Concepts for a Large-Aperture, High Dynamic Range Telescope

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1 Publications of the Astronomical Society of the Pacific, 113: , 2001 December The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A. Concepts for a Large-Aperture, High Dynamic Range Telescope J. R. Kuhn Institute for Astronomy, University of Hawaii, Honolulu, HI 96822; kuhn@ifa.hawaii.edu G. Moretto Astronomical Instrumentation Group, Department of Physics, University of Durham, Durham DH1 3LE, UK; gil.moretto@durham.ac.uk R. Racine Département de Physique, Université de Montréal, Montréal, QC H3C 3J7, Canada; racine@astro.umontreal.ca F. Roddier Institute for Astronomy, University of Hawaii, Honolulu, HI 96822; roddier@ifa.hawaii.edu and R. Coulter Institute for Astronomy, University of Hawaii, Honolulu, HI 96822; coulter@ifa.hawaii.edu Received 2000 December 13; accepted 2001 August 24; published 2001 November 20 ABSTRACT. This paper summarizes concept studies for a large telescope capable of wide-field imaging and of the highest possible dynamic range for photometry and angular resolution. Point-spread functions (PSFs) and scattered light levels at large offsets are computed and compared for four telescopes of the same light-gathering power but with different pupil functions: 1. a reference monolithic mirror telescope with a 17.4 m primary, 2. a segmented mirror telescope (SMT) with a hexagonally segmented primary, 3. a hexagonal off-axis telescope (HOT) with a distributed aperture made of 6 # 6.5 m unobstructed circular mirrors that are identical off-axis sections of a parent 20 m mirror, and 4. a square off-axis telescope (SOT) whose aperture is made of 4 # 8 m off-axis mirrors. The characteristics of the PSFs are examined in the diffraction- and seeing-limited regimes, assuming (1) perfect mirror figure and (2) realistic figure errors (edge defects). The implications of field rotation with an altitude-azimuth mounting are discussed in each case. The implementation of adaptive optics (AO) and the properties of AO-compensated PSFs having a Strehl ratio of 0.5, and of coronagraphic imaging, are also discussed for the four configurations. It is shown that, in the seeing-limited regime and as intuitively expected, the optical performance of all four telescopes is comparable. With higher order adaptive optics and for coronagraphic observations, the SOT and HOT are superior to the SMT. This distinction becomes larger with relaxed constraints on mirror edge-polishing requirements. A full optical design is presented for the novel HOT configuration, and optical fabrication issues are briefly addressed. Finally, science programs and possible instrumentation layouts with the HOT are briefly explored for different modes of operation. It appears that the natural optical bench configuration of the HOT can provide a remarkably versatile and convenient environment for instrument deployment. 1. INTRODUCTION Close attention to active control and to local seeing management in the design and implementation of the current generation of 8 10 m telescopes has set new standards in delivered natural image quality. At good sites, sub half-arcsecond seeing has become the norm rather than the exception it was 20 years ago. Meanwhile, the advent of astronomical adaptive optics (AO) systems has allowed near diffraction-limited performance to be achieved with ground-based telescopes. The next frontier can include the development of telescopes with the highest possible dynamic range, having point-spread functions (PSFs) as clean as possible, while maintaining historical trends to ever larger apertures. Optical technology now allows one to envisage building a telescope that maximizes the PSF core energy and minimizes the scattered light flux in the wings of the PSF (Moretto & Kuhn 1998, 1999, 2000; Kuhn & Hawley 1999; Kuhn & Mor- 1486

2 CONCEPTS FOR LARGE TELESCOPES 1487 Fig. 3. Typical scattered light PSF contributions for a 6.5 m telescope. Fig. 1. Pupil functions for (clockwise from upper left) the SMT, SOT, HOT, and MMT. Each panel corresponds to a physical width of 22 m. etto 2000; Joseph et al. 2000). These are key requirements for achieving high angular and photometric dynamic range. Meanwhile, it seems clear that any telescope with an effective aperture larger than 8 m must use multiple mirrors. Because of the constraints of finite construction resources, it is interesting to ask how the total reflecting surface area should be distributed within a large telescope pupil. Given simultaneous requirements for core image resolution and dynamic range, it is not obvious that a filled (unobstructed or otherwise) circular aperture is optimum. With further constraints imposed by optical fabrication (polishing), mechanical, and structural issues, it is clear that the solution space to this problem is complex. The essential requirement of atmospheric wave front distortion correction (AO) for any large astronomical telescope further complicates the search for an optimal solution. If we allow for interferometric operating modes, where Fig. 2. This shows how the aperture diameter of an obstructed pupil must be scaled to achieve a constant S/N detection in one resolution element, as a function of the obscuration. Curves for field points at the first, second, and third Airy ring are plotted. Fig. 4. Top: Structure function S for a hexagonal segmented mirror with (left) six rings and (right) 11 rings of mirror segments. Maxima are separated by 2l/(a 3). The lower panels show how the zeros of the subaperture diffraction function 0 line up with the peaks (left) when the mirror separation just fills the pupil and (right) when the gaps are 10% of the segment radius.

3 1488 KUHN ET AL. Fig. 5. Core PSF for each telescope plotted over four decades in intensity and for a region 0.18 wide (at a wavelength of 1.6 mm). Clockwise from upper left: SMT, SOT, HOT, and MMT. Fig. 7. Wide-field (1.8) images of the PSF plotted over four decades. Clockwise from upper left: SMT, SOT, HOT, and MMT. Fig. 6. Core PSFs on a linear intensity scale corresponding to Fig. 5. Fig. 8. Wide-field PSF images on a linear intensity scale corresponding to Fig. 7.

