1. Introduction

Because of its quick and remote detection of gas leakages in large-area open spaces, the optical gas imaging (OGI) technique has a pivotal role in refineries, chemical plants, pipelines, and power stations [1–9]. Active OGI techniques include backscatter absorption gas imaging (BAGI) [10–13], tunable diode laser absorption spectroscopy (TDLAS) based tomography [14,15], and single-pixel detector imaging technique with structured illumination tuned by digital micromirror device (DMD) [16]. However, these techniques are unsuitable for unsupervised monitoring of the environment because the powerful lasers require security assurance. Passive OGI has drawn increased attention for gas leakage detection because it uses the ambient background infrared radiation rather than lasers and includes techniques such as Fourier transform infrared spectroscopy [17], dispersive element-based hyperspectral imaging [18–20], and non-dispersive imaging [21–26]. Non-dispersive imaging systems are further divided into monoband, dual-band [22,23], and multiband [24–26] systems.

The monoband system generally utilizes a narrow bandpass (BP) filter that matches the most significant absorption band of a gas [21] to increase the ratio between the gas absorption radiation and total received energy. However, when the plume temperature is close to the ambient temperature, the leaking gas cannot be distinguished from the background. The dual-band OGI system improves the gas detection sensitivity by taking advantage of differential wavebands to decrease the effect of background clutter. In addition,the dual-band OGI can quantitatively measure the gas concentration after calibrating the concentration length and image grayscale. The differential wavebands include the in-band, which covers the strong absorption peak of the gas, and the out-band, which involves the transparent spectra of the gas. By subtracting or dividing the in-band and out-band images, the image contrast of the gas plume is enhanced [27]. The thermal background radiation fluctuations and fixed pattern noise can be eliminated as well.

Gas correlation is a representative dual-band differential OGI technique that employs a gas cell filled with high-concentration gas during a test as the out-band filter. This makes the transmittance of the out-band path opaque precisely at the strong gas absorption lines [28,29]. When gas leakage occurs, even a small difference in the radiant flux between the in-band and out-band paths can be detected by the infrared focal plane array (FPA). However, this technique can only detect a single kind of gas, and the detection accuracy is seriously affected by the overlapping spectral lines of other gases. Wolowelsky et al. applied a voltage-controlled liquid crystal filter to switch the in-band and out-band paths [23]. This has the advantage that the switching frequency can reach up to 100 Hz, and rapidly moving gas plumes can be detected. However, this technology is still being studied in the laboratory, and relevant visualization experiments are not reported.

A multiband OGI system cannot only measure the gas concentration but also identify the gas species. There are two common multiband schemes: division of aperture [24] and division of time [25]. Unfortunately, they are subject to degradation of the spatial resolution or time resolution to some degree. Particularly, these limitations may become serious and reduce the frame rate when a low-cost uncooled infrared focal plane array (FPA) is used owing to its long thermal response constant. Second Sight produced by Bertin in France is a typical six-band OGI system that uses an uncooled infrared FPA, and it has a frame rate of less than 1 fps [26]. Furthermore, this system requires the leaking gas plume to remain stable during the six-band image acquisition; thus, it is more suitable for detecting a large gas leakage than a small gas leakage.

A multiband OGI system using an uncooled infrared FPA has lower frame rate and sensitivity than a cooled one. Thus, to improve the time resolution for detecting a small gas leakage, we propose to combine the Archimedean spiral push-broom filtering (ASPBF) with the electronic pulses scanning row by row of the uncooled FPA. Because the trajectory of an Archimedean spiral over the FPA is approximated as a straight line, the operating mode of ASPBF optically filtering the present row of the FPA and electronically reading out the previous row can be realized to avoid FPA idleness during filter switching and increase the frame rate.

2. Archimedean spiral push-broom multiband thermal imaging system

The filter wheel is a typical scheme for realizing multiband imaging with the division of time. It adopts discrete filtering to ensure incident infrared radiation passing through one filter to reach the FPA simultaneously. Each time, a single filter is involved in the optical path. However, this operating mode causes a low frame rate and FPA idleness during filter switching. We propose the ASPBF mode basing on an Archimedean spiral filtering disk (A-disk) to address these issues. The trajectory of the A-disk spiral push-broom filtering over the FPA can be approximated as a straight line because of the small curvature of the Archimedean spiral. This means that, within a single filtering zone, the A-disk continuously filters over pixels of the FPA row-by-row and seamlessly transits to the next filtering zone without FPA idleness during filter switching. Thus, the system’s frame rate can be increased.

