Abstract

A new method has been developed for testing the optical quality of ground-based telescopes. Aberrations are estimated from wideband long-exposure defocused stellar images recorded with current astronomical CCD cameras. An iterative algorithm is used that simulates closed-loop wave-front compensation in adaptive optics. Compared with the conventional Hartmann test, the new method is easier to implement, has similar accuracy, and provides a higher spatial resolution on the reconstructed wave front. It has been applied to several astronomical telescopes and has been found to be a powerful diagnostic tool for improving image quality.

© 1993 Optical Society of America

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  1. D. Morris, “Phase retrieval in the radio holography of reflector antennas and radio telescopes,” IEEE Trans. Antennas Propag. AP-33, 749–755 (1985).
    [CrossRef]
  2. C. Roddier, F. Roddier, “Combined approach to Hubble Space Telescope wave-front distortion analysis,” Appl. Opt. 32, 2992–3008 (1993).
    [CrossRef] [PubMed]
  3. C. Roddier, F. Roddier, “New optical testing methods developed at the University of Hawaii: results on ground-based telescopes and Hubble Space Telescope,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 37–43 (1991).
    [CrossRef]
  4. A. Behr, “A proposal for the alignment of large telescopes,” Astron. Astrophys. 28, 355–358 (1973).
  5. R. Wilson, “Procedures and formulae for the adjustment of telescopes and analysis of their performance,” memorandum, ESO Telescope Project Division (European Southern Observatory, Garching bei München, Germany, June18, 1980).
  6. F. Roddier, “Curvature sensing and compensation: a new concept in adaptive optics,” Appl. Opt. 27, 1223–1225 (1988).
    [CrossRef] [PubMed]
  7. F. Roddier, “Wavefront sensing and the irradiance transport equation,” Appl. Opt. 29, 1402–1403 (1990).
    [CrossRef] [PubMed]
  8. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,”J. Opt. Soc. Am. 73, 1434–1441 (1983).
    [CrossRef]
  9. N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).
    [CrossRef]
  10. K. Ichikawa, A. Lohmann, M. Takeda, “Phase retrieval based on the irradiance transport equation and the Fourier transform method: experiments,” Appl. Opt. 27, 3433–3436 (1988).
    [CrossRef] [PubMed]
  11. N. Roddier, “Algorithms for wave-front reconstruction out of curvature sensing data,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1542, 120–129 (1991).
    [CrossRef]
  12. F. Roddier, C. Roddier, “Wavefront reconstruction using iterative Fourier transforms,” Appl. Opt. 30, 1325–1327 (1991).
    [CrossRef] [PubMed]
  13. C. Roddier, F. Roddier, A. Stockton, A. Pickles, N. Roddier, “Testing of telescope optics: a new approach,” in Advanced Technology Optical Telescopes IV, D. L. Barr, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.1236, 756–766 (1990).
    [CrossRef]
  14. W. H. Press, B. P. Flannery, S. A. Tenkolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988), p. 104.
  15. R. Noll, “Zernike polynomials and atmospheric turbulence,”J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  16. R. N. Wilson, F. Franzia, P. Giordano, L. Noethe, M. Tarenghi, “Active optics: the NTT and the future,” Messenger (ESO) 53, 1–7 (1988).
  17. D. J. Schroeder, Astronomical Optics (Academic, San Diego, 1987), p. 113.
  18. J. C. Fouéré, G. Ratier, “Report on the optical quality of the primary mirror,” (CFHT primary-mirror acceptance test report) (Canada–France–Hawaii Telescope Project Office, Meudon, France, 1978).
  19. In “Modified F/8 secondary gives excellent images,” CFHT Inform. Bull. 10 (Canada–France–Hawaii Telescope Office, Kamuela, Hawaii, 1984), p. 1.
  20. F. Roddier, “Mirror aberration communication,” Phys. Today 43(11), 117 (1990).
    [CrossRef]
  21. D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992), p. 750.

1993 (1)

1991 (1)

1990 (2)

1988 (3)

1985 (1)

D. Morris, “Phase retrieval in the radio holography of reflector antennas and radio telescopes,” IEEE Trans. Antennas Propag. AP-33, 749–755 (1985).
[CrossRef]

1984 (1)

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).
[CrossRef]

1983 (1)

1976 (1)

1973 (1)

A. Behr, “A proposal for the alignment of large telescopes,” Astron. Astrophys. 28, 355–358 (1973).

Behr, A.

