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Design Considerations for a Highly Segmented Mirror

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Design Considerations for a Highly Segmented Mirror Design considerations for a highly segmented mirror Stephen Padin Design issues for a 30-m highly segmented mirror are explored, with emphasis on parametric models of simple, inexpensive segments. A mirror with many small segments offers cost savings through quantity production and permits high-order active and adaptive wave-front corrections. For a 30-m f͞1.5 parab- oloidal mirror made of spherical, hexagonal glass segments, with simple warping harnesses and three- point supports, the maximum segment diameter is ϳ100 mm, and the minimum segment thickness is ϳ5 mm. Large-amplitude, low-order gravitational deformations in the mirror cell can be compensated if the segments are mounted on a plate floating on astatic supports. Because gravitational deformations in the plate are small, the segment actuators require a stroke of only a few tens of micrometers, and the segment positions can be measured by a wave-front sensor. © 2003 Optical Society of America OCIS codes: 350.1260, 010.1080, 220.4880, 120.4640. 1. Introduction design considerations are explored here for a 30-m Multiple mirrors seem to be the only viable approach f͞1.5 visible and infrared telescope with AO. for optical telescopes with apertures much larger For a large mirror with small segments, the cost than ϳ8 m. Many designs have been proposed, and and complexity of sensors and actuators are key is- these are broadly distinguished by the size of the sues. If gradients in the telescope structural defor- subapertures. The 20–20 telescope elements, which mations are repeatable at the level of ϳ1 ␮m across have seven 8.4-m-diameter segments,1 and the a segment diameter, changes in the segment posi- Phased Array Mirror Extendible Large Aperture tions can be measured by a wave-front sensor instead ͑PAMELA͒, with 8-cm-diameter segments,2–4 repre- of edge sensors. The wave-front sensor could also be sent the extremes of the design space. The Keck shared by a high-order AO system. If segment-to- telescopes, with 1.8-m-diameter segments,5 and the segment piston errors are not repeatable at the level Hobby-Eberly Telescope, with 1.15-m-diameter seg- of approximately half of the wave-front sensor wave- ments,6,7 are the only working multiple-mirror tele- length, an iterative piston-stepping algorithm,9 or scopes. measurements at multiple wavelengths, must be Small segments have potential for a lightweight, used to resolve 2␲ phase ambiguities. The deforma- low-cost telescope mirror and can support adaptive tion gradient constraint is severe, but feasible: Ax- optics ͑AO͒ if the segment diameter is approximately ial gravitational deformation of the primary in the half of the Fried parameter.8 PAMELA addressed 30-m California Extremely Large Telescope ͑CELT͒ some of these issues, using a scaled version of the design is ϳ10-mm p.-p., i.e., ϳ700-␮m p.-p. on 1-m Keck approach with inductive edge sensors and voice scales10; gravitational deformations in the Keck tele- coil actuators, but the large number of edge sensors scopes are repeatable at the level of 1 part per 1000, and high actuator power consumption make the de- so the nonrepeatable deformation in the CELT pri- sign unattractive for a very large mirror. Simpler mary should be Ͻ1-␮m p.-p. on 1-m scales. A thin small-segment schemes are possible, and some of the highly segmented mirror will have low mass, which will help to achieve small, repeatable structural de- formations. Small gravitational deformations on the scale of a segment diameter also allow the mirror to be constructed with small gaps between segments. The author is with the California Institute of Technology, Mail This is important because it gives a low infrared Stop 105-24, 1200 East California Boulevard, Pasadena, California 91125. His e-mail address is [email protected]. background and low diffraction pattern sidelobes. Received 26 July 2002; revised manuscript received 16 Decem- The stroke of the segment actuators is set by grav- ber 2002. itational deformations in the telescope structure, but 0003-6935͞03͞163305-08$15.00͞0 these are mainly on large spatial scales, so it is not © 2003 Optical Society of America efficient for the segments to have expensive, long- 1 June 2003 ͞ Vol. 42, No. 16 ͞ APPLIED OPTICS 3305 stroke actuators. An obvious development is a hier- and the more sparse array of mirror plate cells. Be- archy of actuators, with a few long-stroke actuators cause the mirror plate has a simple force-based sup- compensating most of the structural deformation and port, the number of support points can be large, and short-stroke actuators on each segment providing the plate can then be a fairly thin, lightweight struc- fast