Showing papers on "Wavefront published in 1996"

Imaging Through Turbulence

Abstract: Introduction Overview of the Problem Area Historical Overview of Imaging Through Turbulence Overview of the Book Background: Fourier and Statistical Optics Fourier Optics Statistical Optics Turbulence Effects on Imaging Systems Index of Refraction Fluctuations in the Atmosphere Statistics of Index of Refraction Fluctuations Wave Propagation through Random Media First-Order Turbulence Effects on Incoherent Imaging Modal Expansions of Phase Perturbation Phase Screen Generation Speckle Imaging Techniques Introduction Overview of Speckle Imaging Speckle Interferometry Fourier Phase Estimation Techniques Image Reconstruction for Speckle Imaging Conclusion Adaptive Optical Imaging Systems Introduction Factors that Degrade AOI Systems Performance Adaptive Optical System Components and Models AOI System Performance Modeling Summary Hybrid Imaging Techniques Introduction Deconvolution from Wavefront Sensing Methods Involving Adaptive Optics Conclusion Index

Pupil plane wavefront sensing with an oscillating prism

Abstract: A compact pupil plane wavefront sensor is described, which is able to image on a single detector four images of the pupil, containing information on the gradient of the incoming wavefront. The wavefront sensor consists of a lens relay and an oscillating pyramidal-shaped prism. The gain of the device is driven by the amplitude of the oscillations, while the sampling is determined by the focal length of the lens relay. This wavefront sensor can be conveniently used for astronomical adaptive optics purposes because of its flexibility to match the brightness of the reference source used (varying the sampling) and the seeing conditions (varying the gain).

Wave fields in three dimensions: analysis and synthesis

Abstract: Distributions of wave fields in three-dimensional domains are analyzed, synthesized, and generated experimentally. Fundamental limits are discussed and sampling conditions are derived for their generation, with use of a single diffractive element. A general design procedure, based on optimization algorithms, is developed and implemented. Experimental results show that special three-dimensional light distributions can be achieved with low-information-content elements in on-axis configurations.

Two-dimensional multivalued traveltime and amplitude maps by uniform sampling of a ray field

Abstract: SUMMARY An algorithm for computing multivalued maps for traveltime, amplitude or any other ray-related variable is presented. It is based on a wavefront construction method, where the ray field is decomposed into elementary cells defined by adjacent rays and wavefronts. A sampling criterion for ray density in the phase space is suggested. It is demonstrated that this new criterion ensures uniform ray density over the entire ray field including caustics. The method is applied to complex models.

Estimation of multivalued arrivals in 3D models using wavefront construction—Part I1

Abstract: A new 3D wavefield modelling approach based on dynamic ray tracing is presented. This approach is called wavefront construction, and it can be used in 3D models with constant or smoothly varying material properties (S- and P-velocity and density) separated by smooth interfaces. Wavefronts consisting of rays arranged in a triangular network are propagated stepwise through the model. At each time step, the differences in a number of parameters are checked between each pair of rays on the wavefront. New rays are interpolated whenever this difference between pairs of rays exceeds some predefined maximum value. A controlled sampling of the wavefront at all time steps is thus obtained. Receivers are given multiple-event values by interpolation when the wavefronts pass them. The strength of the wavefront construction method is that it is robust and efficient.

The telescope point spread function

Abstract: New observations are used to accurately define the stellar point spread function produced by atmospheric turbulence at the focus of large telescopes and to compare its profile to those computed from wavefronts characterized by various structure functions Excellent agreement is found with the PSF expected from Kolmogorov statistics, except for the presence of an extended aureole of light which appears to results from a combination of instrumental and atmospheric light scattering Simple yet accurate analytic fits are developed to represent the PSF profile over a range of 15 magnitudes in surface brightness The relation between the Strehl ratio S of the PSF and the value of the parameter D/r0 is re-discussed, both for a natural wavefront and for a wavefront whose variance DeltaN is reduced by an adaptive optics systems A simple expression for S(D/r0, DeltaN) is proposed and shown to yield essentially correct Strehl ratios for any value of the parameters

Heterodyne interferometer with two‐wave mixing in photorefractive crystals for ultrasound detection on rough surfaces

