Showing papers on "Wavefront published in 1990"

Sensitive measurement of optical nonlinearities using a single beam

Abstract: A sensitive single-beam technique for measuring both the nonlinear refractive index and nonlinear absorption coefficient for a wide variety of materials is reported. The authors describe the experimental details and present a comprehensive theoretical analysis including cases where nonlinear refraction is accompanied by nonlinear absorption. In these experiments, the transmittance of a sample is measured through a finite aperture in the far field as the sample is moved along the propagation path (z) of a focused Gaussian beam. The sign and magnitude of the nonlinear refraction are easily deduced from such a transmittance curve (Z-scan). Employing this technique, a sensitivity of better than lambda /300 wavefront distortion is achieved in n/sub 2/ measurements of BaF/sub 2/ using picosecond frequency-doubled Nd:YAG laser pulses. >

Atmospheric wavefront simulation using Zernike polynomials

Abstract: An algorithm is described that simulates atmospherically distorted wavefronts using a Zernike expansion of randomly weighted Karhunen- Loeve functions. Its performance is presented and analyzed, and the program is then used to forecast resulting structure function and Strehl resolution for adaptive optics systems.

Fourier description of digital phase-measuring interferometry

Abstract: A general description of phase measurement by digital heterodyne techniques is presented in which the heterodyning is explained as a filtering process in the frequency domain Examples of commonly used algorithms are given Special emphasis is given to the analysis of systematic errors Gaussian error propagation is used to derive equations for the random phase errors of common algorithms

Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images

Abstract: A new technique of high-resolution imaging through atmospheric turbulence is described. As in speckle interferometry, short-exposure images are recorded, but in addition the associated wave fronts are measured by a Hartmann–Shack wave-front sensor. The wave front is used to calculate the point-spread function. The object is then estimated from the correlation of images and point-spread functions by a deconvolution process. An experimental setup is described, and the first laboratory results, which prove the capabilities of the method, are presented. A signal-to-noise-ratio calculation, permitting a first comparison with the speckle interferometry, is also presented.

Two-dimensional spatial light modulators: a tutorial

Abstract: Two-dimensional spatial light modulators (SLMs) modulate one of the properties of an optical wavefront (amplitude, phase, polarization) as a function of two spatial dimensions and time in response to information-bearing control signals that may be either optical or electrical. These devices form a critical part of optical information processing systems, serving as input transducers as well as performing several basic processing operations on optical wavefronts. A tutorial overview of the 2-D SLMs is given. their applications are outlined, a classification scheme for them is given, and major types of SLMs that are under active development are described. >

Wavefront sensing and the irradiance transport equation

Abstract: Phase retrieval has recently been experimentally demonstrated, using the irradiance transport equation. We show that this equation provides a unified description for incoherent wavefront sensing methods, bringing new insights and opening new prospects in this area.

First diffraction-limited astronomical images with adaptive optics

Abstract: An adaptive optics prototype system has been tested at the 1.52 m telescope of the Observatoire de Haute Provence, resulting in diffraction-limited images at near infrared wavelengths (2.2 to 5 microns). This paper presents the first results and a short analysis, which demonstrate the considerable gain in resolution and sensitivity achieved by this technique. Single stars, close binary stars, and a satellite have been resolved. In some cases another star several arcseconds apart has been used as reference for the wavefront sensing.

Wavefront propagation in an activation model of the anisotropic cardiac tissue: asymptotic analysis and numerical simulations.

Abstract: In this paper we present a macroscopic model of the excitation process in the myocardium. The composite and anisotropic structure of the cardiac tissue is represented by a bidomain, i.e. a set of two coupled anisotropic media. The model is characterized by a non linear system of two partial differential equations of parabolic and elliptic type. A singular perturbation analysis is carried out to investigate the cardiac potential field and the structure of the moving excitation wavefront. As a consequence the cardiac current sources are approximated by an oblique dipole layer structure and the motion of the wavefront is described by eikonal equations. Finally numerical simulations are carried out in order to analyze some complex phenomena related to the spreading of the wavefront, like the front-front or front-wall collision. The results yielded by the excitation model and the eikonal equations are compared.

Hartmann-Shack wavefront sensing and wavefront control algorithm

Abstract: The wavefront sensing and reconstruction algorithms needed for the control signals for the actuators of a deformable mirror when utilizing the Hartmann-Shack wavefront sensing method are discussed. The algorithms determine the actuator's use of the measured data of image displacement to control the mirror. An analysis is presented regarding the limitations inherent in various techniques of wavefront reconstruction. The direct control of subaperture wavefront gradients is discussed, in which a single step replaces the multistep process associated with wavefront reconstruction and decoupling. The single-step process is tested experimentally on a 19-element deformable mirror with subaperture dividing optics and an optical path for purposes of comparison. By increasing the number of fitting terms, coupling can be alleviated, and modal reconstruction is shown to prevent aliasing. Controlling gradients are found to make wavefront correcting more precise by modeling the response function between actuators and subapertures.

