Abstract

We define a signal-to-noise ratio (SNR) for eye aberrometry in terms of the sensor geometry, measurement noise, and population statistics. The overall estimation error is composed of three main contributions: the bias in the estimated modes, the truncation error, and the error due to the noise propagation. This last term can be easily parametrized by the proposed SNR. We compute the overall error as well as the magnitude of its three components for a typical sensor configuration, population statistics, and different SNR. We show that there are an optimum number of Zernike aberration modes to be retrieved in each case.

© 2012 Optical Society of America

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References

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2006 (1)

2005 (1)

2002 (2)

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, J. Opt. Soc. Am. A 19, 2329 (2002).
[CrossRef]

L. N. Thibos, A. Bradley, and X. Hong, Ophthal. Physiol. Opt. 22, 427 (2002).
[CrossRef]

2001 (1)

1999 (1)

1996 (1)

1981 (1)

1976 (1)

Ares, J.

Arines, J.

Bará, S.

Bará, S. X.

Bradley, A.

L. N. Thibos, A. Bradley, and X. Hong, Ophthal. Physiol. Opt. 22, 427 (2002).
[CrossRef]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, J. Opt. Soc. Am. A 19, 2329 (2002).
[CrossRef]

Cheng, X.

Conan, J.-M.

Cox, I. G.

Dai, G.

Díaz-Santana, L.

Fusco, T.

Guirao, A.

Herrmann, J.

Hong, X.

L. N. Thibos, A. Bradley, and X. Hong, Ophthal. Physiol. Opt. 22, 427 (2002).
[CrossRef]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, J. Opt. Soc. Am. A 19, 2329 (2002).
[CrossRef]

Michau, V.

Mugnier, L. M.

Noll, R. J.

Porter, J.

Prado, P.

Rousset, G.

Thibos, L. N.

L. N. Thibos, A. Bradley, and X. Hong, Ophthal. Physiol. Opt. 22, 427 (2002).
[CrossRef]

L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, J. Opt. Soc. Am. A 19, 2329 (2002).
[CrossRef]

Walker, G.

Williams, D. R.

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Figures (3)

Fig. 1.
Fig. 1.

Wavefront sampling array. Only the 145 unvignetted microlenses shown with a blue dot in their center are used in the calculations.

Fig. 2.
Fig. 2.

Global reconstruction error σerr2 for SNR=10 (bold line with circles) and its three contributing terms: truncation error due to the non-estimated modes (dash-dotted w/squares), noise propagation (dashed w/asterisks), and bias in the retrieved modes (dotted w/triangles).

Fig. 3.
Fig. 3.

Relative reconstruction error sqrt (σerr2/trace(Ca)) for different number of estimated radial orders and SNR= (circles), 10 (squares), and 1 (triangles).

Equations (5)

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σerr2=trace[(IRA)Ca(IRA)T]+i=M+1Mai2+σν2trace[RRT],
Σμ2=12N1Ks=12Nk=1Kμs2(k)=12Ns=12Nμs2=12Ntrace[μμT].
SNR=1σν212Ntrace[ACaAT],
σerr2=trace[(IRA)Ca(IRA)T]+i=M+1Mai2+1SNR12Ntrace[ACaAT]trace[RRT].
Ca^=(RA)Ca(RA)T+σν2RRT.

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