Abstract

Light intensity fluctuations and phase randomness in quadrature demodulation disturb the accuracy of frequency modulation spectroscopy. The proposed self-corrected method eliminated these effects: the profile of correctly demodulated signals identified whether a demodulation was phase matched and corrected a phase-mismatched demodulated signal; we extracted the measured signal’s direct current component and corrected the light intensity fluctuation. We conducted theoretical analysis and experimental verification to reduce light-intensity errors by 16.8% under different intensity conditions and obtained spectral features by phase difference corrections under the same measurement conditions. We reduced the effect of light intensity fluctuation and demodulated signals were freed from phase stability limitations.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
  4. J. C. Bloch, R. W. Field, G. E. Hall, and T. J. Sears, “Time-resolved frequency-modulation spectroscopy of photochemical transients,” J. Chem. Phys. 101(2), 1717–1720 (1994).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2018 (1)

L. Wenke, Z. Qiang, D. Xiaozhou, and L. Tieliang, “Influence of temperature-induced cavity length variation in wavelength modulation spectroscopy,” Optik 172, 220–224 (2018).
[Crossref]

2015 (1)

2014 (1)

K. A. Whittaker, J. Keaveney, I. G. Hughes, and C. S. Adams, “The Hilbert transform: Applications to atomic spectra,” Phys. Rev. A 11, 1–16 (2014).

2009 (1)

2008 (1)

J. Wang, J. D. Yu, Y. K. Yong, and T. Imai, “A finite element analysis of frequency–temperature relations of AT-cut quartz crystal resonators with higher-order Mindlin plate theory,” Acta Mech. 199(1–4), 117–130 (2008).
[Crossref]

2006 (1)

2000 (1)

G. E. Hall and S. W. North, “Transient laser frequency modulation spectroscopy,” Annu. Rev. Phys. Chem. 51(1), 243–274 (2000).
[Crossref]

1999 (1)

1998 (1)

1996 (1)

S. W. North, X. S. Zheng, R. Fei, and G. E. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104(6), 2129–2135 (1996).
[Crossref]

1994 (2)

J. C. Bloch, R. W. Field, G. E. Hall, and T. J. Sears, “Time-resolved frequency-modulation spectroscopy of photochemical transients,” J. Chem. Phys. 101(2), 1717–1720 (1994).
[Crossref]

P. H. Moose, “A Technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun. 42(10), 2908–2914 (1994).
[Crossref]

1989 (1)

P. Werle, F. Slemr, M. Gehrtz, and C. Bräuchle, “Quantum-limited FM-spectroscopy with a lead-salt diode laser,” Appl. Phys. B: Photophys. Laser Chem. 49(2), 99–108 (1989).
[Crossref]

1986 (1)

1984 (2)

W. Lenth, “High Frequency Heterodyne Spectroscopy with Current-modulated Diode Lasers,” IEEE J. Quantum Electron. 20(9), 1045–1050 (1984).
[Crossref]

E. A. Whittaker, H. R. Wendt, H. E. Hunziker, and G. C. Bjorklund, “Laser FM spectroscopy with photochemical modulation,” Appl. Phys. B: Photophys. Laser Chem. 35(2), 105–111 (1984).
[Crossref]

1983 (1)

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B: Photophys. Laser Chem. 32(3), 145–152 (1983).
[Crossref]

1980 (1)

Adams, C. S.

K. A. Whittaker, J. Keaveney, I. G. Hughes, and C. S. Adams, “The Hilbert transform: Applications to atomic spectra,” Phys. Rev. A 11, 1–16 (2014).

Bjorklund, G. C.

E. A. Whittaker, H. R. Wendt, H. E. Hunziker, and G. C. Bjorklund, “Laser FM spectroscopy with photochemical modulation,” Appl. Phys. B: Photophys. Laser Chem. 35(2), 105–111 (1984).
[Crossref]

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B: Photophys. Laser Chem. 32(3), 145–152 (1983).
[Crossref]

G. C. Bjorklund, “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett. 5(1), 15–17 (1980).
[Crossref]

Bloch, J. C.

J. C. Bloch, R. W. Field, G. E. Hall, and T. J. Sears, “Time-resolved frequency-modulation spectroscopy of photochemical transients,” J. Chem. Phys. 101(2), 1717–1720 (1994).
[Crossref]

Bräuchle, C.

P. Werle, F. Slemr, M. Gehrtz, and C. Bräuchle, “Quantum-limited FM-spectroscopy with a lead-salt diode laser,” Appl. Phys. B: Photophys. Laser Chem. 49(2), 99–108 (1989).
[Crossref]

Fei, R.

