Showing papers on "Wavefront published in 1998"

Interferogram analysis for optical testing

Abstract: (condensed). Review and Comparison of the Main Interferometric Systems: Two-Wave Interferometers and Configurations Used in Optical Testing. Twyman-Green Interferometer. Fizeau Interferometers. Typical Interferograms in Twyman-Green and Fizeau Interferometers. Lateral Shear Interferometers. Ronchi Test. Hartmann Test. Fringe Projection. Talbot Interferometry and Moire Deflectometry. Common Light Sources Used in Interferometry. Aspherical Compensators and Aspheric Wavefronts. Imaging of the Pupil on the Observation Plane. Multiple-Wavelength Interferometry. Fourier Theory Review: Introduction. Fourier Series. Fourier Transforms. The Convolution of Two Functions. The Cross-Correlation of Two Functions. Sampling Theorem. Sampling of a Periodical Function. Sampling of a Periodical Function with Interval Averaging. Fast Fourier Transform. Digital Image Processing: Introduction. Histogram and Gray-Scale Transformations. Space and Frequency Domain of Interferograms. Digital Processing of Images. Some Useful Spatial Filters. Square Window Filter. Hamming and Hanning Window Filters. Cosinusoidal and Sinusoidal Window Filters. Extrapolation of Fringes Outside of the Pupil. Light Detectors Used To Digitize Images. Fringe Contouring and Polynomial Fitting: Fringe Detection Using Manual Digitizers. Fringe Tracking and Fringe Skeletonizing. Global Polynomial Interpolation. Local Interpolation by Segments. Wavefront Representation by an Array of Gaussians.References. Periodic Signal Phase Detection and Algorithms Analysis: Least Squares Phase Detection of a Sinusoidal Signal. Quadrature Phase Detection of a Sinusoidal Signal. Discrete Low-Pass Filtering Functions. Fourier Description of Synchronous Phase Detection. Synchronous Detection Using a Few Sampling Points. Signal Amplitude Measurement. Characteristic Polynomial of a Sampling Algorithm. General Error Analysis of Synchronous Phase-Detection Algorithms. Some Sources of Phase Error. Shifting Algorithms with Respect to the Phase Origin. Optimization of Phase-Detection Algorithms. Influence of Window Function of Sampling Algorithms. Conclusions. Appendix: Derivative of the Amplitude of the Fourier Transform of the Reference Sampling Functions. References. Phase-Detection Algorithms: General Properties of Synchronous Phase-Detection Algorithms. Three-Step Algorithms To Measure the Phase. Four-Step Algorithms To Measure the Phase. Five-Step Algorithm. Algorithms with Symmetrical N +1 Phase Steps. Combined Algorithms in Quadrature. Detuning-Insensitive Algorithms for Distorted Signals. Algorithms Corrected for Nonlinear Phase-Shifting Error. Continuous Sampling in a Finite Interval. Asynchronous Phase-Detection Algorithms. Algorithm Summary. References. Phase-Shifting Interferometry: Phase-Shifting Basic Principles. An Introduction to Phase Shifting. Phase-Shifting Schemes and Phase Measurement. Heterodyne Interferometry. Phase-lock Detection. Sinusoidal Phase Oscillation Detection. Practical Sources of Phase Error. Selection of the Reference Sphere in Phase-Shifting Interferometry. Paraxial Focus. Best Focus. Marginal Focus. Optimum Tilt and Defocusing in Phase-Shifting Interferometry. References. Spatial Linear and Circular Carrier Analysis: Spatial Linear Carrier Analysis. Space-Domain Phase Demodulation with a Linear Carrier. Basic Space-Domain Phase Demodulation Theory. Circular Spatial Carrier Analysis. Phase Demodulation with a Circular Carrier. Fourier Transform Phase Demodulation with a Linear Carrier. Fourier Transform Phase Demodulation with a Circular Carrier. References. Interferogram Analysis with Moire Methods: Moire Techniques. Moire Formed by Two Interferograms with a Linear Carrier. Moire Formed by Two Interferograms with a Circular Carrier. Summary of Moire Effects. Holographic Interpretation of Moire Patterns. Conclusion. References. Interferogram Analysis without a Carrier: Introduction. Mathematical Model of the Fringes. The Phase Tracker. The N-Dimensional Quadrature Transform. Conclusion. References. Phase Unwrapping: The Phase Unwrapping Problem. Unwrapping Consistent Phase Maps Unwrapping Noisy Phase Maps. Unwrapping Subsampled Phase Maps. Conclusions. References. Wavefront Curvature Sensing: Wavefront Determination by Slope Sensing. Wavefront Curvature Sensing. Wavefront Determination with Defocused Images. Conclusions. References. Index. Short TOC

Liquid-crystal adaptive lenses with modal control.

