Abstract

A 32×32 microelectricalmechanical systems mirror is controlled in a closed-loop adaptive optics test bed with a spatially filtered wavefront sensor (WFS), Fourier transform wavefront reconstruction, and calibration of references with a high-precision interferometer. When correcting the inherent aberration of the mirror, 0.7nm rms phase error in the controllable band is achieved. When correcting an etched phase plate with atmospheric statistics, a dark hole 103 deeper than the uncontrollable phase is produced in the phase power spectral density. Compensation of the mirror’s influence function is done with a Fourier filter, which results in improved loop convergence. Use of the spatial filter is shown to reduce the gain variability of the WFS in a quadcell configuration.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2006 (7)

B. Macintosh, J. Graham, D. Palmer, R. Doyon, D. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, J. K. Wallace, B. Bauman, J. Evans, D. Erikson, K. Morzinski, D. Phillion, L. Poyneer, A. Sivaramakrishnan, R. Soummer, S. Thibault, and J.-P. Véran, “The Gemini planet imager,” Proc. SPIE 6272, 62720L (2006).
[CrossRef]

J. K. Wallace, R. Bartos, S. Rao, R. Samuele, and E. Schmidtlin, “A laboratory experiment for demonstrating post-coronagraph wavefront sensing and control for extreme adaptive optics,” Proc. SPIE 6272, 62722L (2006).
[CrossRef]

L. A. Poyneer, J.-P. Véran, D. Dillon, S. Severson, and B. A. Macintosh, “Wavefront control for the gemini planet imager,” Proc. SPIE 6272, 62721N (2006).
[CrossRef]

K. M. Morzinski, J. W. Evans, S. Severson, B. Macintosh, D. Dillon, D. Gavel, C. Max, and D. Palmer, “Characterizing the potential of MEMS deformable mirrors for astronomical adaptive optics,” Proc. SPIE 6272, 627221 (2006).
[CrossRef]

L. A. Poyneer, B. Bauman, B. A. Macintosh, D. Dillon, and S. Severson, “Experimental demonstration of phase correction with a 32×32 microelectricalmechanical systems mirror and a spatially filtered wavefront sensor,” Opt. Lett. 31, 293-295 (2006).
[CrossRef] [PubMed]

J. W. Evans, B. Macintosh, L. A. Poyneer, K. Morzinski, S. Severson, D. Dillon, D. Gavel, and L. Reza, “Demonstrating sub-nm closed loop MEMS flattening,” Opt. Express 14, 5558-5570 (2006).
[CrossRef] [PubMed]

L. A. Poyneer and B. A. Macintosh, “Optimal Fourier control performance and speckle behavior in high-contrast imaging with adaptive optics,” Opt. Express 14, 7499-7514 (2006).
[CrossRef] [PubMed]

2005 (3)

2004 (4)

L. A. Poyneer and B. Macintosh, “Spatially filtered wave-front sensor for high-order adaptive optics,” J. Opt. Soc. Am. A 21, 810-819 (2004).
[CrossRef]

K. L. Baker, E. A. Stappaerts, D. Gavel, S. C. Wilks, J. Tucker, D. A. Silva, J. Olsen, S. S. Olivier, P. E. Young, M. W. Kartz, L. M. Flath, P. Krulevitch, J. Crawford, and O. Azucena, “Breadboard testing of a phase-conjugate engine with an interferometric wave-front sensor and a microelectromechanical systems-based spatial light modulator,” Appl. Opt. 43, 5585-5593 (2004).
[CrossRef] [PubMed]

B. A. Macintosh, B. Bauman, J. W. Evans, J. R. Graham, C. Lockwood, L. Poyneer, D. Dillon, D. T. Gavel, J. J. Green, J. P. Lloyd, R. B. Makidon, S. Olivier, D. Palmer, M. D. Perrin, S. Severson, A. I. Sheinis, A. Sivaramakrishnan, G. Sommargren, R. Soummer, M. Troy, J. K. Wallace, and E. Wishnow, “Extreme adaptive optics planet imager: overview and status,” Proc. SPIE 5490, 359-369 (2004).
[CrossRef]

