Mitigation of truncation effects in elongated Shack-Hartmann laser guide star wavefront sensor images

Laser guide star Shack-Hartmann wavefront sensor images on extremely large telescopes (ELT) will be significantly elongated due to the off-axis projection of the laser relative to the subapertures. The finite number of pixels of the wavefront sensor detector means the most elongated images will be truncated, introducing errors in the centroid measurements. In this paper, we propose appending to the truncated wavefront sensor image the most likely missing tails from a high-resolution nontruncated reference image, which can be calculated from all of the low-resolution images. We show, via numerical simulation, that we can improve the centroid estimate for the most elongated subapertures on an ELT in the presence of read and photon noise.