Gas Concentration Inversion Method Based on Multiple Harmonic Joint Analysis

Zihuai Liu; Chunhua Yang; Qiwu Luo; Gaofeng Zhu

doi:10.3788/AOS201939.1030001

Journals >Acta Optica Sinica >Volume 39 >Issue 10 >Page 1030001 > Article

Acta Optica Sinica
Vol. 39, Issue 10, 1030001 (2019)

Gas Concentration Inversion Method Based on Multiple Harmonic Joint Analysis

Zihuai Liu^1、***, Chunhua Yang^1、**, Qiwu Luo^1、*, and Gaofeng Zhu²

Author Affiliations

¹School of Automation, Central South University, Changsha, Hunan 410083, China

²School of Information, Hunan University of Humanities, Science and Technology, Loudi, Hunan 417000, China

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DOI: 10.3788/AOS201939.1030001 Cite this Article Set citation alerts

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 Copy Citation Text

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Fig. 1. Relationship between second harmonic peak value and modulation depth

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Fig. 2. Relationship between joint peak value of 2nd-/4th-harmonics and modulation depth

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Fig. 3. Relationship between joint peak value of 2nd-/4th-/6th-harmonics and modulation depth

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Fig. 4. Relationship between joint peak value of 2nd-/4th-/6th-/8th-harmonics and modulation depth

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Fig. 5. Diagram of multiple harmonic joint analysis method

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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 1. Expressions of even harmonic functions with different modulation depths

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 2. Optimal modulation depth, harmonic peak value, and peak value ratio 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

Table 3. Degree of noise suppression under different inversion modes

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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