S. W. North, X. S. Zheng, R. Fei, and G. E. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104(6), 2129–2135 (1996).
[Crossref]

Field, R. W.

J. C. Bloch, R. W. Field, G. E. Hall, and T. J. Sears, “Time-resolved frequency-modulation spectroscopy of photochemical transients,” J. Chem. Phys. 101(2), 1717–1720 (1994).
[Crossref]

Gehrtz, M.

P. Werle, F. Slemr, M. Gehrtz, and C. Bräuchle, “Quantum-limited FM-spectroscopy with a lead-salt diode laser,” Appl. Phys. B: Photophys. Laser Chem. 49(2), 99–108 (1989).
[Crossref]

Hall, G. E.

G. E. Hall and S. W. North, “Transient laser frequency modulation spectroscopy,” Annu. Rev. Phys. Chem. 51(1), 243–274 (2000).
[Crossref]

S. W. North, X. S. Zheng, R. Fei, and G. E. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104(6), 2129–2135 (1996).
[Crossref]

J. C. Bloch, R. W. Field, G. E. Hall, and T. J. Sears, “Time-resolved frequency-modulation spectroscopy of photochemical transients,” J. Chem. Phys. 101(2), 1717–1720 (1994).
[Crossref]

Hall, J. L.

Hanson, R. K.

Hejie, L.

Hughes, I. G.

K. A. Whittaker, J. Keaveney, I. G. Hughes, and C. S. Adams, “The Hilbert transform: Applications to atomic spectra,” Phys. Rev. A 11, 1–16 (2014).

Hunziker, H. E.

E. A. Whittaker, H. R. Wendt, H. E. Hunziker, and G. C. Bjorklund, “Laser FM spectroscopy with photochemical modulation,” Appl. Phys. B: Photophys. Laser Chem. 35(2), 105–111 (1984).
[Crossref]

Imai, T.

J. Wang, J. D. Yu, Y. K. Yong, and T. Imai, “A finite element analysis of frequency–temperature relations of AT-cut quartz crystal resonators with higher-order Mindlin plate theory,” Acta Mech. 199(1–4), 117–130 (2008).
[Crossref]

Jeffries, J. B.

Keaveney, J.

K. A. Whittaker, J. Keaveney, I. G. Hughes, and C. S. Adams, “The Hilbert transform: Applications to atomic spectra,” Phys. Rev. A 11, 1–16 (2014).

Lenth, W.

W. Lenth, “High Frequency Heterodyne Spectroscopy with Current-modulated Diode Lasers,” IEEE J. Quantum Electron. 20(9), 1045–1050 (1984).
[Crossref]

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B: Photophys. Laser Chem. 32(3), 145–152 (1983).
[Crossref]

Levenson, M. D.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B: Photophys. Laser Chem. 32(3), 145–152 (1983).
[Crossref]

Lynds, L.

Ma, L. S.

Moose, P. H.

P. H. Moose, “A Technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun. 42(10), 2908–2914 (1994).
[Crossref]

Nagel, A.

North, S. W.

G. E. Hall and S. W. North, “Transient laser frequency modulation spectroscopy,” Annu. Rev. Phys. Chem. 51(1), 243–274 (2000).
[Crossref]

S. W. North, X. S. Zheng, R. Fei, and G. E. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104(6), 2129–2135 (1996).
[Crossref]

Ortiz, C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B: Photophys. Laser Chem. 32(3), 145–152 (1983).
[Crossref]

Qiang, Z.

L. Wenke, Z. Qiang, D. Xiaozhou, and L. Tieliang, “Influence of temperature-induced cavity length variation in wavelength modulation spectroscopy,” Optik 172, 220–224 (2018).
[Crossref]

Quack, M.

Rieker, G. B.

Sears, T. J.

J. C. Bloch, R. W. Field, G. E. Hall, and T. J. Sears, “Time-resolved frequency-modulation spectroscopy of photochemical transients,” J. Chem. Phys. 101(2), 1717–1720 (1994).
[Crossref]

Slemr, F.

P. Werle, F. Slemr, M. Gehrtz, and C. Bräuchle, “Quantum-limited FM-spectroscopy with a lead-salt diode laser,” Appl. Phys. B: Photophys. Laser Chem. 49(2), 99–108 (1989).
[Crossref]

Suter, M.

Tieliang, L.

