OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 8 — Apr. 16, 2007
  • pp: 4705–4710
« Show journal navigation

Feasibility of symmetry-based speckle noise reduction for faint companion detection

E. E. Bloemhof  »View Author Affiliations


Optics Express, Vol. 15, Issue 8, pp. 4705-4710 (2007)
http://dx.doi.org/10.1364/OE.15.004705


View Full Text Article

Acrobat PDF (244 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Great interest has been focused on the problem of detecting faint companions, possibly including extrasolar planets, very close to other stars. A promising approach involves coupling high-correction adaptive optics to coronagraphs, for which many new and innovative designs have emerged. Detection of faint companions will require suppression of noise due to fluctuating speckles from the remnant fraction of stellar light not adaptively controlled. At high correction, the speckle halo takes on distinct spatial symmetries that may allow partial speckle noise reduction through relatively simple post-processing that rejects one spatial symmetry in the image. This paper quantitatively examines potential companion-detection sensitivity improvements that might be expected, and shows that realistic operational parameters will allow them to be realized.

© 2007 Optical Society of America

1. Introduction

In just over a decade, more than 200 “extrasolar” planets have been discovered orbiting stars other than the sun, chiefly through rather indirect techniques such as radial velocity measurements that detect the recoil of the stellar primary [1

1. J. J. Lissauer, “Extrasolar planets,” Nature 419, 355 (2002). [CrossRef] [PubMed]

]. Efforts are underway to provide direct imaging of planetary and other stellar companions, though this is a challenging undertaking: at visible wavelengths, an earthlike planet may have roughly 10-10 the signal of its parent star. A classical technique for suppressing light from the primary is coronagraphy [2

2. A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552, 397 (2001). [CrossRef]

], and many innovative approaches are under development. Whether on the ground or in space, coronagraphs may be fed by adaptive optics (AO) [3

3. J. W. Hardy, Adaptive Optics for Astronomical Telescopes, (Oxford University Press, New York, 1998).

] to control the wavefront aberrations induced by atmospheric turbulence or by flexure in beamtrain optics, respectively.

2. Symmetry properties of speckles at high correction

2.1 Phase and amplitude speckle symmetries

At high adaptive correction, the speckle halo organizes itself into terms of distinct spatial symmetry, either even or odd, as can be seen by algebraic expansion of the Fourier-optical expression for the image of the bright central star [4–8

4. D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. principle,” Publ. Astron. Soc. Pac. 112, 1479 (2000). [CrossRef]

]. A useful approximation here is

(A+α)eiϕ¯2(A+α)(1+iϕ12ϕ2)¯2A̅22Re{iA¯*Aϕ¯}+Aϕ¯2Re{iA¯*Aϕ2¯}+α¯2+2Re{A¯*α¯}+2Re{iA¯*αϕ¯}+2Re{iAϕ¯α¯*}
(1)

where 0≤A≤1 is the aperture (pupil) function, α<<1 is a small error in transmission amplitude (equivalent to a fractional intensity fluctuation 2α), and (ϕ<<1 is the (small) residual phase. This treatment assumes that all phase and amplitude errors are in the pupil plane. An overbar denotes two-dimensional Fourier transformation, an asterisk denotes complex conjugation, and |Ā|2 is the point-spread function (PSF), much brighter than all the other terms. Several speckle terms containing more factors of the small quantities α or ϕ have been omitted from Eq. (1) because they are generally fainter at high correction. Since A, ϕ, α are real, their Fourier transforms are Hermitian, causing each term to have definite spatial symmetry. For the regimes to be considered in this paper, the brightest phase speckles come from the term linear in ϕ¯ , 2Re{i A̅* ̅}, which is spatially antisymmetric, and the quadratic term |̅|2, which is spatially symmetric. (The 4th term in Eq. (1), -Re{Ā * 2̅}, is primarily a PSF correction plus true speckles that are fainter than those from the quadratic term [8

