Adaptive optics

Adaptive optics (AO) systems measure and correct wavefront aberrations in real time. AO systems usually perform corrections using a small deformable mirror (DM) equipped with tens to hundreds of small actuators, applying corrections at a rate of 10_{− 1000 Hz. This differs from active optics systems, as it is not generally feasible} to modify the shape of large primary mirrors with sufficient accuracy and speed to correct atmospheric wavefront distortions, although some systems have used adaptive secondary mirrors (e.g. Lloyd-Hart et al. 2003, Guerra et al. 2013).

Wavefront aberrations are measured through the observation of a reference source of light, which may be a star (a natural guide star, NGS), or instead artificially gener- ated point of light (a laser guide star, LGS). Measurements are most often performed using a Shack-Hartmann wavefront sensor which consists of an array of small aper- tures or lenses, each of which produces an image of the guide star onto a detector. Due to their small size, the apertures only receive a small portion of the incoming wavefront each; as a result, tip-tilt aberration is dominant, and the image created by each aperture will move on the detector. By measuring the motion of the image from each aperture, the local wavefront tilt can be determined, and the combination of all image shifts allows the 2D profile of the incoming wavefront to be reconstructed. The deformable mirror is then modified to cancel out the measured wavefront aberration, providing a seeing-corrected image to the attached instrument or detector.

Better correction can provided by 1) increasing number of apertures in the Shack- Hartmann array to provide better sampling of the wavefront; 2) adding more actuators in the deformable mirror to provide a more accurate correction of the wavefront; and 3) through higher rates of operation to reduce the residual wavefront errors caused by time delays between sensing and correction. However, each of these changes also comes with drawbacks. Adding additional apertures and actuators increases the required computa- tional difficulty of modelling the wavefront and determining the necessary corrections, noting that only a small fraction of a second is available for each iteration of the algo- rithm. Higher rates of operation also cause such issues by reducing the time available

Figure 2.2: A cartoon illustrating wavefront correction using a deformable mirror. The incoming wavefronts (black) have been perturbed by atmospheric turbulence. Based on information collected by a wavefront sensor (not shown), the deformable mirror (blue) is shaped so as to cancel out the wavefront errors introduced by the atmosphere. The reflected light (red) consists of corrected, plane-parallel wavefronts, which are passed on to another instrument, such as a photometer or a spectrograph.

Image created by Bob Tubbs, released into the public domain via Wikimedia Commons: https://commons.wikimedia.org/wiki/File:Adaptive_optics_correct.png

for each iteration, and also reduce the number of photons collected by the Shack- Hartmann sensor during each exposure. Similarly, providing more apertures divides the same number of incoming photons across a larger number of images, reducing the signal-to-noise (SNR) of the wavefront tilt measurement from each individual aperture. Due to the requirements for sufficient SNR in the wavefront measurements, AO systems are limited to using bright stars for guiding. Whilst the guide star does not need to be the target star, correction becomes increasingly poor outside the isoplanatic angle. In the visible, this limitation results in as little as 0.001% of the sky being available to NGS AO systems due to the sparsity of bright guide stars, depending on the limiting magnitude of the system. This issue is somewhat alleviated by designing an AO system operating in the infrared, where the isoplanatic angle is larger, but even in the best case, only a few percent of the sky remains observable (Rigaut 2015).

2.2.2.1 Laser guide stars

To combat the limited sky available to NGS systems, an artificial guide star can be created using a ground-based laser positioned near the telescope. The concept relies on the laser light being scattered back towards the telescope by atmospheric parti- cles, passing through same turbulent atmosphere as the starlight, allowing wavefront errors to be measured and corrected for (Foy & Labeyrie 1985). In order to achieve a sufficient amount of returned light from high altitude, the wavelength of the laser is carefully chosen to match specific re-emission or scattering mechanisms. The most common choices of mechanism are the sodium resonance, which involves stimulated emission by atmospheric sodium at an altitude of approximately 90km, and Rayleigh scattering, which uses blue or ultraviolet light that is backscattered by the atmosphere at altitudes of 10–30km. Whilst sodium lasers are preferable for seeing correction due to their ability to probe a larger fraction of the atmosphere, the strict wavelength tuning required to exactly match the sodium resonance makes such lasers much more complex – and hence expensive – than Rayleigh scattering lasers.

the column of air that is probed by starlight, the laser is off-axis and cannot be treated as a source at infinity, and hence the laser probes a cone of air that may contain significantly different turbulence; this is known as the cone effect (Foy & Labeyrie 1985). Secondly, the light is not only affected by atmospheric turbulence when passing downwards through the atmosphere, but is also affected when passing upwards before scattering; as a result, an unknown amount of tilt error is introduced to the laser wavefront that is not present in the stellar wavefronts, making it difficult or impossible to correct stellar tip-tilt motion with the LGS alone (Rigaut & Gendron 1992). Other issues present in LGSAO facilities are increased cost and complexity compared to NGS systems, aircraft and satellite avoidance, and the light pollution created by the lasers (adjacent observing facilities can be badly affected by bright laser beams passing through their field of view, as discovered by the NGTS survey, Wheatley et al. 2018).

2.2.2.2 Advances in adaptive optics

In addition to the simple NGS and LGS AO systems discussed above, many variants of the AO concept exist. Rigaut (2015) provides an overview of these advances, with a brief summary being given below:

• Extreme AO (ExAO) focuses on very high quality correction for high contrast imaging close to targets, at the expense of being unable to use a laser guide star due to the cone effect. Several instruments such as SPHERE (Beuzit et al. 2008), GPI (Macintosh et al. 2014), and SCExAO (Martinache & Guyon 2009) utilise this concept, with the main aim being the direct detection of hot, young exoplanets in wide orbits around nearby stars.

• Ground Layer AO (GLAO) corrects only for the atmosphere closest to the tele- scope (the ‘ground layer’), and is able to correct much wider fields of view due to the larger angular extent of turbulence features near the ground, as seen by the telescope. The ground layer contributes a large fraction of the wave- front error, allowing a significant improvement over seeing-limited observations

(Tokovinin 2004).

• Multiple Object AO (MOAO) uses multiple guide stars spread over several arcminutes of sky. Rather than correcting for atmospheric turbulence across the entire field, multiple deformable mirrors are used to correct the light from individual targets. Instruments such as CANARY (Gendron et al. 2011) and RAVEN (Andersen et al. 2012) utilise this concept.

• Multi-Conjugate AO (MCAO) also invokes multiple guide stars and deformable mirrors, aiming to correct the entirety of a wider field of view ('2 arcmin.). The multiple guide stars are used to reconstruct a 3D turbulence profile, with multiple deformable mirrors being used to correct for individual layers of at- mospheric turbulence (Beckers 1988). The concept has been utilised by in- struments such as MAD, which used three natural guide stars (Marchetti et al. 2007), and the GeMS system, with a constellation of LGSs (Neichel et al. 2014).

These improvements on ‘classical’ AO concepts are being actively pursued, with some systems already active on 10m class telescopes, and others in development for both 10m class (e.g. ESO’s Adaptive Optics Facility) and 30m class telescopes, with AO capabilities being considered a fundamental component of the latter.