Showing papers on "Wavefront published in 2008"

Method and apparatus for improving vision and the resolution of retinal images

Abstract: A method of and apparatus for improving vision and the resolution of retinal images is described in which a point source produced on the retina of a living eye by a laser beam is reflected from the retina and received at a lenslet array of a Hartmann-Shack wavefront sensor such that each of the lenslets in the lenslet array forms an aerial image of the retinal point source on a CCD camera located adjacent to the lenslet array. The output signal from the CCD camera is acquired by a computer which processes the signal and produces a correction signal which may be used to control a compensating optical or wavefront compensation device such as a deformable mirror. It may also be used to fabricate a contact lens or intraocular lens, or to guide a surgical procedure to correct the aberrations of the eye. Any of these methods could correct aberrations beyond defocus and astigmatism, allowing improved vision and improved imaging of the inside of the eye.

Resolution of the wavefront set using continuous shearlets

Abstract: It is known that the Continuous Wavelet Transform of a distribution f decays rapidly near the points where f is smooth, while it decays slowly near the irregular points. This property allows the identification of the singular support of f. However, the Continuous Wavelet Transform is unable to describe the geometry of the set of singularities of f and, in particular, identify the wavefront set of a distribution. In this paper, we employ the same framework of affine systems which is at the core of the construction of the wavelet transform to introduce the Continuous Shearlet Transform. This is defined by SH ψ f(a,s,t) = (fψ ast ), where the analyzing elements ψ ast are dilated and translated copies of a single generating function ψ. The dilation matrices form a two-parameter matrix group consisting of products of parabolic scaling and shear matrices. We show that the elements {ψ ast } form a system of smooth functions at continuous scales a > 0, locations t ∈ R 2 , and oriented along lines of slope s ∈ R in the frequency domain. We then prove that the Continuous Shearlet Transform does exactly resolve the wavefront set of a distribution f.

Modern developments in X-ray and neutron optics

Abstract: Theoretical Approaches and Calculations.- X-Ray and Neutron Optical Systems.- The BESSY Raytrace Program RAY.- Neutron Beam Phase Space Mapping.- Raytrace of Neutron Optical Systems with RESTRAX.- Wavefront Propagation.- Theoretical Analysis of X-Ray Waveguides.- Focusing Optics for Neutrons.- Volume Effects in Zone Plates.- Nano-Optics Metrology.- Slope Error and Surface Roughness.- The Long Trace Profilers.- The Nanometer Optical Component Measuring Machine.- Shape Optimization of High Performance X-Ray Optics.- Measurement of Groove Density of Diffraction Gratings.- The COST P7 Round Robin for Slope Measuring Profilers.- Hartmann and Shack-Hartmann Wavefront Sensors for Sub-nanometric Metrology.- Extraction of Multilayer Coating Parameters from X-Ray Reflectivity Data.- Refection/Refraction Optics.- Hard X-Ray Microoptics.- Capillary Optics for X-Rays.- Reflective Optical Arrays.- Reflective Optical Structures and Imaging Detector Systems.- CLESSIDRA: Focusing Hard X-Rays Efficiently with Small Prism Arrays.- Multilayer Optics Developments.- Neutron Supermirror Development.- Stress Reduction in Multilayers Used for X-Ray and Neutron Optics.- Multilayers with Ultra-Short Periods.- Specially Designed Multilayers.- Diffraction Optics.- Diffractive-Refractive Optics: X-ray Crystal Monochromators with Profiled Diffracting Surfaces.- Neutron Multiple Reflections Excited in Cylindrically Bent Perfect Crystals and Their Possible use for High-Resolution Neutron Scattering.- Volume Modulated Diffraction X-Ray Optics.- High Resolution 1D and 2D Crystal Optics Based on Asymmetric Diffractors.- Thermal Effects under Synchrotron Radiation Power Absorption.

Beam scanning-type display device, method, program and integrated circuit

Abstract: A beam scanning-type display device used as a head-mounted display (HMD) or a head-up display (HUD) includes a light source which emits a beam, a scanning unit which performs scanning using the beam emitted from the light source, a deflecting unit which deflects the beam used for the scanning by the scanning unit in the direction toward an eye of a user, and a wavefront shape changing unit which changes the wavefront shape of the beam from the light source so that the beam spot size falls within the predetermined allowable range, and emits the beam to the wavefront shape changing unit.