8. E. E. Bloemhof, “Static point-spread function correction dominating higher-order speckle terms at high adaptive correction,” Opt. Lett. 29, 2333 (2004). [CrossRef] [PubMed]

].) Brightest of the amplitude speckles are the low-order terms |α̅|2 and 2Re{Ā̅* α̅}, each of which is spatially symmetric. The last two amplitude-speckle terms in Eq. (1

1. J. J. Lissauer, “Extrasolar planets,” Nature 419, 355 (2002). [CrossRef] [PubMed]

) are spatially antisymmetric, but are bilinear in the small quantities α, ϕ and so are fainter than the linear phase speckles also retained here. (Later, in §3, simple image processing will remove the symmetric speckle species and leave the antisymmetric behind; the new speckle contrast floor will then be limited by linear phase speckles, the brightest spatially antisymmetric species.)

2.2 Speckle intensity estimates

Linear-term speckles can have negative intensity, but are “pinned” to diffraction rings of the PSF because they contain a multiplicative factor of the PSF amplitude, Ā. So they reduce diffraction-ring brightness locally, keeping total intensity non-negative. Although the total linear-term power in the halo vanishes, speckles fluctuate locally and cause speckle noise or contribute to the speckle-limited imaging contrast. Owing to the amplification by Ā, linear-term speckles will tend to be brightest in the inner halo; being of lowest order in ̅, they will always dominate in the limit of high adaptive correction (|ϕ̅| small). The PSF amplitude Ā for a round unobscured aperture is the familiar Airy amplitude. The “speckle amplitude” ϕ̅ and “intensity speckle amplitude” α¯ may be computed as a function of Strehl ratio (S) and deformable mirror actuator density (D/a, for pupil diameter D and actuator spacing a), which specifies the highest corrected spatial frequency and hence the halo diameter λ/a [9

9. E. E. Bloemhof, “Suppression of speckle noise by speckle pinning in adaptive optics,” Astrophys. J. 582, L59 (2003). [CrossRef]

]:

A̅=[2J1(πλ)πλ];ϕ̅typ(1S)0.342(aD);α̅typα20.342(aαD).
(2)

D/aα is the analogous spatial frequency characterizing intensity variations on the pupil. Typical intensities of individual speckles may be estimated to within a factor of ~2 by combining Eq. (1) and Eq. (2). Speckle noise is then directly proportional to speckle intensity [10

10. 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 (1999). [CrossRef]

]; for space-borne observatories, the speckle intensity level is directly of interest as the speckle-limited imaging contrast. Full numerical simulations of highly-corrected images at various (S, D/a) were made to determine typical degrees of net spatial symmetry in the phase speckle noise variance fraction; an example is shown in Fig. 1.

2.3 Attenuation of linear-term speckles by coronagraph

For faint companion searches, adaptive correction may be coupled to coronagraphs, substantially modifying some speckle intensities. Specifically, speckles from the terms linear in ϕ̅ or in α̅ are suppressed, while quadratic-term speckles are little affected. The linear terms 2Re{ i A̅* ̅} and 2Re{A̅* α̅} contain a factor of the PSF amplitude, Ā, which the coronagraph naturally suppresses in suppressing the on-axis PSF, |Ā|2. The action of the coronagraph at any given position in the focal plane may be described as reducing the PSF from |Ā|2 to a new contrast level C=|Ā|2/R, with the suppression parameter R>1. Then the Airy amplitude Ā and each linear speckle term will be reduced [11

11. E. E. Bloemhof, “Remnant speckles in a highly corrected coronagraph,” Astrophys. J. 610, L69 (2004). [CrossRef]

, 12

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

] by a factor √R. Considering only phase speckles for simplicity, the competition between the odd linear and even quadratic terms determines the net spatial symmetry of the speckle halo. At the highest correction, an adaptively-fed coronagraph is always dominated by antisymmetric linear-term speckles. But for high-performance coronagraphs at moderately high correction, suppression of the linear term will reverse the symmetry at typical operating parameters from antisymmetric to symmetric, with quadratic speckles then dominating.

