Showing papers on "Wavefront published in 1994"

Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor

Abstract: A Hartmann-Shack wave-front sensor is used to measure the wave aberrations of the human eye by sensing the wave front emerging from the eye produced by the retinal reflection of a focused light spot on the fovea. Since the test involves the measurements of the local slopes of the wave front, the actual wave front is reconstructed by the use of wave-front estimation with Zernike polynomials. From the estimated Zernike coefficients of the tested wave front the aberrations of the eye are evaluated. It is shown that with this method, using a Hartmann-Shack wave-front sensor, one can obtain a fast, precise, and objective measurement of the aberrations of the eye.

On the Wave Theory in Heat Conduction

Abstract: This work contains three major components: a thorough review on the research emphasizing engineering applications of the thermal wave theory, special features in thermal wave propagation, and the thermal wave model in relation to the microscopic two-step model. For the sake of convenience, the research works are classified according to their individual emphases. Special features in thermal wave propagation include the sharp wavefront and rate effects, the thermal shock phenomenon, the thermal resonance phenomenon, and reflections and refractions of thermal waves across a material interface. By employing the dual-phase-lag concept, we show that the energy equation may be reduced to that governing the heat transport through the metal lattice in the microscopic two-step model

Acoustic event localization using a crosspower-spectrum phase based technique

Abstract: Linear microphone arrays can be employed for acoustic event localization in a noisy environment using time delay estimation. Three techniques are investigated that allow delay estimation, namely normalized cross correlation, LMS adaptive filters, crosspower-spectrum phase: they are combined with a bidimensional representation, the coherence measure, in order to emphasize information that can be exploited for estimating position of both non-moving and moving acoustic sources. To compare the given techniques, different acoustic sources were considered, that generated events in different positions in space. Expressing performance in terms of accuracy of the wavefront direction angle, experiments showed that the crosspower-spectrum phase based technique outperforms the other two. This technique provided very promising preliminary results also in terms of source position estimation. >

Correction of ultrasonic wavefront distortion using backpropagation and a reference waveform method for time-shift compensation.

Abstract: A model is introduced to describe ultrasonic pulse amplitude and shape distortion as well as arrival time fluctuation produced by propagation through specimens of human abdominal wall. In the model, amplitude and shape distortion develops as the wavefront propagates in a uniform medium after passing through a phase screen that only causes time shifts. This distortion is compensated by a backpropagation of the wavefront using the angular spectrum method. The compensation employed waveforms emitted by a pointlike source and measured after propagation through the tissue. The waveforms were first corrected for geometric path and then were backpropagated over a sequence of increasing distances. At each distance, a waveform similarity factor was calculated to find the backpropagation distance at which the waveforms were most similar. A new method was devised to estimate pulse arrival time for geometric correction as well as to perform time‐shift compensation. The method adaptively derives a reference waveform that is then cross correlated with all the waveforms in the aperture to obtain a surface of arrival times. The surface was smoothed iteratively to remove outlying points due to waveform distortion. The mean (±s.d.) of the waveform similarity factor for 14 specimens was found to be 0.938 (±0.025) initially. After backpropagation of waveforms to the distance of maximum waveform similarity for each specimen, the waveform similarity factor improved to 0.967 (±0.015). The corresponding energy level fluctuation in the wavefront was 4.2 (±0.4) dB initially and became 3.3 (±0.3) dB after backpropagation. For wavefronts focused at 180 mm, the −30 dB mean (±s.d.) effective radius of the focus was 4.2 (±1.2) mm with time‐shift compensation in the aperture and became 2.5 (±0.5) mm with backpropagation followed by time‐shift compensation. These results indicate that a phase screen placed some distance away from the aperture is an improved model for the description of wavefront distortion produced by human abdominal wall and that wavefront backpropagation followed by time‐shift estimation and compensation is an effective method to compensate for such distortion.

Ultrasound synthetic aperture imaging: monostatic approach

Abstract: An ultrasound synthetic aperture imaging method based on a monostatic approach was studied experimentally. The proposed synthetic aperture method offers good dynamical resolution along with fast numerical reconstruction. In this study complex object data were recorded coherently in a two-dimensional hologram using a 3.5 MHz single transducer with a fairly wide-angle beam. Image reconstruction which applies the wavefront backward propagation method and the near-field curvature compensation was performed numerically in a microcomputer using the spatial frequency domain. This approach allows an efficient use of the FFT-algorithms. Because of the simple and fast scanning scheme and the efficient reconstruction algorithms the method can be made real-time. The image quality of the proposed method was studied by evaluating the spatial and dynamical resolution in a waterbath and in a typical tissue-mimicking phantom. The lateral as well as the range resolution (-6 dB) were approximately 1 mm in the depth range of 30-100 mm. The dynamical resolution could be improved considerably when the beam width was made narrower. Although it resulted in a slightly reduced spatial resolution this compromise has to be done for better resolution of low-contrast targets such as cysts. The study showed that cysts as small as 2 mm by diameter could be resolved. >

Analysis of multiconjugate adaptive optics.

