ON-SKY WIDE-FIELD ADAPTIVE OPTICS CORRECTION USING MULTIPLE LASER GUIDE STARS AT THE MMT

The MMT's multiple LGS AO system comprises a laser launch telescope (Stalcup 2006), an adaptive secondary mirror (ASM; Brusa-Zappellini et  al. 1998; Wildi et  al. 2003), a Cassegrain mounted WFS instrument (Lloyd-Hart et  al. 2005, 2006b; Baranec 2007; Baranec et  al. 2007c), and a PC-based real-time reconstructor computer (Vaitheeswaran et  al. 2008). The laser launch telescope, mounted above the MMT's ASM, projects a constellation of five λ = 532 nm Rayleigh LGSs on a regular 2' diameter pentagon with a total on-sky power of 25 W.

The Cassegrain WFS instrument consists of a LGS WFS, a tip-tilt sensor and a NGS WFS. The LGS WFS uses dynamically refocused optics (Georges 2003) and an electronically shuttered CCD to accumulate photon return over a range of 20–29 km from the telescope. Shack–Hartmann patterns for each of the five LGSs are created by a prism array (Putnam et  al. 2004) with 60 subapertures in a hexapolar geometry, and captured at a rate of 400 frames per second. An electron multiplying CCD is used to obtain tip-tilt measurements from a natural star within the 2' LGS constellation at the same rate. The NGS WFS is a traditional 12 × 12 Shack–Hartmann sensor used for system calibration and automatic static aberration correction. The Cassegrain-mounted WFS instrument is designed to accept the current suite of MMT f/15 NGS AO science instruments including PISCES (McCarthy et  al. 2004), Clio (Freed et  al. 2004), ARIES (McCarthy et  al. 1998), and BLINC-MIRAC (Hinz et  al. 2000).

The GLAO correction is calculated by reconstructor matrix multiplication in the PC-based real-time computer from 300 LGS slope pairs, 60 pairs from each of the five laser beacons, as well as a pair of slopes from the fast tip-tilt camera. The reconstructor projects each of the five sets of LGS WFS slope measurements onto an orthonormal basis of disk harmonic (DH) functions (Milton & Lloyd-Hart 2005) in the telescope's pupil. The five LGS wave fronts are averaged by mode to produce an estimate of the ground-layer contribution to atmospheric seeing. Finally, the GLAO modal estimate is converted to actuator displacements which are transmitted to the ASM at the telescope pupil. In addition to an overall system loop gain, separate gains can be applied to the individual DH modes in the reconstruction for fine tuning of the system response. These are obtained from the measured modal closed-loop system response. Measured scale factors for the individual responses of the ASM actuators are also applied to account for variations in the sensitivities of the associated capacitive sensors. The DH basis functions are used instead of the traditional Zernike polynomials since they provide increased loop stability and a lower rms error for a given number of controlled modes. Zernike polynomials have large radial derivatives near the edge of the pupil, particularly for high spatial frequency modes. By contrast, the DH functions have zero radial derivatives at the edge of the pupil, placing less stress on actuators at the outer edge of the ASM and resulting in lower actuator currents and greater loop stability.

The results of the GLAO correction are presented in the context of seeing statistics recorded at the telescope spanning the past 5 yr. Measurements of seeing are made by calculating stellar image widths directly as observed by the Shack–Hartmann WFSs used for the active alignment of the MMT's primary mirror with its f/5 and f/9 secondary mirrors (Pickering et  al. 2004). The sensors do not have the temporal bandwidth to resolve the dynamic atmospheric turbulence so the integrated image widths represent the best-available estimate of seeing. The WFSs currently operate at a mean wavelength of $\overline{\lambda } = 650\,{\rm nm}$ (T. Pickering 2008, private communication) and data comprise ∼ 50,000 individual measurements taken during approximately 800 different nights. Measurements are corrected for airmass (quoted at zenith) and are extrapolated—in an overly conservative way—to infrared wavelengths by a factor of the ratio of wavelengths to the −1/5 power.

