Abstract

Two methods for extracting linewidth estimates from evenly sampled partially coherent signals, where white frequency fluctuations are the major source of noise, are discussed. The first method utilizes the Allan deviation, requiring multiple frequency estimates for each linewidth estimate. The second method utilizes the second-order autoregressive model to provide a linewidth estimate with each frequency estimate. A characterization shows that the latter technique is reliable for short data sets (≤1 s). The application of these techniques to large, quantum-noise-limited ring laser gyroscopes is demonstrated. The results of the analysis compare favorably with a theoretical analysis.

© 2000 Optical Society of America

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References

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  1. J. R. Wilkinson, “Ring lasers,” Prog. Quantum Electron. 11, 1–103 (1987).
    [CrossRef]
  2. W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
    [CrossRef]
  3. F. Aronowitz, Laser Applications: the Laser Gyro (Academic, New York, 1971).
  4. H. Statz, T. A. Dorschner, M. Holtz, I. Smith, The Multioscillator Ring Laser Gyroscope, Vol. 4 of the Laser Handbook (Elsevier, Amsterdam, 1985).
  5. C. H. Rowe, U. K. Schreiber, S. J. Cooper, B. T. King, M. Poulton, G. E. Stedman, “Design and operation of a very large ring laser gyroscope,” Appl. Opt. 38, 2516–2523 (1999).
    [CrossRef]
  6. H. R. Bilger, G. E. Stedman, M. P. Poulton, C. H. Rowe, Z. Li, P. V. Wells, “Ring laser for precision measurement of nonreciprocal phenomena,” IEEE Trans. Instrum. Meas. 42, 407–411 (1993).
    [CrossRef]
  7. G. E. Stedman, “Ring-laser tests of fundamental physics and geophysics,” Rep. Prog. Phys. 60, 615–688 (1997).
    [CrossRef]
  8. G. E. Stedman, H. R. Bilger, Z. Li, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Austr. J. Phys. 46, 87–101 (1993).
  9. R. Anderson, H. R. Bilger, G. E. Stedman, “‘Sagnac’ effect: a century of Earth-rotated interferometers,” Am. J. Phys. 62, 975–985 (1994).
    [CrossRef]
  10. H. R. Bilger, G. E. Stedman, Z. Li, U. Schreiber, M. Schneider, “Ring lasers for Geodesy,” IEEE Trans. Instrum. Meas. 44, 468–470 (1995).
    [CrossRef]
  11. R. S. Gross, “Correspondence between theory and observations of polar motion,” Geophys. J. Int. 109, 162–170 (1992).
    [CrossRef]
  12. R. S. Gross, “Combinations of Earth orientation measurements: SPACE94, COMB94, and POLE94,” J. Geophys. Res. 101, 8729–8740 (1996).
    [CrossRef]
  13. C. P. Wyss, D. N. Wright, B. T. King, D. P. McLeod, S. J. Cooper, G. E. Stedman, “Collision broadening and quantum noise in a very large laser gyroscope,” Opt. Commun. 174, 181–189 (2000).
    [CrossRef]
  14. T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron. QE-16, 1376–1379 (1980).
    [CrossRef]
  15. D. G. Childers, ed., Modern Spectrum Analysis (Institute of Electrical and Electronics Engineers, New York, 1978).
  16. S. B. Kesler, Modern Spectrum Analysis II (Institute of Electrical and Electronics Engineers, New York, 1986).
  17. S. M. Kay, S. L. Marple, “Spectrum analysis—a modern perspective,” Proc. IEEE 69, 1380–1419 (1981); reprinted with related works in Ref. 15.
    [CrossRef]
  18. V. F. Pisarenko, “On the estimation of spectra by means of nonlinear functions of the covariance matrix,” Geophys. J. R. Astron. Soc. 28, 511–531 (1972).
    [CrossRef]
  19. V. F. Pisarenko, “The retrieval of harmonics from a covariance function,” Geophys. J. R. Astron. Soc. 33, 347–366 (1973).
    [CrossRef]
  20. J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A 25, 2214–2225 (1982).
    [CrossRef]
  21. J. D. Cresser, D. Hammonds, W. H. Louisell, P. Meystre, H. Risken, “Quantum noise in ring laser gyros. II. Numerical results,” Phys. Rev. A 25, 2226–2234 (1982).
    [CrossRef]
  22. J. D. Cresser, “Quantum noise in ring laser gyros. III. Approximate analytic results in unlocked region,” Phys. Rev. A 26, 398–409 (1982).
    [CrossRef]
  23. J. D. Cresser, “Theory of the spectrum of the quantised light field,” Phys. Rep. 94, 47–110 (1983).
    [CrossRef]
  24. J. P. Burg, “Maximum entropy spectral analysis,” In Proceedings of the 37th Meeting of the Society of Exploration Geophysicists (Society of Exploration Geophysicists, Tulsa, Okla., 1967); reprinted in Ref. 16.
  25. T. J. Ulrych, T. N. Bishop, “Maximum entropy spectral analysis and autoregressive decomposition,” Rev. Geophys. Space Phys. 13, 183–200 (1975).
    [CrossRef]

