Abstract

Stellar images taken by the Hubble Space Telescope at various focus positions have been analyzed to estimate wave-front distortion. Rather than using a single algorithm, we found that better results were obtained by combining the advantages of various algorithms. For the planetary camera, the most accurate algorithms consistently gave a spherical aberration of −0.290-μm rms with a maximum deviation of 0.005 μm. Evidence was found that the spherical aberration is essentially produced by the primary mirror. The illumination in the telescope pupil plane was reconstructed and evidence was found for a slight camera misalignment.

© 1993 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. F. Roddier, C. Roddier, N. Roddier, “Curvature sensing: a new wave-front sensing method,” in Statistical Optics, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.976, 203–209 (1988).
  3. C. Roddier, F. Roddier, A. Stockton, A. Pickles, “Testing of telescope optics: a new approach,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. End.1236, 756–766 (1990).
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    [CrossRef]
  6. D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D 6, L6–L9 (1973).
    [CrossRef]
  7. D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics. I: Test calculations,” J. Phys. D 6, 2200–2216 (1973).
    [CrossRef]
  8. D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics. II: Sources of error,” J. Phys. D 6, 2217–2225 (1973).
    [CrossRef]
  9. R. H. Boucher, “Convergence of algorithms for phase retrieval from two intensity distributions,” in 1980 International Optical Computing Conference I, W. T. Rhodes, ed., Proc. Soc. Photo-Opt. Instrum. Eng.231, 130–141 (1980).
  10. D. Morris, “Phase retrieval in the radio holography of reflector antennas and radio telescopes,” IEEE Trans. Antennas Propag. AP-33, 749–755 (1985).
    [CrossRef]
  11. C. Roddier, F. Roddier, “Reconstruction of the Hubble Space Telescope mirror figure from out-of-focus stellar images,” in Space Astronomical Telescopes and Instruments, P. Y. Bely, J. B. Breckinridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1494, 78–84 (1991).
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    [CrossRef]
  13. C. Roddier, F. Roddier, “A combined approach to HST wave-front distortion analysis,” in Space Optics, Vol. 19 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 25–27.
  14. C. Burrows, “Algorithms-preliminary results,” in Proceedings of the First Hubble Aberration Recovery Program Workshop, 15–16 November 1990, R. Korechoff, ed. (Jet Propulsion Laboratory, Pasadena, Calif., 1990), paper 8.
  15. V. N. Mahajan, “Zernike annular polynomials for imaging systems with annular pupils,” J. Opt. Soc. Am. 71, 75–85 (1981).
    [CrossRef]
  16. R. Lyon, P. Miller, “Phase retrieval algorithms and results,” in Proceedings of the First Hubble Aberration Recovery Program Workshop, 15–16 November 1990, R. Korechoff, ed. (Jet Propulsion Laboratory, Pasadena, Calif., 1990), paper 13.
  17. C. Roddier, F. Roddier, “New optical testing methods developed at the University of Hawaii: results on ground-based telescopes and the Hubble Space Telescope,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1531, 37–43 (1991).

1988 (2)

L. M. Kani, J. C. Dainty, “Super-resolution using the Gerchberg algorithm,” Opt. Commun. 68, 11–17 (1988).
[CrossRef]

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

1986 (1)

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]

1981 (1)

1973 (3)

D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D 6, L6–L9 (1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics. I: Test calculations,” J. Phys. D 6, 2200–2216 (1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics. II: Sources of error,” J. Phys. D 6, 2217–2225 (1973).
[CrossRef]

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Boucher, R. H.

R. H. Boucher, “Convergence of algorithms for phase retrieval from two intensity distributions,” in 1980 International Optical Computing Conference I, W. T. Rhodes, ed., Proc. Soc. Photo-Opt. Instrum. Eng.231, 130–141 (1980).

Burrows, C.

C. Burrows, “Algorithms-preliminary results,” in Proceedings of the First Hubble Aberration Recovery Program Workshop, 15–16 November 1990, R. Korechoff, ed. (Jet Propulsion Laboratory, Pasadena, Calif., 1990), paper 8.

Dainty, J. C.

L. M. Kani, J. C. Dainty, “Super-resolution using the Gerchberg algorithm,” Opt. Commun. 68, 11–17 (1988).
[CrossRef]

Fienup, J. R.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Kani, L. M.