Adaptive optics for array telescopes using neural-network techniques

Abstract: IMAGES formed by ground-based telescopes are marred by atmospheric 'seeing9. The plane wavefront from an unresolved star is distorted by continually changing turbulent fluctuations in the air's refractive index. Diffraction-limited performance can in principle be recovered through the methods of adaptive optics, in which the instantaneous wavefront shape is sensed and corrected in real-time by deformable optics that cancel the distortion1,2. The highest resolution will be achieved when this technique is applied to multiple-telescope arrays. For such arrays, the biggest errors caused by seeing at infrared wavelengths are the variations in pathlength and wavefront tilt between array elements. We show here that these errors can be derived by an artificial neural network, given only a pair of simultaneous in-focus and out-of-focus images of a reference star formed at the combined focus of all the array elements. We have optimized a neural network appropriate for 2.2-μm wavelength imaging at the Multiple Mirror Telescope in Arizona. Corrections made by moving the beam-combining mirrors will largely recover the diffraction-limited profile, with a resolution of 0.06 arcsec.

Mathematical modeling of the excitation process in myocardial tissue: influence of fiber rotation on wavefront propagation and potential field.

Abstract: In our macroscopic model the heart tissue is represented as a bidomain coupling the intra- and extracellular media. Owing to the fiber structure of the myocardium, these media are anisotropic, and their conductivity tensors have a principal axis parallel to the local fiber direction. A reaction-diffusion system is derived that governs the distribution and evolution of the extracellular and transmembrane potentials during the depolarization phase of the heart beat. To investigate frontlike solutions, the system is rescaled and transformed into a system dependent on a small parameter. Subsequently a perturbation analysis is carried out that yields zero- and first-order approximations called eikonal equations. The effects of the transmural fiber rotation on wavefront propagation and the corresponding potential field, elicited by point stimulations, are investigated by means of numerical simulations.

Microwave tomography: From theory to practical imaging systems

Abstract: This paper deals with numerical processing techniques and practical applications of active microwave imaging. Different wavefront processing are presented, from an immediate use of measured projections to more complex procedures. Both spectral approaches to diffraction tomography and spatial iterative methods for generalized imaging are considered using multi-incidence of multifrequency techniques for 3D and/or 2D objects. The technology of the so-called microwave camera is presented for the fast recording of the scattered field with arrays of probes involving one- or two-dimensional sensors at a single frequency or in a broad-frequency band. Three different systems are depicted: a single-frequency linear sensor devoted to industrial applications (on-line transverse control of conveyed products), a single-frequency planar microwave camera for biomedical applications and research, and a broad-frequency linear microwave camera for civil engineering applications (detection of the rebars in reinforced concrete strctures). Microwave images obtained experimentally with the three systems are presented on configurations of practical interest for each field of application.

Spectral narrowing technique

Abstract: Monochromatic light from a laser gain generator passes through a first aperture to a beam expander which expands the beam width and reduces the angular divergence of the beam The light from the beam expander has a curved wavefront because of (1) light diffraction in the aperture and (2) deviations from planar surfaces in the optical components in the light path The light is then reflected by a first mirror to a grating which has a plurality of steps in a stepped configuration The grating is adjustable curved so that the steps in the grating are parallel to the curved wavefront and so that light from only a particular band of wavelengths is reflected back to the first mirror The light then passes back through the beam expander, which compresses the beam width, to the discharge chamber for further amplification The light then passes through a second aperture to a partially reflecting mirror A portion of the light is reflected by the partial mirror back to the discharge chamber for further amplification The grating curvature is adjustable controlled by an apparatus which contacts the grating at three spaced points and which applies a controlled force to the grating along a line extending between one of the points and a position midway between the other two points The grating curvature may be servoed to maintain the bandwidth of the laser light at a particular value as various components age

Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry.

Abstract: A phase shifting interferometer using a tunable laser as a light source is proposed for measuring shapes of both surfaces of a glass plate and the distribution of refractive index. To separate the superimposed interferograms generated with many wavefronts reflected from the plate, the phase shift associated with the wavelength shift is applied in the phase shifting interferometer with unequal optical paths in testing and reference beams. A laser diode is used for the tunable light source, and the data processing for obtaining phase distribution is based on the least-squares fitting in interferograms. The rms errors of the measurements are <1/50 wavelength for the surface shape, and 10(-5) of the refractive index for a 5-mm thick optical glass plate.

