Chapter 4

Chapter 4, The Point Design

Section 4.6.2: MCAO

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Multi-conjugate adaptive optics (MCAO) can provide near-diffraction-limited atmospheric turbulence compensation across extended fields of view that are considerably larger than the isoplanatic patch size for conventional Adaptive Optics (AO). It is an important capability for GSMT, because it enables new classes of observations not previously feasible with AO, and it provides a significant multi-plexing advantage for many others. But as with virtually all other aspects of GSMT, the achievement of these objectives will require very significant advances beyond the current state-of-the-art. Dramatic improvements have already occurred in the level of maturity of MCAO over the past several years, but this is only the beginning of what will be needed to make MCAO on GSMT a reality.

Many different concepts for MCAO have already been suggested for ELTs (extremely large telescopes) and 8-m class telescopes. Based upon our current understanding of the GSMT science requirements and the various technology options, we believe that the most promising approach is to pursue a scaled-up version of the sodium laser guide star (LGS) MCAO design proposed for Gemini South. Analysis indicates that this configuration can achieve essentially the same performance (in terms of Strehl, field of view, wavelength range, and optical throughput) for D=30-m as for D=8-m, with no increase required in the number of guide stars or deformable mirrors (DMs). A strawman opto-mechanical implementation for GSMT has been developed, and the challenges involved in developing the required very-high-order wavefront sensing and correcting technologies appear manageable if a means can be found to cope with elongated sodium LGSs. Three possible concepts for resolving this complication appear worthy of exploration. Other topics deserving further attention in our baseline concept include:

Section reviews the top-level science requirements for MCAO on GSMT, and sketches our derivation of the resulting AO system parameters and other design requirements. Section summarizes the baseline concepts for the opto-mechanical design of the laser launch system and the AO module. Section contains recommendations for more detailed near-term work. More details on recent progress in modeling and evaluating very-high-order MCAO systems can be found in Appendices 4.6.B, 4.6.C, and 4.6.D. PERFORMANCE AND IMPLEMENTATION REQUIREMENTS

Optimizing an AO system for an increased field of view (FOV) will generally result in reduced resolution. MCAO provide intermediate levels of performance in both of these categories in comparison with two other AO modes planned for GSMT. The Prime Focus AO mode for is intended to yield moderate improvements in seeing over the widest possible field, while the very high order AO coronagraph is designed to obtain the highest resolution achievable over a field of a few arcseconds. The MCAO requirements and design are bounded by these two extremes, yielding a system with near-diffraction-limited performance over an appreciable field while minimizing hardware complexity and technology challenges. Science Requirements

Table 1 outlines the top-level draft science requirements we have assumed for developing a baseline MCAO concept. They are certainly not final, but these representative values serve to illustrate the requirements definition process and lead to a system that is a reasonable starting point for future iterations. The wavelength range, FOV, and Strehl ratio requirements are taken from MCAO for Gemini South. Note that the Strehl values are for delivered imagery under median seeing conditions at zenith, and consequently must include the effects of implementation error sources (optical misalignments, AO system calibration errors, etc.), as well as the residual turbulence-induced phase distortions. Quantitative requirements for PSF (point spread function) uniformity and plate scale stability are difficult to assign before more detailed modeling results on the characteristics of the PSF are available, but it is clear that serious efforts must be made to achieve very good performance with respect to these criteria. Finally, the draft specifications for optical transmittance are "round numbers" derived from the throughput predicted for the Gemini South AO system design.

Wavelength range, µm


Field of view diameter, arcmin2
Mean Strehl over central 1' field
(with bright NGSs for tip-tilt)
0.6 (K)
 0.4 (H)
 0.2 (J)
PSF UniformityTBD (good)
Plate scale stabilityTBD (good)
Optical transmittance0.80 (K)
 0.75 (H)
 0.75 (J)
Table 1 Draft science requirements for MCAO. Derived AO Parameters

Table 2 is a top level summary of the MCAO system's wavefront error budget and the associated AO parameters, including allocations for: (1) fitting error (order of correction); (2) generalized anisoplanatism (DM and guide star configurations); (3) servo lag (control loop bandwidth); (4) WFS (Wave Front Sensor) measurement noise; and (5) higher-order effects and implementation errors. To obtain the Strehl ratios listed in Table 1, the combined optical path difference (OPD) associated with all of these error sources must not exceed 0.25 µm RMS (root mean square), as can be verified using the Maréchal approximation, S = exp[-(2piOPD / lambda)2].

The error budgeting process is still at an early stage, because the modeling and simulation tools needed to comprehensively estimate MCAO performance for GSMT are not yet complete. The modeling that has been accomplished has assumed the Gemini South atmospheric turbulence profile for Cerro Pachón, because this is a well-characterized profile for a good site with which we are familiar. We have recently developed a new simulation to accurately assess error sources (1) and (2), and Gemini South simulation results on the effect of servo lag (error (3)) can also be used for GSMT with reasonable confidence. But the current estimates for the effects of WFS measurement noise and implementation errors are essentially allocations borrowed with only limited justification from Gemini South, and more work is needed to study the impact of elongated LGSs and the dynamic misalignments of the telescope itself.