Abstract: We report on a novel approach to the realization of nematic liquid-crystal (LC) phase correctors to form spherical and cylindrical wave fronts. A LC cell with a distributed reactive electrical impedance was driven by an ac voltage applied to the cell boundary to yield the desired spatial distribution of the refractive index. The two-dimensional function of the phase delay introduced into the light beam depends on the frequency of the ac control voltage, the geometry of the boundary electrode surrounding the LC cell, and the electrical parameters of the cell. We realized a cylindrical adaptive lens with a clear aperture of 15 mm x 4mm and a spherical adaptive lens with circular aperture of 6.5 mm. Both devices are capable of focusing collimated light in the range infinity...0.5 m.

Branch point problem in adaptive optics

Abstract: It is shown that when branch points are present in the phase of a turbulence-distorted optical field, the ability of an adaptive optics system that utilizes a least mean square error type of wave-front reconstructor to sense all of the turbulence-induced phase perturbations is limited. There is a portion of the turbulence-induced phase perturbation, which portion we refer to as the hidden phase, that such a least mean square error type of wave-front reconstructor will, in effect, ignore. It is shown that the presence of branch points indicates that the measured phase-difference vector field cannot be considered to be simply the gradient of some scalar potential—the phase function—but is in part also the curl of a vector potential function. A solution is developed for this vector potential, and from this a simple closed-form solution for the hidden phase is developed. Sample numerical results are presented showing the nature of the hidden phase. Suggestions are provided for a branch-point-tolerant wave-front reconstructor based on use of the closed-form solution for the hidden phase.

Seismic monitoring of diffraction images for detection of local heterogeneities

Abstract: Diffracted waves contain valuable information regarding both the structure and composition of the media they are in In seismic data processing, however, these waves are usually regarded as noise In this paper, we present an attempt to use scattered/diffracted waves for the detection of local heterogeneities The method is based on the detection of diffracted waves by concentrating the signal amplitudes from diffracting points on the seismic section This is done using a correlation procedure that enhances the amplitude of the seismic signal at the location of the diffractors on the common‐diffraction‐point section (D-section) The new local time correction for diffraction traveltime curve parameterization is based on the radius of curvature of the diffracted wavefront and near‐surface velocity We use the idea of seismic monitoring for detection and delineating local objects which may occur within the subsurface resulting from human activity or fast geological processes The method consists of continuou

Traveltimes for infrasonic waves propagating in a stratified atmosphere

Abstract: SUMMARY The tau‐p method of Buland & Chapman (1983) is reformulated for sound waves propagating in a stratified atmosphere under the influence of a height-dependent wind velocity profile. For a given launch angle along a specified azimuth, the ray parameter is redefined to include the influence of the horizontal wind component along the direction of wave propagation. Under the assumption of negligible horizontal wind shear, the horizontal wind component transverse to the ray propagation does not aVect the direction of the wave normal, but displaces the reference frame of the moving wavefront, thus altering the observed incidence azimuth. Expressions are derived for the time, horizontal range, and transverse range of the arriving waves as a function of ray parameter. Algorithms for the location of infrasonic wave sources using the modified tau‐p formulation in conjunction with regional atmospheric wind and temperature data are discussed.

3-D finite-difference elastic wave modeling including surface topography

Abstract: Three‐dimensional finite‐difference (FD) modeling of seismic scattering from free surface topography has been pursued. We have developed exact 3-D free surface topography boundary conditions for the particle velocities. A velocity‐stress formulation of the full elastic wave equations together with the boundary conditions has been numerically modeled by an eighth‐order FD method on a staggered grid. We give a numerical stability criterion for combining the boundary conditions with curved‐grid wave equations, where a curved grid represents the physical medium with topography. Implementation of this stability criterion stops instabilities from arising in areas of steep and rough topographies. We have simulated scattering from teleseismic P-waves using a plane, vertically incident wavefront and real topography from a 40 × 40 km area centered at the NORESS array of seismic receiver stations in southeastern Norway. Synthetic snapshots and seismograms of the wavefield show clear conversion from P-waves to Rg (sh...