A. Behr, “A proposal for the alignment of large telescopes,” Astron. Astrophys. 28, 355–358 (1973).

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Tenkolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988), p. 104.

Fouéré, J. C.

J. C. Fouéré, G. Ratier, “Report on the optical quality of the primary mirror,” (CFHT primary-mirror acceptance test report) (Canada–France–Hawaii Telescope Project Office, Meudon, France, 1978).

Franzia, F.

R. N. Wilson, F. Franzia, P. Giordano, L. Noethe, M. Tarenghi, “Active optics: the NTT and the future,” Messenger (ESO) 53, 1–7 (1988).

Giordano, P.

R. N. Wilson, F. Franzia, P. Giordano, L. Noethe, M. Tarenghi, “Active optics: the NTT and the future,” Messenger (ESO) 53, 1–7 (1988).

Ichikawa, K.

Lohmann, A.

Malacara, D.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992), p. 750.

Morris, D.

D. Morris, “Phase retrieval in the radio holography of reflector antennas and radio telescopes,” IEEE Trans. Antennas Propag. AP-33, 749–755 (1985).
[CrossRef]

Noethe, L.

R. N. Wilson, F. Franzia, P. Giordano, L. Noethe, M. Tarenghi, “Active optics: the NTT and the future,” Messenger (ESO) 53, 1–7 (1988).

Noll, R.

Pickles, A.

C. Roddier, F. Roddier, A. Stockton, A. Pickles, N. Roddier, “Testing of telescope optics: a new approach,” in Advanced Technology Optical Telescopes IV, D. L. Barr, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.1236, 756–766 (1990).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Tenkolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988), p. 104.

Ratier, G.

J. C. Fouéré, G. Ratier, “Report on the optical quality of the primary mirror,” (CFHT primary-mirror acceptance test report) (Canada–France–Hawaii Telescope Project Office, Meudon, France, 1978).

Roddier, C.

C. Roddier, F. Roddier, “Combined approach to Hubble Space Telescope wave-front distortion analysis,” Appl. Opt. 32, 2992–3008 (1993).
[CrossRef] [PubMed]

F. Roddier, C. Roddier, “Wavefront reconstruction using iterative Fourier transforms,” Appl. Opt. 30, 1325–1327 (1991).
[CrossRef] [PubMed]

C. Roddier, F. Roddier, “New optical testing methods developed at the University of Hawaii: results on ground-based telescopes and Hubble Space Telescope,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 37–43 (1991).
[CrossRef]

C. Roddier, F. Roddier, A. Stockton, A. Pickles, N. Roddier, “Testing of telescope optics: a new approach,” in Advanced Technology Optical Telescopes IV, D. L. Barr, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.1236, 756–766 (1990).
[CrossRef]

Roddier, F.

C. Roddier, F. Roddier, “Combined approach to Hubble Space Telescope wave-front distortion analysis,” Appl. Opt. 32, 2992–3008 (1993).
[CrossRef] [PubMed]

F. Roddier, C. Roddier, “Wavefront reconstruction using iterative Fourier transforms,” Appl. Opt. 30, 1325–1327 (1991).
[CrossRef] [PubMed]

F. Roddier, “Mirror aberration communication,” Phys. Today 43(11), 117 (1990).
[CrossRef]

F. Roddier, “Wavefront sensing and the irradiance transport equation,” Appl. Opt. 29, 1402–1403 (1990).
[CrossRef] [PubMed]

F. Roddier, “Curvature sensing and compensation: a new concept in adaptive optics,” Appl. Opt. 27, 1223–1225 (1988).
[CrossRef] [PubMed]

C. Roddier, F. Roddier, A. Stockton, A. Pickles, N. Roddier, “Testing of telescope optics: a new approach,” in Advanced Technology Optical Telescopes IV, D. L. Barr, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.1236, 756–766 (1990).
[CrossRef]

C. Roddier, F. Roddier, “New optical testing methods developed at the University of Hawaii: results on ground-based telescopes and Hubble Space Telescope,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 37–43 (1991).
[CrossRef]

Roddier, N.

N. Roddier, “Algorithms for wave-front reconstruction out of curvature sensing data,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1542, 120–129 (1991).
[CrossRef]

C. Roddier, F. Roddier, A. Stockton, A. Pickles, N. Roddier, “Testing of telescope optics: a new approach,” in Advanced Technology Optical Telescopes IV, D. L. Barr, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.1236, 756–766 (1990).
[CrossRef]

Schroeder, D. J.