Abstract: We investigate a method for widening the compensated field of view of an adaptive-optical telescope with multiple deformable mirrors and an array of artificial guide stars. An ensemble of wavefront sensor measurements, made with the individual guide stars in the array, is used to estimate the contribution of a region of the atmosphere to the cumulative phase distortion. Our analysis includes the effects of measurement noise, wavefront-sensor sampling, and reconstruction of the wave front from slope measurements. We performed numerical computations for an atmosphere consisting of two turbulent layers: one at 1% of the guide-star altitude with 90% of the total turbulence strength and one at 10% of the guide-star altitude with the remaining 10% of the total turbulence strength. If we assume that r0 = 0.15 m and that a photon-limited wave-front sensor detecting 50 photons/r0-sized subaperture is used, the results indicate that a 0.9-m-square telescope with a diagonal field of view of ~92 μrad ≈ 19 arcsec can use two deformable mirrors, four laser guide stars, and a natural tilt reference star to achieve an rms residual phase error that is <λ/7 over its entire field of view.

Phase-diversity wave-front sensor for imaging systems.

Abstract: A phase-diversity wave-front sensor has been developed and tested at the Lockheed Palo Alto Research Labs (LPARL). The sensor consists of two CCD-array focal planes that record the best-focus image of an adaptive imaging system and an image that is defocused. This information is used to generate an object-independent function that is the input to a LPARL-developed neural network algorithm known as the General Regression Neural Network (GRNN). The GRNN algorithm calculates the wave-front errors that are present in the adaptive optics system. A control algorithm uses the calculated values to correct the errors in the optical system. Simulation studies and closed-loop experimental results are presented.

Control of wave-front propagation with diffractive elements.

Abstract: In principle, diffractive elements can be designed to control a propagating wave in three dimensions, but no general procedure has been proposed. We present an iterative method that is suitable for the design of such diffractive elements. The resulting complex amplitude distribution will approach any arbitrary requirement, as much as is permitted by basic physical principles. The problem of “nondiffracting-beam” propagation is analyzed as a special case, and intensity peaks are generated that propagate as much as 4 m with a bounded width. The generality of the method, as compared with other techniques, is demonstrated by the design of an array of nondiffracting beams.

Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object

Abstract: A detailed analysis of the characteristics, regularities, and relationships of the centroiding errors of image spots caused by discrete and limited sampling, photon noise, and readout noise of the detector in a Hartmann-Shack wavefront sensor, wherein an image intensified charge-coupled device used as a photon detector is presented. The theoretical analysis and experimental results herein prove useful for optimum design and application of the sensor.

How to approach the design of a bilateral symmetric optical system

Abstract: A theoretical development is presented for understanding and designing bilateral symmetric optical systems. This development uses concepts familiar to the optical engineer and is an extension to the wave theory of axially symmetric systems. An aberration function is developed and the image position and size, image defects, and aberration fields are discussed. The main dependence of aberrations as a function of system parameters is established by a set of approximate aberration coefficients and some guidelines to approach the design of bilateral symmetric systems are presented.

Internal‐wave effects on 1000‐km oceanic acoustic pulse propagation: Simulation and comparison with experiment

Abstract: A recent 1000‐km acoustic pulse transmission experiment in the Pacific revealed unexpected fluctuations on received wavefronts, including a dominant rapid variation, called the broadband fluctuation, with time scales less than 10 minutes and spatial scales of less than 60 m; a distinct breakdown of the geometrical optics wavefront pattern and broadening of the wavefront near the transmission finale; and a coherent wavefront motion with a timescale near the semi‐diurnal tidal period Parabolic‐equation numerical simulations have been carried out which utilize environmental data and which take into account internal‐wave‐induced sound‐speed perturbations obeying the Garrett–Munk (GM) spectral model It is shown that the effects of internal waves can account for the broadband fluctuations, the breakdown of the geometrical optics pattern, and the wavefront broadening The sensitivity of these fluctuations to internal‐wave energy and modal content is examined The spectral energy in the GM model at tidal period

