Adaptive-optics compensation by distributed beacons for non-kolmogorov turbulence

In optical propagation through atmospheric turbulence, the performance of compensation with adaptive optics depends on a beacon's spatial distribution. With distributed beacons, the inefficiency of the modal correction, which is defined as the ratio of the anisoplanatic error of the jth mode and the Zernike-coefficient variance, is derived by use of the wave-front expansion on the Zernike polynomials for non-Kolmogorov turbulence. Numerical results are presented for laser beam propagation through constant turbulence with an offset point beacon and an on-axis uniform circular beacon. The results show that compensation for an on-axis uniform circular beacon is much more effective than that for an offset point beacon. The low-order modes are much more correlated than the higher-order modes. The larger the power-law exponent of the refractive-index power spectrum beta, the smaller the propagation path length L and the larger the diameter D of the telescope aperture, the more effective the compensation is. For a specific extended degree of beacon for which there are a maximum number of modes N(max) to be corrected, only low-order-correction systems are useful.     

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.     

Tilt angular anisoplanatism and a full-aperture tilt-measurement technique with a laser guide star

A method is presented for sensing atmospheric wave-front tilt from a laser guide star (LGS) by observing a laser beacon with auxiliary telescopes. The analysis is performed with a LGS scatter model and Zernike polynomial expansion of wave-front distortions. It is shown that integration of the LGS image over its angular extent and the position of the auxiliary telescope in an array reduce the tilt sensing error associated with the contribution from the downward path. This allows us to single out only the wave-front tilt of the transmitted beam on the uplink path that corresponds to the tilt for the scientific object. The tilt angular correlation is analyzed in the atmosphere with a finite turbulence outer scale. The tilt correlation angle depends on the angular size of the telescope and the outer scale of turbulence. The tilt sensing error increases with the auxiliary telescope diameter, suggesting that an auxiliary telescope must be small. The Strehl ratio associated with the contribution from the downward path is in the range from 0.1 to 0.9 when the relative telescope diameter D/r(0) varies from 4 to 93 and the turbulence outer scale is in the 10-150-m range. Tilt correction increases the Strehl ratio compared with the uncorrected image for all the system parameters and seeing conditions considered. The method discussed gives a higher performance than the conventional technique, which uses an off-axis natural guide star. A scheme for measuring tilt with a beam projected from a small aperture is described. This scheme allows us to avoid phosphorescence of the main optical train for a sodium LGS.     

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.     

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.     

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.     

Spectrometer slit-power-coupling calculations for natural and laser guide-star adaptive optics

We use numerical calculations to examine the relation between adaptive optics (AO) turbulence compensation and power coupled through a spectrometer slit for both laser and natural guide-star AO systems. The AO system and observing parameters used are relevant to the Gemini-North 8-m telescope. For this study, we separate residual tilt from residual higher-order aberrations to isolate their relative effects under a variety of operating conditions. Our results demonstrate that slit-coupled intensity is not uniquely determined by system Strehl alone; we show that this is due to the differing effects of higher-order and tilt aberrations on the shape of the compensated point-spread function. For the Gemini spectrometer and AO system, the wider point-spread function halo associated with an added residual higher-order aberration reduces slit-coupled intensity more rapidly than a broad point-spread function core induced by residual tilt.     

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.     

Photometric observations of a polychromatic laser guide star

We report the photometric observation of a polychromatic laser guide star (PLGS) using the AVLIS laser at the Lawrence Livermore National Laboratory (LLNL). The process aims at providing a measurement of the tilt of the incoming wave front at a telescope induced by atmospheric turbulence. It relies on the two-photon coherent excitation of the 4D5/2 energy level of sodium atoms in the mesosphere. We used two laser beams at 589 and 569 nm, with a maximum total average output power of approximately 350 W. For the purpose of photometric calibration, a natural star was observed simultaneously through the same instrument as the PLGS at the focus of the LLNL 50-cm telescope. Photometric measurements of the 330-nm return flux confirm our previous theoretical studies that the PLGS process should allow us at a later stage to correct for the tilt at wavelengths as short as approximately 1 microm at good astronomical sites. They show also that, at saturation of two-photon coherent absorption in the mesosphere, the backscattered flux increases by a factor of approximately 2 when the pulse repetition rate decreases by a factor of 3 at constant average power. This unexpected behavior is briefly discussed.     

