Turbulence-induced edge image waviness: theory and experiment

A theoretical model for the edge image waviness effect is developed for the ground-to-ground imaging scheme and validated by use of IR imagery data collected at the White Sands Missile Range. It is shown that angle-of-arrival (AA) angular anisoplanatism causes the phenomenon of edge image waviness and that the AA correlation scale, not the isoplanatic angle, characterizes the edge image waviness scale. The latter scale is determined by the angular size of the imager and a normalized atmospheric outer scale, and it does not depend on the strength of turbulence along the path. Spherical divergence of the light waves increases the edge waviness scale. A procedure for estimating the atmospheric and camera-noise components of the edge image motion is developed and implemented. A technique for mitigation of the edge image waviness that relies on averaging the effects of AA anisoplanatism on the image is presented and validated. The edge waviness variance is reduced by a factor of 2-3. The time history and temporal power spectrum of the edge image motion are obtained. These data confirm that the observed edge image motion is caused by turbulence.     

Control of the unilluminated deformable mirror actuators in an altitude-conjugated adaptive optics system

Off-axis observations made with adaptive optics are severely limited by anisoplanatism errors. However, conjugating the deformable mirror to an optimal altitude can reduce these errors; it is then necessary to control, through extrapolation, actuators that are not measured by the wave-front sensor (unilluminated actuators). In this study various common extrapolation schemes are investigated, and an optimal method that achieves a significantly better performance is proposed. This extrapolation method involves a simple matrix multiplication and will be implemented in ALTAIR, the Gemini North Telescope adaptive optics system located on Mauna Kea, Hawaii. With this optimal method, the relative H-band Strehl reduction due to extrapolation errors is only 5%, 16%, and 30% when the angular distance between the guide source and the science target is 20, 40 and 60 arc sec, respectively. For a site such as Mauna Kea, these errors are largely outweighed by the increase in the size of the isoplanatic field.     

Estimation and correction of ultrasonic wavefront distortion using pulse-echo data received in a two-dimensional aperture

Pulse-echo measurements from random scattering and from a point target have been used to quantify transmitter beam size effects and isoplanatic patch size as well as to evaluate the performance of different aberration compensation techniques. Measurements were made using a single-element transmitter with a diameter of 1/2 in., 1 in., or 2 in., each focused at 3 in. A tissue-mimicking scattering phantom or a point target was used to produce echoes that were received in a two-dimensional aperture synthesized by scanning a linear array. A specimen of abdominal wall was placed in the reception path to produce aberration. B-scan images were formed with no compensation, with time-shift compensation in the receiving aperture, and with backpropagation followed by time-shift compensation. The isoplanatic patch size was estimated by compensating the focus of a test point target with the parameters estimated for an original point target position, and observing the deterioration of compensation effects with increasing distance between the test and the original point targets. The results of the measurements using different transmitter diameters quantify the improvement of time-delay estimation with the increase in wavefront coherence that accompanies decreased transmitter beam size. For seven specimens, the average isoplanatic patch size determined from a 10% increase in the -10 dB effective diameter was 16.7 mm in the azimuthal direction and 39.0 mm in the range direction. These sizes increased after backpropagation to 19.0 mm and 41.4 mm, respectively. For the 1/2 in., 1 in., and 2 in. diameter transmitters, the average contrast ratio improvement was 2.0 dB, 2.1 dB, and 2.8 dB, respectively, with time-shift compensation, and 2.3 dB, 2.7 dB, and 3.5 dB, respectively, with backpropagation of 20 mm followed by time-delay estimation and compensation. The investigation indicates that a tightly focused transmitter beam is necessary to create a scattered wavefront satisfactory for time-shift estimation, the isoplanatic patch is about twice as long in the range direction as in the azimuthal direction, and backpropagation followed by time-shift compensation provides better compensation of distortion than time-shift compensation alone.     

