Adaptive optics are used in ground-based telescopes to directly image extrasolar planets and overcome atmospheric turbulence. Atmospheric turbulence causes distortions that blur planetary images. Adaptive optics systems measure wavefront distortions using a wavefront sensor and correct for them using a deformable mirror in a closed-loop system. This results in sharper, diffraction-limited images that help verify exoplanets. Future extremely large telescopes will use many more actuators on deformable mirrors to provide substantial correction, aiding the search for Earth-like exoplanets.

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Adaptive Optics in Ground Based Telescopes that Directly Image Extrasolar
Planets
Abstract
Even before the invention of the telescope, people have asked whether there are other
worlds like ours. With ground based telescopes scientists are able to search for distant planets
able to sustain life. The main issue surrounding ground based telescopes is the atmospheric
turbulence that can cause unusable planetary images. In this paper I first introduce current and
future methods for detecting and characterizing extra solar planets, focusing on direct imaging.
Next, atmospheric turbulence is discussed in more detail since it is the major issue in direct
imaging. Finally, the paper discusses the technology behind adaptive optics. After the reader is
acquainted with the adaptive optics technology, the paper discusses the reduced negative effects
of atmospheric turbulences thanks to the implementation of adaptive optics. The end result is
“sharp[er] [and more] diffraction limited core” that helps verify the exoplanet’s existence [7].
1.0 Introduction
According to Lagrange and Tinetti, the science of exoplanet discovery aims to uncover
planet formation and evolution, the “diversity of a planetary system”, as well as search for
planets capable of supporting life [3]. Detecting such planets outside of our solar system has
proven to be challenging. Despite the challenge, with the use of current and future developments
in planetary detection technology the “era of exoplanets is well into its golden age” [8]. One
method that has experienced technological improvement over the years has been ground based
direct imaging. In combination with other methods which will be discussed below, direct
imaging maintains “extraordinary potential” for planetary detection as well as “determining
atmospheric composition” of earth like planets [6]. Throughout the rest of the introduction I will
discuss other technologies currently in use and will briefly introduce direct imaging. In the next
section, atmospheric turbulences limiting ground based direct imaging and the use of adaptive
optics to counter turbulence and will be discussed. Finally, the conclusion will summarize the
use of adaptive optics and will briefly mention future projects related to it and exoplanet
discoveries.
In his book, Perryman discuss a number of planetary detection methods including: radial
velocities (Doppler measurements), transits, astrometry, microlensing, and of course, direct

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imaging. Radial velocity has successfully measured masses and periods of planets with masses
greater than of Earth’s [4]. Likewise, transits have successfully measured diameters and periods
of giant planets. Using the same technique, scientists have been able to measure “temperature
distribution, spectral features and thermal inversion” [4]. Despite the available methods and their
relative success in exoplanet discoveries, direct imaging remains very useful. According to
Lagrange, given the period of Saturn, Uranus, and Neptune, radial velocities won’t allow the
timely “characterization of [their orbits]”. Conversely, Lagrange stresses that the aforementioned
measurements can be taken rapidly by using direct imaging. Traub, Oppenheimer, and Lagrange,
agree that the planetary detection methods benefit the discovery and understanding of extrasolar
planets independently from each other. In addition to the various techniques in use, direct
imaging is crucial to our continuing efforts for exoplanet discovery. [4,3]
In its basic definition, direct imaging refers to point source detection using reflected light
from the “parent star” or through its “own thermal emission”, received in visible and infrared
light respectively. With distant planets, the primary aim of direct imaging is to detect and
characterize them through “spectroscopic investigations” in combination with other methods.
Due to an exoplanet’s close proximity to its parent star and earth’s “turbulent atmospheric
refraction”, the desired planet signal is “immersed” in the “stellar glare” [9]. In order to correct
this, scientists equip telescopes with adaptive optics alongside other techniques.
2.0 Atmospheric Turbulence and the Function of Adaptive Optics
According to Oswalt et. all, the presence of star light becomes the dominant source of
noise that impedes the detection of the desired planet. In order to achieve a successful planet
detection, “fluctuations in the wings of the star’s PSF” where the planet is located, need to be
smaller than the signal from the planet [7]. Adaptive optics in combination with other techniques
are used in order to correct stellar glare and atmospheric turbulence; however, without first
countering the effects of atmospheric turbulence ground based imaging becomes fruitless [6].
Temperature variations in the atmosphere produce changes in the refractive index in the
air[1,7]. The magnitude of this change depends on air density and the level of temperature
variation [1]. Ideal light waves incident from the planet and star become “distorted” as they pass
through regions with “variable refractive [indices]” [6]. Atmospheric turbulence limits the
angular resolution, which due to the turbulence is proportional to λ/r0, where r0 is the “lateral

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correlation length of the wavefront” [2]. Instantaneous images that reach the telescope represent
“diffraction-limited duplicates” of the star/planet duo. Each duplicate represents a Fourier
component of the earth’s atmosphere. Together they form an image composed of many “rapidly
moving speckles” [1]. Figure 1a depicts a diffraction limited image acquired without turbulence.
Figure 1b depicts the scattered point spread function as a result of turbulence in the atmosphere.
Unlike speckle imaging, adaptive optics deals with the “perturbed wave fronts” prior to
their integration. Another drawback of using speckle imaging is that the atmosphere limits the
integration time. These limitations are removed with adaptive optics thanks to phase corrections
[2].
Figure 1a (left) and 1b(right) [2]. Image acquisition with (right) and without (left) atmospheric turbulence
In adaptive optics, correcting a final version of the desired image requires the repetitive
measuring of the wavefront’s phase aberration. A wavefront sensor measures the wavefront
phases influenced by the atmospheric turbulence [6,2]. The incoming wavefront is then
compared with a reference in order to produce the pathlength error [1]. Stars located in an ideal
position may act as a wavefront reference [9]. Another option is to use a laser reference beam
[5]. The last step is to create an equal and opposite wavefront phase aberration. This must be