Comments (derived AO parameters)

Overall RMS OPD (Higher order + tip/tilt)


Fitting error


Scaling law (0.5 m actuator pitch--order 60 AO system)
General anisoplanatism


GSMT simulation (3 DMs, 5 sodium LGSs, 3 tip-tilt NGSs)
Servo lag


GS Simulation (800 Hz update rate, 35 Hz bandwidth)
WFS noise


GS Simulation, modified for LGS elongation (50 W LGS)
Higher-order and implementation errors


RSS of below
Higher-order atmospheric effects


Diffraction and 3d LGS


Gemini South wave optics simulation
WFS centroid gain estimation error


GS Tolerance analysis and estimates of seeing variability
LGS focus tracking




From EB1; includes primary, secondary, and alignment


Uncorrectable error


Calibration error


AO implementation


Residual windshake


Tip-tilt servo error; scaled from Gemini MCAO
Uncorrectable mirror figure


Gemini South tolerance analysis
Non-common path calibration error


Gemini South tolerance analysis (flexure/themal)
DM/WFS misregistration


Gemini South tolerance analysis (flexure/themal)
Component nonlinearities



Table 2 MCAO wavefront error budget and derived AO system parameters.

The following subsections provide further information on how the overall error budget has been allocated between the five primary error sources, and how the these values are determined by AO system parameters. Order of Correction

The RMS fitting error associated with the finite spatial resolution of the DM actuators and WFS subapertures can be estimated by the formula OPDfit = (lambda/ 2pi) [0.28 (d/r0)5/3]1/2, where r0 is the atmospheric turbulence effective coherence diameter at the wavelength lambda, d is the DM actuator pitch in telescope output space, and 0.28 is the fitting error coefficient for an AO system employing a Shack-Hartmann WFS and a piezostack DM arranged in the Fried actuator/subaperture geometry.

Median seeing conditions at Cerro Pachón correspond approximately to r0 = 0.16 m at a wavelength of 0.5 µm. Using d = 0.5 m yields OPDfit = 0.109 µm for the value of the fitting error, which is a reasonable fraction of the overall error budget of 0.25 µm. An actuator pitch of 0.5 m corresponds to 61 actuators across the diameter of the beam. Reducing the fitting error to a smaller value by reducing the actuator pitch will: (1) increase the cost and technical risk associated with very-high-order DMs and wavefront sensors; (2) increase the cost and complexity of the real-time wavefront reconstruction electronics; and (3) increase laser power requirements for wavefront sensing with smaller subapertures. Number of Deformable Mirrors and Conjugate Ranges; Guide Star Configuration

These parameters determine OPDaniso, the RMS OPD due to generalized anisoplanatism in the MCAO system. Unlike fitting error, OPDaniso cannot be accurately described by a simple scaling law, and the magnitude of this error must be evaluated via analysis or simulation on a configuration-by-configuration basis. These calculations are difficult for GSMT (and ELTs in general) due to the very high orders of the AO system involved. The most significant obstacle is computing the wavefront control algorithm, because the required number of operations scales with the cube of the number of DM actuators using standard techniques.

We have very recently developed a new sparse matrix method for computing the reconstruction algorithm that breaks this scaling law. With this new approach, the complexity of computing the control algorithm appears to scale with the square of the number of actuators, so that computing and evaluating reconstructors for MCAO systems with up to 2500 DM actuators and 4000 WFS subapertures is now relatively straightforward. We have just begun using these techniques to evaluate MCAO performance, starting with D = 8 and 16 m and a DM-guide star configuration patterned closely after the Gemini South MCAO design. This configuration includes:

We find that the RMS OPD, due to generalized anisoplanatism, is nearly independent of telescope aperture diameter, with OPDaniso = 0.1001 and 0.1016 µm for D = 8 and 16 m, respectively. This result parallels the behavior of classical anisoplanatism in a conventional NGS AO system, where OPDaniso is independent of D once D/r0 is large. The anisoplanatic error extrapolated to D = 30 m is OPDaniso = 0.103 µm. We are now investigating further improvements to computational efficiency and hope to confirm this extrapolated estimate by explicit computation by mid-2002.

Why begin with a point design derived from Gemini South, instead of considering a more ambitious configuration to achieve superior performance? Uniform turbulence correction over a larger FOV would require additional DMs at more closely spaced conjugate ranges. More closely spaced conjugate ranges require a lower magnification ratio to package the DMs without vignetting, and the resulting increase in beam diameter significantly complicates packaging the MCAO optical train. As illustrated below, packaging the optical path with three DMs is already challenging.

