Abstract

Wavelet analyses of tunable diode laser absorption spectroscopy signals were performed. The absorption spectroscopy data were obtained by repeatedly scanning the beams from a tunable diode laser operating in the near infrared across absorption lines of gaseous NH3 contained within a windowed glass tube. The laser was modulated and wavelet analyses of the absorption data were performed. It was observed that harmonic wavelets could simultaneously extract the 1f and 2f harmonics as well as higher-order harmonics from the direct absorption data.

© 2009 Optical Society of America

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References

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  1. M. G. Allen, “Diode laser absorption sensors for gas-dynamic and combustion flows,” Meas. Sci. Technol. 9, 545-562 (1998).
    [CrossRef]
  2. K. Kohse-Höinghaus and J. B. Jeffries, Applied Combustion Diagnostics (Taylor and Francis, 2002).
  3. O. Axner, P. Kluczynski, and A. M. Lindberg, “Theoretical description based on Fourier analysis of wavelength-modulation spectroscopy in terms of analytical and background signals,” Appl. Opt. 38, 5803-5815 (1999).
    [CrossRef]
  4. A. M. Russell and D. A. Torchia, “Harmonic analysis in systems using phase sensitive detectors,” Rev. Sci. Instrum. 33, 442-444 (1962).
    [CrossRef]
  5. G. V. H. Wilson, “Modulation broadening of NMR and ESR line shapes,” J. Appl. Phys. 34, 3276-3285 (1963).
    [CrossRef]
  6. R. Arndt, “Analytical line shapes for Lorentzian signals broadened by modulation,” J. Appl. Phys. 36, 2522-2524 (1965).
    [CrossRef]
  7. P. Kluczynski and O. Axner, “A general non-complex analytical expression for the nth Fourier component of a wavelength-modulated Lorentzian lineshape function,” J. Quant. Spectrosc. Radiat. Transfer 68, 299-317 (2001).
    [CrossRef]
  8. B. D. Shaw, “Analytical evaluation of the Fourier components of wavelength-modulated Gaussian functions,” J. Quant. Spectrosc. Radiat. Transfer 109, 2891-2894 (2008).
    [CrossRef]
  9. J. Reid and D. Labrie, “Second-harmonic detection with tunable-diode lasers--comparison with experiment and theory,” Appl. Phys. B 26, 203-210 (1981).
    [CrossRef]
  10. C. S. Burrus, R. A. Gopinath, and H. Guo, Introduction to Wavelets and Wavelet Transforms--A Primer (Prentice-Hall, 1997).
  11. D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis (Cambridge U. Press, 2000).
  12. L. Lundsberg-Nielsen, F. Hegelund, and F. M. Nicolaisen, “Analysis of the high-resolution spectrum of ammonia (14NH3) in the near-infrared region 6400-6900 cm−1,” J. Mol. Spectrosc. 162, 230-245 (1993).
    [CrossRef]
  13. M. E. Webber, M. D. S. Baer, and R. K. Hanson, “Ammonia monitoring near 1.5 μm with diode-laser absorption sensors,” Appl. Opt. 40, 2031-2042 (2001).
    [CrossRef]
  14. D. E. Newland, “Harmonic wavelet analysis,” Proc. R. Soc. London Ser. A 443, 203-225 (1993).
    [CrossRef]
  15. D. E. Newland, “Harmonic wavelets in vibration and acoustics,” Phil. Trans. R. Soc. London 357, 2607-2625(1999).
    [CrossRef]
  16. Mathematica 5.2, Wolfram Research, Inc., 100 Trade Center Drive, Champaign, Ill. 61820, USA.