2000 (1)

C. P. Wyss, D. N. Wright, B. T. King, D. P. McLeod, S. J. Cooper, G. E. Stedman, “Collision broadening and quantum noise in a very large laser gyroscope,” Opt. Commun. 174, 181–189 (2000).
[CrossRef]

1999 (1)

1997 (1)

G. E. Stedman, “Ring-laser tests of fundamental physics and geophysics,” Rep. Prog. Phys. 60, 615–688 (1997).
[CrossRef]

1996 (1)

R. S. Gross, “Combinations of Earth orientation measurements: SPACE94, COMB94, and POLE94,” J. Geophys. Res. 101, 8729–8740 (1996).
[CrossRef]

1995 (1)

H. R. Bilger, G. E. Stedman, Z. Li, U. Schreiber, M. Schneider, “Ring lasers for Geodesy,” IEEE Trans. Instrum. Meas. 44, 468–470 (1995).
[CrossRef]

1994 (1)

R. Anderson, H. R. Bilger, G. E. Stedman, “‘Sagnac’ effect: a century of Earth-rotated interferometers,” Am. J. Phys. 62, 975–985 (1994).
[CrossRef]

1993 (2)

H. R. Bilger, G. E. Stedman, M. P. Poulton, C. H. Rowe, Z. Li, P. V. Wells, “Ring laser for precision measurement of nonreciprocal phenomena,” IEEE Trans. Instrum. Meas. 42, 407–411 (1993).
[CrossRef]

G. E. Stedman, H. R. Bilger, Z. Li, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Austr. J. Phys. 46, 87–101 (1993).

1992 (1)

R. S. Gross, “Correspondence between theory and observations of polar motion,” Geophys. J. Int. 109, 162–170 (1992).
[CrossRef]

1987 (1)

J. R. Wilkinson, “Ring lasers,” Prog. Quantum Electron. 11, 1–103 (1987).
[CrossRef]

1985 (1)

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[CrossRef]

1983 (1)

J. D. Cresser, “Theory of the spectrum of the quantised light field,” Phys. Rep. 94, 47–110 (1983).
[CrossRef]

1982 (3)

J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A 25, 2214–2225 (1982).
[CrossRef]

J. D. Cresser, D. Hammonds, W. H. Louisell, P. Meystre, H. Risken, “Quantum noise in ring laser gyros. II. Numerical results,” Phys. Rev. A 25, 2226–2234 (1982).
[CrossRef]

J. D. Cresser, “Quantum noise in ring laser gyros. III. Approximate analytic results in unlocked region,” Phys. Rev. A 26, 398–409 (1982).
[CrossRef]

1981 (1)

S. M. Kay, S. L. Marple, “Spectrum analysis—a modern perspective,” Proc. IEEE 69, 1380–1419 (1981); reprinted with related works in Ref. 15.
[CrossRef]

1980 (1)

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron. QE-16, 1376–1379 (1980).
[CrossRef]

1975 (1)

T. J. Ulrych, T. N. Bishop, “Maximum entropy spectral analysis and autoregressive decomposition,” Rev. Geophys. Space Phys. 13, 183–200 (1975).
[CrossRef]

1973 (1)

V. F. Pisarenko, “The retrieval of harmonics from a covariance function,” Geophys. J. R. Astron. Soc. 33, 347–366 (1973).
[CrossRef]

1972 (1)

V. F. Pisarenko, “On the estimation of spectra by means of nonlinear functions of the covariance matrix,” Geophys. J. R. Astron. Soc. 28, 511–531 (1972).
[CrossRef]

Anderson, R.