Table 3 summarizes our thoughts on the choice of guide star technology. In spite of a variety of implementation issues, we believe that sodium LGSs are the only approach capable of achieving the Strehl ratio performance requirements given in Table 1 with a scientifically useful level of sky coverage. Trade studies for MCAO on Gemini South have determined that five sodium LGSs is the minimum number that can be used to control three DMs and obtain near-uniform Strehl ratios over a one-arcminute square field. In passing, we note that "Hybrid" configurations consisting of sodium and Rayleigh LGSs may also be of interest, because such guide star constellations can theoretically estimate tilt anisoplanatism without multiple tip-tilt NGSs, thereby maximizing sky coverage.


1) NaturalNo lasersQuestionable sky coverage (at desired Strehls without a revolutionary WFS)
2) Rayleigh
  1. Mature laser technology
  2. Safe for satellites
  3. Fixed LGS range
  1. Performance questions
  2. Many guide stars required
  3. Optical design questions
  4. Multiple tip-tilt NGS or a higher-order NGS WFS needed for tilt anisoplanatism correction
3) Sodium
  1. Encouraging performance predictions
  2. Few (5) guide stars required
  1. LGS elongation
  2. Immature laser technology
  3. Variable LGS range
  4. Satellite predictive avoidance
  5. See item 4 for Rayleigh LGS Julie McLaughlin
4) Sodium + low-order RayleighOnly 1 tip-tilt NGS needed2) 3 and 3) 1-5
Table 3 Guide star options for MCAO. Control Loop Bandwidth

This parameter determines the RMS OPD due to servo lag in the AO control loop. Performance estimates obtained for Gemini South should give a reasonable estimate for this effect, because the two designs share the same actuator pitch and most of this error derives from the highest spatial frequency wavefront errors that are controlled by the AO system. For a WFS sampling rate of 800 Hz and a conservative control loop bandwidth of 35 Hz, the predicted OPD due to servo lag is OPDservo = 0.026 µm. Wavefront Error Due to Noise

Our estimate for this error is also taken from previous simulations of the Gemini South MCAO system, but we are considerably less comfortable in making this extrapolation. For Gemini South, the predicted wavefront error due to noise is OPDnoise = 0.032 µm RMS for a LGS WFS signal level of 125 photodetection events/cm2/sec. This estimate is based upon detailed wave optics simulations of the wavefront sensing process, including: (1) laser propagation up through the atmosphere; (2) the nonzero depth of the sodium layer; (3) propagation from the LGS back down through the atmosphere and MCAO; and (4) Shack-Hartmann wavefront sensing using 2-x-2 active pixels per subaperture. The LGS WFS signal level corresponds to a laser power of about 10 Watts, assuming near-optimal spectral characteristics for the laser and representative parameters for optical transmittance and sodium column density.

The value of OPDnoise estimated for Gemini South cannot be transferred directly to GSMT, however, because effect (2) will cause significantly greater guide star elongation for a 30-m telescope. For GSMT, the length of the guide star would be greater by a factor of 30/8 = 3.75 if this were the only source of guide star blurring, but we estimate that the actual increase will be closer to a factor of three when diffraction and laser beam quality are taken into account. The wavefront error due to noise would increase proportionately if laser power and LGS WFS design parameters were held constant; increasing the laser power to 50 W per LGS to compensate for the increased elongation yields an estimate of 3 * 0.032 * (10/50)1/2 = 0.043 µm for the value of OPDnoise. More work is obviously needed to reduce this error and/or to be less wasteful of laser power, as described further in Section Higher-Order Effects and Implementation Errors

Higher-order effects and implementation errors (for example, DM-to-WFS misregistration and other AO calibration errors) are allocated a RMS OPD of 0.178 µm, the largest of the five top- level terms in the error budget. The lower portion of Table 2 breaks down this error further into contributions from: (a) higher-order atmospheric effects, (b) telescope errors, (c) instrument errors, and (d) AO implementation errors. The values for (b) are analyzed in EB1 of Section 4.2. The values selected for (c) are simply top-down allocations at this point. The values for (a) and (d) are based upon prior work for Gemini South MCAO, as described in the following paragraphs.

Diffraction and three-dimensional LGSs are sources of higher-order wavefront sensing error, because the Shack-Hartmann sensor is no longer an ideal wavefront gradient sensor when these real-world effects are taken into account. The associated RMS OPD of 0.048 µm has been estimated via detailed simulations for Gemini South that accurately model wave optics propagation in the atmosphere, telescope, and Shack-Hartmann WFS. The corresponding error for GSMT should be similar or perhaps somewhat smaller, because the increased size of the Shack-Hartmann spots due to LGS elongation actually "smoothes out" some of aberrations and nonlinearities associated with diffraction.

The remaining two higher-order effects may be less easily controlled, however. The tilt measurement gain for the LGS WFS must be known accurately, because this sensor will operate slightly off-null due to noncommon path wavefront errors (i.e., imperfections in the LGS WFS optics). Errors in estimating the tilt measurement gain will degrade the accuracy of the calibration offset for the noncommon path errors, and in effect transfer a fraction of these errors into the science path. The estimate of the tilt measurement gain must be updated in real-time as the atmospheric seeing and the distribution of the sodium layer vary. This process may be less accurate for GSMT than for Gemini South due to the increased elongation of the Shack- Hartmann spots. Additional simulations are needed to quantify this effect. Similar comments apply to tracking the mean range to the sodium layer, which must be known accurately to avoid focus biases in the LGS WFS measurements.