L. Wenke, Z. Qiang, D. Xiaozhou, and L. Tieliang, “Influence of temperature-induced cavity length variation in wavelength modulation spectroscopy,” Optik 172, 220–224 (2018).
[Crossref]

Wang, J.

J. Wang, J. D. Yu, Y. K. Yong, and T. Imai, “A finite element analysis of frequency–temperature relations of AT-cut quartz crystal resonators with higher-order Mindlin plate theory,” Acta Mech. 199(1–4), 117–130 (2008).
[Crossref]

Wendt, H. R.

E. A. Whittaker, H. R. Wendt, H. E. Hunziker, and G. C. Bjorklund, “Laser FM spectroscopy with photochemical modulation,” Appl. Phys. B: Photophys. Laser Chem. 35(2), 105–111 (1984).
[Crossref]

Wenke, L.

L. Wenke, Z. Qiang, D. Xiaozhou, and L. Tieliang, “Influence of temperature-induced cavity length variation in wavelength modulation spectroscopy,” Optik 172, 220–224 (2018).
[Crossref]

Werle, P.

P. Werle, F. Slemr, M. Gehrtz, and C. Bräuchle, “Quantum-limited FM-spectroscopy with a lead-salt diode laser,” Appl. Phys. B: Photophys. Laser Chem. 49(2), 99–108 (1989).
[Crossref]

Whittaker, E. A.

E. A. Whittaker, H. R. Wendt, H. E. Hunziker, and G. C. Bjorklund, “Laser FM spectroscopy with photochemical modulation,” Appl. Phys. B: Photophys. Laser Chem. 35(2), 105–111 (1984).
[Crossref]

Whittaker, K. A.

K. A. Whittaker, J. Keaveney, I. G. Hughes, and C. S. Adams, “The Hilbert transform: Applications to atomic spectra,” Phys. Rev. A 11, 1–16 (2014).

Woody, B. A.

Wynands, R.

Xiang, L.

Xiaozhou, D.

L. Wenke, Z. Qiang, D. Xiaozhou, and L. Tieliang, “Influence of temperature-induced cavity length variation in wavelength modulation spectroscopy,” Optik 172, 220–224 (2018).
[Crossref]

Ye, J.

Yong, Y. K.

J. Wang, J. D. Yu, Y. K. Yong, and T. Imai, “A finite element analysis of frequency–temperature relations of AT-cut quartz crystal resonators with higher-order Mindlin plate theory,” Acta Mech. 199(1–4), 117–130 (2008).
[Crossref]

Yu, J. D.

J. Wang, J. D. Yu, Y. K. Yong, and T. Imai, “A finite element analysis of frequency–temperature relations of AT-cut quartz crystal resonators with higher-order Mindlin plate theory,” Acta Mech. 199(1–4), 117–130 (2008).
[Crossref]

Zheng, X. S.

S. W. North, X. S. Zheng, R. Fei, and G. E. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104(6), 2129–2135 (1996).
[Crossref]

Acta Mech. (1)

J. Wang, J. D. Yu, Y. K. Yong, and T. Imai, “A finite element analysis of frequency–temperature relations of AT-cut quartz crystal resonators with higher-order Mindlin plate theory,” Acta Mech. 199(1–4), 117–130 (2008).
[Crossref]

Annu. Rev. Phys. Chem. (1)

G. E. Hall and S. W. North, “Transient laser frequency modulation spectroscopy,” Annu. Rev. Phys. Chem. 51(1), 243–274 (2000).
[Crossref]

Appl. Opt. (4)

Appl. Phys. B: Photophys. Laser Chem. (3)

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, “Frequency modulation (FM) spectroscopy,” Appl. Phys. B: Photophys. Laser Chem. 32(3), 145–152 (1983).
[Crossref]

P. Werle, F. Slemr, M. Gehrtz, and C. Bräuchle, “Quantum-limited FM-spectroscopy with a lead-salt diode laser,” Appl. Phys. B: Photophys. Laser Chem. 49(2), 99–108 (1989).
[Crossref]

E. A. Whittaker, H. R. Wendt, H. E. Hunziker, and G. C. Bjorklund, “Laser FM spectroscopy with photochemical modulation,” Appl. Phys. B: Photophys. Laser Chem. 35(2), 105–111 (1984).
[Crossref]

IEEE J. Quantum Electron. (1)

W. Lenth, “High Frequency Heterodyne Spectroscopy with Current-modulated Diode Lasers,” IEEE J. Quantum Electron. 20(9), 1045–1050 (1984).
[Crossref]

IEEE Trans. Commun. (1)