R. Anderson, H. R. Bilger, G. E. Stedman, “‘Sagnac’ effect: a century of Earth-rotated interferometers,” Am. J. Phys. 62, 975–985 (1994).
[CrossRef]

Aronowitz, F.

F. Aronowitz, Laser Applications: the Laser Gyro (Academic, New York, 1971).

Bilger, H. R.

H. R. Bilger, G. E. Stedman, Z. Li, U. Schreiber, M. Schneider, “Ring lasers for Geodesy,” IEEE Trans. Instrum. Meas. 44, 468–470 (1995).
[CrossRef]

R. Anderson, H. R. Bilger, G. E. Stedman, “‘Sagnac’ effect: a century of Earth-rotated interferometers,” Am. J. Phys. 62, 975–985 (1994).
[CrossRef]

H. R. Bilger, G. E. Stedman, M. P. Poulton, C. H. Rowe, Z. Li, P. V. Wells, “Ring laser for precision measurement of nonreciprocal phenomena,” IEEE Trans. Instrum. Meas. 42, 407–411 (1993).
[CrossRef]

G. E. Stedman, H. R. Bilger, Z. Li, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Austr. J. Phys. 46, 87–101 (1993).

Bishop, T. N.

T. J. Ulrych, T. N. Bishop, “Maximum entropy spectral analysis and autoregressive decomposition,” Rev. Geophys. Space Phys. 13, 183–200 (1975).
[CrossRef]

Burg, J. P.

J. P. Burg, “Maximum entropy spectral analysis,” In Proceedings of the 37th Meeting of the Society of Exploration Geophysicists (Society of Exploration Geophysicists, Tulsa, Okla., 1967); reprinted in Ref. 16.

Chow, W. W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[CrossRef]

Cooper, S. J.

C. P. Wyss, D. N. Wright, B. T. King, D. P. McLeod, S. J. Cooper, G. E. Stedman, “Collision broadening and quantum noise in a very large laser gyroscope,” Opt. Commun. 174, 181–189 (2000).
[CrossRef]

C. H. Rowe, U. K. Schreiber, S. J. Cooper, B. T. King, M. Poulton, G. E. Stedman, “Design and operation of a very large ring laser gyroscope,” Appl. Opt. 38, 2516–2523 (1999).
[CrossRef]

Cresser, J. D.

J. D. Cresser, “Theory of the spectrum of the quantised light field,” Phys. Rep. 94, 47–110 (1983).
[CrossRef]

J. D. Cresser, D. Hammonds, W. H. Louisell, P. Meystre, H. Risken, “Quantum noise in ring laser gyros. II. Numerical results,” Phys. Rev. A 25, 2226–2234 (1982).
[CrossRef]

J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A 25, 2214–2225 (1982).
[CrossRef]

J. D. Cresser, “Quantum noise in ring laser gyros. III. Approximate analytic results in unlocked region,” Phys. Rev. A 26, 398–409 (1982).
[CrossRef]

Dorschner, T. A.

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron. QE-16, 1376–1379 (1980).
[CrossRef]

H. Statz, T. A. Dorschner, M. Holtz, I. Smith, The Multioscillator Ring Laser Gyroscope, Vol. 4 of the Laser Handbook (Elsevier, Amsterdam, 1985).

Gea-Banacloche, J.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[CrossRef]

Gross, R. S.

R. S. Gross, “Combinations of Earth orientation measurements: SPACE94, COMB94, and POLE94,” J. Geophys. Res. 101, 8729–8740 (1996).
[CrossRef]

R. S. Gross, “Correspondence between theory and observations of polar motion,” Geophys. J. Int. 109, 162–170 (1992).
[CrossRef]

Hammonds, D.

J. D. Cresser, D. Hammonds, W. H. Louisell, P. Meystre, H. Risken, “Quantum noise in ring laser gyros. II. Numerical results,” Phys. Rev. A 25, 2226–2234 (1982).
[CrossRef]

Haus, H. A.

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron. QE-16, 1376–1379 (1980).
[CrossRef]

Holtz, M.

H. Statz, T. A. Dorschner, M. Holtz, I. Smith, The Multioscillator Ring Laser Gyroscope, Vol. 4 of the Laser Handbook (Elsevier, Amsterdam, 1985).

Holz, M.

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron. QE-16, 1376–1379 (1980).
[CrossRef]

Kay, S. M.

