Showing papers on "Wavefront published in 2002"

Evaluation of an ultra-wide-band propagation channel

Abstract: This paper describes the results of an ultra-wideband (UWB) propagation study in which arrays of propagation measurements were made. After a description of the propagation measurement technique, an approach to the spatial and temporal decomposition of an array of measurements into wavefronts impinging on the receiving array is presented. Based on a modification of the CLEAN algorithm, this approach provides estimates of time-of-arrival, angle-of-arrival, and waveform shape. This technique is applied to 14 arrays of indoor propagation measurements made in an office/laboratory building. Statistical description of the results is presented, based on a clustering model for multipath effects. The parameters of these statistical models are compared to results derived for narrowband signal propagation in the indoor environment.

Differential x-ray phase contrast imaging using a shearing interferometer

Abstract: An x-ray interferometer has been developed that uses two transmission phase gratings to analyze wave front distortions in the hard x-ray range. The interferometer is insensitive to mechanical drift and vibrations, and it is tunable over a wide range of photon energies. This setup was used for differential phase contrast imaging of low-absorbing test objects. We obtained micrographs with moire fringes of good visibility, which revealed the local phase shift gradient caused by the objects. A comparison with numerically simulated images indicates that quantitative analysis of unknown phase objects is possible.

Adaptive aberration correction in a confocal microscope

Abstract: The main advantage of confocal microscopes over their conventional counterparts is their ability to optically “section” thick specimens; the thin image slices thus obtained can be used to reconstruct three-dimensional images, a capability which is particularly useful in biological applications. However, it is well known that the resolution and optical sectioning ability can be severely degraded by system or specimen-induced aberrations. The use of high aperture lenses further exacerbates the problem. Moreover, aberrations can considerably reduce the number of photons that reach the detector, leading to lower contrast. It is rather unfortunate, therefore, that in practical microscopy, aberration-free confocal imaging is rarely achieved. Adaptive optics systems, which have been used widely to correct aberrations in astronomy, offer a solution here but also present new challenges. The optical system and the source of aberrations in a confocal microscope are considerably different and require a novel approach to wavefront sensing. This method, based upon direct measurement of Zernike aberration modes, also exhibits an axial selectivity similar to that of a confocal microscope. We demonstrate an adaptive confocal fluorescence microscope incorporating this modal sensor together with a deformable membrane mirror for aberration correction. Aberration corrected images of biological specimens show considerable improvement in contrast and apparent restoration of axial resolution.

Tailored freeform optical surfaces

Abstract: Freeform optical surfaces embedded in three-dimensional space, without any symmetry, are tailored so as to solve the archetypal problem of illumination design: redistribute the radiation of a given small light source onto a given reference surface, thus achieving a desired irradiance distribution on that surface. The shape of the optical surface is found by solving a set of partial nonlinear differential equations. For most cases, a few topologically distinct solutions exist, given suitable boundary conditions.

SLODAR: measuring optical turbulence altitude with a Shack–Hartmann wavefront sensor

Abstract: This paper discusses the use of Shack–Hartmann wavefront sensors to determine the vertical distribution of atmospheric optical turbulence above large telescopes. It is demonstrated that the turbulence altitude profile can be recovered reliably from time-averaged spatial cross-correlations of the local wavefront slopes for Shack–Hartmann observations of binary stars. The method, which is referred to as SLODAR, is analogous to the well known SCIDAR scintillation profiling technique, and a calibration against contemporaneous SCIDAR observations is shown. Hardware requirements are simplified relative to the scintillation method, and the number of suitable target objects is larger. The implementation of a Shack–Hartmann based turbulence monitor for use at the William Herschel Telescope is described. The system will be used to optimize adaptive optical observations at the telescope and to characterize anisoplanatic variations of the corrected point spread function.

Method and apparatus for the production of process sensitive lithographic features

Abstract: A method for controlling the variation in process parameters using test structures sensitized to process parameter changes. Wavefront engineering techniques are used to make features of the test structure more sensitive to process changes. Focus and exposure parameters are adjusted in response to the measurements of the test structures. In another embodiment, the wavefront engineering features are placed to permit the test structure appearing on the reticle out of focus. The wavefront engineering feature is an OPC technique applied to the test structure to modify it. The OPC features are applied in an asymmetrical manner to the test structure and enable identifying the direction of process focus changes.