Phase-Shifting Holographic Interferometry

Abstract: Quantitative data can be extracted from holographic interference fringes using Phase-Measurement Interferometry (PMI) techniques. These techniques are used to determine the phase of the secondary interference fringe pattern and can be divided broadly into spatial and temporal techniques. Temporal techniques introduce a known phase shift between the object and reference beams in an interferometer and take a series of data over time as the phase shift is varied. Spatial techniques rely on encoding the phase shift information spatially in a single interferogram by using a large number of fringes as a carrier for the phase information which are generated by tilting the reference wavefront relative to the test wave front. Temporal techniques which process data in electronics are known as heterodyne techniques and were discussed in the last chapter. The processing of spatial phase-measurement data will be discussed in the next chapter. Temporal techniques which process the data analytically on a point-by-point basis will be the concentration of this chapter.

Polarization aberrations. 1. Rotationally symmetric optical systems

Abstract: The polarization in isotropic radially symmetric lens and mirror systems in the paraxial approximation is examined. Polarized aberrations are variations in the phase, amplitude, and polarization state of the electromagnetic field across the exit pupil. Some are dependent on the incident polarization state and some are not. Expressions through fourth order for phase, amplitude, linear diattenuation, and linear retardance aberrations are derived in terms of the chief and marginal ray angles of incidence and the Taylor series expansion coefficients of the Fresnel equations for reflection and transmission at uncoated and thin-film-coated interfaces. Applications to polarization ray tracing are discussed.

SLIDE: subspace-based line detection

Abstract: An analogy is made between each straight line in an image and a planar propagating wavefront impinging on an array of sensors so as to obtain a mathematical model exploited in recent high resolution methods for direction-of-arrival estimation in sensor array processing. The new so-called SLIDE (subspace-based line detection) algorithm then exploits the spatial coherence between the contributions of each line in different rows of the image to enhance and distinguish a signal subspace that is defined by the desired line parameters. SLIDE yields closed-form and high resolution estimates for line parameters, and its computational complexity and storage requirements are far less than those of the standard method of the Hough transform. If unknown a priori, the number of lines is also estimated in the proposed technique. The signal representation employed in this formulation is also generalized to handle grey-scale images as well. The technique has also been generalized to fitting planes in 3-D images. Some practical issues of the proposed technique are given. >

Analysis of fundamental limits to artificial-guide-star adaptive-optics-system performance for astronomical imaging

Abstract: The concept of using the atmospheric backscatter from a pulsed laser as an artificial guide star (AGS) for an adaptive-optics system in an astronomical telescope is analyzed. The extent to which such an AGS can be used to provide the information that is needed for adaptive-optics-system compensation of a wave front that is distorted by propagation through the atmosphere is studied. Attention is directed to the effect of focus anisoplanatism, the measurement error that is introduced when the probe light from the AGS at a finite range travels a different path than does the light from an astronomical object at a larger (infinite) range. Because of focus anisoplanatism there is a residual wave-front error that the wave-front-distortion sensor, relying on the AGS, is unable to sense and for which the adaptive-optics system is therefore unable to compensate. This residual wave-front error has a mean-square value that takes the form σφFA2 = (D/d0)5/3, where d0 is an aperture-diameter-sized quantity that measures the magnitude of the effect of focus anisoplanatism. The value of d0 depends on the vertical distribution of the optical strength of turbulence, the optical wavelength of the imaging system, the zenith angle, and the backscatter altitude. An expression is given for d0, and sample results for d0 are presented. Analytic results are also developed for the effect of focus anisoplanatism on the Strehl definition (or normalized antenna gain) of the imaging system. Numerical results are presented for the normalized antenna gain for a wide variety of backscatter altitudes and for several vertical distributions of the optical strength of turbulence. These results indicate that the diameter dependence of the normalized antenna gain is fully expressed as a function of D/d0. The peak achievable antenna gain is approximately equal to 40% of that of a diffraction-limited system with an aperture diameter that is equal to d0, and the peak is achieved with an actual aperture diameter in the range of (7/6)d0 to (9/6)d0.