Abstract: Heterodyne interferometers using two‐wave mixing in photorefractive cubic crystals for ultrasound detection on rough surfaces are demonstrated. The speckled scattered beam from a rough surface sample interferes with a planar coherent pump beam inside a photorefractive crystal. A third frequency‐shifted beam is used to read the grating. The diffracted readout beam and the transmitted signal beam are wavefront matched, resulting in an optimal heterodyne interference signal. The signal to noise ratio for the two commonly used crystallographic configurations with cubic crystals, G∥〈110〉∥ and G∥〈001〉, where G is the grating wave vector, are investigated. Very good sensitivity is demonstrated for the detection of small amplitude ultrasonic surface displacements.

Ground‐penetrating radar: Wave theory and numerical simulation in lossy anisotropic media

Abstract: Subsurface georadar is a high-resolution technique based on the propagation of high-frequency radio waves. Modeling radio waves in a realistic medium requires the simulation of the complete wavefield and the correct description of the petrophysical properties, such as conductivity and dielectric relaxation. Here, the theory is developed for 2-D transverse magnetic (TM) waves, with a different relaxation function associated to each principal permittivity and conductivity component. In this way, the wave characteristics (e.g., wavefront and attenuation) are anisotropic and have a general frequency dependence. These characteristics are investigated through a plane-wave analysis that gives the expressions of measurable quantities such as the quality factor and the energy velocity. The numerical solution for arbitrary heterogeneous media is obtained by a grid method that uses a time-splitting algorithm to circumvent the stiffness of the differential equations. The modeling correctly reproduces the amplitude and the wavefront shape predicted by the plane-wave analysis for homogeneous media, confirming, in this way, both the theoretical analysis and the numerical algorithm. Finally, the modeling is applied to the evaluation of the electromagnetic response of contaminant pools in a sand aquifer. The results indicate the degree of resolution (radar frequency) necessary to identify the pools and the differences between the anisotropic and isotropic radargrams versus the source-receiver distance.

Shack Hartmann wave-front measurement with a large F-number plastic microlens array.

Abstract: A new plastic microlens array, consisting of 900 lenslets, has been developed for the Shack Hartmann wave-front sensor. The individual lens is 300 μm × 300 μm and has a focal length of 10 mm, which provides the same focal size, 60 μm in diameter, with a constant peak intensity. One can improve the wave-front measurement accuracy by reducing the spot centroiding error by averaging a few frame memories of an image processor. A deformable mirror for testing the wave-front sensor gives an appropriate defocus and astigmatism, and the laser wave front is measured with a Shack Hartmann wave-front sensor. The measurement accuracy and reproducibility of our wave-front sensor are better than λ./20 and λ/50 (λ = 632.8 nm), respectively, in rms.

Liquid-crystal point-diffraction interferometer for wave-front measurements

Abstract: A new instrument, the liquid-crystal point-diffraction interferometer (LCPDI), is developed for the measurement of phase objects. This instrument maintains the compact, robust design of Linnik's point-diffraction interferometer and adds to it a phase-stepping capability for quantitative interferogram analysis. The result is a compact, simple to align, environmentally insensitive interferometer capable of accurately measuring optical wave fronts with very high data density and with automated data reduction. We describe the theory and design of the LCPDI. Afocus shift was measured with the LCPDI, and the results are compared with theoretical results.

Amplitude and phase beam characterization using a two-dimensional wavefront sensor

Abstract: We have developed a two-dimensional Shack-Hartman wavefront sensor that uses binary optic lenslet arrays to directly measure the wavefront slope (phase gradient) and amplitude of the laser beam. This sensor uses an array of lenslets that dissects the beam into a number of samples. The focal spot location of each of these lenslets (measured by a CCD camera) is related to the incoming wavefront slope over the lenslet. By integrating these measurements over the laser aperture, the wavefront or phase distribution can be determined. Since the power focused by each lenslet is also easily determined, this allows a complete measurement of the intensity and phase distribution of the laser beam. Furthermore, all the information is obtained in a single measurement. Knowing the complete scalar field of the beam allows the detailed prediction of the actual beam`s characteristics along its propagation path. In particular, the space- beamwidth product M{sup 2}, can be obtained in a single measurement. The intensity and phase information can be used in concert with information about other elements in the optical train to predict the beam size, shape, phase and other characteristics anywhere in the optical train. We present preliminary measurements of an Ar{sup +} laser beam and associated M{sup 2} calculations.