Ultrahigh-resolution optical coherence tomography with monochromatic and chromatic aberration correction

Abstract: We have developed an improved adaptive optics - optical coherence tomography (AO-OCT) system and evaluated its performance for in vivo imaging of normal and pathologic retina. The instrument provides unprecedented image quality at the retina with isotropic 3D resolution of 3.5 x 3.5 x 3.5 microm(3). Critical to the instrument's resolution is a customized achromatizing lens that corrects for the eye's longitudinal chromatic aberration and an ultra broadband light source (Delta lambda=112 nm lambda(0)= approximately 836 nm). The eye's transverse chromatic aberrations is modeled and predicted to be sufficiently small for the imaging conditions considered. The achromatizing lens was strategically placed at the light input of the AO-OCT sample arm. This location simplifies use of the achromatizing lens and allows straightforward implementation into existing OCT systems. Lateral resolution was achieved with an AO system that cascades two wavefront correctors, a large stroke bimorph deformable mirror (DM) and a micro-electromechanical system (MEMS) DM with a high number of actuators. This combination yielded diffraction-limited imaging in the eyes examined. An added benefit of the broadband light source is the reduction of speckle size in the axial dimension. Additionally, speckle contrast was reduced by averaging multiple B-scans of the same proximal patch of retina. The combination of improved micron-scale 3D resolution, and reduced speckle size and contrast were found to significantly improve visibility of microscopic structures in the retina.

Adaptive optics for structured illumination microscopy

Abstract: We implement wave front sensor-less adaptive optics in a structured illumination microscope. We investigate how the image formation process in this type of microscope is affected by aberrations. It is found that aberrations can be classified into two groups, those that affect imaging of the illumination pattern and those that have no influence on this pattern. We derive a set of aberration modes ideally suited to this application and use these modes as the basis for an efficient aberration correction scheme. Each mode is corrected independently through the sequential optimisation of an image quality metric. Aberration corrected imaging is demonstrated using fixed fluorescent specimens. Images are further improved using differential aberration imaging for reduction of background fluorescence.

Wavefront Optics for Vision Correction

Abstract: This book addresses some of the issues in visual optics with a functional analysis of ocular aberrations, especially for the purpose of vision correction. The basis is the analytical representation of ocular aberrations with a set of orthonormal polynomials, such as Zernike polynomials or the Fourier series. Although the aim of this book is the application of wavefront optics to laser vision correction, most of the theories discussed are equally applicable to other methods of vision correction, such as contact lenses and intraocular lenses.

Full phase and amplitude control of holographic optical tweezers with high efficiency.

Abstract: Recently we demonstrated the applicability of a holographic method for shaping complex wavefronts to spatial light modulator (SLM) systems. Here we examine the potential of this approach for optical micromanipulation. Since the method allows one to shape both amplitude and phase of a trapping light field independently and thus provides full control over scattering and gradient forces, it extends the possibilities of commonly used holographic tweezers systems. We utilize two cascaded phase-diffractive elements which can actually be display side-by-side on a single programmable phase modulator. Theoretically the obtainable light efficiency is close to 100%, in our case the major practical limitation arises from absorption in the SLM. We present data which demonstrate the ability to create user-defined “light pathways” for microparticles driven by transverse radiation pressure.

Wide-angle nonmechanical beam steering using thin liquid crystal polarization gratings

Abstract: We introduce and demonstrate a compact, nonmechanical beam steering device based on liquid Crystal (LC) Polarization Gratings (PGs). Directional control of collimated light is essential for free-space optical communications, remote sensing, and related technologies. However, current beam steering methods often require moving parts, or are limited to small angle operation, offer low optical throughput, and are constrained by size and weight. We employ multiple layers of LCPGs to achieve wide-angle (> ±40°), coarse beam steering of 1550 nm light in a remarkably thin package. LCPGs can be made in switchable or polymer materials, and possess a continuous periodic birefringence profile, that renders several compelling properties (experimentally realized): ~ 100% experimental diffraction efficiency into a single order, high polarization sensitivity, and very low scattering. Light may be controlled within and between the zero- and first-diffraction orders by the handedness of the incident light and potentially by voltage applied to the PG itself. We implement a coarse steering device with several LCPGs matched with active halfwave LC variable retarders. Here, we present the preliminary experimental results and discuss the unique capability of this wide-angle steering.