Wave-front correction by one or more synthetic beacons

Abstract: Adaptive optics has been used in a cooperative mode to measure the phase distortion of the light from a star and to correct its image with a deformable mirror. A wave-front sensor in the adaptive-optics system that measures the phase aberrations requires that an object be fairly bright for accurate performance of the measurement. The use of synthetic beacons provides a means of correcting the images of objects that are too dim to allow one to use their light to provide correction in a cooperative mode. Synthetic beacons at a finite distance do not provide a perfect correction in imaging an object at a greater distance. The error in making a correction with one or more beacons is analyzed. Analytical expressions that can be used to determine performance in a variety of geometries, with various beacon altitudes and numbers, are derived. This analysis is applied to 60-cm and 4-m systems.

Nonuniform muscle fiber orientation causes spiral wave drift in a finite element model of cardiac action potential propagation.

Abstract: Mechanism for Spiral Wave Drift. Introduction: Reentrant tachyarrhythmias are thought to involve spiral waves of excitation and recovery that may be nonstationary. The effect of muscle fiber curvature on spiral and planar wave propagation was studied using a computational model. Methods and Results: Two-dimensional anisotropic cardiac propagation was modeled using a finite element method to solve a modification of the FitzHugh-Nagumo equations. Spiral waves that propagated stably about a fixed core in tissue with a uniform fiber orientation were found to drift at an oblique angle to the fibers when the fibers curved. The drift velocity was linearly related to the fiber angle gradient and was 10% of the longitudinal propagation velocity with a gradient of 4 degree/cm. Planar wavefronts were also affected by fiber curvature. The maximal upstroke rate, propagation velocity, and the action potential amplitude all increased when the fibers curved toward the wavefront and decreased when they curved away. For example, when the fibers curved toward the wavefront with a moderate gradient of 15 degree/cm, maximal upstroke rate increased 74%, transverse propagation velocity increased 65%, and action potential amplitude increased 9%, This phenomenon caused the spiral wave drift: As a spiral wave traverses a cycle, the angle between the wavefront at the wavetip and the fibers changes periodically, thus altering the propagation parameters. These periodic changes affect the instantaneous radius of curvature of the wavetip path, which results in drift. Conclusion: Spiral and planar waves are affected by muscle fiber curvature. The resulting dynamics may be important in determining the lifetime and stability of reentrant arrhythmias.

One dimensional wavefront distortion sensor comprising a lens array system

Abstract: A 1-dimensional sensor for measuring wavefront distortion of a light beam as a function of time and spatial position includes a lens system which incorporates a linear array of lenses, and a detector system which incorporates a linear array of light detectors positioned from the lens system so that light passing through any of the lenses is focused on at least one of the light detectors. The 1-dimensional sensor determines the slope of the wavefront by location of the detectors illuminated by the light. The 1 dimensional sensor has much greater bandwidth that 2 dimensional systems.

Characterization of microlenses using a phase-shifting shearing interferometer

Abstract: A shearing interferometer is proposed for the characterization of microlenses. The optical configuration of the test system enables the measurement of the wave aberrations, the focal length, and the deviations of the lens surface from an ideal sphere. In addition, a quantitative evaluation method is given that enables the calculation of the wave aberrations (e.g., the phase function) from the shearing interferometer data.

Image-spectrum signal-to-noise-ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence

Abstract: Adaptive-optics systems have been used to overcome some of the effects of atmospheric turbulence on large-aperture astronomical telescopes. However, the correction provided by adaptive optics cannot restore diffraction-limited performance, due to discretized spatial sampling of the wavefront, limited degrees of freedom in the adaptive-optics system, and wavefront sensor measurement noise. Field experience with adaptive-optics imaging systems making short-exposure image measurements has shown that some of the images are better than others in the sense that the better images have higher resolution. This is a natural consequence of the statistical nature of the compensated optical transfer function in an adaptive-optics telescope. Hybrid imaging techniques have been proposed that combine adaptive optics and postdetection image processing to improve the high-spatial-frequency information of images. Performance analyses of hybrid methods have been based on prior knowledge of the ensemble statistics of the underlying random process. Improved image-spectrum SNRs have been predicted, and in some cases experimentally demonstrated. In this paper we address the issue of selecting and processing the best images from a finite data set of compensated short-exposure images. Image sharpness measures are used to select the data subset to be processed. Comparison of the image-spectrum SNRs for the cases of processing the entire data set and processing only the selected subset of the data shows a broad range of practical cases where processing the selected subset results in superior SNR.