D. J. Schroeder, Astronomical Optics (Academic, San Diego, 1987), p. 113.

Stockton, A.

C. Roddier, F. Roddier, A. Stockton, A. Pickles, N. Roddier, “Testing of telescope optics: a new approach,” in Advanced Technology Optical Telescopes IV, D. L. Barr, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.1236, 756–766 (1990).
[CrossRef]

Streibl, N.

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).
[CrossRef]

Takeda, M.

Tarenghi, M.

R. N. Wilson, F. Franzia, P. Giordano, L. Noethe, M. Tarenghi, “Active optics: the NTT and the future,” Messenger (ESO) 53, 1–7 (1988).

Teague, M. R.

Tenkolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Tenkolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988), p. 104.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Tenkolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988), p. 104.

Wilson, R.

R. Wilson, “Procedures and formulae for the adjustment of telescopes and analysis of their performance,” memorandum, ESO Telescope Project Division (European Southern Observatory, Garching bei München, Germany, June18, 1980).

Wilson, R. N.

R. N. Wilson, F. Franzia, P. Giordano, L. Noethe, M. Tarenghi, “Active optics: the NTT and the future,” Messenger (ESO) 53, 1–7 (1988).

Appl. Opt. (5)

Astron. Astrophys. (1)

A. Behr, “A proposal for the alignment of large telescopes,” Astron. Astrophys. 28, 355–358 (1973).

IEEE Trans. Antennas Propag. (1)

D. Morris, “Phase retrieval in the radio holography of reflector antennas and radio telescopes,” IEEE Trans. Antennas Propag. AP-33, 749–755 (1985).
[CrossRef]

J. Opt. Soc. Am. (2)

Messenger (ESO) (1)

R. N. Wilson, F. Franzia, P. Giordano, L. Noethe, M. Tarenghi, “Active optics: the NTT and the future,” Messenger (ESO) 53, 1–7 (1988).

Opt. Commun. (1)

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).
[CrossRef]

Phys. Today (1)

F. Roddier, “Mirror aberration communication,” Phys. Today 43(11), 117 (1990).
[CrossRef]

Other (9)

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992), p. 750.

R. Wilson, “Procedures and formulae for the adjustment of telescopes and analysis of their performance,” memorandum, ESO Telescope Project Division (European Southern Observatory, Garching bei München, Germany, June18, 1980).

N. Roddier, “Algorithms for wave-front reconstruction out of curvature sensing data,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1542, 120–129 (1991).
[CrossRef]

C. Roddier, F. Roddier, A. Stockton, A. Pickles, N. Roddier, “Testing of telescope optics: a new approach,” in Advanced Technology Optical Telescopes IV, D. L. Barr, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.1236, 756–766 (1990).
[CrossRef]

W. H. Press, B. P. Flannery, S. A. Tenkolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988), p. 104.

D. J. Schroeder, Astronomical Optics (Academic, San Diego, 1987), p. 113.

J. C. Fouéré, G. Ratier, “Report on the optical quality of the primary mirror,” (CFHT primary-mirror acceptance test report) (Canada–France–Hawaii Telescope Project Office, Meudon, France, 1978).

In “Modified F/8 secondary gives excellent images,” CFHT Inform. Bull. 10 (Canada–France–Hawaii Telescope Office, Kamuela, Hawaii, 1984), p. 1.

C. Roddier, F. Roddier, “New optical testing methods developed at the University of Hawaii: results on ground-based telescopes and Hubble Space Telescope,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 37–43 (1991).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

In the image space (top), the recorded illuminations I1, and I2 appear as defocused stellar images. In the conjugate object space (bottom), they appear as defocused pupil images.

Fig. 2
Fig. 2

Geometrical scheme showing the distortion introduced in plane Pl by a wave-front slope error in pupil plane P0. The ray that would otherwise go through focus F and cross the plane Pl at point N(u,v) will in fact cross the plane at point N′(u,v).

Fig. 3
Fig. 3

CFHT Cassegrain focus phase map with 15 Zernike terms removed. The contour intervals are 0.02 μm. Gray areas are positive; white areas are negative.

Fig. 4
Fig. 4

Reduction of a coma term introduced in the ESO NTT. From left to right: inside-focus image, outside-focus image, normalized difference between the two images (sensor signal), and domain boundaries; from top to bottom: starting data, data after one iteration, and data after six iterations.

