Numerical simulations of multiconjugate adaptive optics wave-front reconstruction on giant telescopes

We present sample Monte Carlo simulation results to illustrate the trends in multiconjugate adaptive optics (MCAO) performance as the telescope aperture diameter increases from 8 to 32 m with all other first-order system parameters held constant. The MCAO system considered includes three deformable mirrors, a 1-arc min square field of view, and five wave-front-sensing references consisting of either natural guide stars or laser guide stars at a range of either 30 or 90 km. The rms residual wave-front error decreases slowly with increasing aperture diameter with natural guide stars, whereas performance degrades significantly with increasing aperture diameter for laser guide stars at 30 km if the number of guide stars is held fixed. Performance with laser guide stars at 90 km is a weak function of telescope aperture diameter in the range from 8 to 32 m, with rms wave-front errors no more than 20% greater than the corresponding natural guide-star case for the same level of wave-front sensor's measurement noise.     

Sky coverage estimates for adaptive optics systems from computations in Zernike space

A sky coverage model for laser guide star adaptive optics systems is proposed. The atmosphere is considered to consist of a finite number of phase screens, which are defined by Zernike basis polynomials, located at different altitudes. These phase screens are transformed to the aperture plane, where they are converted to laser and natural guide star wavefront sensing measurements. These transformations incorporate the cone effect due to guide stars at finite heights, anisoplanatism due to guide stars off axis with respect to the science object, and adaptive optics systems with multiple guide stars. The wavefront error is calculated tomographically with minimum variance estimators derived from the transformation matrices and the known statistical properties of the atmosphere. This sky coverage model provides fast Monte Carlo simulations over random natural guide star configurations, irrespective of telescope diameter. The Monte Carlo simulations outlined show that inclusion of a finite outer scale for the atmosphere significantly reduces the median wavefront error, that increasing the number of laser guide stars in the asterism reduces the median wavefront error, and that a larger natural guide star patrol field provides a smaller median wavefront error when there is a low star density in the field.     

Shack-Hartmann wavefront sensing with elongated sodium laser beacons: centroiding versus matched filtering

We describe modeling and simulation results for the Thirty Meter Telescope on the degradation of sodium laser guide star Shack-Hartmann wavefront sensor measurement accuracy that will occur due to the spatial structure and temporal variations of the mesospheric sodium layer. By using a contiguous set of lidar measurements of the sodium profile, the performance of a standard centroid and of a more refined noise-optimal matched filter spot position estimation algorithm is analyzed and compared for a nominal mean signal level equal to 1000 photodetected electrons per subaperture per integration time, as a function of subaperture to laser launch telescope distance and CCD pixel readout noise. Both algorithms are compared in terms of their rms spot position estimation error due to noise, their associated wavefront error when implemented on the Thirty Meter Telescope facility adaptive optics system, their linear dynamic range, and their bias when detuned from the current sodium profile.     

Centroid gain compensation in Shack-Hartmann adaptive optics systems with natural or laser guide star

In an adaptive optics system with an undersampled Shack-Hartmann wave-front sensor (WFS), variations in seeing, laser guide star quality, and sodium layer thickness and range distance all combine to vary WFS centroid gain across the pupil during an exposure. While using the minimum of 4 pixels per WFS subaperture improves frame rate and read noise, the WFS centroid gain uncertainty may introduce static aberrations and degrade servo loop phase margin. We present a novel method to estimate and compensate WFS gains of each subaperture individually in real time for both natural and laser guide stars.     

Tilt Estimation in Moderate-to-Strong Scintillation

Adaptive optics systems are being applied in ever more challenging environments, for example, the projection of lasers over long horizontal paths through the atmosphere. These long atmospheric paths corrupt the signal received from the beacon and typically yield highly scintillated received wave fronts. Tilt estimation for controlling the fast steering mirror in these systems is complicated by the presence of branch points in the scintillated received wave fronts. In particular, correlation between the tilt and the projected beam's centroid error at the target has been observed in horizontal laser beam projection experiments. The presence of this correlation indicates that better tracking performance should be achievable. We compare the performance of four estimation schemes applied to tilt estimation in a horizontal laser projection system. It is demonstrated that all four schemes underestimate the tilt required to return the laser beam to a target in highly scintillated environments. A method of correcting this tilt is presented, and the expected performance improvement is quantified.     

Effect of wavefront corrugations on fringe motion in an astronomical interferometer with spatial filters

Numerical simulations of atmospheric turbulence and adaptive optics (AO) wavefront correction are performed to investigate the time scale for fringe motion in optical interferometers with spatial filters. These simulations focus especially on partial AO correction, where only a finite number of Zernike modes are compensated. The fringe motion is found to depend strongly on both the aperture diameter and the level of AO correction used. In all the simulations the coherence time scale for interference fringes is found to decrease dramatically when the Strehl ratio provided by the AO correction is < or = 30%. For AO systems that give perfect compensation of a limited number of Zernike modes, the aperture size that gives the optimum signal for fringe phase tracking is calculated. For AO systems that provide noisy compensation of Zernike modes (but are perfectly piston neutral), the noise properties of the AO system determine the coherence time scale of the fringes when the Strehl ratio is < or = 30%.     