Interferometer for precise and flexible asphere testing

Abstract: A novel non-null interferometer for the precise measurement of aspheric surfaces is presented. In contrast to a classical interferometer, where only one test wavefront is used, the proposed system makes use of multiple test beams propagating under different angles through the interferometer. This allows the measurement of aspheric surfaces in a very short time, even for strong aspheres with deviations from the best-fit sphere of up to 900 μm. The non-null test configuration implies that any additional aberrations introduced by the interferometer have to be well characterized to precisely measure the asphere. Experimental measurements of a calibrated non-null interferometer on an aspheric element with 900 μm SAG deviation are presented.

Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry.

Abstract: We assesses the efficiency of x-ray Talbot interferometry (XTI), a technique based on the Talbot effect for measuring a wavefront gradient, in terms of how quickly it can capture a high-quality phase image with a large signal-to-noise ratio for a given incident photon number. Photon statistics cause errors in the phase of the moire fringes and impose a detection limit on the wavefront gradient. The relation between the incident photon number and the detection limit is determined, and a figure of merit of XTI for a monochromatic cone beam is then defined. The dependence of the figure of merit on optical system parameters, such as grating pitch and position, is then discussed. The effects of varying the pattern height and linewidth of the second grating are shown for rectangular and trapezoidal teeth. Finally, we show how to design a practical cone-beam Talbot interferometer for certain boundary conditions.

Seismic ray tracing and wavefront tracking in laterally heterogeneous media

Abstract: Publisher Summary This chapter describes a variety of schemes for tracking the kinematic evolution of high frequency seismic waves in heterogeneous 2-D and 3-D structures. Where possible, the chapter has focused on methods that have been used in practical applications; most of these can be characterized as either ray based or grid based. Ray tracing has traditionally been the method of choice in many seismic applications due to its high accuracy and potential for computational efficiency. Common ray tracing schemes include shooting, bending and pseudo bending. Shooting methods formulate the kinematic ray equation as an initial value problem, which allows a complete ray path to be computed given an initial projection vector. The boundary value problem of locating source-receiver trajectories is typically solved using iterative non-linear strategies, which exploit information from nearby paths to update the projection parameters and better target the receiver. Bending methods perturb the geometry of an initial path joining source and receiver, until it becomes a true (stationary) path, by iteratively solving a boundary value formulation of the ray equations. Pseudo-bending schemes usually represent a path as a series of points, which are perturbed using a simple algorithm based directly on Fermat's principle of stationary time. In practice, the most appropriate scheme for predicting an observational dataset depends on a number of factors including computational efficiency, accuracy, robustness and the type of information that is required.

Ultrafast laser writing of homogeneous longitudinal waveguides in glasses using dynamic wavefront correction.

Abstract: Laser writing of longitudinal waveguides in bulk transparent materials degrades with the focusing depth due to wavefront distortions generated at the air-dielectric interface. Using adaptive spatial tailoring of ultrashort laser pulses, we show that spherical aberrations can be dynamically compensated in optical glasses, in synchronization with the writing procedure. Aberration-free structures can thus be induced at different depths, showing higher flexibility for 3D processing. This enables optimal writing of homogeneous longitudinal waveguides over more significant lengths. The corrective process becomes increasingly important when laser energy has to be transported without losses at arbitrary depths, with the purpose of triggering mechanisms of positive refractive index change.

GRAVITY: getting to the event horizon of Sgr A*

Abstract: We present the second-generation VLTI instrument GRAVITY, which currently is in the preliminary design phase. GRAVITY is specifically designed to observe highly relativistic motions of matter close to the event horizon of Sgr A*, the massive black hole at center of the Milky Way. We have identified the key design features needed to achieve this goal and present the resulting instrument concept. It includes an integrated optics, 4-telescope, dual feed beam combiner operated in a cryogenic vessel; near infrared wavefront sensing adaptive optics; fringe tracking on secondary sources within the field of view of the VLTI and a novel metrology concept. Simulations show that the planned design matches the scientific needs; in particular that 10µas astrometry is feasible for a source with a magnitude of K=15 like Sgr A*, given the availability of suitable phase reference sources.

Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments

Abstract: An algorithm to extract the arbitrary unknown phase shift and then reconstruct the complex object wave in generalized phase-shifting interferometry (GPSI) without the iteration process and measurement of object wave intensity is proposed. This method can be used for GPSI of any frame number >or=2. Both computer simulations with smooth and diffusing object surfaces and optical experiments have verified the effectiveness of this method over a wide range of phase shifts with very satisfactory results.

Characteristics of the human isoplanatic patch and implications for adaptive optics retinal imaging

Abstract: Conventional adaptive optics enables correction of high-order aberrations of the eye, but only for a single retinal point. When imaging extended regions of the retina, aberrations increase away from this point and degrade image quality. The zone over which aberrations do not change significantly is called the "isoplanatic patch." Literature concerning the human isoplanatic patch is incomplete. We determine foveal isoplanatic patch characteristics by performing Hartmann-Shack aberrometry in 1 deg increments in 8 directions on 7 human eyes. Using these measurements, we establish the correction quality required to yield at least 80% of the potential patch size for a given eye. Single-point correction systems (conventional adaptive optics) and multiple-point correction systems (multiconjugate adaptive optics) are simulated. Results are compared to a model eye. Using the Marechal criterion for 555-nm light, average isoplanatic patch diameter for our subjects is 0.80+/-0.10 deg. The required order of aberration correction depends on desired image quality over the patch. For the more realistically achievable criterion of 0.1 mum root mean square (rms) wavefront error over a 6.0-mm pupil, correction to at least sixth order is recommended for all adaptive optics systems. The most important aberrations to target for a multiconjugate correction are defocus, astigmatism, and coma.

Split atmospheric tomography using laser and natural guide stars.

Abstract: Laser guide star (LGS) atmospheric tomography is described in the literature as integrated minimum-variance tomographic wavefront reconstruction from a concatenated wavefront-sensor measurement vector consisting of many high-order, tip/tilt (TT)-removed LGS measurements, supplemented by a few low-order natural guide star (NGS) components essential to estimating the TT and tilt anisoplanatism (TA) modes undetectable by the TT-removed LGS wavefront sensors (WFSs). The practical integration of these NGS WFS measurements into the tomography problem is the main subject of this paper. A split control architecture implementing two separate control loops driven independently by closed-loop LGS and NGS measurements is proposed in this context. Its performance is evaluated in extensive wave optics Monte Carlo simulations for the Thirty Meter Telescope (TMT) LGS multiconjugate adaptive optics (MCAO) system, against the delivered performance of the integrated control architecture. Three iterative algorithms are analyzed for atmospheric tomography in both cases: a previously proposed Fourier domain preconditioned conjugate gradient (FDPCG) algorithm, a simple conjugate gradient (CG) algorithm without preconditioning, and a novel layer-oriented block Gauss-Seidel conjugate gradient algorithm (BGS-CG). Provided that enough iterations are performed, all three algorithms yield essentially identical closed-loop residual RMS wavefront errors for both control architectures, with the caveat that a somewhat smaller number of iterations are required by the CG and BGS-CG algorithms for the split approach. These results demonstrate that the split control approach benefits from (i) a simpler formulation of minimum-variance atmospheric tomography allowing for algorithms with reduced computational complexity and cost (processing requirements), (ii) a simpler, more flexible control of the NGS-controlled modes, and (iii) a reduced coupling between the LGS- and NGS-controlled modes. Computation and memory requirements for all three algorithms are also given for the split control approach for the TMT LGS AO system and appear feasible in relation to the performance specifications of current hardware technology.

