone plate, is used to modulate light rays at appropriate phases in order to obtain constructive interference only at a predetermined portion of the object, including one or more preselected voxels. The rays reflected from (or diffusively transmitted through) the predetermined portion are received simultaneously at a detector, thus providing simultaneously all the data necessary to describe or image the portion. A single detector element may be used to detect the scattered reflected or transmitted light from the portion and to generate a signal representing the amplitude and phase characteristics for the modulation wavefront, thereby to provide absorption (and other) characteristics descriptive of the portion. An array of detectors may be used to detect the light from a plurality of individual voxels simultaneously and to provide such characteristics for each of the voxels. By dynamically controlling the phase and amplitude selecting device, the voxels selected for imaging are changed without mechanical scanning. Light rays having different frequencies may be modulated to provide complete absorption spectra for an arbitrarily selected portion of the object.

Fitting capability of deformable mirror

Abstract: Deformable mirror is the key element for adaptive optical wavefront correction. The number of actuators decides the complexity and cost of adaptive optical system. In this paper computer simulations of wavefront error for fitting different Zernike terms by deformable mirror with different number of actuators are presented. The arrangement of actuator and the influence function of mirror are discussed in respect of fitting error. The minimum number of actuators for fitting different Zernike orders of wavefront are given. Some optical experiments of fitting capability have been done with 19 and 37-element deformable mirrors and a Zygo interferometer.

Design of substrate-mode holographic interconnects with different recording and readout wavelengths

Abstract: A method for recording a substrate-mode holographic interconnect system, composed of two identical holographic optical elements (HOEs) which were recorded on the same plate, has been developed. Since the possible recording wavelengths for efficient holograms are usually different from the readout wavelengths, the holographic elements must be recorded with predistorted wavefronts to assure high diffraction efficiencies and low aberrations. The predistorted wavefronts are derived from simple spherical holograms whose readout geometries differ from those used during recording. The method is illustrated with HOEs recorded at 488 nm and read out at 633 nm. Nearly diffraction-limited imaging and high efficiencies were achieved.

Optical modeling for dynamics and control analysis

Abstract: This paper presents a coordinate-free ray-trace analysis of optical beam trains consisting of mirrors, lenses and reference surfaces. The analysis leads to optical models that can be directly integrated with standard structure and control models for integrated instrument design, analysis and simulation. This capability is required for a coming generation of spaceborn optical instruments which use controlled optical elements supported by flexible structures. New results include analytic formulas for optical sensitivities as functions of structural and control geometric parameters. An example problem calculates a linear (small-motion) optical model, derives optical gains for small- and large-angle controlled mirrors, and shows the propagation of a wavefront.

Measurement of the inhomogeneity of a window

Abstract: We describe three methods to measure the inhomogeneity of a window material. The first method immerses the window in a liquid between two planes. However, this method is inconvenient for some applications. The second method measures the optical figure of the front surface and then measures the return wavefront that transmits through the window and reflects from the rear surface of the window. The advantage of this method is that it can remove the contributions of both the surface figures and the return flat plus the system error of the interferometer. The disadvantage is that a small wedge must be fabricated between the two surfaces to eliminate spurious interference. The third method derives the inhomogeneity of the window material by measuring the optical figure of the front surface of the window and then flipping the mirror to measure the back surface. The advantage of this method is that it is not necessary to have a wedge between the two surfaces. The disadvantage of the window-flipping method is that the contribution of system error can increase.