Isoplanatism in a multiconjugate adaptive optics system

Turbulence correction in a large field of view by use of an adaptive optics imaging system with several deformable mirrors (DM's) conjugated to various heights is considered. The residual phase variance is computed for an optimized linear algorithm in which a correction of each turbulent layer is achieved by applying a combination of suitably smoothed and scaled input phase screens to all DM's. Finite turbulence outer scale and finite spatial resolution of the DM's are taken into account. A general expression for the isoplanatic angle thetaM of a system with M mirrors is derived in the limiting case of infinitely large apertures and Kolmogorov turbulence. Like Fried's isoplanatic angle theta0,thetaM is a function only of the turbulence vertical profile, is scalable with wavelength, and is independent of the telescope diameter. Use of angle thetaM permits the gain in the field of view due to the increased number of DM's to be quantified and their optimal conjugate heights to be found. Calculations with real turbulence profiles show that with three DM's a gain of 7-10x is possible, giving the typical and best isoplanatic field-of-view radii of 16 and 30 arcseconds, respectively, at lambda = 0.5 microm. It is shown that in the actual systems the isoplanatic field will be somewhat larger than thetaM owing to the combined effects of finite aperture diameter, finite outer scale, and optimized wave-front spatial filtering. However, this additional gain is not dramatic; it is less than 1.5x for large-aperture telescopes.     

Methods for correcting tilt anisoplanatism in laser-guide-star-based multiconjugate adaptive optics

Multiconjugate adaptive optics (MCAO) is a technique for correcting turbulence-induced phase distortions in three dimensions instead of two, thereby greatly expanding the corrected field of view of an adaptive optics system. This is accomplished with use of multiple deformable mirrors conjugate to distinct ranges in the atmosphere, with actuator commands computed from wave-front sensor (WFS) measurements from multiple guide stars. Laser guide stars (LGSs) must be used (at least for the forseeable future) to achieve a useful degree of sky coverage in an astronomical MCAO system. Much as a single LGS cannot be used to measure overall wave-front tilt, a constellation of multiple LGSs at a common range cannot detect tilt anisoplanatism. This error alone will significantly degrade the performance of a MCAO system based on a single tilt-only natural guide star (NGS) and multiple tilt-removed LGSs at a common altitude. We present a heuristic, low-order model for the principal source of tilt anisoplanatism that suggests four possible approaches to eliminating this defect in LGS MCAO: (i) tip/tilt measurements from multiple NGS, (ii) a solution to the LGS tilt uncertainty problem, (iii) additional higher-order WFS measurements from a single NGS, or (iv) higher-order WFS measurements from both sodium and Rayleigh LGSs at different ranges. Sample numerical results for one particular MCAO system configuration indicate that approach (ii), if feasible, would provide the highest degree of tilt anisoplanatism compensation. Approaches (i) and (iv) also provide very useful levels of performance and do not require unrealistically low levels of WFS measurement noise. For a representative set of parameters for an 8-m telescope, the additional laser power required for approach (iv) is on the order of 2 W per Rayleigh LGS.     

Shack-Hartmann wavefront estimation with extended sources: anisoplanatism influence

Anisoplanatism limits the correction field of adaptive optics (AO). In the case of Shack-Hartmann measurement performed on extended sources it may also strongly affect wavefront estimation accuracy. An analytical formalism has been previously proposed to quantify anisoplanatism slope measurement error. It is exploited here to derive the most relevant quantity in AO, the wavefront error. Analytical and end-to-end simulation results are compared in three cases: solar observation, weakly perturbed near-to-ground observation, and strongly perturbed near-to-ground observation. In every case, anisoplanatism wavefront error takes significant values. The accuracy of the analytical model is investigated in detail. Three contributions to the slope error previously identified are considered: phase anisoplanatism, scintillation anisoplanatism, and coupling between scintillation and phase anisoplanatism. The influence of both scintillation and coupling contributions to the wavefront error is confirmed here.     

Fundamental limits on isoplanatic correction with multiconjugate adaptive optics

We investigate the performance of a general multiconjugate adaptive optics (MCAO) system in which signals from multiple reference beacons are used to drive several deformable mirrors in the optical beam train. Taking an analytic approach that yields a detailed view of the effects of low-order aberration modes defined over the metapupil, we show that in the geometrical optics approximation, N deformable mirrors conjugated to different ranges can be driven to correct these modes through order N with unlimited isoplanatic angle, regardless of the distribution of turbulence along the line of sight. We find, however, that the optimal deformable mirror shapes are functions of target range, so the best compensation for starlight is in general not the correction that minimizes the wave-front aberration in a laser guide beacon. This introduces focal anisoplanatism in the wave-front measurements that can be overcome only through the use of beacons at several ranges. We derive expressions for the number of beacons required to sense the aberration to arbitrary order and establish necessary and sufficient conditions on their geometry for both natural and laser guide stars. Finally, we derive an expression for the residual uncompensated error by mode as a function of field angle, target range, and MCAO system geometry.     

