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Showing papers on "Wavefront published in 1997"


Journal ArticleDOI
TL;DR: A nematic liquid-crystal spatial light modulator that can be used as a high-precision wave-front control device andWave-front shaping by the production and quantification of the first 15 significant Zernike terms is demonstrated.
Abstract: I describe a nematic liquid-crystal spatial light modulator that can be used as a high-precision wave-front control device. I present results showing the open-loop correction of wave-front aberrations and demonstrate wave-front shaping by the production and quantification of the first 15 significant Zernike terms.

337 citations


Patent
21 Nov 1997
TL;DR: In this paper, a system and method for objective measurement and correction of focusing optical systems comprising optics disposed in the path of the beam (18) which directs the beam through the focusing optical system, e.g., and eye (120) and focuses the beam at its rear portion (122).
Abstract: A system and method for objective measurement and correction of focusing optical systems comprising optics disposed in the path of the beam (18) which directs the beam through the focusing optical system, e.g., and eye (120) and focuses the beam at its rear portion (122). The beam is diffusely reflected back and a wavefront analyzer (26) is disposed in the path of the wavefront projected from the optics and calculates the distortions as an estimate of aberrations of the focusing optical system.

303 citations


Journal ArticleDOI
TL;DR: The theoretical background relating impulse propagation to wavefront curvature is considered and the role of wave front curvature in electrical stimulation, formation of conduction block, and the dynamic behavior of spiral waves is estimated.
Abstract: It is traditionally assumed that impulse propagation in cardiac muscle is determined by the combination of two factors: (1) the active properties of cardiac cell membranes and (2) the passive electrical characteristics of the network formed by cardiac cells. However, advances made recently in the theory of generic excitable media suggest that an additional factor—the geometry of excitation wavefronts—may play an important role. In particular, impulse propagation strongly depends on the wavefront curvature on a small spatial scale. In the heart, excitation wavefronts have pronounced curvatures in several situations including waves initiated by small electrodes, waves emerging from narrow tissue structures, and waves propagating around the sharp edges of anatomical obstacles or around a zone of functional conduction block during spiral wave rotation. In this short review we consider the theoretical background relating impulse propagation to wavefront curvature and we estimate the role of wavefront curvature in electrical stimulation, formation of conduction block, and the dynamic behavior of spiral waves.

270 citations


PatentDOI
TL;DR: A novel interferometer design suitable for highly accurate measurement of wave-front aberrations over a wide range of wavelengths, from visible to x ray is described, applicable to at-wavelength testing of many optical systems, including short-wa wavelength projection lithography optics.
Abstract: Disclosed is a point diffraction interferometer for evaluating the quality of a test optic. In operation, the point diffraction interferometer includes a source of radiation, the test optic, a beam divider, a reference wave pinhole located at an image plane downstream from the test optic, and a detector for detecting an interference pattern produced between a reference wave emitted by the pinhole and a test wave emitted from the test optic. The beam divider produces separate reference and test beams which focus at different laterally separated positions on the image plane. The reference wave pinhole is placed at a region of high intensity (e.g., the focal point) for the reference beam. This allows reference wave to be produced at a relatively high intensity. Also, the beam divider may include elements for phase shifting one or both of the reference and test beams.

247 citations


Journal ArticleDOI
TL;DR: A two-dimensional regularized phase-tracking technique that is capable of demodulating a single fringe pattern with either open or closed fringes and gives the detected phase continuously so that no further unwrapping is needed over the detectedphase.
Abstract: We present a two-dimensional regularized phase-tracking technique that is capable of demodulating a single fringe pattern with either open or closed fringes. The proposed regularized phase-tracking system gives the detected phase continuously so that no further unwrapping is needed over the detected phase.

