Abstract

An adaptive periodic-correlation (APC) algorithm was developed for use in extended-scene Shack–Hartmann wavefront sensors. It provides high accuracy even when the subimages in a frame captured by a Shack–Hartmann camera are not only shifted but also distorted relative to each other. Recently we found that the shift estimate error of the APC algorithm has a component that depends on the content of the extended scene. In this paper, we assess the amount of that error and propose a method to minimize it.

© 2013 Optical Society of America

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References

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  1. I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed., 2nd ed. (Wiley, 1992), pp. 367–396.
  2. S. A. Basinger, D. C. Redding, A. E. Lowman, L. A. Burns, K. Y. Liu, and D. Cohen, “Performance of wavefront sensing and control algorithms on a segmented telescope testbed,” Proc. SPIE 4013, 749–756 (2000).
    [CrossRef]
  3. V. P. Lukin, N. N. Botygina, and P. A. Konyaev, “Wave-front sensors for adaptive optical systems,” Proc. SPIE 7476, 74760L (2009), and some references therein.
    [CrossRef]
  4. L. A. Poyneer, “Scene-based Shack–Hartmann wave-front sensing: analysis and simulation,” Appl. Opt. 42, 5807–5815 (2003).
    [CrossRef]
  5. E. Sidick, J. J. Green, R. M. Morgan, C. M. Ohara, and D. C. Redding, “Adaptive cross-correlation algorithm for extended scene Shack–Hartmann wavefront sensing,” Opt. Lett. 33, 213–215 (2008).
    [CrossRef]
  6. E. Sidick, “Adaptive periodic-correlation algorithm for extended scene Shack–Hartmann wavefront sensing,” in 2011 COSI Topical Meeting (Optical Society of America, 2011), paper CPDP1.
  7. F. Shi, S. Basinger, R. Diaz, H. Tang, R. Lam, E. Sidick, R. Hein, M. Rud, and M. Troy, “Advanced wavefront sensing and control testbed (AWCT),” Proc. SPIE 7739, 77392W1 (2010).
    [CrossRef]
  8. E. Sidick, “Dependence of adaptive cross-correlation algorithm performance on the extended scene image quality,” Proc. SPIE 7093, 70930G1 (2008).
  9. R. M. Morgan, W. K. Wilkie, X. Bao, and E. Sidick, “Actuator fault detection via electrical impedance testing,” Proc. SPIE 6711, 67110A1 (2007).
    [CrossRef]

2010

F. Shi, S. Basinger, R. Diaz, H. Tang, R. Lam, E. Sidick, R. Hein, M. Rud, and M. Troy, “Advanced wavefront sensing and control testbed (AWCT),” Proc. SPIE 7739, 77392W1 (2010).
[CrossRef]

2009

V. P. Lukin, N. N. Botygina, and P. A. Konyaev, “Wave-front sensors for adaptive optical systems,” Proc. SPIE 7476, 74760L (2009), and some references therein.
[CrossRef]

2008

E. Sidick, J. J. Green, R. M. Morgan, C. M. Ohara, and D. C. Redding, “Adaptive cross-correlation algorithm for extended scene Shack–Hartmann wavefront sensing,” Opt. Lett. 33, 213–215 (2008).
[CrossRef]

E. Sidick, “Dependence of adaptive cross-correlation algorithm performance on the extended scene image quality,” Proc. SPIE 7093, 70930G1 (2008).

2007

R. M. Morgan, W. K. Wilkie, X. Bao, and E. Sidick, “Actuator fault detection via electrical impedance testing,” Proc. SPIE 6711, 67110A1 (2007).
[CrossRef]

2003

2000

S. A. Basinger, D. C. Redding, A. E. Lowman, L. A. Burns, K. Y. Liu, and D. Cohen, “Performance of wavefront sensing and control algorithms on a segmented telescope testbed,” Proc. SPIE 4013, 749–756 (2000).
[CrossRef]

Bao, X.

R. M. Morgan, W. K. Wilkie, X. Bao, and E. Sidick, “Actuator fault detection via electrical impedance testing,” Proc. SPIE 6711, 67110A1 (2007).
[CrossRef]

Basinger, S.

F. Shi, S. Basinger, R. Diaz, H. Tang, R. Lam, E. Sidick, R. Hein, M. Rud, and M. Troy, “Advanced wavefront sensing and control testbed (AWCT),” Proc. SPIE 7739, 77392W1 (2010).
[CrossRef]

Basinger, S. A.

