Abstract

In this paper, we propose signal-processing tools adapted to supercontinuum absorption spectroscopy, in order to predict the precision of gas species concentration estimation. These tools are based on Cramer–Rao bounds computations. A baseline-insensitive concentration estimation algorithm is proposed. These calculations are validated by statistical tests on simulated supercontinuum signals as well as experimental data using a near-infrared supercontinuum laser and a grating spectrometer.

© 2012 Optical Society of America

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References

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  1. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
    [CrossRef]
  2. C. Xia, Z. Xu, M. N. Islam, F. L. Terry, M. J. Freeman, A. Zakel, and J. Mauricio, “10.5 watts time-averaged power mid-infrared supercontinuum generation extending beyond 4 m with direct pulse pattern modulation,” IEEE J. Sel. Top. Quantum Electron. 15, 422–434 (2009).
    [CrossRef]
  3. C. Agger, C. Petersen, S. Dupont, H. Steffensen, J. Lyngs, C. Thomsen, J. Thgersen, S. Keiding, and O. Bang, “Supercontinuum generation in ZBLAN fibers-detailed comparison between measurement and simulation,” J. Opt. Soc. Am. B 29, 635–645 (2012).
    [CrossRef]
  4. D. Brown, K. Shi, Z. Liu, and C. Philbrick, “Long-path supercontinuum absorption spectroscopy for measurement of atmospheric constituents,” Opt. Express 16, 8457–8471 (2008).
    [CrossRef]
  5. M. Kumar, M. Islam, F. Terry, M. Freeman, A. Chan, M. Neelakandan, and T. Manzur, “Stand-off detection of solid targets with diffuse reflection spectroscopy using a high-power mid-infrared supercontinuum source,” Appl. Opt. 51, 2794–2807 (2012).
    [CrossRef]
  6. R. Warren, “Optimum detection of multiple vapor materials with frequency-agile lidar,” Appl. Opt. 35, 4180–4193(1996).
    [CrossRef]
  7. S. Yin and W. Wang, “Novel algorithm for simultaneously detecting multiple vapor materials with multiple-wavelength differential absorption lidar,” Chin. Opt. Lett. 4, 360–362 (2006).
  8. Harry L. van Trees, Detection, Estimation, and Modulation Theory (Wiley, 1997).
  9. A. Kudlinski, B. Barviau, A. Leray, C. Spriet, L. Hliot, and A. Mussot, “Control of pulse-to-pulse fluctuations in visible supercontinuum,” Opt. Express 18, 27445–27454 (2010).
    [CrossRef]
  10. B. Wetzel, K. Blow, S. Turitsyn, G. Millot, L. Larger, and J. Dudley, “Random walks and random numbers from supercontinuum generation,” Opt. Express 20, 11143–11152 (2012).
    [CrossRef]
  11. D. M. Brown, A. Willitsford, K. Shi, Z. Liu, and C. R. Philbrick, “Advanced optical techniques for measurements of atmospheric constituents,” in Proceedings of the 28th Annual Review of Atmospheric Transmission Models, Lexington, Massachusetts, June 2006.
  12. C. Lieber and A. Mahadevan-Jansen, “Automated method for subtraction of fluorescence from biological Raman spectra,” Appl. Spectrosc. 57, 1363–1367 (2003).
    [CrossRef]
  13. U. Platt and J. Stutz, “Differential absorption spectroscopy,” in Differential Optical Absorption Spectroscopy, Physics of Earth and Space Environments (Springer Verlag, 2008), pp. 135–174.

2012 (3)

2010 (1)

2009 (1)

C. Xia, Z. Xu, M. N. Islam, F. L. Terry, M. J. Freeman, A. Zakel, and J. Mauricio, “10.5 watts time-averaged power mid-infrared supercontinuum generation extending beyond 4 m with direct pulse pattern modulation,” IEEE J. Sel. Top. Quantum Electron. 15, 422–434 (2009).
[CrossRef]

2008 (1)

2006 (2)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

S. Yin and W. Wang, “Novel algorithm for simultaneously detecting multiple vapor materials with multiple-wavelength differential absorption lidar,” Chin. Opt. Lett. 4, 360–362 (2006).

2003 (1)

1996 (1)

Agger, C.

Bang, O.

Barviau, B.

Blow, K.