Modal compensation and the atmospheric-turbulence outer scale: computer simulations

The influence of the turbulence outer scale on the Strehl ratio obtained with low-order adaptive optics systems is examined by numerical simulation. The Karhunen-Loeve approach is used to generate wave-front samples. A method that allows construction of the outer-scale-dependent Karhunen-Loeve functions is described. It is shown that the Strehl ratio produced by a second-order adaptive optics correction (tip-tilt, defocus, and astigmatism) is affected quite strongly by the finite outer scale. For the higher-order correction, the effect under study is weak and appears only when the outer-scale magnitude becomes less than the aperture diameter. It is also shown that the finite outer scale has a positive effect on the Strehl ratio of the uncorrected long-exposure image.     

Binary phase-only filtering for turbulence compensation in fiber-coupled free-space laser communication systems

Binary wavefront control in the focal plane (i.e., binary phase-only filtering) for partial compensation of atmospheric turbulence in fiber-coupled free-space laser communication systems is investigated. Numerical results from wave-optics simulations show that in an air-to-air scenario, the combination of binary phase-only filtering and centroid tracking provides mean fiber coupling efficiency close to that resulting from ideal least-squares adaptive optics, but without the requirement for direct wavefront sensing. This result suggests a simpler and less computationally demanding turbulence mitigation system that is more readily applied to tactical applications.     

Horizontal Line-of-Sight Turbulence Over Near-Ground Paths and Implications for Adaptive Optics Corrections in Laser Communications

Atmospheric turbulence over long horizontal paths perturbs phase and can also cause severe intensity scintillation in the pupil of an optical communications receiver, which limits the data rate over which intensity-based modulation schemes can operate. The feasibility of using low-order adaptive optics by applying phase-only corrections over horizontal propagation paths is investigated. A Shack-Hartmann wave-front sensor was built and data were gathered on paths 1 m above ground and between a 1- and 2.5-km range. Both intensity fluctuations and optical path fluctuation statistics were gathered within a single frame, and the wave-front reconstructor was modified to allow for scintillated data. The temporal power spectral density for various Zernike polynomial modes was used to determine the effects of the expected corrections by adaptive optics. The slopes of the inertial subrange of turbulence were found to be less than predicted by Kolmogorov theory with an infinite outer scale, and the distribution of variance explained by increasing order was also found to be different. Statistical analysis of these data in the 1-km range indicates that at communications wavelengths of 1.3 mum, a significant improvement in transmitted beam quality could be expected most of the time, to a performance of 10% Strehl ratio or better.     

Adaptive optics technique to overcome the turbulence in a large-aperture collimator

A collimator with a long focal length and large aperture is a very important apparatus for testing large-aperture optical systems. But it suffers from internal air turbulence, which may limit its performance and reduce the testing accuracy. To overcome this problem, an adaptive optics system is introduced to compensate for the turbulence. This system includes a liquid crystal on silicon device as a wavefront corrector and a Shack-Hartmann wavefront sensor. After correction, we can get a plane wavefront with rms of about 0.017 lambda (lambda=0.6328 microm) emitted out of a larger than 500 mm diameter aperture. The whole system reaches diffraction-limited resolution.     

Level crossing statistics for optical beam wander in a turbulent atmosphere with applications to ground-to-space laser communications

Level crossing statistics is applied to the complex problem of atmospheric turbulence-induced beam wander for laser propagation from ground to space. A comprehensive estimate of the single-axis wander angle temporal autocorrelation function and the corresponding power spectrum is used to develop, for the first time to our knowledge, analytic expressions for the mean angular level crossing rate and the mean duration of such crossings. These results are based on an extension and generalization of a previous seminal analysis of the beam wander variance by Klyatskin and Kon. In the geometrical optics limit, we obtain an expression for the beam wander variance that is valid for both an arbitrarily shaped initial beam profile and transmitting aperture. It is shown that beam wander can disrupt bidirectional ground-to-space laser communication systems whose small apertures do not require adaptive optics to deliver uniform beams at their intended target receivers in space. The magnitude and rate of beam wander is estimated for turbulence profiles enveloping some practical laser communication deployment options and suggesting what level of beam wander effects must be mitigated to demonstrate effective bidirectional laser communication systems.     

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.     

