Abstract

We describe a novel method for phasing segmented optics in which the signal is the difference between inside-of-focus and outside-of-focus long-exposure infrared images. A detailed algorithm based on a correlation of this difference image with theoretical images or templates is presented. In a series of tests of this phase discontinuity sensing (PDS) algorithm at the Keck 1 telescope, at a wavelength of 3.3 µm, the rms piston error (averaged over the 36 primary mirror segments) was repeatedly reduced from approximately 240 to 40 nm or less. Furthermore, the PDS phasing solution was consistent with our previous phasing camera results (to within 66-nm rms), providing strong independent confirmation of this earlier approach.

© 1999 Optical Society of America

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  1. G. A. Chanan, M. Troy, F. G. Dekens, S. Michaels, J. Nelson, T. Mast, D. Kirkman, “Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998).
    [CrossRef]
  2. G. A. Chanan, J. E. Nelson, T. S. Mast, P. L. Wizinowich, B. Schaefer, “W. M. Keck Telescope phasing camera system,” in Instrumentation in Astronomy VIII, D. L. Crawford, E. R. Craine, eds., Proc. SPIE2198, 1139–1150 (1994).
    [CrossRef]
  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. SPIE1531, 37–43 (1991).
    [CrossRef]
  4. T. K. Korhonen, “Interferometric method for optical testing and wavefront error sensing,” in Advanced Technology Optical Telescopes II, L. D. Barr, B. Mack, eds., Proc. SPIE444, 249–252 (1983).
    [CrossRef]
  5. F. Roddier, “Curvature sensing and compensation: a new concept in adaptive optics,” Appl. Opt. 27, 1223–1225 (1988).
    [CrossRef] [PubMed]
  6. F. Roddier, “Wavefront sensing and the irradiance transport equation,” Appl. Opt. 29, 1402–1403 (1990).
    [CrossRef] [PubMed]
  7. N. Roddier, “Algorithms for wavefront reconstruction out of curvature sensing data,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE1542, 120–129 (1991).
    [CrossRef]
  8. D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,” J. Opt. Soc. Am. 56, 1372–1384 (1966).
    [CrossRef]
  9. F. Dekens, “Atmospheric characterization for adaptive optics at the W. M. Keck and Hale Telescopes,” Ph.D. dissertation (University of California, Irvine, Irvine, Calif., 1998).
  10. J. E. Nelson, P. R. Gillingham, “Overview of the performance of the W. M. Keck Observatory,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 92–93 (1994).
  11. K. Matthews, B. T. Soifer, “The near infrared camera on the W. M. Keck Telescope,” in Infrared Astronomy with Arrays: the Next Generation, I. S. McLean, ed. (Kluwer Academic, Boston, Mass., 1994), pp. 239–246.
    [CrossRef]
  12. G. Chanan, G. Djorgovski, A. Gleckler, S. Kulkarni, T. Mast, C. Max, J. Nelson, P. Wizinowich, “Adaptive optics for Keck Observatory,” (W. M. Keck Observatory, Kamuela, Hawaii, 1996).
  13. W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1989), pp. 484–487.
  14. P. L. Wizinowich, T. S. Mast, J. E. Nelson, M. DiVittorio, G. A. Chanan, “Optical quality of the W. M. Keck Observatory,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 94–104 (1994).
    [CrossRef]

1998 (1)

1990 (1)

1988 (1)

1966 (1)

Chanan, G.

G. Chanan, G. Djorgovski, A. Gleckler, S. Kulkarni, T. Mast, C. Max, J. Nelson, P. Wizinowich, “Adaptive optics for Keck Observatory,” (W. M. Keck Observatory, Kamuela, Hawaii, 1996).

Chanan, G. A.

