Abstract

The quasi-static aberrations of optical telescopes are often determined using light from a star as the reference wavefront. We calculate the exposure time necessary to determine the amplitude of the phase aberrations for a given telescope to a given accuracy in the presence of atmospheric seeing. We implement a computational simulation of the atmosphere and present the root mean square of the generated wavefront Zernike amplitudes for a given exposure time. We find the exposure time τ required to reach a desired precision is strongly dependent on telescope diameter (τD8/3) and can be many tens of minutes in extreme cases. We present the results so τ can be calculated for a range of telescopes and atmospheric parameters.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. C. West, “Interferometric Hartmann wave-front sensing for active optics at the 6.5 m conversion of the multiple mirror telescope,” Appl. Opt. 41, 3781–3789 (2002).
    [CrossRef] [PubMed]
  2. J. Hill, R. Ragazzoni, A. Baruffolo, C. Biddick, O. Kuhn, E. Diolaiti, D. Thompson, and A. Rakich, “Prime focus active optics with the Large Binocular Telescope,” Proc. SPIE 7012, 70121M (2008).
    [CrossRef]
  3. M. L. Marrero, L. F. R. Ramos, and J. M. R. Ramos, “Static telescope aberration measurement and correction using lucky imaging techniques,” Proc. SPIE 7018, 70183L (2008).
    [CrossRef]
  4. J. A. Koch, R. W. Presta, R. A. Sacks, R. A. Zacharias, E. S. Bliss, M. J. Dailey, M. Feldman, A. A. Grey, F. R. Holdener, and J. T. Salmon, “Experimental comparison of a Shack–Hartmann sensor and a phase-shifting interferometer for large-optics metrology applications,” Appl. Opt. 39, 4540–4546 (2000).
    [CrossRef]
  5. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  6. V. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover, 1967).
  7. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1427–1431(1965).
    [CrossRef]
  8. G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. A 164, 476–490 (1938).
    [CrossRef]
  9. A. Quirrenbach, “Observing through the turbulent atmosphere,” in Principles of Long Baseline Stellar Interferometry, P.Lawson, ed. (NASA, 2000), pp. 71–85.
  10. L. Poyneer, M. van Dam, and J.-P. Véran, “Experimental verification of the frozen flow atmospheric turbulence assumption with use of astronomical adaptive optics telemetry,” J. Opt. Soc. Am. A 26, 833–846 (2009).
    [CrossRef]
  11. D. Dravins, L. Lindegren, E. Mezey, and A. T. Young, “Atmospheric intensity scintillation of stars, I. statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).
    [CrossRef]
  12. V. V. Voitsekhovich, “Outer scale of turbulence: comparison of different models,” J. Opt. Soc. Am. A 12, 1346–1353(1995).
    [CrossRef]
  13. R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
    [CrossRef]
  14. M. C. Roggemann and B. Welsh, Imaging Through Turbulence (CRC, 1996).
  15. W. Swantner and W. W. Chow, “Gram–Schmidt orthonormalization of Zernike polynomials for general aperture shapes,” Appl. Opt. 33, 1832–1837 (1994).
    [CrossRef] [PubMed]
  16. A. Ziad, M. Schöck, G. A. Chanan, M. Troy, R. Dekany, B. F. Lane, J. Borgnino, and F. Martin, “Comparison of measurements of the outer scale of turbulence by three different techniques,” Appl. Opt. 43, 2316–2324(2004).
    [CrossRef] [PubMed]
  17. D. M. Winker, “Effect of a finite outer scale on the Zernike decomposition of atmospheric optical turbulence,” J. Opt. Soc. Am. A 8, 1568–1573 (1991).
    [CrossRef]

2009

2008

J. Hill, R. Ragazzoni, A. Baruffolo, C. Biddick, O. Kuhn, E. Diolaiti, D. Thompson, and A. Rakich, “Prime focus active optics with the Large Binocular Telescope,” Proc. SPIE 7012, 70121M (2008).
[CrossRef]

M. L. Marrero, L. F. R. Ramos, and J. M. R. Ramos, “Static telescope aberration measurement and correction using lucky imaging techniques,” Proc. SPIE 7018, 70183L (2008).
[CrossRef]

2004

2002

2000

1997

D. Dravins, L. Lindegren, E. Mezey, and A. T. Young, “Atmospheric intensity scintillation of stars, I. statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).
[CrossRef]

1995

1994

1992

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

1991

1976

1965

1938

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. A 164, 476–490 (1938).
[CrossRef]

Baruffolo, A.

J. Hill, R. Ragazzoni, A. Baruffolo, C. Biddick, O. Kuhn, E. Diolaiti, D. Thompson, and A. Rakich, “Prime focus active optics with the Large Binocular Telescope,” Proc. SPIE 7012, 70121M (2008).
[CrossRef]

Biddick, C.