Adaptive beam shaping by controlled thermal lensing in optical elements

We describe an adaptive optical system for use as a tunable focusing element. The system provides adaptive beam shaping via controlled thermal lensing in the optical elements. The system is agile, remotely controllable, touch free, and vacuum compatible; it offers a wide dynamic range, aberration-free focal length tuning, and can provide both positive and negative lensing effects. Focusing is obtained through dynamic heating of an optical element by an external pump beam. The system is especially suitable for use in interferometric gravitational wave interferometers employing high laser power, allowing for in situ control of the laser modal properties and compensation for thermal lensing of the primary laser. Using CO(2) laser heating of fused-silica substrates, we demonstrate a focal length variable from infinity to 4.0 m, with a slope of 0.082 diopter/W of absorbed heat. For on-axis operation, no higher-order modes are introduced by the adaptive optical element. Theoretical modeling of the induced optical path change and predicted thermal lens agrees well with measurement.     

Self-referenced interferometry for the characterization of axicon lens quality

A simple interferometer for the characterization of axicon lenses is presented. The phase cone acquired by a wave propagating through an axicon, when interfered with a collinear reference wave, produces a nearly cylindrically symmetric self-referenced interference pattern from which the distortions of the axicon surface may be readily obtained. Comparison with two-dimensional off-axis interferometry is used to validate the self-referenced technique. The measurements are based on retrieval of the accrued spatial phase distribution from interference fringes with on- and off-axis reference beams and are found to be equivalent. We use the ellipticity of the phase maps to qualify axicon lenses, which are expected to exhibit radial symmetry and engage the self-referential capability of the on-axis method to derive deviation maps that characterize the surface quality of the axicons.     

Modal properties of an external diode-laser-array cavity with diffractive mode-selecting mirrors

Coupled mode theory is used to describe the behavior of an external laser cavity consisting of a diode laser array and a diffractive mode-selecting mirror. The mirror is designed to establish a uniform-amplitude, uniform-phase fundamental mode. Coupled mode theory is then used to study the behavior of higher-order modes. We show that the maximum discrimination against higher-order modes occurs when the round-trip cavity length satisfies certain Talbot relations. In addition, this high modal discrimination can be maintained for arrays with large numbers of lasers without incurring significant loss in the fundamental mode.     

Tip-tilt reconstruction with a single dim natural guide star in multiconjugate adaptive optics with laser guide stars

A solution to the problem of detecting the tip-tilt modes in multiconjugate adaptive optics (MCAO) with laser guide stars (LGS) is presented. This solution requires the presence of only a single relatively dim natural guide star (NGS) within the reconstructed field of view (FoV). The dim NGS is used for the reconstruction of the tip-tilt modes on the entire FoV, while the tomographic reconstruction of second-order and higher-order modes is made possible by having an LGS constellation with LGSs at different heights. Due to the relatively low brightness required for the tip-tilt NGS and the large corrected FoV (as compared with the case of conventional adaptive optics) the presented solution provides a means to achieve near-diffraction-limited performance of a 10-m-class telescope in the near infrared over a large portion of the sky. Sky coverage calculations assuming median seeing conditions indicate that this technique could be applied to 75% (95%) of the sky, achieving corrections with an average Strehl ratio approximately 0.42(approximately 0.33) in the 2.2 microm K band across the 1.5' reconstructed FoV.     

