The lattice geometry of Walsh-function-based adaptive optics
We show that there is an intrinsic link between the use of Walsh aberration modes in adaptive optics (AO) and the mathematics of lattices. The discrete and binary nature of these modes means that there are infinite combinations of Walsh mode coefficients that can optimally correct the same aberratio...
| Main Authors: | , , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
MDPI
2022
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| _version_ | 1797107786800168960 |
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| author | Hu, Q Xiao, Y Cui, J Turcotte, R Booth, MJ |
| author_facet | Hu, Q Xiao, Y Cui, J Turcotte, R Booth, MJ |
| author_sort | Hu, Q |
| collection | OXFORD |
| description | We show that there is an intrinsic link between the use of Walsh aberration modes in adaptive optics (AO) and the mathematics of lattices. The discrete and binary nature of these modes means that there are infinite combinations of Walsh mode coefficients that can optimally correct the same aberration. Finding such a correction is hence a poorly conditioned optimisation problem that can be difficult to solve. This can be mitigated by confining the AO correction space defined in Walsh mode coefficients to the fundamental Voronoi cell of a lattice. By restricting the correction space in this way, one can ensure there is only one set of Walsh coefficients that corresponds to the optimum correction aberration. This property is used to enable the design of efficient estimation algorithms to solve the inverse problem of finding correction aberrations from a sequence of measurements in a wavefront sensorless AO system. The benefit of this approach is illustrated using a neural-network-based estimator. |
| first_indexed | 2024-03-07T07:20:45Z |
| format | Journal article |
| id | oxford-uuid:0808f672-82a2-4af4-a2d2-58e56412fbda |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:20:45Z |
| publishDate | 2022 |
| publisher | MDPI |
| record_format | dspace |
| spelling | oxford-uuid:0808f672-82a2-4af4-a2d2-58e56412fbda2022-10-10T16:59:01ZThe lattice geometry of Walsh-function-based adaptive opticsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0808f672-82a2-4af4-a2d2-58e56412fbdaEnglishSymplectic ElementsMDPI2022Hu, QXiao, YCui, JTurcotte, RBooth, MJWe show that there is an intrinsic link between the use of Walsh aberration modes in adaptive optics (AO) and the mathematics of lattices. The discrete and binary nature of these modes means that there are infinite combinations of Walsh mode coefficients that can optimally correct the same aberration. Finding such a correction is hence a poorly conditioned optimisation problem that can be difficult to solve. This can be mitigated by confining the AO correction space defined in Walsh mode coefficients to the fundamental Voronoi cell of a lattice. By restricting the correction space in this way, one can ensure there is only one set of Walsh coefficients that corresponds to the optimum correction aberration. This property is used to enable the design of efficient estimation algorithms to solve the inverse problem of finding correction aberrations from a sequence of measurements in a wavefront sensorless AO system. The benefit of this approach is illustrated using a neural-network-based estimator. |
| spellingShingle | Hu, Q Xiao, Y Cui, J Turcotte, R Booth, MJ The lattice geometry of Walsh-function-based adaptive optics |
| title | The lattice geometry of Walsh-function-based adaptive optics |
| title_full | The lattice geometry of Walsh-function-based adaptive optics |
| title_fullStr | The lattice geometry of Walsh-function-based adaptive optics |
| title_full_unstemmed | The lattice geometry of Walsh-function-based adaptive optics |
| title_short | The lattice geometry of Walsh-function-based adaptive optics |
| title_sort | lattice geometry of walsh function based adaptive optics |
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