25 October 2004 Tomography for multiconjugate adaptive optics systems using laser guide stars
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In this paper we present a solution to the MCAO reconstruction problem using multiple laser guide stars and show that it can be interpreted as a form of back-projection tomography. It is shown that a key intermediate step is to determine a minimum-variance estimate of the index variations over the atmospheric volume. We follow the idea of Tokovinin and Viard [JOSA-A, April 2001] in initially formulating the problem in the Fourier domain; we then extend the interpretation to the spatial domain. The former results were limited to the case of infinite aperture and plane wave beacons, and the statistically optimal wavefront solution was given for a single science direction. The new approach is more general and interpretable as tomographic back-projections, which gives rise to algorithms for the finite aperture, cone (laser) beams, and wide-science-field cases. A fortuitous consequence of this analysis is that a "fast" algorithm suitable for real-time implementation has become evident. The reconstruction requires only filtering and the inversion of small (dimension = number of guidestars) matrices. In simulations, we compare results with those of a spatial domain least-square matrix-inversion method.
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Donald T. Gavel "Tomography for multiconjugate adaptive optics systems using laser guide stars", Proc. SPIE 5490, Advancements in Adaptive Optics, (25 October 2004); doi: 10.1117/12.552402; https://doi.org/10.1117/12.552402

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