Improvements in LC/Electrospray Ion Trap Mass Spectrometry Performance Using an Off-Axis Nebulizer

Charged residues from the electrospray process have been hypothesized to limit the sensitivity and dynamic range of an ion trap mass spectrometry operation. Incorporation of an off-axis nebulizer (positioned 90-95° from the sampling orifice) was found to drastically reduce the detrimental effects caused by the charged particles or droplets compared to typical on-axis nebulization configurations (spraying 10-20° from sampling orifices). The off-axis nebulizer reduced total ion currents that enter the ion trap (through the reduction of charged residues) by a factor of 5-7 while resulting in an increase of analyte [M + H](+) signal by a factor of 6 compared to an on-axis sprayer at flow rates of 20 μL/min. At higher flow rates (e.g., 800 μL/min) these enhancements are more evident. At flows greater than 200 μL/min, off-axis nebulization reduced total ion current that enters the ion trap by a factor of 30 and resulted in a factor of more than 20 increase in [M + H](+) signal relative to on-axis nebulization. Incorporation of the off-axis nebulizer improved the detection limit and precision for determination of dihydroxyvitamin D(3) in plasma compared to on-axis nebulization. The LC/MS/MS detection limits obtained for the off-axis nebulizer on the ion trap was within a factor of 2 from the detection limit determined by the triple quadrupole. The relative standard deviation of the dihydroxyvitamin D(3) determination was less than 8% for both off-axis ion trap and triple-quadrupole determinations.     

Digital holographic microscopy with sequential off-axis illumination directions based on spatial light modulator

Digital holographic microscopy (DHM) with time-sequential off-axis illumination directions can synthesize a large aperture, and thus have a higher spatial resolution than the one with on-axis illumination. In this paper, time-sequential off-axis illumination directions are generated by a spatial light modulator (SLM) in DHM, and the residual phases along different illumination directions are suppressed by using the phase compensation technique, as such the image with resolution enhancement is reconstructed. The usage of SLM enables shifting the illumination for different orientations and phase shifts without mechanical motion. The experiments have been conducted to verify the feasibility of this method on the residual phase suppression.     

Split atmospheric tomography using laser and natural guide stars

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

Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography

By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty.     

弯扭耦合层合板模态特性数值模拟与试验研究

通过不同位置采用对称偏轴铺设纤维实现层合板的弯扭耦合,利用模态试验和有限元数值模拟研究弯扭耦合层合板的振动模态特性。采用单点拾振的方法采集层合板振动数据,分析其固有频率和振型参数,研究不同耦合区域层合悬臂板的模态节线位置,并且与有限元模拟结果进行对比。提出采用模态置信因子(MAC)定量描述层合板的弯扭耦合性能的方法,实现了采用模态特性研究层合板的弯扭耦合效应。结果表明,层合板的耦合效应,在低阶模态时中部耦合板显著,而高阶模态时端部耦合板显著。     

Statistical properties of the Strehl ratio as a function of pupil diameter and level of adaptive optics correction following atmospheric propagation

The propagation of an optical beam through atmospheric turbulence produces wave-front aberrations that can reduce the power incident on an illuminated target or degrade the image of a distant target. The purpose of the work described here was to determine by computer simulation the statistical properties of the normalized on-axis intensity--defined as (D/r0)2 SR--as a function of D/r0 and the level of adaptive optics (AO) correction, where D is the telescope diameter, r0 is the Fried coherence diameter, and SR is the Strehl ratio. Plots were generated of (D/r0)2 (SR) and sigmaSR/(SR), where (SR) and sigma(SR) are the mean and standard deviation, respectively, of the SR versus D/r0 for a wide range of both modal and zonal AO correction. The level of modal correction was characterized by the number of Zernike radial modes that were corrected. The amount of zonal AO correction was quantified by the number of actuators on the deformable mirror and the resolution of the Hartmann wave-front sensor. These results can be used to determine the optimum telescope diameter, in units of r0, as a function of the AO design. For the zonal AO model, we found that maximum on-axis intensity was achieved when the telescope diameter was sized so that the actuator spacing was equal to approximately 2r0. For modal correction, we found that the optimum value of D/r0 (maximum mean on-axis intensity) was equal to 1.79Nr + 2.86, where Nr is the highest Zernike radial mode corrected.     

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.