Mass production and control technology now exists to build telescope primary mirrors out of panels consisting of a large number of small agile segments. This technology will  deliver diffraction limited performance without the need for additional adaptive optics. There is no obvious limitation to the size of telescope that can be built with this technology. A 25 meter version is estimated to cost $250M and could be built within the next decade.
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Over the last two centuries, every increase in telescope size by a factor of two has relied on using a new approach in technology. Sometimes this was because of a fundamental limitation in the available technology, but usually it was because it was too expensive, in both time and money, to use existing technology. Scaling laws also suggest that big telescopes are not cost effective without near diffraction limited imaging. In the past, this meant retrofitting existing telescopes with adaptive optics.  Although telescope primary mirrors are usually figured to an accuracy of a few tens of nanometers, the effect of atmospheric turbulence is to introduce wavefront errors amounting to tens of microns of distortion across the pupil. These distortions are currently removed using expensive, high-performance adaptive optics (AO) systems increasing the cost and complexity of the facility.

The biggest telescopes in the world use either monolithic, lightweighted mirrors (LBT) or an array of 1.8-meter size segments phased using edge sensors (Keck Observatory).  Designers of the next generation of telescopes have concentrated on scaling up these existing designs. The largest project, the E-ELT will build a 42 meter primary mirror and use a total of five mirrors, including  high order adaptive mirrors 2.5 meters in diameter,  to form the final image. However as the size of the telescope increases the effect of gravitational distorting forces and wind loading on the mirror becomes increasing severe; these problems drive up the price and technical risk to the project. The total current cost of  three international telescopes, TMT, GMT, and E-ELT planned to be built in the next decade is  $3B with running costs of over $200M/year. The current ELT designs are already near their limit in size and affordability. 

Astrophysics is moving to an era in which statistical surveys of large numbers of faint objects are required to distinguish between the increasing detailed theoretical models of the evolution of the universe and galaxies. These projects require high spatial resolution and enormous amounts of telescope time. We need to build not just bigger telescopes but more telescopes of large collecting areas that are affordable to build, simple to maintain and available to the general community. More than ever, advances in observational capabilities are going to be driven by access and cost and will require innovation to achieve breakthroughs in telescope technology. This is immensely challenging; the cost of a telescope is the sum of its parts and even dramatic reduction in the cost of one of the system component, such as the primary mirror, may not significantly impact the overall cost. Breakthroughs have to be made across the board.
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Basic Principles of Adaptive Primary Telescope Technology

Advantages of Small Segments

In general, the overall weight of the telescope and size of dome are important factors in reducing cost. The weight of a telescope of given aperture is driven by the weight of the primary and secondary optics, while the size of the dome is driven by the F-ratio of the telescope and the level of wind loading that can be handled by the primary and the telescope structure. Simple scales laws show that the smaller the segments used to build the telescope, the lighter the primary mirror becomes. We can also show that the depth of material that must be removed to introduce the required amount of astigmatism and coma into the segment surface is given by:

                     Amount of material to be removed 

Inasmuch as fabrication costs tend to increase with the amount of optical work required to produce the surface, this equations show that there is a strong advantage in using smaller segments, especially for fast primary F-ratios.The alignment tolerance for skew of the segments on the backing structure are also reduced for smaller segments. 
However, both TMT and E-ELT  are designed to allow operation without high order adaptive optics. The size of the segment then becomes a compromise between the cost of making and supporting the optics and perceived difficulty of controlling a large number of segments. Reducing the size of segments by a factor of two does not appear to bring much benefit in cost if conventional manufacturing technology is used. In a hexagonal structure there are only 6 segments of the same shape and each one requires a substantial support structure.  As a result of trade studies, TMT and E-ELT have chosen the same segment size of 1.44 meters, slightly smaller than those used at Keck. Each segment will use a servo controlled 18 actuator warping harness to improve the figure of each segment of the primary mirror and three servo controlled actuators to align the segments. The design of the actuators is non trivial since each segment weighs about 120kg/m^2 and must be positioned to a few tens of nm.