G. A. Chanan, M. Troy, F. G. Dekens, S. Michaels, J. Nelson, T. Mast, D. Kirkman, “Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998).
[CrossRef]

P. L. Wizinowich, T. S. Mast, J. E. Nelson, M. DiVittorio, G. A. Chanan, “Optical quality of the W. M. Keck Observatory,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 94–104 (1994).
[CrossRef]

G. A. Chanan, J. E. Nelson, T. S. Mast, P. L. Wizinowich, B. Schaefer, “W. M. Keck Telescope phasing camera system,” in Instrumentation in Astronomy VIII, D. L. Crawford, E. R. Craine, eds., Proc. SPIE2198, 1139–1150 (1994).
[CrossRef]

Dekens, F.

F. Dekens, “Atmospheric characterization for adaptive optics at the W. M. Keck and Hale Telescopes,” Ph.D. dissertation (University of California, Irvine, Irvine, Calif., 1998).

Dekens, F. G.

DiVittorio, M.

P. L. Wizinowich, T. S. Mast, J. E. Nelson, M. DiVittorio, G. A. Chanan, “Optical quality of the W. M. Keck Observatory,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 94–104 (1994).
[CrossRef]

Djorgovski, G.

G. Chanan, G. Djorgovski, A. Gleckler, S. Kulkarni, T. Mast, C. Max, J. Nelson, P. Wizinowich, “Adaptive optics for Keck Observatory,” (W. M. Keck Observatory, Kamuela, Hawaii, 1996).

Flannery, B.

W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1989), pp. 484–487.

Fried, D. L.

Gillingham, P. R.

J. E. Nelson, P. R. Gillingham, “Overview of the performance of the W. M. Keck Observatory,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 92–93 (1994).

Gleckler, A.

G. Chanan, G. Djorgovski, A. Gleckler, S. Kulkarni, T. Mast, C. Max, J. Nelson, P. Wizinowich, “Adaptive optics for Keck Observatory,” (W. M. Keck Observatory, Kamuela, Hawaii, 1996).

Kirkman, D.

Korhonen, T. K.

T. K. Korhonen, “Interferometric method for optical testing and wavefront error sensing,” in Advanced Technology Optical Telescopes II, L. D. Barr, B. Mack, eds., Proc. SPIE444, 249–252 (1983).
[CrossRef]

Kulkarni, S.

G. Chanan, G. Djorgovski, A. Gleckler, S. Kulkarni, T. Mast, C. Max, J. Nelson, P. Wizinowich, “Adaptive optics for Keck Observatory,” (W. M. Keck Observatory, Kamuela, Hawaii, 1996).

Mast, T.

G. A. Chanan, M. Troy, F. G. Dekens, S. Michaels, J. Nelson, T. Mast, D. Kirkman, “Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998).
[CrossRef]

G. Chanan, G. Djorgovski, A. Gleckler, S. Kulkarni, T. Mast, C. Max, J. Nelson, P. Wizinowich, “Adaptive optics for Keck Observatory,” (W. M. Keck Observatory, Kamuela, Hawaii, 1996).

Mast, T. S.

G. A. Chanan, J. E. Nelson, T. S. Mast, P. L. Wizinowich, B. Schaefer, “W. M. Keck Telescope phasing camera system,” in Instrumentation in Astronomy VIII, D. L. Crawford, E. R. Craine, eds., Proc. SPIE2198, 1139–1150 (1994).
[CrossRef]

P. L. Wizinowich, T. S. Mast, J. E. Nelson, M. DiVittorio, G. A. Chanan, “Optical quality of the W. M. Keck Observatory,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 94–104 (1994).
[CrossRef]

Matthews, K.

K. Matthews, B. T. Soifer, “The near infrared camera on the W. M. Keck Telescope,” in Infrared Astronomy with Arrays: the Next Generation, I. S. McLean, ed. (Kluwer Academic, Boston, Mass., 1994), pp. 239–246.
[CrossRef]

Max, C.

G. Chanan, G. Djorgovski, A. Gleckler, S. Kulkarni, T. Mast, C. Max, J. Nelson, P. Wizinowich, “Adaptive optics for Keck Observatory,” (W. M. Keck Observatory, Kamuela, Hawaii, 1996).

Michaels, S.

Nelson, J.

