Abstract

We determine the maximum accuracy in the wavelength measurement of finite-bandwidth optical signals. The limit is dependent on the spectral and coherence properties of the optical signal and on the available optical power. We also investigate the effect of finite measurement resolution in the wavelength measurement.

© 2004 Optical Society of America

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References

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  1. M. Teshima, M. Koga, and K. I. Sato, “Performance of multiwavelength simultaneous monitoring circuit employing an arrayed-waveguide grating,” J. Lightwave Technol. 14, 2277–2285 (1996).
    [CrossRef]
  2. M. G. Shim, B. Wilson, E. Marple, and M. Wach, “Study of fiber-optic probes for in vivo medical Raman spectroscopy,” Appl. Spectrosc. 53, 619–627 (1999).
    [CrossRef]
  3. A. D. Kersey, M. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and J. Frieble, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1462 (1997).
    [CrossRef]
  4. S. M. Melle, K. Liu, and R. M. Measures, “A passive wavelength demodulation system for guided-wave Bragg grating sensors,” IEEE Photon. Technol. Lett. 4, 516–518 (1992).
    [CrossRef]
  5. C. G. Atkins, M. A. Putnam, and E. J. Frieble, “Instrumentation for interrogating many-element fiber Bragg grating arrays embedded in fiber/resin composites,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instumentation, W. B. Spillman, Jr., ed., Proc. SPIE 2444, 257–266 (1995).
  6. A. D. Kersey, T. A. Berkoff, and W. W. Morey, “Fiber-optic Bragg grating strain sensor with drift-compensated high-resolution interferometric wavelength-shift detection,” Opt. Lett. 18, 72–74 (1993).
    [CrossRef] [PubMed]
  7. A. D. Kersey, T. A. Berkoff, and W. W. Morey, “Multiplexed fiber Bragg grating strain-sensor system with a fiber Fabry–Perot wavelength filter,” Opt. Lett. 18, 1370–1372 (1993).
    [CrossRef]
  8. M. A. Davis and A. D. Kersey, “Application of a fiber Fourier transform spectrometer to the detection of wavelength-encoded signals from Bragg grating sensors,” J. Lightwave Technol. 13, 1289–1295 (1995).
    [CrossRef]
  9. R. Loudon, The Quantum Theory of Light (Oxford U. Press, Oxford, UK, 2000), Chap. 3, pp. 82–124.
  10. N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989).
    [CrossRef]
  11. S. P. Davis, Diffraction Grating Spectrographs (Holt, Rinehart & Winston, New York, 1970), Chap. 1, pp. 1–12.
  12. D. Zwillinger, CRC Standard Mathematical Tables and Formulae (CRC Press, Boca Raton, Fla., 1996), Chap. 7, p. 583.
  13. I. Bennion, J. A. R. Williams, L. Zhang, K. Sugnden, and N. J. Doran, “UV-written in-fiber Bragg gratings,” Opt. Quantum Electron. 28, 93–135 (1996).
    [CrossRef]

1999 (1)

1997 (1)

A. D. Kersey, M. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and J. Frieble, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1462 (1997).
[CrossRef]

1996 (2)

M. Teshima, M. Koga, and K. I. Sato, “Performance of multiwavelength simultaneous monitoring circuit employing an arrayed-waveguide grating,” J. Lightwave Technol. 14, 2277–2285 (1996).
[CrossRef]

I. Bennion, J. A. R. Williams, L. Zhang, K. Sugnden, and N. J. Doran, “UV-written in-fiber Bragg gratings,” Opt. Quantum Electron. 28, 93–135 (1996).
[CrossRef]

1995 (2)

C. G. Atkins, M. A. Putnam, and E. J. Frieble, “Instrumentation for interrogating many-element fiber Bragg grating arrays embedded in fiber/resin composites,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instumentation, W. B. Spillman, Jr., ed., Proc. SPIE 2444, 257–266 (1995).