Method and apparatus for correcting surface profiles determined by phase-shifting interferometry according to optical parameters of test surface

Abstract: An improvement to phase-shifting interferometry that consists of the addition of a pupil mask with two parallel slits and a polarizer in the optical path of a conventional phase-shifting interferometer. The pupil-mask/polarizer combination is adapted to produce a linearly polarized wavefront of light reaching the sample surface at a predetermined angle of incidence, thereby producing a corresponding phase shift on reflection. The relative orientation of the mask and polarizer can be changed to take measurements with the polarizer parallel or perpendicular to the mask slits, in each case producing a phase shift on reflection related to the test sample's refractive index and extinction coefficient. Four phase-shifting measurements conducted at π/2 intervals for each polarization axis yield sufficient interferometric information to map n, k and the height profile of the sample surface. The preferred mask consists of an opaque disk structure having two opposite annular slits approximately 90-degrees wide and with an outer annular radius approximately twice the size of the inner annular radius.

Wavefront measuring system with integral geometric reference (igr)

Abstract: A geometric sensor includes a Monolithic Lenslet Module (MLM) subaperture array (22) having a plurality of microlenses (40), each of which have an opaque center marking formed concentric with the micolens optical axis (44), at the location of the lens chief ray, to produce an integral geometric reference (IGR) spot pattern of the lens array which is used to correct for sensor errors to an accuracy comparable with that achieved with reference plane wave calibration.

Off-axial HMD optical system consisting of aspherical surfaces without rotational symmetry

Abstract: An off-axial optical system is desirable for a see-through head mounted display (HMD) with a wide field of view (FOV). Using our new off-axial paraxial theory and the fabricating methods, we have achieved to correct the off-axial aberrations of the optical systems which consists of an aspherical surfaces without rotational symmetry. In this paper, we describe 3 types of off-axial HMD optical systems. (1) The first one is a hologram for a monochromatic HMD. The hologram has been recorded the wavefront generated by computer generated hologram. The image spot size is about 15 micrometers over 9 degree FOV. (2) The second one is an aspherical mirror system for a color HMD. The designed image spot size is less than 30 micrometers over 43.5 degree FOV. The shape error of the fabricated mirror is measured by a contact probing from 1.0 micrometers to 1.9 micrometers . The maximum resolution is 36 lp/mm. (3) The last one is a prism with aspherical surfaces, 34 degree FOV and less than 15 mm thickness. The monocular HMD with only 80 g weight has been developed. The line of sight detecting device has been applied as an interactive man-machine interface.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Phase shifting diffraction interferometry for measuring extreme ultraviolet optics

Abstract: Extreme ultraviolet projection lithography operating at a wavelength of 13nm requires surface figure accuracy on each mirror to be better than 0.25nm rms. A new type of interferometry, based on the fundamental process of diffraction, is described that can intrinsically achieve the required accuracy. Applying this principle, two independent spherical wavefronts are generated - one serves as the measurement wavefront and is incident on the optic or optical system under test and the other serves as the reference wavefront. Since they are generated independently their relative amplitude and phase can be controlled, providing contrast adjustment and phase shifting capability. Using diffraction from a single mode optical fiber, different interferometers can be configured to measure individual mirrors or entire imaging systems. Measurement of an EUV projection system is described. 5 refs., 4 figs.

Wavefront direction mapping catheter system

Abstract: A wavefront direction mapping catheter system is disclosed which includes a wire catheter that, when placed on the inner surface of the heart, identifies the direction of the electric field wavefront, and provides output signals for indicating the manner in which a position controller of the system is to be operated for moving the distal tip portion of the catheter toward the source of the wavefront. The distal tip portion of the catheter includes a bipolar electrode array, preferably including first and second pairs of orthogonally arranged bipolar electrodes which provide signals to an analyzer of the system, whereby vector analysis of the wavefront is performed. The signal analysis permits the catheter to be moved toward and positioned at the source of the wavefront or within the wavefront circuit, with the present system thereafter being configured to effect radio frequency energization of the bipolar electrode array for tissue ablation.