and small spatial scale wave-front control. This ture. scheme is particularly appropriate if the mirror is The floating mirror plate averages segment actua- made of several rafts of segments because the low- tor reaction forces over large spatial scales, and the order deformations can be compensated by use of force-based support decouples the mirror plate from actuators on each raft.3 Compensation of low-order the telescope structure. These effects minimize deformations could also be moved to a fairly small control–structure interaction for adaptive correc- active mirror at an image of the primary, leaving just tions, so the segments do not require reaction masses, high-order corrections in the primary. Several dif- and this helps to reduce the cost and mass of the ferent optical designs are possible,11–14 but the mirror. The mirror plate is tightly coupled to the schemes with good image quality have two or three segment actuators, and keeping the natural frequen- additional reflections that cause a significant sensi- cies of the plate modes above the frequencies of adap- tivity degradation for long-wavelength infrared ob- tive corrections is an important constraint on the servations.15 A third option, explored in more detail plate design. The fundamental frequency of the ϳ͑ ͞ ␲͒͑ ͞ ͒1͞2 ϰ 3͞ 2 in this paper, is to mount the small segments on a plate is f1 1 2 K1 m1 , where K1 t1 R1 is 18 ϭ␲ 2 ␳ plate floating in a force field, as in a monolithic mirror the stiffness of the plate ; and m1 R1 t1 , t1, R1, mount ͑Ref. 16 and references therein͒. The plate and ␳ are the mass, thickness, radius, and density of ϰ ͞ 2 supports provide axial and radial forces to compen- the plate, respectively. Thus f1 t1 R1 . Modes sate gravity, so the plate is essentially free of gravi- with Zernike radial degree n have features with a ϳ ͞ tational deformations. This is analogous to a scale size of R1 n, so the natural frequency for ͑ ͒ϰ 2 scheme with raft actuators, but the control require- modes in the nth radial degree is f1 n n . Adap- ments are simpler because the plate supports can all tive corrections must be made on the time scale of exert the same elevation-dependent force. The seg- the wind-crossing time for a mode feature, so the ment actuators can be fairly inexpensive, short- frequency for corrections in the nth radial degree is 17 ͑ ͒ϳ ͞ stroke electrostrictive devices. These are fast fAO n un R1, where u is the wind speed. Be- ͑ ͒͞ ͑ ͒ϰ enough for AO and have low hysteresis so they can be cause f1 n fAO n n, a mirror plate that is not operated without local feedback from sensors on the excited by the lowest-order adaptive corrections will segments. not be excited by higher-order corrections if the The following sections contain an overview of de- coupling between different mirror plate modes is sign issues for a mirror with many small segments small. For a 30-m telescope, and a wind speed of mounted on a floating plate. The material is in 30 msϪ1 in the turbulent atmospheric layers, the three parts: design of the floating plate; parametric frequency of the lowest-order adaptive corrections modeling of a simple, inexpensive segment ͑which is is ϳ2 Hz, so the floating mirror plate should have a the emphasis of this paper͒; and optical alignment fundamental frequency of at least a few hertz. This and AO issues. requires an ϳ1-m-thick steel box-style mirror plate ͑see Fig. 1͒. 2. Floating Mirror Plate The force-based support of the floating mirror plate The classical flotation support for a monolithic mirror offers no resistance to wind buffeting, but wind- can be applied to compensate structural deformations induced deformations in the mirror can be corrected in a segmented mirror telescope. In this scheme, if they are smaller than the stroke of the segment the segments are mounted on a plate floating in an actuators. Position-based support can be applied on astatic, gravity-compensating force field. The shape short time scales to provide wind resistance, but at of the plate is determined only by the support forces the expense of a lower fundamental frequency for the and is independent of deformations in the telescope plate and increased coupling to the telescope struc- structure. This is an important advantage because ture. If the mirror plate is supported by hydraulic the stiffness requirements for the structure can be actuators, the cylinders can be connected to an accu- relaxed. The plate is stiff on small spatial scales, mulator with small orifices to restrict the hydraulic and this helps to minimize piston errors between seg- fluid flow. This couples the mirror plate to the tele- ments. Segment motions that are due to gravity are scope structure on short time scales, and the struc- also small, so the gaps between segments are set ture provides stiffness.
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