2008 (1)

B. D. Shaw, “Analytical evaluation of the Fourier components of wavelength-modulated Gaussian functions,” J. Quant. Spectrosc. Radiat. Transfer 109, 2891-2894 (2008).
[CrossRef]

2001 (2)

P. Kluczynski and O. Axner, “A general non-complex analytical expression for the nth Fourier component of a wavelength-modulated Lorentzian lineshape function,” J. Quant. Spectrosc. Radiat. Transfer 68, 299-317 (2001).
[CrossRef]

M. E. Webber, M. D. S. Baer, and R. K. Hanson, “Ammonia monitoring near 1.5 μm with diode-laser absorption sensors,” Appl. Opt. 40, 2031-2042 (2001).
[CrossRef]

1999 (2)

1998 (1)

M. G. Allen, “Diode laser absorption sensors for gas-dynamic and combustion flows,” Meas. Sci. Technol. 9, 545-562 (1998).
[CrossRef]

1993 (2)

L. Lundsberg-Nielsen, F. Hegelund, and F. M. Nicolaisen, “Analysis of the high-resolution spectrum of ammonia (14NH3) in the near-infrared region 6400-6900 cm−1,” J. Mol. Spectrosc. 162, 230-245 (1993).
[CrossRef]

D. E. Newland, “Harmonic wavelet analysis,” Proc. R. Soc. London Ser. A 443, 203-225 (1993).
[CrossRef]

1981 (1)

J. Reid and D. Labrie, “Second-harmonic detection with tunable-diode lasers--comparison with experiment and theory,” Appl. Phys. B 26, 203-210 (1981).
[CrossRef]

1965 (1)

R. Arndt, “Analytical line shapes for Lorentzian signals broadened by modulation,” J. Appl. Phys. 36, 2522-2524 (1965).
[CrossRef]

1963 (1)

G. V. H. Wilson, “Modulation broadening of NMR and ESR line shapes,” J. Appl. Phys. 34, 3276-3285 (1963).
[CrossRef]

1962 (1)

A. M. Russell and D. A. Torchia, “Harmonic analysis in systems using phase sensitive detectors,” Rev. Sci. Instrum. 33, 442-444 (1962).
[CrossRef]

Allen, M. G.

M. G. Allen, “Diode laser absorption sensors for gas-dynamic and combustion flows,” Meas. Sci. Technol. 9, 545-562 (1998).
[CrossRef]

Arndt, R.

R. Arndt, “Analytical line shapes for Lorentzian signals broadened by modulation,” J. Appl. Phys. 36, 2522-2524 (1965).
[CrossRef]

Axner, O.

P. Kluczynski and O. Axner, “A general non-complex analytical expression for the nth Fourier component of a wavelength-modulated Lorentzian lineshape function,” J. Quant. Spectrosc. Radiat. Transfer 68, 299-317 (2001).
[CrossRef]

O. Axner, P. Kluczynski, and A. M. Lindberg, “Theoretical description based on Fourier analysis of wavelength-modulation spectroscopy in terms of analytical and background signals,” Appl. Opt. 38, 5803-5815 (1999).
[CrossRef]

Baer, M. D. S.

Burrus, C. S.

C. S. Burrus, R. A. Gopinath, and H. Guo, Introduction to Wavelets and Wavelet Transforms--A Primer (Prentice-Hall, 1997).

Gopinath, R. A.

C. S. Burrus, R. A. Gopinath, and H. Guo, Introduction to Wavelets and Wavelet Transforms--A Primer (Prentice-Hall, 1997).

Guo, H.

C. S. Burrus, R. A. Gopinath, and H. Guo, Introduction to Wavelets and Wavelet Transforms--A Primer (Prentice-Hall, 1997).

Hanson, R. K.

Hegelund, F.

L. Lundsberg-Nielsen, F. Hegelund, and F. M. Nicolaisen, “Analysis of the high-resolution spectrum of ammonia (14NH3) in the near-infrared region 6400-6900 cm−1,” J. Mol. Spectrosc. 162, 230-245 (1993).
[CrossRef]

Jeffries, J. B.

K. Kohse-Höinghaus and J. B. Jeffries, Applied Combustion Diagnostics (Taylor and Francis, 2002).

Kluczynski, P.

P. Kluczynski and O. Axner, “A general non-complex analytical expression for the nth Fourier component of a wavelength-modulated Lorentzian lineshape function,” J. Quant. Spectrosc. Radiat. Transfer 68, 299-317 (2001).
[CrossRef]

O. Axner, P. Kluczynski, and A. M. Lindberg, “Theoretical description based on Fourier analysis of wavelength-modulation spectroscopy in terms of analytical and background signals,” Appl. Opt. 38, 5803-5815 (1999).
[CrossRef]

Kohse-Höinghaus, K.