Quantitatively, the degree of symmetry for phase speckles can be evaluated at high correction by considering only linear and quadratic terms, the former attenuated by the factor √R. Then if over many independent realizations of the phase screen an adaptive correction gives antisymmetric speckle noise variance fraction f, which is proportional to the antisymmetric fraction of the squared speckle intensity [10

10. 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 (1999). [CrossRef]

], the coronagraph converts this to a symmetric noise variance fraction f’ given by

f=σ2symmσ2antiR+σ2symm=R(1f)f+R(1f).
(3)

This effect is illustrated in Fig. 1 for R=10 and 100, coronagraphic suppression values representative of extreme ground-based adaptive optics systems now under development.

Fig. 1. Spatially antisymmetric speckle noise variance fraction with no coronagraph (solid curve, “simple imaging”) as a function of Strehl ratio, for fixed D/a=16 (higher future D/a will give higher antisymmetry). Values are averages of many monochromatic short-exposures for small (0.25 λ/D) pixels in the innermost two rings of the PSF. The other two curves show the noise variance, though always antisymmetric at highest correction, becomes symmetric when linear-term speckles are suppressed by a coronagraph with PSF rejection R. (The coronagraph curves consider only linear and quadratic speckle terms, strictly valid only at high correction. For illustration, R is taken to be independent of correction.)

3. Potential gains from symmetry-based speckle noise reduction

To apply these concepts, consider a space-based telescope equipped with a coronagraph but no deformable mirror or other high-order adaptive optics. Phase speckles are caused by slowly-varying telescope aberrations; speckle-limited contrast is simply the typical speckle intensity as a fraction of the peak of the primary star. High-quality conventional optics are assumed (λ/100 rms wavefront, or S~0.996) with spatial frequency content D/a~10. Coronagraph performance is assumed high, suppressing the PSF to contrast ~10-7 on the 4th Airy ring [13

13. A. Chakraborty, L. A. Thompson, and M. Rogosky, “10-7 contrast ratio at 4.5λ/D: New results obtained in laboratory experiments using nanofabricated coronagraph and multi-Gaussian shaped pupil masks,” Opt. Express 13, 2394 (2005). [CrossRef] [PubMed]

] (equivalent to R~7800), giving a predominantly symmetric speckle halo.

Equations (1) and (2) then give the intensities of all relevant phase and amplitude speckles. Near the 4th Airy ring, the pre-coronagraph PSF amplitude is Ā~2.8×10-2. The speckle amplitude is ̅~10-2 anywhere in the halo. Assuming pupil-plane intensity variations of 2.6% [14

14. F. Shi, A. E. Lowman, D. C. Moody, A. F. Niessner, and J. T. Trauger, “Wavefront amplitude variation of TPF’s high-contrast imaging testbed: modeling and experiment,” Proc. SPIE 5905, 59051L-1 (2005). [CrossRef]

] characterized by spatial frequencies ~10 cycles/aperture, the intensity speckle amplitude is α̅~2×10-3 anywhere in the halo. So quadratic-term phase speckles |̅|2 dominate, with intensity (contrast) ~1.2×10-4 , while linear-term phase speckles 2Re{ i Ā * ̅} have intensity ~5×10-7 near the 4th Airy ring. (Note that the PSF amplitude has been reduced by √R to capture the effect of the coronagraph, as discussed in §2.3. Also, each linear-term intensity has been reduced an order of magnitude from the small-pixel, monochromatic values of Eq. (2) to account for partial cancellation over an octave of spectral bandwidth on λ/D pixels.) Quadratic amplitude speckles |α̅|2 will have intensity ~5×10-6 anywhere in the halo, while linear amplitude speckles 2Re{Ā * α̅} will have intensity ~10-7 near the 4th Airy ring.