Brown, D.

Brown, D. M.

D. M. Brown, A. Willitsford, K. Shi, Z. Liu, and C. R. Philbrick, “Advanced optical techniques for measurements of atmospheric constituents,” in Proceedings of the 28th Annual Review of Atmospheric Transmission Models, Lexington, Massachusetts, June 2006.

Chan, A.

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

Dudley, J.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

Dupont, S.

Freeman, M.

Freeman, M. J.

C. Xia, Z. Xu, M. N. Islam, F. L. Terry, M. J. Freeman, A. Zakel, and J. Mauricio, “10.5 watts time-averaged power mid-infrared supercontinuum generation extending beyond 4 m with direct pulse pattern modulation,” IEEE J. Sel. Top. Quantum Electron. 15, 422–434 (2009).
[CrossRef]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

Hliot, L.

Islam, M.

Islam, M. N.

C. Xia, Z. Xu, M. N. Islam, F. L. Terry, M. J. Freeman, A. Zakel, and J. Mauricio, “10.5 watts time-averaged power mid-infrared supercontinuum generation extending beyond 4 m with direct pulse pattern modulation,” IEEE J. Sel. Top. Quantum Electron. 15, 422–434 (2009).
[CrossRef]

Keiding, S.

Kudlinski, A.

Kumar, M.

Larger, L.

Leray, A.

Lieber, C.

Liu, Z.

D. Brown, K. Shi, Z. Liu, and C. Philbrick, “Long-path supercontinuum absorption spectroscopy for measurement of atmospheric constituents,” Opt. Express 16, 8457–8471 (2008).
[CrossRef]

D. M. Brown, A. Willitsford, K. Shi, Z. Liu, and C. R. Philbrick, “Advanced optical techniques for measurements of atmospheric constituents,” in Proceedings of the 28th Annual Review of Atmospheric Transmission Models, Lexington, Massachusetts, June 2006.

Lyngs, J.

Mahadevan-Jansen, A.

Manzur, T.

Mauricio, J.

C. Xia, Z. Xu, M. N. Islam, F. L. Terry, M. J. Freeman, A. Zakel, and J. Mauricio, “10.5 watts time-averaged power mid-infrared supercontinuum generation extending beyond 4 m with direct pulse pattern modulation,” IEEE J. Sel. Top. Quantum Electron. 15, 422–434 (2009).
[CrossRef]

Millot, G.

Mussot, A.

Neelakandan, M.

Petersen, C.

Philbrick, C.

Philbrick, C. R.

D. M. Brown, A. Willitsford, K. Shi, Z. Liu, and C. R. Philbrick, “Advanced optical techniques for measurements of atmospheric constituents,” in Proceedings of the 28th Annual Review of Atmospheric Transmission Models, Lexington, Massachusetts, June 2006.

Platt, U.

U. Platt and J. Stutz, “Differential absorption spectroscopy,” in Differential Optical Absorption Spectroscopy, Physics of Earth and Space Environments (Springer Verlag, 2008), pp. 135–174.

Shi, K.

D. Brown, K. Shi, Z. Liu, and C. Philbrick, “Long-path supercontinuum absorption spectroscopy for measurement of atmospheric constituents,” Opt. Express 16, 8457–8471 (2008).
[CrossRef]

D. M. Brown, A. Willitsford, K. Shi, Z. Liu, and C. R. Philbrick, “Advanced optical techniques for measurements of atmospheric constituents,” in Proceedings of the 28th Annual Review of Atmospheric Transmission Models, Lexington, Massachusetts, June 2006.

Spriet, C.

Steffensen, H.

Stutz, J.

U. Platt and J. Stutz, “Differential absorption spectroscopy,” in Differential Optical Absorption Spectroscopy, Physics of Earth and Space Environments (Springer Verlag, 2008), pp. 135–174.

Terry, F.

Terry, F. L.

C. Xia, Z. Xu, M. N. Islam, F. L. Terry, M. J. Freeman, A. Zakel, and J. Mauricio, “10.5 watts time-averaged power mid-infrared supercontinuum generation extending beyond 4 m with direct pulse pattern modulation,” IEEE J. Sel. Top. Quantum Electron. 15, 422–434 (2009).
[CrossRef]

Thgersen, J.

Thomsen, C.

