Application of Hartmann Linearity Calibrations to ViLLaGEs

We attempt to linearize the output of the Shack-Hartmann wavefront sensor in the ViLLaGEs instrument. ViLLaGEs (Visible Light Laser Guidestar Experiments) is a MEMS-based Adaptive Optics system on the 1 - meter Nickel telescope at Lick Observatory meant to provide correction at visible wavelengths with a 9x9 subaperture Hartmann sensor. We estimate that the open-loop accuracy of ViLLaGEs is ~40 nm. We "calibrate" the Hartmann linearity by raster scanning a tip/tilt mirror downstream of an internal fiber and inverting the resulting signal, forming a lookup table of unbiased tilts. From this calibration, we conclude that nonlinearity is a minor effect in the open-loop operation of ViLLaGEs, on the order of ~15 nm. We show through simulations of Shack-Hartmann sensors that this error is likely due to an internal pupil mask not physically conjugate to the telescope pupil. We test the resulting lookup table on an internal "turbulator" in ViLLaGEs, or a rotating plate meant to simulate the wind-driven atmosphere, and find that the Strehls with and without the lookup table are indistinguishable.