Elevation Limits Due to Pupil Rotation

The Keck 2 laser projection telescope is located along the side of the telescope, 6.2 m from the optical axis, and illuminates a cylinder of Na atoms in the Earth's mesosphere approximately 1 m diameter and 10 km long. The apparent elongation of the laser guide star (LGS) therefore varies across the pupil, reaching ~3.5" at the edge farthest from the projection telescope (see Fig. 1). This elongation pattern remains fixed to the telescope pupil, but varies with the elevation of the telescope and the changing structure of the Na layer.
Fig 1: LGS with primary unstacked

As the LGS is observed by the wavefront sensor (WFS) quad cells, the elongation of the spots induces quasi-static aberrations in the corrected wavefront. The LGS aberrations are sensed by the low-bandwidth wavefront sensor (LBWFS), and corrected by changing the centroid locations to which the spots on the WFS are driven. For targets with sufficiently bright TT references (R<16.0), this dynamic image sharpening is performed continuously during observations. We are currently developing a predictive model of the LGS aberrations, for use on targets with TT references R>16.0, but this has not yet been implemented.

Maximum acceptable pupil rotation rate

When observing in position angle mode (PA fixed on NIRC2), the telescope pupil and LGS elongation pattern will appear to rotate on the WFS. If this rotation is faster than the rate at which we can measure and correct the LGS aberrations, the image quality will suffer. The WFS centroid correction is an iterative process, and ~5 iterations are required to reach convergence.
R magnitude LBWFS integ. (s) Convergence (s)
14.0 20 100
15.0 30 150
16.0 45 225

Table 1: LBWFS convergence time vs. TT reference R mag.

The convergence times listed in Table 1 must be compared with the pupil rotation rate for a given target and the critical rotation angle at which the error in the estimate of the LGS aberrations becomes dominant. Near zenith, 5° pupil rotation will induce a 100 nm wavefront error, while 10° pupil rotation leads to 200 nm of wavefront error.

Figures 2-4 show the region of the sky over which the pupil rotation rate is low enough to allow correction of the LGS aberrations, for TT reference stars R=14,15,16. Orange and red zones mark the regions in which >100 nm and >200 nm of LGS aberrations should be expected. The red region at el>87° represents the "keyhole" region excluded due to telescope azimuth tracking constraints. Depending on the declination of the target, passage through the region of poor correction can last up to 50 minutes (for an R=16.0 TT reference).

Fig 2: R=14.0 TT ref

Fig 3: R=15.0 TT ref

Fig 4: R=16.0 TT ref