Abstract

Digitally enhanced heterodyne interferometry is a laser metrology technique employing pseudo-random codes phase modulated onto an optical carrier. We present the first characterization of the technique’s displacement sensitivity. The displacement of an optical cavity was measured using digitally enhanced heterodyne interferometry and compared to a simultaneous readout based on conventional Pound-Drever-Hall locking. The techniques agreed to within 5 pm/√Hz at 1 Hz, providing an upper bound to the displacement noise of digitally enhanced heterodyne interfer-ometry. These measurements employed a real-time signal extraction system implemented on a field programmable gate array, suitable for closed-loop control applications. We discuss the applicability of digitally enhanced heterodyne interferometry for lock acquisition of advanced gravitational wave detectors.

© 2009 Optical Society of America

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References

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  1. N. Bobroff, "Recent advances in displacement measuring interferometry," Meas. Sci. Technol. 4, 907 (1993).
    [CrossRef]
  2. D. A. Shaddock, "Digitally enhanced heterodyne interferometry," Opt. Lett. 32, 3355-3357 (2007).
    [CrossRef] [PubMed]
  3. O. Lay, S. Dubovitsky, D. A. Shaddock, and B. Ware, "Coherent range-gated laser distance metrology with compact optical head," Opt. Lett. 32, 2933-2935 (2007).
    [CrossRef] [PubMed]
  4. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
    [CrossRef]
  5. O. Lay, Private Communication (2008).
  6. See for example http://www.ligo.caltech.edu/advLIGO/ or A. Weinstein for the LSC, "Advanced LIGO optical configuration and prototyping effort," Class. Quantum Grav. 19, 1575-1584 (2002).
  7. Y. Aso, M. Ando, K. Kawabe, S. Otsuka, and K. Tsubono, "Stabilisation of a Fabry-Perot interferometer using a suspension-point interferometer," Phys. Lett. A 327, 18 (2004).
    [CrossRef]
  8. B. J. J. Slagmolen, G. de Vine, D. S. Rabeling, K. McKenzie, A. J. Mullavey, D. A. Shaddock, D. E. McClelland, M. Evans, and Y. Aso, "Advanced LIGO arm cavity pre-lock acquisition system," http://www.ligo.caltech.edu/docs/T/T080139-00.pdf (2008).

2007 (2)

2004 (1)

Y. Aso, M. Ando, K. Kawabe, S. Otsuka, and K. Tsubono, "Stabilisation of a Fabry-Perot interferometer using a suspension-point interferometer," Phys. Lett. A 327, 18 (2004).
[CrossRef]

1993 (1)

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

1983 (1)

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

Ando, M.

Y. Aso, M. Ando, K. Kawabe, S. Otsuka, and K. Tsubono, "Stabilisation of a Fabry-Perot interferometer using a suspension-point interferometer," Phys. Lett. A 327, 18 (2004).
[CrossRef]

Aso, Y.

Y. Aso, M. Ando, K. Kawabe, S. Otsuka, and K. Tsubono, "Stabilisation of a Fabry-Perot interferometer using a suspension-point interferometer," Phys. Lett. A 327, 18 (2004).
[CrossRef]

Bobroff, N.

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

Drever, R. W. P.

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

Dubovitsky, S.

Ford, G. M.

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

Hall, J. L.

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

Kawabe, K.

Y. Aso, M. Ando, K. Kawabe, S. Otsuka, and K. Tsubono, "Stabilisation of a Fabry-Perot interferometer using a suspension-point interferometer," Phys. Lett. A 327, 18 (2004).
[CrossRef]

Kowalski, F. V.

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

Lay, O.

Munley, A. J.

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

Otsuka, S.

Y. Aso, M. Ando, K. Kawabe, S. Otsuka, and K. Tsubono, "Stabilisation of a Fabry-Perot interferometer using a suspension-point interferometer," Phys. Lett. A 327, 18 (2004).
[CrossRef]

Shaddock, D. A.

Tsubono, K.

Y. Aso, M. Ando, K. Kawabe, S. Otsuka, and K. Tsubono, "Stabilisation of a Fabry-Perot interferometer using a suspension-point interferometer," Phys. Lett. A 327, 18 (2004).
[CrossRef]

Ward, H.

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

Ware, B.

Appl. Phys. B (1)

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

Meas. Sci. Technol. (1)

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

Opt. Lett. (2)

Phys. Lett. A (1)

Y. Aso, M. Ando, K. Kawabe, S. Otsuka, and K. Tsubono, "Stabilisation of a Fabry-Perot interferometer using a suspension-point interferometer," Phys. Lett. A 327, 18 (2004).
[CrossRef]

Other (3)

B. J. J. Slagmolen, G. de Vine, D. S. Rabeling, K. McKenzie, A. J. Mullavey, D. A. Shaddock, D. E. McClelland, M. Evans, and Y. Aso, "Advanced LIGO arm cavity pre-lock acquisition system," http://www.ligo.caltech.edu/docs/T/T080139-00.pdf (2008).

O. Lay, Private Communication (2008).

See for example http://www.ligo.caltech.edu/advLIGO/ or A. Weinstein for the LSC, "Advanced LIGO optical configuration and prototyping effort," Class. Quantum Grav. 19, 1575-1584 (2002).

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Figures (7)

Fig. 1.
Fig. 1.

Digital Interferometer for monitoring displacements of two mirrors, M1 and M2. Signals are isolated by matching the decoding delays to the optical delays. Signals measured at points A, B, C1, C2, D1, and D2 are shown in Table 1.

Fig. 2.
Fig. 2.

Simplified experimental layout of digital interferometry transmission technique for displacement sensitivity measurements.

Fig. 3.
Fig. 3.

Spectral density of the DI measurement of cavity displacement when the cavity is locked using PDH locking. Spectral density averaged for clarity (3x for 0.1> f >1 Hz, and 10x for f >1 Hz). note: The roll-off above 100 Hz is due to the transfer function of the phasemeter.

Fig. 4.
Fig. 4.

Comparison of DI readout (A) and digital implementation of PDH readout (B) with the cavity locked using the analog PDH system. The feature (C) is a calibration peak used to scale the digital PDH readout. The lower noise level of (B) indicates good agreement of analog and digital PDH systems and rules out analog electronic noise in the mixer and controller as the limitation of the DI measurement.

Fig. 5.
Fig. 5.

Single-pass and 4th-round-trip DI measurements when the cavity length is scanned. The cavity length change appears strongly in the phase measurement of the 4th-round-trip but not in the single-pass phase measurement.

Fig. 6.
Fig. 6.

Root power spectral density of data from Fig. 5. The ratio of the 1Hz scan signal sets an upper bound on the crosstalk between channels at less than 10-3 (α > 1000).

Fig. 7.
Fig. 7.

Comparison of (a) DI and (b) PDH signals as the cavity length is scanned over more than one FSR. The techniques differ by 0.6% on the FSR. 1 FSR measured by PDH equal to 1.0063 cycles measured by digital interferometry. Note that the DI readout remains linear over the entire FSR.

Tables (1)

Tables Icon

Table 1. Signals from single-pass beam with matched (middle column) and unmatched (right column) decoding delays. Signals A, B, C1, C2, D1, D2 correspond to the measurement points in Fig. 1.

Equations (4)

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δ ϕ sn = h v p rad / Hz
δL = λ 2 π ( ϕ j ϕ k ) 2 ( j k )
δ L PDH ~ λ 2 π P PDH P DI 2 δθ 2 ( j k ) α
δ L PDH ~ δθ × 670 pm

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