Abstract

We present a robust, dense, and accurate Shack-Hartmann spot dislocation map determination method based on a regularized optical flow algorithm that does not require obtaining the spot centroids. The method is capable to measure in presence of strong noise, background illumination and spot modulating signals, which are typical limiting factors of traditional centroid detection algorithms. Moreover, the proposed approach is able to face cases where some of the reference beam spots have not a corresponding one in the distorted Hartmann diagram, and it can expand the dynamic range of the Shack-Hartmann sensor unwrapping the obtained dense dislocation maps. We have tested the algorithm with both simulations and experimental data obtaining satisfactory results. A complete MATLAB package that can reproduce all the results can be downloaded from [http://goo.gl/XbZVOr].

© 2014 Optical Society of America

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References

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2012 (4)

2011 (1)

2010 (2)

2007 (1)

2005 (1)

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

2004 (1)

2002 (1)

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

1998 (1)

1992 (1)

1988 (1)

R. T. Frankot, R. Chellappa, “A method for enforcing integrability in shape from shading,” IEEE PAMI 10(4), 439–451 (1988).
[CrossRef]

1981 (1)

B. K. P. Horn, B. G. Schunck, “Determining Optical Flow,” Artif. Intell. 17(1-3), 185–203 (1981).
[CrossRef]

Antonio Quiroga, J.

Baker, K. L.

Bauman, B.

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

Belenguer, T.

Carazo, J. M.

Chellappa, R.

R. T. Frankot, R. Chellappa, “A method for enforcing integrability in shape from shading,” IEEE PAMI 10(4), 439–451 (1988).
[CrossRef]

Copland, J.

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

Dainty, C.

Du, Y. Z.

Estrada, J. C.

Flores-Moreno, J. M.

Frankot, R. T.

R. T. Frankot, R. Chellappa, “A method for enforcing integrability in shape from shading,” IEEE PAMI 10(4), 439–451 (1988).
[CrossRef]

Fusco, T.

González-Fernandez, L.

Horn, B. K. P.

B. K. P. Horn, B. G. Schunck, “Determining Optical Flow,” Artif. Intell. 17(1-3), 185–203 (1981).
[CrossRef]

Kanade, T.

B. D. Lucas, T. Kanade, “An iterative image registration technique with an application to stereo vision,” Proc. of Imaging Understanding Workshop 121–130 (1981).

LaFortune, K. N.

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

Lane, R. G.

Leroux, C.

Lindlein, N.

Lucas, B. D.

B. D. Lucas, T. Kanade, “An iterative image registration technique with an application to stereo vision,” Proc. of Imaging Understanding Workshop 121–130 (1981).

Michau, V.

Moallem, M. M.

Navarro, M. A.

Neal, D.

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

Neal, D. N.

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

Nicolle, M.

Palmer, D. W.

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

Pfund, J.

Poyneer, L. A.

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

Quiroga, J. A.

Restrepo, R.

Rousset, G.

Schunck, B. G.

B. K. P. Horn, B. G. Schunck, “Determining Optical Flow,” Artif. Intell. 17(1-3), 185–203 (1981).
[CrossRef]

Schwider, J.

Servin, M.

Servín, M.

Sorzano, C. O. S.

Tallon, M.

Vargas, J.

Appl. Opt. (5)

Artif. Intell. (1)

B. K. P. Horn, B. G. Schunck, “Determining Optical Flow,” Artif. Intell. 17(1-3), 185–203 (1981).
[CrossRef]

IEEE PAMI (1)

R. T. Frankot, R. Chellappa, “A method for enforcing integrability in shape from shading,” IEEE PAMI 10(4), 439–451 (1988).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Proc. SPIE (2)

D. N. Neal, J. Copland, 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, B. Bauman, “Experimental results for correlation-based wavefront sensing,” Proc. SPIE 5894, 58940N (2005).
[CrossRef]

Other (3)

J. Y. Bouguet, “Pyramidal Implementation of the LK Feature Tracker,” Tech. Rep., Intel Corporation, Microprocessor Research Labs (1999).

B. D. Lucas, T. Kanade, “An iterative image registration technique with an application to stereo vision,” Proc. of Imaging Understanding Workshop 121–130 (1981).

