Abstract

We implement a digital fringe-counting technique to measure in real time the relative mirror displacement of a suspended Michelson interferometer with modulated optical path length for oscillations much larger than the laser wavelength (λ). This provides the proper error signal for a servo mechanism that reduces the relative displacement within λ/2. The implemented technique does not require extra optics or polarizers and thus can be used for interferometric gravitational wave detectors as a starting procedure to get the system locked.

© 1994 Optical Society of America

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References

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  1. For a review of GW interferometric detectors see, for example, The Detection of Gravitational Waves, D. G. Blair, ed. (Cambridge U. Press, Cambridge, 1991).
    [CrossRef]
  2. C. Bradaschia, R. Del Fabbro, L. Di Fiore, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, “First results on the electronic cooling of the Pisa seismic noise super-attenuator for gravitational wave detection,” Phys. Lett. A 137, 329–333 (1989).
    [CrossRef]
  3. The Virgo Project, a proposal by a collaboration of 38 physicists of the Italian–French large base interferometric antenna Virgo for GW detection, June 1989, of which F. Barone, L. Di Fiore, L. Milano, and G. Russo are members.
  4. A. Augurio, F. Barone, E. Calloni, L. Di Fiore, L. Milano, G. Russo, S. Solimeno, “Automatic control system for mirrors alignment of interferometric antenna Virgo,” presented at the Sixth Marcel Grossman Meeting on General Relativity, Kyoto, Japan, 23–29 June 1991.
  5. A. Sona, “Laser in metrology: distance measurements,” in Laser Handbook, F. T. Arecchi, E. O. Shulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, pp. 1457–1486.
  6. H. J. Tiziani, “Optical methods for precision measurements,” Opt. Quantum Electron. 21, 253–282 (1989).
    [CrossRef]

1989 (2)

C. Bradaschia, R. Del Fabbro, L. Di Fiore, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, “First results on the electronic cooling of the Pisa seismic noise super-attenuator for gravitational wave detection,” Phys. Lett. A 137, 329–333 (1989).
[CrossRef]

H. J. Tiziani, “Optical methods for precision measurements,” Opt. Quantum Electron. 21, 253–282 (1989).
[CrossRef]

Augurio, A.

A. Augurio, F. Barone, E. Calloni, L. Di Fiore, L. Milano, G. Russo, S. Solimeno, “Automatic control system for mirrors alignment of interferometric antenna Virgo,” presented at the Sixth Marcel Grossman Meeting on General Relativity, Kyoto, Japan, 23–29 June 1991.

Barone, F.

A. Augurio, F. Barone, E. Calloni, L. Di Fiore, L. Milano, G. Russo, S. Solimeno, “Automatic control system for mirrors alignment of interferometric antenna Virgo,” presented at the Sixth Marcel Grossman Meeting on General Relativity, Kyoto, Japan, 23–29 June 1991.

Bradaschia, C.

C. Bradaschia, R. Del Fabbro, L. Di Fiore, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, “First results on the electronic cooling of the Pisa seismic noise super-attenuator for gravitational wave detection,” Phys. Lett. A 137, 329–333 (1989).
[CrossRef]

Calloni, E.

A. Augurio, F. Barone, E. Calloni, L. Di Fiore, L. Milano, G. Russo, S. Solimeno, “Automatic control system for mirrors alignment of interferometric antenna Virgo,” presented at the Sixth Marcel Grossman Meeting on General Relativity, Kyoto, Japan, 23–29 June 1991.

Del Fabbro, R.

C. Bradaschia, R. Del Fabbro, L. Di Fiore, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, “First results on the electronic cooling of the Pisa seismic noise super-attenuator for gravitational wave detection,” Phys. Lett. A 137, 329–333 (1989).
[CrossRef]

Di Fiore, L.

C. Bradaschia, R. Del Fabbro, L. Di Fiore, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, “First results on the electronic cooling of the Pisa seismic noise super-attenuator for gravitational wave detection,” Phys. Lett. A 137, 329–333 (1989).
[CrossRef]

A. Augurio, F. Barone, E. Calloni, L. Di Fiore, L. Milano, G. Russo, S. Solimeno, “Automatic control system for mirrors alignment of interferometric antenna Virgo,” presented at the Sixth Marcel Grossman Meeting on General Relativity, Kyoto, Japan, 23–29 June 1991.

Di Virgilio, A.

C. Bradaschia, R. Del Fabbro, L. Di Fiore, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, “First results on the electronic cooling of the Pisa seismic noise super-attenuator for gravitational wave detection,” Phys. Lett. A 137, 329–333 (1989).
[CrossRef]

Giazotto, A.

C. Bradaschia, R. Del Fabbro, L. Di Fiore, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, “First results on the electronic cooling of the Pisa seismic noise super-attenuator for gravitational wave detection,” Phys. Lett. A 137, 329–333 (1989).
[CrossRef]

Kautzky, H.

C. Bradaschia, R. Del Fabbro, L. Di Fiore, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, “First results on the electronic cooling of the Pisa seismic noise super-attenuator for gravitational wave detection,” Phys. Lett. A 137, 329–333 (1989).
[CrossRef]

Milano, L.

A. Augurio, F. Barone, E. Calloni, L. Di Fiore, L. Milano, G. Russo, S. Solimeno, “Automatic control system for mirrors alignment of interferometric antenna Virgo,” presented at the Sixth Marcel Grossman Meeting on General Relativity, Kyoto, Japan, 23–29 June 1991.

