Abstract

A technique to align automatically the beams of displacement-measuring interferometric gauges is described. The pointing of the launched beam is modulated in a circular pattern, and the resulting displacement signal is demodulated synchronously to determine the alignment error. This error signal is used in a control system that maintains the alignment for maximum path between a pair of fiducial hollow-cube corner retroreflectors, which minimizes sensitivity to alignment drift. The technique is tested on a developmental gauge of the type intended for the Space Interferometry Mission. The displacement signal for the gauge is generated in digital form; and the lock-in amplifier functions of modulation, demodulation, and filtering are all implemented digitally.

© 2002 Optical Society of America

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References

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  1. For more information on the SIM, see http://sim.jpl.nasa.gov .
  2. T. Boker, R. J. Allen, “Imaging and nulling with the Space Interferometer Mission,” Astrophys. J. Suppl. 125(1), 123–142 (1999).
    [CrossRef]
  3. S. Hosoe, “Highly precise and stable displacement-measuring laser interferometer with differential optical paths,” Prec. Eng. 17, 258–265 (1995).
    [CrossRef]
  4. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993).
    [CrossRef]
  5. K. Miyagi, M. Nanami, I. Kobayashi, A. Taniguchi, “A compact optical heterodyne interferometer by optical integration and its application,” Opt. Rev. 4(1A), 133–137 (1997).
  6. S. Shaklan, S. Azevedo, R. Bartos, A. Carlson, Y. Gursel, P. Halverson, A. Kuhnert, Y. Lin, R. Savedra, E. Schmidtlin, “Micro-arcsecond metrology testbed (MAM),” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 100–108 (1998).
    [CrossRef]
  7. K. Kawabe, N. Mio, K. Tsubono, “Automatic alignment-control system for a suspended Fabry-Perot cavity,” Appl. Opt. 33, 5498–5505 (1994).
    [CrossRef] [PubMed]
  8. P. Haschberger, O. Mayer, “Ray tracing through an eccentrically rotating retroreflector used for path-length alteration in a new Michelson interferometer,” J. Opt. Soc. Am. A 8, 1991–2000 (1991).
    [CrossRef]
  9. In addition to this geometric error, there are errors associated with imperfections in the optics, including nonplanar reflecting surfaces, corner gaps, and departures from perfect orthogonality of the surfaces. The latter may be the most significant; if there is a dihedral error ∊ deviation from 90 deg in the orientation of the cube corner faces, Eq. (1) becomes ΔL = L0θ0(Δθ + 2∊). For high-quality retroreflectors, ∊ ≈ 5 µrad.
  10. P. Halverson, D. Johnson, A. Kuhnert, S. Shaklan, R. Spero, “A multichannel phasemeter for picometer precision laser metrology,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi, ed. Proc. SPIE3740, 646–649 (1999).
    [CrossRef]
  11. R. C. Dorf, R. H. Bishop, Modern Control Systems (Prentice-Hall, Englewood Cliffs, N.J., 2001).

1999 (1)

T. Boker, R. J. Allen, “Imaging and nulling with the Space Interferometer Mission,” Astrophys. J. Suppl. 125(1), 123–142 (1999).
[CrossRef]

1997 (1)

K. Miyagi, M. Nanami, I. Kobayashi, A. Taniguchi, “A compact optical heterodyne interferometer by optical integration and its application,” Opt. Rev. 4(1A), 133–137 (1997).

1995 (1)

S. Hosoe, “Highly precise and stable displacement-measuring laser interferometer with differential optical paths,” Prec. Eng. 17, 258–265 (1995).
[CrossRef]

1994 (1)

1993 (1)

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993).
[CrossRef]

1991 (1)

Allen, R. J.

T. Boker, R. J. Allen, “Imaging and nulling with the Space Interferometer Mission,” Astrophys. J. Suppl. 125(1), 123–142 (1999).
[CrossRef]

Azevedo, S.

S. Shaklan, S. Azevedo, R. Bartos, A. Carlson, Y. Gursel, P. Halverson, A. Kuhnert, Y. Lin, R. Savedra, E. Schmidtlin, “Micro-arcsecond metrology testbed (MAM),” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 100–108 (1998).
[CrossRef]

Bartos, R.

S. Shaklan, S. Azevedo, R. Bartos, A. Carlson, Y. Gursel, P. Halverson, A. Kuhnert, Y. Lin, R. Savedra, E. Schmidtlin, “Micro-arcsecond metrology testbed (MAM),” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 100–108 (1998).
[CrossRef]

Bishop, R. H.