As just shown, symmetry-based image processing can deeply suppress speckles. But particularly for faint primary stars, integration times must be long enough to overcome shot (photon) noise on the pre-processing intensity of the brightest speckle species:

tshotSNR2r*CnCS2,
(4)

4. Practical feasibility of symmetry-based speckle noise suppression

Operationally, an image is symmetrized/antisymmetrized by adding/subtracting a spatially inverted copy. This section examines the fundamental photon-noise-limited precision with which this can be done, and shows it is sufficient to realize the gains described in §3. First, in locating the image center, monochromatic diffraction-limited speckles are grossly characterized as Airy patterns of diameter FWHM~1.03/D or as Gaussian spots with HW1/e σsp~FWHM/(2√(ln2))~0.62λ/D. The minimum possible uncertainty in the single-axis centroid location of a Gaussian spot of size σsp when only photon noise is considered is [16

16. S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323 (2006). [CrossRef]

]

σcent=σspNph,
(5)

where Nph= Cnr* t is the number of photons per speckle, Cn the initial contrast, and r* the rate of detected photons from the primary star, as in §3. (Broadband radial speckle streaks are located transversely to roughly this accuracy.) Locating the center between symmetric speckle pairs improves the accuracy by √2, and combining measurements from all speckle pairs in the halo gives a further improvement by √(Nsp/2), where Nsp≈0.342(D/a)2 is the number of speckles in a halo characterized by actuator density (D/a) [17

17. F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” Prog. Opt. 19, 281 (1981). [CrossRef]

]. The overall precision of locating the speckle halo’s center of symmetry is then

Δ=121Nsp2σcent=1NspσspNph=10.342(aD)(0.062λD)Cnr*t.
(6)

The new remnant speckle noise floor due to imperfect subtraction of image and inverted copy, given the misregistration Δ just calculated, is found from a linearization of two shifted Gaussians valid for small arguments: the spurious intensity is I0Δ/σsp, where I0=Cn is the intensity of each Gaussian speckle. The resulting post-processing contrast is

Cn=Δσsp=Cn10.342(aD)1Cnr*t,
(7)

equal to ~10-8 assuming t~100 s for the illustrative space-borne observatory (with initial speckle contrast floor Cn~1.2×10-4) and the representative primary star (r*~3×108 photons/s) of §3. This value is small compared to the final noise contrast limited by linear-term speckles, Cn'~5×10-7, so frame registration accuracy is adequate to realize this speckle contrast improvement. This is an important check on realistic speckle suppression: past studies have assumed perfect image antisymmetrization [18

18. A. Sivaramakrishnan, P. E. Hodge, R B. Makidon, M. D. Perrin, J. P. Lloyd, E. E. Bloemhof, and B. R. Oppenheimer, “The adaptive optics point-spread function at moderate and high Strehl ratios,” Proc. SPIE 4860, 161 (2003). [CrossRef]

] around a numerically-defined image center.

5. Conclusions

More ambitious observatories might incorporate active optics to increase S and D/a, thus reducing the initial speckle-limited contrast Cn. A λ/160 correction (S=0.9985), D/a=100, and R=7800 on the 4th Airy ring imply Cn~5×10-7 and a final contrast Cs=2Cn'~6×10-8, limited by the antisymmetric linear-term phase speckles that survive image processing (Fig. 2). Integration times to overcome speckle and PSF shot noise are still quite short, t~25 seconds.

Fig. 2. Improvement in speckle-limited search contrast with the image antisymmetrization described in §3, as a function of initial correction, for R=7800 on the 4th Airy ring. Also plotted is the potential limit imposed by centroiding errors, as described by Eq. (7), assuming speckle lifetimes of t~1 second. Contrast values are based on the analytic expressions of Eqs. (1) and (2). At the highest correction considered here, giant extrasolar planets are observable.