K. Kohse-Höinghaus and J. B. Jeffries, Applied Combustion Diagnostics (Taylor and Francis, 2002).

Labrie, D.

J. Reid and D. Labrie, “Second-harmonic detection with tunable-diode lasers--comparison with experiment and theory,” Appl. Phys. B 26, 203-210 (1981).
[CrossRef]

Lindberg, A. M.

Lundsberg-Nielsen, L.

L. Lundsberg-Nielsen, F. Hegelund, and F. M. Nicolaisen, “Analysis of the high-resolution spectrum of ammonia (14NH3) in the near-infrared region 6400-6900 cm−1,” J. Mol. Spectrosc. 162, 230-245 (1993).
[CrossRef]

Newland, D. E.

D. E. Newland, “Harmonic wavelets in vibration and acoustics,” Phil. Trans. R. Soc. London 357, 2607-2625(1999).
[CrossRef]

D. E. Newland, “Harmonic wavelet analysis,” Proc. R. Soc. London Ser. A 443, 203-225 (1993).
[CrossRef]

Nicolaisen, F. M.

L. Lundsberg-Nielsen, F. Hegelund, and F. M. Nicolaisen, “Analysis of the high-resolution spectrum of ammonia (14NH3) in the near-infrared region 6400-6900 cm−1,” J. Mol. Spectrosc. 162, 230-245 (1993).
[CrossRef]

Percival, D. B.

D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis (Cambridge U. Press, 2000).

Reid, J.

J. Reid and D. Labrie, “Second-harmonic detection with tunable-diode lasers--comparison with experiment and theory,” Appl. Phys. B 26, 203-210 (1981).
[CrossRef]

Russell, A. M.

A. M. Russell and D. A. Torchia, “Harmonic analysis in systems using phase sensitive detectors,” Rev. Sci. Instrum. 33, 442-444 (1962).
[CrossRef]

Shaw, B. D.

B. D. Shaw, “Analytical evaluation of the Fourier components of wavelength-modulated Gaussian functions,” J. Quant. Spectrosc. Radiat. Transfer 109, 2891-2894 (2008).
[CrossRef]

Torchia, D. A.

A. M. Russell and D. A. Torchia, “Harmonic analysis in systems using phase sensitive detectors,” Rev. Sci. Instrum. 33, 442-444 (1962).
[CrossRef]

Walden, A. T.

D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis (Cambridge U. Press, 2000).

Webber, M. E.

Wilson, G. V. H.

G. V. H. Wilson, “Modulation broadening of NMR and ESR line shapes,” J. Appl. Phys. 34, 3276-3285 (1963).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

J. Reid and D. Labrie, “Second-harmonic detection with tunable-diode lasers--comparison with experiment and theory,” Appl. Phys. B 26, 203-210 (1981).
[CrossRef]

J. Appl. Phys. (2)

G. V. H. Wilson, “Modulation broadening of NMR and ESR line shapes,” J. Appl. Phys. 34, 3276-3285 (1963).
[CrossRef]

R. Arndt, “Analytical line shapes for Lorentzian signals broadened by modulation,” J. Appl. Phys. 36, 2522-2524 (1965).
[CrossRef]

J. Mol. Spectrosc. (1)

L. Lundsberg-Nielsen, F. Hegelund, and F. M. Nicolaisen, “Analysis of the high-resolution spectrum of ammonia (14NH3) in the near-infrared region 6400-6900 cm−1,” J. Mol. Spectrosc. 162, 230-245 (1993).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

P. Kluczynski and O. Axner, “A general non-complex analytical expression for the nth Fourier component of a wavelength-modulated Lorentzian lineshape function,” J. Quant. Spectrosc. Radiat. Transfer 68, 299-317 (2001).
[CrossRef]

B. D. Shaw, “Analytical evaluation of the Fourier components of wavelength-modulated Gaussian functions,” J. Quant. Spectrosc. Radiat. Transfer 109, 2891-2894 (2008).
[CrossRef]

Meas. Sci. Technol. (1)

