Abstract

We present a Shack–Hartmann (SH) centroid detection algorithm capable to measure in presence of strong noise, background illumination and spot modulating signals, which are typical limiting factors of traditional centroid detection algorithms. The proposed method is based on performing a normalization of the SH pattern using the spiral phase transform method and Fourier filtering. The spot centroids are then obtained using global thresholding and weighted average methods. We have tested the algorithm with simulations and experimental data obtaining satisfactory results. A complete MATLAB package that can reproduce all the results can be downloaded from [http://goo.gl/o2JhD].

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  10. http://goo.gl/o2JhD .

2010

2007

2005

J. Villa, I. De la Rosa, G. Miramontes, and J. A. Quiroga, “Phase recovery from a single fringe pattern using an orientational vector-field-regularized estimator,” J. Opt. Soc. Am. A 22, 2766–2773 (2005).
[CrossRef]

L. A. Poyneer, D. W. Palmer, K. N. LaFortune, and B. Bauman, “Experimental results for correlation-based wavefront sensing,” Proc. SPIE 5894, 58940N (2005).
[CrossRef]

2004

2002

D. N. Neal, J. Copland, and D. Neal, “Shack–Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
[CrossRef]

2001

1996

1992

Baker, K. L.

Bauman, B.

L. A. Poyneer, D. W. Palmer, K. N. LaFortune, and B. Bauman, “Experimental results for correlation-based wavefront sensing,” Proc. SPIE 5894, 58940N (2005).
[CrossRef]

Bone, D. J.

Copland, J.

D. N. Neal, J. Copland, and D. Neal, “Shack–Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
[CrossRef]

Dainty, C.

De la Rosa, I.

Fusco, T.

LaFortune, K. N.

L. A. Poyneer, D. W. Palmer, K. N. LaFortune, and B. Bauman, “Experimental results for correlation-based wavefront sensing,” Proc. SPIE 5894, 58940N (2005).
[CrossRef]

Lane, R. G.

Larkin, K. G.

Leroux, C.

Michau, V.

Miramontes, G.

Moallem, M. M.

Neal, D.

D. N. Neal, J. Copland, and D. Neal, “Shack–Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
[CrossRef]

Neal, D. N.

D. N. Neal, J. Copland, and D. Neal, “Shack–Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
[CrossRef]

Nicolle, M.

Oldfield, M. A.

Palmer, D. W.

L. A. Poyneer, D. W. Palmer, K. N. LaFortune, and B. Bauman, “Experimental results for correlation-based wavefront sensing,” Proc. SPIE 5894, 58940N (2005).
[CrossRef]

Poyneer, L. A.

L. A. Poyneer, D. W. Palmer, K. N. LaFortune, and B. Bauman, “Experimental results for correlation-based wavefront sensing,” Proc. SPIE 5894, 58940N (2005).
[CrossRef]

Quiroga, J. A.

Rousset, G.

Strobel, B.

Tallon, M.

Villa, J.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Proc. SPIE

D. N. Neal, J. Copland, and D. Neal, “Shack–Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, 148–160 (2002).
[CrossRef]

L. A. Poyneer, D. W. Palmer, K. N. LaFortune, and B. Bauman, “Experimental results for correlation-based wavefront sensing,” Proc. SPIE 5894, 58940N (2005).
[CrossRef]

Other

http://goo.gl/o2JhD .

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Figures (5)

Fig. 1.
Fig. 1.

(a) Simulated Hartmann pattern affected by noise, background and modulation signals, (b) recovered normalized SH pattern and the obtained centroids, and (c) computed modulation map B˜.

Fig. 2.
Fig. 2.

(a) Simulated wavefront error (ΔW), (b) its derivatives in the x axis, and (c) y axis, respectively.

Fig. 3.
Fig. 3.

Difference between the ground truth and obtained centroids in the x and y axis when it is used with the proposed (a) SPT, (b) WCOG, and (c) ICOG approaches.

Fig. 4.
Fig. 4.

(a) Root-mean-square error versus noise level, (b) spot size, and (c) wavefront error dynamic ranges for the different methods.

Fig. 5.
Fig. 5.

(a) Real Hartmann pattern, (b) recovered normalized pattern and obtained centroids, and (c) B˜ map.

Equations (16)

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[ΔW]ij=[(ΔWxΔWy)]ij=[1f(ΔxΔy)]ij,
I(x,y)=A(x,y)+B(x,y)cos[Φ(x,y)]+η(x,y),
I˜=Bcos[Φ]=FT1[H·FT[I]],
H=exp[(RR0)2/2σ2],
SPT[I˜]=iexp(iD)Bsin(Φ),
SPT[·]=FT1[(Rx+iRyRx2+Ry2)FT[·]].
D=arctan(yΦ/xΦ).
θ=arctan(yI˜/xI˜).
D=θ+α,α={0π,
exp(iD)=±exp(iθ).
Q[I˜]=Bsin(Φ)=iexp(iD)SPT[I˜],
Q^[I˜]=iexp(iθ)SPT[I˜].
Φ(x,y)=±arctan[Q^[I˜(x,y)]I˜(x,y)].
In=cos[Φ(x,y)]=cos[arctan[Q^[I˜]I˜]].
B˜=Q^[I˜]2+I˜2.
xc=x,yxInB˜/x,yInB˜yc=x,yyInB˜/x,yInB˜.

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