Data were taken to compare seeing-limited imaging with that of tip-tilt only and GLAO-corrected imaging. The images were captured with the science instrument PISCES, a near-infrared camera with a 110'' field of view and a plate scale of 107 mas per pixel. Observations comprised consecutive 1 s exposures, with a rate of approximately 14 exposures per minute. During subsequent analysis, exposures were first background subtracted and flat fielded, then averaged to simulate a long exposure. Sky de-rotation was then applied post facto for images with more than one object. All images were taken with a standard K_s or λ = 2.14 μm narrowband filter. Image widths were calculated using the MOFFAT radial fit tool in the imexam package of IRAF.

The first astronomical targets observed on the night of 2008 February 19 were a series of single stars ranging in visual magnitude from 8 to 10, all with a declination of approximately +40°. The stars were located approximately in the center of the laser beacon constellation with tip-tilt sensing done using the target star. Figures 2 and 3 show examples of the stellar PSF during seeing-limited, tip-tilt only, and the GLAO correction at K_s and λ = 2.14 μm. Each image is an average of approximately 60 1 s exposures.

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Star 1 has a seeing-limited FWHM of 070, while the closed-loop PSF has a FWHM of 033, a reduction of the image width of 53%, with a factor of 2.3 increase in relative peak intensity. The GLAO-corrected PSF shows some asymmetry which is similar in each of the 60 exposures used to create the mean image in Figure 2 indicating that the system was limited by uncorrected noncommon path errors. The reduction in image width with GLAO can be compared with the cumulative seeing distribution measured at the MMT as presented in Figure 4. The GLAO correction represents an effective improvement in seeing from somewhat worse than median for the site, at the 58th percentile, to excellent, at the fourth percentile.

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During observations of star 2, the GLAO correction was modest. A 10% decrease in image width was observed with the tip-tilt only correction; however, with full ground-layer correction, the FWHM of the image is reduced by 35%, from 060 to 039. This corresponds to an effective seeing improvement from the 42nd to the 9th percentile.

Although the results from the 2008 February telescope run demonstrate successful closed-loop GLAO operation, the level of correction did not achieve the final expected system performance of 01–02 images in the K band. This is attributable to three factors. Time to implement and test the system for measuring and correcting noncommon path and other static aberrations was cut short due to inclement weather. This feature was implemented and initial testing was completed in the subsequent 2008 May run. Second, and more seriously, there were random network transmission delays and dropouts in the tip-tilt control loop, which unbeknownst to us at the time, severely affected loop stability. In addition, the elevation axis servo control system of the MMT telescope was exhibiting technical problems resulting in the amplification of wind-driven oscillations at 2.25 Hz. The AO loop gain had to be significantly reduced in the presence of the latter two factors in order to maintain stable closed-loop GLAO operation, compromising the final level of image correction.

Additional observations were carried out in 2008 May in order to implement and test automated static aberration correction with the NGS WFS and to characterize the uniformity of the GLAO-corrected PSF over the 110'' field. Unfortunately, these results were again severely affected by the tip-tilt network issues and continuing problems with the MMT telescope elevation axis servo control system. Automated static aberration correction for the MMT LGS WFS system is achieved by measuring the difference in the long-term average open-loop and closed-loop GLAO aberrations of the tip-tilt star with the NGS WFS, similar to the quasistatic calibration with the Keck LGS AO system (van Dam et  al. 2006). The change in the mean NGS WFS slopes is reconstructed to produce a modal estimate of the quasistatic nonatmospheric aberrations. These modal corrections are converted to LGS WFS centroid offsets using the LGS WFS influence matrix. Finally, these offsets are used to shift the zero points of the LGS WFS slope calculation during GLAO closed-loop operation.

Data were taken of an m_V = 9 star (20^h01^m1672, 20°41'298, J2000) with many field stars seen in the 110'' PISCES field of view. Figure 5 shows an image of the field, with brighter stars magnified, shown both uncorrected and with ground-layer correction. The stellar images are rescaled in intensity for clarity. Both corrected and uncorrected data are averages of 70 1 s exposures with the narrowband λ = 2.14 μm filter. Tip-tilt signals were obtained from the bright star in the center of the field, which was also used to sense static aberrations. Image improvement was again modest: the tip-tilt star has a measured FWHM of 070 in open loop and 055 in GLAO closed loop, a decrease of only 21%. Over the entire field, both the uncorrected and GLAO corrected PSFs are fairly constant, with a mean seeing-limited FWHM of 072 ±  001 for the brightest 12 stars in this field and a mean GLAO-corrected FWHM of 058 ±  003 for the same stars. In contrast to the results from the February run in Figure 2, the corrected PSFs are round, showing the effect of removing the static aberration by reference to the NGS WFS. We expect a substantial overall improvement in the PSF FWHM during future observations now that the vibration issues have been resolved and we are able to increase the GLAO loop gain, however, a decrease in closed-loop PSF uniformity may be seen due to anisoplanatic effects.

