Abstract

An alignment-sensing scheme for all significant angular degrees of freedom of a power-recycled Michelson interferometer with Fabry–Perot cavities in the arms was tested on a tabletop interferometer. The response to misalignment of all degrees of freedom was measured at each sensor, and good agreement was found between measured and theoretical values.

© 1998 Optical Society of America

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  1. R. Weiss, “Electromagnetically coupled broadband gravitational antenna,” MIT Res. Lab. Electron. Q. Prog. Rep. 105, 54–76 (1972).
  2. A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
    [CrossRef] [PubMed]
  3. See, for example, R. W. P. Drever, “Interferometric detectors for gravitational radiation,” in Gravitational Radiation, N. Deruelle, T. Piran, eds. (North-Holland, Dordrecht, The Netherlands, 1983), pp. 321–338.
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    [CrossRef]
  5. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
    [CrossRef]
  6. P. Fritschel, N. Mavalvala, D. Shoemaker, D. Sigg, M. Zucker, G. González, “Alignment of an interferometric gravitational wave detector,” Appl. Opt. 37, 6734–6747 (1998).
    [CrossRef]
  7. D. Z. Anderson, “Alignment of resonant optical cavities,” Appl. Opt. 23, 2944–2949 (1984);N. Sampas, D. Z. Anderson, “Stabilization of laser beam alignment to an optical resonator by heterodyne detection of off-axis modes,” Appl. Opt. 29, 394–403 (1990).
    [CrossRef] [PubMed]
  8. E. Morrison, B. J. Meers, D. I. Robertson, H. Ward, “Experimental demonstration of an automatic alignment system for optical interferometers,” Appl. Opt. 33, 5037–5040 (1994);E. Morrison, B. J. Meers, D. I. Robertson, H. Ward, “Automatic alignment of optical interferometers,” Appl. Opt. 33, 5041–5049 (1994).
    [CrossRef] [PubMed]
  9. A. E. Siegman, Lasers (University Science, California, 1986) pp. 682–685.
  10. M. W. Regehr, F. J. Raab, S. E. Whitcomb, “Demonstration of a power-recycled Michelson interferometer with Fabry–Perot arms by frontal modulation,” Opt. Lett. 20, 1507–1509 (1995).
    [CrossRef] [PubMed]
  11. D. Sigg, N. Mavalvala, J. Giaime, P. Fritschel, D. Shoemaker, “Signal extraction in a power-recycled Michelson interferometer with Fabry–Perot arm cavities by use of multiple-carrier frontal modulation scheme,” Appl. Opt. 37, 5687–5693 (1998).
    [CrossRef]
  12. N. Mavalvala, “Alignment issues in laser interferometric gravitational-wave detectors,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1997).
  13. Y. Hefetz, N. Mavalvala, D. Sigg, “Principles of calculating alignment signals in complex resonant optical interferometers,” J. Opt. Soc. Am. B 14, 1597–1605 (1997).
    [CrossRef]

1998

1997

1995

1994

1992

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

1984

1983

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

1982

A. Schenzle, R. DeVoe, G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25, 2606–2621 (1982).
[CrossRef]

1972

R. Weiss, “Electromagnetically coupled broadband gravitational antenna,” MIT Res. Lab. Electron. Q. Prog. Rep. 105, 54–76 (1972).

Abramovici, A.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Althouse, W. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Anderson, D. Z.

Brewer, G.

A. Schenzle, R. DeVoe, G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25, 2606–2621 (1982).
[CrossRef]

DeVoe, R.

A. Schenzle, R. DeVoe, G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25, 2606–2621 (1982).
[CrossRef]

Drever, R. W. P.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

See, for example, R. W. P. Drever, “Interferometric detectors for gravitational radiation,” in Gravitational Radiation, N. Deruelle, T. Piran, eds. (North-Holland, Dordrecht, The Netherlands, 1983), pp. 321–338.

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Fritschel, P.

Giaime, J.

González, G.

Gürsel, Y.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Hefetz, Y.

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Kawamura, S.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Mavalvala, N.

Meers, B. J.

Morrison, E.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Raab, F. J.

M. W. Regehr, F. J. Raab, S. E. Whitcomb, “Demonstration of a power-recycled Michelson interferometer with Fabry–Perot arms by frontal modulation,” Opt. Lett. 20, 1507–1509 (1995).
[CrossRef] [PubMed]

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Regehr, M. W.

Robertson, D. I.

Schenzle, A.

A. Schenzle, R. DeVoe, G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25, 2606–2621 (1982).
[CrossRef]

Shoemaker, D.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, California, 1986) pp. 682–685.

Sievers, L.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Sigg, D.

Spero, R. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Thorne, K. S.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Vogt, R. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Ward, H.

Weiss, R.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

R. Weiss, “Electromagnetically coupled broadband gravitational antenna,” MIT Res. Lab. Electron. Q. Prog. Rep. 105, 54–76 (1972).

Whitcomb, S. E.

M. W. Regehr, F. J. Raab, S. E. Whitcomb, “Demonstration of a power-recycled Michelson interferometer with Fabry–Perot arms by frontal modulation,” Opt. Lett. 20, 1507–1509 (1995).
[CrossRef] [PubMed]

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Zucker, M.

Zucker, M. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. B

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

J. Opt. Soc. Am. B

MIT Res. Lab. Electron. Q. Prog. Rep.

R. Weiss, “Electromagnetically coupled broadband gravitational antenna,” MIT Res. Lab. Electron. Q. Prog. Rep. 105, 54–76 (1972).

Opt. Lett.

Phys. Rev. A

A. Schenzle, R. DeVoe, G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25, 2606–2621 (1982).
[CrossRef]

Science

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Other

See, for example, R. W. P. Drever, “Interferometric detectors for gravitational radiation,” in Gravitational Radiation, N. Deruelle, T. Piran, eds. (North-Holland, Dordrecht, The Netherlands, 1983), pp. 321–338.

A. E. Siegman, Lasers (University Science, California, 1986) pp. 682–685.

N. Mavalvala, “Alignment issues in laser interferometric gravitational-wave detectors,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1997).

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Figures (2)

Fig. 1
Fig. 1

Overview of the experiment. The length sensors and wave-front sensors (WFS i ) are placed at three signal detection ports. An antireflection-coated pellicle beam splitter is used to pick off a tiny fraction of the light inside the power-recycling cavity.

Fig. 2
Fig. 2

Dominant elements of the alignment-sensitivity matrix compared with the values predicted by the model. Calculated values are along the horizontal axis, and the vertical axis corresponds to measured values. (All values are given in arbitrary units.) Each wave-front sensor is designated by a different symbol; the error bars are explained in the text.

Equations (1)

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WFS i     j   A ij Θ j   cos η i - η ij cos Ω i t - ϕ ij ,

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