On-sky measurement accuracy of Keck telescope segment surface errors

We quantify the accuracy of the Keck telescope segment surface figure measurements made on sky by the Phasing Camera System (PCS), a Shack-Hartmann wavefront sensor that uses long integration times to average over the effects of atmospheric turbulence. These measurements are used to determine the settings for warping harnesses that significantly reduce the segment surface errors. When a series of six measurements is performed on the same segment in rapid succession, the Root Mean Square (RMS) segment surface, as reconstructed by 2nd through 4th order Zernike polynomials, is determined with an accuracy of 6.0 ‡ 3.2 nm (error on the mean). However, when we compare measurements on the same segment separated by several hours the inferred surface RMS accuracy is 9.0 ‡ 5.0 nm, or 50% larger. This suggests that there are systematic errors on the order of 7 nm that vary throughout the night. In this paper we investigate and quantify the potential causes of these systematic errors, which together with statistical errors, constitute a fundamental limit for the performance of segment warping harnesses. Such measurements are currently the baseline warping harness inputs for the Thirty Meter Telescope and the European Extremely Large Telescope.