Abstract

In a previous paper, we described a successful technique, the broadband algorithm, for phasing the primary mirror segments of the Keck telescopes to an accuracy of 30 nm. Here we describe a complementary narrow-band algorithm. Although it has a limited dynamic range, it is much faster than the broadband algorithm and can achieve an unprecedented phasing accuracy of approximately 6 nm. Cross checks between these two independent techniques validate both methods to a high degree of confidence. Both algorithms converge to the edge-minimizing configuration of the segmented primary mirror, which is not the same as the overall wave-front-error-minimizing configuration, but we demonstrate that this distinction disappears as the segment aberrations are reduced to zero.

© 2000 Optical Society of America

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References

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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) [Paper 1].
  2. G. A. Chanan, M. Troy, “Strehl ratio and modulation transfer function for segmented mirror telescopes as functions of segment phase error,” Appl. Opt. 38, 6642–6647 (1999).
    [CrossRef]
  3. J. E. Nelson, T. S. Mast, S. M. Faber, “The design of the Keck Observatory and Telescope,” (W. M. Keck Observatory, Kamuela, Hawaii1985).
  4. R. W. Cohen, T. S. Mast, J. E. Nelson, “Performance of the W. M. Keck Telescope active mirror control system,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 105–116 (1994).
    [CrossRef]
  5. G. A. Chanan, T. S. Mast, J. E. Nelson, “Keck telescope primary mirror segments: initial alignment and active control,” in European Southern Observatory Conference on Very Large Telescopes and their Instrumentation, M.-H. Ulrich, ed. (Garching, Germany, 1988), pp. 421–428.
  6. G. A. Chanan, J. Nelson, T. Mast, P. Wizinowich, B. Schaefer, “The 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]
  7. G. A. Chanan, “Design of the Keck Observatory alignment camera,” in Precision Instrument Design, T. C. Bristow, A. E. Hatheway, eds., Proc. SPIE1036, 59–70 (1988).
    [CrossRef]
  8. W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, New York, 1989), pp. 484–487.
  9. W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, New York, 1989), pp. 52–64, 515–520.
  10. M. G. Lofdahl, H. Eriksson, “Resolving piston ambiguities when phasing a segmented mirror,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE 4013 (to be published).
  11. J. E. Nelson, Lick Observatory, University of California, Santa Cruz, Calif. 95064 (personal communication, 1998).

1999 (1)

1998 (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) [Paper 1].

Chanan, G. A.

G. A. Chanan, M. Troy, “Strehl ratio and modulation transfer function for segmented mirror telescopes as functions of segment phase error,” Appl. Opt. 38, 6642–6647 (1999).
[CrossRef]

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) [Paper 1].

G. A. Chanan, T. S. Mast, J. E. Nelson, “Keck telescope primary mirror segments: initial alignment and active control,” in European Southern Observatory Conference on Very Large Telescopes and their Instrumentation, M.-H. Ulrich, ed. (Garching, Germany, 1988), pp. 421–428.

G. A. Chanan, J. Nelson, T. Mast, P. Wizinowich, B. Schaefer, “The 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]

G. A. Chanan, “Design of the Keck Observatory alignment camera,” in Precision Instrument Design, T. C. Bristow, A. E. Hatheway, eds., Proc. SPIE1036, 59–70 (1988).
[CrossRef]

Cohen, R. W.

R. W. Cohen, T. S. Mast, J. E. Nelson, “Performance of the W. M. Keck Telescope active mirror control system,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 105–116 (1994).
[CrossRef]

Dekens, F. G.

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) [Paper 1].

Eriksson, H.

M. G. Lofdahl, H. Eriksson, “Resolving piston ambiguities when phasing a segmented mirror,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE 4013 (to be published).

Faber, S. M.

J. E. Nelson, T. S. Mast, S. M. Faber, “The design of the Keck Observatory and Telescope,” (W. M. Keck Observatory, Kamuela, Hawaii1985).

Flannery, B.

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

W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, New York, 1989), pp. 52–64, 515–520.

Kirkman, D.

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) [Paper 1].

Lofdahl, M. G.

M. G. Lofdahl, H. Eriksson, “Resolving piston ambiguities when phasing a segmented mirror,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE 4013 (to be published).

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) [Paper 1].