Optical Wavefront Reconstruction: Theory and Numerical Methods

Abstract: Optical wavefront reconstruction algorithms played a central role in the effort to identify gross manufacturing errors in NASA's Hubble Space Telescope (HST). NASA's success with reconstruction algorithms on the HST has led to an effort to develop software that can aid and in some cases replace complicated, expensive, and error-prone hardware. Among the many applications is HST's replacement, the Next Generation Space Telescope (NGST). indent This work details the theory of optical wavefront reconstruction, reviews some numerical methods for this problem, and presents a novel numerical technique that we call extended least squares. We compare the performance of these numerical methods for potential inclusion in prototype NGST optical wavefront reconstruction software. We begin with a tutorial on Rayleigh--Sommerfeld diffraction theory.

Polarization imaging by use of digital holography

Abstract: We present what we believe to be a new digital holographic imaging method that is able to determine simultaneously the distributions of intensity, phase, and polarization state at the surface of a specimen on the basis of a single image acquisition. Two reference waves with orthogonal polarization states interfere with the object wave to create a hologram that is recorded on a CCD camera. Two wave fronts, one for each perpendicular polarization state, are numerically reconstructed in intensity and phase. Combining the intensity and the phase distributions of these two wave fronts permits the determination of all the components of the Jones vector of the object-wave front. We show that this method can be used to image and measure the distribution of the polarization state at the surface of a specimen, and the obtained results indicate that precise quantitative measurements of the polarization state can be achieved. An application of the method to image the birefringence of a stressed polymethyl methacrylate sample is presented.

Methods and apparatus for splitting, imaging, and measuring wavefronts in interferometry

Abstract: Apparatus for splitting, imaging, and measuring wavefronts with a reference wavefront and an object wavefront. A wavefront-combining element receives and combines into a combined wavefront an object wavefront from an object and a reference wavefront. A wavefront-splitting element splits the combined wavefront into a plurality of sub-wavefronts in such a way that each of the sub-wavefronts is substantially contiguous with at least one other sub-wavefront. The wavefront-splitting element may shift the relative phase between the reference wavefront and the object wavefront of the sub-wavefronts to yield a respective plurality of phase-shifted sub-wavefronts. The wavefront-splitting element may then interfering the reference and object wavefronts of the phase-shifted sub-wavefronts to yield a respective plurality of phase-shifted interferograms. An imaging element receives and images the phase-shifted interferograms. A computer connected to the imaging element measures various parameters of the objects based on the phase-shifted interferograms. Examples of measurements include flow parameters such as the concentrations of selected gaseous species, temperature distributions, particle and droplet distributions, density, and so on. In addition to flow parameters, the displacement (e.g., the vibration) and the profile of an object may be measured.

Spectral anomalies at wave-front dislocations.

Abstract: In a recent Letter, Gbur, Visser, and Wolf [Phys Rev Lett 88, 013901 (2002)] predict that remarkable spectral changes can take place in the neighborhood of phase singularities of a diffracted focused wave We report here the experimental observation of this anomalous spectral behavior and show that this is a general characteristic of optical vortices Using a high-resolution interferometric technique, we are able to measure directly both the spectral intensity distribution and the spectral phase at the singular points of optical waves

Method for the generation of arbitrary complex vector wave fronts

Abstract: We describe an extremely versatile method that permits the accurate generation of arbitrary complex vector wave fields. We implement the scheme using a reconfigurable binary optical element that also permits additional fine tuning, such as aberration correction, to be performed. As examples we demonstrate the generation of both azimuthally and radially polarized beams.

Travelling fronts for the KPP equation with spatio-temporal delay

Abstract: We study an integro-differential equation based on the KPP equation with a convolution term which introduces a time-delay in the nonlinearity. Special attention is paid to the question of the existence of travelling wavefront solutions connecting the two uniform steady states and their qualitative form. Motivated by the analogue between steady travelling fronts and heteroclinic orbits of an associated ordinary differential equation, we prove, using a geometric singular perturbation analysis, that steady travelling wavefront solutions persist when the delay is suitably small, for a class of convolution kernels. These travelling fronts are qualitatively similar to the well known KPP wavefront. The effect of finite and large delay is studied numerically and we find that this introduces qualitative changes to the fronts but that the front remains robust. A numerical integration of the initial-value problem confirms the qualitative shape of these fronts and suggests that - even for large delay - they may be temporally stable. Finally we show that in the discrete delay case the non-zero uniform state can be driven unstable. In this case a travelling wavefront can leave in its wake a periodic travelling wave moving with a different speed.