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During these observations, the NGS WFS was passively collecting data in both open- and closed-loop operations of the tip-tilt star at 180 frames per second. These data have been analyzed to evaluate the closed-loop performance in a manner independent of static aberrations. Table 1 shows the rms modal amplitudes reconstructed from the NGS WFS measurements, grouped by radial order. We show the more familiar Zernike modes rather than the DH modes used in the real-time control. GLAO-corrected 42% of the measured total rms wave front error, with a reduction in the modes controlled by the LGS WFS (orders 2–8) of 38%, consistent with previous open-loop studies of GLAO performance at the MMT (Baranec et  al. 2007c). However, the reduction of 43% for the tip-tilt modes is much lower than the greater than 80% correction obtained in previous analyses and attributable to the low tip-tilt loop gains and the servo oscillations experienced during this run. Note that even though there was a resonance in the telescope's elevation drive, the total power in the orthogonal tilt modes were quite similar during both open- and closed-loop observations, differing by at most 11%, and as a consequence would not have affected an asymmetry in the stellar PSFs.

There were two different control loops used in the closed-loop GLAO system: one for the NGS tip-tilt sensor and the other for the high-order LGS WFS. Both loops used an integral control law and had a sample rate of 400 Hz. The tip-tilt loop was unfortunately hindered by two technical issues. It was discovered during an examination of telemetry data that there were randomly varying network delays and dropouts in the transmission of the tip-tilt data between the tip-tilt sensor and real-time wave front reconstruction computer. This would cause the tip-tilt control loop to act erratically and not follow the atmospheric tip-tilt signal. In addition, the 2.25 Hz tilt signal produced by the oscillating elevation drive increased the required actuator stroke at the edges of the ASM. With the combination of these effects, the ASM would quickly hit its safety limits for voice coil actuator current at the edges, breaking the loop—for even modest gains in the tip-tilt loop. To maintain closed-loop operation for any appreciable amount of time, the gain was severely reduced, compromising correction. Figure 6 shows the open- and closed-loop power spectra for selected Zernike modes as measured by the NGS WFS. The power spectra show that despite low gain the GLAO control is removing a significant portion of the aberrations at very low frequencies, below ∼1 Hz, for the tip-tilt modes, and even a 46% reduction in the 2.25 Hz oscillation in elevation. The random network transmission delays, however, created a large overshoot in higher frequencies, hindering the ability to recover good image quality.

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The disturbance-rejection frequency response of high-order loop, which was not affected by the tip-tilt issues, was modeled at different gain values (Figure 7). At a gain of 0.15, the disturbance rejection bandwidth is ∼20 Hz with a low-frequency slope of 20 dB/decade. To maintain the closed-loop operation of the AO system during observations, the overall system gain was reduced to approximately 0.015. At this gain, the bandwidth is limited, in the range of 3–5 Hz. The power spectra of higher-order modes (e.g., for the astigmatism modes shown in Figure 6) show correction out to a higher bandwidth of ∼2.5 Hz due to the limited influence from the elevation servo resonance. While it is possible that the bandwidth of the higher-order modes could have been improved by taking advantage of the mode-dependent gains, a conservative approach to controlling the ASM was adopted, and only the overall system gain was adjusted to achieve loop stability. With the elevation axis servo oscillation issue now resolved, we expect the closed-loop bandwidth during future observations to increase to ∼20 Hz once the loop gain is increased to 0.15 and the modal gains are fine tuned. We intend to also implement a more sophisticated proportional-integral-derivative controller which should further increase the bandwidth of the controller to ∼30 Hz, significantly reducing the residual wave front error.

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