G. A. Chanan, J. Nelson, T. Mast, P. Wizinowich, B. Schaefer, “The 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]

Mast, T. S.

R. W. Cohen, T. S. Mast, J. E. Nelson, “Performance of the W. M. Keck Telescope active mirror control system,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 105–116 (1994).
[CrossRef]

J. E. Nelson, T. S. Mast, S. M. Faber, “The design of the Keck Observatory and Telescope,” (W. M. Keck Observatory, Kamuela, Hawaii1985).

G. A. Chanan, T. S. Mast, J. E. Nelson, “Keck telescope primary mirror segments: initial alignment and active control,” in European Southern Observatory Conference on Very Large Telescopes and their Instrumentation, M.-H. Ulrich, ed. (Garching, Germany, 1988), pp. 421–428.

Michaels, S.

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) [Paper 1].

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) [Paper 1].

G. A. Chanan, J. Nelson, T. Mast, P. Wizinowich, B. Schaefer, “The 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]

Nelson, J. E.

G. A. Chanan, T. S. Mast, J. E. Nelson, “Keck telescope primary mirror segments: initial alignment and active control,” in European Southern Observatory Conference on Very Large Telescopes and their Instrumentation, M.-H. Ulrich, ed. (Garching, Germany, 1988), pp. 421–428.

J. E. Nelson, T. S. Mast, S. M. Faber, “The design of the Keck Observatory and Telescope,” (W. M. Keck Observatory, Kamuela, Hawaii1985).

R. W. Cohen, T. S. Mast, J. E. Nelson, “Performance of the W. M. Keck Telescope active mirror control system,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 105–116 (1994).
[CrossRef]

J. E. Nelson, Lick Observatory, University of California, Santa Cruz, Calif. 95064 (personal communication, 1998).

Press, W.

W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, New York, 1989), pp. 52–64, 515–520.

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

Schaefer, B.

G. A. Chanan, J. Nelson, T. Mast, P. Wizinowich, B. Schaefer, “The 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]

Teukolsky, S.

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

W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, New York, 1989), pp. 52–64, 515–520.

Troy, M.

G. A. Chanan, M. Troy, “Strehl ratio and modulation transfer function for segmented mirror telescopes as functions of segment phase error,” Appl. Opt. 38, 6642–6647 (1999).
[CrossRef]

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) [Paper 1].

Vetterling, W.

W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, New York, 1989), pp. 52–64, 515–520.

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

Wizinowich, P.

G. A. Chanan, J. Nelson, T. Mast, P. Wizinowich, B. Schaefer, “The 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]

Appl. Opt. (2)

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) [Paper 1].

G. A. Chanan, M. Troy, “Strehl ratio and modulation transfer function for segmented mirror telescopes as functions of segment phase error,” Appl. Opt. 38, 6642–6647 (1999).
[CrossRef]

Other (9)

J. E. Nelson, T. S. Mast, S. M. Faber, “The design of the Keck Observatory and Telescope,” (W. M. Keck Observatory, Kamuela, Hawaii1985).

R. W. Cohen, T. S. Mast, J. E. Nelson, “Performance of the W. M. Keck Telescope active mirror control system,” in Advanced Technology Optical Telescopes V, L. M. Stepp, ed., Proc. SPIE2199, 105–116 (1994).
[CrossRef]

G. A. Chanan, T. S. Mast, J. E. Nelson, “Keck telescope primary mirror segments: initial alignment and active control,” in European Southern Observatory Conference on Very Large Telescopes and their Instrumentation, M.-H. Ulrich, ed. (Garching, Germany, 1988), pp. 421–428.

G. A. Chanan, J. Nelson, T. Mast, P. Wizinowich, B. Schaefer, “The 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]

G. A. Chanan, “Design of the Keck Observatory alignment camera,” in Precision Instrument Design, T. C. Bristow, A. E. Hatheway, eds., Proc. SPIE1036, 59–70 (1988).
[CrossRef]

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

W. Press, B. Flannery, S. Teukolsky, W. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, New York, 1989), pp. 52–64, 515–520.

M. G. Lofdahl, H. Eriksson, “Resolving piston ambiguities when phasing a segmented mirror,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE 4013 (to be published).

