Abstract

High-contrast imaging with adaptive optics (AO) for planet detection requires a sophisticated AO control system to provide the best possible performance. We evaluate the performance improvements in terms of residual error and point-spread function intensity provided by optimal Fourier control using detailed end-to-end simulation. Intensity, however, is not the final measure of system performance. We explore image contrast through analysis and simulation results, showing that speckles caused by atmospheric errors behave very differently in a temporal fashion from speckles caused by wavefront sensor noise errors.

© 2006 Optical Society of America

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References

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  1. J. Schneider, The Extrasolar Planets Encyclopaedia, Tech. rep. (CNRS-LUTH, Paris Observatory, 2006), http://vo.obspm.fr/exoplanetes/encyclo/catalog.php.
  2. 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]
  3. L. A. Poyneer and J.-P. Véran, "Optimal modal Fourier transform wave-front control," J. Opt. Soc. Am. A 22, 1515-1526 (2005).
    [CrossRef]
  4. 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. 596, 702-712 (2003).
    [CrossRef]
  5. L. A. Poyneer, D. T. Gavel, and J. M. Brase, "Fast wavefront reconstruction in large adaptive optics systems with use of the Fourier transform," J. Opt. Soc. Am. A 19, 2100-2111 (2002).
    [CrossRef]
  6. E. Gendron and P. Léna, "Astronomical adaptive optics, 1: Modal control optimization," Astron. Astrophys. 291, 337-347 (1994).
  7. P.-Y. Madec, "Control Techniques," in Adaptive Optics in Astronomy, F. Roddier, ed. (Cambridge University Press, 1999) pp. 131-154.
  8. A. Tokovinin, "Modeling turbulence profile for GLAO," Tech. rep. (Gemini Observatory, 2004).
  9. E. M. Johansson and D. T. Gavel, "Simulation of stellar speckle imaging," in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE 1237 (1994) pp. 372-383.
    [CrossRef]
  10. S. B. Howell, Handbook of CCD Astronomy (Cambridge University Press, 2000).
  11. J. J. Green and S. B. Shaklan, "Optimizing coronagraph designs to minimize their contrast sensitivity to loworder optical aberrations," in Techniques and Instrumentation for Detection of Exoplanets, D. R. Coulter, ed., Proc. SPIE 5170 (2003) pp. 25-37.
    [CrossRef]
  12. B. L. Ellerbroek, "Linear systems modeling of adaptive optics in the spatial-frequency domain," J. Opt. Soc. Am. A 22, 310-322 (2005).
    [CrossRef]
  13. L. Jolissaint, J.-P. Véran, and R. Conan, "Analytical modeling of adaptive optics: foundations of the phase spatial power spectrum approach," J. Opt. Soc. Am. A 23, 382-394 (2006).
    [CrossRef]
  14. C. Aime and R. Soummer, "The usefulness and limits of coronagraphy in the presence of pinned speckles," Astrophys. J. 612, L85-L88 (2004).
    [CrossRef]
  15. M. P. Fitzgerald and J. R. Graham, "Speckle statistics in adaptively corrected images," Astrophys. J. 637, 541-547 (2006).
    [CrossRef]
  16. R. Racine, G. A. H. Walker, D. Nadeau, R. Doyon, and C. Marois, "Speckle noise and the detection of faint companions," Publ. Astron. Soc. Pac. 111, 587-594 (1999).
    [CrossRef]
  17. B. Macintosh, L. A. Poyneer, A. Sivaramakrishnan, and C. Marois, "Speckle lifetimes in high-contrast adaptive optics," in Astronomical Adaptive Optics Systems and Applications II, R. K. Tyson andM. Llyod-Hart, eds., Proc. SPIE 5903 (2005) p. 59030J.
    [CrossRef]
  18. A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-time Signal Processing (Prentice Hall, 1999).

