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In Zernike modal wavefront reconstruction algorithm, because of a certain number of the low Zernike modes is selected subjective for making up the reconstruction model, the modes confusion and modes coupling will produced, the accuracy reduction of wavefront reconstruction is deduced. According to the minimal description length principal, a principle can balance the model error against model size so as to prevent the model from overfitting. The reconstruction model is selected by top-down method, and Levenberg-Marquardt nonlinear optimization algorithm is applied to the solution of reconstruction coefficients, then the wavefronts reconstruction is realized. Under different noise conditions, the reconstruction algorithm is validated with the numerical simulation of the wavefront reconstruction of uniform amplitude incidence beam, the results indicate: Zernike modal wavefront reconstruction algorithm based on the model selection can improve the wavefront reconstruction accuracy, and algorithm possesses the property of resistance to noise.
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Keywords:
- wavefront reconstruction /
- model selection /
- minimum description length /
- nonlinear optimization
[1] Yang G Z, Gu B Y (in Chinese) [杨国桢, 顾本源 1981 物理学报 30 411]
[2] Zhao C, Burge H
[3] Li X Y, Jiang W H 2002 Acta Opt. Sin. 10 1236 (in Chinese) [李新阳, 姜文汉 2002 光学学报 10 1236]
[4] Roberts J, Dekany R, Burruss R
[5] Upton R, Ellerbroek B 2004 Opt. Lett. 24 2840
[6] Rissanen J 1986 Ann. Statis. 14 1080
[7] Rissanen J
[8] Judd K, Mees A 1995 Physica D 82 426
[9] Judd K, Mees A 1998 Physica D 120 273
[10] Noll R J 1976 J. Opt. Soc. Am. 66 207
[11] Nakamura T, Judd, Mees A 2003 Int. J. Bifurcat. Chaos 13 1263
[12] Nakamura T, Kilminster D, Judd K, Mees A 2004 Int. J. Bifurcat. Chaos 14 1129
[13] Nocedal J, Wright S J 2000 Numerical Optimization (2nd Ed.) (New York: Springer) pp367-370
[14] Gao Q, Liao T H, Cui Y F 2008 Opt. Lett. 33 1899
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[1] Yang G Z, Gu B Y (in Chinese) [杨国桢, 顾本源 1981 物理学报 30 411]
[2] Zhao C, Burge H
[3] Li X Y, Jiang W H 2002 Acta Opt. Sin. 10 1236 (in Chinese) [李新阳, 姜文汉 2002 光学学报 10 1236]
[4] Roberts J, Dekany R, Burruss R
[5] Upton R, Ellerbroek B 2004 Opt. Lett. 24 2840
[6] Rissanen J 1986 Ann. Statis. 14 1080
[7] Rissanen J
[8] Judd K, Mees A 1995 Physica D 82 426
[9] Judd K, Mees A 1998 Physica D 120 273
[10] Noll R J 1976 J. Opt. Soc. Am. 66 207
[11] Nakamura T, Judd, Mees A 2003 Int. J. Bifurcat. Chaos 13 1263
[12] Nakamura T, Kilminster D, Judd K, Mees A 2004 Int. J. Bifurcat. Chaos 14 1129
[13] Nocedal J, Wright S J 2000 Numerical Optimization (2nd Ed.) (New York: Springer) pp367-370
[14] Gao Q, Liao T H, Cui Y F 2008 Opt. Lett. 33 1899
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