The final section of Table 2 summarizes the wavefront errors associated with imperfect engineering of the AO system itself. These include: (a) uncorrectable mirror figure errors; (b) uncalibrated noncommon path error due to flexure and temperature variations; and (c) DM-to- WFS misregistration errors caused by initial misalignments, flexure, and thermal effects. The values used have been taken from a detailed tolerance analysis of the opto-mechanical design for Gemini South MCAO. Such an analysis will eventually be required for GSMT, but the results may be similar due to the parallel approach taken to the optical design. Implementation Requirements Opto-Mechanical Interfaces

The MCAO optical system forms an optical relay between the GSMT itself and a science instrument. It will be mounted in the space reserved for instrumentation behind the GSMT primary mirror, following a fold mirror located on the telescope optical axis. The telescope optical design defines the location of the input image and pupil planes. The corrected science beam must be output to the instrument along the elevation axis of the telescope. There are no exact constraints upon the locations of the output pupil and focal planes. Mass and center of gravity constraints are to be determined.

The beam diameter in the MCAO system must be small enough to allow the optical system to be packaged behind the primary mirror, including the natural and LGS wavefront sensing paths. However, the spacing of the three DMs optically conjugate to ranges of 0, 5, and 10 km must be great enough to allow reasonable angles of incidence. Because the longitudinal magnification in an optical system is the square of the transverse magnification, this is always possible provided that the beam diameter is not too small. Atmospheric Dispersion Compensation

The optical path for the science instrument must include elements for an atmospheric dispersion compensator (ADC) that provides correction to a small part of the diffraction-limited blur diameter in J, H, and K bands at a zenith angle of 45 degrees. One-tenth of the blur diameter ranges from about 0.9 milliarcseconds (mas) in J to about 1.5 mas in K. Adjusting the ADC as a function of zenith angle must not shift the output pupil, and should ideally not shift the instrument line of sight. Atmospheric dispersion compensation is only required one band at a time, not for all bands simultaneously.

An ADC is clearly not required for the narrowband LGS WFS optical path. An ADC is required for the NGS WFS optical path, but excellent compensation is not required because the width of the visible guide star image will not be significantly improved over the ambient seeing. Special Issues and Requirements for Sodium Laser Guide Stars LGS Elongation and Laser Power

As mentioned previously, the elongation of a sodium LGS increases almost in proportion with telescope aperture diameter due to the nonzero thickness of the sodium layer. This increases the wavefront estimation error due to noise for a fixed LGS signal level, and complicates accurate calibration of the LGS WFS due to temporal variations in the distribution and mean range of the sodium layer. Several options have been suggested to minimize these effects, as summarized and discussed below.

  1. Increased laser power In an ideal world, LGS WFS measurement accuracy could be maintained by increasing the LGS signal level to compensate for the increased spot size. However, laser power would need to increase roughly in proportion to the square of the spot size, corresponding to an increase from 10 to 90 W for the factor of three increase in LGS elongation between Gemini and GSMT. This is wasteful and may not be feasible. It also fails to address the calibration issues associated with elongated LGS.

  2. Improved wavefront sensors To the best of our knowledge, there is no alternative WFS concept that is better adapted to working with extended, spatially incoherent sources than the Shack-Hartmann WFS. Performance with extended objects can be improved, however, by using more than 2-x-2 pixels per subaperture and employing a more sophisticated spot tracking algorithm. A higher resolution wavefront sensor may also improve calibration accuracy. Wavefront sensing simulations using representative sodium layer intensity profiles are needed to quantify the potential improvement in sensing and calibration accuracy that might be achieved using this approach.

  3. Rebalancing the control bandwidth and error budget Additional improvements may be possible by reducing the AO control loop bandwidth and increasing the DM actuator pitch (and WFS subaperture width) to optimize system performance at an increased WFS noise level. This trade study should be straightforward, if computationally intensive, once the existing GSMT MCAO simulation is upgraded to model the closed-loop case.

  4. Novel laser pulse formats With a laser pulse length of a few microseconds or less, it is theoretically possible to eliminate LGS elongation by tracking the pulse (in focus) as it transits the sodium layer. The pulse repetition interval should be no shorter than the duration of the backscattered signal for a single pulse, which is about 100 microseconds for a 10-km thick sodium layer at a zenith angle of 45 degrees. A pulse length of 5-10 microseconds would be short enough to significantly reduce the elongation, while providing a high enough duty cycle to minimize concern over saturation effects. Note that this approach also greatly simplifies LGS calibration for the range and distribution of the sodium layer, provided that the WFS focus adjustment is properly synchronized to the pulse. No such pulse format has yet been investigated for sodium lasers. Preliminary calculations and tests at Steward Observatory suggest that a mechanical zoom focus adjustment is probably feasible, and electro-optical approaches may be feasible as well.