2006 (2)

2005 (2)

2004 (2)

C. Aime and R. Soummer, "The usefulness and limits of coronagraphy in the presence of pinned speckles," Astrophys. J. 612, L85-L88 (2004).
[CrossRef]

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]

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. 596, 702-712 (2003).
[CrossRef]

2002 (1)

1999 (1)

R. Racine, G. A. H. Walker, D. Nadeau, R. Doyon, and C. Marois, "Speckle noise and the detection of faint companions," Publ. Astron. Soc. Pac. 111, 587-594 (1999).
[CrossRef]

1994 (1)

E. Gendron and P. Léna, "Astronomical adaptive optics, 1: Modal control optimization," Astron. Astrophys. 291, 337-347 (1994).

Aime, C.

C. Aime and R. Soummer, "The usefulness and limits of coronagraphy in the presence of pinned speckles," Astrophys. J. 612, L85-L88 (2004).
[CrossRef]

Brase, J. M.

Conan, R.

Doyon, R.

R. Racine, G. A. H. Walker, D. Nadeau, R. Doyon, and C. Marois, "Speckle noise and the detection of faint companions," Publ. Astron. Soc. Pac. 111, 587-594 (1999).
[CrossRef]

Ellerbroek, B. L.

Fitzgerald, M. P.

M. P. Fitzgerald and J. R. Graham, "Speckle statistics in adaptively corrected images," Astrophys. J. 637, 541-547 (2006).
[CrossRef]

Gavel, D. T.

Gendron, E.

E. Gendron and P. Léna, "Astronomical adaptive optics, 1: Modal control optimization," Astron. Astrophys. 291, 337-347 (1994).

Graham, J. R.

M. P. Fitzgerald and J. R. Graham, "Speckle statistics in adaptively corrected images," Astrophys. J. 637, 541-547 (2006).
[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. 596, 702-712 (2003).
[CrossRef]

Jolissaint, L.

Léna, P.

E. Gendron and P. Léna, "Astronomical adaptive optics, 1: Modal control optimization," Astron. Astrophys. 291, 337-347 (1994).

Macintosh, B.

Makidon, R. B.

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. 596, 702-712 (2003).
[CrossRef]

Marois, C.

R. Racine, G. A. H. Walker, D. Nadeau, R. Doyon, and C. Marois, "Speckle noise and the detection of faint companions," Publ. Astron. Soc. Pac. 111, 587-594 (1999).
[CrossRef]

Nadeau, D.

R. Racine, G. A. H. Walker, D. Nadeau, R. Doyon, and C. Marois, "Speckle noise and the detection of faint companions," Publ. Astron. Soc. Pac. 111, 587-594 (1999).
[CrossRef]

Oppenheimer, B. R.

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. 596, 702-712 (2003).
[CrossRef]

Perrin, M. D.

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. 596, 702-712 (2003).
[CrossRef]

Poyneer, L. A.

Racine, R.

R. Racine, G. A. H. Walker, D. Nadeau, R. Doyon, and C. Marois, "Speckle noise and the detection of faint companions," Publ. Astron. Soc. Pac. 111, 587-594 (1999).
[CrossRef]

Sivaramakrishnan, A.

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. 596, 702-712 (2003).
[CrossRef]

Soummer, R.

C. Aime and R. Soummer, "The usefulness and limits of coronagraphy in the presence of pinned speckles," Astrophys. J. 612, L85-L88 (2004).
[CrossRef]

Véran, J.-P.

Walker, G. A. H.

R. Racine, G. A. H. Walker, D. Nadeau, R. Doyon, and C. Marois, "Speckle noise and the detection of faint companions," Publ. Astron. Soc. Pac. 111, 587-594 (1999).
[CrossRef]

Astron. Astrophys. (1)

E. Gendron and P. Léna, "Astronomical adaptive optics, 1: Modal control optimization," Astron. Astrophys. 291, 337-347 (1994).

