Abstract

Dispersed fringe sensing (DFS) is an efficient and robust method for coarse phasing of segmented primary mirrors (from one quarter of a wavelength to as much as the depth of focus of a single segment, typically several tens of microns). Unlike phasing techniques currently used for ground-based segmented telescopes, DFS does not require the use of edge sensors in order to sense changes in the relative heights of adjacent segments; this makes it particularly well suited for phasing of space-borne segmented telescopes, such as the James Webb Space Telescope. We validate DFS by using it to measure the piston errors of the segments of one of the Keck telescopes. The results agree with those of the Shack-Hartmann-based phasing scheme currently in use at Keck to within 2% over a range of initial piston errors of ±16 μm.

© 2004 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).
    [CrossRef]
  2. G. A. Chanan, C. Ohara, M. Troy, “Phasing the mirror segments of the Keck telescopes II: the narrow-band phasing algorithm,” Appl. Opt. 39, 4706–4714 (2000).
    [CrossRef]
  3. G. Chanan, M. Troy, E. Sirko, “Phase discontinuity sensing: a method for phasing segmented mirrors in the infrared,” Appl. Opt. 38, 704–713 (1999).
    [CrossRef]
  4. F. Shi, D. C. Redding, C. W. Bowers, A. E. Lowman, S. A. Basinger, T. A. Norton, P. Petrone, P. S. Davila, M. E. Wilson, R. A. Boucarut, “DCATT dispersed fringe sensor: modeling and experimenting with the transmissive phase plates,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 757–762 (2000).
    [CrossRef]
  5. F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiments on NGST’s Wavefront Control Testbed,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 318–328 (2002).
    [CrossRef]
  6. 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]
  7. J. E. Nelson, T. S. Mast, S. M. Faber, “The design of the Keck Observatory and Telescope,” Keck Observatory Report 90 (W. M. Keck Observatory, Kamuela, Hawaii, 1985).

2000 (1)

1999 (1)

1998 (1)

Basinger, S. A.

F. Shi, D. C. Redding, C. W. Bowers, A. E. Lowman, S. A. Basinger, T. A. Norton, P. Petrone, P. S. Davila, M. E. Wilson, R. A. Boucarut, “DCATT dispersed fringe sensor: modeling and experimenting with the transmissive phase plates,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 757–762 (2000).
[CrossRef]

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiments on NGST’s Wavefront Control Testbed,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 318–328 (2002).
[CrossRef]

Boucarut, R. A.

F. Shi, D. C. Redding, C. W. Bowers, A. E. Lowman, S. A. Basinger, T. A. Norton, P. Petrone, P. S. Davila, M. E. Wilson, R. A. Boucarut, “DCATT dispersed fringe sensor: modeling and experimenting with the transmissive phase plates,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 757–762 (2000).
[CrossRef]

Bowers, C. W.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiments on NGST’s Wavefront Control Testbed,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 318–328 (2002).
[CrossRef]

F. Shi, D. C. Redding, C. W. Bowers, A. E. Lowman, S. A. Basinger, T. A. Norton, P. Petrone, P. S. Davila, M. E. Wilson, R. A. Boucarut, “DCATT dispersed fringe sensor: modeling and experimenting with the transmissive phase plates,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 757–762 (2000).
[CrossRef]

Burns, L. A.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiments on NGST’s Wavefront Control Testbed,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 318–328 (2002).
[CrossRef]

Chanan, G.

Chanan, G. A.

Davila, P. S.

F. Shi, D. C. Redding, C. W. Bowers, A. E. Lowman, S. A. Basinger, T. A. Norton, P. Petrone, P. S. Davila, M. E. Wilson, R. A. Boucarut, “DCATT dispersed fringe sensor: modeling and experimenting with the transmissive phase plates,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 757–762 (2000).
[CrossRef]

Dekens, F. G.

Faber, S. M.

J. E. Nelson, T. S. Mast, S. M. Faber, “The design of the Keck Observatory and Telescope,” Keck Observatory Report 90 (W. M. Keck Observatory, Kamuela, Hawaii, 1985).

