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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).