J. E. Nelson, Lick Observatory, University of California, Santa Cruz, Calif. 95064 (personal communication, 1998).

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Figures (7)

Fig. 1
Fig. 1

Geometry of the primary mirror of the Keck telescopes, showing the 78 circular subapertures that sample the intersegment edges in the phasing procedure. Each segment is 0.9 m on a side. The subapertures are 12 cm in diameter. The 35 peripheral subapertures are used for pupil registration. The six subapertures on the innermost edges (not shown) are obscured by the tertiary mirror and secondary baffles and are not used in the phasing procedure.

Fig. 2
Fig. 2

Theoretical diffraction patterns (monochromatic light) for a split circular subaperture of radius a with a physical step δ between the two halves given by kδ = 0, π/11, 2π/11, … , 10π/11. The boxes are 15/ka rad on a side.

Fig. 3
Fig. 3

Measured narrow-band edge height (at a single wavelength of 852 nm) versus edge height predicted from the previous broadband phasing run for a series of eight narrow-band phasing runs taken during the night of 25–26 August 1999 on Keck 1. The rss of the differences between corresponding measurements is 19 nm. Agreement of each individual pair of measurements to within ±100 nm (dashed lines) is necessary to insure against aliasing errors in the narrow-band measurements.

Fig. 4
Fig. 4

Two-wavelength narrow-band edge-height measurements (Keck 1, 25–26 August 1999) interpreted as two single-wavelength measurements (at 852 and 651 nm) as a consistency check. The RSS of the differences between corresponding measurements is 12 nm; this implies a phasing accuracy of 6 nm (for single-wavelength phasing), which is approximately what is achieved. Agreement of the individual measurements to within ±50 nm (dashed lines) is necessary to insure the correct two-wavelength solution. Only three points (squares) out of 624 lie outside of this range.

Fig. 5
Fig. 5

(a) Measured two-wavelength narrow-band edge height [from Eqs. (15) and (16)] versus edge height predicted from the previous broadband phasing run (Keck 1, 25–26 August 1999). The two wavelengths were 852 and 651 nm. The RSS of the differences between corresponding measurements is 29 nm. As predicted, the three discrepant measurements of Fig. 4 (shown again as squares) yield incorrect solutions. (b) Same as (a), except with discrepant measurements corrected as described in the text. The RSS of the differences is now 16 nm.

Fig. 6
Fig. 6

Residual edge height (after phasing) for the 78 intersegment edges for a series of 43 narrow-band phasing runs on Keck 1. Error bars represent the rms variation from run to run (not the error on the mean). The fact that the variations are small shows that the residuals result principally from (fixed) segment aberrations, rather than from random errors in tip-tilt alignment or phasing.

Fig. 7
Fig. 7

Close-up of narrow-band phasing CCD image (a) for nominal phased configuration and (b) for simulated perfect segments. Note the much more uniformly symmetric appearance of the subimages in (b). The elliptical subimage at the lower right in both images is used for pupil alignment and does not contain phasing information.

Tables (2)

Tables Icon

Table 1 Keck 1 One-Filter Narrow-Band Phasing Results from 25–26 August 1999

Tables Icon

Table 2 Keck 1 Two-Filter Narrow-Band Phasing Results from 25–26 August 1999

Equations (21)

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S=1+exp-σ2n-1n,
fρ; kδ=expikδη0; ρaexp-ikδη<0; ρa0ρ>a,
fˆw; kδ=2πa20π0a coskδ+kρ·wρdρdθ,
Iw; kδ=fˆ2w; kδ.
Iw; kδ=cos kδ fˆw; 0+sin kδ fˆw; π/22,
fˆw; 0=2a20a J0kρwρdρ,
Iw; 0=2J1kawkaw2,
fˆ(w; π2=-2πa20π0a sinkρ·wρdρdθ
=2π0πu cos u-sin uu2dθ,
y=-163πδa
r=ixi-x¯yi-y¯ixi-x¯21/2iyi-y¯21/2.
pij-pij=δj;  j=1, , 78,
i pi=0;  i=1, , 36.
Δδj=δj-pij*-pij*,
h=z1+1/2mλ1,
h=z2+1/2nλ2.
δz=1/2mλ1-nλ2,
1<λ2λ1<32
j+1j<λ2λ1<jj-1.
-jλ14<h<jλ14   for j odd
-j-1λ24<h<j-1λ24,  for j even.

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