Kirkman, D.

Lowman, A. E.

F. Shi, D. C. Redding, C. W. Bowers, A. E. Lowman, S. A. Basinger, T. A. Norton, P. Petrone, P. S. Davila, M. E. Wilson, R. A. Boucarut, “DCATT dispersed fringe sensor: modeling and experimenting with the transmissive phase plates,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 757–762 (2000).
[CrossRef]

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiments on NGST’s Wavefront Control Testbed,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 318–328 (2002).
[CrossRef]

Mast, T.

Mast, T. S.

J. E. Nelson, T. S. Mast, S. M. Faber, “The design of the Keck Observatory and Telescope,” Keck Observatory Report 90 (W. M. Keck Observatory, Kamuela, Hawaii, 1985).

Michaels, S.

Nelson, J.

Nelson, J. E.

J. E. Nelson, T. S. Mast, S. M. Faber, “The design of the Keck Observatory and Telescope,” Keck Observatory Report 90 (W. M. Keck Observatory, Kamuela, Hawaii, 1985).

Norton, T. A.

F. Shi, D. C. Redding, C. W. Bowers, A. E. Lowman, S. A. Basinger, T. A. Norton, P. Petrone, P. S. Davila, M. E. Wilson, R. A. Boucarut, “DCATT dispersed fringe sensor: modeling and experimenting with the transmissive phase plates,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 757–762 (2000).
[CrossRef]

Ohara, C.

Ohara, C. M.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiments on NGST’s Wavefront Control Testbed,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 318–328 (2002).
[CrossRef]

Petrone, P.

F. Shi, D. C. Redding, C. W. Bowers, A. E. Lowman, S. A. Basinger, T. A. Norton, P. Petrone, P. S. Davila, M. E. Wilson, R. A. Boucarut, “DCATT dispersed fringe sensor: modeling and experimenting with the transmissive phase plates,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 757–762 (2000).
[CrossRef]

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiments on NGST’s Wavefront Control Testbed,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 318–328 (2002).
[CrossRef]

Redding, D. C.

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiments on NGST’s Wavefront Control Testbed,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 318–328 (2002).
[CrossRef]

F. Shi, D. C. Redding, C. W. Bowers, A. E. Lowman, S. A. Basinger, T. A. Norton, P. Petrone, P. S. Davila, M. E. Wilson, R. A. Boucarut, “DCATT dispersed fringe sensor: modeling and experimenting with the transmissive phase plates,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 757–762 (2000).
[CrossRef]

Shi, F.

F. Shi, D. C. Redding, C. W. Bowers, A. E. Lowman, S. A. Basinger, T. A. Norton, P. Petrone, P. S. Davila, M. E. Wilson, R. A. Boucarut, “DCATT dispersed fringe sensor: modeling and experimenting with the transmissive phase plates,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 757–762 (2000).
[CrossRef]

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiments on NGST’s Wavefront Control Testbed,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 318–328 (2002).
[CrossRef]

Sirko, E.

Troy, M.

Wilson, M. E.

F. Shi, D. C. Redding, C. W. Bowers, A. E. Lowman, S. A. Basinger, T. A. Norton, P. Petrone, P. S. Davila, M. E. Wilson, R. A. Boucarut, “DCATT dispersed fringe sensor: modeling and experimenting with the transmissive phase plates,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 757–762 (2000).
[CrossRef]

Appl. Opt. (3)

Other (4)

F. Shi, D. C. Redding, C. W. Bowers, A. E. Lowman, S. A. Basinger, T. A. Norton, P. Petrone, P. S. Davila, M. E. Wilson, R. A. Boucarut, “DCATT dispersed fringe sensor: modeling and experimenting with the transmissive phase plates,” in UV, Optical, and IR Space Telescopes and Instruments, J. B. Breckinridge, P. Jakobsen, eds., Proc. SPIE4013, 757–762 (2000).
[CrossRef]

F. Shi, D. C. Redding, A. E. Lowman, C. W. Bowers, L. A. Burns, P. Petrone, C. M. Ohara, S. A. Basinger, “Segmented mirror coarse phasing with a dispersed fringe sensor: experiments on NGST’s Wavefront Control Testbed,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 318–328 (2002).
[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]

J. E. Nelson, T. S. Mast, S. M. Faber, “The design of the Keck Observatory and Telescope,” Keck Observatory Report 90 (W. M. Keck Observatory, Kamuela, Hawaii, 1985).