However, as the segment size is reduced to  about 0.3  meter, new methods of fabrication, testing and support are possible and the use of small, agile segments impacts almost every aspect of telescope design.  At these sizes we can also literally mass produce light-weighted segment, greatly simplify the support structures and use low cost, highly reliable voice coils to move the segments. These segments can then be assembled to form panels of convenient size (typically 10 m^2) for installation on the telescope. Low fabrication cost is only the first advantage of this technology. With suitable control techniques, many of them already necessary for the conventional adaptive optics control in the telescope system, we can take out the effect of wind forces and atmospheric turbulence on the image quality and build telescopes with faster optics and smaller domes. The only downside is that the telescope is now totally dependent on the control system, we are committed to "fly by wire " technology.
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Compensating for the Effects of Wind and Atmospheric Turbulence

The forces required to move a segment so as to correct for atmospheric disturbances are surprisingly small. Atmospheric turbulence displaces the wavefront by about 1 radian/coherence distance/coherence time. This corresponds to a displacement of about 0.1 micron every 10 millisecond for a 30 cm size segment. The mean acceleration under these conditions is about 10^-3m/sec^2. We need to update the positions every millisecond if we wish to correct for atmospheric turbulence with a 100 Hz bandwidth. If we assume that we have to move the 0.1 micron at a much faster speed of 1 millisecond (rather than 10 millisecond)  the force required during this time is  only 0.4N for a 2 kg segment and the average power needed to drive the segment is still less than 20 mW. This conservative calculation shows that the maximum heat generated by adaptive control of the segments will be < 1 watt/m^2, which is  less than the heat required to track typical fluctuations in air temperature. The force and power levels  required to correct for wind are about the same order. The high bandwidth of the system ( ≈ 100 Hz) means that:
(1)  the controls system automatically corrects for gravitational and wind deflections.

 (2) also allows correction for the effect  for atmospheric turbulence on the wavefront so that an additional adaptive optics system is not required.

 (3) the primary mirror shape no longer depends on the stability of the backing structure.

Structural deformations increase with telescope size. Because wind and atmospheric turbulence follow a power law, with more energy at lower frequencies, there is some bending of the structure on largest spatial scales. The dynamic range of the segment motion ( of order a few mm )  must be sufficient  to correct for structural deformation. The type of material used for the backing structure is also important. The movement of the segments to correct for wind and atmospheric turbulence transmits energy into the backing structure which must ultimately be dissipated as heat. Structural materials with high damping, such as carbon fiber, are desirable for this application and this technology is economic for light weight segments.The maximum displacement over a panel size of 4 meters is much less than this ( typically < 50 microns ) and it is also possible to control each panel with a bandwith of order 1 Hz to take out large scale deformations due to gravity and wind in some hierarchical design.
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ATLAS ( Adaptive Telescope using a Large Array of Segments)
ATLAS drawing
ATLAS is an acronym for Adaptive Telescope using a Large Array of Segments. A CAD drawing, prepared by William Boettinger and Tom Fornek, working at the Argonne National Laboratory, is shown left. ATLAS is designed as a survey telescope aimed at statistical surveys of objects at high red shifts. Most of the objects of interest are galaxies or proto galaxies with angular sizes of about 1 microradian and are thus over-resolved at the diffraction limit of the telescope. For this application the use of a single laser guide star provides sufficient resolution and wide field for the science goals at lowest cost and complexity. In the future, its field of view can be expanded at the expense of resolution by only correcting the ground layer. This is useful for spectroscopic surveys in the visible and near infra-red.  Much higher  performance will be obtained over small angles using a bright star as the wavefront sensing source. In this later configuration the telescope will be able to search for, and image, planets orbiting other nearby stars.
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Summary of the Design