R. C. Dorf, R. H. Bishop, Modern Control Systems (Prentice-Hall, Englewood Cliffs, N.J., 2001).

Bobroff, N.

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993).
[CrossRef]

Boker, T.

T. Boker, R. J. Allen, “Imaging and nulling with the Space Interferometer Mission,” Astrophys. J. Suppl. 125(1), 123–142 (1999).
[CrossRef]

Carlson, A.

S. Shaklan, S. Azevedo, R. Bartos, A. Carlson, Y. Gursel, P. Halverson, A. Kuhnert, Y. Lin, R. Savedra, E. Schmidtlin, “Micro-arcsecond metrology testbed (MAM),” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 100–108 (1998).
[CrossRef]

Dorf, R. C.

R. C. Dorf, R. H. Bishop, Modern Control Systems (Prentice-Hall, Englewood Cliffs, N.J., 2001).

Gursel, Y.

S. Shaklan, S. Azevedo, R. Bartos, A. Carlson, Y. Gursel, P. Halverson, A. Kuhnert, Y. Lin, R. Savedra, E. Schmidtlin, “Micro-arcsecond metrology testbed (MAM),” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 100–108 (1998).
[CrossRef]

Halverson, P.

S. Shaklan, S. Azevedo, R. Bartos, A. Carlson, Y. Gursel, P. Halverson, A. Kuhnert, Y. Lin, R. Savedra, E. Schmidtlin, “Micro-arcsecond metrology testbed (MAM),” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 100–108 (1998).
[CrossRef]

P. Halverson, D. Johnson, A. Kuhnert, S. Shaklan, R. Spero, “A multichannel phasemeter for picometer precision laser metrology,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi, ed. Proc. SPIE3740, 646–649 (1999).
[CrossRef]

Haschberger, P.

Hosoe, S.

S. Hosoe, “Highly precise and stable displacement-measuring laser interferometer with differential optical paths,” Prec. Eng. 17, 258–265 (1995).
[CrossRef]

Johnson, D.

P. Halverson, D. Johnson, A. Kuhnert, S. Shaklan, R. Spero, “A multichannel phasemeter for picometer precision laser metrology,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi, ed. Proc. SPIE3740, 646–649 (1999).
[CrossRef]

Kawabe, K.

Kobayashi, I.

K. Miyagi, M. Nanami, I. Kobayashi, A. Taniguchi, “A compact optical heterodyne interferometer by optical integration and its application,” Opt. Rev. 4(1A), 133–137 (1997).

Kuhnert, A.

P. Halverson, D. Johnson, A. Kuhnert, S. Shaklan, R. Spero, “A multichannel phasemeter for picometer precision laser metrology,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi, ed. Proc. SPIE3740, 646–649 (1999).
[CrossRef]

S. Shaklan, S. Azevedo, R. Bartos, A. Carlson, Y. Gursel, P. Halverson, A. Kuhnert, Y. Lin, R. Savedra, E. Schmidtlin, “Micro-arcsecond metrology testbed (MAM),” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 100–108 (1998).
[CrossRef]

Lin, Y.

S. Shaklan, S. Azevedo, R. Bartos, A. Carlson, Y. Gursel, P. Halverson, A. Kuhnert, Y. Lin, R. Savedra, E. Schmidtlin, “Micro-arcsecond metrology testbed (MAM),” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 100–108 (1998).
[CrossRef]

Mayer, O.

Mio, N.

Miyagi, K.

K. Miyagi, M. Nanami, I. Kobayashi, A. Taniguchi, “A compact optical heterodyne interferometer by optical integration and its application,” Opt. Rev. 4(1A), 133–137 (1997).

Nanami, M.

K. Miyagi, M. Nanami, I. Kobayashi, A. Taniguchi, “A compact optical heterodyne interferometer by optical integration and its application,” Opt. Rev. 4(1A), 133–137 (1997).

Savedra, R.

S. Shaklan, S. Azevedo, R. Bartos, A. Carlson, Y. Gursel, P. Halverson, A. Kuhnert, Y. Lin, R. Savedra, E. Schmidtlin, “Micro-arcsecond metrology testbed (MAM),” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 100–108 (1998).
[CrossRef]

Schmidtlin, E.

S. Shaklan, S. Azevedo, R. Bartos, A. Carlson, Y. Gursel, P. Halverson, A. Kuhnert, Y. Lin, R. Savedra, E. Schmidtlin, “Micro-arcsecond metrology testbed (MAM),” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 100–108 (1998).
[CrossRef]

Shaklan, S.