S. A. Basinger, D. C. Redding, A. E. Lowman, L. A. Burns, K. Y. Liu, and D. Cohen, “Performance of wavefront sensing and control algorithms on a segmented telescope testbed,” Proc. SPIE 4013, 749–756 (2000).
[CrossRef]

Botygina, N. N.

V. P. Lukin, N. N. Botygina, and P. A. Konyaev, “Wave-front sensors for adaptive optical systems,” Proc. SPIE 7476, 74760L (2009), and some references therein.
[CrossRef]

Burns, L. A.

S. A. Basinger, D. C. Redding, A. E. Lowman, L. A. Burns, K. Y. Liu, and D. Cohen, “Performance of wavefront sensing and control algorithms on a segmented telescope testbed,” Proc. SPIE 4013, 749–756 (2000).
[CrossRef]

Cohen, D.

S. A. Basinger, D. C. Redding, A. E. Lowman, L. A. Burns, K. Y. Liu, and D. Cohen, “Performance of wavefront sensing and control algorithms on a segmented telescope testbed,” Proc. SPIE 4013, 749–756 (2000).
[CrossRef]

Diaz, R.

F. Shi, S. Basinger, R. Diaz, H. Tang, R. Lam, E. Sidick, R. Hein, M. Rud, and M. Troy, “Advanced wavefront sensing and control testbed (AWCT),” Proc. SPIE 7739, 77392W1 (2010).
[CrossRef]

Ghozeil, I.

I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed., 2nd ed. (Wiley, 1992), pp. 367–396.

Green, J. J.

Hein, R.

F. Shi, S. Basinger, R. Diaz, H. Tang, R. Lam, E. Sidick, R. Hein, M. Rud, and M. Troy, “Advanced wavefront sensing and control testbed (AWCT),” Proc. SPIE 7739, 77392W1 (2010).
[CrossRef]

Konyaev, P. A.

V. P. Lukin, N. N. Botygina, and P. A. Konyaev, “Wave-front sensors for adaptive optical systems,” Proc. SPIE 7476, 74760L (2009), and some references therein.
[CrossRef]

Lam, R.

F. Shi, S. Basinger, R. Diaz, H. Tang, R. Lam, E. Sidick, R. Hein, M. Rud, and M. Troy, “Advanced wavefront sensing and control testbed (AWCT),” Proc. SPIE 7739, 77392W1 (2010).
[CrossRef]

Liu, K. Y.

S. A. Basinger, D. C. Redding, A. E. Lowman, L. A. Burns, K. Y. Liu, and D. Cohen, “Performance of wavefront sensing and control algorithms on a segmented telescope testbed,” Proc. SPIE 4013, 749–756 (2000).
[CrossRef]

Lowman, A. E.

S. A. Basinger, D. C. Redding, A. E. Lowman, L. A. Burns, K. Y. Liu, and D. Cohen, “Performance of wavefront sensing and control algorithms on a segmented telescope testbed,” Proc. SPIE 4013, 749–756 (2000).
[CrossRef]

Lukin, V. P.

V. P. Lukin, N. N. Botygina, and P. A. Konyaev, “Wave-front sensors for adaptive optical systems,” Proc. SPIE 7476, 74760L (2009), and some references therein.
[CrossRef]

Morgan, R. M.

E. Sidick, J. J. Green, R. M. Morgan, C. M. Ohara, and D. C. Redding, “Adaptive cross-correlation algorithm for extended scene Shack–Hartmann wavefront sensing,” Opt. Lett. 33, 213–215 (2008).
[CrossRef]

R. M. Morgan, W. K. Wilkie, X. Bao, and E. Sidick, “Actuator fault detection via electrical impedance testing,” Proc. SPIE 6711, 67110A1 (2007).
[CrossRef]

Ohara, C. M.

Poyneer, L. A.

Redding, D. C.

E. Sidick, J. J. Green, R. M. Morgan, C. M. Ohara, and D. C. Redding, “Adaptive cross-correlation algorithm for extended scene Shack–Hartmann wavefront sensing,” Opt. Lett. 33, 213–215 (2008).
[CrossRef]

S. A. Basinger, D. C. Redding, A. E. Lowman, L. A. Burns, K. Y. Liu, and D. Cohen, “Performance of wavefront sensing and control algorithms on a segmented telescope testbed,” Proc. SPIE 4013, 749–756 (2000).
[CrossRef]

Rud, M.

F. Shi, S. Basinger, R. Diaz, H. Tang, R. Lam, E. Sidick, R. Hein, M. Rud, and M. Troy, “Advanced wavefront sensing and control testbed (AWCT),” Proc. SPIE 7739, 77392W1 (2010).
[CrossRef]

Shi, F.