G. A. Chanan, M. Troy, F. G. Dekens, S. Michaels, J. Nelson, T. Mast, D. Kirkman, “Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998).
[CrossRef]

G. Chanan, G. Djorgovski, A. Gleckler, S. Kulkarni, T. Mast, C. Max, J. Nelson, P. Wizinowich, “Adaptive optics for Keck Observatory,” (W. M. Keck Observatory, Kamuela, Hawaii, 1996).

Nelson, J. E.

G. A. Chanan, J. E. Nelson, T. S. Mast, P. L. Wizinowich, B. Schaefer, “W. M. Keck Telescope phasing camera system,” in Instrumentation in Astronomy VIII, D. L. Crawford, E. R. Craine, eds., Proc. SPIE2198, 1139–1150 (1994).
[CrossRef]

P. L. Wizinowich, T. S. Mast, J. E. Nelson, M. DiVittorio, G. A. Chanan, “Optical quality of the W. M. Keck Observatory,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 94–104 (1994).
[CrossRef]

J. E. Nelson, P. R. Gillingham, “Overview of the performance of the W. M. Keck Observatory,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 92–93 (1994).

Press, W.

W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1989), pp. 484–487.

Roddier, C.

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. SPIE1531, 37–43 (1991).
[CrossRef]

Roddier, F.

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, “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. SPIE1531, 37–43 (1991).
[CrossRef]

Roddier, N.

N. Roddier, “Algorithms for wavefront reconstruction out of curvature sensing data,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE1542, 120–129 (1991).
[CrossRef]

Schaefer, B.

G. A. Chanan, J. E. Nelson, T. S. Mast, P. L. Wizinowich, B. Schaefer, “W. M. Keck Telescope phasing camera system,” in Instrumentation in Astronomy VIII, D. L. Crawford, E. R. Craine, eds., Proc. SPIE2198, 1139–1150 (1994).
[CrossRef]

Soifer, B. T.

K. Matthews, B. T. Soifer, “The near infrared camera on the W. M. Keck Telescope,” in Infrared Astronomy with Arrays: the Next Generation, I. S. McLean, ed. (Kluwer Academic, Boston, Mass., 1994), pp. 239–246.
[CrossRef]

Teukolsky, S.

W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1989), pp. 484–487.

Troy, M.

Vetterling, W.

W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1989), pp. 484–487.

Wizinowich, P.

G. Chanan, G. Djorgovski, A. Gleckler, S. Kulkarni, T. Mast, C. Max, J. Nelson, P. Wizinowich, “Adaptive optics for Keck Observatory,” (W. M. Keck Observatory, Kamuela, Hawaii, 1996).

Wizinowich, P. L.

G. A. Chanan, J. E. Nelson, T. S. Mast, P. L. Wizinowich, B. Schaefer, “W. M. Keck Telescope phasing camera system,” in Instrumentation in Astronomy VIII, D. L. Crawford, E. R. Craine, eds., Proc. SPIE2198, 1139–1150 (1994).
[CrossRef]

P. L. Wizinowich, T. S. Mast, J. E. Nelson, M. DiVittorio, G. A. Chanan, “Optical quality of the W. M. Keck Observatory,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 94–104 (1994).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

Other (10)

G. A. Chanan, J. E. Nelson, T. S. Mast, P. L. Wizinowich, B. Schaefer, “W. M. Keck Telescope phasing camera system,” in Instrumentation in Astronomy VIII, D. L. Crawford, E. R. Craine, eds., Proc. SPIE2198, 1139–1150 (1994).
[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. SPIE1531, 37–43 (1991).
[CrossRef]

T. K. Korhonen, “Interferometric method for optical testing and wavefront error sensing,” in Advanced Technology Optical Telescopes II, L. D. Barr, B. Mack, eds., Proc. SPIE444, 249–252 (1983).
[CrossRef]

F. Dekens, “Atmospheric characterization for adaptive optics at the W. M. Keck and Hale Telescopes,” Ph.D. dissertation (University of California, Irvine, Irvine, Calif., 1998).

J. E. Nelson, P. R. Gillingham, “Overview of the performance of the W. M. Keck Observatory,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 92–93 (1994).

