Correction Method for Cavity Ring-Down Time Measurement Based on Wiener Deconvolution Transform

Lingxiao Cheng; Haiyang Qi; Songjie Yang; Jieling Xie; Sumei Liu; Xiaowei Guo; Bo Li; Sunqiang Pan

doi:10.3788/AOS241782

Acta Optica Sinica, Volume. 45, Issue 5, 0512002(2025)

Correction Method for Cavity Ring-Down Time Measurement Based on Wiener Deconvolution Transform

Lingxiao Cheng¹, Haiyang Qi², Songjie Yang³, Jieling Xie³, Sumei Liu², Xiaowei Guo², Bo Li^1、**, and Sunqiang Pan^2、*

Author Affiliations

¹School of Physics, Zhejiang University of Technology, Hangzhou 310023, Zhejiang , China

²Zhejiang Institute of Quality Sciences, Hangzhou 310018, Zhejiang , China

³Hangzhou Pengpu Technology Co., Ltd, Hangzhou 310052, Zhejiang , China

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Figures & Tables(18)

Fig. 1. Response process of detector system for signal

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Fig. 2. Measured ring-down signals with different bandwidths. (a) Full-process response curves; (b) normalized ring-down curves; (c) fitting residuals

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Fig. 3. Simulation of ring-down time and absorption spectra for different bandwidths. (a) Ring-down time for different bandwidths; (b) absorption spectra for different bandwidths

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Fig. 4. Simulation of relative measurement errors of different bandwidths

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Fig. 5. Simulation of deconvolution restoration. (a) 2 μs ring-down curve restoration; (b) 10 μs ring-down curve restoration; (c) 35 μs ring-down curve restoration

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Fig. 6. Diagram of CRDS system

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Fig. 7. Step response curve of the detector

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Fig. 8. Amplitude-frequency response of the detector system

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Fig. 9. Full ring-down signal

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Fig. 10. Compensation of typical measured ring-down curves

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Fig. 11. Measurement results and reduction of empty-cavity ring-down time

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Fig. 12. Real-time temperature and pressure measurements. (a) Real-time temperature measurements; (b) real-time pressure measurements

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Fig. 13. Compensation of measured spectra. (a) Ring-down time before and after compensation; (b) fitting curves of absorption spectra before and after compensation

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Table 1. Simulation results of absorption spectral areas and volume fractions of gas for different bandwidths
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Table 1. Simulation results of absorption spectral areas and volume fractions of gas for different bandwidths
Bandwidth /MHz
Area of spectrum /
（10^-7 cm^-2）
Volume
fraction /10^-6
Deviation /
%
10 1.42 328.55 0.0182
1 1.41 324.13 1.3633
0.4 1.33 307.17 6.5245

Table 2. Parameters of ring-down curves before and after compensation

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Table 2. Parameters of ring-down curves before and after compensation

Original ring-down time / $μ s$	Ring-down curve	$τ$ / $μ s$	Relative measurement error /%	Residual /arb.units
2	Before compensation	2.9321	46.60	0.0220
2	After compensation	2.0243	1.22	0.0085
10	Before compensation	10.4044	4.04	0.0113
10	After compensation	9.9843	0.16	0.0088
35	Before compensation	35.2146	0.61	0.0102
35	After compensation	35.0097	0.03	0.0080

Table 3. Parameters of typical ring down curves before and after compensation
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Table 3. Parameters of typical ring down curves before and after compensation
Ring-down curve $τ$ / $μ s$ Residual RMS /V
Before compensation 35.1011 0.0113
After compensation 34.2512 0.0052

Table 4. Measurement and compensation results of empty-cavity ring-down time
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Table 4. Measurement and compensation results of empty-cavity ring-down time
Ring-down
curve
Average ring-
down time / $μ s$
Standard
deviation / $μ s$
Average residual /V
Before compensation 35.3101 0.2674 0.0116
After compensation 34.3807 0.1477 0.0059

Table 5. Parameters of spectra before and after compensation
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Table 5. Parameters of spectra before and after compensation
Spectrum
Measured concentration /
10^-8
Absolute error /
10^-6
Relative error /%
Before compensation 5.6719 29.81 4.99
After compensation 5.9552 1.48 0.25

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Lingxiao Cheng, Haiyang Qi, Songjie Yang, Jieling Xie, Sumei Liu, Xiaowei Guo, Bo Li, Sunqiang Pan. Correction Method for Cavity Ring-Down Time Measurement Based on Wiener Deconvolution Transform[J]. Acta Optica Sinica, 2025, 45(5): 0512002

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