Figure 1 shows three different positions of the FPA relative to a four-zone A-disk in which each zone is an independent filter. The position of the FPA relative to the A-disk is a prerequisite to achieve stable push-broom filtering. When the A-disk rotates counterclockwise at a constant angular velocity, one filtering spiral (e.g., the green spiral in Figs. 1(a)–1(c)) should lie in one row of the FPA. Therefore, position $P_B$ (Fig. 1(b)) is superior to $P_A$ (Fig. 1(a)) or $P_C$ (Fig. 1(c)) in which the filtering spiral crosses several rows of the FPA and cannot cover a single row completely.

 

Fig. 1 (a)–(c) Three different positions of the FPA relative to a four-zone A-disk in which each zone is an independent filter and position $P_B$ is superior to $P_A$ or $P_C$ for stable push-broom filtering. (d)-(e) The yellow filtering zone starts (the green spiral) and ends (the red spiral) the push-broom filtering for the first row of the FPA.

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Figures 1(d) and 1(e) illustrate how an FPA is filtered at position $P_B$ by one of the ASPBF filtering zones (e.g., the yellow region in Fig. 1). As the A-disk rotates counterclockwise, the first row of the FPA is firstly filtered by the green spiral (Fig. 1(d)). Then, its pixels start to continuously receive the incident infrared radiation penetrating the yellow filtering zone until the red spiral (Fig. 1(e)) arrives. Other rows of the FPA are filtered in the same way. For an uncooled FPA based on the thermoelectric effect, the resistance of the pixels change because of the absorption of the filtered radiation. The variations in the resistance are integrated at the integration capacities biased with pulse voltages. Then, the electrical signals are read out by a readout integrated circuit (ROIC) row by row (i.e. electronic pulses scanning row by row mode). Although each row of the FPA is filtered by the whole yellow zone, its signal is only effectively biased and read out during the filtering of the next row. This implies that each row of pixels operates in the mode of optically filtering the present row and electronically reading out the previous row. When the yellow zone finishes filtering, the A-disk seamlessly transits to the next filtering zone and starts to filter the first row of the FPA.

Therefore, there are two crucial principles when designing an ASPBF multiband thermal imaging system for gas leakage detection:

2.1. Mathematical model and parameter optimization for ASPBF

Figure 2 shows a single A-disk filtering zone. The rectangle represents an FPA with $\text{m}\times \text{n}$ pixels. The dotted spiral across the central pixel $M$ of the first row indicates a special Archimedean spiral during the rotation of the A-disk. The Cartesian coordinates are defined by the center of the A-disk being the origin $O$. The OX axis is also defined as a polar axis. The rows and columns of the FPA are parallel with the axes X and Y. $P(u,v)$ represents the pixel of the u-th row and v-th column on the FPA. Its corresponding polar coordinates are denoted as $(r_P,{\theta }_P)$. The FPA’s upper-left pixel $H(1,1)$ has the polar coordinates ($r_H,$${\theta }_H$). The A-disk rotates counterclockwise at the constant angular velocity $\omega$.

 

Fig. 2 Single A-disk filtering zone and its geometric relationship with the FPA. The blue rectangle represents the FPA with $\text{m}\times \text{n}$ pixels. The center of the A-disk O is the origin of Cartesian coordinates. $r_H$ and ${\theta }_H$ are the polar radius and polar angle of the FPA’s upper-left pixel $H(1,1)$. M(1,m/2) is the center pixel of the first row of the FPA. ${\theta }_0$ is the initial polar angle of the red dotted Archimedean spiral. The A-disk rotates counterclockwise at the constant angular velocity ω.

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Mathematical models for ASPBF were established to consider the mismatch between the optical filtering and electronic readout of each pixel of the FPA. Among these models, time-variant variables are of great importance. By minimizing the mismatch, the optimal Archimedean spiral parameter, rotational angular velocity of the A-disk, and relative positions of the A-disk and FPA are derived.

The trajectory of the Archimedean spiral is a function of time and can be expressed as

The time span of the Archimedean spiral trajectory traveling over the pixel $P(u, v)$ from the initial angle ${\theta }_0$ can be defined as

The pixels of the FPA are read out equidistantly row-by-row by the ROIC. $T_{line}$ is assumed to be the line readout period of the ROIC. The readout time of the pixel $P(u,v)$ on the FPA can be calculated as

Because of the bent Archimedean spiral, some pixels are electronically read earlier, whereas others are later than the optical filtering. Thus, the time offset of the pixel $P(u,v)$ that is caused by the asynchronization between the A-disk filtering and ROIC readout can be expressed as