Astrophys. J. (3)

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. 596, 702-712 (2003).
[CrossRef]

C. Aime and R. Soummer, "The usefulness and limits of coronagraphy in the presence of pinned speckles," Astrophys. J. 612, L85-L88 (2004).
[CrossRef]

M. P. Fitzgerald and J. R. Graham, "Speckle statistics in adaptively corrected images," Astrophys. J. 637, 541-547 (2006).
[CrossRef]

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

Publ. Astron. Soc. Pac. (1)

R. Racine, G. A. H. Walker, D. Nadeau, R. Doyon, and C. Marois, "Speckle noise and the detection of faint companions," Publ. Astron. Soc. Pac. 111, 587-594 (1999).
[CrossRef]

Other (8)

B. Macintosh, L. A. Poyneer, A. Sivaramakrishnan, and C. Marois, "Speckle lifetimes in high-contrast adaptive optics," in Astronomical Adaptive Optics Systems and Applications II, R. K. Tyson andM. Llyod-Hart, eds., Proc. SPIE 5903 (2005) p. 59030J.
[CrossRef]

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

P.-Y. Madec, "Control Techniques," in Adaptive Optics in Astronomy, F. Roddier, ed. (Cambridge University Press, 1999) pp. 131-154.

A. Tokovinin, "Modeling turbulence profile for GLAO," Tech. rep. (Gemini Observatory, 2004).

E. M. Johansson and D. T. Gavel, "Simulation of stellar speckle imaging," in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. SPIE 1237 (1994) pp. 372-383.
[CrossRef]

S. B. Howell, Handbook of CCD Astronomy (Cambridge University Press, 2000).

J. J. Green and S. B. Shaklan, "Optimizing coronagraph designs to minimize their contrast sensitivity to loworder optical aberrations," in Techniques and Instrumentation for Detection of Exoplanets, D. R. Coulter, ed., Proc. SPIE 5170 (2003) pp. 25-37.
[CrossRef]

J. Schneider, The Extrasolar Planets Encyclopaedia, Tech. rep. (CNRS-LUTH, Paris Observatory, 2006), http://vo.obspm.fr/exoplanetes/encyclo/catalog.php.

Supplementary Material (2)

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Figures (8)

Fig. 1.
Fig. 1.

Block diagram of the AO control system for a complex Fourier modal coefficient. All modal signals are complex-valued. The WFS, FTR, and DM units are boxed off.

Fig. 2.
Fig. 2.

Optimal gain filters for a range of NGS magnitudes and two frame rates. The filters are centered so that the lowest frequency is in the middle. The optimal gain varies with modal spatial frequency, spanning in most cases a range of 0.4 gain units.

Fig. 3.
Fig. 3.

[Animated Figure: 1.3 MB] Gain optimization that reduces temporal errors in the PSF, I = 5, 2 kHz case.

Fig. 4.
Fig. 4.

[Animated Figure: 1.9 MB] Gain optimization that reduces noise errors in the PSF, I = 8, 2 kHz case.

Fig. 5.
Fig. 5.

Short and long exposure PSFs from the end-to-end simulation. Both have the same standard deviation of intensity in the controllable region (dark hole) but a planet is more easily detected in the long exposure image.

Fig. 6.
Fig. 6.

(a) (left) PSF intensity at a location 0.45” above the PSF core, sampled at 100 Hz. Atmosphere is for simulation with no WFS noise. WFS noise line for simulation with no atmospheric error. (b) (right) the estimated temporal PSDs for PSF intensity at the same location as shown in (a).

Fig. 7.
Fig. 7.

(a) (left) estimated intensity variances as a function of exposure time, calculated with Eq. 13 and the data shown in Fig. 6b. The WFS noise has the 1/T drop-off, but the atmospheric variance is flat before dropping off after 0.25 seconds. (b) (right) Intensity variances drawn from a spatially-averaged contrast metric at 0.45” distance for cumulative exposures of increasing length. Atmosphere data points are over 12 difference atmospheres, with error bars. These results, determined with a completely different method, confirm the results shown (a).

Fig. 8.
Fig. 8.