  ATLAS has a circular entrance pupil 25 meters in diameter with a central obscuration of 5 meters and primary mirror focal length of 20 meters. 
ATLAS  is similar in appearance to large sub millimeter telescopes such as CCAT. The primary mirror consists of 84 panels arranged in a radial configuration. However, instead of the panels being monolithic, they are build from between 38 and 72 segments each about 0.3 m square and each being able to be moved over a distance of a few millimeters with a small signal bandwidth of about 100 Hz. Each panel will weigh about the same as a single segment of the Keck telescope (400 kg) and will be about 6 m^2 in area. There are only 5 different types of panel. Replacement panels will be available and each panel will be designed to enable rapid replacement for maintainence, recoating and repair.  The primary mirror therefore consists of 4944 individual segments,  provide ~10,000 degrees of freedom. There will typically be 32 different segment shapes, requiring the manufacture of hundreds of identical segments. The backing structure that supports the panels will be built composite material( black) and will itself be supported by a steel azimuth structure. The secondary mirror is small and highly lightweighted, so as to reduce the mass at the ends of the secondary support structure. The outer two rings of panels are clear of obstruction and avoid the entire pupil being divided into discrete quadrants. This benefits adaptive control of the primary mirror.
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Control of the Primary Mirror Surface


The most important difference between ATLAS design and conventional telescopes is that the control bandwidth of the segments is much higher than the lowest resonances of the telescope structure. This is in contrast, for instance, to Keck, where the structural rigidly of the primary mirror is largely determined by the backing structure. The actuators that position the mirror segments only correct for slow distortions of the structure due to gravity or thermal effects. In the ATLAS design we attempt to control the surface to an accuracy of a few tens of nanometers against a backing structure that is compliant on medium and large spatial scales.
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Design of the Individual Segments
 Segment and support design
The original design of the segments used a lightweighted Pyrex  substrate, mounted on three, two point, wiffle trees. FEA analysis enabled us to design a segment with a surface figure under gravity of 15 nm peak to valley and a mass of 2 kg for a 32 cm square substrate. A lever system within each wiffle tree provided in an astatic support system, requiring minimal drive current to the voice coils when under static gravity loads. 

Lee Holloway, a professor at University of Illinois at Urbana, modeled the response of the segment  to a command to a 1 micron step displacement ( blue line below). Also shown are the response of its neighbors to this step input (insert).

 A compliant backing structure can potentially introduce coupling between the segments. If one segment position is changed in a step displacement, its control system applies forces to the segment and reaction forces are transmitted to the backing structure and thence to its neighbors.  Lee modeled five segments in a line on backing structure with an assumed compliance similar to the ANL model.Segment response to step input The results are shown below left. This figure gives the response of one segment to a step displacement (blue curve). Also shown in the insert are the disturbances of neighboring  segments separated by one  through five segment distances due to this displacement. Typical movement of neighboring segments are 10 nm and are damped out in 20 milliseconds.

More realistic simulations, in which the segments are directly exposed to 5 m/s winds were as undertaken by Professor Holloway. The wind power followed a von Karman turbulent power spectrum with a break frequency of 0.3 Hz  This simulations gave rms segment motions of less than 15 nm. This wind speed corresponds to a force of a few N/m2 and is considerably higher than the forces needed to correct for atmospheric turbulence.

Several Pyrex substrates were made for the project. However, the wiffle design is relatively complex and its internal resonances were shown to affect the servo performance. Also, because the back is open, this design is not particularly strong for its weight and Pyrex has sufficient thermal expansion to raise potential problems. We have since developed and built a new technology using pneumatic pistons as a support for a thin plate of zero expansion material. The prototype system is shown below using 9 pistons as the support. These pistons are connected to the substrate via a magnetic coupling, allowing the substrate to be removed for servicing. This design  also provides astatic support and a degree of internal damping of the substrate. The pressure to the air pistons is controlled so that the mean current sent to the voice coils is zero.