4 CONCEPTS FOR LARGE TELESCOPES 1489 Fig. 9. Cross section of the PSFs for all four telescope configurations. u-v plane image reconstruction is performed (as one reconstructs radio wavelength array image data), then distinctions between interferometric instruments and conventional filledaperture astronomical telescopes are blurred. Although there are general arguments (Fienup 2000; Fiete et al. 2000) that show how sparse apertures can affect detected image quality, we are concerned here with the design of a versatile astronomical facility whose performance should not be dependent on specific image reconstruction techniques. Consequently, to achieve excellent image performance with any possible source, we consider optical concepts that are nearly filled-aperture, having filling factors larger than 50%. Fig. 10. Same as Fig. 9 but orthogonal PSF cross section.

5 1490 KUHN ET AL. Fig. 11. Radial average of the PSF for all telescope configurations. How should mirror segments in a large realistic optical/ IR astronomical telescope be arranged to optimize the PSF characteristics while allowing buildable AO systems? At one extreme, using mirror segments that minimize their edge-toarea ratio, we are likely to be limited by fabrication issues to 8 m diameter monolithic optics. Off-axis mirrors of 6.5 m diameter based on parent optics of unity focal ratio and as large as 22 m diameters are quite feasible, while 8 m diameters are also likely but will require some additional effort to devise testing procedures (J. Espiard 2000, private communication). Fig. 12. Cross section of the wider field PSFs for all four telescope configurations.

6 CONCEPTS FOR LARGE TELESCOPES 1491 Fig. 13. Same as Fig. 12 but orthogonal PSF cross section. At the other extreme of small mirror segments, it is almost certainly wasteful to consider segments much smaller than the expected atmospheric Fried length (r 0 ) given the diffractive losses and additional handling expense of a large number of mirror segments. The maximum size of the aperture we consider here has been guided in part by the historical growth rate in previous large telescopes and by the level of our expectations for funding resources that could be applied to a project of this magnitude. By considering perfect theoretical, and current real, tele- Fig. 14. Radial average of the wider field PSFs for all telescope configurations.

7 1492 KUHN ET AL. Fig. 17. Modeled edge errors for the SMT. multimirror off-axis telescope configuration and illustrates its performance. We favor this design, in part, because of its optical versatility and its various modes of scientific operations, which are briefly described in 5 and 6. Fig. 15. Extrafocal Keck images were registered and differenced to reveal local estimates of wave front curvature errors (M. Northcott 2000, private communication). Edge errors between mirrors appear to have a scale perpendicular to many of the mirror edges of 5 cm and amplitude of about one wave. scopes below, we are arguing for what the next generation of large telescope could look like. In 2 we model various PSFs with pupils of different geometries and levels of residual mirror figuring errors and under different observing conditions. All telescopes described below require off-axis mirror segments, but we use the term off-axis telescope (OAT) to refer to designs that are dependent on the fabrication of large off-axis mirrors. Section 3 discusses issues related to AO. Section 4 develops a full optical design for one possible version of a 2. THE QUEST FOR THE BEST PSF At the most fundamental level, the dynamic range of an image is limited by diffraction effects in the optical instrument or telescope. We shall therefore first calculate and compare the diffraction patterns for various pupil geometries, assuming perfect optics ( 2.1) and then realistic levels of optical figure errors ( 2.2). Atmospheric turbulence degrades the diffractionlimited PSF. We extend the calculations to include the effects of both natural ( 2.3) and partly compensated turbulence ( 2.4). Coronagraphic imaging is modeled and discussed in 2.5. Our comparison baseline follows from an impractical but simple and conventional geometry. We explore three more realistic alternatives for a large telescope pupil, all providing Fig. 16. Left: AO PSF of the Keck telescope in the H band displayed over two decades (M. Liu 2001, private communication). Right: Same data with the circular average subtracted from the PSF. Each panel corresponds to 2.2.

8 CONCEPTS FOR LARGE TELESCOPES 1493 Fig. 18. Left: SMT PSF with no edge errors. Right: SMT PSF with 0.1 wave rms edge errors. The intensity display range is four decades. identical light-gathering power and similar diffraction-limited resolution: 1. a monolithic mirror telescope (MMT [note, not multiple mirror telescope ]) with 17.4 m primary, 2. a segmented mirror telescope (SMT) with a hexagonally segmented primary, 3. a hexagonal off-axis telescope (HOT) with a distributed aperture made of 6 # 6.5 m unobstructed circular mirrors that are identical off-axis sections of a parent 20 m mirror, and 4. a square array telescope (SOT) whose aperture is made of 4 # 8 m off-axis mirrors. Figure 1 illustrates the pupil functions for these telescopes. The conventional MMT, despite the current impossibility of its optical manufacturing and mechanical construction, provides a useful and familiar basis of comparison for the other alternatives. It has a large central obstruction (7 m in diameter or 40% of the 17.4 m aperture) in order to make the telescope capable of a 1 field of view (FOV) without vignetting for survey work. The four orthogonal support struts of the secondary unit have a projected (and perhaps optimistically narrow) width of 20 mm, as scaled from extant 8 m telescopes. This affects the intensity and angular scale of the four familiar diffraction spikes. The fractional diffracted flux is proportional to the fraction of the pupil area obstructed by the struts, which is 0.21% of the 200 m 2 clear area for the MMT. The SMT pupil geometry is inspired from the Keck telescopes. The mirror segments and the global outline of the pupil are hexagonal. The face-to-face extent of the pupil is 16.6 m, which, with 21% of the area occulted by the secondary assem- Fig. 19. Circular average of the SMT PSF with and without 0.1 wave rms of segment edge errors. Fig. 20. Atmospheric phase error ( r0 p 0.8 m) across each pupil. The intensity scale range corresponds to about 10 waves of phase error. Clockwise from upper left: SMT, SOT, HOT, and MMT.