207 citations


Journal ArticleDOI
TL;DR: In this article, a method for extracting object visibilities from data provided by a long baseline interferometer, where the beams are spatially filtered by single-mode fibers and interferograms are obtained as scans around the zero optical pathlength difference.
Abstract: A method is given for extracting object visibilities from data provided by a long baseline interferometer, where the beams are spatially filtered by single-mode fibers and interferograms are obtained as scans around the zero optical pathlength difference. It is shown how the signals can be corrected from the wavefront perturbations caused by atmospheric turbulence. If the piston perturbations are also removed, then the corrected data contain both spatial and spectral information on the source (double Fourier interferometry). When the piston cannot be removed, object phase and spectral information are lost, and the observable (free of detector noise bias) is the squared modulus of the coherence factor, integrated over the optical bandpass. In a fiber interferometer this quantity leads to very accurate object visibility measurements because the transfer function does not involve an atmospheric term. The analysis also holds for a more classical pupil plane interferometer which does not take advantage of the spatial filtering capability of single-mode fibers. In that case however, the transfer function includes a turbulence term that needs to be calibrated by statistical methods.

184 citations


Journal ArticleDOI
TL;DR: In this article, a method to estimate the PSF related to each image, using data from the adaptive optics control computer, namely, the wavefront sensor measurements and the commands to the deformable mirror, accumulated in synchronization with the acquisition, is presented.
Abstract: Astronomical images obtained with adaptive optics systems can be enhanced by using image restoration techniques. However, this usually requires an accurate knowledge of the system point-spread function (PSF) which is variable in time. We present a method to estimate the PSF related to each image, using data from the adaptive optics control computer, namely, the wave-front sensor measurements and the commands to the deformable mirror, accumulated in synchronization with the acquisition. This method requires no extra observing time and has been successfully tested on PUEO, the Canada–France–Hawaii Telescope adaptive optics system. With this system, accurate PSF estimations could be achieved for guide stars of magnitude 13 or brighter.

178 citations


Journal ArticleDOI
TL;DR: Experimental verification of an extended depth of focus (EDF) system with near-diffraction-limited performance capabilities is reported with a number of images from various optical systems using the phase plate, thus demonstrating the success of this EDF system.
Abstract: We report experimental verification of an extended depth of focus (EDF) system with near-diffraction-limited performance capabilities. Dowski and Cathey [Appl. Opt.34, 1859–1866 (1995)] described the theory of this system in detail. We can create an EDF system by modifying a standard incoherent optical system with a special cubic phase plate placed at the aperture stop. We briefly review the theory and present the first optical experimental verification of this EDF system. The phase plate codes the wave front, producing a modified optical transfer function. Once the image is transformed into digital form, a signal-processing step decodes the image and produces the final in-focus image. We have produced a number of images from various optical systems using the phase plate, thus demonstrating the success of this EDF system.

168 citations


Journal ArticleDOI
TL;DR: In this paper, the authors describe the development of an experimental system for ultrasound computed tomography and its application to breast imaging and their methods of high-speed data acquisition are presented.
Abstract: This report describes the development of an experimental system for ultrasound computed tomography and its application to breast imaging. Details of the system design and methods of high-speed data acquisition are presented. The method uses low-power discrete frequency sound in the range of 0.3–1.2 MHz, two cylindrical arrays of 512 and 1024 PZT transducers, high spatial sampling of the wavefront, and unique diffraction tomographic reconstruction methods. One transducer at a time is activated and allowed to reach steady state at which point the remaining measure phase and amplitude of the ultrasound signal. A total of 64 MB of data are acquired in <1 s for the 512-element array and 128 MB in <3 s for the 1024 array. Several algorithms have been developed to produce the diffraction tomogram which is reconstructed as either a 512 × 512 or 1024 × 1024 matrix of the scattering potential of the object dependent on speed of sound and attenuation. The effects of aberration are greatly diminished by a hybrid iterative algorithm. To date, human images have been made of the female breast which show good depiction of glandular structures and differentiation of gland and fat, and the coronal format provides a novel of the entire breast in life-size display. The results demonstrate that the technique provides a unique quantitative ultrasound image with high resolution over a very large global field of view of the breast. The method shows promise for improved imaging of the breast. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8: 137–147, 1997