A prototype segment Photo of prototype segmentis shown right. In this design a 3/8 inch plate is used as the segment substrate. FEA analysis of the plate give a peak to valley deflection of 10 nm under a vertical gravity load (see below). 4 voice coils are used to drive the segment in tip tilt and piston over a 5 mm distance. Use of 4 voice coils enables the segment to operate even if one voice coil or drive fails. The servo is being designed so that the segment will still operate, with some acceptable loss of performance, if any one voice coil fails.FEA of segment

The cost of voice coils, support and inductive sensors is estimated at  $1K/segment in volume production. The cost of building panels from these segments, including the servo systems, is predicted to be in the range $40K to $50K/m^2.
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Optical Fabrication

A number of new polishing technologies have been proposed in recent years aimed at high volume production of light-weighted mirror blanks. The most conservative option, and the one chosen for the base plan, is to use the Keck bend and polish technique, use a spherical planetary lapping machine to polish the surface. For our segments, the direction of astigmatism always lies along a radius vector, so it can be introduced easily and accurately by applying a bending moment along opposite sides of the segments prior to polishing. FEA analysis of this design gives a fit of better than 100 nm to the ideal aspheric surface for all segments types. We plan to make the faceplate of the segment slightly oversize and cut it to the appropriate shape after polishing using a water jet. Residual aberrations will then be corrected by Ion polishing or similar technique. Nelson has reported that a  0.025 m diameter Ion beam can remove 5 x10^11 micrometer^3/day, so that in principle we can process 600 m^2,starting with an initial surface error of 200 nm, in less than 6 months with a single polishing station
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Optical Testing

Optical testing is a large part of the conventional cost of fabricating mirrors. ATLAS has two important advantages compared to other approaches. The 25m meter version of ATLAS uses only 32 different segment shapes to make up  primary and requires on average about 200 identical segments. The project will carefully prepare a concave master for each shape and we have designed a testing procedure that will make surface measurements with an absolute accuracy better than 20 nm. These masters will be provided to the optical fabricators and the profile of each segment shape will be measured against this master using a Fizeau interferometer. This approach will allow the project to provide the optical fabrication vendor with known reference surfaces, greatly improving the certainty that the optics are generated to the optical prescription and allowing multiple vendors to fabricate the optics. Once the segments have been fabricated they will be instrumented with edge sensors, assembled into panels, aligned, and tested as a unit using a large flat as an autocollimator.
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Adaptive Optics Strategy

Adaptive optics is an intrinsic feature of ATLAS technology and a requirement for the science for which it is intended. No technical breakthroughs in AO technology and practice are needed, but a reliable AO system is essential. In following sections we will discuss specific approaches to critical subsystems including wavefront sensors and laser beacons. In this section, we discuss our overall plan for a staged implementation of ATLAS AO that will enable a productive science program from first light.
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Stage 1:    Natural Guide Star AO

The first AO system used on ATLAS will use bright natural guide stars to commission the system and carry out necessary on-sky development of the  telescope system. We would like to achieve a wavefront error of 250nm early in the commissioning of ATLAS corresponding to a 65% Strehl ratio at 2.4 micron. We expect to improve the performance for bright sources to 150 nm (86% Strehl ratio at 2.4 micron) over time. However the main goal will be to implement the single sodium guide star AO outlined below.
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Stage 2:    Single Sodium Guide Star AO

Many of the science drivers for ATLAS can be achieved using a single laser guide star. Although the cone effect degrades the on-axis Strehl ratio of a laser guide star system, the field of view of correction is increased. This is discussed in detail by Mathew Britten and Keith Taylor. In the first figure, reproduced from their paper, shows the calculated value of d0 and a pictorial explanation of why the isoplanatic angle is increased.

Do plot after Britton and Taylor

The error due to the cone effect is formally given by (Telescope diameter/d0)^5/3 in units of rad^2. A telescope of diameter d0 has a wavefront error of 1 radian^2. The diagram on the right shows schematically that, for images off- axis, at least some parts of the wavefront are better corrected than for an AO system driven by a natural guide star. Britton and Taylor calculate the point spread functions for an AO system limited by the cone effect for various field angles and telescope sizes

PSF of SLGSAO After Britton andc Taylor
The cone effect is bigger for bigger telescopes. However, the Strehl ratio improvement, between the Single laser guide star corrected image and the seeing limited image, increases with telescope diameter . Although the on-axis Strehl ratio is only 10% @ 1.65 micron with this  correction, the intensity of the diffraction-limited core of the image is about two orders of magnitude greater than that of the natural-seeing image over an arc minute field. The following table shows that ~50% of the light is concentrated within a 0.1 arcsecond radius aperture on axis.