Multi-frame blind deconvolution with linear equality constraints

Abstract: The Phase Diverse Speckle (PDS) problem is formulated mathematically as Multi Frame Blind Deconvolution (MFBD) together with a set of Linear Equality Constraints (LECs) on the wavefront expansion parameters. This MFBD--LEC formulation is quite general and, in addition to PDS, it allows the same code to handle a variety of different data collection schemes specified as data, the LECs, rather than in the code. It also relieves us from having to derive new expressions for the gradient of the wavefront parameter vector for each type of data set. The idea is first presented with a simple formulation that accommodates Phase Diversity, Phase Diverse Speckle, and Shack--Hartmann wavefront sensing. Then various generalizations are discussed, that allows many other types of data sets to be handled. Background: Unless auxiliary information is used, the Blind Deconvolution problem for a single frame is not well posed because the object and PSF information in a data frame cannot be separated. There are different ways of bringing auxiliary information to bear on the problem. MFBD uses several frames which helps somewhat, because the solutions are constrained by a requirement that the object be the same, but is often not enough to get useful results without further constraints. One class of MFBD methods constrain the solutions by requiring that the PSFs correspond to wavefronts over a certain pupil geometry, expanded in a finite basis. This is an effective approach but there is still a problem of uniqueness in that different phases can give the same PSF. Phase Diversity and the more general PDS methods are special cases of this class of MFBD, where the observations are usually arranged so that in-focus data is collected together with intentionally defocused data, where information on the object is sacrificed for more information on the aberrations. The known differences and similarities between the phases are used to get better estimates.

Objective Lens, Optical Element, Optical Pick-Up Apparatus and Optical Information Recording and/or Reproducing Apparatus Equipped Therewith

Abstract: A hybrid objective lens has a refractive lens and a diffractive optical element constructed by plural coaxial ring-shaped zones on at least one optical surface thereof. When n1, n2 and n3 each is a diffraction order of a diffracted ray having a maximum light amount among diffracted rays of each of first, second and third light flux having wavelength λ1, λ2 and λ3 when respective light flux comes to be incident into the diffractive structure respectively, the following formulas are satisfied: |n1|>|n2|, and |n1|>|n3|, and the hybrid objective lens converges a n1-th, n2-th and n3-th order diffracted ray of the first, second and third light flux onto an information recording plane of each of the first, second ant third optical information recording medium respectively so as to form an appropriate wavefront within respective prescribed necessary image side numerical apertures.

Spot size and quality of scanning laser correction of higher-order wavefront aberrations.

Abstract: Purpose To investigate the effect of laser spot size on the outcome of aberration correction with scanning laser corneal ablation. Setting Cleveland Clinic Foundation, Cleveland, Ohio, USA. Methods Corrections of wavefront aberrations of Zernike modes from the second to eighth order were simulated. Gaussian and top-hat beams of 0.6 to 2.0 mm full-width-half-maximum diameters were modeled. The fractional correction and secondary aberration (distortion) were evaluated. Results Using a distortion/correction ratio of less than 0.5 as a cutoff for adequate performance, a 2.0 mm or smaller beam was adequate for spherocylindrical correction (Zernike second order), a 1.0 mm or smaller beam was adequate for correction of up to fourth-order Zernike modes, and a 0.6 mm or smaller beam was adequate for correction of up to sixth-order Zernike modes. Conclusions Since ocular aberrations above the Zernike fourth order are relatively insignificant in normal eyes, current scanning lasers with a beam diameter of 1.0 mm or less are theoretically capable of eliminating most higher-order aberrations.

