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

1. Introduction

Gas leak infrared imaging detection technology has been one of the most effective gas leak detection technologies mainly because of its capabilities of high efficiency, remote detection, dynamic imaging, and other significant advantages. Gas leak infrared imaging detection technology can be mainly divided into two categories, active imaging technology, based on the absorption of the laser radiation, and passive imaging technology, based on the radiation of the gas itself and the absorption of the background radiation. Of these, the latter has been an important research direction and its market share continues to grow, since illumination of the radiation source and a reflective background are not necessary. However, there is no standard method for evaluating the performance of GLIIDSs (gas leak infrared imaging detection systems). Three common methods are often adopted currently. The first is to continue using the evaluation metrics of thermal imaging systems [1–3], such as NETD (noise equivalent temperature difference) and NESR (noise equivalent spectral radiance). The second method is NECL (noise equivalent concentration path length) [4–6], which represents the gas concentration integral value along the LOS (line of sight) of the system when the SNR (signal-to-noise ratio) is equal to one. Compared with the first method, the second one is more reasonable and widely used because it takes into account the infrared absorption characteristics of the gas. However, the influence from the size of the gas plume is not considered. The third method is to specify a detection limit of a certain gas, usually in the form of the MLDR (minimum detectable leak rate) [7,8]. Although this is a rough method, it has been adopted by manufacturers and vendors for the intuitive and perceivable nature of its evaluation. Due to the lack of comprehensively considering 1) the gas infrared absorption characteristics and 2) the size and distance of the gas plume, which are factors that cannot be ignored, none of the above-mentioned methods can accurately and comprehensively evaluate the performance of GLIIDS.

In fact, the MRTD (minimum resolvable temperature difference) is also one of the most important parameters that quantify the performance of thermal imaging systems, besides those mentioned above. The MRTD is a comprehensive evaluation parameter that includes both the temperature resolution and the spatial resolution. It has the mutual performance model, the measurement method, and the specific device. Because of the very similar application mode of GLIIDS and the conventional thermal imaging system, the MRGC (minimum resolvable gas concentration) model is established based on the MRTD model in this paper. The simulation and experimental results demonstrate the effectiveness of the proposed MRGC performance evaluation method.

2. MRTD definition and analysis

According to the definition in [9], with unlimited viewing time and optimization of controls, the observers observe the standard four-bar pattern on the screen, which has a 7:1 length-to-width aspect ratio, with a planar blackbody background (Fig. 1).The temperature difference between the target and background keeps increasing from zero, until the observers confirm that the four-bar target can be distinguished (with 50% probability). At this time, the temperature difference is MRTD(f) at the spatial frequency f. Obviously the MRTD contains not only the temperature resolution and the spatial resolution of the thermal imaging system, but also subjective factors associated with the observers. The MRTD is one of the most important indexes for evaluating the performance of thermal imaging systems. To date, the MRTD mathematical model has been established and the generic MRTD measurement method and equipment have been developed; the MRTD has become the industry-standard performance measure for thermal imaging systems.

Fig. 1 Image of the four-bar pattern.

Download Full Size | PDF

According to the ideas used in the MRTD derivation [10], the MRTD is the temperature difference between the blackbody target and background when the image SNR perceived by the human eye (that is, the visual SNR) is greater than or equal to the visual threshold SNR.

Generally, the target image SNR that the system receives can be expressed as

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

According to the imaging relationship, Eq. (1) can be specifically expressed as

\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

where D₀ is the aperture of the optical system; α and β are the opening angles of the target to the system; A_d is the area of the detector; Δf is the noise equivalent bandwidth; [λ₁, λ₂] is the spectral response band of the system; D*(λ) is the specific detectivity of the detector; τ_a(λ) is the spectral transmittance of the atmosphere; and τ₀(λ) is spectral transmittance of the optical system. ΔM_t-b is the spectral radiation difference between the target and background,

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

where T_t and T_b are the temperatures of the target and background; ε_t(λ) and ε_b(λ) are the spectral emissivities of the target and background; and M(λ,T) is the blackbody spectral emittance at the temperature T (Planck’s radiation law):

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

where c₁ = 3.74 × 10⁻¹⁶ (W·m²) and c₂ = 1.44 × 10⁻² (m·K) are the first and second radiation constants, respectively.