  5. Multiple launch telescopes In principle, there should be little or no reduction in WFS measurement accuracy when using an elongated LGS for the tilt in the direction orthogonal to the elongation. It may therefore be advantageous to project additional LGSs from multiple launch telescopes located around the periphery of the GSMT primary mirror. Each laser beacon provides accurate tip-tilt measurements in both dimensions near its launch telescope, and accurate measurements in one (subaperture-dependent) dimension across the remainder of the aperture. It is hypothesized that a sufficient number of launch telescopes will provide accurate measurements in both dimensions over the full aperture. This approach obviously increases the number of lasers, launch telescopes, wavefront sensors, and overall system complexity, and we do not believe that it would be cost-effective for GSMT. It may be worth considering for apertures that are even larger.

At this point, we are basing our AO performance estimates and laser system requirements on option 1. We intend to study options 2 and 3 during the next phase of the effort. Optical Design

The range to the sodium layer varies with time and the telescope zenith angle, from a minimum of about 85 km at zenith to a maximum of 200 km at 60 degrees. This translates to a huge variation in the location of the intermediate image of the guide star, and this must be accommodated by a focus adjustment in the LGS WFS foreoptics. Any wavefront aberrations and pupil distortion induced by using the common path portion of the MCAO designat finite conjugates must also be compensated, either by canceling aberrations in the LGS WFS optical design or through very accurate software calibration. We have proof-of-concept optical designs that satisfy this requirement for Gemini South, but the magnitude of the aberrations to be compensated for a 30- m GSMT will be significantly larger. IMPLEMENTATION CONCEPT AO Module Opto-Mechanical Design Optical Design Approach

The baseline optical design for the GSMT MCAO system is modeled upon MCAO for Gemini South. It consists of two off-axis paraboloid mirrors enclosing numerous optical elements: three DMs, atmospheric dispersion corrector prisms, a tip-tilt mirror, beamsplitters, and auxiliary optical sections that provide visible wavelength foci for the natural- and LGS wavefront sensors.

The parent telescope, illustrated in Figure 1, consists of a 30-m diameter, f/1, paraboloidal primary mirror, and a 2-m diameter hyperboloidal secondary mirror. Without AO, its image quality would be seeing-limited to approximately 0.5 arcseconds. The diffraction-limited spot size for a 30-m telescope at 1.6 microns wavelength is 0.026 arcseconds, which corresponds to the approximate geometric spot size of the Cassegrain telescope at ± 1 arcminute off-axis. The nominal RMS wavefront quality over this FOV is shown in Figure 2. Geometrical spot diagrams are presented in Figure 3.

Figure 1 Optical Layout of 30-m Cassegrain GSMT. Figure 2 Theoretical wavefront quality vs. field of view of the GSMT telescope.  The wavelength is 1.6 µm. Figure 3 Geometrical spot diagrams for the GSMT telescope.  The circles indicate the Airy disk at 1.6 µm.

The foundation of the AO module is a relay formed by two off-axis paraboloids, OAP1 and OAP2, which transfer the f/18.75 Cassegrain focus to an f/38 output on an outward-curving (convex) Science Focus approximately 640 mm in diameter, with a 3-m radius of curvature. The exit pupil lies approximately 48 m away, toward the telescope. The image is perpendicular to the axis, but this design has slightly anamorphic properties so that object-to-image mapping is not entirely uniform. The maximum distortion is approximately 0.48%.

Figure 4 illustrates one candidate folding of the MCAO science path. Figure 5 and Figure 6 are side and top views of this implementation, together with the GSMT Cassegrain telescope. The actual physical layout of these many components has been a difficult task, because they must be assembled within a "pancake" behind the GSMT primary that is punctured with numerous posts. Threading the multiple optical paths was a particular challenge, but Figure 7 illustrates that the design can be folded into the available space.

Figure 4 Candidate MCAO science path, including atmospheric dispersion correctors. Figure 5 Side cutaway of GSMT telescope and MCAO fundamentals. Figure 6 End view, looking toward GSMT secondary mirror, of basic MCAO components. Figure 7 Layout of MCAO components behind GSMT primary. Science path white; WFS path red. Adaptive Optics Functions

Wavefront correction

The two OAPs enclose a collimated optical path that serves as a location for all of the wavefront sensing and correcting functions provided by MCAO. Three DMs are presently conjugate to altitudes of 9, 4.5, and 0 km. The zero altitude mirror is known as DM0. Its diameter is 500 mm, virtually the smallest possible size based on the distances to the remaining two DMs, which require increasingly large angles of incidence as the beam size is made smaller. The image of DM0 will be transferred by reimaging optics to an array of Shack-Hartmann lenses in each LGS wavefront sensor.