T. Bifano, P. Bierden, and J. Perreault, “Micromachined deformable mirrors for dynamic wavefront control,” Proc. SPIE 5553, 1-16 (2004).
[CrossRef]

2003 (1)

M. D. Perrin, A. Sivaramakrishnan, R. B. Makidon, B. R. Oppenheimer, and J. R. Graham, “The structure of high strehl ratio point-spread functions,” Astrophys. J. Lett. 596, 702-712 (2003).
[CrossRef]

2002 (3)

A. Sivaramakrishnan, J. P. Lloyd, P. Hodge, and B. A. Macintosh, “Speckle decorrelation and dynamic range in speckle noise-limited imaging,” Astrophys. J. Lett. 581, L59-L62(2002).
[CrossRef]

G. E. Sommargren, D. W. Phillion, M. A. Johnson, N. Q. Nguyen, A. Barty, F. J. Snell, D. R. Dillon, and L. S. Bradsher, “100-picometer interferometry for EUVL,” Proc. SPIE 4688, 316-328 (2002).
[CrossRef]

L. A. Poyneer, D. T. Gavel, and J. M. Brase, “Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform,” J. Opt. Soc. Am. A 19, 2100-2111 (2002).
[CrossRef]

2000 (1)

Appl. Opt. (1)

Astrophys. J. Lett. (2)

A. Sivaramakrishnan, J. P. Lloyd, P. Hodge, and B. A. Macintosh, “Speckle decorrelation and dynamic range in speckle noise-limited imaging,” Astrophys. J. Lett. 581, L59-L62(2002).
[CrossRef]

M. D. Perrin, A. Sivaramakrishnan, R. B. Makidon, B. R. Oppenheimer, and J. R. Graham, “The structure of high strehl ratio point-spread functions,” Astrophys. J. Lett. 596, 702-712 (2003).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Express (2)

Opt. Lett. (2)

Proc. SPIE (8)

L. A. Poyneer, J.-P. Véran, D. Dillon, S. Severson, and B. A. Macintosh, “Wavefront control for the gemini planet imager,” Proc. SPIE 6272, 62721N (2006).
[CrossRef]

K. M. Morzinski, J. W. Evans, S. Severson, B. Macintosh, D. Dillon, D. Gavel, C. Max, and D. Palmer, “Characterizing the potential of MEMS deformable mirrors for astronomical adaptive optics,” Proc. SPIE 6272, 627221 (2006).
[CrossRef]

B. A. Macintosh, B. Bauman, J. W. Evans, J. R. Graham, C. Lockwood, L. Poyneer, D. Dillon, D. T. Gavel, J. J. Green, J. P. Lloyd, R. B. Makidon, S. Olivier, D. Palmer, M. D. Perrin, S. Severson, A. I. Sheinis, A. Sivaramakrishnan, G. Sommargren, R. Soummer, M. Troy, J. K. Wallace, and E. Wishnow, “Extreme adaptive optics planet imager: overview and status,” Proc. SPIE 5490, 359-369 (2004).
[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]

B. Macintosh, J. Graham, D. Palmer, R. Doyon, D. Gavel, J. Larkin, B. Oppenheimer, L. Saddlemyer, J. K. Wallace, B. Bauman, J. Evans, D. Erikson, K. Morzinski, D. Phillion, L. Poyneer, A. Sivaramakrishnan, R. Soummer, S. Thibault, and J.-P. Véran, “The Gemini planet imager,” Proc. SPIE 6272, 62720L (2006).
[CrossRef]

T. Bifano, P. Bierden, and J. Perreault, “Micromachined deformable mirrors for dynamic wavefront control,” Proc. SPIE 5553, 1-16 (2004).
[CrossRef]

J. K. Wallace, R. Bartos, S. Rao, R. Samuele, and E. Schmidtlin, “A laboratory experiment for demonstrating post-coronagraph wavefront sensing and control for extreme adaptive optics,” Proc. SPIE 6272, 62722L (2006).
[CrossRef]

G. E. Sommargren, D. W. Phillion, M. A. Johnson, N. Q. Nguyen, A. Barty, F. J. Snell, D. R. Dillon, and L. S. Bradsher, “100-picometer interferometry for EUVL,” Proc. SPIE 4688, 316-328 (2002).
[CrossRef]

Other (3)

J. W. Evans, “High-contrast imaging using adaptive optics for extrasolar planet detection,” Ph.D. dissertation (University of California, 2006).

