Multiple Deformable Mirrors Research Articles

Differential optical transfer function (dOTF) broad-spectrum wavefront sensing using integral field unit spectroscopy

Context. Detecting and characterizing Earth-like exoplanets is a critical scientific goal for the next generation of telescopes. However, current direct imaging instruments are hindered by evolving noncommon path aberrations (NCPAs), which lead to persistent speckles in the images. The differential optical transfer function (dOTF) is an image-based, noniterative, and model-independent wavefront sensor that combines differential images to estimate the complex field of the pupil. Aims. Given the objective of spectrally characterizing exoplanets to discern their composition and potentially detect biosignatures, we aim to explore the integration of the dOTF sensing method with an integral field unit (IFU) spectrograph. An IFU spectrograph generates a spectral data cube that contains diverse spectral information within a single dataset. Combining these two concepts is expected to improve the efficiency with which NCPAs can be spectrally measured and characterized. Methods. This Letter presents an implementation strategy for integrating dOTF and IFU spectroscopy data, enabling estimations of the electric field at various wavelengths simultaneously. Results. This method is specifically optimized to provide the most effective combination with minimal hardware requirements. It involves the use of multiple simultaneous deformable mirror actuator displacements in conjunction with an adapted Lyot stop employing a circular variable filter. Conclusions. The dOTF wavefront sensor coupled with an IFU spectrograph promises to be rapid and efficient, capable of measuring NCPAs across the entire spectrum provided by the spectrograph. Because the combination of dOTF and IFU spectroscopy is immediately applicable, it is of potential interest for various present-day on-sky instruments, as well as future IFU-based instruments coupled to the next generation of extremely large telescopes (ELTs).

Experience with wavefront sensor and deformable mirror interfaces for wide-field adaptive optics systems

Recent advances in adaptive optics (AO) have led to the implementation of wide field-of-view AO systems. A number of wide-field AO systems are also planned for the forthcoming Extremely Large Telescopes. Such systems have multiple wavefront sensors of different types, and usually multiple deformable mirrors (DMs). Here, we report on our experience integrating cameras and DMs with the real-time control systems of two wide-field AO systems. These are CANARY, which has been operating on-sky since 2010, and DRAGON, which is a laboratory adaptive optics real-time demonstrator instrument. We detail the issues and difficulties that arose, along with the solutions we developed. We also provide recommendations for consideration when developing future wide-field AO systems.

Optimal mirror deformation for multi conjugate adaptive optics systems

Multi conjugate adaptive optics (MCAO) is a system planned for all future extremely large telescopes to compensate in real-time for the optical distortions caused by atmospheric turbulence over a wide field of view. The principles of MCAO are based on two inverse problems: a stable tomographic reconstruction of the turbulence profile followed by the optimal alignment of multiple deformable mirrors (DMs), conjugated to different altitudes in the atmosphere. We present a novel method to treat the optimal mirror deformation problem for MCAO. Contrary to the standard approach where the problem is formulated over a discrete set of optimization directions we focus on the solution of the continuous optimization problem. In the paper we study the existence and uniqueness of the solution and present a Tikhonov based regularization method. This approach gives us the flexibility to apply quadrature rules for a more sophisticated discretization scheme. Using numerical simulations in the context of the European extremely large telescope we show that our method leads to a significant improvement in the reconstruction quality over the standard approach and allows to reduce the numerical burden on the computer performing the computations.

Interferometric nulling limits with tip-tilt-piston deformable mirrors and a pinhole spatial filter array

We explore the use of hexagonal segment tip-tilt-piston deformable mirrors alone and paired with pinhole spatial filter arrays for high-order wavefront correction of nulling interferometers used for visible light study of exoplanetary systems at 107 to 1010 contrast within regions extending ∼0.1 to 6 arc s from a parent star. A similar system has been proposed using a single-mode fiber array as an alternative to using multiple deformable mirrors to correct both phase aberrations and balance electric field amplitude, the benefit being drastically reduced component and control complexity. Performance is compared using measured deformable mirror data for hexagonal arrays consisting of a number of rings NR=2 to 18, emphasizing the trade between throughput and the additional contrast gained from suppressing wavefront errors introduced by the deformable mirror at spatial frequencies Λ≥NR that are otherwise present in the image at corresponding field locations. Taking into account effects of loss of throughput and vignetting, the nulled signal-to-noise ratio is shown to improve for filtered systems in the outer portion of the field of view. Modeled performance shows no significant change in signal-to-noise in the inner field of view.

Polychromatic Compensation of Propagated Aberrations for High‐Contrast Imaging

We describe the influence of Fresnel propagation in apodized-pupil coronagraphs and introduce a methodology to compensate for propagated wavefront aberrations. We start from the Fresnel integral and derive an analytical closed form for the propagated field at an arbitrary distance from a pupil. In a second part, we show that the propagation of the coronagraphic term can be neglected with sufficiently oversized optics. Then we derive a λ-Fourier expansion of the aberration at an arbitrary plane in the optical train of a telescope. Finally, we present a series of wavefront actuators, based on multiple deformable mirrors, that possess adequate chromatic behavior to correct for the dominant terms of this expansion.