A tip-tilt mirror is required due to the limited dynamic range of the DM actuators. As with the Gemini South MCAO design, this mirror is located relatively close to a pupil to minimize the pupil motion on the LGS wavefront sensors induced by tip-tilt corrections. (These corrections will be offloaded to the telescope secondary mirror at a reasonably high bandwidth to prevent large displacements from accumulating.) The bandwidth requirements for this mirror will be determined by windshake rather than by turbulence-induced tip-tilt, because the PSD of the latter disturbance becomes more benign with increasing telescope aperture diameter. A reflective relay could be included after DM0 to produce a small pupil solely for the purpose of fast tip-tilt correction, but this approach would add additional optical surfaces and reduce throughput.

Wavefront sensing

In addition to the deformable and tip-tilt mirrors, we must include beamsplitters to separate the science IR light from the visible light used for wavefront sensing, and then separate the visible light into two bands: 589 nm from sodium guide stars, and the balance from NGSs. The two bands must be separated efficiently, not only to make best use of the radiation in each band, but so that the LGS light does not impair the ability to track faint guide stars.

The first beamsplitter, made from water-free fused silica to enhance its performance through the K-band, transmits the science path and reflects "visible" light to a third off-axis paraboloid, OAP3. As the visible light heads to a focus, it is divided by a second beamsplitter into the NGS and LGS wavefront sensing channels. This element is made from ordinary optical fused silica or selected optical glass, with a wedged and curved second surface to correct astigmatism in the transmitted beam. Driven by "Rugate" filter considerations, the broadband transmitted beam will go to the NGS wavefront sensors. The reflected narrowband light at 589 nm goes to the LGS refocusing optics and finally to the Shack-Hartmann wavefront sensors.

The MCAO baseline design system employs five sodium LGSs, arrayed in a 1-arcminute square pattern with stars at each corner and a fifth in the middle. According to the Zenith angle, the distance to the laser-generated stars will range from 85 km at zenith to 200 km at the maximum zenith angle and sodium layer elevation. The Cassegrain telescope defocuses by 3.5 m at 90 km range, compared to its focus at true infinity. No longer used at null conjugates, the dual-OAP relay introduces serious image and pupil aberrations, which change significantly with the LGS slant range. This causes difficulties for any optical relay that must image light from the laser stars onto the Shack-Hartmann wavefront sensor optics.

Several possible candidates for dealing with the aberrations and focal position vs. LGS range exist. One that we currently favor is termed the "zoom optics," a relay whose purpose is to maintain plate scale, focal position, and exit pupil distance at an intermediate focal surface. A preliminary design is indicated in Figure 8. All four lenses are made from optical glass, which is V- coated at 589 nm for maximum efficiency. Although the details remain to be settled, the outermost lenses are fixed in location, while the inner two, which comprise a zoom kernel, move in a nonlinear relationship with each other.

Field masks are employed at the zoom optics focal plane (actually a curved surface) to reduce stray light, and the images of each LGS are then transferred with individual collimator optics that form images of DM0 onto the five Shack-Hartmann lenslets at a constant magnification. Complications exist in forming high-quality images and maintaining good pupil alignment. These requirements were addressed successfully in the Gemini South MCAO design, but the aberrations to be corrected may be even larger for GSMT.

A second candidate, which becomes attractive in view of the very large beam and focal plane sizes, involves the use of one or more flat and curved mirrors acting as a "trombone," and variable aberration correctors to provide a fixed, partially corrected intermediate focal surface. This is less ideal than the zoom lens concept in that it places demands on the Shack-Hartmann collimator optics to deal with not-insignificant shifts in intermediate image plane scale and exit pupil location. It may still represent a means for obtaining superior performance. Indeed, it may be that the refractive optical elements can be nearly eliminated, with the S-H arrays being the only remaining lenses.

The NGS path is comparatively straightforward, and can be implemented at a later date following the approach developed for the Gemini South MCAO system.

Figure 8  LGS WFS zoom optical system forms a fixed intermediate focal plane.

Atmospheric dispersion correction

The telescope is intended to operate at zenith angles as large as 65 degrees, with excellent optical performance required as low as 45 degrees. Owing to the large beam sizes of 500 mm, the atmospheric dispersion correctors are uncommonly large, precluding the use of certain favored materials such as calcium fluoride. GSMT therefore intends to depart from conventional ADC design so that singlet prisms of Cleartran (heat clarified ZnS), rather than bonded doublets, are used. The optical axis of the system is consequently deflected in proportion to the amount of dispersion correction required. This is corrected with additional "wobbling" folding mirrors that restore the optical axis to the second off-axis parabola.

A second advantage in using Cleartran is that it also provides a useful degree of atmospheric dispersion compensation at visible wavelengths. The performance achieved is less than ideal, but it will be satisfactory for wavefront sensing purposes. This reduces the complexity of the NGS path and makes its optical quality higher than was possible in Gemini South. Provided that the scattering associated with Cleartran is deemed acceptable, this approach eliminates the need for an additional ADC in the NGS WFS optical path.