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Figures (9)

Fig. 1
Fig. 1

Theoretical fringe visibility curves for the three different edge orientations.

Fig. 2
Fig. 2

Simulated fringe formation for the three different edge orientations for an edge height of +4 μm. The display is logarithmically stretched to accentuate the diffraction effects. From bottom to top, the three pairs of fringes correspond to edge orientations of -60°, 0°, and +60°, respectively. In each pair, the lower fringe is the result of discrete sampling and illustrates the buildup of the fringe, whereas the upper one shows the fully dispersed fringe that results from dense wavelength sampling. Note that for edges oriented at +60° and for positive edge heights, the individual diffraction patterns are oriented so that they tend to fill in the dark bands on each fringe and thus to reduce the visibility. A similar effect occurs for edges oriented at -60° and negative edge heights.

Fig. 3
Fig. 3

Geometry of the primary mirror of the Keck telescopes, showing the 12 circular subapertures that sample the intersegment edges in the DFS mask. Each segment (A-D) is 0.90 m on a side. The subapertures are 12 cm in diameter. The 18 peripheral subapertures are used for pupil registration. The location of the grism with respect to the subapertures is indicated by the gray rectangle.

Fig. 4
Fig. 4

Edge-height distribution for all experimental trials.

Fig. 5
Fig. 5

Sample DFS image showing 12 dispersed fringes from the intersegment edges as well as 18 peripheral spots (undispersed) used for pupil registration. The display has been stretched in order to accentuate the fringes.

Fig. 6
Fig. 6

Sample DFS signal intensities for edge 3 (at an orientation of 0°), depicting a range of piston values. The corresponding fits to Eq. (14) are also shown. The upper-left plot is an example of two segments that are nearly phased; such results are discarded by the fitting algorithm because the calculated fringe contrast is too low. Also, as the absolute piston value increases, the fringe visibility decreases as a result of the limited spectral resolution, thereby defining the DFS capture range.

Fig. 7
Fig. 7

DFS measurements compared with PCS measurements, excluding the data points corresponding to the three regions of reduced sensitivity, as described in the text. The best straight-line fit yields a slope that is close to unity (0.980 ± 0.001) and a systematic offset of -0.031 ± 0.008 μm.

Fig. 8
Fig. 8

Comparison of the fringe visibility for positive edge heights (left column) and negative edge heights (right column) for various edge orientations. For edge orientations of ±60° (but not for 0°), the fringe visibility is sensitive to the sign of the edge height, as shown in the middle row (60° edge orientation) and bottom row (-60° edge orientation).

Fig. 9
Fig. 9

DFS detection error (relative to PCS) versus edge height, excluding the data points corresponding to the three regions of reduced sensitivity. The best straight-line fit is also plotted.

Tables (1)

Tables Icon

Table 1 Summary of DFS Intersegment Height Measurementsa

Equations (15)

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Iω; kδ=fˆω; 0coskδ+fˆω; π/2sinkδ2,
Iω; kδ=I1ω+I2ωsin2kδ+I3ωcos2kδ,
γ=Imax-Imin/Imax+Imin.
I12=I22+I32.
λx=λ0+λx x=λ0+C0x,
Iω= I1ω-ω+I2ω-ωsin2kδ+I3ω-ωcos2kδdx,
k-k=C0k02x-x/2π,
λ/d  δ/λ.
Iiω=gxhiy,
gx=exp-x2/2σ2,
h12=h22+h32.
Iω=I0y1+exp-α2cos2kδ+ϕy,
α22πC0σδ/λ02.
Iω=I01+γ cos2kδ+ϕy,
δ00.23λ0d/C0.

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