        Field angle radius (arcsecond)
        0.05 arcsec aperture
       0.1 arcsec aperture

This performance means that the telescope can be efficiently coupled to a spectrograph or integral field unit. We should also note that, although a 1 arcminute field of view seems small, the resolution is still of order 10 milliarcseond in the near infra-red and that we will require about over 10000x10000 pixels to sample the field of view.
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Stage 3:    Ground Layer AO (GLAO)

Much wider fields can be obtained at visible wavelengths with some improvement over non-AO performance, by only correcting the wavefront for ground layer turbulence. We can achieve this using a single laser by nutating the beam about the optical axis and providing image motion compensation before the wavefront sensor. Rayleigh beacons provide an alternate method of achieving this performance. At mid-latitude sites, GLAO can reduce the width of the point spread function by 10-50%, depending on distance from the optical axis, wavelength, and seeing conditions. Such a modest reduction in performance requires careful scientific justification. However gains could be much larger for sites on the Antarctic Plateau, where the ground layer and boundary layer are extremely thin and the free-air seeing is  low, resolutions of 0.1 arcsecond over a 30 arcminute field of view appear possible. Such a telescope would greatly outperform any planned telescope located at other sites on earth.
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Stage 4:   Multibeacon, Single/Multi DM laser guide star

Use of multiple beacons will enable us to significantly improve imaging performance. By using multiple beacons and wavefront sensors we can reduce the cone effect. Using more beacons may not require more laser power because the effect of spot elongation, which drives the laser power requirement, can also be reduced with suitable placement of laser beams and control algorithms. Use of short pulse laser systems may also provide increased performance with lower laser power, although this technology still has to be developed. Although the most efficient way of reducing the Cone effect has yet to be worked out by the AO community, multi laser guide star with a single adaptive primary should give a wavefront error of between 100 and 150 nm over a field of view of a few tens of arcsecond. A small number of natural stars are still required to implement this improvement, limiting access to about 50% of the sky. In the more distant future,  the ATLAS primary mirror will be used correct for ground layer turbulence and additional deformable mirrors (DMs) conjugate to high-altitude layers will be located between the primary mirror and the science instrument. This will allow us to have diffraction limited imaging over a wider field of view. Planning for this mode will only start once first generation systems have been successfully demonstrated on existing 8 to 10 meter telescopes.
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Wavefront Measurement

There are a number of different ways of providing the signals to control the positions of the segments. The Keck telescope was designed to use only edge sensors, but has very successfully also used Shack-Hartmann wavefront sensors and a natural guide star to observe the relative positions of the edges of the hexagonal mirror. This optical technique works well with broad band sources, such as stars, but can only determine the position, modulo half a wavelength, for single frequency sources such as a sodium guide star. Extension of the dynamic range can be made using a second wavelength, such as the Potassium line guide star at 766 nm to achieve lock. The lower brightness of this laser guide star is acceptable since we can use longer time scales to determine the number of wavelengths shift between segment edges. We propose, however, to use a combination of edge sensors and an optical wavefront sensor provide the error signals. We are developing a low cost wide band inductive sensor with a noise floor of about 3 nm/√Hz. This will be used to provide edge sensing information, measuring the differences between the corners of neighboring segments.  We will use a laser guide star to drive the optical wavefront sensor.
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Laser Power Requirements