L. M. Kani, J. C. Dainty, “Super-resolution using the Gerchberg algorithm,” Opt. Commun. 68, 11–17 (1988).
[CrossRef]

Lyon, R.

R. Lyon, P. Miller, “Phase retrieval algorithms and results,” in Proceedings of the First Hubble Aberration Recovery Program Workshop, 15–16 November 1990, R. Korechoff, ed. (Jet Propulsion Laboratory, Pasadena, Calif., 1990), paper 13.

Mahajan, V. N.

Miller, P.

R. Lyon, P. Miller, “Phase retrieval algorithms and results,” in Proceedings of the First Hubble Aberration Recovery Program Workshop, 15–16 November 1990, R. Korechoff, ed. (Jet Propulsion Laboratory, Pasadena, Calif., 1990), paper 13.

Misell, D. L.

D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D 6, L6–L9 (1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics. I: Test calculations,” J. Phys. D 6, 2200–2216 (1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics. II: Sources of error,” J. Phys. D 6, 2217–2225 (1973).
[CrossRef]

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]

Pickles, A.

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

Roddier, C.

F. Roddier, C. Roddier, N. Roddier, “Curvature sensing: a new wave-front sensing method,” in Statistical Optics, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.976, 203–209 (1988).

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

C. Roddier, F. Roddier, “Reconstruction of the Hubble Space Telescope mirror figure from out-of-focus stellar images,” in Space Astronomical Telescopes and Instruments, P. Y. Bely, J. B. Breckinridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1494, 78–84 (1991).

C. Roddier, F. Roddier, “A combined approach to HST wave-front distortion analysis,” in Space Optics, Vol. 19 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 25–27.

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

Roddier, F.

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

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

C. Roddier, F. Roddier, “A combined approach to HST wave-front distortion analysis,” in Space Optics, Vol. 19 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 25–27.

C. Roddier, F. Roddier, “Reconstruction of the Hubble Space Telescope mirror figure from out-of-focus stellar images,” in Space Astronomical Telescopes and Instruments, P. Y. Bely, J. B. Breckinridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1494, 78–84 (1991).

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

F. Roddier, C. Roddier, N. Roddier, “Curvature sensing: a new wave-front sensing method,” in Statistical Optics, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.976, 203–209 (1988).

Roddier, N.

F. Roddier, C. Roddier, N. Roddier, “Curvature sensing: a new wave-front sensing method,” in Statistical Optics, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.976, 203–209 (1988).

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Stockton, A.

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

Wackerman, C. C.

Appl. Opt. (1)

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. (1)

J. Opt. Soc. Am. A (1)

J. Phys. D (3)

D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D 6, L6–L9 (1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics. I: Test calculations,” J. Phys. D 6, 2200–2216 (1973).
[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics. II: Sources of error,” J. Phys. D 6, 2217–2225 (1973).
[CrossRef]

Opt. Commun. (1)

L. M. Kani, J. C. Dainty, “Super-resolution using the Gerchberg algorithm,” Opt. Commun. 68, 11–17 (1988).
[CrossRef]

Optik (Stuttgart) (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Other (8)

R. Lyon, P. Miller, “Phase retrieval algorithms and results,” in Proceedings of the First Hubble Aberration Recovery Program Workshop, 15–16 November 1990, R. Korechoff, ed. (Jet Propulsion Laboratory, Pasadena, Calif., 1990), paper 13.

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

C. Roddier, F. Roddier, “Reconstruction of the Hubble Space Telescope mirror figure from out-of-focus stellar images,” in Space Astronomical Telescopes and Instruments, P. Y. Bely, J. B. Breckinridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1494, 78–84 (1991).

C. Roddier, F. Roddier, “A combined approach to HST wave-front distortion analysis,” in Space Optics, Vol. 19 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 25–27.

C. Burrows, “Algorithms-preliminary results,” in Proceedings of the First Hubble Aberration Recovery Program Workshop, 15–16 November 1990, R. Korechoff, ed. (Jet Propulsion Laboratory, Pasadena, Calif., 1990), paper 8.

F. Roddier, C. Roddier, N. Roddier, “Curvature sensing: a new wave-front sensing method,” in Statistical Optics, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.976, 203–209 (1988).