Turitsyn, S.

van Trees, Harry L.

Harry L. van Trees, Detection, Estimation, and Modulation Theory (Wiley, 1997).

Wang, W.

Warren, R.

Wetzel, B.

Willitsford, A.

D. M. Brown, A. Willitsford, K. Shi, Z. Liu, and C. R. Philbrick, “Advanced optical techniques for measurements of atmospheric constituents,” in Proceedings of the 28th Annual Review of Atmospheric Transmission Models, Lexington, Massachusetts, June 2006.

Xia, C.

C. Xia, Z. Xu, M. N. Islam, F. L. Terry, M. J. Freeman, A. Zakel, and J. Mauricio, “10.5 watts time-averaged power mid-infrared supercontinuum generation extending beyond 4 m with direct pulse pattern modulation,” IEEE J. Sel. Top. Quantum Electron. 15, 422–434 (2009).
[CrossRef]

Xu, Z.

C. Xia, Z. Xu, M. N. Islam, F. L. Terry, M. J. Freeman, A. Zakel, and J. Mauricio, “10.5 watts time-averaged power mid-infrared supercontinuum generation extending beyond 4 m with direct pulse pattern modulation,” IEEE J. Sel. Top. Quantum Electron. 15, 422–434 (2009).
[CrossRef]

Yin, S.

Zakel, A.

C. Xia, Z. Xu, M. N. Islam, F. L. Terry, M. J. Freeman, A. Zakel, and J. Mauricio, “10.5 watts time-averaged power mid-infrared supercontinuum generation extending beyond 4 m with direct pulse pattern modulation,” IEEE J. Sel. Top. Quantum Electron. 15, 422–434 (2009).
[CrossRef]

Appl. Opt. (2)

Appl. Spectrosc. (1)

Chin. Opt. Lett. (1)

IEEE J. Sel. Top. Quantum Electron. (1)

C. Xia, Z. Xu, M. N. Islam, F. L. Terry, M. J. Freeman, A. Zakel, and J. Mauricio, “10.5 watts time-averaged power mid-infrared supercontinuum generation extending beyond 4 m with direct pulse pattern modulation,” IEEE J. Sel. Top. Quantum Electron. 15, 422–434 (2009).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (3)

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

Other (3)

U. Platt and J. Stutz, “Differential absorption spectroscopy,” in Differential Optical Absorption Spectroscopy, Physics of Earth and Space Environments (Springer Verlag, 2008), pp. 135–174.

D. M. Brown, A. Willitsford, K. Shi, Z. Liu, and C. R. Philbrick, “Advanced optical techniques for measurements of atmospheric constituents,” in Proceedings of the 28th Annual Review of Atmospheric Transmission Models, Lexington, Massachusetts, June 2006.

Harry L. van Trees, Detection, Estimation, and Modulation Theory (Wiley, 1997).

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Figures (18)

Fig. 1.
Fig. 1.

Supercontinuum signal (simulation): 501 sampling points, 1 nm FWHM resolution, SNR=70. The gas mixture is made of H2O (50,000 ppm.m) and CH4 (100,000 ppm.m). The black dashed curve is the baseline; the blue curve is the signal S.

Fig. 2.
Fig. 2.

Transmission (simulation): 2001 sampling points, 2 nm FWHM resolution, without noise. Gas species: H2O (2000 and 20,000 ppm.m). The transmission is computed with and without the approximation.

Fig. 3.
Fig. 3.

Histogram of si/si at 1300 nm (measured with 1 nm FWHM resolution) showing supercontinuum relative amplitude fluctuations. The standard deviation is 1.4% (SNR=si/σsi70).

Fig. 4.
Fig. 4.

Noise variance as a function of the mean optical power P measured at 1300 nm with a 1 nm resolution and plotted in logarithmic scale. When the multiplicative noise dominates: SNR=1/α70.

Fig. 5.
Fig. 5.

Signal-to-noise ratio evaluated on 466 acquisitions. Inset: example of measured signal.

Fig. 6.
Fig. 6.

Baseline filtering technique. Left: discrete Fourier transform of the signal logarithm. Right: filter transfer function and filtered Fourier transform.

Fig. 7.
Fig. 7.

Simulation of a baseline-filtered signal. The original signal is shown in Fig. 1 and the cut-off frequency is νc=0.5nm1.