M. A. Davis and A. D. Kersey, “Application of a fiber Fourier transform spectrometer to the detection of wavelength-encoded signals from Bragg grating sensors,” J. Lightwave Technol. 13, 1289–1295 (1995).
[CrossRef]

1993 (2)

1992 (1)

S. M. Melle, K. Liu, and R. M. Measures, “A passive wavelength demodulation system for guided-wave Bragg grating sensors,” IEEE Photon. Technol. Lett. 4, 516–518 (1992).
[CrossRef]

1989 (1)

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989).
[CrossRef]

Askins, C. G.

A. D. Kersey, M. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and J. Frieble, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1462 (1997).
[CrossRef]

Atkins, C. G.

C. G. Atkins, M. A. Putnam, and E. J. Frieble, “Instrumentation for interrogating many-element fiber Bragg grating arrays embedded in fiber/resin composites,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instumentation, W. B. Spillman, Jr., ed., Proc. SPIE 2444, 257–266 (1995).

Bennion, I.

I. Bennion, J. A. R. Williams, L. Zhang, K. Sugnden, and N. J. Doran, “UV-written in-fiber Bragg gratings,” Opt. Quantum Electron. 28, 93–135 (1996).
[CrossRef]

Berkoff, T. A.

Davis, M.

A. D. Kersey, M. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and J. Frieble, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1462 (1997).
[CrossRef]

Davis, M. A.

M. A. Davis and A. D. Kersey, “Application of a fiber Fourier transform spectrometer to the detection of wavelength-encoded signals from Bragg grating sensors,” J. Lightwave Technol. 13, 1289–1295 (1995).
[CrossRef]

Doran, N. J.

I. Bennion, J. A. R. Williams, L. Zhang, K. Sugnden, and N. J. Doran, “UV-written in-fiber Bragg gratings,” Opt. Quantum Electron. 28, 93–135 (1996).
[CrossRef]

Frieble, E. J.

C. G. Atkins, M. A. Putnam, and E. J. Frieble, “Instrumentation for interrogating many-element fiber Bragg grating arrays embedded in fiber/resin composites,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instumentation, W. B. Spillman, Jr., ed., Proc. SPIE 2444, 257–266 (1995).

Frieble, J.

A. D. Kersey, M. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and J. Frieble, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1462 (1997).
[CrossRef]

Kersey, A. D.

A. D. Kersey, M. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and J. Frieble, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1462 (1997).
[CrossRef]

M. A. Davis and A. D. Kersey, “Application of a fiber Fourier transform spectrometer to the detection of wavelength-encoded signals from Bragg grating sensors,” J. Lightwave Technol. 13, 1289–1295 (1995).
[CrossRef]

A. D. Kersey, T. A. Berkoff, and W. W. Morey, “Fiber-optic Bragg grating strain sensor with drift-compensated high-resolution interferometric wavelength-shift detection,” Opt. Lett. 18, 72–74 (1993).
[CrossRef] [PubMed]

A. D. Kersey, T. A. Berkoff, and W. W. Morey, “Multiplexed fiber Bragg grating strain-sensor system with a fiber Fabry–Perot wavelength filter,” Opt. Lett. 18, 1370–1372 (1993).
[CrossRef]

Koga, M.

M. Teshima, M. Koga, and K. I. Sato, “Performance of multiwavelength simultaneous monitoring circuit employing an arrayed-waveguide grating,” J. Lightwave Technol. 14, 2277–2285 (1996).
[CrossRef]

Koo, K. P.

A. D. Kersey, M. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and J. Frieble, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1462 (1997).
[CrossRef]

LeBlanc, M.

A. D. Kersey, M. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and J. Frieble, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1462 (1997).
[CrossRef]

Liu, K.

S. M. Melle, K. Liu, and R. M. Measures, “A passive wavelength demodulation system for guided-wave Bragg grating sensors,” IEEE Photon. Technol. Lett. 4, 516–518 (1992).
[CrossRef]

Marple, E.

Measures, R. M.

S. M. Melle, K. Liu, and R. M. Measures, “A passive wavelength demodulation system for guided-wave Bragg grating sensors,” IEEE Photon. Technol. Lett. 4, 516–518 (1992).
[CrossRef]

Melle, S. M.

S. M. Melle, K. Liu, and R. M. Measures, “A passive wavelength demodulation system for guided-wave Bragg grating sensors,” IEEE Photon. Technol. Lett. 4, 516–518 (1992).
[CrossRef]

Morey, W. W.

Olsson, N. A.

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989).
[CrossRef]

Patrick, H. J.

A. D. Kersey, M. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and J. Frieble, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1462 (1997).
[CrossRef]

Putnam, M. A.

A. D. Kersey, M. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and J. Frieble, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1462 (1997).
[CrossRef]

C. G. Atkins, M. A. Putnam, and E. J. Frieble, “Instrumentation for interrogating many-element fiber Bragg grating arrays embedded in fiber/resin composites,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instumentation, W. B. Spillman, Jr., ed., Proc. SPIE 2444, 257–266 (1995).

Sato, K. I.

M. Teshima, M. Koga, and K. I. Sato, “Performance of multiwavelength simultaneous monitoring circuit employing an arrayed-waveguide grating,” J. Lightwave Technol. 14, 2277–2285 (1996).
[CrossRef]

Shim, M. G.

Sugnden, K.

I. Bennion, J. A. R. Williams, L. Zhang, K. Sugnden, and N. J. Doran, “UV-written in-fiber Bragg gratings,” Opt. Quantum Electron. 28, 93–135 (1996).
[CrossRef]

Teshima, M.

M. Teshima, M. Koga, and K. I. Sato, “Performance of multiwavelength simultaneous monitoring circuit employing an arrayed-waveguide grating,” J. Lightwave Technol. 14, 2277–2285 (1996).
[CrossRef]

Wach, M.

Williams, J. A. R.

I. Bennion, J. A. R. Williams, L. Zhang, K. Sugnden, and N. J. Doran, “UV-written in-fiber Bragg gratings,” Opt. Quantum Electron. 28, 93–135 (1996).
[CrossRef]

Wilson, B.

Zhang, L.

I. Bennion, J. A. R. Williams, L. Zhang, K. Sugnden, and N. J. Doran, “UV-written in-fiber Bragg gratings,” Opt. Quantum Electron. 28, 93–135 (1996).
[CrossRef]

Appl. Spectrosc. (1)

IEEE Photon. Technol. Lett. (1)

S. M. Melle, K. Liu, and R. M. Measures, “A passive wavelength demodulation system for guided-wave Bragg grating sensors,” IEEE Photon. Technol. Lett. 4, 516–518 (1992).
[CrossRef]

J. Lightwave Technol. (4)

M. A. Davis and A. D. Kersey, “Application of a fiber Fourier transform spectrometer to the detection of wavelength-encoded signals from Bragg grating sensors,” J. Lightwave Technol. 13, 1289–1295 (1995).
[CrossRef]

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989).
[CrossRef]

A. D. Kersey, M. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and J. Frieble, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1462 (1997).
[CrossRef]

M. Teshima, M. Koga, and K. I. Sato, “Performance of multiwavelength simultaneous monitoring circuit employing an arrayed-waveguide grating,” J. Lightwave Technol. 14, 2277–2285 (1996).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

I. Bennion, J. A. R. Williams, L. Zhang, K. Sugnden, and N. J. Doran, “UV-written in-fiber Bragg gratings,” Opt. Quantum Electron. 28, 93–135 (1996).
[CrossRef]

Proc. SPIE (1)

C. G. Atkins, M. A. Putnam, and E. J. Frieble, “Instrumentation for interrogating many-element fiber Bragg grating arrays embedded in fiber/resin composites,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instumentation, W. B. Spillman, Jr., ed., Proc. SPIE 2444, 257–266 (1995).

Other (3)

R. Loudon, The Quantum Theory of Light (Oxford U. Press, Oxford, UK, 2000), Chap. 3, pp. 82–124.

S. P. Davis, Diffraction Grating Spectrographs (Holt, Rinehart & Winston, New York, 1970), Chap. 1, pp. 1–12.

D. Zwillinger, CRC Standard Mathematical Tables and Formulae (CRC Press, Boca Raton, Fla., 1996), Chap. 7, p. 583.

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Figures (4)

Fig. 1
Fig. 1

Typical power spectrum of an optical signal that could be measured to determine the mean wavelength λm. The bandwidth of the spectrum is given by Δλw. g(λ) is the spectral line-shape function.