For the blackbody target and background in the laboratory [assuming that ε_t(λ) = ε_b(λ) = 1 and τ_a(λ) = τ₀(λ) = 1], ΔM_t-b can be rewritten as

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

where ΔT = T_t -T_b is the temperature difference between the target and background.

The visual SNR is

\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}

where p_corr(f) is a filtering function related to the modulation transfer function MTF_s(f) of the imaging system, the modulation transfer function MTF_eye(f) of the human eye, the human-eye–matched filter, and other correction factors. For the first- and second-generation thermal imaging systems, p_corr(f) can be found in Refs [9]. and [10].

When the visual SNR is equal to the visual threshold SNR (SNR_DT), ΔT is MRTD, which can be obtained from Eq. (1) and Eq. (6):

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}

3. MRGC model

There are significant differences in radiation characteristics between the gas and the blackbody target or other common targets (generally, a graybody). On the one hand, the spectral emissivity of the gas target, which is a selective radiator, varies greatly at different wavelengths. On the other hand, a part of the background radiation can still pass through the gas plume and be received by the system after being absorbed and attenuated. Furthermore, the gas has a strong selective absorption characteristic for infrared radiation (Fig. 2 shows part of the absorption spectrum of ethylene). For the detection by imaging of a gas plume with a spatial distribution, the judgment criterion is also the human observation. Therefore, the evaluation principle is similar to that of the MRTD. However, since the target and background of the MRTD measurement are blackbody, the radiation and absorption characteristics of the gas are not considered and cannot be directly applied to evaluate the gas imaging detection.

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

Download Full Size | PDF

In order to take advantage of the MRTD model and take into account the radiation and absorption characteristics of the gas, a MRGC performance evaluation model of GLIIDSs is established by redesigning the MRTD measurement target and method.

3.1 MRGC definition and measurement method

As is shown in Fig. 3 and Fig. 4, a specially designed infrared gas chamber with a thickness l is inserted into the space between the target blackbody and the background blackbody of the ordinary planar differential blackbody source. The front and rear windows of the gas chamber are made of infrared-transmitting materials (e.g., ZnSe or Ge), and on the windows are antireflection coatings covering the working wavelength range, where the transmission spectrum of the window/coating combination is designed to be as flat as possible. Thus the hollow pattern of the background blackbody, which was previously used as the measurement target, is covered by the gas chamber, and the gas can become the measurement target. The frame of the gas chamber is made of poor thermal-conductivity material to deduce the influence to the gas temperature from the frame. There are gas inlet, outlet and mounting holes for the gas concentration meter and thermometer on the frame. The target radiation of the MRGC measurement consists of 1) the radiation from the target blackbody after being attenuated by the gas in the chamber and 2) the radiation from the gas itself. The background radiation is still from the background blackbody.

Fig. 3 MRGC measurement target and gas chamber.

Download Full Size | PDF

Fig. 4 Schematic diagram of the MRTD measurement system.

Download Full Size | PDF

Figure 4 shows the schematic diagram of the MRTD measurement system; the MRGC is defined according to the following measurement method:

The compositions of air, such as carbon dioxide or moisture, can emit or absorb the infrared radiation. To avoid the interference from air, the infrared gas chamber and the pipeline need to be cleaned with the carrier gas (e.g., nitrogen) that does not emit or absorb infrared radiation;
Before the chamber is filled with ethylene, the temperature difference between the target blackbody and the background blackbody needs to be set at a fixed and appropriate value, so that the video images are uniform and the four-bar target cannot be observed (the influence of the infrared windows is eliminated).
To measure a gas where the gas temperature is T_gas, gradually adjust the gas concentration c in the infrared gas chamber, until the observer confirms that the four-bar gas pattern with a spatial frequency f can be distinguished (with 50% probability). At this time, for the gas temperature T_gas, the product of the gas concentration c and the thickness l of the gas chamber is MRGC(f, T_gas), in units of ppm·m.