J. Marzat, Y. Dumortier, and A. Ducrot, “Real-time dense and accurate parallel optical flow using CUDA,” WSCG2009 105–111. (2009).

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Figures (11)

Fig. 1
Fig. 1

Simulated reference (a) and distorted (b) Hartmann pattern affected by noise, background and modulation signals.

Fig. 2
Fig. 2

Theoretical dislocation maps Δx (a) and Δy (d) and displacements obtained by the optical flow approach (b) and (e) without Zernike fitting. In (c) and (d) we show the dislocation maps after performing a Zernike fitting.

Fig. 3
Fig. 3

Simulated reference (a) and distorted (b) Hartmann pattern shown in Fig. 1 with the detected centroids marked with white squares.

Fig. 4
Fig. 4

Obtained rms results for different NSRs obtained from the Δx and Δy maps computed without ((a) and (b)), and with ((c) and (d)) Zernike fitting.

Fig. 5
Fig. 5

Simulated reference (a) and distorted (b) Hartmann patterns obtained from a NSR of 158%.

Fig. 6
Fig. 6

Obtained rms results for different NSRs obtained from the Δx and Δy maps (a)-(b), and percentage of detected centroids (c).

Fig. 7
Fig. 7

Obtained dislocation maps Δx (a) and Δy (d) by the proposed optical flow algorithm when the simulated wavefront error dynamic range exceeded the limited dynamic range of the SH sensor. In (b) and (e) it is shown the obtained results after unwrapping the dislocation maps, and in (c) and (f) the theoretical dislocation maps.

Fig. 8
Fig. 8

Quadratic wrapped phase-shift introduced in the SLM.

Fig. 9
Fig. 9

Obtained reference (a) and distorted (b) Hartmann spot diagrams obtained by the commercial Shack-Hartmann device.

Fig. 10
Fig. 10

Wavefront error computed by the commercial HASO3 sensor.

Fig. 11
Fig. 11

Wavefront error computed by the proposed Optical Flow algorithm.

Equations (11)

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[ ΔW ] ij = [ ( ΔW x ΔW y ) ] ij = [ 1 f ( Δx Δy ) ] ij
I( x+Δx,y+Δy,t+Δt )I( x,y,t )+ I x Δx+ I y Δy+ I t Δt
I( x+Δx,y+Δy,t+Δt )=I( x,y,t )
I x u+ I y v+ I t =0
I x ( x ˜ , y ˜ )u+ I y ( x ˜ , y ˜ )v= I t ( x ˜ , y ˜ )
Ax=b ( I x ( x ˜ 1 , y ˜ 1 ) I y ( x ˜ 1 , y ˜ 1 ) ... ... I x ( x ˜ N , y ˜ N ) I y ( x ˜ N , y ˜ N ) )( u( x 0 , y 0 ) v( x 0 , y 0 ) )=( I t ( x ˜ 1 , y ˜ 1 ) ... I t ( x ˜ N , y ˜ N ) )
x= ( A T A ) 1 ( A T b ) ( u( x 0 , y 0 ) v( x 0 , y 0 ) )= ( i ( I x ( x ˜ i , y ˜ i ) ) 2 i I x ( x ˜ i , y ˜ i ) I y ( x ˜ i , y ˜ i ) ... ... i I x ( x ˜ i , y ˜ i ) I y ( x ˜ i , y ˜ i ) i ( I y ( x ˜ i , y ˜ i ) ) 2 ) 1 ( i I x ( x ˜ i , y ˜ i ) I t ( x ˜ i , y ˜ i ) ... i I y ( x ˜ i , y ˜ i ) I t ( x ˜ i , y ˜ i ) )
I( ( x+Δ x k )+Δ x k+1 ,( y+Δ y k )+Δ y k+1 ,t+Δt )=I( x,y,t )
Δx= k=1 N i Δ x k , Δy= k=1 N i Δ y k
I n ( ( x+Δ x n1 )+Δ x n ,( y+Δ y n1 )+Δ y n ,t+Δt )= I n ( x,y,t )
Δx= n=0 N p 1 Δ x n , Δy= n=0 N p 1 Δ y n

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