9 1494 KUHN ET AL. Fig. 23. Diffraction-limited core PSF for MMT and 1000-actuator core PSF from HOT, SMT, and SOT. Fig. 21. Natural seeing wide-field PSF plotted over four decades and Clockwise from upper left: SMT, SOT, HOT, and MMT. bly (the center and two rings of segments), leaves a 200 m 2 clear aperture. There are six 13 mm wide secondary support struts parallel to the segments edges and with their outer ends projected at the centers of the six pupil faces. This arrangement, also adopted for the Keck telescopes, minimizes light loss and diffraction effects. They obstruct 0.19% of the clear area. The choice of a segment size for a real SMT is a thorny issue. It involves considerations of diffraction effects, optical quality, mechanical support and control, cost, and serviceability. We cannot address all these questions here, and we limit our exploration to how diffraction effects and optical figure errors affect the PSF. We must first adopt a gap width between segments. We set this at 0.7% of the hexagon side length a, close to the Keck value. This implies that 0.6% of the pupil area is lost to gaps. Note that this is 3 times the area blocked by the secondary struts. The mirror segment size itself is a fundamental concern since the edges can be difficult to polish accurately and cannot be masked (without large diffracted energy losses) as is sometimes Fig. 22. Plots of the atmospheric PSFs for all pupil configurations and the SMT with edge errors. Fig. 24. Lyot coronagraph pupil-plane images using a 1000-actuator AO system.

10 CONCEPTS FOR LARGE TELESCOPES 1495 Fig. 25. Expected coronagraphic scattered light attenuation for 0.11 radius occulter and 1000-actuator AO systems. Fig. 26. Same as Fig. 25 but for 4000-actuator AO systems. Fig. 27. The HOT concept uses six subapertures, shown here in the narrow-field mode.

11 1496 KUHN ET AL. TABLE 1 HOT Narrow-Field Configurations Design M2-PF (m) Blur (arcsec) M2 Diameter (mm) NFM NFM NFM Fig. 29. NFM-6 geometrical spot diagrams computed across a 3 # 3 FOV. Fig. 28. HOT narrow-field mode (NFM-6) concept. M2 can be as small as 0.4 m in diameter or composed of six 140 mm optics. done with monolithic primaries. Mirrors with larger edge-toarea ratios scatter more energy. On the other hand, smaller and thinner segments may be more economical. We shall therefore explore two segment diameters 2a in our PSF studies: m segments on six rings and m elements on 11 rings. The details of a particular HOT optical prescription that we call a high dynamic range telescope and its conceptual mechanical design are discussed in 4. Here we consider the pupil geometry only inasmuch as it affects the characteristics of the PSF. The HOT pupil is simply six 6.5 m off-axis circular mirrors with centers equally spaced on a 13.5 m diameter circle. These mirrors are identical sections of a parent 20 m mirror about whose optical axis this composite telescope is arranged. There are no central obstruction or strut shadows. The SOT configuration is a four-element variant of the clearpupil HOT concept. The four segments are 8 m in diameter, to provide a 200 m 2 clear area. The square defined by the mirror centers is 9.2 m on a side, leading to a 21.1 m parent for the pupil. As we show below, this is the most compact configu-

12 CONCEPTS FOR LARGE TELESCOPES 1497 Surface Radius (mm) TABLE 2 Optical Prescription for HOT NFM-6 Thickness a (mm) Conic Constant Clear Aperture Parent Surface M # 6.5mF/ mF/1 M # m F/ m F/0.85 FP # 288 mm 2 Note. The effective focal length is 330 m, yielding a focal ratio of F/15 and plate scale of mm 1. a Parent vertex mirrors M to M distance along system optical axis. i i 1 ration possible with a nonobstructing 5.1 m secondary. This configuration offers diffraction-limited performance comparable to the HOT but with fewer subapertures Diffraction-limited PSFs The Fraunhofer diffraction patterns for these pupils are most expeditiously computed analytically from standard diffraction theory (Born & Wolf 1987). Indeed, qualitative illustrations of similar patterns can readily be found in most optics textbooks. It may be useful to first briefly recall some general properties of these patterns. An unobstructed circular pupil of diameter D generates the well-known Airy pattern: a central core of FWHM about l/d surrounded by diffraction rings whose peak intensities are enveloped by an r 3 profile. With a central obstruction of kd,the core becomes slightly narrower, its central intensity is reduced 2 2 by a factor (1 k ), the inner diffraction ring is enhanced, and the envelope of the outer rings becomes gradually shallower and would develop an r 1 profile if k approached unity: Obstructions produce brighter diffraction rings. Obstruction causes sidelobe confusion (directly proportional to the brightness enhancement e of the diffraction sidelobes), and at best the background noise is increased by the square root of this enhancement if a perfect PSF subtraction can be achieved (which is obviously problematic). The signal-to-noise ratio (S/N) for background-limited detection of a point-source PSF in the diffraction regime is proportional to the pupil area divided by the background noise under the PSF. This noise increases as e but is independent of the pupil area the PSF area shrinks as the collecting area increases. An equivalent dynamic range would then be had, at the same offsets in l/d units, with a clear pupil area smaller by a factor of 1/ e. To give a simple example, in the case of a central obstruction, Figure 2 shows the ratio of the obstructed-to-unobstructed aperture diameter required to achieve a constant S/N at the first three diffraction rings as a function of the central obstruction factor k c. The calculations take into account the flux reduction by the obstruction. Any obstruction makes the first ring brighter, and large values of k c are detrimental over the whole PSF (although specific diffraction rings can be marginally attenuated for some ranges of k c ). Linear pupil features, such as straight edges or spider/strut shadows of length l and of spacing or width w, generate the 2 familiar (sin X/X), X p pl/w spikes orthogonal to their length. Their total flux is proportional to area lw, and their intensity at zero offset is proportional to that area squared. Their envelope falls off as r 2, and, at a given offset, the energy per unit length in a spike is proportional to the length l of the feature while the maximum intensity is proportional to l 2. With any reasonable central obstruction, the spikes dominate the scattered light at large offsets. Figure 3 plots the typical radial variation in scattered light surface brightness for a conventional 6.5 m aperture telescope. With an altitude-azimuth (alt-az) mounted telescope, a PSF adorned with such spikes rotates on the detector during an exposure. The intensity profile of the smear then follows an r 3 law, as in the case of a circular(ized) pupil. If the angle of rotation is limited or the rotation speed variable, this diffuse light will vary in azimuth. Diffraction spikes reduce the dynamic range along their lengths. Kuhn & Hawley (1999) showed how faint-object detection thresholds in a typical observation will be degraded by bright stars well beyond the FOV. We note here (and discuss below) that these obstructions also affect the performance of the AO wave front reconstruction, since these areas within the pupil where information about the wave front slope or curvature is lost can affect the wave front reconstruction. The diffraction pattern from the telescope pupil P(v) can be described as the product of a single subaperture diffraction pattern O(v) (an Airy function for all but the SMT) times a periodic structure function determined by the offset vectors between subapertures S(v). Here v represents the small angle coordinates in the image plane we have P p SO. If each mirror segment is displaced from the optical axis of the telescope by a vector displacement a in a hexagonal pattern (as for the HOT), then 2 S(v) p [cos kav x cos kav x/2 cos (ka 3v y/2)] describes a function that is a regular, infinite hexagonal pattern with angular spacing between maxima of v m p 2l/(a 3), where k p 2p/l and a is the displacement magnitude. A square subaperture displacement pattern generates a square lattice structure 2 function, S(v) p (cos kavx cos kav y), with a spacing between peaks of v m p l/(a 2). The interferometric (structure function) image core resolution is characterized by the angular distance between the central peak of S and its first zero. For the hexagonal telescope this is