Hot-air optical turbulence generator for the testing of adaptive optics systems: principles and characterization

A statistically repeatable, hot-air optical turbulence generator, based on the forced mixing of two air flows with different temperatures, is described. Characterization results show that it is possible to generate any turbulence strength up to CN2 Dh approximately 6 x 10(-10) m1/3, allowing a ratio of beam diameter to Fried's parameter as large as D/r0 approximately 25 for one crossing through the turbulator or D/r0 approximately 38 for two crossings. The outer scale (L0 approximately 133 +/- 60 mm) is found to be compatible with the turbulator mixing chamber size (170 mm), and the inner scale (l0 approximately 7.6 +/- 3.8 mm) is compatible with the values in the literature for the free atmosphere. The temporal power spectrum analysis of the centroid of the focused image shows good agreement with Kolmogorov's theory. Therefore the device can be used with confidence to emulate realistic turbulence in a controlled manner. A calibrated CN2 profile, both in layer altitude and strength, is necessary for the testing of off-axis adaptive optics correction (multiconjugate adaptive optics). Testing was done to calibrate the CN2 profile using the slope detection and ranging technique. The first results, with only one layer, show the validity of the approach and indicate that a multiple-pass scheme is viable with a few modifications of the current setup.     

Sky coverage modeling for the whole sky for laser guide star multiconjugate adaptive optics

The scientific productivity of laser guide star adaptive optics systems strongly depends on the sky coverage, which describes the probability of finding natural guide stars for the tip/tilt wavefront sensor(s) to achieve a certain performance. Knowledge of the sky coverage is also important for astronomers planning their observations. In this paper, we present an efficient method to compute the sky coverage for the laser guide star multiconjugate adaptive optics system, the Narrow Field Infrared Adaptive Optics System (NFIRAOS), being designed for the Thirty Meter Telescope project. We show that NFIRAOS can achieve more than 70% sky coverage over most of the accessible sky with the requirement of 191 nm total rms wavefront.     

Multilateration with the wide-angle airborne laser ranging system: positioning precision and atmospheric effects

Numerical simulations based on previously validated models for the wide-angle airborne laser ranging system are used here for assessing the precision in coordinate estimates of ground-based cube-corner retroreflectors (CCR's). It is shown that the precision can be optimized to first order as a function of instrument performance, number of laser shots (LS's), and network size. Laser beam divergence, aircraft altitude, and CCR density are only second-order parameters, provided that the number of echoes per LS is greater than 20. Thus precision in the vertical is ~1 mm, with a signal-to-noise ratio of 50 at nadir, a 10-km altitude, a 20 degrees beam divergence, and ~5 x 10(3) measurements. Scintillation and fair-weather cumulus clouds usually have negligible influence on the estimates. Laser biases and path delay are compensated for by adjustment of aircraft offsets. The predominant atmospheric effect is with mesoscale nonuniform horizontal temperature gradients, which might lead to biases near 0.5 mm.     

Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction

We introduce a multigrid preconditioned conjugate-gradient (MGCG) iterative scheme for computing open-loop wave-front reconstructors for extreme adaptive optics systems. We present numerical simulations for a 17-m class telescope with n = 48756 sensor measurement grid points within the aperture, which indicate that our MGCG method has a rapid convergence rate for a wide range of subaperture average slope measurement signal-to-noise ratios. The total computational cost is of order n log n. Hence our scheme provides for fast wave-front simulation and control in large-scale adaptive optics systems.     

Adaptive optics and ground-to-space laser communications

The relationships between laser communication system parameters and adaptive optics system parameters are addressed. Improvement in optical signal propagation between space-based receivers and ground-based transmitters is possible with adaptive optics systems that compensate for a few degrees of freedom. Beginning with the relationship between optical signal fade and surge and the atmospheric log-amplitude variance and coupling to expressions that combine adaptive optics systems performance with the reduction in log-amplitude variance, system level examinations of the effects of adaptive optics can be done. Examples are given that show the advantageous reduction in signal fade and surge when adaptive optics are built into the optical system.     

Adaptive control in an adaptive optics experiment

This paper presents results from an adaptive optics experiment in which an adaptive control loop augments a classical adaptive optics feedback loop. Closed-loop wavefront errors measured by a self-referencing interferometer are fed back to the control loops, which drive a membrane deformable mirror to correct the wavefront. The paper introduces new frequency-weighted deformable mirror modes used as the control channels and new wavefront sensor modes for analyzing the performance of the control loops. The corrected laser beam also is imaged by a diagnostic target camera. The experimental results show reduced closed-loop wavefront errors and correspondingly sharper diagnostic target images produced by the adaptive control loop as compared with the classical AO loop.     

激光大气传输光斑统计概率接收孔径效应

本文综合考虑湍流大气对激光斑纹强度、光束传输方向的调制作用和有限接收孔径的光强起伏、相位起伏平滑作用等因素,从理论上研究了激光斑纹强度、相位起伏概率密度函数和孔径平滑作用,求得了高阶强度矩的孔径平滑因子。     

Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm

To achieve its full diffraction limit in the infrared, the primary mirror of the Keck telescope (now telescopes) must be properly phased: The steps or piston errors between the individual mirror segments must be reduced to less than 100 nm. We accomplish this with a wave optics variation of the Shack-Hartmann test, in which the signal is not the centroid but rather the degree of coherence of the individual subimages. Using filters with a variety of coherence lengths, we can capture segments with initial piston errors as large as +/-30 microm and reduce these to 30 nm--a dynamic range of 3 orders of magnitude. Segment aberrations contribute substantially to the residual errors of approximately 75 nm.