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applied to the incoming wavefronts so that by superposition the aberrations cancel out [5].
Figure 2 [2] Various types of flexible mirrors compensating wavefront phase aberrations
Each atmospheric phase is corrected by a deformable mirror. Ribak states that these
mirrors are “usually made by a piezoelectric actuator.” Such an arrangement is advantageous
since displacement becomes directly proportional to applied voltage. As is shown in Figure 2
above, mirror designs can vary from “separate pieces,” to a “continuous thin sheet,” to a single
piezoelectric material where the “electrodes are drilled into it” [2]. Current flexible mirrors use
around 200 actuators while higher end telescopes use many more. Sensor measurements and
actuator corrections are made in the frequencies on the order of 1 kHz [9]. The remaining piece
of the system is the servo control loop that continually measures the wavefronts and corrects
accordingly. An example of this closed loop system incorporating the wavefront sensor, mirrors,
and image detectors is discussed below.
A very basic setup for a telescope with adaptive optics includes the use the wavefront
sensor, adaptive mirrors, beam splitter, control system with feedback, as well as a camera to
capture the final image. Looking at Figure 3 below, the reader notices the distorted light from the
telescope hitting the deformable mirror, reflecting off the mirror, and hitting the beam-splitter. At
this point, part of the light reaches the wavefront sensor where the phase difference is calculated
based on one of the aforementioned references. Through the feedback control, appropriate signal
values are transmitted to the mirror in order to cancel out wavefront phase aberrations caused by
the atmospheric turbulence. The flexible mirror interprets these signals as voltage values causing

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the actuators to perform accordingly. As light travels through the telescope, the mirror flexes
appropriately in order to compensate for phase aberrations. Finally, light is transmitted through
the beam splitter and a compensated image is formed at our camera sensor [9]. As mentioned
before, the process is repeated every thousand(s) of a second in order to account for the
continuously changing atmospheric turbulence.
Oswalt et. al and Hardy describe the impact of adaptive optics in order to correct
planetary imaging. Hardy mentions that the “peak intensity” of the desired planetary image is
increased in reference to the sky background. Additionally, Oswalt et. al. state that after adaptive
optics correction, the PSF contains a “sharp [and] diffraction limited core.” They go on to
describe the factors that limit adaptive optics compensation which include: wavefront adjustment
errors due to finite sampling and correcting elements, time lag errors in the loop, wavefront
sensing due to lack of photons, and control loop alignment and calibration.
Figure 3 [9] Adaptive Optics system incorporating a flexible mirror, a
wavefront sensor, and a feedback control system.

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Conclusion
As the search for extrasolar planet continues, scientists continue to use various techniques
for planetary detection and characterization. It is evident that in combination with the older,
conventional methods, direct imaging must be implemented to increase our chances of detecting
exoplanets. Current telescopes employing ground based imaging techniques are limited by the
image blurs caused by atmospheric turbulences. Adaptive optics aims to solve this problem.
Very simply, adaptive optics uses the principle of superposition in order to apply an equal and
opposite wavefront phase aberration with the purpose of canceling out undesired effects caused
by atmospheric turbulences. The three main components of an adaptive optics system include: a
wavefront sensor, a deforming mirror, and the feedback system. Traub. et. al discuss the
employment of adaptive optics in the planned Thirty Meter Telescope(TMT), Giant Magellan
Telescope(GMT), as well as the European Extremely Large Telescope(E-ELT). As the names
may imply, a number of actuators in the order of 10^4 will be used to provide substantial
correction for the E-ELT [9]. The challenges of these planned telescopes remain the same;
however, with improving technology the aim is to detect planets that Oswalt et. al regard as
“Earth-twin[s].”

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References:
[1] “Adaptive Optics for Astronomical Telescopes”, Hardy, J., Oxford University Press, UK
(1998).
[2] “Atmospheric Turbulence, Speckle, and Adaptive Optics”, E. RIBAK, Annals of the New
York Academy of Sciences, 808: 193–204, (1997).
[3] “Direct Imaging of Exoplanets”, Anne-Marie Lagrange, Philosophical Transactions of the
Royal Society A, 372, pp 10 (2014).
[4] “Direct Imaging of Exoplanets”, Wesley A. Traub, Ben. R. Oppenheimer, S.Seager, ed
(Tucson: Univ.Arizona Press; 2010).
[5] “Galactic planetary science”, Giovanna Tinetti, Philosophical Transactions of the Royal
Society A, 372, (2014).
[6] “Ground-based imaging of extrasolar planets using adaptive optics”, J.R.P. Angel, Nature,
368, (1994)
[7] “Imaging Exoplanets. The Role of Small Telescopes”, Ben. R. Oppenheimer, A.
Sivaramakrishan, R.B. Makidon, Terry Oswalt, ed.(New York: Kluwer Academic Publishers),
The Future of Small Telescopes, Vol. 3, Chapter 10, p.157-174, (2003).
[8] “Probing an Extrasolar Planet”, Mark S. Marley, Science, 339, (2013).
[9] “The exoplanet handbook”, Perryman M., Cambridge University Press. Cambridge, UK
(2011).