MRGC performance evaluation model of gas leak infrared imaging detection system

Jiakun Li; Weiqi Jin; Xia Wang; Xu Zhang

doi:10.1364/OE.22.0A1701

Optics Express
Vol. 22,
Issue S7,
pp. A1701-A1712
(2014)
•https://doi.org/10.1364/OE.22.0A1701

MRGC performance evaluation model of gas leak infrared imaging detection system

Jiakun Li, Weiqi Jin, Xia Wang, and Xu Zhang

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Jiakun Li, Weiqi Jin, Xia Wang, and Xu Zhang, "MRGC performance evaluation model of gas leak infrared imaging detection system," Opt. Express 22, A1701-A1712 (2014)

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Abstract

Gas leak infrared imaging detection technology has become one of the most effective means to detect gas leaks. We propose a novel MRGC (minimum resolvable gas concentration) model that is suitable for evaluating the performance of passive GLIIDSs (gas leak infrared imaging detection systems). An MRGC equivalent calculation method and a direct MRGC measurement method based on the MRTD (minimum resolvable temperature difference) model are also proposed. The MRGC measurement system is designed and built. The measured and calculated results are in good agreement, which verifies the MRGC model’s correctness and demonstrates the effectiveness of the MRGC performance evaluation method.

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Fig. 1 Image of the four-bar pattern.

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Fig. 2 Part of the infrared absorption spectrum of ethylene (1ppm·m@296K, Pacific Northwest National Laboratory).

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Fig. 3 MRGC measurement target and gas chamber.

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Fig. 4 Schematic diagram of the MRTD measurement system.

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Fig. 5 Plot of the simulated MRTD(f) curve.

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Fig. 6 Plot of the simulated MRGC(f, T_gas) surface.

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Fig. 7 Plots of the simulated MRGC(f) curves for various gas temperatures.

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Fig. 8 Plot of the relationship between MRGC(f₀) and the gas temperature T_gas (the blue curve). The red vertical line is the asymptote T_gas = 300 K.

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Fig. 9 Block diagram of the MRGC measurement system.

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Fig. 10 Setup of the MRGC measurement system.

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Fig. 11 Results of the calculated and measured MRGC of ethylene [T_gas ≈293.15 ± 0.2 K; the green line is the calculated MRGC value (corresponding to the left axis), the red line is the measured MRGC value (corresponding to the left axis), and the blue line is the measured negative MRTD value (corresponding to the right axis)].

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Equations (15)

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{SNR}_{0} = \frac{V_{s}}{V_{n}} = \frac{Δ T}{NETD}

\frac{V_{s}}{V_{n}} = \frac{D_{0}^{2} α β}{4 {(A_{d} Δ f)}^{1 / 2}} \int_{λ_{1}}^{λ_{2}} D^{*} (λ) τ_{α} (λ) τ_{0} (λ) Δ M_{t - b} d λ

Δ M_{t - b} = ε_{t} (λ) M (λ, T_{t}) - ε_{b} (λ) M (λ, T_{b})

M (λ, T) = \frac{c_{1}}{λ^{5}} \frac{1}{\exp (c_{2} / λ T) - 1}

Δ M_{t - b}^{b} = M (λ, T_{t}) - M (λ, T_{b}) \approx \frac{\partial}{\partial T} M (λ, T_{b}) Δ T

\begin{matrix} {SNR}_{V} (f) = p_{corr} (f) \cdot {SNR}_{0} = p_{corr} (f) \cdot \frac{D_{0}^{2} α β}{4 {(A_{d} Δ f)}^{1 / 2}} \int_{λ_{1}}^{λ_{2}} D^{*} (λ) Δ M_{t - b} d λ \\ = p_{corr} (f) \cdot Δ T \cdot \frac{D_{0}^{2} α β}{4 {(A_{d} Δ f)}^{1 / 2}} \int_{λ_{1}}^{λ_{2}} D^{*} (λ) \frac{\partial M (λ, T_{b})}{\partial T} d λ \end{matrix}

MRTD (f) = \frac{{SNR}_{DT} \cdot NETD}{p_{corr} (f)} = \frac{{SNR}_{DT}}{p_{corr} (f) \cdot \frac{D_{0}^{2} α β}{4 {(A_{d} Δ f)}^{1 / 2}} \int_{λ_{1}}^{λ_{2}} D^{*} (λ) \frac{\partial M (λ, T_{b})}{\partial T} d λ}

{SNR}_{V} = p_{corr} \cdot \frac{V_{s}}{V_{n}}

Δ M_{gas-b} = [1 - τ_{gas} (λ)] M (λ, T_{gas}) + τ_{gas} (λ) M (λ, T_{t}) - M (λ, T_{b})

τ_{gas} (λ) = \exp [- α_{gas} (λ) c l]

Δ M_{gas-b} (λ) = [1 - τ_{gas} (λ)] [M (λ, T_{gas}) - M (λ, T_{b})]

{SNR}_{V} (f) = p_{corr} (f) \cdot \frac{D_{0}^{2} α β}{4 {(A_{d} Δ f)}^{1 / 2}} \int_{λ_{1}}^{λ_{2}} D^{*} (λ) [1 - τ_{gas} (λ)] [M (λ, T_{gas}) - M (λ, T_{b})] d λ

MRTD (f) \approx \frac{c l \int_{λ_{1}}^{λ_{2}} D^{*} (λ) α_{gas} (λ) [M (λ, T_{gas}) - M (λ, T_{b})] d λ}{\int_{λ_{1}}^{λ_{2}} D^{*} (λ) \frac{\partial M (λ, T_{b})}{\partial T} d λ}

MRGC (f, T_{gas}) = c_{\min} \cdot l = MRTD (f) \cdot \frac{\int_{λ_{1}}^{λ_{2}} D^{*} (λ) \frac{\partial M (λ, T_{b})}{\partial T} d λ}{\int_{λ_{1}}^{λ_{2}} D^{*} (λ) α_{gas} (λ) [M (λ, T_{gas}) - M (λ, T_{b})] d λ}

\int_{λ_{1}}^{λ_{2}} D^{*} (λ) Δ M_{gas-b} d λ = \int_{λ_{1}}^{λ_{2}} D^{*} (λ) Δ M_{t - b}^{b} d λ

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