High‐Resolution Images of Orbital Motion in the Trapezium Cluster: First Scientific Results from the Multiple Mirror Telescope Deformable Secondary Mirror Adaptive Optics System1

We present the first scientific images obtained with a deformable secondary mirror adaptive optics (AO) system. We utilized the 6.5 m Multiple Mirror Telescope adaptive optics system to produce high-resolution (FWHM ¼ 0>07) near-infrared (1.6 lm) images of the young (� 1 Myr) Orion Trapezium � 1 Ori cluster members. A combination of high spatial resolution and high signal-to-noise ratio allowed the positions of these stars to be measured to within � 0>003 accuracies. We also present slightly lower resolution (FWHM � 0>085) images from Gemini with the Hokupa‘a AO system as well. Including previous speckle data from Weigelt et al., we analyze a 6 yr baseline of high-resolution observations of this cluster. Over this baseline we are sensitive to relative proper motions of only � 0>002 yr � 1 (4.2 km s � 1 at 450 pc). At such sensitivities we detect orbital motion in the very tight � 1 Ori B2-B3 (52 AU separation) and � 1 Ori A1-A2 (94 AU separation) systems. The relative velocity in the � 1 Ori B2-B3 system is 4:2 � 2: 1k m s � 1 . We observe 16:5 � 5: 7k m s � 1 of relative motion in the � 1 Ori A1-A2 system. These velocities are consistent with those independently observed by Schertl et al. with speckle interferometry, giving us confidence that these very small (� 0>002 yr � 1 ) orbital motions are real. All five members of the � 1 Ori B system appear likely gravitationally bound (B2-B3 is moving at � 1.4 km s � 1 in the plane of the sky with respect to B1, where Vesc � 6k m s � 1 for the B group). The very lowest mass member of the � 1 Ori B system (B4) has K 0 � 11:66 and an estimated mass of � 0.2 M� . Very little motion (4 � 15 km s � 1 ) of B4 was detected with respect to B1 or B2; hence, B4 is possibly part of the � 1 Ori B group. We suspect that if this very low mass member is physically associated, it most likely is in an unstable (nonhierarchical) orbital position and will soon be ejected from the group. The � 1 Ori B system appears to be a good example of a star formation ‘‘ minicluster,’’ which may eject the lowest mass members of the cluster in the near future. This ‘‘ ejection ’’ process could play a major role in the formation of low-mass stars and brown dwarfs. Subject headings: binaries: general — instrumentation: adaptive optics — stars: evolution — stars: formation — stars: low-mass, brown dwarfs On-line material: color figures

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.

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.

Some computational problems arising in adaptive optics imaging systems

Recently there has been growing interest and progress in using numerical linear algebra techniques in adaptive optics imaging control computations. Real-time adaptive optics is a means for enhancing the resolution of ground based, optical telescopes beyond the limits previously imposed by the turbulent atmosphere. An adaptive optics system automatically corrects for light distortions caused by the medium of transmission. The system measures the characteristics of the phase of the arriving wavefront and corrects for the degradations by means of one or more deformable mirrors controlled by special purpose computers. No attempt is made in this paper to give a comprehensive survey of recent numerical linear applications in optical imaging. Rather, two fairly representative applications are discussed in some detail. The following research topics in the area of adaptive optics control systems, each involving the formulation and numerical solution of difficult problems in numerical linear algebra, are described: (1) Jacobi-like eigenvalue computations for multiple bandwidth deformable mirror control methods, and (2) covariance matrix computations for performance modeling of adaptive optics systems using fast Hankel transforms.

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.

Optimizing closed-loop adaptive-optics performance with use of multiple control bandwidths

The performance of a closed-loop adaptive-optics system may in principle be improved by selection of distinct and independently optimized control bandwidths for separate components, or modes, of the wave-front-distortion profile. We describe a method for synthesizing and optimizing a multiple-bandwidth adaptive-optics control system from performance estimates previously derived for single-bandwidth control systems operating over a range of bandwidths. The approach is applicable to adaptive-optics systems that use either one or several wave-front sensing beacons and also to systems that include multiple deformable mirrors for atmospheric-turbulence compensation across an extended field of view. Numerical results are presented for the case of an atmospheric-turbulence profile consisting of a single translating phase screen with Kolmogorov statistics, a Shack–Hartmann wave-front sensor with from 8 to 16 subapertures across the aperture of the telescope, and a continuous-face-sheet deformable mirror with actuators conjugate to the corners of the wave-front-sensor subapertures. The use of multiple control bandwidths significantly relaxes the wave-front-sensor noise level that is permitted for the adaptive-optics system to operate near the performance limit imposed by fitting error. Nearly all of this reduction is already achieved through the use of a control system that uses only two distinct bandwidths, one of which is the zero bandwidth.

Analysis of multiconjugate adaptive optics

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