3.2 MRGC model

According to the definition of the MRGC, the same condition that the visual SNR be greater than or equal to the visual threshold SNR needs to be met when the human eye is able to distinguish the four-bar gas pattern. Combining Eq. (1) and Eq. (6) yields:

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

For the gas target and blackbody background, the spectral radiation difference of Eq. (3) needs to be rewritten as

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

where τ_gas(λ) is the spectral transmissivity of the gas; assume that the gas concentration is uniformly distributed, according to the Beer–Lambert law:

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

where α_gas(λ) is the spectral absorption coefficient, c is the gas concentration, and l is the path length along the LOS. For a given type of gas, α_gas(λ) can be obtained from the gas infrared spectral database (e.g. the Russian Information System Spectroscopy of Atmospheric Gases) if the state parameters (the temperature and the pressure) of the gas are known.

Since the influence of the gas chamber is corrected and the measurement is carried out in the laboratory, we can assume that T_t = T_b, τ_a(λ) = τ₀(λ) = 1. Thus, Eq. (9) becomes

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

Substituting Eq. (2) and Eq. (11) into Eq. (8) yields:

{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

As the gas concentration is low when measuring the MRGC, τ_gas(λ) can be approximated by the first-order minima of the Taylor expansion. Then, using Eq. (7), Eq. (12) becomes

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}

So the MRGC can be expressed as

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}

where c_min is the minimum gas concentration in units of ppm corresponding to the path length l when the human eye can distinguish the four-bar gas pattern.

4. MRGC equivalent calculation method

It is known from the definitions and models of the MRTD and the MRGC that the radiation difference between the target and background that the same system receives is the only factor that affects the observer’s visual SNR under the same laboratory conditions (assuming that τ_a(λ) = τ₀(λ) = 1). This means that when

\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

the visual perception of the human eye is the same. Therefore, we propose the MRGC equivalent calculation method based on the MRTD:

Obtain the MRTD(f) at different spatial frequencies by measurement or simulation when the target blackbody temperature T_t and background blackbody temperature T_b are known.
If the spectral response band [λ₁, λ₂] and the specific detectivity D*(λ) are known, the minimum resolvable radiation difference can be calculated by substituting T_b and T_t = T_b-MRTD(f) into the right side of Eq. (15). (When the gas leaks out of the pipeline or the gas tank, it expands and absorbs heat. So the gas temperature is lower than that of the environment and the background.)
Under the same measurement conditions (that is, the target frequency f and the background blackbody T_b are the same), the gas concentration c can be calculated from Eq. (15) by substituting the gas temperature T_gas, the spectral absorption coefficient α_gas(λ), and the path length l into the left side of Eq. (15). Then the value of MRGC(f, T_gas) can be obtained.
(4) The MRGC(f, T_gas) surface (or discrete measured values thereof) of the gas to be measured can be calculated based on the MRTD(f) curve (or discrete measured values thereof).

Without loss of generality, we carried out the MRGC equivalent calculation in detail to describe this method by using the uncooled long-wave infrared imaging system (D*(λ) = D*) to detect ethylene. We assume that the spectral response band of the thermal imaging system is 8.0 µm–12.0 µm, the pixel size is 17 µm × 17 µm, and the focal length is 25 mm. Thus, the characteristic frequency f₀ is 0.735 cycles/mrad (f₀ = 2DAS, where DAS is the field angle of a single detector element on the objective lens); the background blackbody temperature T_b is 300 K; and the path length of the gas chamber, l, is 0.1 m. The simulated MRTD(f) curve is shown in Fig. 5.The MRGC(f, T_gas) surface for ethylene can be calculated (Fig. 6).