141 citations


Patent
23 Oct 1997
TL;DR: In this article, a reticle consisting of a multiplicity of small openings corresponding to separate and distinguishable points is put in the reticle plane, and a corresponding array of spots are created at the image plane of the optical system.
Abstract: A reticle consisting of a multiplicity of small openings corresponding to separate and distinguishable points is put in the reticle plane. This reticle is imaged down through an opening O in aperture plate AP. A corresponding multiplicity of spots are created at the image plane of the optical system. These spots have spot centroids relative to the original separate and distinguishable points in the reticle. These points, however, are deviated from their diffraction limited positions by the average of gradφ(u)) over the corresponding ray bundle. The opening O in the aperture plate samples a discrete portion of the entrance pupil. With points spread out over an area of size 2*NAo*za, ray bundles with chief rays covering the entire entrance pupil will be projected down to image plane IP. The above outlined procedure is extended to analyzing the wavefront at a multiplicity of field points over the entire lens train. The process includes using an aperture plate AP consisting of a multiplicity of openings O. Each opening O is centered underneath a neighborhood of points that is accepted into the entrance pupil of the imaging objective. Points passing through all openings O will produce in the wafer plane a number of spot arrays corresponding to the number of openings O. The totality of all the arrays of spots whose centroids can be measured and reconstructed yield an aberrated wavefront φ(u;x) at a number of discrete field points x.

130 citations


Journal ArticleDOI
TL;DR: The application of the angular spectrum method to other kinds of boundary conditions is discussed, as is the relationship between wave backpropagation, phase conjugation, and the time-reversal mirror.
Abstract: Wave backpropagation is a concept that can be used to calculate the excitation signals for an array with programmable transmit waveforms to produce a specified field that has no significant evanescent wave components. This concept can also be used to find the field at a distance away from an aperture based on measurements made in the aperture. For a uniform medium, three methods exist for the calculation of wave propagation and backpropagation: the diffraction integral method, the angular spectrum method, and the shift-and-add method. The boundary conditions that are usually implicitly assumed by these methods are analyzed, and the relationship between these methods are explored. The application of the angular spectrum method to other kinds of boundary conditions is discussed, as is the relationship between wave backpropagation, phase conjugation, and the time-reversal mirror. Wave backpropagation is used, as an example, to calculate the excitation signals for a ring transducer to produce a specified pulsatile plane wave with a limited spatial extent.

Journal ArticleDOI
TL;DR: In this article, a double-pulsed holographic system is described where two separate holograms of an object under test are recorded within a few microseconds using a CCD-camera and stored in a frame grabber.

Journal ArticleDOI
TL;DR: The potential of wavefront shaping with liquid-crystals for modulating the eye's refractive state was evaluated and spatial undersampling of the wavefront retardation function by the discrete array of liquid crystal cells was traced.
Abstract: We evaluated the potential of wavefront shaping with liquid-crystals for modulating the eye's refractive state. A spatial light modulator with 127 liquid crystals cells was imaged in the entrance pupil of the eye and programmed to induce prismatic, spherical, and astigmatic refractive changes. Psychophysical evaluation of these optical effects was in agreement with expectations for prisms up to approximately 0.08 D and for lenses up to approximately 1.5 D. These maximum dioptric values represent wavefront retardation of about 3 to 4 wavelengths of 584 nm light across a 3-mm diameter pupil. Optical aliasing of high-power prisms was traced to spatial undersampling of the wavefront retardation function by the discrete array of liquid crystal cells. Undersampling may also be the factor which limits the useful dioptric range of the technique.

Patent
03 Jun 1997
TL;DR: In this article, a holographic optical device with a light transmissive substrate and a second holographic element also carried by the substrate but laterally offset from the first is described.
Abstract: A holographic optical device having a light transmissive substrate with a first holographic optical element carried by the substrate, and a second holographic optical element also carried by the substrate but laterally offset from the first holographic optical element. The first holographic optical element diffracts waves from each data point in a display source into a collimated plane wave such that the plane wave is trapped inside the substrate by internal reflection, and the first holographic optical element also corrects field aberrations over the entire field of view by being recorded using at least one aspheric wavefront. The second holographic optical element diffracts the trapped plane waves out of the substrate.