In the event that ZnS is not a satisfactory choice for some reason (efficiency of coatings, cost, or size limitations), a fallback position would be to design singlet prisms from water-free fused silica. Unfortunately, the dispersion properties of silica are not so favorable, and the ADCs would need to be rotated separately for each spectral band, rather than correcting them simultaneously as is possible with Cleartran. A separate set of ADCs would also be required for the NGS path because the dispersion of silica is a poor match with the atmosphere at visible wavelengths. Science Path Optical Performance

The theoretical design performance of the science path, with ADCs included and compensating atmospheric dispersion at 45 degrees zenith angle, is shown in Figures 9 and 11. The spacing between OAP1 and OAP2 is such that the field aberrations are minimized, resulting in extremely small wavefront errors and high Strehl ratio. The Strehl ratio as a function of field is shown in Figure 10. The correction provided by the singlet prism is excellent because near-to-thermal infrared (IR) materials, such as Cleartran, lack the absorption that induces a rapid change in the refractive index with respect to wavelength. This is the bane of all ADC designs.

Figure 9 Wavefront error vs. field of view for the science path. Figure 10   Strehl ratio vs. field angle for J, H, and K. Figure 11 Spot diagrams in H, J, and K bands at a single ADC setting at Z = 45 degrees. The circles indicate the Airy disk at 1.6 microns. Science Path Throughput and Emissivity

Although final information remains to be obtained on the optical properties of Cleartran and the coating efficiencies achievable with it, Table 4 presents our current calculations for science path throughput and emissivity. These predictions are slightly inferior to the values for Gemini South due to the additional mirrors required to compensate for the line of sight deviations induced by the singlet ADCs. We intend to explore alternate design approaches to see if the total number of surfaces can be reduced.

Wavelength, µm1.001.652.202.20 (emissivity)
Per reflection 0.979 0.986 0.987 0.013
Per air-glass interface0.9910.9870.9890.011
Beamsplitter (net)0.9300.9600.9650.022
Overall for 11 reflections0.7920.8560.8660.143
Overall without ADC 0.7360.8220.1650.139
Overall for 4 ADC air-glass interfaces0.9650.9490.9570.044
Overall with ADC 0.7100.7800.8000.209
Table 4 Throughput and emissivity estimates for the GSMT MCAO science path. Laser Launch System(s)

The laser launch telescope (LLT) design developed for MCAO on Gemini South can also be used with this point design, because the geometries of the guide star constellations on the sky are identical. A somewhat smaller launch telescope may actually be acceptable because the minimum size of the guide stars has been significantly increased due to elongation. The LLT must be located behind the GSMT secondary mirror to minimize this elongation for subapertures at the edge of the primary mirror. It is highly unlikely that the laser system itself can be located behind the secondary, and a beam transfer optics (BTO) system must be provided to relay the beams from the laser sources to the LLT.

An additional launch system would be required if Raleigh guide stars are included in the LGS constellation. This telescope should also be mounted behind the GSMT secondary to reduce LGS elongation effects. In this case, it might actually be possible to mount the lasers at this location, because the commercially available, doubled or tripled Nd:YAG lasers that are suitable for generating Rayleigh guide stars are highly compact and efficient. ISSUES FOR NEAR-TERM WORK Modeling and Simulation

Further progress in verifying and refining the MCAO error budget given in Table 2 above will require detailed analysis and simulation of the AO control loop, combined with inputs provided by telescope modeling, a tolerance analysis of the MCAO opto-mechanical design, and measurements of sodium layer dynamics. This process will follow the approach already taken for the Gemini South MCAO preliminary design review (PDR), including: (2) trade studies to optimize first-order AO system parameters; (2) detailed simulation of higher-order effects such as diffraction and three-dimensional LGSs; and (3) simulation of implementation error sources, such as the noncommon path wavefront errors predicted by the opto-mechanical tolerance analysis. For GSMT, we will also add (4) simulation of advanced wavefront sensor concepts suitable for use with extended LGSs, and (5) studies of hybrid sodium/Rayleigh guide star constellations.

The AO analysis and simulation tools already developed for Gemini South MCAO are generally scalable to GSMT, with the important exception that new methods are needed to efficiently compute and apply wavefront control algorithms for the much larger number of DM actuators and WFS subapertures. As described previously, we have recently made important progress in efficiently computing open-loop wavefront estimation algorithms for very-high-order AO systems, and can compute such an algorithm for a MCAO system on an intermediate 16-m telescope in about two hours. Two extensions are needed to efficiently compute control algorithms for a 30-m GSMT: (1) upgrading our computer to 4 GB of RAM and (2) generalizing our new methods for computing open-loop wavefront estimation algorithms to the case of closed-loop wavefront control. We estimate that we can compute a control algorithm for MCAO on a 30-m GSMT in about 20 hours using a 1 GHz Pentium IV with 4 GB of RAM. Even if this estimate is overly optimistic, we can still generate the performance estimates for MCAO on GSMT by simulating a 16-m system, provided that the thickness of the sodium layer is doubled to yield the correct magnitude of LGS elongation. AO Module Opto-Mechanical Design