Optimal filter for phase correction of anisoplanatism

An optimal filter algorithm for adaptive optics provides a powerful method for phase correction for propagation through the Earth's turbulent atmosphere involving anisoplanatism. In the new algorithm the outward phase correction is the sum of the product of a weighting function (the optimal filter) and all the wave-front measurements at the pupil, greatly improving the Strehl ratio. Two simplified cases are presented for illustration: (1) a collimated beam traversing a layer of uniform isotropic turbulence (angle anisoplanatism) and (2) focus anisoplanatism. It compares favorably with tomographic techniques. The technique can be extended to the case of thick, strong turbulence in the far field of a subaperture of an adaptive optics system.     

Including outer scale effects in zonal adaptive optics calculations

Mellin transform techniques are applied to evaluate the covariance of the integrated turbulence-induced phase distortions along a pair of ray paths through the atmosphere from two points in a telescope aperture to a pair of sources at finite or infinite range. The derivation is for the case of a finite outer scale and a von Karman turbulence spectrum. The Taylor hypothesis is assumed if the two phase distortions are evaluated at two different times and amplitude scintillation effects are neglected. The resulting formula for the covariance is a power series in one variable for the case of a fixed atmospheric wind velocity profile and a power series in two variables for a fixed wind-speed profile with a random and uniformly distributed wind direction. These formulas are computationally efficient and can be easily integrated into computer codes for the numerical evaluation of adaptive optics system performance. Sample numerical results are presented to illustrate the effect of a finite outer scale on the performance of natural and laser guide star adaptive optics systems for an 8-m astronomical telescope. A hypothetical outer scale of 10 m significantly reduces the magnitude of tilt anisoplanatism, thereby improving the performance of a laser guide star adaptive optics system if the auxiliary natural star used for full-aperture tip/tilt sensing is offset from the science field. The reduction in higher-order anisoplanatism that is due to a 10-m outer scale is smaller, and the off-axis performance of a natural guide star adaptive optics system is not significantly improved.     

Measurements of r(0) and theta(0) : two decades and 18 sites

We present a statistical analysis of r (0) and theta(0) measurements collected over the last 2 decades at 18 different sites. Although the site altitudes varied from sea level to 3 km, the major distinguishing feature between average r(0) values was the presence or absence of a turbulent, atmospheric boundary layer above the surface. For locations without a strong boundary-layer inversion, the mean coherence length, r(0), was 93 +/- 6 mm and the mean isoplanatic angle, theta(0), was 9.4 +/- 0.5 murad. Where a boundary-layer inversion was present, the corresponding values for r(0) and theta(0) were 53 +/- 2 mm and 6.5 +/- 0.5 murad, respectively.     

Analysis of modes and behavior of a multiconjugate adaptive optics system

We study the so-called three-dimensional mapping of turbulence, a method solving the cone effect (or focus anisoplanatism) by using multiple laser guide stars (LGSs). This method also permits a widening of the corrected field of view much beyond the isoplanatic field. Multiple deformable mirrors, conjugated to planes at chosen altitudes among the turbulent layers, are used to correct in real time the wave fronts measured from the LGSs. We construct an interaction matrix describing the multiconjugate adaptive optics system and analyze the eigenmodes of the system. We show that the global tilt mode is singular because it cannot be localized in altitude, so that it must be corrected only once at any altitude. Furthermore, when the tilt from the LGS cannot be measured, the singularity of the global tilt yields the delocalization of particular forms of defocus and astigmatism. This imposes the use of a single natural guide star located anywhere in the corrected field to measure these modes. We show as an example that the cone effect can be corrected with a Strehl of 0.8 with four LGSs (tilt ignored) on an 8-m telescope in the visible when a single laser star provides a Strehl of 0.1. The maximum field of view of 100 arc sec in diameter can be reconstructed with an on-axis Strehl ratio of 30%. We also show that the measurement of the height of the layers can be done with current techniques and that additional layers, not accounted for, do not significantly degrade the performance in the configuration that we model.     