Agile holographic optical phased array device and applications

Abstract: A device that provides light beam switching, agile steering of the light beam over a range of angles, and generation of arbitrary wavefront shapes with high spatial and temporal resolution. The agile device can include a volume diffractive structure comprising Bragg planes having one refractive index and the Bragg planes separated by regions containing an active optical medium. Electrodes (which may be the Bragg planes themselves, or may be arrayed adjacent to the active optical medium) are used to control the electric field intensity and direction across the structure, and thereby control the diffraction efficiency of the structure and the local phase delay imposed on a diffracted wavefront. Means are provided for addressing the many thousands of electrodes required for precise and rapid wavefront control. Applications include free-space atmospheric optical communications, near-eye displays, direct-view 3D displays, optical switching, and a host of other applications.

Repeatability of corneal first-surface wavefront aberrations measured with Pentacam corneal topography.

Abstract: Purpose To assess the repeatability of corneal wavefront aberrations derived from Pentacam (Oculus) corneal topography. Setting Flinders Eye Centre, Flinders Medical Centre, Bedford Park, South Australia, Australia. Methods Forty-five normal participants and 10 participants with keratoconus were tested. Intraobserver and interobserver repeatability was determined using 4 observers within and between sessions. Topographical maps were exported to external software, and corneal first-surface wavefront aberrations were calculated using a 10th-order Zernike expansion over a 6.0 mm optical zone. Repeatability was determined with Bland-Altman limits of agreement and expressed as the coefficient of repeatability (COR). Results Initial data showed high wavefront aberrations in normal participants and poor repeatability. Topographical maps showed extrapolated topography in zones without data acquisition; maps with less than 6.0 mm of complete data were excluded in the final analysis. The mean wavefront aberrations for normal participants remained high, but repeatability improved. The COR relative to the magnitude of wavefront aberrations was high (average 100%) across all modal pairs and orders, although best for total higher-order root mean square. Participants with keratoconus had higher magnitude wavefront aberrations and poorer repeatability but similar COR to average wavefront aberration ratios. Examination of raw elevation data showed poor repeatability. Conclusions Wavefront aberrations calculated from Pentacam corneal topography were large in magnitude, and reliability was poor, largely due to variability in corneal elevation data. Intraobserver and interobserver reliability within and between sessions was comparable. The Pentacam was not reliable in measuring corneal wavefront aberrations.

Wavefront error correction and Earth-like planet detection by a self-coherent camera in space

Abstract: Context. In the context of exoplanet detection, the performance of coronagraphs is limited by wavefront errors. Aims. To remove efficiently the effects of these aberrations using a deformable mirror, the aberrations themselves must be measured in the science image to extremely high accuracy. Methods. The self-coherent camera which is based on the principle of light incoherence between star and its environment can estimate these wavefront errors. This estimation is derived directly from the encoded speckles in the science image, avoiding differential errors due to beam separation and non common optics. Results. Earth-like planet detection is modeled by numerical simulations with realistic assumptions for a space telescope. Conclusions. The self-coherent camera is an attractive technique for future space telescopes. It is also one of the techniques under investigation for the E-ELT planet finder the so-called EPICS.

Stability of strong travelling waves for a non-local time-delayed reaction-diffusion equation

Abstract: The paper is concerned with a non-local time-delayed reaction–diffusion equation. We prove the (time) asymptotic stability of a travelling wavefront without a smallness assumption on its wavelength, i.e. the so-called strong wavefront, by means of the (technical) weighted energy method, when the initial perturbation around the wave is small. The exponential convergent rate is also given. Selection of a suitable weight plays a key role in the proof.

Specification and Control of Mid-Spatial Frequency Wavefront Errors in Optical Systems

Abstract: This paper is an introduction to the specification and tolerancing of Mid-spatial frequency (MSF) ripple or waviness. We begin with an introduction to the definition of ripple, spatial frequencies, and MSF ripple as a class of surface error (as opposed to figure or form, roughness, and surface imperfections or defects.) We then cover the derivation of spatial frequency bands of interest, specifications methods and notations, and relative amplitudes for typical manufacturing processes.