S. M. Kay, S. L. Marple, “Spectrum analysis—a modern perspective,” Proc. IEEE 69, 1380–1419 (1981); reprinted with related works in Ref. 15.
[CrossRef]

Kesler, S. B.

S. B. Kesler, Modern Spectrum Analysis II (Institute of Electrical and Electronics Engineers, New York, 1986).

King, B. T.

C. P. Wyss, D. N. Wright, B. T. King, D. P. McLeod, S. J. Cooper, G. E. Stedman, “Collision broadening and quantum noise in a very large laser gyroscope,” Opt. Commun. 174, 181–189 (2000).
[CrossRef]

C. H. Rowe, U. K. Schreiber, S. J. Cooper, B. T. King, M. Poulton, G. E. Stedman, “Design and operation of a very large ring laser gyroscope,” Appl. Opt. 38, 2516–2523 (1999).
[CrossRef]

Li, Z.

H. R. Bilger, G. E. Stedman, Z. Li, U. Schreiber, M. Schneider, “Ring lasers for Geodesy,” IEEE Trans. Instrum. Meas. 44, 468–470 (1995).
[CrossRef]

H. R. Bilger, G. E. Stedman, M. P. Poulton, C. H. Rowe, Z. Li, P. V. Wells, “Ring laser for precision measurement of nonreciprocal phenomena,” IEEE Trans. Instrum. Meas. 42, 407–411 (1993).
[CrossRef]

G. E. Stedman, H. R. Bilger, Z. Li, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Austr. J. Phys. 46, 87–101 (1993).

Louisell, W. H.

J. D. Cresser, D. Hammonds, W. H. Louisell, P. Meystre, H. Risken, “Quantum noise in ring laser gyros. II. Numerical results,” Phys. Rev. A 25, 2226–2234 (1982).
[CrossRef]

J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A 25, 2214–2225 (1982).
[CrossRef]

Marple, S. L.

S. M. Kay, S. L. Marple, “Spectrum analysis—a modern perspective,” Proc. IEEE 69, 1380–1419 (1981); reprinted with related works in Ref. 15.
[CrossRef]

McLeod, D. P.

C. P. Wyss, D. N. Wright, B. T. King, D. P. McLeod, S. J. Cooper, G. E. Stedman, “Collision broadening and quantum noise in a very large laser gyroscope,” Opt. Commun. 174, 181–189 (2000).
[CrossRef]

Meystre, P.

J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A 25, 2214–2225 (1982).
[CrossRef]

J. D. Cresser, D. Hammonds, W. H. Louisell, P. Meystre, H. Risken, “Quantum noise in ring laser gyros. II. Numerical results,” Phys. Rev. A 25, 2226–2234 (1982).
[CrossRef]

Pedrotti, L. M.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[CrossRef]

Pisarenko, V. F.

V. F. Pisarenko, “The retrieval of harmonics from a covariance function,” Geophys. J. R. Astron. Soc. 33, 347–366 (1973).
[CrossRef]

V. F. Pisarenko, “On the estimation of spectra by means of nonlinear functions of the covariance matrix,” Geophys. J. R. Astron. Soc. 28, 511–531 (1972).
[CrossRef]

Poulton, M.

Poulton, M. P.

H. R. Bilger, G. E. Stedman, M. P. Poulton, C. H. Rowe, Z. Li, P. V. Wells, “Ring laser for precision measurement of nonreciprocal phenomena,” IEEE Trans. Instrum. Meas. 42, 407–411 (1993).
[CrossRef]

G. E. Stedman, H. R. Bilger, Z. Li, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Austr. J. Phys. 46, 87–101 (1993).

Risken, H.

J. D. Cresser, D. Hammonds, W. H. Louisell, P. Meystre, H. Risken, “Quantum noise in ring laser gyros. II. Numerical results,” Phys. Rev. A 25, 2226–2234 (1982).
[CrossRef]

Rowe, C. H.

C. H. Rowe, U. K. Schreiber, S. J. Cooper, B. T. King, M. Poulton, G. E. Stedman, “Design and operation of a very large ring laser gyroscope,” Appl. Opt. 38, 2516–2523 (1999).
[CrossRef]

H. R. Bilger, G. E. Stedman, M. P. Poulton, C. H. Rowe, Z. Li, P. V. Wells, “Ring laser for precision measurement of nonreciprocal phenomena,” IEEE Trans. Instrum. Meas. 42, 407–411 (1993).
[CrossRef]

G. E. Stedman, H. R. Bilger, Z. Li, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Austr. J. Phys. 46, 87–101 (1993).