Apparatus and method for determining objective refraction using wavefront sensing

Abstract: An apparatus for determining the objective refraction of a patient's eye includes a transparent window and a wavefront measurement device that determines aberrations in a return beam from the patient's eye after the beam passes through a corrective test lens in the apparatus. The wavefront measurement device outputs an instant display representative of the quality of vision afforded the patient through the test lens. The display can be a representation of a Snellen chart, convoluted with the optical characteristics of the patient's vision, an overall quality of vision scale or the optical contrast function, all based on the wavefront measurements of the patient's eye. The examiner may use the display information to conduct a refraction examination and other vision tests without the subjective response from the patient.

Aberration correction spectacle lens

Abstract: A novel method for the design and construction of a spectacle lens for the correction of human vision, including the correction of high order aberrations. The lens enables the provision of super-normal vision using spectacles. Different lenses are described for use at a partial or a fuller field of view. The method applies corrective measures based on data obtained from high order wave front measurements of the subject's eye. According to one method, the Modulation Transfer Function (MTF) of the overall eye and lens optical system is optimized. According to another method, the optimization is performed on the wavefront of the overall eye and lens optical system. Both methods use weighted functions in the optimization procedure. This method of high order aberration correction is also applicable for the design of contact lenses and intra-ocular lenses, and for the execution of refractive eye surgery.

Adaptive optic correction using microelectromechanical deformable mirrors

Abstract: A micromachined deformable mirror (μ-DM) for optical wavefront correction is described. Design and manufacturing approaches for μ-DMs are detailed. The μ-DM employs a flexible silicon membrane supported by mechanical attachments to an array of electrostatic parallel plate actuators. Devices are fabricated through surface micromachining using polycrystalline silicon thin films. μ-DM membranes measuring 2 mm×2 mm×2 μm, supported by 100 actuators are described. Figures of merit include stroke of 2 μm, resolution of 10 nm, and frequency bandwidth dc to 7 kHz in air. The devices are compact, inexpensive to fabricate, exhibit no hysteresis, and use only a small fraction of the power required for conventional DMs. Performance of an adaptive optics system using a μ-DM is characterized in a closed-loop control experiment. Significant reduction in quasistatic wavefront phase error is achieved. Advantages and limitations of μ-DMs are described in relation to conventional adaptive optics systems and to emerging applications of adaptive optics such as high-resolution correction, small-aperture systems, and optical communication.

Lithographic projection apparatus, a grating module, a sensor module, a method of measuring wave front aberrations

Abstract: A lithographic projection apparatus including an illumination system; a support structure for holding a mask; a substrate table for holding a substrate; a projection system for projecting a pattern onto a target portion of the substrate; and an interferometric measurement system for measuring wave front aberrations of the projection system, characterized in that the interferometric measurement system including: a grating, featuring a grating pattern in a grating plane, said grating being movable into and out of the projection beam, such that the grating plane is substantially coincident with said object plane; a pinhole, featuring a pinhole pattern in a pinhole plane and arranged in a pinhole plate, said pinhole being movable into and out of the projection beam, such that the pinhole plane is substantially coincident with a plane downstream of the projection system and optically conjugate to said object plane, and a detector with a detector surface substantially coincident with a detection plane, said detection plane located downstream of the pinhole at a location where a spatial distribution of the electric field amplitude of the projection beam is substantially a Fourier transformation of a spatial distribution of the electric field amplitude of the projection beam in the pinhole plane.

Tomographic wavefront analysis system and method of mapping an optical system

Abstract: A method of measuring aberrations of a three-dimensional structure of an optical system, such as an eye, includes creating a plurality of light beams, optically imaging the light beams and projecting the light beams onto different locations in an optical system, receiving scattered light from each of the locations, and detecting individual wavefronts of the scattered light. The plurality of light beams may be created and projected simultaneously or sequentially. A system for measuring aberrations of a three-dimensional structure of an optical system includes a light source creating a plurality of light beams, an optical imaging system optically imaging the light beams and projecting the light beams onto different locations in the target optical system, and a wavefront sensor receiving scattered light from each of the locations and detecting individual wavefronts of the scattered light.

Virtual ultrasound sources in high-resolution ultrasound imaging

Abstract: This paper investigates the concept of virtual source elements. It suggests a common framework for increasing the resolution, and penetration depth of several imaging modalities by applying synthetic aperture focusing (SAF). SAF is used either as a post focusing procedure on the beamformed data, or directly on the raw signals from the transducer elements. Both approaches increase the resolution. The paper shows that in one imaging situation, there can co-exist different virtual sources for the same scan line - one in the azimuth plane, and another in the elevation. This property is used in a two stage beamforming procedure for 3D ultrasound imaging. The position of the virtual source, and the created waveform are investigated with simulation, and with pulse-echo measurements. There is good agreement between the estimated wavefront and the theoretically fitted one. Several examples of the use of virtual source elements are considered. Using SAF on data acquired for a conventional linear array imaging improves the penetration depth for the particular imaging situation from 80 to 110 mm. The independent use of virtual source elements in the elevation plane decreases the respective size of the point spread function at 100 mm below the transducer from 7mm to 2 mm.

A finite element method for an eikonal equation model of myocardial excitation wavefront propagation

Abstract: An efficient finite element method is developed to model the spreading of excitation in ventricular myocardium by treating the thin region of rapidly depolarizing tissue as a propagating wavefront. The model is used to investigate excitation propagation in the full canine ventricular myocardium. An eikonal-curvature equation and an eikonal-diffusion equation for excitation time are compared. A Petrov--Galerkin finite element method with cubic Hermite elements is developed to solve the eikonal-diffusion equation on a reasonably coarse mesh. The oscillatory errors seen when using the Galerkin weighted residual method with high mesh Peclet numbers are avoided by supplementing the Galerkin weights with C0 functions based on derivatives of the interpolation functions. The ratio of the Galerkin and supplementary weights is a function of the Peclet number such that, for one-dimensional propagation, the error in the solution is within a small constant factor of the optimal error achievable in the trial space. An ...

Method and apparatus for measuring wavefront aberrations

Abstract: An apparatus and method for measuring wavefront aberrations. A beam splitter separates the aberrated wavefront into two components, mirror arrays focus each of the components to a plurality of discrete lines with the discrete lines of one component having a different orientation than the discrete lines of the other component, and an imaging device detects the discrete lines to determine wavefront aberrations. The method includes separating the wavefront into two components, focusing each of the components into a plurality of discrete lines with the discrete lines of one component having a different orientation than the discrete lines of the other component, and detecting information related to the discrete lines.

Extended source pyramid wave-front sensor for the human eye.

Abstract: We describe a new wave-front sensor based on the previously proposed pyramid sensor. This new sensor uses an extended source instead of a point-like source avoiding in this manner the oscillation of the pyramid. After an introductory background the sensor functioning is described. Among other possible optical testing uses, we apply the sensor to measure the wave-front aberration of the human eye. An experimental system built to test this specific application is described. Results obtained both in an articficial eye and in a real eye are presented. A discussion about the sensor characteristics, the experimental results and future work prospects is also included.

Scanning interferometer for aspheric surfaces and wavefronts

Abstract: Interferometric scanning method(s) and apparatus for measuring optics either having aspherical surfaces or that produce aspherical wavefronts. A test optic is aligned and moved with respect to a scanning axis relative to the origin of a known spherical wavefront that is generated with a reference surface to intersect the test optic at the apex of the aspherical surface and at radial zones where the spherical wavefront and the aspheric surface possess common tangents. The test surface is imaged onto a space resolving detector to form interferograms containing phase information about the differences in optical path length between the reference surface and the test surface while the axial distance which the test optic moves relative to the spherical reference surface is interferometrically measured. The deviation in the shape of the aspheric surface from its design in a direction normal to the aspheric surface is determined and reported.

Integrated wavefront-directed topography-controlled photoablation

Abstract: A system and method combining wavefront analysis with narrow-beam scanning photoablation where optimal corneal topography is first calculated then followed by real-time topographic feedback controlled photoablation Eye movement and beam position sensing to within a tolerance of 5 μm are provided by high speed digital computation in conjunction with specialized charge coupled devices Lasers of three different wavelengths—one low-powered pulsed ultraviolet, a second continuous visible band type, and a pulsed infrared type are combined together into narrow beams whereupon a scanning mechanism generates coaxial collimated beams for the functions of ablation, beam position sensing, and fundus spot imaging Transepithelial ablation is performed utilizing the same CCD used for wavefront analysis by switching between two dichroic mirrors The light source for the raster videokeratography topography means is the UV laser used for ablation