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing (Prentice Hall, 1999).

J. W. Evans, Lawrence Livermore National Laboratory, Livermore, Calif. 94550 (personal communication, 2007).

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Figures (11)

Fig. 1
Fig. 1

LAO test bed for control of a 32 × 32 MEMS mirror. The PSDI provides a sub-nm measurement of the residual wavefront. It is also used as the source for the spatially filtered WFS, which is used with FTR to control the MEMS.

Fig. 2
Fig. 2

Radial averages of the spatial PSD of residual error in the case of flattening the MEMS. WFS–FTR control achieves a total of 0.9 nm rms error in the controllable band, with most of the region corrected to a level of 0.5 nm rms or less.

Fig. 3
Fig. 3

Microscope image of physical spatial filter overlaid on ideal shape. The actual field stop has rounded edges as is not quite square. Image courtesy of Scott Severson, University of California, Santa Cruz and UCO/Lick Observatory.

Fig. 4
Fig. 4

Radial averages of the spatial PSD of residual error in the case of flattening the MEMS after calibration of references. WFS–FTR control now achieves 0.7 nm rms error at all controllable frequencies, with some of the region corrected to a level of 0.25 nm rms or less.

Fig. 5
Fig. 5

Tip–tilt removed phase aberration (nm) induced by etched phase plate, as measured by PSDI. The high-frequency ripple is from the surface of the MEMS, and the phase discontinuities are clearly visible.

Fig. 6
Fig. 6

Radial averages of the spatial PSD of residual error in the case of correcting an atmosphere-like phase plate. The WFS– FTR loop was run with the best references from flattening the MEMS, resulting is a clear dark hole, but not nearly as good as with the PSDI.

Fig. 7
Fig. 7

Radial averages of the spatial PSD of residual error in the case of correcting an atmosphere-like phase plate after calibration of references. The WFS–FTR references were updated using the residual phase measurements provided by the PSDI. This substantially improves the depth of the dark hole, and most of it is corrected to the 0.5 nm rms level, equivalent to the PSDI correction.

Fig. 8
Fig. 8

Modal gains due to MEMS response for Fourier modes of k = 0 . The dashed curve shows the modal gains after a Gaus sian fit to the MEMS response is used to precompensate phase commands.

Fig. 9
Fig. 9

Normalized power in a Fourier mode as the closed loop converges, based on PSDI measurements of residual phase at each time step. Fourier mode [ 0 , 12 ] has estimated closed-loop modal gains of 0.12 (uncompensated) and 0.41 (compensated). Straight gray lines indicate theoretical convergence.

Fig. 10
Fig. 10

Spatial PSD of residual phase on MEMS without (“No comp.”) and with (“Comp.”) MEMS compensation. With the MEMS compensation filter, the dark hole forms rapidly at all spatial frequencies. Log color scale from 0.25 to 8.0 nm rms error.

Fig. 11
Fig. 11

WFS image for two different subapertures. Log color scale with WFS CCD counts spline interpolated for smoothness; actual pixels are nearly twice Nyquist sampled. For a subaperture with a discontinuous phase, the spatial filter dramatically improves spot shape but cannot completely make it diffraction limited. For a smooth, regular phase aberration, the spatial filter further refines the spot PSF.

Tables (2)

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Table 1 WFS Centroid for Subimages Binned to 8 × 8 Pixels

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Table 2 WFS Centroid for Subimages Binned to 2 × 2 Pixel Quadcell

Equations (1)

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G d [ k , l ] = 2.5 exp ( k 2 + l 2 121 )

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