13 1498 KUHN ET AL. Fig. 30. NFM encircled energy performance: (a): radial distribution of the enclosed energy and the diffraction-limited performance of the system in a 10 # 10 field. The dashed gray lines indicate the diffraction limits at 700, 900, and 1250 nm. (b): Encircled energy spot profiles across a 3 FOV. v0 p 0.38l/a. The SOT has less resolution v0 p 0.5l/a for the same mirror offset a. The core image concentration might be described by the ratio of the distance between maxima to the resolution width, v m/v0. This is 3.0 for the HOT but more than twice as small (1.4) for the square array. The larger number of mirrors in the hexagonal array improves the interferometric core image resolution and mitigates image confusion caused by the lattice structure of S. Circular subaperture mirrors have a diffraction pattern O(v) with circular (Airy function) symmetry and zeros at v p 1.22, 2.22, 3.24, in units of l/d, where D is the sub- aperture diameter. Since the total telescope PSF is the product of O and S, we can further minimize multiple-order confusion by arranging for the minima in O to coincide with maxima in S. With circular subapertures, complete cancellation of all noncentral maxima is not possible, but we can pick a and D to 3 minimize the near-central maxima while relying on the 1/v falloff of O to attenuate larger angle structure function maxima. Since subapertures cannot overlap, the HOT must have a 1 D, and the SOT has a D. By aligning the second Airy ring of O with the second hexagonal ring of maxima in S, we obtain the most compact HOT, with a p 1.04D. Matching the first Airy ring with the SOT s second structure function maxima yields the most compact SOT, having a p 0.82D. The maximum diameter of the array (the parent diameter) in either configuration is Dp p 2a D. Thus, geometrically comparable SOT and HOT telescopes can be constructed from, correspondingly, D p 6.5 m or D p 8 m mirror segments. The parent diameter (which determines the largest off-axis polishing distance) would be 21.1 m for SOT and 20 m for HOT, either configuration yielding subaperture mirrors that are manufacturable. The SMT telescope is constructed from several rings of small hexagonal mirrors offset over multiple hexagonal displacement patterns. The SMT PSF can then be calculated from functions O and S as the HOT and SOT PSFs were determined. As we have seen, the structure function for a hexagonal ring of displacements is a hexagonal pattern in angle coordinates. Additional rings of mirror offsets cause the peaks in the hexagonal lattice of S to sharpen. Figure 4 shows six- and 11-ring hexagonal segmented mirror structure functions. Ridges between peaks in the structure function are about 10 3 of the peak amplitude. When the hexagonal mirror segment radius r fills out the pupil plane with r p a/ 3 (a is the mirror displacement distance), the zeros of O coincide with the noncentral peaks of the structure function. Thus, mirror gaps cause r! a/ 3, so peaks in the structure function will not coincide precisely with diffraction function zeros and the telescope PSF will exhibit spurious secondary peaks. Gaps in SMT mirror segments produce secondary PSF speckles on a hexagonal lattice with angular spacing of 2l/(a 3). Figure 4 shows how the O function zeros coincide with a six-ring structure function when the gaps are small and when the gaps are 0.1a. A problematic characteristic of an array s PSF is that the sidelobes take the form of speckles that are fainter but similar to the central core of the PSF. This can lead to confusion in the study of faint pointlike sources, a problem that does not arise with the diffraction rings of a filled circular pupil. It follows from the above considerations that, in principle, the highest dynamic range PSF is provided by a single unobstructed circular pupil giving a pure Airy pattern. This is especially true if the telescope operation will lead to PSF rotation.