The opto-mechanical point design presented in Section is an "existence proof" for implementing MCAO on GSMT, but some amount of exploration is desirable to investigate the feasibility of other designs with fewer surfaces and improved optical throughput. The aberrations in the LGS WFS optical path must be evaluated in greater detail, particularly the variations in the pupil distortion and noncommon path error as a function of LGS range. The NGS WFS optical path still needs to be designed, including an atmospheric dispersion corrector for the 0.4-1.0 µm spectral range. Work on the optical bench and other aspects of the mechanical design can begin once the optical design is complete. This will include a detailed tolerance analysis to evaluate the impact of flexure and thermal variations on noncommon path wavefront errors and DM-to-WFS misregistration. Tolerancing an optical system becomes more subtle when AO are involved, because the analysis must account for how errors in the wavefront sensing path impact the performance of the science path through the action of the AO control loop. This issue has already been studied in detail for the Gemini South MCAO system, and the methods and software tools developed are directly transferable to GSMT. AO Module Component Development Deformable Mirrors

The DMs appearing in the MCAO point design are essentially extrapolations of the conventional zonal DMs in use today. The actuator pitch (measured at the DM and not converted to primary mirror space) is 0.5/60 = 0.0825 m, which falls in the range of 7-9 cm typical of many existing DMs. The area of the mirror and the number of actuators required are approximately a factor of four greater than the 941-channel DMs presently is use for USAF AO systems at the Starfire Optical Range (SOR) and Mt. Haleakela (AEOS). Both mirrors feature uniform actuator influence functions with about 7% cross coupling and ±2 µm dynamic range. These parameters are fully acceptable for GSMT, provided that a comparatively low-order adaptive secondary mirror with a larger dynamic range can correct the lowest-order modes of atmospheric turbulence. The SOR mirror includes about four detached actuators, while all actuators are functional for AEOS. It might be useful to obtain ROM quotes on the mirrors required for GSMT, possibly by funding a modest design study. Tip-Tilt Mirror

The current optical design includes a fast tip-tilt mirror with a clear aperture larger than 500 mm. This is beyond the current state-of-the-art, although fast tip-tilt mirrors have been demonstrated with clear apertures of about 250 mm and resonant frequencies of about 500 Hz. The bandwidth and dynamic range requirements for this mirror will be determined by windshake, and more work is needed to determine the input tip-tilt disturbance spectra and assess the potential performance of "extreme" tip-tilt mirrors. Wavefront Sensors

As stated previously, we believe that Shack-Hartmann (SH) sensors remain the preferred approach for high-order LGS wavefront sensing, primarily because the guide star is a spatially incoherent, extended source with little high spatial frequency content. For current SH WFS designs with 4 x 4 pixels per subaperture, CCD arrays with 2562 pixels would suffice for a WFS with 60 x 60 subapertures as required for the current point design. This is a factor of two increase in size over the 1282 arrays presently in use for the SOR and AEOS wavefront sensors with 32 x 32 subapertures. Using larger arrays to resolve the elongated LGS would be more challenging, with an upper bound of about 15362 on the potential number of pixels (1.5k2) set by Nyquist-rate sampling of a three-arcsecond elongate LGS as imaged by a 0.5-m subaperture. Analysis and simulations should be performed to assess (1) tip-tilt measurement accuracy as a function of LGS signal level, detector read noise, and pixel FOV, together with (2) sensitivity to variations in the sodium layer distribution. Measurements to characterize the thickness and variability of the sodium layer should continue, and the possibility of closed-loop LGS AO tests on a 4-8-m class telescope with guide star elongation induced by an appropriately displaced laser launch telescope should also be considered. The likely development costs and technical challenges for larger high- speed (600-1000 kHz), low noise (4-6 e-) CCD arrays should also be assessed. Real-Time Control Algorithms and Electronics

The requirement to implement a wavefront control algorithm for MCAO on GSMT is challenging but not impossible. The computational burden for a conventional control algorithm will be greater by approximately a factor of 200 than for MCAO on Gemini South, based on the relative numbers of actuators and subapertures in the two systems. This would correspond to about 1800 G4 power PC processors on perhaps 450 boards using today's technology, which seems wasteful.

Ways to possibly reduce the necessary volume of electronics include:

  1. Some reduction can be expected due to continuing improvements in commercial electronics.

  2. New wavefront control algorithms, such as the sparse matrix methods described in Appendices 4.6.A and 4.6.B, may be more computationally efficient than conventional matrix multiply techniques. At present, most of these approaches still suffer from increased signal processing latency, because the majority of the computations must wait until the full WFS measurement vector is available, and they are less straightforward to parallelize.

  3. Field programmable gate array (FPGA) technology may offer significant reductions in signal processing time at some penalty in control algorithm flexibility. Laser System and Beam Transfer Optics

The BTO system design for the Gemini LGS systems employs mirrors, which introduce complications in terms of optical transmittance, scattered light, beam quality, and reliability. Fiber lasers and/or fiber BTO systems could eliminate these issues if they can be demonstrated at the required wavelengths and power levels. This is an important area for any laser research and development work that might be funded in connection with GSMT.

March 2002