Abstract

In this work, a new approach, a method using artificial neural networks was applied to reconstruct the wavefront. First, the optimal structure of neural networks was found. Then, the networks were trained on both noise-free and noisy spot patterns. The results of the wavefront reconstruction with artificial neural networks were compared to those obtained through the least square fit and singular value decomposition method.

© 2006 Optical Society of America

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References

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2003

2002

L. N. Thibos, A. Bradley, and X. Hong, "A statistical model of the aberration structure of normal, well-corrected eyes," Ophthalmic Physiol. Opt. 22, 427-433 (2002).
[CrossRef] [PubMed]

Y. Yasuno, T. Yatagai, T. F. Wiesendanger, A. K. Ruprecht, and H. J. Tiziani, "Aberration measurement from confocal axial intensity response using neural network," Opt. Express 10, 1451-1457 (2002).
[PubMed]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, "Statistical variation of aberration structure and image quality in a normal population of healthy eyes," J. Opt. Soc. Am. A 19, 2329-2348 (2002).
[CrossRef]

J. F. Castej´on-Moch´on, N. L´opez-Gil, A. Benito, P. Artal, "Ocular wave-front statistics in a normal young population," Vis. Res. 42, 1611-1617 (2002).Q1
[CrossRef] [PubMed]

2001

1999

S. Walczak, N. Cerpa, "Heuristic principles for the design of artificial neural networks," Information and Software Technology 41, 107-117 (1999).
[CrossRef]

1997

1994

1993

1980

1979

1977

Artal, P.

J. F. Castej´on-Moch´on, N. L´opez-Gil, A. Benito, P. Artal, "Ocular wave-front statistics in a normal young population," Vis. Res. 42, 1611-1617 (2002).Q1
[CrossRef] [PubMed]

Barrett, T. K.

Benito, A.

J. F. Castej´on-Moch´on, N. L´opez-Gil, A. Benito, P. Artal, "Ocular wave-front statistics in a normal young population," Vis. Res. 42, 1611-1617 (2002).Q1
[CrossRef] [PubMed]

Bille, J.

Bradley, A.

L. N. Thibos, A. Bradley, and X. Hong, "A statistical model of the aberration structure of normal, well-corrected eyes," Ophthalmic Physiol. Opt. 22, 427-433 (2002).
[CrossRef] [PubMed]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, "Statistical variation of aberration structure and image quality in a normal population of healthy eyes," J. Opt. Soc. Am. A 19, 2329-2348 (2002).
[CrossRef]

Castej´on-Moch´on, J. F.

J. F. Castej´on-Moch´on, N. L´opez-Gil, A. Benito, P. Artal, "Ocular wave-front statistics in a normal young population," Vis. Res. 42, 1611-1617 (2002).Q1
[CrossRef] [PubMed]

Cerpa, N.

S. Walczak, N. Cerpa, "Heuristic principles for the design of artificial neural networks," Information and Software Technology 41, 107-117 (1999).
[CrossRef]

Cheng, X.

Cubalchini, R.

Fried, D.

Goelz, S.

Gox, I. G.

Grimm, B.

Guirao, A.

Hong, X.

L. N. Thibos, A. Bradley, and X. Hong, "A statistical model of the aberration structure of normal, well-corrected eyes," Ophthalmic Physiol. Opt. 22, 427-433 (2002).
[CrossRef] [PubMed]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, "Statistical variation of aberration structure and image quality in a normal population of healthy eyes," J. Opt. Soc. Am. A 19, 2329-2348 (2002).
[CrossRef]

L´opez-Gil, N.

J. F. Castej´on-Moch´on, N. L´opez-Gil, A. Benito, P. Artal, "Ocular wave-front statistics in a normal young population," Vis. Res. 42, 1611-1617 (2002).Q1
[CrossRef] [PubMed]

Liang, J.

Montera, D. A.

Nirmaier, T.

Porter, J.

Pudasaini, G.

Roggemann, M. C.

Ruck, D. W.

Ruprecht, A. K.

Sandier, D. G.

Southwell, W. H.

Thibos, L. N.

L. N. Thibos, A. Bradley, and X. Hong, "A statistical model of the aberration structure of normal, well-corrected eyes," Ophthalmic Physiol. Opt. 22, 427-433 (2002).
[CrossRef] [PubMed]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, "Statistical variation of aberration structure and image quality in a normal population of healthy eyes," J. Opt. Soc. Am. A 19, 2329-2348 (2002).
[CrossRef]

Tiziani, H. J.

Walczak, S.

S. Walczak, N. Cerpa, "Heuristic principles for the design of artificial neural networks," Information and Software Technology 41, 107-117 (1999).
[CrossRef]

Welsh, B. M.

Wiesendanger, T. F.

Williams, D. R.

Yasuno, Y.

Yatagai, T.

Appl. Opt.

Information and Software Technology

S. Walczak, N. Cerpa, "Heuristic principles for the design of artificial neural networks," Information and Software Technology 41, 107-117 (1999).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Ophthalmic Physiol. Opt.

L. N. Thibos, A. Bradley, and X. Hong, "A statistical model of the aberration structure of normal, well-corrected eyes," Ophthalmic Physiol. Opt. 22, 427-433 (2002).
[CrossRef] [PubMed]

Opt. Express

Vis. Res.

J. F. Castej´on-Moch´on, N. L´opez-Gil, A. Benito, P. Artal, "Ocular wave-front statistics in a normal young population," Vis. Res. 42, 1611-1617 (2002).Q1
[CrossRef] [PubMed]

Other

J. W. Clark, T. Lindenau, M. L. Ristig, Scientific Applications of Neural Nets (Springer, 1998).

C. Bishop, Neural Networks for Pattern Recognition (Clarendon Press, Oxford, 1995).

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Figures (7)

Fig. 1.
Fig. 1.

A simple neuron model.

Fig. 2.
Fig. 2.

The principle of training.

Fig. 3.
Fig. 3.

One example of the validation after training on the noise-free patterns. The generated noise-free and reconstructed wavefronts are shown.

Fig. 4.
Fig. 4.

The average RMS errors demonstrating the effect of different network architecture on the performance of the wavefront reconstruction.

Fig. 5.
Fig. 5.

Two results of the validation after the training on the noisy patterns. The noisy patterns were presented to the network.

Fig. 6.
Fig. 6.

An example of the wavefront validation with three different reconstruction methods: LSF, SVD, and ANN. The neural network has 90 neurons in the hidden layer.

Fig. 7.
Fig. 7.

The comparison among the evaluation methods - LSF, SVD, and ANN. The x-axis corresponds to the dynamic magnitude of the noise, the y-axis shows the errors of each low-order Zernike coefficient. The numbering of Zernike coefficients: z1, z2 - tilt and tip, z3 and z5 - astigmatism, z4 - defocus.

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