K. Matthews, B. T. Soifer, “The near infrared camera on the W. M. Keck Telescope,” in Infrared Astronomy with Arrays: the Next Generation, I. S. McLean, ed. (Kluwer Academic, Boston, Mass., 1994), pp. 239–246.
[CrossRef]

G. Chanan, G. Djorgovski, A. Gleckler, S. Kulkarni, T. Mast, C. Max, J. Nelson, P. Wizinowich, “Adaptive optics for Keck Observatory,” (W. M. Keck Observatory, Kamuela, Hawaii, 1996).

W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1989), pp. 484–487.

P. L. Wizinowich, T. S. Mast, J. E. Nelson, M. DiVittorio, G. A. Chanan, “Optical quality of the W. M. Keck Observatory,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 94–104 (1994).
[CrossRef]

N. Roddier, “Algorithms for wavefront reconstruction out of curvature sensing data,” in Active and Adaptive Optical Systems, M. A. Ealey, ed., Proc. SPIE1542, 120–129 (1991).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Primary mirror of the Keck telescope, showing the segment geometry and numbering scheme.

Fig. 2
Fig. 2

Numerically generated difference images at 3.3 µm across the diameter of a dephased Keck telescope. The piston errors were drawn from a flat distribution between +400 and -400 nm. The solid curve corresponds to r 0(0.5 µm) = 20 cm; the dashed curve corresponds to r 0(0.5 µm) = 10 cm. The difference image depends fairly sensitively on r 0 under these circumstances.

Fig. 3
Fig. 3

Numerically generated out-of-focus image of a perfectly phased Keck mirror, with parameters as in Table 1.

Fig. 4
Fig. 4

Numerically generated out-of-focus image of the Keck telescope with segment 13 pistoned by λ/8. Note that the resulting diffraction effects are well localized at a position that has an obvious correspondence with the position of the segment in the pupil (Fig. 1).

Fig. 5
Fig. 5

Upper curve is the piston error as calculated from the correlation coefficient [Eq. (10)] versus the true piston error. The straight line of unit slope is drawn for reference. The lower curve is 0.7 times the upper curve. This lower curve provides a useful estimate of the piston error for purposes of the algorithm because it is accurate at small piston errors and underestimates the desired correction for large errors. This deliberate undershoot stabilizes the algorithm.

Fig. 6
Fig. 6

(a) Typical initial piston error configuration corresponding to a flat distribution of errors from -λ/8 to +λ/8 (-400 to +400 nm). (b) The corresponding numerically generated out-of-focus image.

Fig. 7
Fig. 7

Same as Fig. 6 but after a ten-iteration simulation of the PDS algorithm. Note the change in scale.

Fig. 8
Fig. 8

(a) Initial out-of-focus image (actual data) for the trial Random1 in Table 2. (b) The same as (a) but from numerically generated data. (This random mirror configuration is the same as the initial configuration used in the simulation of Fig. 6.) The close correspondence between (a) and (b) confirms that PDS converges to the correct phasing solution.

Fig. 9
Fig. 9

Upper curve is the residual piston error as a function of iteration number for the trial Random1 in Table 2. The lower curve is the same as the upper curve, and for the same initial configuration of piston errors, but for numerically generated data. Note that the numerical data (which exclude the effects of detector noise, segment aberrations, etc.) converge only slightly faster than the real sequence.

Tables (2)

Tables Icon

Table 1 Instrumental and Observing Parameters

Tables Icon

Table 2 Summary of the Phase Discontinuity Sensing Runs

Equations (11)

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

S=I+-I-I++I-.
Aˆω= expikρ·ω+2ikεdxdy,
ε±=εlρ24f2,
Sω, kδ=sin2kδSω, π/4.
fλD  Dlf.
r0λ  D.
λ  λ0Dr0λ05/6.
λD  s206265,
Δa=206265mλNs.
p=λ8 cη, ξ,
cη, ξ=Σηij-η¯ξij-ξ¯Σξij-ξ¯2.

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