14 CONCEPTS FOR LARGE TELESCOPES 1499 Fig. 31. WFM layout; the effective focal length is EFL p 41,838 mm, resulting in an F/1.90 focal ratio and a plate scale of 4.93 mm 1. The position of the tertiary mirror M3 and focal plane FP were constrained during these optimizations. For a reflecting telescope, such a pupil is provided by a single off-axis monolithic primary mirror. The intensity of the diffraction rings can be attenuated by pupil apodization. This entails a loss of light, which is often considered objectionable, and a slight loss in resolution. Apodization of a pupil image can be incorporated in dedicated coronagraphic imagers, which are briefly modeled below. With this background in mind, we examine the diffraction PSFs for the four pupils described above and illustrated in Figure 1. Figure 5 shows diffraction-limited images of a point source at 1.6 mm for all configurations. Each of the four subpanels shows a field 0.18 wide, has the same logarithmic intensity scale, and displays four decades. Figure 6 shows these PSFs on a linear scale. A wide-field (1.8) view of the logarithmic and linear PSFs is shown in Figures 7 and 8. The hexagonal pattern in the SMT and HOT PSFs follows from the mirror structure function, while the starlike flare of the SMT versus the nearly circular pattern of the HOT are consequences of the straight edges versus circular subaperture diffraction patterns of the hexagonal versus circular mirror segments. Radial profiles of the diffracted light for the telescopes are illustrated in Figures 9 and 10. A more representative measure of diffraction (illustrated in Fig. 11) follows from the circular average of the PSF since any large telescope is likely to require an alt-az mount and will produce either a rotating pupil or field at the detector. Figures 12, 13, and 14 show the corresponding radial variation over 0.5. While the average first diffraction minimum in the HOT is lowest of any nonmonolithic pupil Surface Radius (mm) TABLE 3 Optical Prescription for HOT-WFM Thickness a (mm) Conic Constant Clear Aperture Parent Surface M # 6.50mF/ mF/1 M A b 6 # 2.34mF/3.00 7mF/1 M m F/1.49 FP... Flat 730# 730 mm 2 Note. The system effective focal length is EFL p 41,838 mm, giving a system focal ratio of F/1.90 and plate scale of S p 4.93 mm 1. a Parent vertex mirrors M to M distance along system optical axis. i i 1 b A hyperboloid plus fourth-order polynomial deformation.

15 1500 KUHN ET AL. Fig. 33. Variation in WFM optical performance versus M2 M3 distance. Fig. 32. WFM geometrical spot performance. Spot diagrams are computed across the 1 # 1 field. configuration, there are no spectacular differences between the diffractive PSFs given our assumption here of perfect optics and small SMT mirror gaps Effects of Optical Figure Errors Off-axis optics are difficult to make whether circular or hexagonal. At some level, polishing defects are bound to remain. However, since all parent primary mirrors discussed here have similar sizes and prescriptions, we will assume that the amplitudes of surface errors are comparable in all cases and, aside from edge-specific defects, introduce no significant differences in the imaging performance. Figure 3 shows how optics as smooth as the Hubble Space Telescope contribute to scattered light. The question of segment edges should however be addressed in more detail because the different segmentations lead to large differences in edge-to-area ratio between the pupils. Segment edges, circular or linear, constitute mechanical surface discontinuities that are inherently challenging to polish without introducing optical surface irregularities. This is the well-known turned edge problem. The technique of ion polishing has been used to touch up segment edges with considerable success, notably for the Keck telescopes. It remains to be seen whether ion-polishing techniques can be applied with sufficient spatial resolution and dynamic range to eliminate edge-specific errors in future large-array segmented telescopes. M. Northcott (2000, private communication) has analyzed extrafocal Keck/Low-Resolution Imaging Spectrograph images to quantify residual wave front errors. Figure 15 shows a peculiar hexagonal-pattern wave front curvature error, which may be due to mirror edge errors. While there is no reported evidence of edge polish errors in the Keck mirrors, the PSF structure in Figure 16 is quite similar to the modeled PSF structure we obtain with mirror edge errors in SMT pupil configurations. The representative H-band PSF, obtained with AO (M. Liu 2001, private communication) and displayed in Figure 16, shows the corresponding hexagonally distributed peaks (now streaks because of the finite wavelength bandwidth) that are characteristic of the SMT. Similar to the effect of edge gaps, which allow diffraction structure function peaks to leak into the PSF, edge errors would generate peaks in the net telescopic PSF. It seems likely that the question of mirror edge polishing will be a key issue in understanding how future large telescope pupils should be arrayed. One approach to exploring these effects is a direct simulation of randomly turned up or down edge errors. Because the SMT has the largest edge-area ratio, it is instructive to use it as our baseline for edge error PSF

16 CONCEPTS FOR LARGE TELESCOPES 1501 Fig. 34. Permanently mounted HOT design combining WFM NFM. The distance from the vertex of WFM-M3 to WFM-M2 is m, and the vertex distance from NFM-M2 to its FP is 6 m. The distance from M1 vertex to WFM-M2 is 15.5 m, and the M1 vertex to NFM-M2 is 22.4 m. The NFM design produces subaperture-m2 mirrors of 140 mm diameter. The diameter for WFM-M3 is 7.0 m, and the subaperture mirrors are 2.34 m. calculations. Figure 17 shows our model for these errors. Each segment has a 5 cm random, linear, turned up or down edge that generates a 0.1 wave rms figure error over the edge region. Figure 18 shows how these errors contribute to the hexagonal residual speckle pattern in the SMT PSF. Figure 19 shows that most of the enhanced scattered light appears outside of the core image but can degrade the PSF by as much as 1 order of magnitude within 2 of the central peak. Comparable edge errors in the MMT, HOT, or SOT yield a PSF degradation that is a factor of 3 4 smaller. The effects of segment misalignment (lateral, rotational, and piston errors) will also provide important constraints on telescope design. Interpreting these errors also requires a careful understanding of the likely mechanical performance of the telescope mirror support structure, which goes beyond the scope of this paper PSFs under Natural Seeing Conditions While any large-aperture telescope will certainly depend on AO for narrow-field observations, its wide-field PSF performance may be defined by the natural seeing conditions. To account for the effects of the atmosphere, we have added a Kolmogorov phase screen with a Fried length of 0.8 m at 1.6 mm to the perfect optics pupils. Figure 20 shows the pupil-plane phase errors over a display range of about 10 waves. This corresponds to median seeing conditions (0.4 FWHM in the H band) at good sites. Since this is a much coarser resolution