Montelatici, V.

C. Bradaschia, R. Del Fabbro, L. Di Fiore, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, “First results on the electronic cooling of the Pisa seismic noise super-attenuator for gravitational wave detection,” Phys. Lett. A 137, 329–333 (1989).
[CrossRef]

Passuello, D.

C. Bradaschia, R. Del Fabbro, L. Di Fiore, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, “First results on the electronic cooling of the Pisa seismic noise super-attenuator for gravitational wave detection,” Phys. Lett. A 137, 329–333 (1989).
[CrossRef]

Russo, G.

A. Augurio, F. Barone, E. Calloni, L. Di Fiore, L. Milano, G. Russo, S. Solimeno, “Automatic control system for mirrors alignment of interferometric antenna Virgo,” presented at the Sixth Marcel Grossman Meeting on General Relativity, Kyoto, Japan, 23–29 June 1991.

Solimeno, S.

A. Augurio, F. Barone, E. Calloni, L. Di Fiore, L. Milano, G. Russo, S. Solimeno, “Automatic control system for mirrors alignment of interferometric antenna Virgo,” presented at the Sixth Marcel Grossman Meeting on General Relativity, Kyoto, Japan, 23–29 June 1991.

Sona, A.

A. Sona, “Laser in metrology: distance measurements,” in Laser Handbook, F. T. Arecchi, E. O. Shulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, pp. 1457–1486.

Tiziani, H. J.

H. J. Tiziani, “Optical methods for precision measurements,” Opt. Quantum Electron. 21, 253–282 (1989).
[CrossRef]

Opt. Quantum Electron. (1)

H. J. Tiziani, “Optical methods for precision measurements,” Opt. Quantum Electron. 21, 253–282 (1989).
[CrossRef]

Phys. Lett. A (1)

C. Bradaschia, R. Del Fabbro, L. Di Fiore, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, “First results on the electronic cooling of the Pisa seismic noise super-attenuator for gravitational wave detection,” Phys. Lett. A 137, 329–333 (1989).
[CrossRef]

Other (4)

The Virgo Project, a proposal by a collaboration of 38 physicists of the Italian–French large base interferometric antenna Virgo for GW detection, June 1989, of which F. Barone, L. Di Fiore, L. Milano, and G. Russo are members.

A. Augurio, F. Barone, E. Calloni, L. Di Fiore, L. Milano, G. Russo, S. Solimeno, “Automatic control system for mirrors alignment of interferometric antenna Virgo,” presented at the Sixth Marcel Grossman Meeting on General Relativity, Kyoto, Japan, 23–29 June 1991.

A. Sona, “Laser in metrology: distance measurements,” in Laser Handbook, F. T. Arecchi, E. O. Shulz-Dubois, eds. (North-Holland, Amsterdam, 1972), Vol. 2, pp. 1457–1486.

For a review of GW interferometric detectors see, for example, The Detection of Gravitational Waves, D. G. Blair, ed. (Cambridge U. Press, Cambridge, 1991).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Input signal simulating a mirror oscillation. (b) Corresponding output of the fringe counter.

Fig. 2
Fig. 2

Experimental setup: BS, beam splitter; PD, photodiode; PS, position-sensing device; PZT, piezoelectric transducer; A, loop amplifier and current driver; M, mirror.

Fig. 3
Fig. 3

Measured interferometer (a) output and (b) recovered displacement in number of fringes, with the mirror free to oscillate along the optical axis.

Fig. 4
Fig. 4

Same as Fig. 3 but with a shorter record length (200 ms).

Fig. 5
Fig. 5

Measured interferometer (a) output and (b) recovered displacement in number of fringes, with the control loop closed. The oscillation is reduced to plus or minus one fringe.

Equations (11)

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P = P 0 2 ( 1 + C cos ϕ ) ,
ϕ = ϕ 0 + 4 π λ x ( t ) .
ϕ m = ϕ 0 + 4 π λ x ( t ) + m sin ( Ω m t ) .
P = P 0 2 ( 1 + C { cos [ ϕ 0 + 4 π λ x ( t ) ] J 0 ( m ) + 2 n = 1 J 2 n ( m ) cos ( 2 n Ω m t ) - 2 sin [ ϕ 0 + 4 π λ x ( t ) ] × n = 0 J 2 n + 1 ( m ) sin [ ( 2 n + 1 ) Ω m t ] } ) .
V dc = A 1 P 0 2 { 1 + C J 0 ( m ) cos [ ϕ 0 + 4 π λ x ( t ) ] } ,
V m = - A 2 P 0 C J 1 ( m ) sin [ ϕ 0 + 4 π λ x ( t ) ] ,
V ˙ dc = - A 1 P 0 2 C J 0 ( m ) sin [ ϕ 0 + 4 π λ x ( t ) ] 4 π λ x ˙ ( t ) .
V ˙ DC V m = 2 π A 1 J 0 ( m ) λ A 2 J 1 ( m ) x ˙ ( t ) = K x ˙ ( t ) ,
N = N + ( V ˙ dc / V m ) / V ˙ dc / V m .
V l = V min + 0.25 ( V max - V min ) ,
V u = V min + 0.75 ( V max - V min ) ,

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