Suppressing speckles by exploiting their spatial symmetries at high adaptive correction is an inherently simple and reliable approach requiring image processing but no special hardware. Strong suppression is available at corrections contemplated for space-borne coronagraphic observatories, and the photon fluxes typical of stars that are candidates to have exoplanets are sufficient to permit that suppression to be realized. Use of the symmetry-based techniques presented here on an uncorrected but high-quality space-based telescope could significantly enhance companion detection with no special hardware beyond the coronagraph, making it a potentially interesting addition to a general-purpose observatory.

Acknowledgments

The research described in this publication was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

References and links

1.

J. J. Lissauer, “Extrasolar planets,” Nature 419, 355 (2002). [CrossRef] [PubMed]

2.

A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, “Ground-based coronagraphy with high-order adaptive optics,” Astrophys. J. 552, 397 (2001). [CrossRef]

3.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes, (Oxford University Press, New York, 1998).

4.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. principle,” Publ. Astron. Soc. Pac. 112, 1479 (2000). [CrossRef]

5.

E. E. Bloemhof, R. G. Dekany, M Troy, and B. R. Oppenheimer, “Behavior of remnant speckles in an adaptively corrected imaging system,” Astrophys. J. 558, L71 (2001). [CrossRef]

6.

A. Boccaletti, P. Riaud, and D. Rouan, “Speckle symmetry with high-contrast coronagraphs,” Publ. Astron. Soc. Pac. 114, 132 (2002). [CrossRef]

7.

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 (2003). [CrossRef]

8.

E. E. Bloemhof, “Static point-spread function correction dominating higher-order speckle terms at high adaptive correction,” Opt. Lett. 29, 2333 (2004). [CrossRef] [PubMed]

9.

E. E. Bloemhof, “Suppression of speckle noise by speckle pinning in adaptive optics,” Astrophys. J. 582, L59 (2003). [CrossRef]

10.

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 (1999). [CrossRef]

11.

E. E. Bloemhof, “Remnant speckles in a highly corrected coronagraph,” Astrophys. J. 610, L69 (2004). [CrossRef]

12.

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

13.

A. Chakraborty, L. A. Thompson, and M. Rogosky, “10-7 contrast ratio at 4.5λ/D: New results obtained in laboratory experiments using nanofabricated coronagraph and multi-Gaussian shaped pupil masks,” Opt. Express 13, 2394 (2005). [CrossRef] [PubMed]

14.

F. Shi, A. E. Lowman, D. C. Moody, A. F. Niessner, and J. T. Trauger, “Wavefront amplitude variation of TPF’s high-contrast imaging testbed: modeling and experiment,” Proc. SPIE 5905, 59051L-1 (2005). [CrossRef]

15.

A. Quirrenbach, “Coronagraphic methods for the detection of terrestrial planets,” conclusions from a workshop held at Leiden Univ., Feb. 2–6, 2004; preprint at (http://arXiv.org/astro-ph/0502254) (2005).

16.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323 (2006). [CrossRef]

17.

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” Prog. Opt. 19, 281 (1981). [CrossRef]

18.

A. Sivaramakrishnan, P. E. Hodge, R B. Makidon, M. D. Perrin, J. P. Lloyd, E. E. Bloemhof, and B. R. Oppenheimer, “The adaptive optics point-spread function at moderate and high Strehl ratios,” Proc. SPIE 4860, 161 (2003). [CrossRef]

19.

J. T. Trauger, C. Burrows, B. Gordon, J. J. Green, A. E. Lowman, D. Moody, A. F. Niessner, F. Shi, and D. Wilson, “Coronagraph contrast demonstrations with the high-contrast imaging testbed,” Proc. SPIE 5487, 1330 (2004). [CrossRef]

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(030.6140) Coherence and statistical optics : Speckle
(350.1260) Other areas of optics : Astronomical optics

ToC Category:
Adaptive Optics

History
Original Manuscript: January 22, 2007
Revised Manuscript: March 13, 2007
Manuscript Accepted: March 20, 2007
Published: April 3, 2007