17 1502 KUHN ET AL. Fig. 35. Full HOT optical layout. Bottom left corner: M2-WFM is composed of six subaperture mirrors, and they can be separately folded up or down like petals on a flower out of the way of the NFM light path. At the top left of the figure we see the six narrow-field subaperture mirrors that are 140 mm in diameter and the unobstructed prime focus. than the diffraction limit of 0.02 for these pupils, no differences in performance should be detectable in the image cores. The level and shape of the diffraction spikes and scattered light well beyond the telescope diffraction limit are affected. Figure 21 shows the PSF over four decades and The circular averaged PSF is displayed in Figure 22. Scattered light differences between telescope pupils are apparent beyond a few arcseconds of the image core. The worst case occurs for the SMT mirror with edge errors: scattered light is about 1.5 mag brighter than other configurations beyond AO-compensated PSFs To examine the PSFs with AO compensation, we model the optical system as if it estimates the atmospheric phase errors using an interpolating function between a sufficient number of points ( actuators ) to achieve a compensated Strehl of 0.5. An equivalent procedure would have been to attenuate, in the phase screen, a sufficient number of lower order Zernike modes to the variance of the first noncompensated higher degree mode in order to reduce the residual wave front variance to 0.7 rad 2. According to the weights of the modes under Kolmogorov turbulence by Noll (1976), the attenuation of 160 modes would be required. This hypothetical AO system is quite respectable by today s standards. It is not unreasonable to expect its availability on m telescopes, given the current rapid development of AO technology. Thus, Figure 23 shows the expected core PSF on each telescope from a 1000-actuator system with R0 p 0.8 m at a wavelength of 1.6 mm. We shall return below to the relative complexities of AO implementation on the SMT and OATs Coronagraphic PSFs The diffracted PSF flux can be attenuated by a coronagraph. When the Strehl is large, this leads to a significant reduction of the background noise in the PSF wings and greatly facilitates the study of crowded, faint image features. The coronagraph reduces scattered light by reimaging the object through a pupil (Lyot) mask that blocks some of the diffracted light from the

18 CONCEPTS FOR LARGE TELESCOPES 1503 Fig. 36. HOT primary mirror M1 surface. (a): Deviation from the best-fit sphere for the parent primary mirror, a pure paraboloid. The shaded region indicates the radial extent of each subaperture of the parent mirror. (b): Geometry of each of the subapertures. Each of the six 6.5 m diameter subapertures define an F/3.38 beam that intersects at the telescope prime focus 0.4 m below the secondary mirror vertex. pupil edges. In the conventional Lyot coronagraph, a small occulting disk in the focal plane blocks the PSF light across a few Airy rings. Its effect is to high-pass filter pupil-plane spatial frequencies. In the pupil image, formed by transfer optics, the energy in the diffraction rings and spikes is preferentially directed toward the images of the diffracting pupil discontinuities (pupil edges, support struts). Thus, the image looks like a strioscopic rendition of the pupil discontinuities. In the presence of atmospheric turbulence, a phase contrast image of the atmospheric wave front is produced (Fig. 24). A Lyot mask somewhat smaller than the pupil image itself, and possibly including broad struts or obstructions, is placed at the pupil image to block the strioscopic light. Thereby, much of the on-axis point-source light diffracted by the pupil discontinuities is removed. Other coronagraphic designs involving apodized or phase masks (cf. Roddier & Roddier 1997) may yield improved coronagraphic performance over limited passbands, but, since we are primarily interested in intercomparing the performance of these optical configurations, we will not consider other designs here.

19 1504 KUHN ET AL. Fig. 37. HOT-NFM secondary mirror M2 surface showing the deviation from the best-fit sphere for the parent secondary mirror, a pure conic ellipsoid with its major axis on the optical axis. The shaded region indicates the radial extent of each subaperture of the parent mirror. With a traditional MMT, the simplicity of the pupil image allows the Lyot mask to be very efficient. With an SMT, however, the adjacency of the subpupils (segments) makes it difficult to efficiently mask their edges, except at the periphery of the pupil: attenuation of the diffraction pattern is then less Fig. 38. HOT-WFM secondary mirror M2 surface showing the sag shape and aspheric departure. M2 naturally divides into 6 # 2.34 m mirrors.

20 CONCEPTS FOR LARGE TELESCOPES 1505 efficient. For the HOT and SOT configurations, the required Lyot mask geometry is slightly more complex than for the MMT, but no struts or linear segment gaps need to be masked. We model the performance of an SMT and OATs with a Lyot coronagraph in both the simple, fully diffraction limited case and in the case of AO-compensated atmospheric wave fronts. In each case our image-plane mask occults a disk of radius The Lyot mask is constructed by decreasing the linear size of each subaperture or segment by 5%. Struts are masked by expanding their thickness by a factor of 5 in the Lyot mask. In the case of the SMT this results in a mask that occults all segment boundaries. It is not clear that this is a practical solution, but it does treat the SMT conservatively. Without AO, under normal seeing conditions, the coronagraphic attenuation of the PSF light beyond the occulting disk is minimal and the attenuation is not a function of the optical pupil configuration. With the 1000-actuator AO system described above, we begin to see differences in the scattered PSF attenuation. Figure 25 shows the circular average of the attenuation of scattered light from the SMT and HOT configurations (corresponding curves for SOT and MMT are not noticeably different than the HOT result). We note that beyond about 1.5 the coronagraphic attenuation of the HOT is better than the segmented mirror telescope. It is possible that future AO systems will use thousands of actuators to achieve very high Strehl ratio. We note that with a 4000-actuator AO system the attenuation improves but with noticeably better coronagraphic attenuation for the HOT within 1 and beyond 1.5 (Fig. 26). Fig. 39. HOT-WFM tertiary mirror M3 surface showing the sag shape and aspheric departure Lessons from PSF Studies All configurations have very similar imaging performance under atmospheric conditions. Except in very specific diffractive performance details, there are only small PSF distinctions between the MMT and OAT configurations, although the difference between these and the SMT configuration grows with improved AO and as segment edge-polishing requirements are relaxed. For high-order coronagraphic AO uses, the OATs may even achieve several magnitudes of scattered light suppression compared to an SMT (for the same level of effort in their AO and coronagraph designs). It is possible that dark spots in the actual (measured) telescope PSFs could be used to improve the dynamic range for some specific and well-defined detection problems. With higher order AO systems the advantages of the larger circular segments will be more decisive. Such high-order systems will be available during the lifetime of currently planned m telescopes. The scientific benefits to be reaped fully justify building telescopes capable of best reaping them. Given these differences between the SMT and OATs, it is useful to further explore the geometrical optics performance and some optical configuration advantages of a distributed pupil design. Since the optical configuration of segmented mirror systems like Keck have been described elsewhere (Dierickx & Gilmozzi

