- Previous Article
- IPI Home
- This Issue
-
Next Article
Computing the fibre orientation from Radon data using local Radon transform
Cumulative wavefront reconstructor for the Shack-Hartmann sensor
1. | Industrial Mathematics Institute, Johannes Kepler University Linz, A-4040 Linz, Austria, Austria |
2. | Industrial Mathematics Institute, Johannes Kepler University Linz A-4040 Linz |
3. | MathConsult GmbH, Altenbergerstrae 69, A-4040 Linz, Austria |
References:
[1] |
J. M. Beckers, Increasing the size of the isoplanatic patch with multi-conjugate adaptive optics, in "Proc. European Southern Observatory Conf. and Workshop on Very Large Telescopes and Their Instrumentation'' (ed. M. H. Ulrich), Vol. 30, (1988), 693-703. |
[2] |
M. A. Davison, The ill-conditioned nature of the limited angle tomography problem, SIAM J. Appl. Math., 43 (1983), 428-448.
doi: 10.1137/0143028. |
[3] |
B. L. Ellerbroek, Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques, J. Opt. Soc. Am., 19 (2002), 1803-1816.
doi: 10.1364/JOSAA.19.001803. |
[4] |
B. L. Ellerbroek and C. R. Vogel, Simulations of closed-loop wavefront reconstruction for multiconjugate adaptive optics on giant telescopes, in "Proc. SPIE vol 5169-23," Adaptive Optics System Technologies II, (2003), 206-217.
doi: 10.1117/12.506580. |
[5] |
B. L. Ellerbroek and C. R. Vogel, Inverse problems in astronomical adaptive optics, Inverse Problems, 25 (2009), 063001, 37 pp. |
[6] |
H. Engl, M. Hanke and A. Neubauer, "Regularization of Inverse Problems,'' Mathematics and its Applications, 375, Kluwer Academic Publishers Group, Dordrecht, 1996. |
[7] |
D. L. Fried, Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements, J. Opt. Soc. Am., 67 (1977), 370-375.
doi: 10.1364/JOSA.67.000370. |
[8] |
L. Gilles, Order $N$ sparse minimum-variance open-loop reconstructor for extreme adaptive optics, Opt. Lett., 28 (2003), 1927-1929.
doi: 10.1364/OL.28.001927. |
[9] |
L. Gilles, Closed-loop stability and performance analysis of least-squares and minimum-variance control algorithms for multi-conjugate adaptive optics, Appl. Opt., 44 (2004), 993-1002.
doi: 10.1364/AO.44.000993. |
[10] |
L. Gilles, C. R. Vogel and B. L. Ellebroek, Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction, J. Opt. Soc. Am. A, 19 (2002), 1817-1822.
doi: 10.1364/JOSAA.19.001817. |
[11] |
J. Herrmann, Least-squares wave front errors of minimum norm, J. Opt. Soc. Am., 70 (1980), 28-35.
doi: 10.1364/JOSA.70.000028. |
[12] |
A. Neubauer, On the ill-posedness and convergence of the Shack-Hartmann based wavefront reconstruction, J. Inv. Ill-Posed Problems, 18 (2010), 551-576.
doi: 10.1515/JIIP.2010.025. |
[13] |
L. A. Poyneer, D. T. Gavel and J. M. Brase, Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform, J. Opt. Soc. Am. A, 19 (2002), 2100-2111.
doi: 10.1364/JOSAA.19.002100. |
[14] |
L. A. Poyneer and J.-P. Véran, Optimal modal Fourier transform wave-front control, J. Opt. Soc. Am. A, 22 (2005), 1515-1526.
doi: 10.1364/JOSAA.22.001515. |
[15] |
F. Roddier, "Adaptive Optics in Astronomy,'' Cambridge University Press, Cambridge, New York, 1999.
doi: 10.1017/CBO9780511525179. |
[16] |
M. C. Roggemann and B. M. Welsh, "Imaging Through Turbulence,'' CRC Press, Boca Raton, Florida, 1996. |
[17] |
E. Thiébaut and M. Tallon, Fast minimum variance wavefront reconstruction for extremely large telescopes, J. Opt. Soc. Am. A, 27 (2010), 1046-1059.
doi: 10.1364/JOSAA.27.001046. |
[18] |
C. R. Vogel and Q. Yang, Multigrid algorithm for least-squares wavefront reconstruction, Applied Optics, 45 (2006), 705-715.