Fig. 5
Fig. 5

Four independent estimates of the ESO NTT mirror figure. Top: residual signal; bottom: associated phase map (15 first Zernike terms removed).

Fig. 6
Fig. 6

ESO NTT mirror figure (15 first Zernike terms removed). Contour plot (top) and cross section (bottom). The cross section was taken on four independent phase maps, along the vertical dashed line shown on the contour plot. The contour plot shows the average phase map. The contour intervals are 0.04 μm. Gray areas are positive; white areas are negative.

Fig. 7
Fig. 7

Coma measured at different field positions at the prime foxus of the NASA/Infrared Telescope. Coordinates are given in CCD pixel units. One pixel corresponds to 0.728 arcsec on the sky. (a) For each field position A, a vector is drawn parallel to the coma, with its origin at point A and its length proportional to the amount of coma. For a perfect measurement all the extremities B should fall at the same point (telescope optical axis); (b) the enlarged portion of the field shows that all the extremities fall within 2.5 pixel of their center of gravity, which indicates a 45-nm peak uncertainty on the coma values.

Fig. 8
Fig. 8

Effect of the secondary-mirror position on spherical aberration. Spherical aberration was measured for two different focus position M and N on the CTIO 4-m telescope (stars). The horizontal scale shows the encoder value for the secondary-mirror position. The dashed line indicates the expected theoretical variation of the spherical aberration as a function of focus position. The best focus position (free from spherical aberration) is found to be at the encoder value 134.

Fig. 9
Fig. 9

Estimated primary-mirror figure of the Hale telescope after removal of 22 Zernike terms. White lines show the mirror honeycomb structure.

Fig. 10
Fig. 10

Point-spread function associated with the phase map shown in Fig. 9.

Fig. 11
Fig. 11

Estimated encircled energies for the CFHT. The curves show our estimate from data taken at the prime focus with coma, astigmatism, and spherical aberrations removed (solid curve) and at the Cassegrain focus with coma removed (dashed curve). The experimental points are from a Shack–Hartmann spot diagram obtained during the primary-mirror acceptance test (asterisks) and later at the Cassegrain focus (crosses).

Tables (4)

Tables Icon

Table 1 Analytic Expression of the First- and Second-Order Terms of the Jacobian of the Trainsformation

Tables Icon

Table 2 Example of Aberrations Retrieved from Simulated Data

Tables Icon

Table 3 Aberrations Retrieved at the ESO NTT with a Known Coma Introduced, along with Results of the ESO Shack–Hartmann Sensor

Tables Icon

Table 4 Mean Difference and rms Dispersion between the ESO Shack–Hartmann Sensor and the Out-of-Focus-Image Method

Equations (20)

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

I / z = - ( I · W + I 2 W ) ,
I = - I 0 n ^ δ c
I z = I 0 W n δ c - I 0 P 2 W ,
I 1 = I 0 - I z Δ z ,
I 2 = I 0 + I z Δ z .
S = I 1 - I 2 I 1 + I 2 = 1 I 0 I z Δ z .
S = ( W n δ c - P 2 W ) Δ z .
( Δ z + f ) l = f 2 .
Δ z = f ( f - l ) l .
S = f ( f - l ) l ( W n δ c - P 2 W ) .
NN : - f - l R | W / x W / y .
δ N : - f ( f - l ) l 1 R 2 | W / x W / y ;
{ x = x + C W ( x , y ) / x y = y + C W ( x , y ) / y ,
C = - f ( f - l ) l 1 R 2 .
I ( x , y ) d 2 N = I ( x , y ) d 2 N = I ( x , y ) J d 2 N ,
J = | x / x x / y y / x y / y | ;
I ( x , y ) / I ( x , y ) = J = | 1 + C 2 W / x 2 C 2 W / x y C 2 W / x y 1 + C 2 W / y 2 | .
I ( x , y ) = I ( x , y ) { 1 + C ( 2 W x 2 + 2 W y 2 ) + C 2 [ 2 W x 2 2 W y 2 - ( 2 W x y ) 2 ] } .
Δ F = 16 ( f / D ) 2 Z 4 .
Z 11 = m ( m 2 - 1 ) 6 × 128 F 3 F p [ 1 + 2 ( m - 1 ) ( m - β ) ] d S ,

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