Abstract

The noise characteristics of a compact high-resolution Shack–Hartmann wavefront sensor with an extended pupil to sensor distance have been measured. The standard deviation, σ, of the angular position error caused by random noise conforms to theoretical predictions of discrete detector arrays described by σtot=λ/D(ω/SNR+η/Vs), where ω is the position error constant, SNR is the signal-to-noise ratio, η is the geometric aperture constant, and Vs is the sum of the signal’s total counts. The agreement both confirms the theoretical derivation of this useful formula and shows that measurement of ocular aberrations under laboratory conditions at working distances greater than 30cm introduces negligible additional error.

© 2010 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]

2008 (2)

K. M. Hampson, “Adaptive optics and vision,” J. Mod. Opt. 55, 3425–3467 (2008).
[CrossRef]

C. Li, H. Xian, C. Rao, and W. Jiang “Measuring statistical error of Shack–Hartmann wavefront sensor with discrete detector arrays,” J. Mod. Opt. 55, 2243–2255 (2008).
[CrossRef]

2000 (1)

1999 (1)

1997 (1)

1994 (2)

1992 (1)

1982 (1)

Artal, P.

Bille, J.

Cao, G.

G. Cao and X. Yu “Accuracy analysis of Hartmann–Shack wavefront sensor operated with a faint object,” Opt. Eng. 33, 2331–2335 (1994).
[CrossRef]

Dayton, D.

Fried, D. L.

Goelz, S.

Gonglewski, J.

Grimm, B.

Hampson, K. M.

K. M. Hampson, “Adaptive optics and vision,” J. Mod. Opt. 55, 3425–3467 (2008).
[CrossRef]

Jiang, W.

C. Li, H. Xian, C. Rao, and W. Jiang “Measuring statistical error of Shack–Hartmann wavefront sensor with discrete detector arrays,” J. Mod. Opt. 55, 2243–2255 (2008).
[CrossRef]

C. Rao, W. Jiang, and N. Ling, “Measuring the power-law exponent of an atmospheric turbulence phase power spectrum with a Shack–Hartmann wave-front sensor,” Opt. Lett. 24, 1008–1010 (1999).
[CrossRef]

Li, C.

C. Li, H. Xian, C. Rao, and W. Jiang “Measuring statistical error of Shack–Hartmann wavefront sensor with discrete detector arrays,” J. Mod. Opt. 55, 2243–2255 (2008).
[CrossRef]

Liang, J.

Ling, N.

Pierson, B.

Prieto, P. M.

Rao, C.

C. Li, H. Xian, C. Rao, and W. Jiang “Measuring statistical error of Shack–Hartmann wavefront sensor with discrete detector arrays,” J. Mod. Opt. 55, 2243–2255 (2008).
[CrossRef]

C. Rao, W. Jiang, and N. Ling, “Measuring the power-law exponent of an atmospheric turbulence phase power spectrum with a Shack–Hartmann wave-front sensor,” Opt. Lett. 24, 1008–1010 (1999).
[CrossRef]

Spielbusch, B.

Tyler, G. A.

Vargas-Martin, F.

Williams, D. R.

Xian, H.

C. Li, H. Xian, C. Rao, and W. Jiang “Measuring statistical error of Shack–Hartmann wavefront sensor with discrete detector arrays,” J. Mod. Opt. 55, 2243–2255 (2008).
[CrossRef]

Yu, X.

G. Cao and X. Yu “Accuracy analysis of Hartmann–Shack wavefront sensor operated with a faint object,” Opt. Eng. 33, 2331–2335 (1994).
[CrossRef]

J. Mod. Opt. (2)

K. M. Hampson, “Adaptive optics and vision,” J. Mod. Opt. 55, 3425–3467 (2008).
[CrossRef]

C. Li, H. Xian, C. Rao, and W. Jiang “Measuring statistical error of Shack–Hartmann wavefront sensor with discrete detector arrays,” J. Mod. Opt. 55, 2243–2255 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Eng. (1)

G. Cao and X. Yu “Accuracy analysis of Hartmann–Shack wavefront sensor operated with a faint object,” Opt. Eng. 33, 2331–2335 (1994).
[CrossRef]

Opt. Lett. (2)

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Figures (2)

Fig. 1
Fig. 1

Experimental setup for measurement of angular position error caused by random noise using a compact high-resolution wavefront sensor at the 35 cm range.

Fig. 2
Fig. 2

(a) Example image with high SNR ( 31 average of all subapertures) acquired by the compact high-resolution wavefront sensor. (b) Example image with low signal to noise ratio ( SNR 6 ). (c) Surface plot of a single subaperture from (a). (d) Surface plot of a single subaperture from (b). (e) Measured results showing the average of the RMS error in the x and y directions as a function of SNR for a lenslet detector scale of 27 × 27 pixels. The two components of Eq. (6) are plotted individually (dashed curves) and then summed (solid curve).

Equations (8)

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σ = 3 π 16 · λ D · 1 SNR ,
( x i , y i ) = ( x n m I n m I n m , y n m I n m I n m ) ,
I ( ϑ ) = I 0 ( sin ( π L 1 sin θ 1 / λ ) π L 1 sin θ 1 / λ ) 2 ( sin ( π L 2 sin θ 2 / λ ) π L 2 sin θ 2 / λ ) 2 ,
I = I 0 ( r 2 2 σ 2 ) = I 0 ( ( f tan θ 1 ) 2 2 ( λ f / D n ) 2 ) ,
ϕ c s 2 = G s 2 V s ,
ϕ c r 2 = L 1 L 2 N r 2 ( L 1 2 1 ) 12 V r 2 ,
σ tot = λ D ( ω SNR + η V s ( 1 / 2 ) ) ,
ω = ( ( L 2 1 ) 12 L 2 ) 1 / 2 l / f λ / D · L 2 N b ( L 2 N b + V s 1 / 2 )

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