Abstract

The process of lock acquisition in a high-finesse suspended Fabry–Perot cavity used in the LIGO 40-m interferometer is numerically simulated. The simulation, including a model of the cavity optical transient response as the mirrors swing through resonance, demonstrates that acquisition of lock by the controller depends on the relative velocity of the mirrors and establishes a threshold velocity below which acquisition may take place. The model results are used to implement a real-time controller that analyzes the transient response, extracts the mirror velocity, and then guides the mirrors into resonance with relative velocity under the threshold. The result is a factor-of-10 decrease in the experimentally observed acquisition time.

© 1995 Optical Society of America

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  1. A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
    [CrossRef] [PubMed]
  2. A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
    [PubMed]
  3. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
    [CrossRef]

1992

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

1983

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Abramovici, A.

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Althouse, W.

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Camp, J.

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Drever, R.

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Durance, D.

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Giaime, J.

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Gillespie, A.

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Gursel, Y.

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (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, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Kawamura, S.

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Kuhnert, A.

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Lyons, T.

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Raab, F. J.

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Savage, R. L.

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Shoemaker, D.

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Sievers, L.

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Spero, R.

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Thorne, K.

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Vogt, R.

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Weiss, R.

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Whitcomb, S.

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Zucker, M.

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

Appl. Phys. B

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Science

A. Abramovici, W. Althouse, R. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, Science 256, 325 (1992).
[CrossRef] [PubMed]

Other

A. Abramovici, W. Althouse, J. Camp, D. Durance, J. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “Improved sensitivity in the LIGO 40-meter interferometer“ submitted toScience.
[PubMed]

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Figures (6)

Fig. 1
Fig. 1

Feedback configuration used to control the 40-m cavity length.

Fig. 2
Fig. 2

Illustration of the optical response model: (a) First two beams used in sum to calculate the cavity electric field at time t. The ith beam enters the cavity at time (t), where τ = 2L/c. The mirror motion affects the path length. (b) Simulated transient error signal for a relative velocity of 1 μm/s.

Fig. 3
Fig. 3

Phase-plane plots showing trajectories for three different initial velocities approaching resonance: below threshold, threshold, and above threshold.

Fig. 4
Fig. 4

Block diagram of the staged digital/analog controller. ADC, analog-to-digital converter; DAC, digital-to-analog converter.

Fig. 5
Fig. 5

Measured velocity distribution before the applied pulse (as the cavity first approaches resonance) and after the applied pulse (as the cavity returns to the resonance condition).

Fig. 6
Fig. 6

Comparison of experimental acquisition time with analog and staged digital/analog controllers.

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