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

Download Full Size | PDF

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

Download Full Size | PDF

Here we demonstrate the equivalent calculation method at the characteristic frequency f₀: As MRTD(f₀) = 0.70 K, the target blackbody temperature is T_t = 300–0.70 K = 299.30 K. By substituting the above parameters into the right side of Eq. (15), the minimum resolvable radiation difference of the target blackbody and background blackbody can be calculated to be 1.3805 (W × m⁻² × µm⁻¹). We assume that the ethylene in the gas chamber is uniformly distributed in space and that its temperature T_gas is 290 K; then, we retrieve the spectral absorption coefficient α_gas(λ) from the gas infrared spectral database, and thus the MRGC(f₀, T_gas) value can be calculated from Eq. (15) to be 1.0439 × 10³ ppm·m.

Since the spectral absorption coefficient is closely related to the gas temperature, it affects the spectral transmissivity indirectly. Furthermore, according to Eq. (9), the gas temperature affects both the radiation of the gas itself and the radiation passing through the gas from the background. Figure 7 shows the MRGC(f) curves of ethylene at different gas temperatures. It can be seen that the MRGC increases with spatial frequency and that the smaller the temperature difference is between the gas and the background blackbody, the faster the MRGC increases. When the spatial frequency is fixed (e.g., at f₀), the nonlinear relationship between MRGC(f₀) and T_gas is as shown in Fig. 8,MRGC(f₀) increases with the gas temperature approaching the background temperature (the blue curve). The red vertical line representing T_gas = 300 K is the asymptote, which means that no matter how high the gas concentration is (here the maximum gas concentration is 1 million ppm under normal pressure), the system cannot detect the four-bar gas pattern. Hence, in order to use the MRGC model to evaluate GLIIDSs more conveniently, the gas temperature needs to be set at an appropriate value by considering the ability of the equipment to control and regulate the gas concentration and temperature, so that more accurate evaluation results can be acquired. Similarly, as an example, to select MRTD(f₀) as the single performance index of thermal imaging systems, the single performance index for GLIIDSs can be chosen to be MRGC(f₀, T_b-5 K).

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

Download Full Size | PDF

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.

Download Full Size | PDF

5. MRGC measurement system and results

By redesigning the target of the MRTD measurement system in Section 2 (Fig. 3 and Fig. 4), we designed and built a setup of the MRGC measurement system. As is shown in Fig. 9, the system mainly includes a concentration-adjusting chamber, a copper heat exchanger, a thermostatic water bath, an infrared gas chamber (thickness: l = 3.935 × 10⁻² m; diameter: 88mm; working wavelength range: 3.0 µm – 12.0 µm; material of the frame: polymethyl methacrylate, thermal-conductivity: 19 W/m/K), a planar differential blackbody source, a gas circulation micro-pump, a gas concentration meter, a thermometer, and a barometer. Nitrogen (N₂) is used as the carrier gas and to clean the pipeline. By changing the ratio between the nitrogen and the gas to be measured, the desired gas concentration can be obtained. The temperature of the gas flowing through the copper heat exchanger can be controlled by adjusting the water temperature of the thermostatic water bath. The gas circulation micro-pump cannot only make the system a closed-cycle cooling system but also keep the gas concentration uniform when the exhaust pipe is turned off. It should be noted that the thickness of the gas chamber needs to be moderate in the current structure of the MRGC measurement system. If it is too thin, a very high gas concentration is required and the measurement accuracy of the concentration meter is reduced. Even worse, the required concentration may be outside of the range of the meter, preventing it from being measured. While, if it is too thick, the accuracy of the MRGC measurement will be affected since the FOV (field of view) of the thermal imaging system is hard to cover with the infrared gas chamber.

Fig. 9 Block diagram of the MRGC measurement system.