D(u,v) affects the infrared radiation reaching the FPA through one filtering zone. So, the fluctuation of D(u,v) induces non-uniformity of the output signals from the FPA. This kind of non-uniformity is systematic noise and can only be minimized rather than be avoided because the Archimedean spiral is not strictly a straight line. We define the non-uniformity ($NU$) as

Figures 3(a) and 3(b) illustrate the $N{U}_{min}$ values with the corresponding FPA’s location $r_H$ and ${\theta }_H$ at three different characteristic parameters. As the characteristic parameter $\chi$ increases, $N{U}_{min}$ increases. Furthermore, for a certain characteristic parameter $\chi$, a larger $r_H$ leads to a smaller $N{U}_{min}$. This is because a larger $\chi$ or $r_H$ means a smaller curvature of the Archimedean spiral, which makes the trajectory over the FPA closer to a straight line.

 

Fig. 3 Sets of the optimum parameters FPA position $(r_H,{\theta }_H)$ and frame rate $\text{fps}$ when $NU$ takes the minimum value. $N{U}_{min}$ varies with the (a) $r_H$, (b) ${\theta }_H$ and (c) frame rate of the ASPBF imaging system at three different values for the characteristic parameter $\chi$. The red dots represent the theoretical working points.

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The frame rate of the ASPBF imaging system is proportional to the rotational angular velocity $\omega$ and can be expressed as $N\frac{\omega }{2\pi }$, where N is the number of filtering zones on the A-disk. Figure 3(c) shows that fast frame rate will lead to high non-uniformity. The reason is that fast frame rate causes the discrepancy between the rotation angular velocity ω of the A-disk and the speed of readout. At a constant frame rate, such as 10 fps, large $\text{χ}$ value will causes high non-uniformity. It signifies that large $\text{χ}$ value corresponds to small radius of the A-disk but high non-uniformity. Inversely, small $\text{χ}$ value corresponds to large radius of the A-disk but low non-uniformity. However, a large A-disk is not desirable for building up a compact imaging system. Therefore, the four parameters ($r_H,{\theta }_H, \chi , \omega$) should be balanced to realize a compact system with an acceptable frame rate and non-uniformity.

2.2. Selection of differential wavebands of the A-disk for gas leakage detection

The infrared image of a small-leakage gas plume has a weak signal and low contrast against the background. The traditional approach to improve the visualization of a gas plume is to use a narrow BP filter. However, an uncooled FPA is hampered by low sensitivity, so the narrow BP filter further limits the incident infrared radiation and decreases the signal-to-noise ratio (SNR). Therefore, we applied differential technology between wideband longwave-pass filters to improve the contrast of the gas plume while maintaining a high $\text{SNR}$. One of the filtering zones of the A-disk serves as the out-band filter, which handles the transparent spectra of the gas. The remaining filtering zones acts as in-band filters to cover the strong absorption peaks of the gases. In particular, note that the gas absorption peaks are located at non-overlapping spectral regions of the in-band and out-band filtering zones, as shown in Fig. 4(a).

 

Fig. 4 (a) Schematic diagrams of the in-band and out-band filtering zones of the A-disk, their spectral transmittance curves, and the gas absorption peak. (b) Schematic diagram of the ASPBF imaging system for gas detection.

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The spectral emissivity of the background (generally a gray body) varies slowly, while the gas plume is a selective radiator and its spectral emissivity changes greatly at different wavelengths. Therefore, the difference between the in-band and out-band background radiation is almost constant, while the difference between the gas plumes of the two bands varies dramatically. After subtraction or division is performed between the in-band and out-band images, the contrast between the gas plume and background can be enhanced. Furthermore, a gas plume that is hard to distinguish from the background in the in-band image becomes distinguishable.

The selection of the differential wavebands affects the gas detection sensitivity. We propose selecting the wavebands by weighting the gas contrast and $\text{SNR}$ of the differential image. In Fig. 4(b), the line of sight of the gas detection can be classified into two paths: the background path (BG path) and plume path (plume path). To connect the received infrared radiation with the parameters of the plume and background, we first make the following assumptions:

Under these assumptions, the received infrared radiation power from the plume and BG paths are each calculated by integrating the spectral radiation exitance within transparent filtering bands.