Fig. 2
Fig. 2

Spectrometer configuration for the measurement of an optical spectrum. Light from a single-mode source is expanded and collimated onto a two-dimensional diffraction grating. The angle of diffraction is dependent on the wavelength of the signal. The diffracted light is focused onto an array of photodetectors to obtain the spectral information of the optical signal. The individual photodetectors are referenced by their index number i, i+1, and so on.

Fig. 3
Fig. 3

Wavelength measurement resolution for a 0.2-nm FWHM signal and a 10-nm measurement range. Resolutions for a sinc2( ) and a Gaussian-shaped power spectrum are shown as well as the difference between a signal from a coherent and incoherent light source. The decreased resolution for incoherent pulsed light with a duty cycle of 1% is also shown.

Fig. 4
Fig. 4

Ratio in wavelength measurement resolution between a sinc2( ) and a Gaussian-shaped power spectrum as a function of the full-scale measurement range. The Gaussian provides much better resolution for large measurement ranges. The dashed curve indicates that values there are approximate because assumptions in the text are less accurate in this regime.

Equations (32)

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ΔtΔν14πorΔtΔλλ024πc,
λm=i=-niλin,
(λm-λm)=i=-ni(λi-λm)n.
(λm-λm)=i=-niiΔλdn,
VAR(λm)=λm2-λm2=Δλd2n2i=-i2VAR(ni),
VAR(ni)=ni+ni2Γ,
Γ=cΔλdDλm2Be,
VAR(λm)=Δλd2n2i=-i2ni+λm2BecΔλdDi=-i2ni2.
ni=nΔλdg(iΔλd)i=-g(iΔλd)Δλd,
-iΔλdg(iΔλd)Δλd=0.
VAR(λm)=1ni=-(iΔλd)2gˆ(iΔλd)Δλd+λm2BecDi=-(iΔλd)2gˆ2(iΔλd)Δλd,
VAR(λm)=1n-λ2gˆ(λ)dλ+λm2BecD-λ2gˆ2(λ)dλ.
λm-λm=1nk=-kΔλdj=-xkj.
VAR(λm)=1n2j=-VARk=-kΔλdxkj,
=1n2j=-k=-k2ΔλdVAR(xkj)+ikikΔλd2COV(xkj, xij),
xkj2=l=0xkj2(nj=l)P(nj=l),
=l=0[lpk(1-pk)+l2pk2]P(nj=1),
xkj2=njpk(1-pk)+nj2pk2,
VAR(xkj)=njpk(1-pk)+VAR(nj)pk2.
xkjxijki=l=0xkjxij(nj=l)P(nj=l),
=-njpkpi+ni2pkpi,
COV(xkj, xij)=-njpkpi+VAR(nj)pkpi.
VAR(λm)=1n2j=-njk=-(kΔλd)2pk+[VAR(nj)-nj]k=-kΔλdpki=-iΔλdpi.
k=-kΔλdpk=jΔλs,
k=-(kΔλd)2pk=k=-(kΔλd)2h(kΔλd)Δλd+(jΔλs)2,
VAR(λm)=j=-gˆ(jΔλs)Δλsnk=-(kΔλd)2hˆ(kΔλd)Δλd+1n2j=-VAR(nj)(jΔλs)2.
VAR(λm)=1n-λ2hˆ(λ)dλ+1n-λ2gˆ(λ)dλ+λm2BecD-λ2gˆ2(λ)dλ.
gˆ(λ)=2Δλwln 2π1/2 exp-2(ln 2λ)1/2Δλw2,
gˆ(λ)=Δλw2.78πλ2sin22.78λΔλw.
Δλm,Gaus=0.42Δλw2(n)1/2,Δλm,sinc=0.34(ΔλtΔλw)1/2(n)1/2.
Δλm,min=0.24λm(ΔλwBe)1/2(cD)1/2
Δλm,sincΔλm,Gaus=0.8ΔλtΔλw1/2.

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