Contrast of 2 s PSF, before and after gain optimization. (a) (left) Slice along y-axis through butterfly region. Gain optimization has improved contrast by a factor of 2. (b) (right). Slice along x-axis through region of little atmospheric error. Gain optimization has decreased contrast by a factor of 1.5.

Equations (26)

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ϕ [ t ] = x [ t ] g rx + y [ t ] g ry ,
g rx = 1 g d ( g wx * g wx 2 + g wy 2 ) ,
g ry = 1 g d ( g wy * g wx 2 + g wy 2 ) .
C ( z ) = g 1 c z 1 ,
SNR F I = 0.146202 ( 10 9 0.4 I ) F ( 0.146202 ( 10 9 0.4 I ) F + 256 ) 1 2 ,
P ε ( ω ) = P m ( ω ) 1 + c 2 2 c cos ω ) 1 + c 2 + g 2 2 c ( 1 + g ) cos ω ) + 2 gcos 2 ω ) .
σ ε 2 = 1 2 π π π P ε ( ω ) .
P nx ( ω ) = P ny ( ω ) = σ n 2 2 .
P ε ( ω ) = σ n 2 2 g 2 ( g rx g d 2 + g ry g d 2 ) 1 + c 2 + g 2 2 c ( 1 + g ) cos ( ω ) + 2 gcos ( 2 ω ) .
σ ε 2 = σ n 2 2 g 2 ( g rx g d 2 + g ry g d 2 ) g 2 ( 1 + g ) ( 1 g ) ( 1 + g ) 2 c 2 ( 1 g ) .
p N [ t ] = 1 T l = 0 T 1 i [ t l ] .
P p , T ( ω ) = P i ( ω ) 1 T 2 [ sin ( ωT 2 ) sin ( ω 2 ) ] 2 .
σ p , T 2 = { 1 2 π 1 T 2 π π P i ( ω ) [ sin ( ωT 2 ) sin ( ω 2 ) ] 2 } m i 2 ,
P X Y = A X Y + jA X Y * Φ X Y 0.5 A X Y * Φ X Y * Φ X Y + 2 .
P A 2 + 2 Im { A [ A * Φ * ] } + A * Φ 2 Re { A [ A * Φ * * Φ * ] }
+ Im { [ A * Φ ] [ A * Φ * * Φ * ] } + 0.25 A * Φ * Φ 2
ϕ x y t = ε cos [ t ] cos ( 2 π D [ kx + ly ] ) + ε sin [ t ] sin ( 2 π D [ kx + ly ] ) ,
Φ X Y t = 1 2 { ε [ t ] δ ( X λk D , Y λl D ) * ε * [ t ] δ ( X + λk D , Y + λl D ) } .
i k , t [ t ] A 2 k l A k l ε sin [ t ] + ε [ t ] 2 4 .
σ ε 2 = σ ε , cos 2 + σ ε , sin 2 .
E [ i ] = A 2 k l + σ ε 2 4 .
σ i 2 = 1 8 { σ ε , cos 4 + σ ε , sin 4 + 2 ( E [ cs ] ) 2 } + A 2 k l σ ε , sin 2 .
E [ i ] = A 2 k l + 1 4 ( σ ε 1 2 + σ ε 2 2 ) .
σ i 1 2 = 1 8 { σ ε 1 , cos 4 + σ ε 1 , sin 4 + 2 ( E [ c 1 s 1 ] ) 2 } + A 2 k l σ ε 1 , sin 2 ,
σ i 2 2 = 1 8 { σ ε 2 , cos 4 + σ ε 2 , sin 4 + 2 ( E [ c 2 s 2 ] ) 2 } + A 2 k l σ ε 2 , sin 2 .
σ i 2 = σ i 1 2 + σ i 2 2 + { 1 4 ( σ ε 1 , sin 2 + σ ε 2 ,cos 2 + σ ε 1 , sin 2 σ ε 2 , sin 2 ) + 1 2 E [ c 1 s 1 ] E [ c 2 s 2 ] } .

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