F. Shi, S. Basinger, R. Diaz, H. Tang, R. Lam, E. Sidick, R. Hein, M. Rud, and M. Troy, “Advanced wavefront sensing and control testbed (AWCT),” Proc. SPIE 7739, 77392W1 (2010).
[CrossRef]

Sidick, E.

F. Shi, S. Basinger, R. Diaz, H. Tang, R. Lam, E. Sidick, R. Hein, M. Rud, and M. Troy, “Advanced wavefront sensing and control testbed (AWCT),” Proc. SPIE 7739, 77392W1 (2010).
[CrossRef]

E. Sidick, “Dependence of adaptive cross-correlation algorithm performance on the extended scene image quality,” Proc. SPIE 7093, 70930G1 (2008).

E. Sidick, J. J. Green, R. M. Morgan, C. M. Ohara, and D. C. Redding, “Adaptive cross-correlation algorithm for extended scene Shack–Hartmann wavefront sensing,” Opt. Lett. 33, 213–215 (2008).
[CrossRef]

R. M. Morgan, W. K. Wilkie, X. Bao, and E. Sidick, “Actuator fault detection via electrical impedance testing,” Proc. SPIE 6711, 67110A1 (2007).
[CrossRef]

E. Sidick, “Adaptive periodic-correlation algorithm for extended scene Shack–Hartmann wavefront sensing,” in 2011 COSI Topical Meeting (Optical Society of America, 2011), paper CPDP1.

Tang, H.

F. Shi, S. Basinger, R. Diaz, H. Tang, R. Lam, E. Sidick, R. Hein, M. Rud, and M. Troy, “Advanced wavefront sensing and control testbed (AWCT),” Proc. SPIE 7739, 77392W1 (2010).
[CrossRef]

Troy, M.

F. Shi, S. Basinger, R. Diaz, H. Tang, R. Lam, E. Sidick, R. Hein, M. Rud, and M. Troy, “Advanced wavefront sensing and control testbed (AWCT),” Proc. SPIE 7739, 77392W1 (2010).
[CrossRef]

Wilkie, W. K.

R. M. Morgan, W. K. Wilkie, X. Bao, and E. Sidick, “Actuator fault detection via electrical impedance testing,” Proc. SPIE 6711, 67110A1 (2007).
[CrossRef]

Appl. Opt.

Opt. Lett.

Proc. SPIE

S. A. Basinger, D. C. Redding, A. E. Lowman, L. A. Burns, K. Y. Liu, and D. Cohen, “Performance of wavefront sensing and control algorithms on a segmented telescope testbed,” Proc. SPIE 4013, 749–756 (2000).
[CrossRef]

V. P. Lukin, N. N. Botygina, and P. A. Konyaev, “Wave-front sensors for adaptive optical systems,” Proc. SPIE 7476, 74760L (2009), and some references therein.
[CrossRef]

F. Shi, S. Basinger, R. Diaz, H. Tang, R. Lam, E. Sidick, R. Hein, M. Rud, and M. Troy, “Advanced wavefront sensing and control testbed (AWCT),” Proc. SPIE 7739, 77392W1 (2010).
[CrossRef]

E. Sidick, “Dependence of adaptive cross-correlation algorithm performance on the extended scene image quality,” Proc. SPIE 7093, 70930G1 (2008).

R. M. Morgan, W. K. Wilkie, X. Bao, and E. Sidick, “Actuator fault detection via electrical impedance testing,” Proc. SPIE 6711, 67110A1 (2007).
[CrossRef]

Other

E. Sidick, “Adaptive periodic-correlation algorithm for extended scene Shack–Hartmann wavefront sensing,” in 2011 COSI Topical Meeting (Optical Society of America, 2011), paper CPDP1.

I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed., 2nd ed. (Wiley, 1992), pp. 367–396.

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Figures (18)

Fig. 1.
Fig. 1.

Measured extended-scene SHC image. The red circle indicates the boundary of a 6126-cell area used in this study. The white and the yellow squares indicate the two 100×100 pixel areas shown in Fig. 2 below. The white circle near the center of the image indicates the location of the reference cell. The x and y axes are in pixels.

Fig. 2.
Fig. 2.

Subimages inside the white (left) and the yellow (right) boxes in Fig. 1. The red and the yellow squares indicate 32×32 pixel and 16×16 pixel cell areas, respectively. The x and y axes are in pixels.

Fig. 3.
Fig. 3.

OPD map obtained in a differential mode ES-SHS experiment using the extended-scene target shown in Figs. 1 and 2.

Fig. 4.
Fig. 4.

Image-shift diagram resulted in the OPD map shown in Fig. 3. The four boxes with different colors indicate the boundaries of the four areas corresponding to the four poked actuators.