J. Hill, R. Ragazzoni, A. Baruffolo, C. Biddick, O. Kuhn, E. Diolaiti, D. Thompson, and A. Rakich, “Prime focus active optics with the Large Binocular Telescope,” Proc. SPIE 7012, 70121M (2008).
[CrossRef]

Bliss, E. S.

Borgnino, J.

Chanan, G. A.

Chow, W. W.

Dailey, M. J.

Dainty, J. C.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Dekany, R.

Diolaiti, E.

J. Hill, R. Ragazzoni, A. Baruffolo, C. Biddick, O. Kuhn, E. Diolaiti, D. Thompson, and A. Rakich, “Prime focus active optics with the Large Binocular Telescope,” Proc. SPIE 7012, 70121M (2008).
[CrossRef]

Dravins, D.

D. Dravins, L. Lindegren, E. Mezey, and A. T. Young, “Atmospheric intensity scintillation of stars, I. statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).
[CrossRef]

Feldman, M.

Fried, D. L.

Glindemann, A.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Grey, A. A.

Hill, J.

J. Hill, R. Ragazzoni, A. Baruffolo, C. Biddick, O. Kuhn, E. Diolaiti, D. Thompson, and A. Rakich, “Prime focus active optics with the Large Binocular Telescope,” Proc. SPIE 7012, 70121M (2008).
[CrossRef]

Holdener, F. R.

Koch, J. A.

Kuhn, O.

J. Hill, R. Ragazzoni, A. Baruffolo, C. Biddick, O. Kuhn, E. Diolaiti, D. Thompson, and A. Rakich, “Prime focus active optics with the Large Binocular Telescope,” Proc. SPIE 7012, 70121M (2008).
[CrossRef]

Lane, B. F.

Lane, R. G.

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Lindegren, L.

D. Dravins, L. Lindegren, E. Mezey, and A. T. Young, “Atmospheric intensity scintillation of stars, I. statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).
[CrossRef]

Marrero, M. L.

M. L. Marrero, L. F. R. Ramos, and J. M. R. Ramos, “Static telescope aberration measurement and correction using lucky imaging techniques,” Proc. SPIE 7018, 70183L (2008).
[CrossRef]

Martin, F.

Mezey, E.

D. Dravins, L. Lindegren, E. Mezey, and A. T. Young, “Atmospheric intensity scintillation of stars, I. statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).
[CrossRef]

Noll, R. J.

Poyneer, L.

Presta, R. W.

Quirrenbach, A.

A. Quirrenbach, “Observing through the turbulent atmosphere,” in Principles of Long Baseline Stellar Interferometry, P.Lawson, ed. (NASA, 2000), pp. 71–85.

Ragazzoni, R.

J. Hill, R. Ragazzoni, A. Baruffolo, C. Biddick, O. Kuhn, E. Diolaiti, D. Thompson, and A. Rakich, “Prime focus active optics with the Large Binocular Telescope,” Proc. SPIE 7012, 70121M (2008).
[CrossRef]

Rakich, A.

J. Hill, R. Ragazzoni, A. Baruffolo, C. Biddick, O. Kuhn, E. Diolaiti, D. Thompson, and A. Rakich, “Prime focus active optics with the Large Binocular Telescope,” Proc. SPIE 7012, 70121M (2008).
[CrossRef]

Ramos, J. M. R.

M. L. Marrero, L. F. R. Ramos, and J. M. R. Ramos, “Static telescope aberration measurement and correction using lucky imaging techniques,” Proc. SPIE 7018, 70183L (2008).
[CrossRef]

Ramos, L. F. R.

M. L. Marrero, L. F. R. Ramos, and J. M. R. Ramos, “Static telescope aberration measurement and correction using lucky imaging techniques,” Proc. SPIE 7018, 70183L (2008).
[CrossRef]

Roggemann, M. C.

M. C. Roggemann and B. Welsh, Imaging Through Turbulence (CRC, 1996).

Sacks, R. A.

Salmon, J. T.

Schöck, M.

Swantner, W.

Tatarskii, V. V. I.

V. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover, 1967).

Taylor, G. I.

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. A 164, 476–490 (1938).
[CrossRef]

Thompson, D.

J. Hill, R. Ragazzoni, A. Baruffolo, C. Biddick, O. Kuhn, E. Diolaiti, D. Thompson, and A. Rakich, “Prime focus active optics with the Large Binocular Telescope,” Proc. SPIE 7012, 70121M (2008).
[CrossRef]

Troy, M.

van Dam, M.

Véran, J.-P.

Voitsekhovich, V. V.

Welsh, B.

