Gas Concentration Inversion Method Based on Multiple Harmonic Joint Analysis

Table 1. Expressions of even harmonic functions with different modulation depths
View table
Table 1. Expressions of even harmonic functions with different modulation depths
S_i(0,m) Expression
S₂(0,m) $\frac{2}{m^{2}} (2 - \frac{2 + m^{2}}{\sqrt[]{1 + m^{2}}})$
S₄(0,m) - $\frac{2}{m^{4}} [4 (2 + m^{2}) - \frac{8 + 8 m^{2} + m^{4}}{\sqrt[]{1 + m^{2}}}]$
S₆(0,m) $\frac{2}{m^{6}} [2 (16 + 16 m^{2} + 3 m^{4}) - \frac{32 + 48 m^{2} + 18 m^{4} + m^{6}}{\sqrt[]{1 + m^{2}}}]$
S₈(0,m) - $\frac{2}{m^{8}} [8 (16 + 24 m^{2} + 10 m^{4} + m^{6}) - \frac{128 + 256 m^{2} + 160 m^{4} + 32 m^{6} + m^{8}}{\sqrt[]{1 + m^{2}}}]$

Table 2. Optimal modulation depth, harmonic peak value, and peak value ratio under different inversion modes
View table
Table 2. Optimal modulation depth, harmonic peak value, and peak value ratio under different inversion modes
Mode m_optimal S_i(i=2,4,6,8) S_i/S₂(i=2,4,6,8)
2nd-harmonics 2.198 0.343 1.000
2nd-/4th-harmonics 2.829 0.500 1.458
2nd-/4th-/6th-harmonics 3.407 0.592 1.726
2nd-/4th-/6th-/8th-harmonics 3.950 0.653 1.904

Table 3. Degree of noise suppression under different inversion modes
View table
Table 3. Degree of noise suppression under different inversion modes
Mode η_i /%
2nd-harmonics 0
2nd-/4th-harmonics 31.38
2nd-/4th-/6th-harmonics 42.03
2nd-/4th-/6th-/8th-harmonics 47.45

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Zihuai Liu, Chunhua Yang, Qiwu Luo, Gaofeng Zhu. Gas Concentration Inversion Method Based on Multiple Harmonic Joint Analysis[J]. Acta Optica Sinica, 2019, 39(10): 1030001

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Paper Information

Category: Spectroscopy

Received: Mar. 25, 2019

Accepted: May. 23, 2019

Published Online: Oct. 9, 2019

The Author Email: Zihuai Liu (liuzihuai@csu.edu.cn), Chunhua Yang (ychh@csu.edu.cn), Qiwu Luo (luoqiwu_csu@163.com)

DOI:10.3788/AOS201939.1030001

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Expressions of even harmonic functions with different modulation depths

Table 1. Expressions of even harmonic functions with different modulation depths

Table 2. Optimal modulation depth, harmonic peak value, and peak value ratio under different inversion modes

Table 2. Optimal modulation depth, harmonic peak value, and peak value ratio under different inversion modes

Table 3. Degree of noise suppression under different inversion modes

Table 3. Degree of noise suppression under different inversion modes