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Pixel processing for laser guide star (LGS) Shack-Hartman wavefront sensor (WFS) is often based on center of gravity with thresholding (tCoG) algorithm, which yields close to linear response but with zero point corrupted by the shape of the source (sodium profile). The spot truncation due to the limited field of view of the WFS sub-apertures, as well as non-common path aberration (NCPA) further complicate the problem. Natural guide star (NGS) based truth wavefront sensors (TWFS) are therefore often used to correct the resulting aberrations, and multiple such TWFS are required to control anisoplanatism effects when there are multiple LGS. In this paper, we demonstrate a novel algorithm that reconstructs the sodium profile from time averaged subaperture images of one or multiple LGS WFS using a system imaging model which can then be used to improve the pixel processing by correcting the tCoG reference vector. It forgoes the need for using any NGS based TWFS for sodium profile induced aberrations and a single TWFS would then be sufficient to monitor optics effects. The reconstructed sodium profile can also be used to build constrained matched filters, a novel pixel processing algorithm alternative to tCoG that requires accurate knowledge of the subaperture reference images and their derivatives and has yet to be demonstrated on sky. Consequently, this new sodium profile reconstruction algorithm eliminates the need for dithering LGS spots on sky, which greatly simplifies the implementation of matched filtering, and also provides better performance. All the pixel processing optimizations can be done with a modern CPU at around 0.1 Hz update rate as a background process for the real time controller. The simulations we have done are for center launch LGS, but we are confident the profile estimation algorithm should work equally well if not better for side launch LGS even when there is truncation.
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