ADAPTIVE OPTICS FOR ESO'S VERY LARGE TELESCOPE (VLT) PROJECT Fritz Merkle European Southern Observatory Karl-Schwarzschild-Str. 2 D-8046 Garching Fed. Rep. Germany May 1986 VLT REPORT No. 47 ADAPTIVE OPTICS FOR ESO'S VERY LARGE TELESCOPE (VLT) PROJECT Fritz Merkle Abstract Imaging in ground-based astronomy is limited by the transmission of the light through the turbulent atmosphere. Adaptive optics offers the possibility to overcome these limitations. It employs a real-time phase compensation with a phase shifting optical element, which is usually a deformable mirror. The information for the control of the mirror surface is gained from a wavefront sensor. This report describes the principles of adaptive optics and its application in astronomy. It gives an overview over the major elements like the wavefront correction devices, the wavefront sensors, and control systems. The performance of adaptive systems and the requirements in astronomy are discussed and guidelines for the implementation of this technology in ESO's Very Large Telescope given. Table of Contents 1 Introduction 1 2 Principles of Adaptive Optics 4 3 Adaptive Optics in Astronomy 9 4 Strategy for Seeing Optimization 10 5 Elements of an Adaptive System 14 5.1 Wavefront Correction Device 14 5.2 Wavefront Sensor 17 5.2.1 Shearing-Interferometer 17 5.2.2 Shack-Hartmann Sensor 19 5.3 Control System 22 6 Performance of an Adaptive System 22 7 Requirements for Adaptive Correction in Astronomy 24 8 Adaptive Optics for the VLT 28 9 Conclusion 31 References 32 1 1 Introduction A perfect astronomical telescope should have a theoretical angular resolu­ tion of A ~a = 1.22 D (in Radians) (A: wavelength, D: telescope diameter), where ~a is the radius of the first dark ring of the Airy disc. This would lead to the resolution values dis­ played in figure 1 for different telescope diameters. However, in practice the imaging quality of ground-based telescopes is degraded by the transmission of the light from the astronomical object through the turbulent atmosphere of the earth. The reason for this degradation is a random spatial and tem­ poral wavefront perturbation induced by the turbulences in the different layers of the atmosphere. In addition to this, also the aberrations of the optical elements of the telescope contribute to the degradation. All these .... ..u III u ....... t c: ~ 10-2 +,t-,'-+-'1f---/+-+----+------l ::::J C III ...QI ... IV ~ 10-3+--+/-+-----1---+-----( c: IV 10- 4 L----t---+---t----' 0.1 1 10 100 1000 [/Lm] Wavelength - Figure 1: Angular resolution of an astronomical tf']pscope in the absence of any atmospheric and instrumental distortion of the light transmission (The angular resolution is given as radius of the. first dark ring in the Airy disc.) 2 1 INTRODUCTION wavefront perturbations together result in a complex phase aberration <P(r, t) - z'A(r, t) of the light beam. The real part <P(r, t) represents the phase shift of the wavefront, usually called"seeing" , while the imaginary part A( r, t) is a mea­ sure for the intensity fluctuations across the aperture plane, called "scintil­ lation". Figure 2 displays the influence of phase distortions on the image quality, which is commonly described with the Strehl ratio S: S = peak z'rradz'ance z'n the j oeaL pLane peak z'rradz'ance dz'j jractz'on hm£ted o t= « ex: 0.5 ...J :I: w ex: ~ VI O'--------I--- L----.J o 0.05 01 RMS ERROR [wave~ Figure 2: Image quality vs. the RMS wavefront error. The image quality is given by the Strehl ratio S. It is possible to correct the phase shift with a technique called adaptive optics [Hardy 1978, Pearson 1979, Merkle 1983a). The basic principle of adaptive optics is to use a phase shifting optical element, which can be controlled in space and time in order to compensate the atmospheric phase shift (see fig.ure 3). A correction of the scintillation would require a spatially and temporally controllable apodization element. Thus, a system for the fu 11 correction of the aberrations applies a compensation equal to -<P(r, t) + z'J.tA{r, t) 3 WAVEFRONT CONTROL OBJECT IMAGE WAVEFRONT SENSOR CONTROL SYSTEM Figure 3: Principle of active/adaptive optical correction system. (J.L : dimensionless intensity scaling factor). For most of the imaging prob­ lems, especially with very large telescopes, the phase correction part is sufficient and for technical reasons its realization is much easier than the correction of the intensity fluctuations. The field of adaptive optics is in astronomy often divided [Woolf 1984] in the so-called "active optics': which is used for the figure correction of the telescope optics and the "adaptive optics" for the correction of atmospheric effects. In this definition the field of active optics is just a special case of the general principle of