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.     

Approach for reconstructing anisoplanatic adaptive optics images

Atmospheric turbulence corrupts astronomical images formed by ground-based telescopes. Adaptive optics systems allow the effects of turbulence-induced aberrations to be reduced for a narrow field of view corresponding approximately to the isoplanatic angle theta(0). For field angles larger than theta(0), the point spread function (PSF) gradually degrades as the field angle increases. We present a technique to estimate the PSF of an adaptive optics telescope as function of the field angle, and use this information in a space-varying image reconstruction technique. Simulated anisoplanatic intensity images of a star field are reconstructed by means of a block-processing method using the predicted local PSF. Two methods for image recovery are used: matrix inversion with Tikhonov regularization, and the Lucy-Richardson algorithm. Image reconstruction results obtained using the space-varying predicted PSF are compared to space invariant deconvolution results obtained using the on-axis PSF. The anisoplanatic reconstruction technique using the predicted PSF provides a significant improvement of the mean squared error between the reconstructed image and the object compared to the deconvolution performed using the on-axis PSF.     

大尺度二维直线度测量仪的研制

研制出一种新的基于离轴成像技术的远距离、大范围二维直线度测量仪。仪器的直线基准为整形的十字线激光光束,光电二维位置敏感元件采用互相正交的线阵CCD,所设计的带有狭缝的离轴光学系统,避开激光十字线光束的能量中心,以使线阵CCD输出信号不会出现饱和现像,从而扩大了测量距离,保证了测量精度。该仪器能在0-20m测量范围连续测量二维直线度,其直线度可达0-70mm,精度优于0.1mm。实际的多次室外环境测量表明,该仪器可适应不同天气环境下的野外作业。     

Design of a compact off-axis two-mirror freeform infrared imager with a wide field of view

With the development of modern precision optical fabrication and measurement technologies, optical freeform surfaces have been widely employed in different applications, especially in off-axis reflective optical systems. For an infrared optical system operating in the long-wavelength spectrum, compactness, brightness, and a wide field of view are key requirements for military surveillance or scene sensing. In this paper, we present an off-axis two-mirror freeform infrared imager with compactness and brightness. It has a large pupil of size 12?mm and a fast focal ratio of 2.2 over a wide 23° diagonal field of view, as well as good image quality. XY-polynomial freeform surfaces are applied to the viewing mirror and focusing mirror. The multiple degrees of freedom of optical freeform surfaces are very helpful for off-axis aberration correction and improving the optical performance over the entire pupil across the full field of view. The overall dimension of our designed freeform infrared imager is about 30?mm by 30?mm by 30?mm, which is elegantly miniaturized. The final designed results of a reflective freeform infrared imager are demonstrated and discussed in detail.     

Michelson wide-field stellar interferometry: principles and experimental verification

A new interferometric technique for Michelson wide-field interferometry is presented that consists of a Michelson pupil-plane combination scheme in which a wide field of view can be achieved in one shot. This technique uses a stair-shaped mirror in the intermediate image plane of each telescope in the array, allowing for simultaneous correction of the differential delay for the on-axis and off-axis image positions. Experimental results in a laboratory setup show that it is possible to recover the fringes of on-axis and off-axis stars with an angular separation of 1 arc min simultaneously and with a similar contrast. This new technique represents a considerable extension of the field of view of an interferometer without the need for extra observation time.     

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.     

Adaptive-optics performance of Antarctic telescopes

The performance of natural guide star adaptive-optics systems for telescopes located on the Antarctic plateau is evaluated and compared with adaptive-optics systems operated with the characteristic mid-latitude atmosphere found at Mauna Kea. A 2-m telescope with tip-tilt correction and an 8-m telescope equipped with a high-order adaptive-optics system are considered. Because of the large isoplanatic angle of the South Pole atmosphere, the anisoplanatic error associated with an adaptive-optics correction is negligible, and the achievable resolution is determined only by the fitting error associated with the number of corrected wave-front modes, which depends on the number of actuators on the deformable mirror. The usable field of view of an adaptive-optics equipped Antarctic telescope is thus orders of magnitude larger than for a similar telescope located at a mid-latitude site; this large field of view obviates the necessity for multiconjugate adaptive-optics systems that use multiple laser guide stars. These results, combined with the low infrared sky backgrounds, indicate that the Antarctic plateau is the best site on Earth at which to perform high-resolution imaging with large telescopes, either over large fields of view or with appreciable sky coverage. Preliminary site-testing results obtained recently from the Dome Concordia station indicate that this site is far superior to even the South Pole.     

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.     

Off-axis detection and characterization of laser beams in the maritime atmosphere

Remote detection and characterization of laser beams propagating in maritime atmospheres is discussed. A model for off-axis scattered laser light based on Mie scattering from maritime aerosols is presented and compared with angle and time-resolved measurements from a pulsed laser source. We demonstrate that the direction of the source can be determined from the angle-resolved intensity and that the beam direction can be determined from arrival times of the scattered signals if the position of the laser source is known.     

Prediction of wave-front sensor slope measurements with artificial neural networks

For adaptive optical systems to compensate for atmospheric turbulence effects, the wave-front perturbation must be measured with a wave-front sensor (WFS) and corrected with a deformable mirror. One limitation in this process is the time delay between the measurement of the aberrated wave front and implementation of the proper correction. Statistical techniques exist for predicting the atmospheric aberrations at the time of correction based on the present and past measured wave fronts. However, for the statistical techniques to be effective, key parameters of the atmosphere and the adaptive optical system must be known. These parameters include the Fried coherence length r(0), the atmospheric wind-speed profile, and the WFS slope measurement error. Neural networks provide nonlinear solutions to adaptive optical problems while offering the possibility to function under changing seeing conditions without actual knowledge of the current state of the key parameters. We address the use of neural networks for WFS slope measurement prediction with only the noisy WFS measurements as inputs. Where appropriate, we compare with classical statistical-based methods to determine if neural networks offer true benefits in performance.     