Signal and resolution enhancements in dual beam optical coherence tomography of the human eye.

Abstract: In the past 10 years, a dual beam version of partial coherence interferometry has been developed for measuring intraocular distances in vivo with a precision on the order of 0.3 to 3 mm. Two improvements of this technology are described. A special diffractive optical element allows matching of the wavefronts of the divergent beam reflected at the cornea and the parallel beam reflected at the retina and collimated by the optic system of the eye. In this way, the power of the light oscillations of the interfering beams incident on the photodetector is increased and the signal-to-noise ratio of in vivo measurements to the human retina is improved by 20 to 25 dB. By using a synthesized light source consisting of two spectrally displaced superluminescent diodes with an effective bandwidth of 50 nm, and by compensating for the dispersive effects of the ocular media, it was possible to record the first optical coherence tomogram of the retina of a human eye in vivo with an axial resolution of ; 6t o 7 m m. This is a twofold improvement over the current technology. © 1998 Society of Photo-Optical Instrumentation Engineers. [S1083-3668(98)01601-3]

Control of chromatic focal shift through wave-front coding.

Abstract: Control of chromatic aberration through purely optical means is well known. We present a novel, to our knowledge, optical–digital method of controlling chromatic aberration. The optical–digital system, which incorporates a cubic phase-modulation (CPM) plate in the optical system and postprocessing of the detected image, effectively reduces a system’s sensitivity to misfocus in general or axial (longitudinal) chromatic aberration, in particular. A fully achromatic imaging system (one that is corrected for a continuous range of wavelengths) can be achieved by initial optimization of the optical system for all aberrations except chromatic aberration. The chromatic aberration is corrected by the inclusion of the CPM plate and postprocessing.

Comparison of the eye’s wave-front aberration measured psychophysically and with the Shack–Hartmann wave-front sensor

Abstract: The Shack-Hartmann wave-front sensor offers many theoretical advantages over other methods for measuring aberrations of the eye; therefore it is essential that its accuracy be thoroughly tested. We assessed the accuracy of a Shack–Hartmann sensor by directly comparing its measured wave-front aberration function with that obtained by the Smirnov psychophysical method for the same eyes. Wave-front profiles measured by the two methods agreed closely in terms of shape and magnitude with rms differences of ∼λ/2 and ∼λ/6 (5.6-mm pupil) for two eyes. Primary spherical aberration was dominant in these profiles, and, in one subject, secondary coma was opposite in sign to primary coma, thereby canceling its effect. Discovery of an unusual, subtle wave-front anomaly in one individual further demonstrated the accuracy and sensitivity of the Shack–Hartmann wave-front sensor for measuring the optical quality of the human eye.

Display apparatus including grating light-valve array and interferometric optical system

Abstract: Display systems employ a planar grating light-valve (GLV) array as a spatial light-modulator for representing an image to be displayed The systems rely for image representation on the position of moveable reflective elements of the GLV array, which move through planes parallel to the plane of the array The moveable elements provide, from an incident phase-constant wavefront, a reflected phase-modulated wavefront representing the image to be displayed The displayed image is provided by interferometrically combining the phase-modulated wavefront with a reference wavefront also formed, directly or indirectly, from the incident phase-constant wavefront

Optical interferometer employing multiple detectors to detect spatially distorted wavefront in imaging of scattering media

Abstract: There is disclosed an optical measurement device which is based on optical interference and it uses a light beam which is radiated to and transmitted through or reflected by a sample, especially a light scattering medium to optically measure the sample. The amount of signal lights effective for optical heterodyne detection is increased, while speckle noises are averaged out. On an observation plane of a concerned point arranged are plural detector elements. From signals obtained by the respective detector elements, an optical signal of the concerned point is obtained.

Dynamic wave-front generation for the characterization and testing of optical systems.

