Fast iterative optimal estimation of turbulence wavefronts with recursive block Toeplitz covariance matrix
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The estimation of a corrugated wavefront after propagation through the atmosphere is usually solved optimally with a Minimum-Mean-Square-Error algorithm. The derivation of the optimal wavefront can be a very computing intensive task especially for large Adaptive Optics (AO) systems that operates in real-time. For the largest AO systems, efficient optimal wavefront reconstructor have been proposed either using sparse matrix techniques or relying on the fractal properties of the atmospheric...[Show more]
dc.contributor.author | Conan, Rodolphe | |
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dc.coverage.spatial | Montreal, Canada | |
dc.date.accessioned | 2015-12-10T23:17:53Z | |
dc.date.created | June 22-27 2014 | |
dc.identifier.isbn | 9780819496164 | |
dc.identifier.uri | http://hdl.handle.net/1885/65392 | |
dc.description.abstract | The estimation of a corrugated wavefront after propagation through the atmosphere is usually solved optimally with a Minimum-Mean-Square-Error algorithm. The derivation of the optimal wavefront can be a very computing intensive task especially for large Adaptive Optics (AO) systems that operates in real-time. For the largest AO systems, efficient optimal wavefront reconstructor have been proposed either using sparse matrix techniques or relying on the fractal properties of the atmospheric wavefront. We propose a new method that exploits the Toeplitz structure in the covariance matrix of the wavefront gradient. The algorithm is particularly well-suited to Shack-Hartmann wavefront sensor based AO systems. Thanks to the Toeplitz structure of the covariance, the matrices are compressed up to a thousand-fold and the matrix-to-vector product is reduced to a simple one-dimension convolution product. The optimal wavefront is estimated iteratively with the MINRES algorithm which exhibits better convergence properties for ill-conditioned matrices than the commonly used Conjugate Gradient algorithm. The paper describes, in a first part, the Toeplitz structure of the covariance matrices and shows how to compute the matrix-to-vector product using only the compressed version of the matrices. In a second part, we introduced the MINRES iterative solver and shows how it performs compared to the Conjugate Gradient algorithm for different AO systems. | |
dc.publisher | SPIE | |
dc.relation.ispartofseries | Adaptive Optics Systems IV | |
dc.source | Proceedings of SPIE - The International Society for Optical Engineering, vol 9148 | |
dc.title | Fast iterative optimal estimation of turbulence wavefronts with recursive block Toeplitz covariance matrix | |
dc.type | Conference paper | |
local.description.notes | Imported from ARIES | |
local.description.refereed | Yes | |
dc.date.issued | 2014 | |
local.identifier.absfor | 020102 - Astronomical and Space Instrumentation | |
local.identifier.ariespublication | a383154xPUB1099 | |
local.type.status | Published Version | |
local.contributor.affiliation | Conan, Rodolphe, College of Physical and Mathematical Sciences, ANU | |
local.description.embargo | 2037-12-31 | |
local.identifier.doi | 10.1117/12.2054472 | |
dc.date.updated | 2015-12-10T10:02:19Z | |
local.identifier.scopusID | 2-s2.0-84922687795 | |
Collections | ANU Research Publications |
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