Agile beam steering using binary optics microlens arrays

Abstract: Agile steering of a helium-neon laser beam (X = 632.8 nm) has been demonstrated using a complementary pair of 5-cm-aperture binary optic microlens arrays in the Galilean telescope geometry. Segmentation of a collimated input beam by illuminating approximately 60,000 /5 microlenses of 200-jim diameter and parabolic phase profile results in nearly aberration free beam steering over an 1 1° field of view for 100- pm lateral displacements of one array relative to the other. Wavefront quality and steering efficiency of the deflected beam has been measured as a function of steering angle and is compared to a simple theoretical model.

Modelling curved surface wave paths: membrane surface wave synthetics

Abstract: SUMMARY Earth's heterogeneity near the surface is so severe that surface waves with period 20 s exhibit complicated propagation effects such as curved paths and multiple rays. In order to take account of these effects, a new method to analyse surface waves is developed. the method, which we call the membrane surface wave method, is an approximation to the Green's function method in a 3-D medium and is valid for a laterally, smoothly varying media. We also present the formulae to invert the seismograms. As an example, we apply the method to a preliminary California model. Use of the method for the forward calculation shows that heterogeneity in the model is so severe that the wavefront due to the Whittier Narrows earthquake is split in two by the time it reaches the San Francisco Bay area. the kernels in the inverse formula to the six Berkeley stations show curved paths, multipathings and finite wavelength effects and visually demonstrate how waves sample the medium. the method is attractive in that these complications cause no problems in its application.

Boundary value ray tracing in a heterogeneous medium: a simple and versatile algorithm

Abstract: SUMMARY Traveltime calculations in 3-D velocity models have become more commonplace during the past decade or so. Many schemes have been developed to deal with the initial value problem, which consists of tracing rays from a known source position and trajectory usually towards some distant surface. Less attention has been given to the more difficult problem of boundary value ray tracing in 3-D. In this case, source and receiver positions are known and one, or more, minimum time paths are sought between fixed endpoints. A new technique for boundary value ray tracing is proposed. The scheme uses a common numerical integration technique for solving the initial value problem and iteratively updates the take-off angles until the ray passes through the receiver. This type of ‘shooting’ technique is made efficient by using expressions describing the geometrical spreading of the wavefront to determine the relationship between the ray position at any time and the take-off angles from the source. The use of numerical integration allows the method to be compatible with a wide variety of structures. These include models with velocity varying smoothly as a function of position and those with arbitrarily orientated surfaces of discontinuity. An examination of traveltime accuracy is given as well as a discussion of efficiency for a few classes of velocity model. To improve upon the first guess pair of take-off angles, a small-scale non-linear inverse problem must be solved. The difference between the receiver position and the arrival point of a ray, on a plane through the receiver, describe a mis-match surface as a function of the two take-off angles of the ray. The shape of this surface can possess local minima and multiple ‘global’ minima even for relatively simple 1-D velocity models. Its study provides some insight into the non-linearities of a small-scale geophysical inverse problem.

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

Optical distortion coefficients of high-power laser windows

Abstract: This paper concerns the problem of describing and evaluating thermal lensing phenomena that occur as a result of the absorption of laser light in solid windows. The aberration function expansion method is applied for deriving the two optical distortion coefficients x+ and xthat characterize the degradation in light intensity at the Gaussian focus of an initially diffraction-limited laser beam passing through a weakly absorbing stress-birefringent window. In a pulsed mode of operation, the concept of an effective optical distortion coefficient Xeff, which properly combines the coefficients x+ and x- in terms of potential impact on focal irradiances, then leads to the definition of a figure of merit for distortion. The theory and calculations presented in this and earlier papers provide simple analytical tools for predicting the optical performance of a windowmaterial candidate in a specific system's environment.

Analysis of spatial pseudodepolarizers in imaging systems

Abstract: The objective of a number of optical instruments is to measure the intensity accurately without bias as to the incident polarization state. One method to overcome polarization bias in optical systems is the insertion of a spatial pseudodepolarizer. Both the degree of depolarization and image degradation (from the polarization aberrations of the pseudodepolarizer) are analyzed for two depolarizer designs: (1) the Cornu pseudodepolarizer, effective for linearly polarized light, and (2) the dual Babinet compensator pseudodepolarizer, effective for all incident polarization states. The image analysis uses a matrix formalism to describe the polarization dependence of the diffraction patterns and optical transfer function.