Abstract: We describe a simple method for generating known optical aberrations dynamically, using a ferroelectric liquid-crystal spatial light modulator. Aberrations inherent in the optical system are measured and corrected, and as an example Kolmogorov turbulence is simulated for aperture sizes D/r(0) from 0 to 30, varying at frame rates up to 2.5 kHz. A measure of wave-front generation efficiency is introduced and is shown to be better than 86% for Kolmogorov phase screens with D/r(0) in the range from 0 to 30.

Measuring shape and deformation of small objects using digital holography

Abstract: Micro-systems engineering is a fast growing technology with a wide variety of different materials. The task to ensure reliability and precision of the products needs the precise knowledge of the materials' properties, which is too less in dimensions smaller than one millimeter at the moment. Because properties determined at much larger specimen cannot be scaled down without any experimental result, simple and robust methods to analyze the materials' shape and deformation under a given load must be developed. Holographic interferometry and optical contouring techniques are widely used as highly sensitive and contactless methods for deformation and shape analysis. To get a full 3d-information of the object's surface, however, requires a complex optical setup with at least three illumination directions. Especially when small objects like micro-components have to be examined, the ordinary use of conventional holography becomes more and more a problem. In that case digital Holography can be used as a fast, simple and robust method. It replaces the classic holographic recording media by a CCD matrix. The whole reconstruction process of the interference phase is done by computer. Compact and very simple setups can be achieved by use of fiber optics. Several experiments realized in an optimized setup by using four illumination directions are presented to show the advantages of digital holography for the investigation of microsystems. This new technique is applied to components with lateral extensions from 0.1 m to 0.001 m to examine their shape and their full three dimensional deformation under a given mechanical load. The results are compared with computer simulations using FEM. For compound Si/Ni microbeams Young's modulus was determined as an example for this technology of measurement.

In-line digital holographic interferometry.

Abstract: An optical system based on in-line digital holography for the evaluation of deformations is described. In-line holograms are recorded on a CCD chip. The problem of overlapping twin images typical for the in-line arrangement is solved by digital reconstruction and filtering of the unwanted wave fronts. Two separate interferograms of an object under test in its undeformed and deformed states are recorded each on a CCD chip. The phases of the two wave fronts are obtained from the complex amplitudes of the digital reconstructed wave fronts, and the deformation is calculated from the phase differences. Experimental results are presented.

The effect of abdominal wall morphology on ultrasonic pulse distortion. Part II. Simulations

Abstract: Wavefront propagation through the abdominal wall was simulated using a finite-difference time-domain implementation of the linearized wave propagation equations for a lossless, inhomogeneous, two-dimensional fluid as well as a simplified straight-ray model for a two-dimensional absorbing medium. Scanned images of six human abdominal wall cross sections provided the data for the propagation media in the simulations. The images were mapped into regions of fat, muscle, and connective tissue, each of which was assigned uniform sound speed, density, and absorption values. Propagation was simulated through each whole specimen as well as through each fat layer and muscle layer individually. Wavefronts computed by the finite-difference method contained arrival time, energy level, and wave shape distortion similar to that in measurements. Straight-ray simulations produced arrival time fluctuations similar to measurements but produced much smaller energy level fluctuations. These simulations confirm that both fat and muscle produce significant wavefront distortion and that distortion produced by fat sections differs from that produced by muscle sections. Spatial correlation of distortion with tissue composition suggests that most major arrival time fluctuations are caused by propagation through large-scale inhomogeneities such as fatty regions within muscle layers, while most amplitude and waveform variations are the result of scattering from smaller inhomogeneities such as septa within the subcutaneous fat. Additional finite-difference simulations performed using uniform-layer models of the abdominal wall indicate that wavefront distortion is primarily caused by tissue structures and inhomogeneities rather than by refraction at layer interfaces or by variations in layer thicknesses.

Rigorous method for compensation selection and alignment of microlithographic optical systems

Abstract: The assembly of an optical system requires the correction of aberrations in the entire imaging field by making selected rigid-body motions of the optical elements. We present a rigorous method for determining which adjustment motions, called compensators, to use for alignment. These compensators are found by employing techniques from linear algebra that choose the most independent vectors from a set which are interdependent. The method finds the smallest number of compensators to correct for misalignments of a given magnitude. As an example the method is applied to a four-mirror scanning ring-field EUV lithography system. It is shown that out of 32 degrees of freedom in the configuration of the optical elements, only eight compensators are required on the optics. By adjusting these compensators a misaligned configuration giving a 30 {lambda} wavefront error can be assembled to {lambda}/50 in the absence of measurement noise.