P. H. Moose, “A Technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun. 42(10), 2908–2914 (1994).
[Crossref]

J. Chem. Phys. (2)

J. C. Bloch, R. W. Field, G. E. Hall, and T. J. Sears, “Time-resolved frequency-modulation spectroscopy of photochemical transients,” J. Chem. Phys. 101(2), 1717–1720 (1994).
[Crossref]

S. W. North, X. S. Zheng, R. Fei, and G. E. Hall, “Line shape analysis of Doppler broadened frequency-modulated line spectra,” J. Chem. Phys. 104(6), 2129–2135 (1996).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Lett. (1)

Optik (1)

L. Wenke, Z. Qiang, D. Xiaozhou, and L. Tieliang, “Influence of temperature-induced cavity length variation in wavelength modulation spectroscopy,” Optik 172, 220–224 (2018).
[Crossref]

Phys. Rev. A (1)

K. A. Whittaker, J. Keaveney, I. G. Hughes, and C. S. Adams, “The Hilbert transform: Applications to atomic spectra,” Phys. Rev. A 11, 1–16 (2014).

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Figures (7)

Fig. 1.
Fig. 1. Demodulated signals with different phase differences. The vertical line is the extreme point frequency of each signal, and the auxiliary line is the equal frequency line.
Fig. 2.
Fig. 2. Algorithm for phase determination with Ieli and Qeli data.
Fig. 3.
Fig. 3. Schematic diagram of experiment setup based on FMS.
Fig. 4.
Fig. 4. The recorded (a) DC terms (b), demodulated I, and (c) demodulated Q of atmospheric water absorbance around 7185.58cm−1 by FMS descript in Fig. 3. The scanning frequency is 10 Hz, the modulation frequency is 0.88 GHz, the modulation index is 2, T = 297.05 K, P = 1 atm, and the effective optical path L = 40 cm, 10 times average sampling.
Fig. 5.
Fig. 5. The real demodulated signals and the corrected demodulated signals by using DC term. (a) I-channel (b) Q-channel. S1: Laboratory air, S2: Laboratory outside air; I: I-channel, Q: Q-channel; Real: The real demodulated signals (left vertical axis); Corrected: the corrected demodulated signals by using DC term (right vertical axis)
Fig. 6.
Fig. 6. Sums of correlation coefficient of the corrected demodulated signals using a Lorentzian line shape fitting. The step interval of the phase difference θ is 0.1°.
Fig. 7.
Fig. 7. The (a) absorption and (b) dispersion components of the demodulated signals were restored.

Tables (1)

Tables Icon

Table 1. Absorbance of water vapor, intensity of the demodulated signal, and corrected intensity of the demodulated signal of laboratory air (S1) and laboratory outside air (S2)

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

I mod ( t ) = I 0 exp ( 2 δ 0 ) DC component + I 0 exp ( 2 δ 0 ) [ ( δ 1 δ 1 ) M cos ω m t + ( ϕ 1 + ϕ 1 2 ϕ 0 ) M sin ω m t ] AC component ,
I F M ( ω ) = I 0 exp ( 2 δ 0 ) γ M [ cos θ ( δ 1 δ 1 ) + sin θ ( ϕ 1 + ϕ 1 2 ϕ 0 ) ] , and
Q F M ( ω ) = I 0 exp ( 2 δ 0 ) γ M [ sin θ ( δ 1 δ 1 ) cos θ ( ϕ 1 + ϕ 1 2 ϕ 0 ) ] .
I e l i ( ω ) = I F M ( ω ) /[ I 0 exp ( 2 δ 0 ) ] = γ M [ cos θ ( δ 1 δ 1 ) + sin θ ( ϕ 1 + ϕ 1 2 ϕ 0 ) ] , and
Q e l i ( ω ) = Q F M ( ω ) / [ I 0 exp ( 2 δ 0 ) ] = γ M [ sin θ ( δ 1 δ 1 ) cos θ ( ϕ 1 + ϕ 1 2 ϕ 0 ) ] .
{ U = ± 2 n 2 2 4 n 4 + n 2 + 1 6 , n = Δ v L 2 ω m exp { 16 ln 2 ω m Δ v D 2 U } = U + ω m U ω m
A F M = γ M ( δ 1 δ 1 ) = cos θ I e l i + sin θ Q e l i ,and
D F M = γ M ( ϕ 1 + ϕ 1 2 ϕ 0 ) = sin θ I e l i cos θ Q e l i .
R ( X , Y ) = C o v ( X , Y ) V a r ( X ) V a r ( Y )