Abstract

Adaptive optics takes its servo feedback error cue from a wavefront sensor. The common Hartmann–Shack spot grid that represents the wavefront slopes is usually analyzed by finding the spot centroids. In a novel application, we used the Fourier decomposition of a spot pattern to find deviations from grid regularity. This decomposition was performed either in the Fourier domain or in the image domain, as a demodulation of the grid of spots. We analyzed the system, built a control loop for it, and tested it thoroughly. This allowed us to close the loop on wavefront errors caused by turbulence in the optical system.

© 2007 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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2006 (3)

2004 (2)

A. Talmi and E. N. Ribak, "Direct demodulation of Hartmann-Shack patterns," J. Opt. Soc. Am. A 21, 632-639 (2004).
[CrossRef]

Y. Carmon and E. N. Ribak, "Fast Fourier demodulation," Appl. Phys. Lett. 84, 4656-4657 (2004).
[CrossRef]

2003 (2)

E. N. Ribak, "Separating atmospheric layers in adaptive optics," Opt. Lett. 28, 613-615 (2003).
[CrossRef] [PubMed]

Y. Carmon and E. N. Ribak, "Phase retrieval by demodulation of a Hartmann-Shack sensor," Opt. Commun. 215, 285-288 (2003).
[CrossRef]

2001 (1)

1998 (1)

1994 (1)

1988 (1)

1980 (1)

1977 (1)

Adler, J.

S. Zommer, E. N. Ribak, S. G. Lipson, and J. Adler, "Simulated annealing in ocular adaptive optics," Opt. Lett. 31, 939-941 (2006).

Artal, P.

Åström, K. J.

K. J. Åström and B. Wittenmark, Computer-Controlled Systems: Theory and Design, 3rd ed. (Prentice-Hall, 1997), p. 512.

Baum, G.

Bauman, B.

Carmon, Y.

Y. Carmon and E. N. Ribak, "Fast Fourier demodulation," Appl. Phys. Lett. 84, 4656-4657 (2004).
[CrossRef]

Y. Carmon and E. N. Ribak, "Phase retrieval by demodulation of a Hartmann-Shack sensor," Opt. Commun. 215, 285-288 (2003).
[CrossRef]

Dillon, D.

Fernández, E. J.

Fried, D. L.

Glazer, O.

O. Glazer, "Construction of a control loop for an adaptive optical system," M.Sc. thesis (Technion, Haifa, Israel, 2005).

Iglesias, I.

Lipson, S. G.

S. Zommer, E. N. Ribak, S. G. Lipson, and J. Adler, "Simulated annealing in ocular adaptive optics," Opt. Lett. 31, 939-941 (2006).

Macintosh, B. A.

Poyneer, L. A.

Ribak, E. N.

Roddier, F.

F. Roddier, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).

Schwartz, C.

Severson, S.

Southwell, W. H.

Srour, O.

Takahashi, T.

Takajo, H.

Talmi, A.

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, 1998).

Wittenmark, B.

K. J. Åström and B. Wittenmark, Computer-Controlled Systems: Theory and Design, 3rd ed. (Prentice-Hall, 1997), p. 512.

Zommer, S.

S. Zommer, "Simulated annealing in adaptive optics for imaging the eye retina," M.Sc. thesis (Technion, Haifa, Israel, 2005).

S. Zommer, E. N. Ribak, S. G. Lipson, and J. Adler, "Simulated annealing in ocular adaptive optics," Opt. Lett. 31, 939-941 (2006).

Zon, N.

Appl. Phys. Lett. (1)

Y. Carmon and E. N. Ribak, "Fast Fourier demodulation," Appl. Phys. Lett. 84, 4656-4657 (2004).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (5)

Opt. Commun. (1)

Y. Carmon and E. N. Ribak, "Phase retrieval by demodulation of a Hartmann-Shack sensor," Opt. Commun. 215, 285-288 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Other (6)

R. K. Tyson, Principles of Adaptive Optics, 2nd ed. (Academic, 1998).

O. Glazer, "Construction of a control loop for an adaptive optical system," M.Sc. thesis (Technion, Haifa, Israel, 2005).

K. J. Åström and B. Wittenmark, Computer-Controlled Systems: Theory and Design, 3rd ed. (Prentice-Hall, 1997), p. 512.

S. Zommer, "Simulated annealing in adaptive optics for imaging the eye retina," M.Sc. thesis (Technion, Haifa, Israel, 2005).

S. Zommer, E. N. Ribak, S. G. Lipson, and J. Adler, "Simulated annealing in ocular adaptive optics," Opt. Lett. 31, 939-941 (2006).

F. Roddier, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).

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Figures (8)

Fig. 1
Fig. 1

Plant (controlled process) and sensor.

Fig. 2
Fig. 2

Block diagram of the feedback control system.

Fig. 3
Fig. 3

Stability and high-frequency performance areas in the ( k p , k a ) plane.

Fig. 4
Fig. 4

Optical system. A collimated, wide laser beam enters from the bottom right and splits (in beam splitter BS2) into either a reference channel or a deformable mirror channel. Light from the unblocked arm returns into the wavefront sensor (WFS: Hartmann–Shack lenslet array and camera). An image of the corrected laser beam is split (in beam splitter BS1) into another camera. Turbulence is added between the lenses in front of the deformable mirror.

Fig. 5
Fig. 5

(Color online) Selected part of the Fourier transform of the current measurement of the wavefront (less a reference array). Only the imaginary part of two lobes is shown, corresponding to the x and the y slopes. On top is a square of 25 pixels of the 0, 1 lobe, below it the square of the 1, 0 lobe.

Fig. 6
Fig. 6

(Color online) Hartmann pattern filtered by smoothing: y-slope response to a single actuator ( 0.3   μm stroke, 15   mm mirror diameter). The Hartmann pattern is grabbed, multiplied by the exponential of its base frequency, smoothed, and its phase extracted. The slope is sampled at 25 spots inside this pattern (left panel). After subtraction of the reference image (flat surface) we get the control signal input (right panel).

Fig. 7
Fig. 7

(Color online) Screen shot of the first six modes converging to their final values within five iterations for k p = 0.3 and k a = 0.3 . Inset cuts through the laser input images for three iterations when they reduce to diffraction size (bottom curve). To better see the width, the camera was overexposed, and the top of the diffraction images was saturated.

Fig. 8
Fig. 8

(Color online) Comparison of the simulation of the control system response (right panel) and the experiment (left panel), a screen shot of the first six modes and their convergence under mild turbulence for k p = 0.25 and k a = 0.4 .

Equations (5)

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E ( z ) = S ( z ) [ R a ( z ) D ( z ) ] + T ( z ) H # N ( z ) ,
C 1 ( z ) = z 1 k p ( 1 + k a z z 1 ) I ,
k p > 1 , k p k a > 0 ,
k p ( 2 + k a ) < 2 α 1 + α ,
k p ( 2 + k a ) > 2 α 1 α , if   α < 1 2 .

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