Widening the effective field of view of adaptive-optics telescopes by deconvolution from wave-front sensing: average and signal-to-noise ratio performance

A fundamental problem of adaptive-optics systems is the very narrow corrected field of view that can be obtained because turbulence is extended in altitude throughout the atmosphere. The correctable field of view is of the order of 5-10 μrad at visible wavelengths and increases as the wavelength increases. Previous concepts to broaden the corrected field of view have been hardware oriented, requiring multiple wave-front sensor (WFS) measurements to control multiple deformable mirrors. We analyze the average and the signal-to-noise-ratio performance of an image measurement and postprocessing technique that uses simultaneous measurements of a short-exposure compensated image measured in an off-axis direction; an additional WFS measurement is taken in the off-axis direction. Results are presented for infinite-altitude WFS beacons driving both the WFS for the adaptive optics and the WFS looking in the off-axis direction, a variety of seeing and WFS light-level conditions, and off-axis angles from two to six times the isoplanatic angle. This technique improves the average effective transfer function out to a field angle of at least six times the isoplanatic angle while providing a higher signal-to-noise ratio in the spatial frequency domain.     

Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing

Adaptive optics provides a real-time compensation for atmospheric turbulence that severely limits the resolution of ground-based observation systems. The correction quality relies on a key component, that is, the wavefront sensor (WFS). When observing extended sources, WFS precision is limited by anisoplanatism effects. Anisoplanatism induces a variation of the turbulent phase and of the collected flux in the field of view. We study the effect of this phase and scintillation anisoplanatism on wavefront analysis. An analytical expression of the error induced is given in the Rytov regime. The formalism is applied to a solar and an endoatmospheric observation. Scintillation effects are generally disregarded, especially in astronomical conditions. We shall prove that this approximation is not valid with extended objects.     

Two-dimensional radiographic imaging analysis

Two-dimensional imaging properties of locally isotropic and isoplanatic point spread functions are described in a general radiographic context. In particular, the radiographic response to a two-dimensional wedge-shaped object is shown to possess several properties which enable the identification of the wedge corner on the image, thereby alleviating the need for image enhancement techniques. Extensions to the location of flat-edged boundaries are also discussed. The potential dimensioning application of this analysis lies in the precise and objective location of points of interest on radiographs of more complex two-dimensional objects.     

Rainbow scattering by a coated sphere

We examine the behavior of the first-order rainbow for a coated sphere by using both ray theory and Aden-Kerker wave theory as the radius of the core a(12) and the thickness of the coating δ are varied. As the ratio δ/a(12) increases from 10(-4) to 0.33, we find three classes of rainbow phenomena that cannot occur for a homogeneous-sphere rainbow. For δ/a(12) ? 10(-3), the rainbow intensity is an oscillatory function of the coating thickness, for δ/a(12) ≈ 10(-2), the first-order rainbow breaks into a pair of twin rainbows, and for δ/a(12) ≈ 0.33, various rainbow-extinction transitions occur. Each of these effects is analyzed, and their physical interpretations are given. A Debye series decomposition of coated-sphere partial-wave scattering amplitudes is also performed and aids in the analysis.     

凤凰木种子毒蛋白的高效液相色谱研究

本文介绍用HPGFC对凤凰木种子中提取的三种毒蛋白分别进行色谱分析。并对分离的蛋白峰进行紫外光谱扫描来确认蛋白的纯度。根据标准分子量曲线,分别得到它们的分子量并与SDS-PAGF所得分子量进行比较,用柱后衍生法测定了三个蛋白各自的氨基酸组成。     

System design considerations to improve isoplanatism for adaptive optics retinal imaging

