The subaperture images in Shack–Hartmann wavefront sensors are elongated when using sodium laser guide stars, due to the parallax effect and the nonzero thickness of the sodium layer. This elon gation increases the measurement error in each subaperture and introduces a correlation between the measurements in the orthogonal x and y pixel axes. We show, via end-to-end numerical simulations, that including these errors in a matrix-vector-multiply maximum a posteriori reconstructor sig nificantly improves the expected performance of a laser tomography adaptive optics system for the $42\mathrm{m}$ diameter European Extremely Large Telescope. In particular, including this noise-weighted re construction shows the detected photon requirement is similar for both central and side launch of the sodium lasers.

© 2010 Optical Society of America

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