Sanders, V. E.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[CrossRef]

Schleich, W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[CrossRef]

J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A 25, 2214–2225 (1982).
[CrossRef]

Schneider, M.

H. R. Bilger, G. E. Stedman, Z. Li, U. Schreiber, M. Schneider, “Ring lasers for Geodesy,” IEEE Trans. Instrum. Meas. 44, 468–470 (1995).
[CrossRef]

Schreiber, U.

H. R. Bilger, G. E. Stedman, Z. Li, U. Schreiber, M. Schneider, “Ring lasers for Geodesy,” IEEE Trans. Instrum. Meas. 44, 468–470 (1995).
[CrossRef]

Schreiber, U. K.

Scully, M. O.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57, 61–104 (1985).
[CrossRef]

J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A 25, 2214–2225 (1982).
[CrossRef]

Smith, I.

H. Statz, T. A. Dorschner, M. Holtz, I. Smith, The Multioscillator Ring Laser Gyroscope, Vol. 4 of the Laser Handbook (Elsevier, Amsterdam, 1985).

Smith, I. W.

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron. QE-16, 1376–1379 (1980).
[CrossRef]

Statz, H.

T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron. QE-16, 1376–1379 (1980).
[CrossRef]

H. Statz, T. A. Dorschner, M. Holtz, I. Smith, The Multioscillator Ring Laser Gyroscope, Vol. 4 of the Laser Handbook (Elsevier, Amsterdam, 1985).

Stedman, G. E.

C. P. Wyss, D. N. Wright, B. T. King, D. P. McLeod, S. J. Cooper, G. E. Stedman, “Collision broadening and quantum noise in a very large laser gyroscope,” Opt. Commun. 174, 181–189 (2000).
[CrossRef]

C. H. Rowe, U. K. Schreiber, S. J. Cooper, B. T. King, M. Poulton, G. E. Stedman, “Design and operation of a very large ring laser gyroscope,” Appl. Opt. 38, 2516–2523 (1999).
[CrossRef]

G. E. Stedman, “Ring-laser tests of fundamental physics and geophysics,” Rep. Prog. Phys. 60, 615–688 (1997).
[CrossRef]

H. R. Bilger, G. E. Stedman, Z. Li, U. Schreiber, M. Schneider, “Ring lasers for Geodesy,” IEEE Trans. Instrum. Meas. 44, 468–470 (1995).
[CrossRef]

R. Anderson, H. R. Bilger, G. E. Stedman, “‘Sagnac’ effect: a century of Earth-rotated interferometers,” Am. J. Phys. 62, 975–985 (1994).
[CrossRef]

H. R. Bilger, G. E. Stedman, M. P. Poulton, C. H. Rowe, Z. Li, P. V. Wells, “Ring laser for precision measurement of nonreciprocal phenomena,” IEEE Trans. Instrum. Meas. 42, 407–411 (1993).
[CrossRef]

G. E. Stedman, H. R. Bilger, Z. Li, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Austr. J. Phys. 46, 87–101 (1993).

Ulrych, T. J.

T. J. Ulrych, T. N. Bishop, “Maximum entropy spectral analysis and autoregressive decomposition,” Rev. Geophys. Space Phys. 13, 183–200 (1975).
[CrossRef]

Vetharaniam, I.

G. E. Stedman, H. R. Bilger, Z. Li, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Austr. J. Phys. 46, 87–101 (1993).

Wells, P. V.

G. E. Stedman, H. R. Bilger, Z. Li, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Austr. J. Phys. 46, 87–101 (1993).

H. R. Bilger, G. E. Stedman, M. P. Poulton, C. H. Rowe, Z. Li, P. V. Wells, “Ring laser for precision measurement of nonreciprocal phenomena,” IEEE Trans. Instrum. Meas. 42, 407–411 (1993).
[CrossRef]

Wilkinson, J. R.

J. R. Wilkinson, “Ring lasers,” Prog. Quantum Electron. 11, 1–103 (1987).
[CrossRef]

Wright, D. N.

C. P. Wyss, D. N. Wright, B. T. King, D. P. McLeod, S. J. Cooper, G. E. Stedman, “Collision broadening and quantum noise in a very large laser gyroscope,” Opt. Commun. 174, 181–189 (2000).
[CrossRef]

Wyss, C. P.

