Abstract
This paper develops a compensation algorithm based on Linear–Quadratic–Gaussian (LQG) control system design whose parameters are determined (in part) by a model of the atmosphere. The model for the atmosphere is based on the open-loop statistics of the atmosphere as observed by the wavefront sensor, and is identified from these using an auto-regressive, moving average (ARMA) model. The (LQG) control design is compared with an existing compensation algorithm for a simulation developed at ESO that represents the operation of MACAO adaptive optics system on the 8.2 m telescopes at Paranal, Chile.
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References
Anderson, B. D. O. and Moore, J. B.: 1990, Optimal Control: Linear Quadratic Methods, Prentice-Hall, Englewood Cliffs.
Craven-Bartle, T. V., Dorn, R. J. and Beletic, J. W.: 2000, P. L. Wizinowich (ed.), Proc. SPIE 4007, 444–451.
Dai, G.-M.: 1995, J. Opt. Soc. Am. A 12, 2182–2193.
Dessenne, C., Madec, P.-Y. and Rousset, G.: 1997, Opt. Lett. 22, 1535–1537.
Dessenne, C., Madec, P.-Y. and Rousset, G.: 1998, Appl. Opt. 37, 4623–4633.
Donaldson, R., Bonaccini, D., Brynnel, J., Buzzoni, B., Close, L. M., Delabre, B., Dupuy, C., Farinato, J., Fedrigo, E., Hubin, N. N., Marchetti, E., Stroebele, S. and Tordo, S.: 2000, P. L. Wizinowich (ed.), Proc. SPIE 4007, 82–89.
Duchene, G., Ghez, A. M. and McCabe, C.: 2002, Astrophys. J. 568, 771–778.
Ellerbroek, B. L.: 1994, J. Opt. Soc. Am. A 11, 783–805.
Franklin, G. F., Powell, J. D. and Emami-Naeini, A.: 1998, Feedback Control of Dynamic Systems, Addison-Wesley, Reading, USA.
Gendron, E. and Lèna, P.: 1994, Astron. Astrophy. 291, 337–347.
Gendron, E. and Lèna, P.: 1995, Astron. Astrophy. Suppl. Ser. 111, 153–167.
Hackenberg,W., Eckart, A., Davies, R. J., Rabien, S., Ott, T., Kasper, M., Hippler, S. and Quirrenbach, A.: 2000, Astron. Astrophy. 363, 41–61.
Kasper,M. E.: 2000, Optimization of an Adaptive Optics System and its Application to High-Resolution Imaging Spectroscopy of T Tauri.Ph.D. Thesis, University of Heidelberg, Germany.
Kokotović, P. K.: 1972, in J. B. Cruz, Jr (ed.), Feedback Systems, McGraw-Hill, New York, 99–137.
Kwakernaak, H. and Sivan, R.: 1972, Linear Optimal Control Systems,Wiley-Interscience, NewYork.
Law, N. F. and Lane, R. G.: 1996, Opt. Commun. 126, 19–24.
Ljung, L.: 1987, System Identification: Theory for the User, Prentice-Hall, Englewood Cliffs, USA.
MATLAB: 1996, MATLAB: Control System Toolbox, The Mathworks, Natick, USA.
Noll, R.-J.: 1976. J. Opt. Soc. Am. 66, 207–211.
Paschall, R. N. and Anderson, D. J.: 1993, Appl. Opt. 32, 6347–6358.
Phillips, R. G.: 1980, Int. J. Control 31, 765–780.
Roddier, C., Roddier, F., Northcott, J. E., Graves, J. E. and Jim, K.: 1996, Astrophy. J. 463, 326–335.
Roddier, F.: 1988, Appl. Opt. 27, 1223–1225.
Sannuti, P. and Kokotović, P. K.: 1969, IEEE Trans. Autom. Control AC-14, 15–21.
Tatarski, V.I.: 1961, R. A. Silverman (translation), Wave Propagation in a Turbulent Medium, Dover Publications, New York.
Tyson, R.K.: 1991, Principles of Adaptive Optics, Academic Press, San Diego.
Veran, J.-P., Rigaut, F., Maitre, H. and Rouan, D.: 1997, J. Opt. Soc. Am. A 14, 3057.
Wallner, E. P.: 1983, J. Opt. Soc. Am. A 73, 1771–1776.
Wild, W. J.: 1996, Opt. Lett. 21, 1433–1435.
Wirth, A., Navetta, J., Looze, D. P., Hippler, S., Glindemann, A. and Hamilton, D.: 1998, Appl. Opt. 37, 4586–4597.
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Looze, D.P., Kasper, M., Hippler, S. et al. Optimal Compensation and Implementation for Adaptive Optics Systems. Experimental Astronomy 15, 67–88 (2003). https://doi.org/10.1023/B:EXPA.0000036150.62118.64
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DOI: https://doi.org/10.1023/B:EXPA.0000036150.62118.64