If a laser is fired from a position close to the optical axis, it will appear as an elongated image at the edge of the telescope pupil ( the obliquity effect). A 15 meter telescope will have a maximum laser guide star dimension of 2 arcseconds in the radial direction and a 25 meter telescope over 3 arcsecond. To obtain an estimate of the laser guide star brightness needed for the project we can carry out the following calculation. The noise propagator of an optimal least squares estimator of the wavefront,  based on the number of measurements required (about 50,000), is 1.3 times the phase difference measurement variance across a subaperture. A typical error budget for the wavefront estimation is 60nm.  Assuming that we can use edge sensors to measure the position difference of segments to 30 nm with a 100 Hz bandwidth, the laser guide star wavefront system should be able to measure the phase difference to 52 nm across a segment. This corresponds to an error in determining the position of the laser guide star of 0.16 microradians.  For a single beacon launched near the optical axis of the telescope, the obliquity effect produces a spot with about 10 microradians FWHM at the edge of the field of a 15 meter telescope. This requires a signal/noise for the position measurement of at least 60 over a measuring interval of a few milliseconds. This topic is discussed in more detail on the laser guide star page.

The reference design will use the pulsed sum frequency laser technology developed for Palomar Observatory. This laser currently operates at 8 watt, generating 150 microsecond long pulses at a 400 Hz rep rate. The laser upgrade for this project will provide additional solid state amplifiers on the output stages of the two IR oscillators. It will improve the chirping and backpumping technology already demonstrated at the Observatory and will run higher frequencies. We expect to obtain a return of at least 1 Million photons/sec/m^2/watt with this laser, based on our current experience at Palomar, at a sodium column density of 4 x 10^13 atoms/m^2. For a 15 meter telescope under conditions of low sodium abundance, we believe that we can obtain this level of performance with a pulsed sum frequency laser with chirping and back pumping generating 30-40 watts.  Over 100 watts of power will be required for a single beacon controlling a 25 meter telescope and it seems likely that some multiple beacon approach will be needed for telescopes of this size. All laser guide star systems need a few faint, natural guide stars, to remove very low order wavefront errors and a comprehensive design study needs to be completed to determine the best configuration of laser guides to remove the cone effect.
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  Telescope Structure

The requirements for the telescope structure are similar to those for telescopes designed for submillimeter wavelengths. We expect to be able to draw on a reservoir of community, especially the 25 meter CCAT,  and industry expertise to aid in estimating costs and fabrication times, so the risks associated with this part of the project will be low.

A  conceptual design telescope structure was carried out at the Argonne National Laboratory in 2005. This study  gives some idea of the design, weight and cost of the different parts of the telescope. The primary mirror structure and secondary mirror supports are carried on a square space frame made from carbon fiber, as is shown below. The four secondary support arms are held at the edges of the square box structure and pass through the primary mirror panels before meeting at an apex behind the secondary mirror. The Alt-Az mount is a steel space frame structure.

Alt-AzThe segments are supported on a backing structure that contains the electronics, cooling, and communication needed to drive the segments, together, they form a modular panel. The panels are carried by the primary mirror support truss, a 10-ton carbon-fiber structure attached to the box frame. Cassegrain instruments will be accommodated within a large volume near the center of mass below the primary mirror. They will be mounted and demounted by means of an elevator through a 6.5x6.5-m hole in the pier.
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Cost Estimate

Weight (tons)
Est Cost (2007)
Segment support
Panel structure
Control Electronics
Panel backing structure
Secondary support
Lightweight secondary
Alt-Az mount and drive
Laser system
Wavefront sensor
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Many people have contributed to the ideas in the design of ATLAS including:
Technical Section: Bill Boettinger (ANL), Abhijit Chakraborty(UIUC), Tom Fornek (ANL), Al Harper (UC), Leland Holloway (UIUC),  Laird Thompson (UIUC), Petros Voulgaris (UIUC)
Science Section: Al Harper (UC), Richard Kron (UC), Jason Tumlinson (YU), Mel Ulmer (NW), Don York (UC)

The laser would not have been built without the hard work of Viswa Velur ( CalTech) and the advice and support of Antonin Bouchez and Richard Dekany (CalTech). Partial funding for the laser at Palomar Observatory was provided by Cal Tech.

Single laser guide star performance figures are taken from a paper "SLGLAO" by Matthew Britton and Keith Taylor ( Cal Tech)

Support of this work by University of Chicago, Argonne National Laboratory and the National Science Foundation is gratefully acknowledged.
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6:46 pm Feb 23 2010 Edward Kibblewhite