Journal ArticleDOI
TL;DR: In this paper, the effects of ocean internal waves on long-range acoustic pulse propagation from a geometrical-optics point of view are investigated, and it is concluded that the observed depth diffusion of energy in the late-arriving portion of the timefront is a result of refraction, not diffraction, and the strength of the rays' sensitivity to initial conditions depend on the average (range-independent) sound-speed profile, on the range from the source to the receiver, and on the internal-wave spectral model, but not on specific realization of the
Abstract: This work presents an analysis of the effects of ocean internal waves on long-range acoustic pulse propagation from the geometrical-optics point of view. The chaotic behavior of rays and the microfolding of timefronts are investigated. The extent of the region of the timefront in which strongly chaotic rays appear, and the strength of the rays’ sensitivity to initial conditions, are found to depend on the average (range-independent) sound-speed profile, on the range from the source to the receiver, and on the internal-wave spectral model, but not on the specific realization of the internal waves. For a particular experiment (SLICE89), it is concluded that the observed depth diffusion of energy in the late-arriving portion of the timefront is a result of refraction (of geometrical-optics rays), not diffraction. It is found that internal-wave effects cause an upper turning point of a ray to be spread to the extent of 10 km horizontally and 100 m vertically, which affects the resolution of ocean-acoustic tomography. The validity and usefulness of ray-based, semi-classical (WKB) waveforms to represent received arrivals are evaluated by comparing with waveforms generated with multifrequency, parabolic-equation simulations. Center frequencies of 250 Hz and 1000 Hz with 100-Hz bandwidth are used. The semi-classical waveforms reproduce the correct arrival time and temporal shape of almost all arrivals, even those that are made of dozens of microrays induced by the internal waves. The overall intensities of the 1000-Hz arrivals are reasonably accurate, while the 250-Hz intensities show differences of order 5 dB.

Journal ArticleDOI
TL;DR: In this article, a simple wave packet along with the complex time of a Gaussian beam in free space is expressed, which gives all the information about the spatial and temporal behaviors of the pulse.
Abstract: By using a different initial value from the previous treatments, we reveal that the pulsed Gaussian beam in free space can be expressed as a simple wave packet along with the complex time, which gives all the information about the spatial and temporal behaviors of the pulse. Then the space-time profiles of a space-time Gaussian pulse are studied. It is shown that even when the pulse propagates in free space, there exist couplings among the beam parameters in space and time. The spot-size-related couplings enlarge the temporal domain (TD) spatial size of the pulse and lessen the carrier frequency of the pulse of the paraxial points, and the wavefront-related couplings bend the transverse spatial shape of the pulse with the wavefront.

Proceedings ArticleDOI
01 Nov 1997
TL;DR: In this paper, an x-ray long trace profiler (XLTP) was proposed to measure surface slope errors with precision and accuracy better than 25 nrad (rms) and 50 nrad(mis), respectively, with alateral resolution of 5 mm in the meridional and less than I mm in a sagittal direction.
Abstract: In this paper we describe an x-ray long trace profiler (XLTP) that takes an x-ray synchrotron beam as a wavefrontreference. According to results of experiments conducted on the Optics Beamline at the ESRF, this instrument allows us tomeasure surface slope errors with precision and accuracy better than 25 nrad (rms) and 50 nrad (mis), respectively, with alateral resolution of 5 mm in the meridional and less than I mm in the sagittal direction.A very similar technique was developed to figure in situ mirrors mounted on mechanical benders into a stigmatic shape formicrofocusing purposes. Micron spot sizes were achieved without difficulty and submicron precision should be possible.The technique is particularly useful if energy tunability is needed. The emphasis has been put on automation and speed ofthe measurement.Keywords: Surface metrology, x-ray mirrors, active optics, microfocusing, synchrotron radiation, multilayers. 1. INTRODUCTION In the light of recent experiments using coherence it became evident that x-ray mirrors for synchrotron radiation are still notgood enough"2. The quality of mirrors and of multilayer substrates must be extremely high to preserve the coherence ofthird generation synchrotron sources. This also applies to focusing and spherical waves. For example, in microdiffractionexperiments applied, e.g., to high pressure studies, the microimage of the source, regarding both the small size and thepurity, should not be degraded by the focusing optics. Whereas highly perfect single crystals do not affect coherence, theslope errors of the best presently available mirrors and multilayer imperfections have shown to deteriorate the phasecontrast significantly. In the following we will briefly recall what are the requirements for mirror quality.A height error Lz of a surface reflecting x-rays at a grazing angle generates a peak-to-valley (PV) phase distortion Ltp