M. G. Allen, “Diode laser absorption sensors for gas-dynamic and combustion flows,” Meas. Sci. Technol. 9, 545-562 (1998).
[CrossRef]

Phil. Trans. R. Soc. London (1)

D. E. Newland, “Harmonic wavelets in vibration and acoustics,” Phil. Trans. R. Soc. London 357, 2607-2625(1999).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

D. E. Newland, “Harmonic wavelet analysis,” Proc. R. Soc. London Ser. A 443, 203-225 (1993).
[CrossRef]

Rev. Sci. Instrum. (1)

A. M. Russell and D. A. Torchia, “Harmonic analysis in systems using phase sensitive detectors,” Rev. Sci. Instrum. 33, 442-444 (1962).
[CrossRef]

Other (4)

K. Kohse-Höinghaus and J. B. Jeffries, Applied Combustion Diagnostics (Taylor and Francis, 2002).

C. S. Burrus, R. A. Gopinath, and H. Guo, Introduction to Wavelets and Wavelet Transforms--A Primer (Prentice-Hall, 1997).

D. B. Percival and A. T. Walden, Wavelet Methods for Time Series Analysis (Cambridge U. Press, 2000).

Mathematica 5.2, Wolfram Research, Inc., 100 Trade Center Drive, Champaign, Ill. 61820, USA.

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Figures (6)

Fig. 1
Fig. 1

Schematic of the WMS experimental setup.

Fig. 2
Fig. 2

Representative output from the photodiode without modulation of the laser.

Fig. 3
Fig. 3

Representative output from the photodiode with modulation of the laser.

Fig. 4
Fig. 4

Representative 2 f output from the lock-in amplifier.

Fig. 5
Fig. 5

Representative harmonic wavelet analysis results for different bandpass ranges.

Fig. 6
Fig. 6

Comparison of results from the wavelet analyses with (a)  H 1 , (b)  H 2 , and (c)  H 3 coefficients obtained with a Voigt absorption profile.

Equations (18)

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I ( ν ) = I 0 ( ν ) exp ( α L ) .
α = 1 L ln ( I I 0 ) = 1 L ( 1 I I 0 ) .
ν = ν ¯ + ε cos ( ω t ) .
α = n = 0 H n cos ( n ω t ) ,
H 0 = 1 2 π 0 2 π α d θ ,
H n = 1 π 0 2 π α cos ( n θ ) d θ , n 1.
α [ ν ¯ + ε cos ( θ ) ] = α ( ν ¯ ) + ε cos ( θ ) d α d ν | ν = ν ¯ + ε 2 cos 2 ( θ ) 2 d 2 α d ν 2 | ν = ν ¯ + ... .
π H 2 = α ( ν ¯ ) 0 2 π cos ( 2 θ ) d θ + ε d α d ν | ν = ν ¯ 0 2 π cos ( θ ) cos ( 2 θ ) d θ + ε 2 2 d 2 α d ν 2 | ν = ν ¯ 0 2 π cos 2 ( θ ) cos ( 2 θ ) d θ + ε 3 6 d 3 α d ν 3 | ν = ν ¯ 0 2 π cos 3 ( θ ) cos ( 2 θ ) d θ + ε 4 24 d 4 α d ν 4 | ν = ν ¯ 0 2 π cos 4 ( θ ) cos ( 2 θ ) d θ + ... .
H 2 = ε 2 4 d 2 α d ν 2 | ν = ν ¯ + ε 4 48 d 4 α d ν 4 | ν = ν ¯ + ε 6 1536 d 6 α d ν 6 | ν = ν ¯ + ε 8 92160 d 8 α d ν 8 | ν = ν ¯ + ... .
H 2 = ε 2 4 d 2 α d ν 2 | ν = ν ¯ .
W ( a , b ) = α ( t ) 1 b φ ( t a b ) d t .
φ ( t ) d t = 0 ,
| φ ( t ) | 2 d t < ,
0 | φ ¯ ( f ) | 2 f d f < .
φ ¯ ( f ) = φ ( t ) exp ( 2 π i f t ) d t .
φ ( t ) = exp ( 4 π i t ) exp ( 2 π i t ) 2 π i t .
f min = S N 2 j 1 ,
f max = S N 2 j .

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