Fig. 5.
Fig. 5.

Distribution of the radial image shifts corresponding to the four areas in Fig. 4. The different colors of these four datasets correspond to the colors of the four areas in Fig. 4.

Fig. 6.
Fig. 6.

OPD maps obtained in a differential mode ES-SHS experiment from a pair of point-source spot image frames. In the figure title, the “PS” means “point source,” and the “ES” means “extended scene.” Listed in the x-label are the RMS values of the corresponding OPD maps.

Fig. 7.
Fig. 7.

(a) RMS values of the OPD maps versus actuator commands. The figure insert shows an example of the OPD maps obtained in this “actuator linearity” experiment. The “Iter” in the figure legend lists the values of the number of peak-finding iterations used, and the pink curve marked as “APC” was obtained with the standard APC algorithm. (b) Percentage error versus actuator commands defined as 100×ΔRMS/(RMS)APC, where ΔRMS represents the RMS values of the ΔOPD=(OPD)APC-(OPD)Iter with Iter=1, 2, and 4, and the (RMS)APC is the RMS value of the (OPD)APC, the OPD map obtained with the standard APC algorithm.

Fig. 8.
Fig. 8.

32×32 pixel reference cells of the seven pairs of extended-scene image frames used to obtain the results in Figs. 7(a) and 7(b).

Fig. 9.
Fig. 9.

512×512 pixel satellite photo. The yellow box shows a 65×65 pixel subimage. The x and y axes are in pixels.

Fig. 10.
Fig. 10.

65×65 pixels subimage corresponding to the yellow box in Fig. 9. The red and the yellow boxes indicate 32×32 pixel and 16×16 pixel cells, respectively.

Fig. 11.
Fig. 11.

Part of a measured point-source spot image.

Fig. 12.
Fig. 12.

Extended-scene subimage array obtained from the convolution of the two images shown in Figs. 7 and 8.

Fig. 13.
Fig. 13.

Shift estimate error of the image shifts between Figs. 11 and 12.

Fig. 14.
Fig. 14.

Histograms of the RMS values of the before correction and after correction radial shift estimate errors, (Δx⃗see2+Δy⃗see)1/2 and (Δx⃗c2+Δy⃗c)1/2.

Fig. 15.
Fig. 15.

Histograms of the linear-fit coefficients [a1,b1] of [Δx⃗see,Δy⃗see].

Fig. 16.
Fig. 16.

Histograms of the mean values (biases) [a0,b0] of [Δx⃗see,Δy⃗see].

Fig. 17.
Fig. 17.

Fractional parts of (a) xr and (b) yr of the reference image used to obtain the result shown in Fig. 3. They are in pixels. The cells whose data are missing in these two plots are the “bad cells” that are excluded during the analysis of the measured images.

Fig. 18.
Fig. 18.

(a) X-shifts, Δx⃗wfe, and (b) y-shifts, Δy⃗wfe, of the case where actuator command=0.5[a.u.]. The x and y axes are in pixels.

Tables (3)

Tables Icon

Table 1. Several Parameters of the Image Shifts Estimated from the Reference and the Test Images Used in Fig. 3a

Tables Icon

Table 2. Histogram of Peak-Finding Iteration Number Needed During the Position Estimate of 6125 Test Cells Relative to a Single Reference Cella

Tables Icon

Table 3. Several Parameters of the Image Shifts Estimated from the Reference and the Test Images Used in Fig. 7(a)a

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

Δxij=jδxij,Δyij=jδyij.
S^ij(u,v)=S^i(u,v)exp[j2π(Δxiju+Δyijv)].
ε⃗=q⃗p⃗.
ε⃗=ε⃗wfe+ε⃗scene+ε⃗algor=ε⃗wfe+ε⃗see,
p⃗=P⃗+δp⃗.
Δx⃗see=a1δx⃗r+Δx⃗scat+a0Δy⃗see=b1δy⃗r+Δy⃗scat+b0.
Δx⃗c=Δx⃗seea1δx⃗r=Δx⃗scat+a0Δy⃗c=Δy⃗seeb1δy⃗r=Δy⃗scat+b0,
ε⃗ε⃗wfe.
Δx⃗wfe=A1δx⃗r+Δx¯scat+A0Δy⃗wfe=B1δy⃗r+Δy¯scat+B0,
Δr⃗lin=(A1δx⃗r)2+(B1δy⃗r)2Δr⃗wfe=(Δx⃗wfe)2+(Δy⃗wfe)2RMSRatio=RMS{Δr⃗lin}/RMS{Δr⃗wfe},

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