Citation
E. E. Bloemhof, "Feasibility of symmetry-based speckle noise reduction for faint companion detection," Opt. Express 15, 4705-4710 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-8-4705


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. J. Lissauer, "Extrasolar planets," Nature 419, 355 (2002). [CrossRef] [PubMed]
  2. A. Sivaramakrishnan, C. D. Koresko, R. B. Makidon, T. Berkefeld, and M. J. Kuchner, "Ground-based coronagraphy with high-order adaptive optics," Astrophys. J. 552, 397 (2001). [CrossRef]
  3. J. W. Hardy, Adaptive Optics for Astronomical Telescopes, (Oxford University Press, New York, 1998).
  4. D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, "The four-quadrant phase-mask coronagraph. I. principle," Publ. Astron. Soc. Pac. 112, 1479 (2000). [CrossRef]
  5. E. E. Bloemhof, R. G. Dekany, M Troy, and B. R. Oppenheimer, "Behavior of remnant speckles in an adaptively corrected imaging system," Astrophys. J. 558, L71 (2001). [CrossRef]
  6. A. Boccaletti, P. Riaud, and D. Rouan, "Speckle symmetry with high-contrast coronagraphs," Publ. Astron. Soc. Pac. 114, 132 (2002). [CrossRef]
  7. 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 (2003). [CrossRef]
  8. E. E. Bloemhof, "Static point-spread function correction dominating higher-order speckle terms at high adaptive correction," Opt. Lett. 29, 2333 (2004). [CrossRef] [PubMed]
  9. E. E. Bloemhof, "Suppression of speckle noise by speckle pinning in adaptive optics," Astrophys. J. 582, L59 (2003). [CrossRef]
  10. 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 (1999). [CrossRef]
  11. E. E. Bloemhof, "Remnant speckles in a highly corrected coronagraph," Astrophys. J. 610, L69 (2004). [CrossRef]
  12. C. Aime and R. Soummer, "The usefulness and limits of coronagraphy in the presence of pinned speckles," Astrophys. J. 612, L85 (2004). [CrossRef]
  13. A. Chakraborty, L. A. Thompson, and M. Rogosky, "10-7 contrast ratio at 4.5λ/D: New results obtained in laboratory experiments using nanofabricated coronagraph and multi-Gaussian shaped pupil masks," Opt. Express 13, 2394 (2005). [CrossRef] [PubMed]
  14. F. Shi, A. E. Lowman, D. C. Moody, A. F. Niessner, and J. T. Trauger, "Wavefront amplitude variation of TPF's high-contrast imaging testbed: modeling and experiment," Proc. SPIE 5905, 59051L-1 (2005). [CrossRef]
  15. A. Quirrenbach, "Coronagraphic methods for the detection of terrestrial planets," conclusions from a workshop held at Leiden Univ., Feb. 2-6, 2004; preprint at (http://arXiv.org/astro-ph/0502254) (2005).
  16. S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, "Comparison of centroid computation algorithms in a Shack-Hartmann sensor," Mon. Not. R. Astron. Soc. 371, 323 (2006). [CrossRef]
  17. F. Roddier, "The effects of atmospheric turbulence in optical astronomy," Prog. Opt. 19, 281 (1981). [CrossRef]
  18. A. Sivaramakrishnan, P. E. Hodge, R. B. Makidon, M. D. Perrin, J. P. Lloyd, E. E. Bloemhof, and B. R. Oppenheimer, "The adaptive optics point-spread function at moderate and high Strehl ratios," Proc. SPIE 4860, 161 (2003). [CrossRef]
  19. J. T. Trauger, C. Burrows, B. Gordon, J. J. Green, A. E. Lowman, D. Moody, A. F. Niessner, F. Shi, and D. Wilson, "Coronagraph contrast demonstrations with the high-contrast imaging testbed," Proc. SPIE 5487, 1330 (2004). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1. Fig. 2.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited