Abstract

A modulation–demodulation scheme substantially enhances diffusion-dominated–adaptive-interferometric sensitivity. The path length sensitivity is improved by converting a quadratic small-signal response, easily drowned in system noise, to a linear response by mixing with a strong phase modulation. This conversion also shifts low-frequency signals away from 1/f noise. Experimental results show 180fm/Hz displacement sensitivity for a 5  Hz signal with a few milliwatts of optical power, an improvement of 3 orders of magnitude over the unenhanced system.

© 2007 Optical Society of America

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References

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  1. D. Z. Anderson and J. Feinberg, "Optical novelty filters," IEEE J. Quantum Electron. 25, 635-647 (1989).
    [CrossRef]
  2. P. Delaye, L. A. de Montmorillon, and G. Roosen, "Transmission of time-modulated optical signals through an absorbing photorefractive crystal," Opt. Commun. 118, 154-164 (1995).
    [CrossRef]
  3. A. A. Kamshilin and A. I. Grachev, "Adaptive interferometer based on wave mixing in a photorefractive crystal under alternating electric field," Appl. Phys. Lett. 81, 2923-2925 (2002).
    [CrossRef]
  4. B. R. Pouet, R. Ing, S. Krishnaswamy, and D. Royer, "Heterodyne interferometer with two-wave mixing in photorefractive crystals for ultrasound detection on rough surfaces."Appl. Phys. Lett. 69, 3782-3784 (1996).
    [CrossRef]
  5. V. Petrov, C. Denz, J. Petter, and T. Tschudi, "Enhancing the sensitivity of an adaptive holographic interferometer using non-Bragg diffraction orders," Opt. Lett. 22, 1902-1904 (1997),
    [CrossRef]
  6. P. C. D. Hobbs, "Ultrasensitive laser measurements without tears," Appl. Opt. 36, 903-920 (1997).
    [CrossRef] [PubMed]
  7. D. Z. Anderson, R. W. Brockett, and N. Nuttall, "Information dynamics of photorefractive two-beam coupling," Phys. Rev. Lett. 82, 1418-1421 (1999).
    [CrossRef]

2002 (1)

A. A. Kamshilin and A. I. Grachev, "Adaptive interferometer based on wave mixing in a photorefractive crystal under alternating electric field," Appl. Phys. Lett. 81, 2923-2925 (2002).
[CrossRef]

1999 (1)

D. Z. Anderson, R. W. Brockett, and N. Nuttall, "Information dynamics of photorefractive two-beam coupling," Phys. Rev. Lett. 82, 1418-1421 (1999).
[CrossRef]

1997 (2)

1996 (1)

B. R. Pouet, R. Ing, S. Krishnaswamy, and D. Royer, "Heterodyne interferometer with two-wave mixing in photorefractive crystals for ultrasound detection on rough surfaces."Appl. Phys. Lett. 69, 3782-3784 (1996).
[CrossRef]

1995 (1)

P. Delaye, L. A. de Montmorillon, and G. Roosen, "Transmission of time-modulated optical signals through an absorbing photorefractive crystal," Opt. Commun. 118, 154-164 (1995).
[CrossRef]

1989 (1)

D. Z. Anderson and J. Feinberg, "Optical novelty filters," IEEE J. Quantum Electron. 25, 635-647 (1989).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. A. Kamshilin and A. I. Grachev, "Adaptive interferometer based on wave mixing in a photorefractive crystal under alternating electric field," Appl. Phys. Lett. 81, 2923-2925 (2002).
[CrossRef]

B. R. Pouet, R. Ing, S. Krishnaswamy, and D. Royer, "Heterodyne interferometer with two-wave mixing in photorefractive crystals for ultrasound detection on rough surfaces."Appl. Phys. Lett. 69, 3782-3784 (1996).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Z. Anderson and J. Feinberg, "Optical novelty filters," IEEE J. Quantum Electron. 25, 635-647 (1989).
[CrossRef]

Opt. Commun. (1)

P. Delaye, L. A. de Montmorillon, and G. Roosen, "Transmission of time-modulated optical signals through an absorbing photorefractive crystal," Opt. Commun. 118, 154-164 (1995).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

D. Z. Anderson, R. W. Brockett, and N. Nuttall, "Information dynamics of photorefractive two-beam coupling," Phys. Rev. Lett. 82, 1418-1421 (1999).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of the improved holographic interferometer using a kilohertz reference signal and dual synchronous demodulation of the mixed signal. The ω S = 2 π × 5 Hz signal generator is only used for calibration purposes.

Fig. 2
Fig. 2

Evolution of field vectors with a single small signal. The unenhanced signal [Eq. (5)] arises from the | sum | 2 of the projection of the signal's second-harmonic ( m = 2 ) and ( ) port field vectors onto the ( ) axis.

Fig. 3
Fig. 3

Evolution of field vectors with modulation-enhanced sensitivity. The enhanced signal [Eq. (9)] arises from the | sum | 2 of the projection of the signal's first-harmonic and reference field vectors onto the ( ) axis.

Equations (9)

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[ E + E ] = [ E + 0 exp [ i δ S sin ( ω S t ) ] E 0 ] .
ρ = 1 I [ | E ω + | 2 ω E ω + ω E ω * ω E ω + * ω E ω | E ω | 2 ] 1 I [ | E + | 2 E + E * E E + * | E | 2 ] ,
T [ cos ( β ) sin ( β ) sin ( β ) cos ( β ) ] .
I = | E | 2 = | E + sin ( θ 0 ) + E cos ( θ 0 ) | 2 .
I 2 ω = 2 E + 0 E 0 J 2 [ δ S ( t ) ] sin ( 2 θ 0 ) cos ( 2 ω S t ) .
[ E + E ] = { E + 0 exp [ i ( δ S sin ( ω S t ) ) ] E 0 exp [ i ( δ R sin ( ω R t ) ) ] } ,
ρ = 1 I [ | E ω + | 2 ω E ω + ω E ω * ω E ω + * ω E ω | E ω | 2 ] 1 I [ | E + | 2 ω E ω + E ω * ω E ω + * E ω | E | 2 ] .
β = { arctan [ e Λ L tan ( θ 0 ) ] θ 0 } | Λ L > 10 θ 0 ,
I sum / dif = 2 E + 0 E 0 J 1 [ δ S ( t ) ] J 1 ( δ R ) sin ( 2 θ 0 ) × cos [ ( ω S ± ω M ) t ] .

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