S. Shaklan, S. Azevedo, R. Bartos, A. Carlson, Y. Gursel, P. Halverson, A. Kuhnert, Y. Lin, R. Savedra, E. Schmidtlin, “Micro-arcsecond metrology testbed (MAM),” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 100–108 (1998).
[CrossRef]

P. Halverson, D. Johnson, A. Kuhnert, S. Shaklan, R. Spero, “A multichannel phasemeter for picometer precision laser metrology,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi, ed. Proc. SPIE3740, 646–649 (1999).
[CrossRef]

Spero, R.

P. Halverson, D. Johnson, A. Kuhnert, S. Shaklan, R. Spero, “A multichannel phasemeter for picometer precision laser metrology,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi, ed. Proc. SPIE3740, 646–649 (1999).
[CrossRef]

Taniguchi, A.

K. Miyagi, M. Nanami, I. Kobayashi, A. Taniguchi, “A compact optical heterodyne interferometer by optical integration and its application,” Opt. Rev. 4(1A), 133–137 (1997).

Tsubono, K.

Appl. Opt. (1)

Astrophys. J. Suppl. (1)

T. Boker, R. J. Allen, “Imaging and nulling with the Space Interferometer Mission,” Astrophys. J. Suppl. 125(1), 123–142 (1999).
[CrossRef]

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

Meas. Sci. Technol. (1)

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993).
[CrossRef]

Opt. Rev. (1)

K. Miyagi, M. Nanami, I. Kobayashi, A. Taniguchi, “A compact optical heterodyne interferometer by optical integration and its application,” Opt. Rev. 4(1A), 133–137 (1997).

Prec. Eng. (1)

S. Hosoe, “Highly precise and stable displacement-measuring laser interferometer with differential optical paths,” Prec. Eng. 17, 258–265 (1995).
[CrossRef]

Other (5)

For more information on the SIM, see http://sim.jpl.nasa.gov .

S. Shaklan, S. Azevedo, R. Bartos, A. Carlson, Y. Gursel, P. Halverson, A. Kuhnert, Y. Lin, R. Savedra, E. Schmidtlin, “Micro-arcsecond metrology testbed (MAM),” in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE3350, 100–108 (1998).
[CrossRef]

In addition to this geometric error, there are errors associated with imperfections in the optics, including nonplanar reflecting surfaces, corner gaps, and departures from perfect orthogonality of the surfaces. The latter may be the most significant; if there is a dihedral error ∊ deviation from 90 deg in the orientation of the cube corner faces, Eq. (1) becomes ΔL = L0θ0(Δθ + 2∊). For high-quality retroreflectors, ∊ ≈ 5 µrad.

P. Halverson, D. Johnson, A. Kuhnert, S. Shaklan, R. Spero, “A multichannel phasemeter for picometer precision laser metrology,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi, ed. Proc. SPIE3740, 646–649 (1999).
[CrossRef]

R. C. Dorf, R. H. Bishop, Modern Control Systems (Prentice-Hall, Englewood Cliffs, N.J., 2001).

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Figures (6)

Fig. 1
Fig. 1

Path-length insensitivity to reflector angle α and lateral translation bf.

Fig. 2
Fig. 2

Dependence of pointing error on cos θ.

Fig. 3
Fig. 3

Measured optical path in response to variation of launch angles. (a) Contours of equal optical path, as a function of the tip-tilt launcher angles θ and ϕ. The contours are spaced by 0.01 cycles of phase, or 6.6 nm. (b) The ϕ = 0 slice through the data in (a) and the calculated cosine dependence of the optical path on θ.

Fig. 4
Fig. 4

Control system for alignment of metrology beams to cube corner vertices. (One of two controlled axes is shown.) Thin and medium lines represent digital and analog signals, respectively. The phase meter measures the phase difference between two photodiode signals: one that detects the interfered beam that has traversed the path between the corner cubes (signal) and one that detects the short-path interference within the launcher optics (reference). The laser diode transmitter and quadrant photodiode receiver provide an out-of-loop monitor of control system performance. DAC, digital-to-analog converter.

Fig. 5
Fig. 5

Step response of the pointing control system. The dashed curve is the optical lever response, and the solid curve is the correction signal. At t = 27 s, a disturbance of 80 µrad was injected when we applied a step change in the PZT actuator voltage. At t = 55 s, a similar disturbance was applied in the opposite direction.

Fig. 6
Fig. 6

Long-term stability of the beam pointing. The solid curve is the optical lever response, and the dotted curve is the phase meter output measurement of the optical path difference (OPD).

Equations (4)

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

ΔL=-L0θ0Δθ.
GH=k1+sτ,
Cs=GHs1+GHs.
pt=k1+k1-exp- 1+ktτ.

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