Simultaneous sodium profile estimation and LGS SH-WFS pixel processing optimization using LGS sub-aperture images

Abstract

Image displacement pixel processing for laser guide star (LGS) Shack–Hartmann wavefront sensors (WFS) is often based upon a center of gravity with thresholding [thresholded CoG (tCoG)] algorithm. This method yields a nearly linear response to the sub-aperture wavefront gradient, but suffers from zero-point biases due to sodium profile variability and the resulting changes in the shape of the LGS sub-aperture images. This effect interacts with additional biases due to the image truncation caused by the limited field of view of the WFS sub-apertures, as well as from WFS non-common path aberration (NCPA). Natural guide star (NGS) truth wavefront sensors (TWFS) have been proposed to correct for the resulting aberrations in the reconstructed wave-front, and multiple such TWFS would be required to control anisoplanatism effects when there are multiple LGS. We describe a novel algorithm that estimates the sodium profile from time averaged sub-aperture images of one or multiple LGS using a system imaging model. This estimate can then be used to correct for the zero-point bias by adjusting the tCoG reference vector. This eliminates the need for an NGS TWFS to detect sodium profile induced aberrations, and a single TWFS with faint NGS would then be sufficient to monitor any variations in NCPA if needed, which greatly improves the sky coverage. The reconstructed sodium profile can also be used to build constrained matched filters, a noise-optimal alternative to tCoG that requires accurate knowledge of the sub-aperture LGS images and their spatial derivatives (and has yet to be demonstrated on sky). This new sodium profile reconstruction algorithm consequently eliminates the need for dithering LGS spots on sky to determine these derivatives, which greatly simplifies the implementation of matched filtering and also provides better performance. All of the necessary sodium profile estimation, bias computations, and matched filter optimizations can be done with a modern CPU (e.g., Intel Core i7-11700) at around a 0.1-Hz update rate as a background process for the real time controller. Our simulations of this new method are for center launch LGS, but we are confident the profile estimation algorithm will work equally well if not better for side launch LGS, even when there is increased image truncation.