Download Full Size | PDF

The MRGC of ethylene is characterized by the measurement system (Fig. 10).The imaging detection capability of the uncooled thermal imaging system mentioned in Section 4 is tested at different spatial frequencies. The temperature of ethylene is about 293.15 ± 0.2 K under standard atmospheric pressure. Because there are not enough four-bar target patterns with different sizes, a collimating optical system is not used. Instead, the thermal imaging system directly faces the planar differential blackbody source, the background blackbody of which completely covers the FOV. The four-bar targets with simulated different spatial frequencies can be obtained by continually changing the distance. Since the temperature of the gas leaking out is usually lower than that of the environment in practical applications, the negative MRGC value is measured and compared with the negative MRTD value measured under the same conditions. When performing the MRTD measurement, the infrared gas chamber is still included and cleaned by N₂, so that the influence of the radiation attenuation by the infrared windows is eliminated.

Fig. 10 Setup of the MRGC measurement system.

Download Full Size | PDF

The MRGC direct measurement method procedure is as follows:

Before the chamber is filled with ethylene, regulate the temperature difference between the target blackbody and the background blackbody of the planar differential blackbody source, so that the video images are uniform and the four-bar target cannot be observed.
Keep increasing the concentration of the ethylene with fixed temperature slowly, until the observer confirms that the four-bar gas pattern can be distinguished (50% probability). Record the frequency of the target and the state parameters of the gas and the environment. At this time, the product of the gas concentration, c, and the thickness of the gas chamber, l, is equal to the MRGC.

The measured MRGC value (red), the measured MRTD value (blue), and the calculated MRGC value (green) of ethylene are given in Fig. 11.Because the range of the gas concentration meter is limited and the significance of measuring the target with low temperature difference at high spatial frequency is not so great, the experiment only measured the MRGC for the spatial frequency range 0.2f₀–0.6f₀. Obviously, the measured and calculated values are in good agreement, which verifies the correctness of the MRGC performance evaluation model. The errors fluctuate within ± 20%. The maximum error is 18.26% at the spatial frequency of 0.214f₀. The main reasons for the errors are as follows:

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)].

Download Full Size | PDF

An error of a theoretical nature arises from the assumptions of 1) a small temperature difference for the MRTD model and 2) an absorption that is not strong for the MRGC model.
The fact that the measurement results depend on the observation and determination of the human eyes can lead to a potential measurement error, which is usually more than 20%.
Due to the limits on the system’s ability to control and measure the gas temperature, the actual gas temperature has a fluctuation of ± 2%.
The ethylene concentration meter has a measurement error of ± 3%.
There are other sources of error such as the fluctuation of the gas pressure and the non-uniformity of the thermal imaging system.

From the MRGC measurement and analysis, it can be seen that:

The MRGC measurement system is able to comprehensively and directly evaluate the performance of GLIIDSs. It is expected to become the standard measurement equipment for infrared imaging detection, similar to the MRTD.
Because 1) the MRGC measurement system is complicated, 2) many state parameters need to be controlled, and most of all 3) dedicated gas concentration meters with large dynamic ranges are required, application of this system is limited. While the MRGC equivalent calculation method can easily give the MRGC value of a GLIIDS, since most of the gas infrared absorption spectrum has been measured, which avoids the requirement of complex equipment for the direct measurement method. Therefore, the cost of the equivalent calculation method is quite low.
• Although the measurement results show that the MRGC value of a GLIIDS is much greater than the detection threshold of the common single-gas detectors, the detection efficiency of a GLIIDS is much higher, and there are significant advantages in aspects such as detection speed and intuitiveness. This is because the work modes are different: single-point detectors are based on the diffusion of the leaking gas (the response speed of which greatly depends on the leak rate), the leak amount, and the distance between the detector and the leak source, while the GLIIDS directly detects the leak source through imaging.