Theoretical study of parametric frequency and wavefront conversion in nonlinear holograms

Abstract: Third-order mixing of arbitrary beams of pump and second-harmonic light gives rise to a spatially periodic DC polarization whose noninversion symmetry and periodicity are correct for quasi-phase matching of the pump and second harmonic. Under appropriate conditions in certain materials, e.g., optical fibers, X/sup (2)/ forms in proportion to this DC polarization, resulting in a nonlinear hologram that can be used to recreate a second-harmonic image from a reference pump beam. Distributed feedforward and feedback reconstruction of plane waves by slab-shaped nonlinear holograms is analyzed, and expressions for the field profiles and conversion efficiencies are derived. In the DFB case at high fixed pump intensities, multistable states of conversion efficiency exist. The higher order states display catastrophes in their transverse amplitude distributions. >

Apparatus for sensing wavefront aberration

Abstract: A wavefront aberration sensor includes a beam splitter, one or more aberration sensor modules and a photodetector for sensing total light power. The aberration sensor modules each provide two voltage outputs from a pair of photodetectors. Differences in the voltage pairs are normalized by the total light power to represent signed aberration amplitudes of phase aberrations present in an input optical beam. The aberration amplitudes may be combined in a digital computer to provide a reconstructed wavefront.

Motionless parallel readout head for an optical disk recorded with arrayed one-dimensional holograms

Abstract: A motionless parallel head reads an optical disk having an active surface encoded with an arrayed multiplicity of one-dimensional holograms. Each 1-D hologram is a computer-encoded representation of, typically, one 128 pixel slice of an image. A group, typically 128, 1-D holograms are positionally distributed, and positionally shifted or staggered one to the next, radially along the disk's active surface so as to fit a complete radius. Typically 14,000 groups are circumferentially-displaced around a 51/4" Compact Disk (CD), forming a herringbone pattern. During readout the encoded CD is simultaneously illuminated along the entirety of one of its radius lines within which a group of holographic data blocks are fitted. The illuminated group of holographic data blocks are optically transformed in parallel by one or more lenses, and preferably by a Hybrid refractive/diffractive Optical Lens (HOL), so as to two-dimensionally spatially encode the wavefront of the light beam by which the group of holographic data blocks was illuminated. The 2-D spatially-encoded light beam is detectable by an array of light detectors. When the disk is rotated then sucessive groups of holographic data blocks that are fitted along successive radius lines are successively retrieved, group by group, at a typically 1.1 Gbyte/sec rate. Such an optical memory is useable as the secondary storage of a high performance optoelectronic associative memory system.

Method of examining an optical component

Abstract: The invention is directed to a method for testing optical components and tests can be made on aspherical surfaces or, more specifically, on aspherical wavefronts. For this purpose, the collimator of an interferometer which generates the test wave is displaced relative to the test component and interferograms are electronically registered by means of an image sensor in different positions of the collimator and are stored as light path length differences between the test beam and the comparison beam for the individual image points of each interferogram. The relative position between the collimator and the test component is additionally measured with high precision. Thereafter, the light path length differences which were measured interferometrically are compared with desired light path length differences computed for the different positions of the collimator or determined by calibration. From this comparison, the aspheric form of the wavefront of the test component is computed. For this computation, the measured values obtained for the different component regions of the test component are integrated over the entire surface of the test component with the measured regions being those wherein the test wave falls essentially perpendicularly onto the surface of the test component.

Constrained shear mode modulator

Abstract: A new mounting configuration for piezoelectric shear mode elements is described. The element is mounted in a cantilever beam fashion. The polarization axis forms an acute angle with the mounting surface normal. A reflective electrode is affixed to a first surface of the element. The first surface normal is perpendicular to the polarization axis. A second electrode is affixed to a second surface which is parallel to the first surface. A voltage is applied across the reflective electrode and the second electrode to generate strain in the element. This results in a deflection of the reflective electrode, phase modulating electromagnetic and/or acoustic wavefronts incident on the reflective electrode. Stress distribution and hence phase modulation properties may be influenced using this mounting technique. Elements may be coupled end to end to form new devices. Anti-parallel polarization coupled elements exhibit large rates of change of deflection. These elements may be formulated by a ferroelectric inversion layer. A support structure design and a reflective electrode overhang concept are introduced. Arrays using these concepts with the mounting technique described are able to reduce electrical interference without compromising spatial resolution.