Wavefront amplitude distribution in the female breast

Abstract: Ultrasound measurements of a large population of wavefronts transmitted through female breasts at 3 and 4 MHz show that the wavefront amplitude distribution is close to Rayleigh. This finding is consistent with a fully developed scatter field, implying that the scatter energy removed from the coherent incident beam dominates the wavefront. The wavefront received from an inhomogeneous medium is the superposition of an incident wave plus a scattered wave. If the scattered field is weak, the received field is dominated by the incident field and the wavefront amplitude distribution is Rician. If the scattered field is strong, the received field is primarily the scattered field and the wavefront amplitude distribution is Rayleigh. If, in addition to scattering, refraction between bodies of different refractive indexes occurs, the total net effect on the wavefront amplitude distribution is the same as for strong scattering. This is what we have observed in the highly refractive female breast. This result has implications for the design of high lateral‐resolution echo scanners that will incorporate adaptive phase deaberration algorithms. The published algorithms were developed for weak scattering and therefore may not be powerful enough. Alternatives have to be found to deaberrate the severe wavefront distortion in the breast.

Full-aperture interferometric test of convex secondary mirrors using holographic test plates

Abstract: Convex secondary mirrors are notoriously difficult to fabricate because of the tremendous cost and difficulty of making accurate measurements of the optical surfaces The new 65- and 8-m-class telescopes require secondary mirrors that are larger, more aspheric, and more accurately figured than those for existing telescopes The challenge of measuring these giant optics has spurred the development of a new measurement technique using holographic test plates This test uses a full-aperture test plate with a computer-generated hologram fabricated onto the spherical reference surface When supported a few millimeters from the secondary and properly illuminated with laser light, an interference pattern is formed that shows the secondary surface errors The hologram consists of annular rings of metal drawn onto the curved test plate surface using a custom-built writing machine The accuracy of the surface measurement using this technique is expected to be 35 nm P-V and 6 nm rms for a 165-m secondary mirror for the MMT Considerably higher accuracy is expected for less aspheric surfaces© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering Downloading of the abstract is permitted for personal use only

Anisoplanatic effects in finite-aperture optical systems

Abstract: Modal decomposition of the phase variance between the wave front that is sampled to make a correction and the desired wave front allows inappropriate piston and tilt terms to be excluded from statistical estimates. Mathematical techniques that were developed for calculating Zernike-mode covariances for multiaperture optical systems lead to statistical expressions for angular and focal anisoplanatism and combinations thereof. The 5/3-law dependence that characterizes the angular dependence and also appears in connection with the standard Greenwood frequency is shown to be an artifact of infinite outer scale that is entirely removable by exclusion of the piston. Large piston and/or tilt components significantly affect critical angle and frequency estimates under conditions of practical interest. A finite inner scale or the removal of high-frequency components also produces a characteristic deviation from the 5/3 power law, including a substantial quadratic region for small angles.

Phase-shifting errors in interferometric tests with high-numerical-aperture reference surfaces

Abstract: The errors introduced by moving a spherical reference surface to generate a phase shift between the beams in a Fizeau interferometer are discussed.

Wavefront reconstruction optics for use in a disk drive position measurement system

Abstract: An optical measurement system for use in a data recording disk drive includes wavefront reconstruction optics which correct and compensate for aberrations in laser beams reflected from radial and linear diffraction gratings. The reconstruction optics include two spherical lenses and two reflectors, one of each positioned on each side of a diffraction grating. Light directed from a laser beam toward the grating diffracts into a +1 order component directed at the first set of reconstruction optics and into a -1 order component directed at the second set of reconstruction optics. The reconstruction optics compensate for the variable yaw angle caused by a linear grating and for the optical wavefront aberrations caused by a radial grating. Use of the reconstruction optics permits an optical measurement system in a data recording disk drive to accurately measure the position of either a linear or rotary actuator and to generate a precise reference clock for use in timing the recording of servo information to the data recording disk.

Optimization method and device for direct measurement of an optical component

Abstract: A method and device for measurement of the geometrical or optical structure of an optical component such as a lens or a mold for making lens are provided. The method comprises the steps of illuminating the optical component to be measured with incident light having a known wavefront, measuring, in a given plane, the maps of the wavefront slopes of the light, after reflection at or transmission by the optical component, and deducing the surface topography or refraction index map of the optical component to be measured from the measurements of the slope maps by the application of at least one calculating procedure. The calculating procedure comprises a step in which a result surface is initialized using a simple starting surface SD' and at least one optimization step; each optimization step involves calculation of the value of a merit function representative of the departure between the result surface and the surface to be measured of the optical component and, minimization of said value varying said result surface, said variation being expressed in the form of at least one intermediate surface Si.