6. Conclusion

A concept and model for the MRGC performance evaluation of GLIIDSs is proposed in this paper. The MRGC model takes into account the environmental (the temperature of the background blackbody and the target blackbody) and gas-state (the gas temperature, pressure and concentration) parameters, the size of the gas plume (the four-bar gas pattern with a spatial frequency), and other factors that influence the MRGC measurement; Both the MRGC direct measurement method and the MRGC equivalent calculation method are first proposed and are able to evaluate the performance of GLIIDSs. The MRGC measurement system is designed and built. The direct measurement and equivalent calculation results for ethylene are in good agreement with errors of less than ± 20%, which verifies the correctness of the model and the effectiveness of the MRGC performance evaluation method.

The error of the MRGC measurement system can be further reduced by using more sophisticated gas concentration meters and temperature control equipment. The system is expected to become the standard measurement equipment for GLIIDSs. In addition, the MRGC equivalent calculation method, which is able to provide the MRGC value of most dangerous gases based on the traditional MRTD measurement system and the gas infrared absorption spectrum database, has great potential for practical applications.

Acknowledgments

This work was supported by the Key Project of the Natural Science Foundation of Beijing, China (Grant No. 4121002). The authors would like to thank Dr. Liu Yang and Dr. Xia Runqiu for their help in the system design and testing.

References and links

1. B. R. Cosofret, C. M. Gittins, and W. J. Marinelli, “Visualization and tomographic analysis of chemical vapor plumes via LWIR imaging Fabry-Perot spectrometry,” Proc. SPIE 5584, 112–121 (2004).

2. V. Farley, A. Vallières, M. Chamberland, A. Villemaire, and J.-F. Legault, “Performance of the FIRST, a longwave infrared hyperspectral imaging sensor,” Proc. SPIE 6398, 63980T (2006).

3. S. Sabbah, R. Harig, P. Rusch, J. Eichmann, A. Keens, and J.-H. Gerhard, “Remote sensing of gases by hyperspectral imaging: system performance and measurements,” Opt. Eng. 51(11), 111717 (2012). [CrossRef]

4. J. Sandsten, P. Weibring, H. Edner, and S. Svanberg, “Real-time gas-correlation imaging employing thermal background radiation,” Opt. Express 6(4), 92–103 (2000). [CrossRef] [PubMed]

5. B. R. Cosofret, W. J. Marinelli, T. E. Ustun, C. M. Gittins, M. T. Boies, M. F. Hinds, D. C. Rossi, R. L. Coxe, S. D. Chang, B. D. Green, and T. Nakamura, “Passive infrared imaging sensor for standoff detection of methane leaks,” Proc. SPIE 5584, 93–99 (2004).

6. E. Naranjo, S. Baliga, and P. Bernascolle, “IR gas imaging in an industrial setting,” Proc. SPIE 7661, 76610K (2010).

7. N. Hagen, R. T. Kester, C. G. Morlier, J. A. Panek, P. Drayton, D. Fashimpaur, P. Stone, and E. Adams, “Video-rate spectral imaging of gas leaks in the longwave infrared,” Proc. SPIE 8710, 871005 (2013).

8. R. Benson, R. Madding, R. Lucier, J. Lyons, and P. Czerepuszko, “Standoff passive optical leak detection of volatile organic compounds using a cooled InSb based infrared imager,” in AWMA 99th Annual Meeting, Papers (2006), 06-A-131.

9. J. M. Lloyd, Thermal Imaging Systems (Plenum, 1975).

10. M. C. Dudzik, ed., Electro-Optical Systems Design, Analysis, and Testing, Vol. 4 of The Infrared and Electro-Optical System Handbook (SPIE, 1993).

MRGC performance evaluation model of gas leak infrared imaging detection system

Abstract

1. Introduction

2. MRTD definition and analysis

3. MRGC model

3.1 MRGC definition and measurement method

3.2 MRGC model

4. MRGC equivalent calculation method

5. MRGC measurement system and results

6. Conclusion

Acknowledgments

References and links

Cited By

Figures (11)

Equations (15)

Optics Express