M. C. Roggemann and B. Welsh, Imaging Through Turbulence (CRC, 1996).

West, S. C.

Winker, D. M.

Young, A. T.

D. Dravins, L. Lindegren, E. Mezey, and A. T. Young, “Atmospheric intensity scintillation of stars, I. statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).
[CrossRef]

Zacharias, R. A.

Ziad, A.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Proc. R. Soc. A

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. A 164, 476–490 (1938).
[CrossRef]

Proc. SPIE

J. Hill, R. Ragazzoni, A. Baruffolo, C. Biddick, O. Kuhn, E. Diolaiti, D. Thompson, and A. Rakich, “Prime focus active optics with the Large Binocular Telescope,” Proc. SPIE 7012, 70121M (2008).
[CrossRef]

M. L. Marrero, L. F. R. Ramos, and J. M. R. Ramos, “Static telescope aberration measurement and correction using lucky imaging techniques,” Proc. SPIE 7018, 70183L (2008).
[CrossRef]

Publ. Astron. Soc. Pac.

D. Dravins, L. Lindegren, E. Mezey, and A. T. Young, “Atmospheric intensity scintillation of stars, I. statistical distributions and temporal properties,” Publ. Astron. Soc. Pac. 109, 173–207 (1997).
[CrossRef]

Waves Random Media

R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Other

M. C. Roggemann and B. Welsh, Imaging Through Turbulence (CRC, 1996).

A. Quirrenbach, “Observing through the turbulent atmosphere,” in Principles of Long Baseline Stellar Interferometry, P.Lawson, ed. (NASA, 2000), pp. 71–85.

V. V. I. Tatarskii, Wave Propagation in a Turbulent Medium (Dover, 1967).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Instantaneous Zernike coefficient amplitude a 4 for Z 4 for one realization of the atmosphere (solid line). Also shown is the RMS σ 4 ( t ) of all 10 3 realizations in the simulation (dashed lines). (b) RMS σ 4 ( τ ) of all 10 3 realizations of Z 4 after an exposure of length τ (solid line). The τ constant and τ 0.5 power law regions are indicated (dashed lines). Both (a) and (b) have the zero line included for reference (dot-dashed line).

Fig. 2
Fig. 2

RMS of Zernike mode coefficients σ j ( τ ) after an integration time τ for Z 4 66 , relating to Zernike radial modes n = 2 , 3 , , 10 (solid line). The τ constant and τ 0.5 power law regions are indicated (dashed line).

Fig. 3
Fig. 3

(a) Value of σ 4 ( τ ) in nanometers for several well-known telescopes with respect to exposure time τ, r 0 ( λ = 500 nm ) = 0.14 m , and v = 10 ms 1 for the Kolmogorov model. (b) Value of σ 4 ( τ ) in nanometers for the 30 m ELT under the same conditions as in (a), but with the inclusion of a finite outer scale L 0 . The Kolmogorov model ( L 0 = ) is included for comparison.

Fig. 4
Fig. 4

Autocorrelation of σ j ( τ ) for Z 4 66 , representing radial order n = 2 , 3 , , 10 (solid lines). The positive region of the graph indicates a correlation as expected for τ τ bp , while the negative region indicates an anticorrelation. A value of zero (dashed line) indicates no correlation, as would be expected for τ τ bp .

Tables (2)

Tables Icon

Table 1 Ordering of the First 10 Zernike Modes

Tables Icon

Table 2 Initial RMS σ j ( 0 ) , Break Point τ bp , and the Coefficients A n

Equations (12)

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

D ϕ ( r ) = | ϕ ( r ) ϕ ( r + r ) | 2 ,
D ϕ ( r ) = 6.88 ( | r | r 0 ) 5 / 3 ,
Φ ϕ K ( κ ) = 0.0229 r 0 5 / 3 κ 11 / 3 ,
Φ ϕ v K ( κ , L 0 ) = 0.0229 r 0 5 / 3 ( κ 2 + 1 L 0 2 ) 11 / 6 .
a j ( t ) = p q φ screen ( t , p , q ) Z j ( p , q ) ,
a j ( τ ) = 1 N t t = 0 N t ( τ ) a j ( t ) .
σ j ( τ ) = | a j ( τ ) | 2 ,
r 0 = N l N l 3 / 5 r 0 .
σ j ( 0 ) = | a j ( 0 ) | 2 ,
a j ( τ ) = a j ( 0 ) .
τ σ ^ j = A n [ σ ^ j ( r 0 D ) 5 / 6 ] 2 ( D v ) = A n D 8 / 3 r 0 5 / 3 v 1 σ ^ j 2 ,
R j ( τ ) = 1 σ j 2 [ a j ( t ) μ j ] [ a j ( t + τ ) μ j ] ,

Metrics