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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

Abstract: The branch of physical and quantum optics studying the evolution of optical vortices and their derivation in various optical systems [ 11 had acquired the name “Singular Optics” after M.Soskin’s suggestion in 1999 [2]. Now this new discipline embraces the great verity of linear and nonlinear unusual optical phenomena including the processes inside laser cavity, subwavelength dislocation reactions in evanescent waves, singular fiber optics and many others. In the given paper we shall restrict our review to singular fiber optics. The aim of our paper is to elucidate the main problems of singular optics of fiee space and homogeneous isotropic media and to consider the most arduous topics of the vortex behavior in guiding inhomogeneous media both subjected to various perturbations and in the steady state [3-51. Optical Vortices in Free Space As the rule, the optical vortices cannot exist in fkee space independently on specific conditions. They are born and annihilated either inside the laser cavity due to special introcavity gadgets or at the expense of diffkaction processes on computer generated holograms, . optical wedges and other phase optical obstacles. Nevertheless, the main properties of the vortex generated by the laser or something else way are simpler to study as fast as it propagates through free space. In concordance with Berry [l] one defines the wavefront singularities the following way: . It means that the wavefront dislocation manifests itself at such places only where the real and imaginary parts of the wave function are simultaneously vanished. Each of the above equations represents the surface in the space. The intersection of these surfaces makes up the space trajectory, which the wavefront dislocation is propagated along. Provided that an optical axis and this trajectory coincide with each other, the phase singularity calls the pure screw dislocation or an optical vortex. An orthogonal optical axis and phase trajectory correspond to the pure edge wavefront dislocation or the transverse optical vortex. the mixed screw-edge dislocation is the result of an arbitrary location ofthe axis and trajectory. Optical vortices (pure screw dislocations) are carried over by Laguerre-Gaussian beams being the solutions of the parabolic wave equations so that their wave function has the form: .I

Abstract: A wavefront measuring system and method for detecting phase aberrations in wavefronts that are reflected, transmitted through internally reflected within objects sought to be measured which includes placing a reticle (20) in the path of a return beam from the object (12), and placing a detector (22) at a diffraction pattern self-imaging plane relative to the reticle (20). A set of known polynomials is fitted to the wavefront phase gradient to obtain polynomial coefficients that describe aberrations in the object.

Abstract: A free-space optical data transmission system, comprised of first and second transceivers (10, 10') spaced a distance from each other and having telescopes (14,14') aimed at each other. Each transceiver (10, 10') has a transmitter (T, T') for transmitting data-encoded light from its telescope (14) to the other telescope (14'), and a receiver (R, R') for receiving light from the other telescope. Each transceiver (10, 10') has a wavefront sensor (WFS, WFS') for determining the curvature of the wavefront of light transmitted between the telescopes, which may be distorted by atmospheric aberrations; and a deformable curvature mirror (DM, DM') connected to the wavefront sensor (WFS,WFS') and in the path of the data-encoded light for modifying the wavefront curvature of the light in response to the wavefront sensor (WFS, WFS'). Preferably, each transceiver (10, 10') has an arrangement for separating the transmitted and received light waves for bidirectional transmission.

Abstract: A method for computing the visual performance of a human or animal subject based on objective measurements of visual refraction, including higher order aberrations, includes measuring wavefront aberrations of a subject ocular pupil, computing a point-spread-function from the measured pupil aberration, providing a test image, and convolving the test image with the point-spread-function. A simulated image may be produced from the convolution result of the test image with the point-spread-function. One or more specific terms of the point-spread-function may be subtracted therefrom prior to the convolving step to simulate an effect of a correcting means, such as spectacles lenses, contact lenses, or laser surgery. A best correction for a given subject may be determined by adjusting the terms that are subtracted to optimize the resultant image.

Abstract: A method of wavefront (100) analysis including applying a transform to the wavefront, applying a plurality of different phase changes (110, 112, 114) to the transformed wavefront (108), obtaining a plurality of intensity maps (130, 132, 134) wherein the plurality of different phase changes are applied to region of the transformed wavefront, corresponding to a shape of the light source.

Abstract: Classical single-mode fiber interferometers, using one fiber per aperture, have very limited imaging capabilities and small field of view. Observations of extended sources (resolved by one aperture) cannot be fully corrected for wavefront aberrations: accurate measurements of object visibilities are then made very difficult from ground-based fiber interferometers. These limitations are very severe for the new generation of interferometers, which make use of large telescopes equipped with adaptive optics, but can be overcome by using several fibers per aperture. This technique improves the wide field imaging capabilities of both ground-based and space interferometers.

Abstract: A scanning laser ophthalmoscope incorporates adaptive optics to compensate for wavefront aberrations in the eye. Light from a light source is scanned onto the retina. Light reflected from the retina is detected for imaging and is also used for wavefront sensing. The sensed wavefront aberrations are used to control an adaptive optic device, such as a deformable mirror, disposed in the path of the light from the source in order to compensate for the aberrations.

Abstract: The simulation of micro-optical systems, especially those including microlens arrays, is still a challenging task. There are of course traditional methods which can be applied under certain circumstances. This paper will discuss several geometrical optical and diffraction-based methods for the simulation of micro-optical systems. A simple paraxial geometrical optical matrix theory will be extended to the simulation of off-axis optical elements. Ray tracing will be used to model incoherent micro-optical systems. The propagation of Gaussian beams through off-axis optical systems using differential ray tracing will be discussed. The angular spectrum of plane waves will be used to propagate a scalar complex wave amplitude in free space simulating non-paraxial diffraction effects. Finally, a model will be proposed which combines ray tracing and wave propagation methods by converting a complex wave amplitude into rays and vice versa. In the case of wavefront warping a decomposition of the wave into elementary waves has to be performed. This combined model can take into account non-paraxial effects such as aberrations of optical elements and also diffraction effects.

Abstract: Summary We present a technique to measure the wavefront in the exit pupil of a microscope to determine the microscope’s three-dimensional point spread function (PSF) experimentally. The wavefront yields the microscope PSF through a Fourier transform that models propagation of light from the exit pupil to the image plane. A Shack–Hartmann wavefront sensor is used to measure the wavefront shape by recording lateral displacements of a grid of focused spots created by a lenslet array. The displacement of each spot is related to the local wavefront slope. Thus, with appropriate sampling across the exit pupil, the entire wavefront can be reconstructed. This technique does not require the use of a sub-resolution object to obtain the three-dimensional microscope PSF. Consequently, larger, brighter fluorescent objects may be imaged, thereby reducing the requirements for detector sensitivity and leading to a three-fold increase in the axial range over which the PSF is measured. The Shack–Hartmann technique results in a description of the PSF as a continuous function whose sampling is not dependent on the size of the CCD pixels. The Shack–Hartmann sensor is not limited by the numerical aperture of the objective and can easily be calibrated to measure the PSF at any wavelength.