Adaptive optical module

Abstract: The invention pertains to the field of controllable optics and can be used for manipulating a radiation wave front or for correcting phase distortions in optical equipment and in a wide range of systems including industrial laser systems, optical telescopes of different spectral ranges, and optical guidance and tracking systems. The invention in essence lies in improving the range and precision of the phase distortion correction while also increasing the maximum permissible power of the radiation used and simplifying the adaptive optical system. This has been achieved by using in the adaptive optical module a dynamic adjusting head in which is mounted a deformable dimorphic mirror, coolable if necessary, in the form of a semi-passive dimorphic structure containing a system of multiple-layer piezo-elements, a radiation detector in the form of a hexagonal photodiode lattice and hexagonal lens lattice. All the optical elements of the module including the radiation detector can be fitted in the same housing provided with inlet and outlet optical windows. In addition, the proposed design increases the sensitivity and reliablility of the adaptive optical module, and significantly increases its operational potential.

Method for electro-optically rendering a holographic image

Abstract: A display method for producing a plurality of different views of an object scene simultaneously is provided. A series of two-dimensional projections of an object is produced for the plane of a display device. Wavefront interference information, independent of the two-dimensional projections is produced for an intermediate plane. The two-dimensional projections and the wavefront interference information are combined to create a diffraction grating in the display device to provide a holographic image of the object scene from a number of positions relative to the display device.

Adaptive optics for astronomy: theoretical performance and limitations

Abstract: We investigate the theoretical performance of adaptive optics correction for imaging in astronomy. Image improvements are calculated as a function of the fundamental limitations imposed by anisoplanatic effects, and photon and detector noise in wavefront sensing. In contrast to previous studies, which have concentrated mainly on predicting Strehl ratio improvements, we calculate the adaptively corrected point­ spread function explicitly. The shape of the point-spread function, and encircled energy widths, is crucial in astronomical applications such as photometry and spectroscopy. The analysis therefore allows a detailed assessment of the potential benefits of adaptive optics for astronomical applications, and provides an important tool for system design.

Defocusing of a converging electromagnetic wave by a plane dielectric interface

Abstract: We study how a converging spherical wave gets distorted by a plane dielectric interface. The fields in the second medium are obtained by evaluating the m-theory diffraction integral on the interface. The loss of intensity and the form of the intensity distribution are investigated. Examples are presented for various refractive-index contrasts and depths of focus. In general the intensity gets spread out over a volume that is large compared with the case without refractive-index contrast. It was found that moving the focusing lens a distance d toward the interface does not result in an equal shift of the intensity profile. This latter point has important practical implications.

Algebraic decay and variable speeds in wavefront solutions of a scalar reaction-diffusion equation

Abstract: Wavefront solutions of scalar reaction-diffusion equations have been intensively studied for many years. There are two basic cases, typified by quadratic and cubic kinetics. An intermediate case is considered in this paper, namely, u l = u xx + u 2 (1 − u). It is shown that there is a unique travelling-wave solution, with a speed 1/√2, for which the decay to zero ahead of the wave is exponential with x. Moreover, numerical evidence is presented which suggests that initial conditions with such exponential decay evolve to this travelling-wave solution, independently of the half-life of the initial decay. It is then shown that for all speeds greater than 1/√2 there is also a travelling-wave solution, but that these faster waves decay to zero algebraically, in proportion to 1/x. The numerical evidence suggests that initial conditions with such a decay rate evolve to one of these faster waves; the particular speed depends in a simple way on the details of the initial condition. Finally, initial conditions decaying algebraically for a power law other than 1/x are considered. It is shown numerically that such initial conditions evolve either to an algebraically decaying travelling wave, or in some cases to a wavefront whose shape and speed vary as a function of time. This variation is monotonic and can be quite pronounced, and the speed is a function of u as well as of time. Using a simple linearization argument, an approximate formula is derived for the wave speed which compares extremely well with the numerical results. Finally, the extension of the results to the more general case of u l = u xx + u m (1 − u), with m > 1, is discussed.