C. P. Wyss, D. N. Wright, B. T. King, D. P. McLeod, S. J. Cooper, G. E. Stedman, “Collision broadening and quantum noise in a very large laser gyroscope,” Opt. Commun. 174, 181–189 (2000).
[CrossRef]

Am. J. Phys. (1)

R. Anderson, H. R. Bilger, G. E. Stedman, “‘Sagnac’ effect: a century of Earth-rotated interferometers,” Am. J. Phys. 62, 975–985 (1994).
[CrossRef]

Appl. Opt. (1)

Austr. J. Phys. (1)

G. E. Stedman, H. R. Bilger, Z. Li, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Austr. J. Phys. 46, 87–101 (1993).

Geophys. J. Int. (1)

R. S. Gross, “Correspondence between theory and observations of polar motion,” Geophys. J. Int. 109, 162–170 (1992).
[CrossRef]

Geophys. J. R. Astron. Soc. (2)

V. F. Pisarenko, “On the estimation of spectra by means of nonlinear functions of the covariance matrix,” Geophys. J. R. Astron. Soc. 28, 511–531 (1972).
[CrossRef]

V. F. Pisarenko, “The retrieval of harmonics from a covariance function,” Geophys. J. R. Astron. Soc. 33, 347–366 (1973).
[CrossRef]

IEEE J. Quantum Electron. (1)

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H. R. Bilger, G. E. Stedman, M. P. Poulton, C. H. Rowe, Z. Li, P. V. Wells, “Ring laser for precision measurement of nonreciprocal phenomena,” IEEE Trans. Instrum. Meas. 42, 407–411 (1993).
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R. S. Gross, “Combinations of Earth orientation measurements: SPACE94, COMB94, and POLE94,” J. Geophys. Res. 101, 8729–8740 (1996).
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Opt. Commun. (1)

C. P. Wyss, D. N. Wright, B. T. King, D. P. McLeod, S. J. Cooper, G. E. Stedman, “Collision broadening and quantum noise in a very large laser gyroscope,” Opt. Commun. 174, 181–189 (2000).
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Figures (3)

Fig. 1
Fig. 1

Stability of C-I is shown in the form of an Allan deviation for data collected on 12 October 1998 starting at 16:33:00 (New Zealand Daylight Time). Frequency estimates are made with the waveform fitting to 1-s segments of data; the waveform is sampled at 1 kHz. The insert illustrates the T -1/2 power-law dependence for short measurement times.

Fig. 2
Fig. 2

Analysis scheme. The parameters A, C, f 0, and β in Eq. (17) can be chosen so that the resulting waveform represents the stored waveform as closely as possible. ADC, analog-to-digital converter.

Fig. 3
Fig. 3

Results of the linewidth estimation for both methods. (a) The initial method provides an independent measure of linewidth Γ1, which should be compared with (b) the AR(2) estimates Γ2, which are presented for β = 0.035. (c) The distributions of the two methods where the distribution of Γ2 is shown by a dashed curve for β = 0.045 (left) and β = 0.025 (right).

Equations (19)

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Δfrms=12πω32PQ2T1/2,
Γ=12πω32PQ2.
Γ=12πω2tffsrQP0.
σ2=1nk=1nyk-y¯2,
σA2=12n-1k=1n-1yk+1-yk2,
limn σA2=limn σ2
xt+a1xt-1+a2xt-2=t
a2<1, a2+1>|a1|.
Sf=12π2σ2|1+a1 exp2iπf+a2 exp4iπf|2.
f0=12πcos-1-a1a2+14a2,
δ=12π {cos-1cos2πf0-ζ-cos-1cos2πf0+ζ},
ζ=4a2-a121/21-a24a2
Sf=18πa22σ2cos2πf-cos2πf02+ζ2,
Ea1, a2=12N-2t=3NXt+a1Xt-1+a2Xt-22+Xt-2+a1Xt-1+a2Xt2,
-a11, 2+1, 0-2 1, 10, 0+2, 22, 1+0, 1=20, 2-0, 0-2, 2,-2a11, 12, 1+0, 1-a2=1,
m, n=t=3N Xt-mXt-n.
Xj=C+Asin2πf0tj+ϕj+βrj,
ϕj=2πγτ k=1j sk,
δ¯=α1γ+α2β2,

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