LGSAO Basics and System Description

Astronomical observations using natural guide star (NGS) adaptive optics are limited to areas of the sky within ~30 arcseconds of a fairly bright star (R<13.5 using the Keck system). This leaves 99% of the sky beyond the reach of AO. The W. M. Keck Observatory now provides a sodium (Na) laser guide star on the Keck II telescope to dramatically expand the sky area accessible by AO observations.

In the upper part of the Earth's mesosphere (90±10 km altitude), there is a 5-10 km thick layer rich in Na atoms, deposited by the ablation of micrometeorites. These atoms can be excited and caused to radiate by sponateous emission by projecting a 10-14 Watt pulsed laser tuned to the Na D atomic transition (589 nm) in the direction of the science target. The magnitude of this artificial guide star corresponds to 9.5<V<11.0 and varies with laser power, beam collimation, and Na column density.

There are four fundamental differences between the operation of the Keck AO system using the LGS with respect to that using an equivalent-magnitude NGS:

1. The laser beam and the light returned to the telescope from the LGS travel upward and downward along the same path. Consequently no tip-tilt (TT) measurement can be derived from observations of the LGS, and a separate natural TT reference near the science target must be used. This object can be fainter than that required for full NGSAO correction, and may also be further from the science target. A TT controller (STRAP) with 4 avalanche photo-diodes in a quad-cell arrangement is used to measure the atmospheric TT (see Fig. 2).

Fig. 2: Keck LGSAO control loops
2. The laser guide star is not located at infinity, but at a finite and slowly varying altitude. Though it can be used to measure the rapid atmospheric focus variations due to turbulence, it cannot be used to measure the absolute focus of the telescope. The TT reference is therefore also used to measure the telescope focus, by diverting a small fraction of its light to the low-bandwidth wavefront sensor (LBWFS, see Fig. 2). The focus of the TT reference recorded by the LBWFS is then used to drive the position of the WFS of a focus stage to track the altitude of the sodium layer.

3. Another consequence of the finite altitude of the LGS is reduced performance due to the cone effect, also known as focal anisoplanatism. The atmospheric volume in which a star's wavefront is distorted by turbulence is cylindrical, while that over which the wavefront of the LGS is distorted is conical (with the apex at the altitude of the Na layer). Some fraction of the turbulence affecting the science target will therefore not be sensed by the wavefront measurement of the LGS, and the AO-corrected image quality will consequently be reduced.

Fig. 3: Image of LGS with primary unstacked
4. The images of the laser guide star are not point-like since they are being produced in an atmospheric Na layer 5-10 km thick. The apparent size of the LGS will therefore vary across the telescope pupil as a function of the distance from the laser launch telescope. This effect can be mitigated by applying a deformable mirror (DM) loop gain which varies across the telescope pupil (see Fig. 3).

Factors limiting system performance

1. Seeing
The AO correction achievable with LGSAO is somewhat more sensitive to seeing than that of NGSAO, due to the blurring of the upward-propagating laser beam under turbulent conditions. The signal-to-noise ratio (SNR) of the wavefront measurement on the LGS will be proportional to the reciprocal of its apparent size, which will be dramatically increased under poor seeing conditions. The Keck LGSAO system has been successfully operated in visible (0.5 micron) seeing between 0.3" and 0.9". Performance estimates given in this document apply to visible seeing of 0.6", approximately the median for the Keck 2 telescope.

2. Laser beam quality
The dye laser used in the Keck 2 LGSAO system must be realigned before each observing run. The delivered beam quality depends critically on the success of this alignment procedure, and the seeing conditions. Analysis of images of the LGS taken with the telescope primary unstacked in Dec. 2003 and Feb. 2004 indicate that its size recorded by the segment nearest the launch telescope can be approximated closely by a spot with intrinsic FWHM = 1.1", convolved twice by the visible seeing (once for each passage through the atmosphere). Thus, on a night with 0.5" seeing, the FWHM of the laser guide star was 1.3"x1.3" in the best unstacked image, and up to 2.8"x1.3" at the far edge of the pupil. The wavefront measurement error will be linearly proportional to the LGS spot size.

3. Returned power
The power returned from the sodium layer is a function of the projected laser power, the frequency tuning and pulse format of the laser, and the density of the sodium layer. The average power output of the laser is generally 10-14 W. No evidence has yet been seen of saturation of the Na layer, where a sufficient fraction of the atoms are excited to their upper state to cause a non-linearity in the returned power with respect to the projected power. The return has however been observed to vary by over a factor of 4 from run to run, from a median of 230 counts per subaperture at 672 Hz framerate in September 2003 (equivalent to V=8.8) to 70 counts per subaperture at 500 Hz framerate in February 2004 (equivalent to V=10.0). The SNR of the wavefront measurement is proportional to the counts per subaperture.

4. TT reference magnitude
The magnitude of the TT reference determines the quality of the tip-tilt control, but not the control of higher order modes. Thus the image degradation suffered with a faint TT reference is a broadening of the PSF core, rather than a reduction in the ratio of the power in the core to that in the halo, as is the case with a faint NGS. The TT bandwidth and measurement noise both increase for fainter stars, and begin to dominate the error budget for TT references with R>15. The LGSAO system has been operated for science with TT reference stars as faint as R=18.2 (07/26/04). Note that the PSF when using faint TT reference stars has a unique structure, since high-order aberations are still well corrected. This results in a PSF with little power in the seeing-limited halow, but no clear diffraction-limited core.

4. TT reference separation
We have measured the isokinetic angle, the angle at which the phase becomes decorrelated by 1 radian rms due only to TT, to be 72" at 2.1 microns on one occasion (07/27/04). This may not be typical. Above a separation of ~40", tilt anisoplanatism becomes a dominant term in the LGSAO error budget. Under most circumstances, the science object will be kept near the telescope optical axis (or NIRC2 detector center), while the TSS stage translates the STRAP TT controller and LBWFS across the focal plane to reach the TT reference. Certain regions of the TSS focal plane are currently inacessible due to vigneting (see TSS view), thus the PA of the NIRC2 detector may be constrained for TT references >10" from the science target.

6. Elevation
As with seeing, the corrected image quality is more strongly dependent on elevation in LGSAO than in NGSAO. Under median seeing conditions on 02/04/04, LGSAO corrected images with a V=15 TT reference at 49° elevation had a Strehl of only 0.06, while that near zenith with a similar TT reference was 0.15. We are prohibited from projecting the laser below 20° elevation.

7. Pointing accuracy
Since TT control is performed by the STRAP controller, which rides on the TSS positioning stage, placement of the the science object on the NIRC2 detector is determined by the TSS stage rather than the FSMs as is the case for NGSAO. TSS stage motions have proven to be repeatable to ~4 microns rms, corresponding to 3 mas on sky. However, we have found that the image stability error (somehow produced by STRAP) does not allow us to implementat compensation for differential atmospheric refraction (DAR). We are actively working on this issue. In the meantime, this will restrict the positioning accuracy and the single-frame exposure times during 2005A shared-risk science observations.

For more information please contact Al Conrad, Jim Lyke or R. Campbell : (randyc, aconrad or jlyke @keck.hawaii.edu).