The effect of random isotropic inhomogeneities on the phase velocity of seismic waves

Abstract: In this paper we study, theoretically and numerically, the influence of 2-D and 3-D random isotropic stationary inhomogeneities on the phase velocities of the transmitted compressional wavefield of an initially plane (or spherical) wave. Due to scattering by the inhomogeneities the wavefield becomes distorted as the wave propagates through the medium. The traveltimes fluctuate when considering different wavefield registrations acquired at the points of surfaces that are parallel to the wavefront of the initial wave. It is usually observed that the slowness obtained from the averaged traveltime differs from the averaged slowness of (he medium. In the geophysical lilerature this effect has been termed the ‘velocity shift’. Using the Rytov approximation we establish formulas for the frequency- and travel-distance-dependent phase velocity of the transmitted wavefield in 2-D and 3-D randomly inhomogeneous media. We also compare our analytical results with finite-difference simulations. Good agreement between numerical simulations and theory is observed. The low-frequency limit of our analytical results coincides with the known effective-medium limit of the phase velocity in statistically isotropic inhomogeneous fluids with constant densities. In the high-frequency limit our results coincide with the results previously obtained by the ray-perturbation theory. However, in contrast to the ray theory, our description is not restricted to media with differentiate correlation functions of fluctuations. Moreover, our results quantify the frequency dependence of the velocity shift in the intermediate-frequency range. This frequency dependence is of major importance for estimating this effect in realistic situations.

Power spectral density specifications for high-power laser systems

Abstract: This paper describes the use of Fourier techniques to characterize the transmitted and reflected wavefront of optical components. Specifically, a power spectral density (PSD), approach is used. High power solid-state lasers exhibit non-linear amplification of specific spatial frequencies. Thus, specifications that limit the amplitude of these spatial frequencies are necessary in the design of these systems. Further, NIF optical components have square, rectangular or irregularly shaped apertures with major dimensions up to 800 nm. Components with non-circular apertures can not be analyzed correctly with Zernicke polynomials since these functions are an orthogonal set for circular apertures only. A more complete and powerful representation of the optical wavefront can be obtained by Fourier analysis in 1 or 2 dimensions. The PSD is obtained from the amplitude of frequency components present in the Fourier spectrum. The shape of a resultant wavefront or the focal spot of a complex multi-component laser system can be calculated and optimize using PSDs of the individual optical components which comprise the system. Surface roughness can be calculated over a range of spatial scale-lengths by integrating the PSD. FInally, since the optical transfer function of the instruments used to measure the wavefront degrades at high spatial frequencies, the PSD of an optical component is underestimated. We can correct for this error by modifying the PSD function to restore high spatial frequency information. The strengths of PSD analysis are leading us to develop optical specifications incorporating this function for the planned National Ignition Facility.

Automated pupil remapping with binary optics

Abstract: Methods and apparatuses for pupil remapping employing non-standard lenslet shapes in arrays; divergence of lenslet focal spots from on-axis arrangements; use of lenslet arrays to resize two-dimensional inputs to the array; and use of lenslet arrays to map an aperture shape to a different detector shape. Applications include wavefront sensing, astronomical applications, optical interconnects, keylocks, and other binary optics and diffractive optics applications.

Design of a Holographically Recorded Plane Grating with a Varied Line Spacing for a Soft X-ray Grazing-Incidence Monochromator

Abstract: A new design concept is presented for a plane grating with a varied line spacing for the Monk–Gillieson mounting monochromator. A light path function including both a spherical mirror and a varied-line-spacing grating is defined to optimize groove parameters. Aspheric wavefront recording optics are utilized to fabricate a grating holographically. Ray-tracing results show that the varied-line-spacing grating eliminates aberrations significantly and affords a high resolving power as a total optical system of a soft X-ray grazing-incidence monochromator. The effects of errors in recording parameters and in the radius of the spherical mirror are described, and possible ways to compensate for these errors are discussed.