Journal ArticleDOI
TL;DR: In this article, the statistical properties of the wave front impacted by atmospheric turbulence are deduced from the calculation of the two-dimensional spatial covariance and the temporal cross-spectrum of the angle-of-arrival fluctuations with a finite outer scale over a pair of circular pupils.
Abstract: Theoretical investigations of the statistical properties of the wave front perturbed by atmospheric turbulence are presented. They are deduced from the calculation of the two-dimensional spatial covariance and the temporal cross spectrum of the angle-of-arrival fluctuations with a finite outer scale over a pair of circular pupils as in the case of the grating scale monitor or any other Shack–Hartmann-type sensor. Both calculations lead to integral expressions that are numerically evaluated and hold for any baseline vector in the mean wave-front plane. It is proposed to retrieve the wave-front outer scale L0 from estimations of this two-dimensional spatial covariance, normalized by the angle-of-arrival structure function. To eliminate instrument vibration errors, the covariance and the structure function are estimated from measurements obtained by mechanically independent and mechanically coupled devices, respectively. The angle-of-arrival temporal cross spectrum is calculated for any mean wind velocity vector. It is shown that the baseline component in the mean wind direction affects the phase of the angle-of-arrival temporal cross spectrum, whereas the component in the perpendicular direction affects the modulus. From simultaneous measurements of the phase of the angle-of-arrival temporal cross spectrum obtained with two nonparallel baselines, one can calculate the mean wind speed and direction, which allows estimation of the coherence time for techniques of optical observation at high angular resolution through the atmosphere.

Proceedings ArticleDOI
23 Sep 1997
TL;DR: In this paper, a Fourier series (FS) is used to represent the wavefront phase as a two dimensional periodic function and the period of the function is chosen to be much larger than the outer scale of the turbulence and thus the FS accurately represents the power in the low spatial frequencies of the hurricane wavefront.
Abstract: Anew Fourier Series atmospheric phase screen generator is introduced. A Fourier Series (FS) is used to represent the wavefront phase as a two dimensional periodic function. The period of the function is chosen to be much larger than the outer scale of the turbulence and thus the FS accurately represents the power in the low spatial frequencies of the wavefront. The accuracy of the representation of the high spatial frequencies is determined by the number of terms used in the FS expansion. The FS based screen generator is capable of simulating atmospheric-induced wavefront phase distortions arising from temporal and/or anisoplanatic conditions. Both the spatial and temporal correlations between wavefront phases screens separated by time and/or angle are properly modeled. The conventional approach of simulating temporal evolution by making a large phase screen and then shifting is avoided. The phase screen generator is presented in an extremely compact and simple vector notation that lends itself for almost immediate implementation on modern mathematical analysis software packages.

Journal ArticleDOI
TL;DR: A modified phase reconstruction formula is presented by which the noise in the reconstructed phase map is reduced, and it is shown that these errors become minimal for a spatial phase-shift angle of 2pi/3.
Abstract: The advantages of spatial phase shifting (SPS) compared with temporal phase shifting in the field of electronic speckle pattern interferometry are described. Some periodic phase reconstruction errors occurring in SPS are discussed. It is shown that these errors become minimal for a spatial phase-shift angle of 2π/3. Furthermore, a modified phase reconstruction formula is presented by which the noise in the reconstructed phase map is reduced.