21 1506 KUHN ET AL. Fig. 40. HOT optical support structure concept. 2000), our discussion below centers on an HOT-style telescope configuration. 3. ADAPTIVE OPTICS IMPLEMENTATION WITH DISTRIBUTED PUPILS A challenge to AO implementation on large-aperture telescopes is the high dynamic range required from the wave front correction scheme and deformable mirror. This is so because the rms phase fluctuations due to the atmosphere between points 5/6 separated a distance d is approximately (d/r 0) rad (Kolmogorov 1941; Tatarski 1961). Thus, the actuator displacement range required from a deformable mirror increases nearly linearly with the telescope aperture. For r p 0.8 m turbulence, 0 a 20 m telescope must correct an rms wave front distortion of 2.5 waves: The dynamic range of the required wave front correction is therefore 15 mm or 20 waves for a deformable mirror used in the H band. In distributed pupil telescopes, it is possible to separately correct the largest component of the turbulence, the phase and tilt differences between subapertures, with a physically distinct low-order correction scheme. One technique for doing this is described by Roddier (2000). Adaptive optics and active alignment systems are fundamental components of a telescope design. Hopefully, before 20 m class telescopes are completed, multiconjugate and tomographic techniques will be devised to extend their useful diffraction-limited FOV. For example, Fusco (2000, unpub-

22 CONCEPTS FOR LARGE TELESCOPES 1507 lished) estimated how the FOV of a telescope such as the HOT could be improved with three guide stars. With a 2 guide star separation the expected FOV is 2 3 across. Larger apertures naturally improve the isoplanatic FOV for multiple guide star AO systems. It is notable that in 0.5 seeing and at a wavelength of about 3.5 mm a distributed pupil 20 m telescope can approach its diffraction limit of 0.04 with only tip-tilt correction of the wave fronts from its individual 6.5 m segments and adequate pupil phasing. The technology for maintaining optical alignment of mirror segments at a level much less than a wavelength is now well demonstrated at the Keck telescopes (see Chanan & Ohara 2000). Likewise, either active referenced mirror alignment techniques or indirect optical methods (see Roddier 2000) can be used to achieve the phasing required for the distributed mirror segments. An interesting feature of the distributed optical configurations is that current AO and segment phasing technology is sufficient to realize the effective resolution of the parent primary mirror aperture. The HOT AO system, for instance, when considered as six cophased 6.5 m pupil systems, is little more complex than current large telescope AO systems. The UH/IfA curvature system on the Gemini telescope will shortly use an 85-actuator system capable of a 0.7 Strehl at D/r0 p 6.5/0.8 p 8. Finally, we must consider the effect of edges and gaps in the pupil domain on the wave front reconstruction algorithm that any AO system uses. In the case of, for example, the SMT we might expect realistic wave front reconstructors to lose information over the small segment gaps where wave front tilt or curvature information is lost or requires additional algorithm complexity to extract. Simple time-dependent wave front reconstruction simulations using the above parameters and a moving atmospheric phase screen show a higher temporal bandwidth in the speckle pattern of SMT than the OATs or MMT pupils. We attribute this to the shorter travel time of an atmospheric wave front cell across a pupil boundary where wave front phase information is lost (i.e., the ratio of the smallest mirror segment length and the phase screen pattern velocity). It seems likely that high-order AO correction on an SMT will require a higher temporal control loop bandwidth for this reason. Technical problems must be solved in order to implement the active and adaptive optics systems that are essential for any large telescope. One immediate advantage of larger mirror segments is that fewer mechanical degrees of freedom must be controlled, since the number of mirror edge actuators and sensors decreases with larger segments and fewer mirrors. Maintaining a short thermal time constant for the primary optics implies the same mirror thickness for either configuration and a constant radial actuator areal density. The implied high geometric aspect ratio of the OAT designs may thus incur greater handling risk. 4. OPTICS The OAT (HOT and SOT) pupil configurations can lead to important optical and mechanical advantages. We illustrate these points with more detailed geometrical descriptions of the HOT optics needed to achieve wide- and narrow-field operation. We note that the HOT pupil described below uses a p 1.19D in order to simplify the straw man mechanical structure Narrow-Field Mode The overall size of the fictitious OAT parent optic is a critical telescope parameter. For telescopes with a net aperture range of m it is efficient to use a single parabolic parent mirror shape, from which identical subapertures are extracted. Either conventional active closed-loop metrology for optics alignment or interferometric beam-combining techniques would then be used to form a common image. The parent mirror is of course never physically generated, but it defines the common geometry of each subaperture. Our choice of 6.5 m off-axis segments was determined from currently available polishing technology for off-axis optics, and cost concerns. Discussion with manufacturers led us to believe that segment diameters could vary, probably with predictable costs, up to 8 m for a 30 m diameter parent. Of course, the parent optic of the off-axis mirrors will be constrained by the physical envelope of the telescope enclosure; greater off-axis distances could be accommodated in larger designs. Our choice of a parabolic primary is driven by several technical considerations. These include the existence of a real prime focus, the possibility of efficient coronagraphic observing, and the natural ability to also achieve wide-field performance using two additional mirrors. The telescope narrow-field mode (NFM) uses a two-mirror Gregorian optical configuration. The parent is a 22 m F/1 parabola from which we use an array of 6 # 6.5 m off-axis sections. One could also use only one of the six segments, which could be superpolished for enhancing the imaging performance without structure function sidelobes. The optical path beyond the prime focus will be completely accessible along a structural optical bench that is parallel to the parent optical axis and is outside of the optical path of the decentered light path from each 6.5 m off-axis primary mirror segment. The NFM illustrated in Figure 27 was optimized to produce an F/15 system across a 3 # 3 FOV, with an effective focal length (EFL) of 330 m and a scale of S p mm 1.Very small secondary mirror (M2) segments are possible. In this way any instrument that requires an FOV smaller than a few minutes of arc can use a secondary mirror comparable to the size of its internal optics. Since the light path is fully accessible beyond M2 without obstructing the primary mirror, astronomical instruments may be designed to include their own specialized secondary mirror or mirror segments and would be suited for implementing cryogenic or adaptive secondary optics as subcomponents. Designs with a larger M2 would allow a