Exact ray-trace beam for an off-axis paraboloid surface

When an off-axis paraboloidal mirror focuses a parallel beam, the image is formed on one side of the optical axis. For a tilted beam focused by an off-axis paraboloidal mirror, the focus is no longer pointlike (not considering the diffraction effect); rather, it is a distorted spot. This is due to the inherent aberrations of the surface. In addition, there is a change in the focus position. We calculate by exact ray-trace equations the modified wave-front aberration and express it in power series. Our formulation uses the optical path variation along a defined principal ray that we relate to the parameter that describe the surface and the beam angle of incidence. We designate this ray as that reflected by the center of the entrance pupil and field of view. We employ the direction cosines of the principal ray to compute the wave-front aberration function of a beam reflected by an off-axis paraboloid.     

Optical control of the Advanced Technology Solar Telescope

The Advanced Technology Solar Telescope (ATST) is an off-axis Gregorian astronomical telescope design. The ATST is expected to be subject to thermal and gravitational effects that result in misalignments of its mirrors and warping of its primary mirror. These effects require active, closed-loop correction to maintain its as-designed diffraction-limited optical performance. The simulation and modeling of the ATST with a closed-loop correction strategy are presented. The correction strategy is derived from the linear mathematical properties of two Jacobian, or influence, matrices that map the ATST rigid-body (RB) misalignments and primary mirror figure errors to wavefront sensor (WFS) measurements. The two Jacobian matrices also quantify the sensitivities of the ATST to RB and primary mirror figure perturbations. The modeled active correction strategy results in a decrease of the rms wavefront error averaged over the field of view (FOV) from 500 to 19 nm, subject to 10 nm rms WFS noise. This result is obtained utilizing nine WFSs distributed in the FOV with a 300 nm rms astigmatism figure error on the primary mirror. Correction of the ATST RB perturbations is demonstrated for an optimum subset of three WFSs with corrections improving the ATST rms wavefront error from 340 to 17.8 nm. In addition to the active correction of the ATST, an analytically robust sensitivity analysis that can be generally extended to a wider class of optical systems is presented.     

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.     

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.     

A method for single image restoration based on the principal ergodic

We present a method to extract from a single image both object and point spread function using low contrast features of an extended field of view. Invoking the principal ergodic on stochastic turbulent phenomena, we show that the aberration parameters, characteristics of the earth's turbulence, can be recovered from multiple features within an isoplanatic patch. The ensemble statistics is replacing the spatial statistics of a single realization to derive an equivalent modulation transfer function and to apply usual deconvolution techniques such as Richardson-Lucy algorithms. The reliability of this postprocessing treatment has been tested on synthetic data, on solar granulation observations performed at La Lunette Jean Rosch du Pic du Midi, and during the event of the Venus transit at La Tour Solaire de Meudon.     

基于图像处理的超声探头声场测量

在超声无损探测中,探头的性能好坏直接制约着整个检测系统的性能。论文以超声探头的声场特性为研究对象：首先建立探头的声场特性参数体系,然后采用球靶法进行C扫描成像,接着对声场图像进行预处理及二值化、边缘检测及特征提取,获得探头的近场长度、孔径大小和声束半扩散角等性能参数,根据实际检测的声场参数来指导超声无损检测。最后通过实验来验证了该方法的有效性。     

Hybrid digital holographic imaging system for three-dimensional dense particle field measurement

To apply digital holography to the measurement of three-dimensional dense particle fields in large facilities, we have developed a hybrid digital holographic particle-imaging system. The technique combines the advantages of off-axis (side) scattering in suppressing speckle noise and on-axis (in-line) recording in lowering the digital sensor resolution requirement. A camera lens is attached to the digital sensor to compensate for the weak object wave from side scattering over a large recording distance. A simple numerical reconstruction algorithm is developed for holograms recorded with a lens without requiring complex and impractical mathematical corrections. We analyze the effect of image sensor resolution and off-axis angle on system performance and quantify the particle positioning accuracy of the system. The holographic system is successfully applied to the study of inertial particle clustering in isotropic turbulence.     

Lateral scanning white-light interferometer

White-light vertical scanning interferometry is a well-established technique for retrieving the three-dimensional shapes of small objects, but it can measure only areas as big as the field of view of the instrument. For bigger fields a stitching algorithm must be applied, which often can be a source of errors. A technique in which the object is scanned laterally in front of an instrument with a tilted coherence plane is described. It permits measurements at higher speeds while measurement accuracy is retained and eliminates the need for stitching in one direction. Experimental confirmation is provided.     

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.     

Off-axis notched strength of fiber–metal laminates and a formula for predicting anisotropic size effect

Experimental and theoretical studies of the effects of notch size and fiber orientation on the off-axis notched strength of the fiber–metal laminate GLARE-3 have been conducted. The notched strength decreased with increasing notch size, regardless of the fiber orientation. The notch sensitivity in GLARE-3 was highest in the fiber direction, and it decreased with increasing fiber orientation angle to the lowest in the 45° direction. A new multiaxial criterion for the tensile failure of notched orthotropic fiber composites was developed from a phenomenological point of view. From the proposed multiaxial failure criterion, an anisotropic size effect law for predicting the off-axis notched strength of orthotropic composite laminates was derived. By comparison with the experimental results on GLARE-3, it was demonstrated that the anisotropic size effect law can accurately and efficiently predict the off-axis notched strength of GLARE-3, regardless of the notch size and fiber orientation.