Atmospheric wavefront simulation and Zernike polynomials

Abstract: An algorithm is described which simulates atmospherically distorted wavefronts using a Zernike expansion of randomly weighted Karhunen-Loeve functions. Its performance are presented and analyzed thereafter. The program is then used to forecast resulting structure function and Strehl resolution for adaptive optics systems.

Wavefront sensing and correction with deformable mirror

Abstract: A closed loop system sends one portion of a coherent laser beam along a first path and another portion of the beam along a second path which is directed at a mirror formed on piezoelectric membrane. After reflection, both return beams are mixed on a photodetector array and the array output is analyzed to determine the values of a charge distribution on the piezoelectric membrane which will null or maintain constant the phase of the mixed beam.

Linearly focusing grating coupler for integrated-optic parallel pickup

Abstract: Parallel pickup of optical digital data is attractive in optical memory applications. In order to construct a parallel pickup device with integrated optics, the use of a linearly focusing grating coupling (LFGC) was proposed and discussed. A guided wave in a slab waveguide is diffracted by the LFGC to be focused to a line in the air. The linearly focused wave is reflected by a recorded medium, such as an optical card, and is coupled by the same LFGC back into the waveguide. The backcoupling of the LFGC was discussed for parallel pickup of 8-μm-sized marks, and it was experimentally confirmed that the virtual images of the marks can be formed in the waveguide.

Ring waves on the surface of shear flows: a linear and nonlinear theory

Abstract: A theory is presented which describes the propagation of a ring wave on the surface of a flow which moves with some prescribed velocity profile. The problem is formulated in suitable far-field variables (which give the concentric KdV equation for a stationary flow), but allowance is made for the fact that the wavefront is no longer circular

Z-Scan: A Simple And Sensitive Technique For Nonlinear Refraction Measurements

Abstract: We describe a sensitive technique for measuring nonlinear refraction in a variety of materials that offers simplicity, sensitivity and speed. The transmittance of a sample is measured through a finite aperture in the far-field as the sample is moved along the propagation path (z) of a focused Gaussian beam. The sign and magnitude of the nonlinearity is easily deduced from such a transmittance curve (Z-scan). Employing this technique a sensitivity of better than λ/300 wavefront distortion is achieved in n2 measurements of BaF2 using picosecond frequency doubled Nd:YAG laser pulses.

Designing holographic lenses with different recording and readout wavelengths

Abstract: A method for designing and recording transmission holographic lenses, having low aberrations and high diffraction efficiencies, in the presence of a recording–readout wavelength shift, is presented. The method is based on a recursive design technique, in which the final hologram is recorded with complex wave fronts that are derived from intermediate holograms. The design is illustrated for a lens with an f-number of 2.5 and a large offset angle, recorded at 488 nm and read out at 633 nm. A nearly diffraction-limited spot size and an efficiency of >80% are measured.

Measurement accuracy of semiconductor LDA systems

Abstract: A laser Doppler anemometer with a laser diode as the light source, has several advantages: i.e., low power consumption, compactness, and low cost. In order to be fully benefitted by these favorable characteristics, the measurement uncertainty, associated with wavefront distortion in the measuring volume, should be minimized. Furthermore, proper attention should be given to system misalignment caused by external perturbations, such as thermal expansion of the diode-collimator assembly. These considerations lead to a computational procedure for optimizing the layout of the semiconductor LDA system. Calculations are based on a generalized relation for fringe non-uniformity combined with a simulation model for the anemometry system. For this purpose, the optical field of a laser diode is described satisfactorily as a product of a Gaussian and a truncated Lorentzian distribution. The influence of various design parameters is examined by means of an extensive computational study as well as experimental evaluation involving precise scanning of the measuring volume. The performance is improved by employing a small focal length collimator and a large focal length front lens. For measurement of turbulence intensities smaller than 1%, it may become necessary to collect the signals in the side scatter and to use a frequency-domain signal processor. For such an application, temperature control may also be necessary, but it should be applied to the entire diode-collimator assembly and not just to the laser diode as suggested in previous publications.

Segmented mirrors for atmospheric compensation

Abstract: An optical wavefront propagating through the atmosphere will be perturbed by local variations in the refractive index ofthe atmospheric gases. When accumulated over long optical path distances they will impart a spatial and temporally random distortion to the wavefront. These distortions have a characteristic spatial coherence length r0 and an atmospheric decorrelation time T0. In directed energy applications, atmospheric distortions can reduce the peak target energy densities of larger diameter laser beams by orders of magnitude. The problem is not solved through the use of larger apertures; once the aperture size increases beyond one or two r0, the far-field spot remains constant in size. Hence, for large aperture systems, the overall performance is set by the spatial coherence of the atmosphere and not by the system's exit pupil.