23 1508 KUHN ET AL. more conventional configuration with instruments mounted behind the primary mirror. A single NFM-M2 mirror is possible, but for tip-tilt and alignment purposes it may be useful to use six separate off-axis mirrors for the secondary optics. In this case each M2 subaperture illumination pattern must not touch. This yields a constraint on the FOV and the distance of the parent M2 vertex from the prime focus (PF), here designated M2-PF. Several optimizations (Table 1) were done as a function of the distance between the M2 vertex and the focal plane, M2-FP. In Table 1 the blur is computed from the 80% encircled energy diameter. The shortest possible design was obtained with M2-FP of 6 m, which we designate NFM-6 below. Its optical prescription is presented in Table 2, and the layout of NFM-6 is shown in Figure 28. The distance between the prime focus and Gregorian focal plane (FP) here is 5600 mm with an effective focal distance of 330 m and a system focal ratio of F/15. This is not the optimal Gregorian design for the NFM because it was designed with the constraint of a small M2 and short PF-FP distance. Other optimizations were done for longer designs: M2-FP varying from 8.0 to 18 m, which requires a larger secondary mirror, as described above, but which yields better performance than the shorter NFM-6 design. In all NFM optimizations the M2 mirror is a concave oblate ellipsoid with small variations of the conic constant (less than 1%). The Gregorian focal surface is concave down with a radius of curvature of about 0.5 m. This can be corrected within the instruments as is often done for existing telescopes. Figure 29 shows the NFM-6 geometrical spot performance across a 3 FOV. The design space for the NFM allows several mechanical options to be explored. The best design would be determined by considering the mechanical constraints imposed by a versatile optical configuration that allows both wide- and narrow-field performance with minimal configuration change overhead. Over a small FOV, suitable for AO and coronagraphy, the image must be diffraction limited. This is achieved even with the most compact NFM-6 design. Figure 30 shows that this design on a 10 # 10 FOV is diffraction limited to wavelengths as short as the R band (700 nm) Wide-Field Mode To provide a wide-field imaging and spectroscopic mode (WFM), we considered F/1.9 systems that were optimized over a 1 # 1 and a 2 # 2 FOV with a scale of 4.93 mm 1.A 3 FOV is also possible with some image degradation at the field edges. The requirement for fast optics is driven by the need to develop an affordable (0.7 m diameter) focal plane. Using the NFM 6 # 6.5 m off-axis primary mirror described above we, obtain an off-axis Paul-Baker configuration by adding convex secondary (M2-WFM) and concave tertiary (M3-WFM) corrector mirrors. A conventional Paul-Baker configuration produces excellent correction across a wide FOV but suffers from significant obscuration because of the large secondary and tertiary mirrors (see Moretto & Kuhn 2000). With an OAT configuration, the secondary (M2-WFM) and tertiary (M3-WFM) mirrors can be placed outside of the optical path of each 6.5 m primary mirror segment. Different WFM configurations have been considered: (1) a shorter telescope design using a shorter distance between the M1 vertex and M2-WFM, (2) a shorter corrector design that uses a smaller distance between M2-WFM and M3-WFM vertices, and (3) smaller diameter mirrors for M2-WFM and M3- WFM. The optimum WFM design uses a longer configuration with an M2 M3 distance of 24 m (WFM-24). In this case the tertiary mirror (M3-WFM) is located 8.9 m behind the primary mirror M1 vertex, and the M2-WFM vertex is 15.5 m from the M1 vertex, as shown in Figure 31. The M2-WFM diameter is 7 m, but only six off-axis sections of the secondary mirror (M2-NFM) are illuminated. Thus, M2-WFM can be built from an array of six small off-axis mirrors each 2.3 m in diameter. The M3- WFM diameter is 7 m and is a single mirror. Table 3 displays the optical prescription for WFM-24. The resulting geometrical spot performance across this large field is excellent. Figure 32 shows the WFM spots with a detail of the central spot pattern. Several designs were optimized as a function of the M2 M3 distance while keeping M1 M2 close to m. A comparison of the blur diameter optical performance is shown in Figure 33. The figure shows the trend in the mean values of the blur circle diameter for 80% and 50% of encircled energy for the eight spot positions at the edge of the flat 1 # 1 FOV. The longdesign (WFM-24) performance is represented by the two points at the bottom right side of Figure 33. The distance M1 M2 is not constant as M2 M3 varies, but ranges between 18 and 19.4 m. The figure shows that designs with M2 M3 larger than about 12 m achieve seeing-limited optical performance across the 1 FOV. The solution for a 2 # 2 field requires M2 mirror segments that are 2.6 m in diameter and an M3 that is 8.1 m. The mean rms and 80% energy spot diameters across the field in this design are 0.30 and Mounting WFM and NFM The open pupil structure allows access to the OAT optical path along an optical bench that extends up through the core of the telescope. This makes it feasible to design a telescope that can change from NFM to WFM without perturbing the instruments or optics. Thus, we envision a telescope facility that has NFM and WFM instruments permanently mounted, along with all secondary optics, on a central core of the optics support structure (OSS) truss. As we show below, it is possible to design an OSS that accommodates WFM and NFM optics by folding the six M2-WFM mirror segments up or down like petals on a flower. This mechanical structure will be actively stiff and should simultaneously support all optics and NFM instruments.