Journal ArticleDOI
TL;DR: In this article, a theoretical formulation is proposed to describe a time-reversal process in a solid medium with two propagation modes, longitudinal and transverse waves, installed in a fluid which is in contact with the solid through a plane interface parallel to the TRM.
Abstract: In this paper, a theoretical formulation is proposed to describe a time-reversal process in a solid medium with two propagation modes, longitudinal and transverse waves. A plane time-reversal mirror (TRM) is used, installed in a fluid which is in contact with the solid through a plane interface parallel to the TRM. The basic approach is similar to the case of a plane fluid–fluid interface [D. Cassereau and M. Fink, J. Acoust. Soc. Am. 96, 3145–3154 (1994)]; it is extended to take into account the different wave types. It is shown that the TRM is able to recreate properly in time and space the reversed fields of the longitudinal wave and the vertical polarization SV of the transverse waves, but not the horizontal polarization SH. The focusing quality of the backpropagating waves is limited by their respective wavelengths, so the slower SV wave can be better focused. Additional, unwanted wavefronts are created in the solid, too, but they are of weak amplitude and they are not focused. Numerical simulations illustrate the dependence of the focal pattern on parameters like distance–source interface, size, and eccentricity of the mirror.

Journal ArticleDOI
TL;DR: In contrast to numerical methods for beam shaping, analytical beam shaping consists of two steps: first, finding a purely geometrical distortion between the input plane and the output plane redistributing the intensity of the incoming wave front; and, second, computing a phase-only element realizing this coordinate transform.
Abstract: In contrast to numerical methods for beam shaping, analytical beam shaping consists of two steps: first, finding a purely geometrical distortion between the input plane and the output plane redistributing the intensity of the incoming wave front; and, second, computing a phase-only element realizing this coordinate transform. For the latter the method of stationary phase may be applied. The known classes of possible analytical wave transformation are extended to comprise separable and isotropic super-Gaussian-to-super-Gaussian conversion as well as transformation of Gaussian arrays to super-Gaussian distributions, and vice versa. The resulting optical phase elements contain no spiral phase dislocation and may thus be realized as refractive or diffractive elements. In addition, the outgoing wave front does not contain spiral phase dislocations.

Proceedings ArticleDOI
01 Nov 1997
TL;DR: In this article, a stitching interferometer for large plano surfaces, using a standard commercial'small' diameter phase-shifting interferer, is presented. But the system is completely automated, using PC computer to acquire and stitch measurements together to produce the original large surface.
Abstract: The manufacture of modern optical components often requires the se of high performance interferometers, usually based on phase-shifting techniques. However, there is currently no commercial phase-shifting interferometer having the capacity to measure large parts, such as those found in inertial confinement lasers and other large systems, with the required high spatial resolution. In order to circumvent the restrictions on the size of standard interferometers, we have designed and built a stitching interferometer for large plano surfaces, using a standard commercial 'small' diameter phase-shifting interferometer. The system is completely automated, using a PC computer to acquire and stitch measurements together to produce the original large surface. The advantages of this technique are low cost, small size, and preservation of spatial resolution. Also, smaller propagation distance means better handling of the smaller spatial periods. One such system has been in actual use for the characterization of large size mirrors since December 1994. In this paper, we shall look at the design of the system and produce, as an example, actual measurements performed on a PHEBUS laser slab polished more than a decade ago. The interferogram shows extraordinary features never seen before in such detail.

Journal ArticleDOI
TL;DR: A novel method of determining phase from a modulated intensity pattern is described, where a line integral of the gradient of the phase is used to reconstruct the phase, eliminating the necessity for complex methods of phase unwrapping.
Abstract: A novel method of determining phase from a modulated intensity pattern is described. A line integral of the gradient of the phase is used to reconstruct the phase, eliminating the necessity for complex methods of phase unwrapping. The new algorithm can be used with any technique that experimentally or theoretically yields the cosine and sine or the tangent of the phase. This phase-reconstruction process works effectively even in the regions of high-intensity gradients and is insensitive to the profile of the illuminating beams and to the shape of the domain boundaries.

