• Chinese Optics Letters
  • Vol. 19, Issue 3, 031201 (2021)
Shaomin Li and Liqun Sun*
Author Affiliations
  • State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China
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    DOI: 10.3788/COL202119.031201 Cite this Article Set citation alerts
    Shaomin Li, Liqun Sun. Natural logarithm wavelength modulation spectroscopy[J]. Chinese Optics Letters, 2021, 19(3): 031201 Copy Citation Text show less
    Absorption coefficient of water vapor around 1392 nm (P = 1 atm, T = 296 K) based on HITRAN[19]. The non-absorbing region is indicated by the dotted rectangle.
    Fig. 1. Absorption coefficient of water vapor around 1392 nm (P = 1 atm, T = 296 K) based on HITRAN[19]. The non-absorbing region is indicated by the dotted rectangle.
    Second harmonic R2f demodulated from the absorption signal.
    Fig. 2. Second harmonic R2f demodulated from the absorption signal.
    Schematic of the experiment setup.
    Fig. 3. Schematic of the experiment setup.
    Detected signal from the photodetector. The non-absorbing region is indicated by the dotted rectangle.
    Fig. 4. Detected signal from the photodetector. The non-absorbing region is indicated by the dotted rectangle.
    Response of ln-WMS-2f (black dots) and WMS-2f (red inverted triangles). The black line represents the linear fit of ln-WMS-2f versus volume fraction.
    Fig. 5. Response of ln-WMS-2f (black dots) and WMS-2f (red inverted triangles). The black line represents the linear fit of ln-WMS-2f versus volume fraction.
    (a) η retrieved with the η-seeking algorithm during 90 s of continuous measurement (0.1 s per measurement); (b) frequency distribution histogram of η; (c) mean of R1fNA for each measurement. The integral time of each point is 0.1 s.
    Fig. 6. (a) η retrieved with the η-seeking algorithm during 90 s of continuous measurement (0.1 s per measurement); (b) frequency distribution histogram of η; (c) mean of R1fNA for each measurement. The integral time of each point is 0.1 s.
    1. Initializeη=0, stride s=π/4, threshold ε=103, residuals r=1.
    2. while r>ε, repeat :
    3. R1fNA=(lnItNA×cos(ωt+η))lowpass
    4. R1fNA[F]=(lnItNA×cos(ωt+η+s))lowpass
    5. R1fNA[B]=(lnItNA×cos(ωt+ηs))lowpass
    6. if|R1fNA|<|R1fNA[F]|and|R1fNA|<|R1fNA[B]|:
    7.   rmeanof|R1fNA|
    8. else :
    9.   if|R1fNA[F]|<|R1fNA|and|R1fNA[F]|<|R1fNA[B]| :
    10.    rmeanof|R1fNA[F]|
    11.    ηη+s
    12.   else :
    13.    rmeanof|R1fNA[B]|
    14.    ηηs
    15.   ss/2
    Table 1. Pseudocode of η-Seeking Algorithm
    Shaomin Li, Liqun Sun. Natural logarithm wavelength modulation spectroscopy[J]. Chinese Optics Letters, 2021, 19(3): 031201
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