adaptive optics at low spatial and temporal frequencies. However, in optical and control engineering the distinction is different. Here, active optical systems or the active components thereof are capable of reshaping a wavefront by adding a set of controllable path differences. No closed loop servo control that operates on the actual wavefront error information is present. An adaptive optical system includes a closed loop phase error sensor that acts to drive a set of path differences to zero. Therefore, the terminology used in astronomy is in some sens contradictory to the technical definition but useful to identify the different applications, mainly because the ways of their technical realization are quite different. The scope of this paper is the field of adaptive optics for atmospheric turbulence correction. During the last 10 years the techniques of adaptive optics have been developed, mainly for laser beam transmission through the turbulent at­ mosphere. Although most of the developments have been made in the United Sta.tes (at companies like ITEK, Lockheed, United Technologies, AVCO Everett, The Aerospace Corp., AOA, and others), there are some promising activities in Europe (CGE, ONERA (France), MBB, and Diehl 4 2 PRINCIPLE OF ADAPTIVE OPTICS (FRG)). The transfer of these techniques to the astronomical field is not straight forward, mainly because of the very low light levels compared with laser applications and the large apertures of the astronomical telescopes. However, the progress in wavefront-sensor technology and the availability of fast computers to cope with the large number of corrections at large aper­ tures has opened the technical feasibility of adaptive optics to astronomy. New ideas came up to overcome the intensity problems, like shooting laser beams to the higher atmosphere to create an artificial star-like reference sources. The intention of this report is to introduce the techniques of adaptive optics and its implication to astronomy. The chapters 2 and 3 will give an introduction to principles of adaptive optics. Chapter 4 describes correction strategies and chapter 5 the the basic elements of an adaptive system. The performance of an adaptive system is evaluated in chapter 6. Chapter 7 and 8 describe the requirements for the design of an adaptive system in astronomy and, especially, with respect to ESO's Very Large Telescope (VLT) project. 2 Principle of Adaptive Optics An adaptive optical system (see figure 4) contains four basic elements: an optical train and image detector, a wavefront sensor, a servo-control system, and a phase-shifting optical element. The distortion of the received wave­ front is usually compensated by reflecting the light beam on a deformable mirror. The surface of this mirror is adjusted in real-time to compensate the path length aberrations. The information required to deform the mirror is obtained by analyzing the light beam with a wavefront sensor. A map of wavefront errors is then derived at each instant of time. Using this error map. the control system determines the signals required to drive the phase shifting optical element and to null the phase aberrations by closing the adaptive loop. The phase correction values can be obtained by expanding the phase-correction function N <l> (r, t) = L an (t) f n(7'1 n=l in a spatially (fn(r)) and temporally (an(t)) dependent function. The spa­ tial functions might represent zones or mode of the aperture, resulting in a zonal or modal correction strategy. 5 LIGHT FROM THE TELESCOPE CLOSED LOOP (- ~-t=I""L I CONTROL SYSTEM I I ~ I I I I I I WAVEFRONT l_ SENSOR Figure 4: Principle of the application of adaptive optics in astronomy. The complexity and design of an adaptive system depends of the aper­ ture size D of the telescope, the direction of the optical path specified by the zenith angle, and the atmospheric conditions. The atmospheric condi­ tions are usually described with the atmospheric turbulent refractive-index structure constant C~ [see Roddier 19811 which is a function of the height h above the ground. Figure 5 (left) shows a model of the vertical profile of the C~ distribution of as a function of altitude h for day and night time [Fried 1982~ and some measurements of C~ in Europe [Barletti 1976, (right). The resulting seeing conditions are often characterized by the scaling parameter 2 TO = [0.423k ~ C~(h) dh] -3/5 with 7r k = 2- >. (A: wavelength, R: height of the atmosphere) called atmospheric corre­ leation length or coherence diameter. It was introduced by Fried in 1965 [Fried 1965]. The size of the resulting seeing disc is then in the order of A/TO' 6 2 PRINCIPLE OF ADAPTIVE OPTICS , ::" IE-13 10- 1 ~ N < u 1E-'" 10- 1, Cl: W c~ (Z), t- W ~2Il I: . 1~-15 < 10- 1, Cl: < 0.. w Cl: lE-le "AVG" -, :0 10.