Journal ArticleDOI
Joseph J. M. Braat1
TL;DR: Analytical expressions for the wave-front aberration coefficients up to the sixth order are derived and are of importance when reading an optical disk through its substrate or when using a plane-parallel plate as a beam splitter.
Abstract: An expression is given for the aberration imparted by a tilted plane-parallel plate to a converging or diverging pencil of rays. Analytical expressions for the wave-front aberration coefficients up to the sixth order are derived. These expressions, among others, are of importance when reading an optical disk through its substrate or when using a plane-parallel plate as a beam splitter. Differences with previous expressions from the literature are noted.

Proceedings ArticleDOI
01 Dec 1997
TL;DR: In this paper, the appearance of wave front dislocations under interference among beams with simple wave fronts is considered and it is shown that even two beams with the smooth wave fonts is possible the formation of dislocation screw type.
Abstract: The appearance of wave front dislocations under interference among beams with simple wave fronts is considered. It is shown, that even two beams with the smooth wave fonts is possible the formation of dislocations screw type. The screw dislocations are formed in cross point of lines of equal amplitude of beams and minimum of an interference pattern.

Journal ArticleDOI
TL;DR: A novel method of time resolving the amplitude and phase of a transient nonlinear-optical polarization, based on Fourier transformation of a spectral interference pattern, is discussed and it is shown that with this technique the delay at which the polarization is generated can be retrieved.
Abstract: A novel method of time resolving the amplitude and phase of a transient nonlinear-optical polarization, based on Fourier transformation of a spectral interference pattern, is discussed. We show that with this technique the delay at which the polarization is generated can be retrieved. The method is demonstrated in a transient four-wave-mixing experiment on a dye solution.

Proceedings ArticleDOI
07 Jul 1997
TL;DR: In this paper, the authors show how aberrations can affect the choice of optimum NA and partial coherence for a given reticle object when considering critical dimension uniformity and depth of focus.
Abstract: This paper shows, that as resolution is pushed into regions below 0.6 (lambda) /NA, understanding the effects of wavefront aberrations is crucial to producing stepper systems that can meet end-user requirements. We show how aberrations can affect the choice of optimum NA and partial coherence for a given reticle object when considering critical dimension uniformity and depth of focus. The ability to measure the complete wavefront and extract meaningful full-field aberration data is shown using an advanced through-the-lens interferometer that operates at the wavelength and bandwidth of the lithographic radiation. The impact of aberrations an image quality criteria is shown through a sensitivity analysis using an imaging approximation model that represents various image criteria as a weighted sum of aberration coefficients. The validity and use of such a model is shown by correlation to full- field experimental measurements.

Journal ArticleDOI
TL;DR: In this paper, a method is proposed to calculate and measure impulse responses in an enclosure along closely spaced receiver arrays, where instead of using a sparse distribution of receiver positions with single microphones, as is common practice now, arrays of microphones are applied to register the complex sound fields within enclosures.
Abstract: A method is proposed to calculate and measure impulse responses in an enclosure along closely spaced receiver arrays. Hence, instead of using a sparse distribution of receiver positions with single microphones, as is common practice now, arrays of microphones are applied to register the complex sound fields within enclosures. This way, there is a strong spatial correlation between adjacent responses, enabling one to analyze individual reflected wavefronts. It is shown that visualization of the recorded data in a two-dimensional domain, defined by detector position and travel time, gives a significantly improved insight in the structure of complex sound fields. This insight is further increased by applying the linear Radon transform (plane wave decomposition), yielding a representation of the data in the so-called ray parameter versus intercept time domain.

Journal ArticleDOI
TL;DR: In this article, it was shown that the nature of the contrast in the images is determined by the ratio between the local wavefront curvature and the width of the crystal rocking curve.
Abstract: Perfect crystals have recently been used as X-ray wavefront analysers to help produce phase-contrast images of non-periodic objects. Such images are essentially the maps of the phase gradients introduced in a plane X-ray wave upon passage through a weakly absorbing object. We show that the nature of the contrast in the images is determined by the ratio between the local wavefront curvature and the width of the crystal rocking curve. Depending on this ratio being small or large, two quite distinct regimes for image formation can be identified, namely the differential phase-contrast mode and the refractometric mode. We derive simple analytical formulae which can be used for the analysis of X-ray images of phase objects obtained in these two regimes.