Fig. 8.
Fig. 8.

Signal-processing diagram.

Fig. 9.
Fig. 9.

Relative bias between exact H2O CPL and linearly estimated CPL for increasing concentration values and several resolutions (FWHM in nm). Here, the linear estimator was applied to a simulated signal between 1300 and 1500 nm (without noise).

Fig. 10.
Fig. 10.

Transmission (simulation) of each gas species: 1001 sampling points, 1 nm FWHM resolution, without noise. This figure shows the interferences between the various absorption lines.

Fig. 11.
Fig. 11.

Supercontinuum signal (simulation): 1001 sampling points, 1 nm FWHM resolution, SNR=70. The mixture is composed of CH4 (1000 ppm.m), H2O (2,500,000 ppm.m), CO2 (165,000 ppm.m) and NH3 (7500 ppm.m).

Fig. 12.
Fig. 12.

Histograms of the statistical tests on the simulated signals and Gaussian curve.

Fig. 13.
Fig. 13.

Experimental setup used to measure H2O and CH4 concentration using a supercontinuum laser source.

Fig. 14.
Fig. 14.

Supercontinuum signal (measurement): 501 sampling points, 1 nm FWHM resolution, SNR=130. The gas mixture is made of H2O (numerous peaks beyond 1340 nm) and CH4 (isolated peak at 1330 nm).

Fig. 15.
Fig. 15.

Example of fit on measured spectrum, νs=0.5nm1.

Fig. 16.
Fig. 16.

Histogram of experimental estimations compared and ideal histogram shapes (Gaussian with CRB standard deviation). The statistical standard deviation (σstat) and the CRB values are also displayed.

Fig. 17.
Fig. 17.

CPL estimations of CH4 and H2O as a function of time.

Fig. 18.
Fig. 18.

Moisture meter measurement with error bars (red), converted in ppm, and the supercontinuum absorption spectroscopy concentration estimation (blue) as a function of the time.

Tables (2)

Tables Icon

Table 1. Mean and Standard Deviation (ppm.m) of the Estimates for 5000 Noise Realizations (SNR=70)

Tables Icon

Table 2. True CPL products, CRB After and Before the Filtering Stage (ppm.m), and CRB ratios (SNR=70), Showing the Impact of the Filtering Stage on Performances

Equations (28)

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CRBn=(F1)nn,
Fkl=2lCkCl,
l(C1,,CN)=lnPS1,,SM(s1,,sM|C1,,CN),
si=a0i·Ti+ni,
Ti=++exp(n=1NHn(λ)Cn)g(λiλ)dλ,
Tiapprox=exp(n=1NCn+Hn(λ)g(λiλ)dλ).
PS1(si)=12πσi2exp((sisi)22σi2),
σi2=αisi2+βisi+γi,
SNR=siσi2=(1αi+βi/si+γi/si2)1/2.
l(C1,...,CN)=i=1M12ln(2πσi2)(sisi)22σi2.
Fkl=i=1MsiCksiCl(1σi2+12(2αisi+βiσi2)2).
Fkl=i=1M1αi(1TiTiCk)(1TiTiCl).
Fkl=i=1M(a0iTi)2γi(1TiTiCk)(1TiTiCl)
Fkl=i=1MSNRi2(1TiTiCk)(1TiTiCl).
lnsi=lna0i+lnTi+ln(1+nia0iTi).
h(ν)=1rect(ν/νc),
si=Ti+ni.
lnsi=lna0i+lnTi+mi,withmi=ni/a0iTi.
si=FHP(lnsi)=Ti.
σsi2=νs/2νs/2PSD|h(ν)|2dν.
Psi(si)ω2SNR22πexp(ω2SNR2(siTi)22).
sisj=νs/2νs/2PSD|h(ν)|2ei2πν(λiλj)dν.
FklFilteri=1Mω2SNR2[FHP(1TTCk)]λi[FHP(1TTCl)]λi.
si=[FHP(ln+exp(n=1NHn(λ)Cn)g(λλ)dλ)]|λi.
si=n=1NH˜inCn,
H˜in=[FHP(+Hn(λ)g(λλ)dλ)]|λi.
C^=(H˜TH˜)1H˜TS,
δ^C1=(H˜TH˜)1H˜TS1.

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