CANARY: the on-sky NGS/LGS MOAO demonstrator for EAGLE

Abstract: EAGLE is a multi-object 3D spectroscopy instrument currently under design for the 42-metre European Extremely Large Telescope (E-ELT). Precise requirements are still being developed, but it is clear that EAGLE will require (~100 x 100 actuator) adaptive optics correction of ~20 - 60 spectroscopic subfields distributed across a ~5 arcminute diameter field of view. It is very likely that LGS will be required to provide wavefront sensing with the necessary sky coverage. Two alternative adaptive optics implementations are being considered, one of which is Multi-Object Adaptive Optics (MOAO). In this scheme, wavefront tomography is performed using a set of LGS and NGS in either a completely open-loop manner, or in a configuration that is only closed-loop with respect to only one DM, probably the adaptive M4 of the E-ELT. The fine wavefront correction required for each subfield is then applied in a completely open-loop fashion by independent DMs within each separate optical relay. The novelty of this scheme is such that on-sky demonstration is required prior to final construction of an E-ELT instrument. The CANARY project will implement a single channel of an MOAO system on the 4.2m William Herschel Telescope. This will be a comprehensive demonstration, which will be phased to include pure NGS, low-order NGS-LGS and high-order woofer-tweeter NGS-LGS configurations. The LGSs used for these demonstrations will be Rayleigh systems, where the variable range-gate height and extension can be used to simulate many of the LGS effects on the E-ELT. We describe the requirements for the various phases of MOAO demonstration, the corresponding CANARY configurations and capabilities and the current conceptual designs of the various subsystems.

Reconstruction of the optical system of the human eye with reverse ray-tracing

Abstract: We present a practical method for reconstructing the optical system of the human eye from off-axis wavefront measurements. A retinal beacon formed at different locations on the retina allows probing the optical structure of the eye by the outgoing beams that exit the eye through the dilated pupil. A Shack-Hartmann aberrometer measures the amount of wave aberrations in each beam at the exit pupil plane. Wavefront data obtained at different oblique directions is used for tomographic reconstruction by optimizing a generic eye model with reverse ray-tracing. The multi-configuration system is constructed by tracing pre-aberrated beams backwards from each direction through the exit pupil into the optical system of the aberrometer followed by the generic eye model. Matching all wave aberrations measured at each field point is equivalent to minimizing the size of the beacon spots on the retina. The main benefit of having a personalized eye model is the ability to identify the origin of the ocular aberrations and to find the optimal way for their correction.

Coherent diffractive imaging using phase front modifications.

Abstract: We introduce a coherent diffractive imaging technique that utilizes multiple exposures with modifications to the phase profile of the transmitted wave front to compensate for the missing phase information. This is a single spot technique sensitive to both the transmission and phase shift through the sample. Along with the details of the method, we present results from the first proof of principle experiment. The experiment was performed with 6.0 keV x rays, in which an estimated spatial resolution of 200 nm was achieved.

Differential Phase X-ray Imaging Microscopy with X-ray Talbot Interferometer

Abstract: A new type of differential phase X-ray imaging microscopy attained by combination of an X-ray imaging microscope and an X-ray Talbot interferometer is described. An X-ray Talbot interferometer was set up so that a moire-fringe pattern appeared on the image plane of an X-ray imaging microscope. The wavefront inclination (differential phase shift) caused by a weakly absorbing polymer sample was measured from the fringes using the fringe-scanning method and with a spatial resolution of 1 µm. Phase tomography was also performed and the internal structures of a piece of polymer blend were depicted.

Design of electromagnetic refractor and phase transformer using coordinate transformation theory.

Abstract: We designed an electromagnetic refractor and a phase transformer using form-invariant coordinate transformation of Maxwell’s equations. The propagation direction of electromagnetic energy in these devices can be modulated as desired. Unlike the conventional dielectric refractor, electromagnetic fields at our refraction boundary do not conform to the Snell’s law in isotropic materials and the impedance at this boundary is matched which makes the reflection extremely low; and the transformation of the wave front from cylindrical to plane can be realized in the phase transformer with a slab structure. Two dimensional finite-element simulations were performed to confirm the theoretical results.

Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures.

Abstract: Wave-front engineering for nonlinear optical interactions was discussed. Using Huygens-Fresnel principle we developed a general theory and technique for domain engineering with conventional quasi-phase-matching (QPM) structures being the special cases. We put forward the concept of local QPM, which suggests that the QPM is fulfilled only locally not globally. Experiments agreed well with the theoretical prediction. The proposed scheme integrates three optical functions: generating, focusing, and beam splitting of second-harmonic wave, thus making the device more compact.