doi: 10.1364/AO.45.000705. |
[19] |
Q. Yang, C. R. Vogel and B. L. Ellerbroek, Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography, Applied Optics, 45 (2006), 5281-5293.
doi: 10.1364/AO.45.005281. |
show all references
References:
[1] |
J. M. Beckers, Increasing the size of the isoplanatic patch with multi-conjugate adaptive optics, in "Proc. European Southern Observatory Conf. and Workshop on Very Large Telescopes and Their Instrumentation'' (ed. M. H. Ulrich), Vol. 30, (1988), 693-703. |
[2] |
M. A. Davison, The ill-conditioned nature of the limited angle tomography problem, SIAM J. Appl. Math., 43 (1983), 428-448.
doi: 10.1137/0143028. |
[3] |
B. L. Ellerbroek, Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques, J. Opt. Soc. Am., 19 (2002), 1803-1816.
doi: 10.1364/JOSAA.19.001803. |
[4] |
B. L. Ellerbroek and C. R. Vogel, Simulations of closed-loop wavefront reconstruction for multiconjugate adaptive optics on giant telescopes, in "Proc. SPIE vol 5169-23," Adaptive Optics System Technologies II, (2003), 206-217.
doi: 10.1117/12.506580. |
[5] |
B. L. Ellerbroek and C. R. Vogel, Inverse problems in astronomical adaptive optics, Inverse Problems, 25 (2009), 063001, 37 pp. |
[6] |
H. Engl, M. Hanke and A. Neubauer, "Regularization of Inverse Problems,'' Mathematics and its Applications, 375, Kluwer Academic Publishers Group, Dordrecht, 1996. |
[7] |
D. L. Fried, Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements, J. Opt. Soc. Am., 67 (1977), 370-375.
doi: 10.1364/JOSA.67.000370. |
[8] |
L. Gilles, Order $N$ sparse minimum-variance open-loop reconstructor for extreme adaptive optics, Opt. Lett., 28 (2003), 1927-1929.
doi: 10.1364/OL.28.001927. |
[9] |
L. Gilles, Closed-loop stability and performance analysis of least-squares and minimum-variance control algorithms for multi-conjugate adaptive optics, Appl. Opt., 44 (2004), 993-1002.
doi: 10.1364/AO.44.000993. |
[10] |
L. Gilles, C. R. Vogel and B. L. Ellebroek, Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction, J. Opt. Soc. Am. A, 19 (2002), 1817-1822.
doi: 10.1364/JOSAA.19.001817. |
[11] |
J. Herrmann, Least-squares wave front errors of minimum norm, J. Opt. Soc. Am., 70 (1980), 28-35.
doi: 10.1364/JOSA.70.000028. |
[12] |
A. Neubauer, On the ill-posedness and convergence of the Shack-Hartmann based wavefront reconstruction, J. Inv. Ill-Posed Problems, 18 (2010), 551-576.
doi: 10.1515/JIIP.2010.025. |
[13] |
L. A. Poyneer, D. T. Gavel and J. M. Brase, Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform, J. Opt. Soc. Am. A, 19 (2002), 2100-2111.
doi: 10.1364/JOSAA.19.002100. |
[14] |
L. A. Poyneer and J.-P. Véran, Optimal modal Fourier transform wave-front control, J. Opt. Soc. Am. A, 22 (2005), 1515-1526.
doi: 10.1364/JOSAA.22.001515. |
[15] |
F. Roddier, "Adaptive Optics in Astronomy,'' Cambridge University Press, Cambridge, New York, 1999.
doi: 10.1017/CBO9780511525179. |
[16] |
M. C. Roggemann and B. M. Welsh, "Imaging Through Turbulence,'' CRC Press, Boca Raton, Florida, 1996. |
[17] |
E. Thiébaut and M. Tallon, Fast minimum variance wavefront reconstruction for extremely large telescopes, J. Opt. Soc. Am. A, 27 (2010), 1046-1059.
doi: 10.1364/JOSAA.27.001046. |
[18] |
C. R. Vogel and Q. Yang, Multigrid algorithm for least-squares wavefront reconstruction, Applied Optics, 45 (2006), 705-715.
doi: 10.1364/AO.45.000705. |
[19] |
Q. Yang, C. R. Vogel and B. L. Ellerbroek, Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography, Applied Optics, 45 (2006), 5281-5293.