Part II: Tracing and interpolation1

Abstract: The numerical tracing of short ray segments and interpolation of new rays between these ray segments are central constituents of the wavefront construction method. In this paper the details of the ray tracing and ray-interpolation procedures are described. The ray-tracing procedure is based on classical ray theory (high-frequency approximation) and it is both accurate and efficient. It is able to compute both kinematic and dynamic parameters at the endpoint of the ray segments, given the same set of parameters at the starting point of the ray. Taylor series are used to approximate the raypath so that the kinematic parameters (new position and new ray tangent) may be found, while a staggered finite-difference approximation gives the dynamic parameters (geometrical spreading). When divergence occurs in some parts of the wavefront, new rays are interpolated. The interpolation procedure uses the kinematic and dynamic parameters of two parent rays to estimate the initial parameters of a new ray on the wavefront between the two rays. Third-order (cubic) interpolation is used for interpolation of position, ray tangent and take-off vector from the source) while linear interpolation is used for the geometrical spreading parameters.

Host-pathogen systems in a spatially patchy environment.

Abstract: A discrete model for a host-pathogen system is developed and is used to represent the dynamics in each patch within a landscape of n x n patches. These patches are linked by between-generation dispersal to neighbouring patches. Important results (compared to similar 'coupled map lattice' studies) include an increase in the likelihood of metapopulation extinction if the natural loss of pathogen particles is low, and the observation of a radial wave pattern (not previously reported) where the wavefront propagates uniformly from a central focus. This result has additional significance in that it permits the system to exhibit 'intermittency' between two quasi-stable spatial patterns: spirals and radial waves. With intermittent behaviour, the dynamics may look consistent when viewed at one time scale, but over a longer time scale they can alter dramatically and repeatedly between the two patterns. There is also evidence of clear links between spatial structure and temporal metapopulation behaviour in both the intermittent and 'pure' regions, verified by results from an algorithmic complexity measure and a spectral analysis of the temporal dynamics.

Two dimensional interferometer array

Abstract: Apparatus and a processing method that determine accurate angle of arrival data indicative of the direction to an emitter. An accurate angle of to the emitter using four antennas and receiver channels (processor). The present invention provides for an ambiguity function that is an implementation of a four-channel two-dimensional interferometer array. The interferometer array and method provide for a reference antenna and second, third and fourth antennas disposed in a predetermined plane with the reference antenna and offset from the reference antenna at locations such that no two antennas lie along a straight line that includes the reference antenna. Receivers are coupled to the antennas for detecting RF energy derived therefrom. Phase comparators make three phase difference measurements (φ 1 , φ 2 and φ 3 ). A processor performs ambiguity elimination and angle determination computations to determine azimuth and elevation angle of arrival data indicative of the direction of arrival of energy derived from the emitter. The processing method is implemented in the processor and computes an ambiguity factor relating the spatial locations of the antenna, looks up the ambiguity factor value in a precomputed ambiguity table and find the associated factors N 2 and N 3 , which correspond to a respective number of integer cycles of RF energy that can occur from the time a plane wavefront hits one of the antennas until this wavefront hits the reference antenna, computes two unambiguous phase values, and computes azimuth and elevation angles to the emitter.

On the effect of diffraction on traveltime measurements

Abstract: SUMMARY All observed waves are of finite frequency and are sensitive to a finite volume of the medium through which they pass. Diffraction causes a loss of information about time contained in the initial front of a wavefield (often referred to as wavefront healing). This effect depends upon frequency and propagation distance and imposes a low-pass filter on the spatial resolution of time measurements. A sequence of canonical, numerical experiments that simulate the diffraction of a perturbed plane wave at a fixed distance is described. Traveltimes are measured using a variety of techniques on a range of waveforms. It is empirically verified that a single Fresnel zone describes the spatial filtering effect of the propagation of a broad-band wavefield, even in the regime where the initial time perturbation cannot be represented by a linear perturbation term. For narrow-band wavefields, more Fresnel zones come into play as the bandwidth is reduced. Measurements of time include a component of signal-generated noise coherent over a small scale which scales with the Fresnel zone. It is found that, for traveltimes measured by automated picking, the width of the Fresnel zone is described by a time delay of (&I< T/4 (here T is one period). On the other hand, the width of the Fresnel zone for traveltimes measured by correlation is wider, characterized by a time delay of ldtl < T/4.