Adaptive optics (AO) retinal images are limited by anisoplanatism; wavefront shape varies across the field of view such that only a limited area can achieve diffraction-limited image quality at one time. We explored three alternative AO modalities designed to reduce this effect, drawn from work in astronomy. Optical design analysis and computer modeling was undertaken to predict the benefit of each modality for various schematic eyes and various complexities of the imaging system. Off-axis performance was found to be limited by system parameters and not by the eye itself, due to the inherent off-axis characteristics of the eye's gradient index lens. This rendered the alternative AO modalities ineffectual compared with conventional AO but did suggest several methods by which anisoplanatism may be reduced by altering the design of conventional AO systems. Several of these design possibilities were explored with further modeling. The best-performing method involved the replacement of system lenses with gradient index versions inspired by the human eye lens. Mirror-based relay optics also demonstrated good off-axis performance, but their advantage was lost in regions of the system suffering from uncorrected higher-order aberration. Incorporating "off-the-plane" beam deviations ameliorated this loss substantially. In this work we also show, to our knowledge for the first time, that the ideal location of a single AO corrector need not lie in the pupil plane.     

Bootstrap beacon creation for overcoming the effects of beacon anisoplanatism in a laser beam projection system

We address the problem of using adaptive optics to deliver power from an airborne laser platform to a ground target through atmospheric turbulence under conditions of strong scintillation and anisoplanatism. We explore three options for creating a beacon for use in adaptive optics beam control: scattering laser energy from the target, using a single uncompensated Rayleigh beacon, and using a series of compensated Rayleigh beacons. We demonstrate that using a series of compensated Rayleigh beacons distributed along the path provides the best beam compensation.     

Wave Theory for a Simple Lens

A new wave theory describing image formation by a simple lens is formulated in the angular spectrum representation. It is closely related to Luneburg's theory of instrumental optics but is free of certain geometrical approximations made in his theory. The validity of Luneburg's essentially geometrical treatment of the lens aperture is discussed and the approximations involved are found to be justified for isoplanatic optical systems with small numerical aperture. Some concepts usually found in lens theories based on geometrical optics are seen to have analogues in the present wave theory. In particular, a connection is made between homogeneous plane waves in an angular spectrum expansion of the field and the light rays belonging to a family of rays that pass through the lens. The fundamental relations assumed in Fourier optics are shown to follow from this theory when they are applied to the special case of isoplanatic optical systems with small numerical aperture. The image field of a scalar dipole formed by a diffraction-limited lens is calculated using these results.     

Measurement of Surface Topography,Packing Density,and Surface Charge Distribution of an Electrostatically Deposited Powder Layer by Image Analysis of Fluorescent Latex Spheres

A novel method of nonintrusive measurement of surface profile, packing density, and surface charge distributions of a powder layer deposited on a substrate is reported. The method employs the deposition of electrostatically charged monodispersed fluorescent latex spheres (FLS), approximately 2 m in diameter, on the surface of: (1) the substrate before deposition, (2) the powder layer after deposition, and (3) the film formed by curing the powder layer. The surface topography in all cases was mapped using an epi-fluorescent microscope with a vertical resolution of - 2 m in the z axis and - 10 m in the x and y axes. An area of 1 cm 2 1 cm is scanned in 1 mm segments, providing approximately 100 data points per cm 2 for the surface topography. For each measurement of surface topography, the substrate was positioned on the microscope stage in a manner such that the reference points (x, y, and z) remained the same for all measurements of the substrate. The surface profiles, with respect to the same reference points, were plotted using Origin 6.0 software for 3D presentation of the topography. The method was also applied to map the surface charge density distribution of electrostatically charged surfaces. The FLS imaging method provides a new tool for examination of surface profiles, packing density, and charge distribution of powder layers on a microscopic scale not provided by optical or atomic force/electrostatic force microscopy (AFM/EFM). While AFM and EFM are very effective in providing similar information with nanometer resolution, they cannot be directly applied on a larger macroscopic scale to study powder layers and for a larger surface area (up to 1 cm 2 or greater) involving deposited particles in the range of 1-50 m in diameter. For AFM, the range in the z-axis is limited to - 3 m and the x-y scan area is limited to 100 m 2 100 m. The FLS method has a much wider range but it is operated manually; an automated scanning process is required for rapid measurement. A comparison of the FLS and EFM techniques as they apply to analyzing charge distribution on coal surfaces is presented.