doi: 10.1364/AO.45.005281. |
[1] |
Michael Herty, Giuseppe Visconti. Kinetic methods for inverse problems. Kinetic and Related Models, 2019, 12 (5) : 1109-1130. doi: 10.3934/krm.2019042 |
[2] |
Guanghui Hu, Peijun Li, Xiaodong Liu, Yue Zhao. Inverse source problems in electrodynamics. Inverse Problems and Imaging, 2018, 12 (6) : 1411-1428. doi: 10.3934/ipi.2018059 |
[3] |
Colin Guillarmou, Antônio Sá Barreto. Inverse problems for Einstein manifolds. Inverse Problems and Imaging, 2009, 3 (1) : 1-15. doi: 10.3934/ipi.2009.3.1 |
[4] |
Sergei Avdonin, Pavel Kurasov. Inverse problems for quantum trees. Inverse Problems and Imaging, 2008, 2 (1) : 1-21. doi: 10.3934/ipi.2008.2.1 |
[5] |
Maciej Zworski. A remark on inverse problems for resonances. Inverse Problems and Imaging, 2007, 1 (1) : 225-227. doi: 10.3934/ipi.2007.1.225 |
[6] |
Zhi-An Wang. Wavefront of an angiogenesis model. Discrete and Continuous Dynamical Systems - B, 2012, 17 (8) : 2849-2860. doi: 10.3934/dcdsb.2012.17.2849 |
[7] |
Janne M.J. Huttunen, J. P. Kaipio. Approximation errors in nonstationary inverse problems. Inverse Problems and Imaging, 2007, 1 (1) : 77-93. doi: 10.3934/ipi.2007.1.77 |
[8] |
Gunther Uhlmann, Jian Zhai. Inverse problems for nonlinear hyperbolic equations. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 455-469. doi: 10.3934/dcds.2020380 |
[9] |
Masoumeh Dashti, Stephen Harris, Andrew Stuart. Besov priors for Bayesian inverse problems. Inverse Problems and Imaging, 2012, 6 (2) : 183-200. doi: 10.3934/ipi.2012.6.183 |
[10] |
Xiaosheng Li, Gunther Uhlmann. Inverse problems with partial data in a slab. Inverse Problems and Imaging, 2010, 4 (3) : 449-462. doi: 10.3934/ipi.2010.4.449 |
[11] |
Sergei A. Avdonin, Sergei A. Ivanov, Jun-Min Wang. Inverse problems for the heat equation with memory. Inverse Problems and Imaging, 2019, 13 (1) : 31-38. doi: 10.3934/ipi.2019002 |
[12] |
Tony Liimatainen, Lauri Oksanen. Counterexamples to inverse problems for the wave equation. Inverse Problems and Imaging, 2022, 16 (2) : 467-479. doi: 10.3934/ipi.2021058 |
[13] |
Manuel Gutiérrez. Lorentz geometry technique in nonimaging optics. Conference Publications, 2003, 2003 (Special) : 386-392. doi: 10.3934/proc.2003.2003.386 |
[14] |
Gang Bao. Mathematical modeling of nonlinear diffracvtive optics. Conference Publications, 1998, 1998 (Special) : 89-99. doi: 10.3934/proc.1998.1998.89 |
[15] |
Zheng-Ru Zhang, Tao Tang. An adaptive mesh redistribution algorithm for convection-dominated problems. Communications on Pure and Applied Analysis, 2002, 1 (3) : 341-357. doi: 10.3934/cpaa.2002.1.341 |
[16] |
Luís Tiago Paiva, Fernando A. C. C. Fontes. Adaptive time--mesh refinement in optimal control problems with state constraints. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 4553-4572. doi: 10.3934/dcds.2015.35.4553 |
[17] |
François Monard, Guillaume Bal. Inverse diffusion problems with redundant internal information. Inverse Problems and Imaging, 2012, 6 (2) : 289-313. doi: 10.3934/ipi.2012.6.289 |
[18] |
Johannes Elschner, Guanghui Hu. Uniqueness in inverse transmission scattering problems for multilayered obstacles. Inverse Problems and Imaging, 2011, 5 (4) : 793-813. doi: 10.3934/ipi.2011.5.793 |
[19] |
Gabriel Peyré, Sébastien Bougleux, Laurent Cohen. Non-local regularization of inverse problems. Inverse Problems and Imaging, 2011, 5 (2) : 511-530. doi: 10.3934/ipi.2011.5.511 |
[20] |
Simopekka Vänskä. Stationary waves method for inverse scattering problems. Inverse Problems and Imaging, 2008, 2 (4) : 577-586. doi: 10.3934/ipi.2008.2.577 |
2020 Impact Factor: 1.639
Tools
Metrics
Other articles
by authors
[Back to Top]