Generation of third-order spherical and coma aberrations by use of radially symmetrical fourth-order lenses

Abstract: We have extended the method of Alvarez [J. Am. Optom. Assoc. 49, 24 (1978)] to generate a variable magnitude of third-order spherical and/or coma aberration by using a combination of fourth-order plates with a magnification system. The technique, based on the crossed-cylinder aberroscope, is used to measure the wave-front aberration generated by the plates. The method has been applied to correct the third-order spherical aberration generated by an artificial eye as well as the coma produced by a progressive addition ophthalmic lens. The simplicity of the method and its relatively low cost make it attractive for partial correction of the aberrations of the eye.

Estimation and correction of ultrasonic wavefront distortion using pulse-echo data received in a two-dimensional aperture

Abstract: Pulse-echo measurements from random scattering and from a point target have been used to quantify transmitter beam size effects and isoplanatic patch size as well as to evaluate the performance of different aberration compensation techniques. Measurements were made using a single-element transmitter with a diameter of 1/2 in., 1 in., or 2 in., each focused at 3 in. A tissue-mimicking scattering phantom or a point target was used to produce echoes that were received in a two-dimensional aperture synthesized by scanning a linear array. A specimen of abdominal wall was placed in the reception path to produce aberration. B-scan images were formed with no compensation, with time-shift compensation in the receiving aperture, and with backpropagation followed by time-shift compensation. The isoplanatic patch size was estimated by compensating the focus of a test point target with the parameters estimated for an original point target position, and observing the deterioration of compensation effects with increasing distance between the test and the original point targets. The results of the measurements using different transmitter diameters quantify the improvement of time-delay estimation with the increase in wavefront coherence that accompanies decreased transmitter beam size. For seven specimens, the average isoplanatic patch size determined from a 10% increase in the -10 dB effective diameter was 16.7 mm in the azimuthal direction and 39.0 mm in the range direction. These sizes increased after backpropagation to 19.0 mm and 41.4 mm, respectively. For the 1/2 in., 1 in., and 2 in. diameter transmitters, the average contrast ratio improvement was 2.0 dB, 2.1 dB, and 2.8 dB, respectively, with time-shift compensation, and 2.3 dB, 2.7 dB, and 3.5 dB, respectively, with backpropagation of 20 mm followed by time-delay estimation and compensation. The investigation indicates that a tightly focused transmitter beam is necessary to create a scattered wavefront satisfactory for time-shift estimation, the isoplanatic patch is about twice as long in the range direction as in the azimuthal direction, and backpropagation followed by time-shift compensation provides better compensation of distortion than time-shift compensation alone.

Laser-based ultrasound detection using photorefractive quantum wells

Abstract: We demonstrate a laser-based adaptive ultrasonic homodyne receiver using dynamic holography in AlGaAs/GaAs photorefractive multiple quantum wells. The dynamic hologram acts as an adaptive beamsplitter that compensates wavefront distortions in the presence of speckle and requires no path-length stabilization. The photorefractive quantum wells have the unique ability to achieve maximum linear homodyne detection regardless of the value of the photorefractive phase shift by tuning the excitonic spectral phase. We achieve a root mean square noise-equivalent surface displacement of 6.7×10−7 A(W/Hz)1/2.

Phase-mapping of periodically domain-inverted LiNbO3 with coherent X-rays

Abstract: A varying refractive index across a wavefront leads to a change in the direction of propagation of the wave. This provides the basis for phase-contrast imaging of transparent or weakly absorbing materials with highly coherent X-ray beams. Lattice distortions can also change the direction of propagation of a wave field diffracted from a crystal. Here we report the use of this principle to effect phase-contrast imaging of the domain structure of a ferroelectric material, lithium niobate. A periodically domain-inverted structure for quasi-phase-matching of second-harmonic generation is created in this material, in which the direction of spontaneous polarization is sequentially inverted. Because of complex interactions during domain-inversion processing, this is accompanied by lattice distortions across the domain walls. These distortions split the diffracted wavefront of a beam of coherent X-rays from an advanced synchrotron source, giving rise to a pattern of interference that reflects the underlying pattern of lattice distortions. These results show that this phase-contrast imaging technique with sub-micrometre spatial resolution permits the non-destructive, highly sensitive phase-mapping of various structural defects and distortions introduced into materials during processing.

