Adaptive optics are by now a well-established part of astronomical instrumentation. Every large ground-based observatory operates AO facilities to extend the range of application of their instruments to observations at high angular resolution. This section will therefore only summarize the basics of this technique and the interested reader is recommended to refer to the pertinent literature (e.g.Beckers 1993;Hartmann 1998;Davies & Kasper 2012, and references therein). The focus of this chapter shall be on the use of adaptive optics with near-infrared spectroscopy, which is described in the subsequent sections.
The Earth’s atmosphere is subject to turbulences caused by patches of air of different temperatures, densities, and humidity, causing a constant change of the refractive index n
Tip Tilt mirror Deformable Mirror Science Camera Wavefront Sensor Computer Distorted wavefront
Figure 2.1: Schematic diagram of an Adaptive Optics system integrated into the light path of a telescope. The distorted light enters the telescope, is reflected via the tip-tilt mirror and a deformable mirror onto a beam splitter that redirects part of the light to a wavefront sensor and lets the rest pass to the science camera. The signal from the wavefront sensor is measured, interpreted, and forwarded to the tip-tilt and deformable mirrors which flatten the incoming wavefront.
of interest. The imposed chaotic wavefront distortions of theseturbulence cells – caused by the fact that the speed of light in air is a function of temperature – cause a seeing-induced
full width at half-maximum FWHMseeing = λ/r0 which is equal to a value of ∼000.7 at a
wavelength ofλ = 2.2µm, assuming the canonical value ofr02.2µm≈0.6 m for the size of the turbulence cells, called Fried parameter r0 (see e.g. Fried 1965; Glindemann et al. 2000).
This is rather large compared to the width of the ideal diffraction limited point spread function (PSF) of a circular telescope aperture of width D, calledAiry function, of
FWHMAiry= 1.03 λ
D (2.1)
which returns a more than ten times better resolution of FWHM = 000.06 at λ= 2.2µm with current 8 m telescopes. While the theoretical diffraction limit becomes smaller with decreasing wavelength the seeing limit is larger at optical wavelengths due to the wavelength dependence of the Fried parameter ofr0∝λ6/5 (Fried 1965; Karo & Schneiderman 1978).
To recover the full angular resolution power of large ground-based telescopes, adaptive optics are included in the light path after entering the telescope and before light enters the science part of the instrument. A sketch of the basic setup is presented in Fig. 2.1. The basic principle relies on the fact that the shape of the distorted wavefront can be
measured and corrected in real-time. Reflection off adeformable mirror (DM)2, adapted to assume the measured shape, leaves the reflected wavefront ideally with no atmospherically induced aberrations. The quality of the correction is limited by the fact that turbulent changes in the atmosphere happen on rather short timescales. The typical coherence time
τ0 ≈r0/|v|, i.e., the time during which the aberrations through the atmosphere can be
assumed to be constant, is on the order of a few times 10 ms (assuming a wind speed v
of a few 10 ms−1,Beckers 1993; Glindemann et al. 2000). This is the maximum time that is available between measuring the shape of the wavefront and its correction. Corrections that are applied slower than the coherence time can at best partly correct the imposed aberrations since the atmosphere already changed significantly.
The demands on the wavefront measuring routine are accordingly high: at a rate of up to 1 kHz it needs to take an acquisition of the incoming wavefront, determine its shape, and pass this information to the deformable mirror. This requires a suitable wavefront reference which is ideally (i) a point source above the atmosphere (to be able to assume that the undisturbed wavefront is approximately flat and passed all of the medium that generates the turbulences), (ii) which provides enough light to be imaged with millisecond snapshots, and (iii) that is close enough to the scientific object of interest to experience the same aberrations. This is usually provided by a star within 3000 of the science target3
with a minimum brightness determined by the used instrumentation, e.g., V <16.7 mag or
K <12–13 mag in the case of NACO/VLT (see Sect. 2.3.1).
To measure the shape of the wavefront, so-called wavefront sensors are used which receive part of the light reflected from the deformable mirror. Three principally differ- ent designs are currently favored: Shack-Hartmann-type, curvature sensing, and Pyra- mid wavefront sensors. The first two are used by the NAOS (Sect. 2.3.1) and SINFONI (Sect.2.3.2) adaptive optics modules, respectively. Shack-Hartmann wavefront sensors use arrays of lenses (so called lenslets) to measure the distortion of individual parts of the wavefront. While the undistorted wavefront passing the lenslet array creates a regular pat- tern of spots on a CCD, wavefront aberrations cause a displacement of the individual spots. This displacement is converted into a distortion model which is used as an input signal for the actuators of the DM. Curvature sensing exploits the fact that a distorted wavefront will not focus exactly in the focal plane like in the undistorted case. Measurement of an increase of the intensity in front of or behind the focal plane indicates the degree and shape of a distortion and is passed on to the DM to correct the incoming wave. Limitations of both techniques are the high demand on computing power to update the correct shape of the DM within a coherence period and the limited number of actuators that can be placed
2The “Tip” and “Tilt” signals, i.e., uniform gradients of the wavefront in x and y direction, often
require the use of a separate optical component, e.g., aTip-Tilt mirror, since they are typically too large for correction with the DM.
3The quality of the correction is a function of the size of theisoplanatic angle, i.e., the angle under which
two sources show correlated atmospheric aberrations, and the angular distance between the reference and science target. The closer the reference the better the correction. Ideally the reference and science target are identical.
on the DM to correct for high-order aberrations4.
The performance of adaptive optics can be measured by means of theStrehl Ratio, which is defined as the ratio of the measured and theoretical, purely diffraction-limited peak flux of a point source. While seeing-limited Strehl ratios are typically less than a few per cent, AO-corrected observations can improve the Strehl ratio to more than 40% at λ= 2µm, depending on reference source brightness and seeing conditions. At these high Strehl ratios, the angular resolution is nearly identical to the theoretical resolution power of the telescope (see e.g.Le Louarn et al. 1998). The correction is wavelength-dependent due to an increase of the coherence times and lengths with wavelength. Accordingly, high Strehl ratios are mainly obtained at infrared wavelengths, while optical corrections require comparably large instrumental and computing effort to achieve even minor improvements. Already over a wavelength range from∼2.2µm (K-band) to ∼1.25µm (J-band), the typical Strehl value can decrease from ideally &50% down to .10%. A Strehl ratio <100% implies that the detected flux is not distributed in the shape of an ideal Airy pattern. In fact, the shape of an AO PSF can be described as a superposition of a diffraction-limited core and a seeing-limited “halo”.
The above describes the basic concept and characteristics of reducing the impact of atmospheric turbulence on ground-based astronomical observations with adaptive optics. Constraints on the applicability of this concept to a particular scientific question arise, however, for example from the limited sky coverage due to guide star magnitude limits, the improvable Strehl ratio in particular at short wavelengths, or the small isoplanatic angle. Concepts to tackle these and other points do exist and are either already in use or are currently being installed (Laser guide star AO,ground-layer AO; e.g.Wizinowich et al. 2006;Rabien et al. 2010), have proven their feasibility (multi-conjugate AO;Beckers 1988; Marchetti et al. 2003), or are planned for special purposes such as the direct imaging of planets (extreme AO; e.g. Sauvage et al. 2010).