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

R. H. Boucher, “Convergence of algorithms for phase retrieval from two intensity distributions,” in 1980 International Optical Computing Conference I, W. T. Rhodes, ed., Proc. Soc. Photo-Opt. Instrum. Eng.231, 130–141 (1980).

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Figures (23)

Fig. 1
Fig. 1

Flow chart of the modified Misell algorithm.

Fig. 2
Fig. 2

Ray tracing showing the effect of spherical aberration at the focal plane of the Hubble Space Telescope (courtesy A. Vaughan). The modified Misell algorithm was applied to images labeled (1), (2), (3) taken at 0.487 μm at secondary mirror positions of +250, −90, and −260.

Fig. 3
Fig. 3

Example of pupil image reconstructed from a single Gerchberg–Saxton iteration.

Fig. 4
Fig. 4

Reconstructed wave-front surface showing wave-front error residuals after removal of the spherical aberration.

Fig. 5
Fig. 5

Linear regression showing the observed defocus terms in micrometers rms as a function of the secondary mirror position in micrometers. Data taken at 0.487 μm (crosses), 0.889 μm (squares), and 0.631 μm(triangles).

Fig. 6
Fig. 6

Star image positions actually measured (dots) and estimated from reconstructed pupil configurations (crosses with error boxes).

Fig. 7
Fig. 7

Image w33410 as observed.

Fig. 8
Fig. 8

Image w33410 as computed from the model.

Fig. 9
Fig. 9

Comparison between observed (dotted curve) and computed (solid curve) image w33410. The horizontal scale is in arcseconds.

Fig. 10
Fig. 10

Image w29822 as observed.

Fig. 11
Fig. 11

Image w29822 as computed from the model.

Fig. 12
Fig. 12

Comparison between observed (dotted curve) and computed (solid curve) image w29822. The horizontal scale is in arcseconds.

Fig. 13
Fig. 13

Comparison between observed (dotted curve) and computed solid curve) image w22718. The computed image is either unblurred (left) or blurred (right). The horizontal scale is in arcseconds.

Fig. 14
Fig. 14

Image w30014 as observed.

Fig. 15
Fig. 15

Image w30014 as directly computed from the model.

Fig. 16
Fig. 16

Image w30014 as computed from the model with additional blur to simulate the effect of telescope jitter.

Fig. 17
Fig. 17

Secondary mirror x slopes estimated from wave-front differences.

Fig. 18
Fig. 18

Secondary mirror y slopes estimated from wave-front differences.

Fig. 19
Fig. 19

Secondary mirror figure reconstructed from the slopes shown in Figs. 17 and 18.

Fig. 20
Fig. 20

Contour plots Showing the difference N1 between the observed and the computed images as a function of Z11 and Z4, with (left) and without (right) taking telescope jitter into account. The top row shows simulations with a black dot at the correct values.

Fig. 21
Fig. 21

Z11 and Z4 estimated at focus position −260 with norms N1 (triangles), N2 (stars), and N3 (crosses) for various levels of blur in the observed and computed images (see text). The black dot shows the exact Z11 and Z4 values for simulations (left two columns).

Fig. 22
Fig. 22

Z11 and Z4 estimated at focus position −90 with norms N1 (triangles), N2 (stars), and N3 (crosses) for various levels of blur in the observed and computed images (see text). The black dot shows the exact Z11 and Z4 values for simulations (left two columns).

Fig. 23
Fig. 23

Z11 and Z4 estimated at focus position +250 with norms N1 (triangles), N2 (stars), and N3 (crosses) for various levels of blur in the observed and computed images (see text). The black dot shows the exact Z11 and Z4 values for simulations (left two columns).

Tables (5)

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Table 1 Hubble Space Telescope Data Used In This Study

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Table 2 Camera Pupil Offset as a Function of Star Coordinates

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Table 3 Location of the Three Clamps Holding the Primary Mirror

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Table 4 Image Pairs Shifted in the x Direction

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Table 5 Image Pairs Shifted in the y Direction

Equations (1)

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N 1 = Σ I - S , N 2 = [ Σ ( I - S ) 2 ] 1 / 2 , N 3 = Σ ( I - S ) 2 ,

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