A study of degraded light coupling into single-mode fibers

Abstract: Because they have demonstrated very high visibility accuracies and have greatly simplified conventional interferometric recombination devices, single-mode fibers are being seriously considered in several optical interferometry projects. This paper deals with light coupling into single-mode fibers. An analytical expression of the coupling efficiency is derived for the monochromatic case. Then, the effect of purely static aberrations is considered. Finally, coupling in the presence of atmospheric turbulence is investigated for long exposure times. Using temporal sequencies of turbulent wavefronts, simulations are performed for a wide range of seeing conditions with both uncorrected turbulence and various levels of correction by an adaptive optics system.

Beam characterization by wavefront sensor

Abstract: An apparatus and method for characterizing an energy beam (such as a laser) with a two-dimensional wavefront sensor, such as a Shack-Hartmann lenslet array. The sensor measures wavefront slope and irradiance of the beam at a single point on the beam and calculates a space-beamwidth product. A detector array such as a charge coupled device camera is preferably employed.

Algorithm to increase the largest aberration that can be reconstructed from Hartmann sensor measurements

Abstract: Conventional Hartmann sensor processing relies on locating the centroid of the image that is formed behind each element of a lenslet array. These centroid locations are used for computing the local gradient of the incident aberration, from which the phase of the incident wave front is calculated. The largest aberration that can reliably be sensed in a conventional Hartmann sensor must have a local gradient small enough that the spot formed by each lenslet is confined to the area behind the lenslet: If the local gradient is larger, spots form under nearby lenslets, causing a form of cross talk between the wave-front sensor channels. We describe a wave-front reconstruction algorithm that processes the whole image measured by a Hartmann sensor and a conventional image that is formed by use of the incident aberration. We show that this algorithm can accurately estimate aberrations for cases in which the aberration is strong enough to cause many of the images formed by individual lenslets to fall outside the local region of the Hartmann sensor detector plane defined by the edges of a lenslet.

Wavefront Sensing and Control for the Next Generation Space Telescope

Abstract: The Next Generation Space Telescope will depart from the traditional means of providing high optical quality and stability, namely use of massive structures. Instead, a benign orbital environment will provide stability for a large, flexible, lightweight deployed structure, and active wavefront controls will compensate misalignments and figure errors induced during launch and cool-down on orbit. This paper presents a baseline architecture for NGST wavefront controls, including initial capture and alignment, segment phasing, wavefront sensing and deformable mirror control. Simulations and analyses illustrate expected scientific performance with respect to figure error, misalignments, and thermal deformation.

Effects of phase shifts on four-beam interference patterns.

Abstract: An analysis of the effects of relative phase changes on the interference pattern formed by the coherent addition of four plane waves is presented. We focus on the configuration in which four plane waves converge at equal angles along two orthogonal planes, an arrangement that is potentially useful for printing arrays of microstructures in resist. We show that, depending on the set of polarization vectors chosen, the shape of the interference pattern is a strong function of the phase difference between each pair of beams. If all the beams have the same phase constant, an intensity distribution that is perfectly modulated and that exhibits strong contrast is produced. However, if the phase constant of any one of the beams is shifted by pi from this condition, a pattern with degraded modulation and significantly weaker contrast is formed. We discuss the implication of these results on lithographic applications of multiple-beam patterns. Further, we show that the sensitivity to phase is a general property of all interference patterns formed by four or more intersecting coherent wave fronts that have collinear electric-field components.

Nonlinear holographic imaging of phase errors

Abstract: Experimental measurements and computer simulations of nonlinear holographic imaging of phase errors in laser beams are presented. The computer models are found to accurately predict the results of the experiments. Comparison with similar results by use of amplitude scatterers reveals that the image location (along the propagation path) is the same for phase and amplitude scatterers. However, the intensity and fluence of the image of a phase scatterer are significantly larger, indicating that phase objects pose a larger damage threat to optical components.