Here, ${\text{A}}_{\text{d}}$ is the area of one pixel. $F_{\#}$ and ${\tau }_{optical}$ are the F number and transmittance, respectively, of the optical lens. ${\tau }_{filter}\left(\lambda \right)$ represents the spectral transmittance of the inserted filters. The spectral range of the in-band filter is $\left[{\lambda }_{in-band},{\lambda }_{off}\right]$, while that of the out-band is $\left[{\lambda }_{out-band},{\lambda }_{off}\right]$. ${\tau }_{gas}\left(\lambda \right)=e^{-\alpha \left(\lambda \right)c\cdot L}$ is the spectral transmittance of the gas plume, which is determined by the gas concentration length $c\cdot L$ and absorbance coefficient $\alpha \left(\lambda \right)$. $T_B$ and $T_{gas}$ are the temperatures of the background and gas. $M_{\lambda }\left(T_B\right)$ and $M_{\lambda }\left(T_{gas}\right)$ are the background’s and gas’s blackbody spectral radiation exitances at the temperatures $T_B$ and $T_{gas}$, respectively. ${\epsilon }_B$ is the background emissivity. The absorbance coefficient $\alpha \left(\lambda \right)$ can be acquired from an infrared spectral library [30].

The integration intervals of Eqs. (8) and (9) are determined by the cut-on and cut-off wavelengths, respectively, of the filtering zones. The gas contrast of the differential image is expressed according to the Weber contrast:

However, differential processing will accumulate random noise and reduce the SNR. We define the SNR in the differential image as

The selection of the differential wavebands immune to the temperature differences between $T_B$ and $T_{gas}$ (ΔT) but only sensitive to the gas absorption is desired for the optical gas imaging system. It signifies that this system can be applied in situations with varying temperature differences. Therefore, we elaborately design an F1-score factor to quantitatively evaluate the combined effects of $CO{N}_{diff}$ and $SN{R}_{diff}$ on the ASPBF imaging system. Meanwhile, the F1-score should lead to the same differential wavebands at the varying ΔTs for one specific gas. The $F1$-score factor is based on the normalized $CO{N}_{diff}$ and $SN{R}_{diff}$:

The maximum $F1$-score implies that the ASPBF imaging system achieved a good gas contrast and SNR simultaneously. We selected the optimal differential wavebands of the A-disk for gas leakage detection based on the maximum $F1$-score.

We took an uncooled vanadium oxide (VOx) infrared FPA with a typical $\text{NETD}$ of $40\text{mK}@303\text{K}$ as an example. When it is used to detect ethylene (C₂H₄) gas leakage at $T_B=303\text{ K}$, $T_{gas}=296\text{ K}$ and with the concentration length of C₂H₄ gas of 5000 ppm·m, ${\text{CON}}_{\text{diff}}$, ${\text{SNR}}_{\text{diff}}$, and $F1$-score vary along the different cut-on wavelengths of the in-band and out-band (${\text{λ}}_{\text{in}-\text{band}}$ and ${\text{λ}}_{\text{out}-\text{band}}$), as shown in Figs. 5(a)–5(c). The transmittance of C₂H₄ gas with an absorption peak at 10.55 μm is shown in Fig. 5(d).

 

Fig. 5 (a–c) Distributions of $CO{N}_{diff}$, $SN{R}_{diff}$, and $F1$-score with variations in the cut-on wavelengths ${\lambda }_{in-band}$ and ${\lambda }_{out-band}$ at a C₂H₄ concentration length of 5000 ppm·m, background temperature of 303 K, and gas temperature of 296 K. Black square: maximum value and corresponding cut-on wavelengths of the in-band and out-band. (d) Transmittance of C₂H₄ gas with an absorption peak at 10.55 µm. (e) The maximum $F1$-score values vary at different ΔTs. (f) The cut-on wavelengths ${\lambda }_{in-band}$ and ${\lambda }_{out-band}$ corresponding to the maximum $F1$-score at different ΔTs.

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In Fig. 5(a), ${\text{CON}}_{\text{diff}}$ reached a maximum of 0.097 at ${\text{λ}}_{\text{in}-\text{band}}=10.50 \mu \text{m}$ and ${\text{λ}}_{\text{out}-\text{band}}=10.55 \mu \text{m}$. However, the corresponding ${\text{SNR}}_{\text{diff}}$ was only 2.41. Similarly, when ${\text{SNR}}_{\text{diff}}$ reached a maximum of 55.58 at ${\text{λ}}_{\text{in}-\text{band}}=9.70\mu \text{m}$ and ${\text{λ}}_{\text{out}-\text{band}}=13.50\mu \text{m}$ (Fig. 5(b)), the corresponding ${\text{CON}}_{\text{diff}}$ was only 0.030. $F1$-score reached a maximum of 0.3 at ${\text{λ}}_{\text{in}-\text{band}}=9.70 \mu \text{m}$ and ${\text{λ}}_{\text{out}-\text{band}}=11.55\mu \text{m}$, as shown in Fig. 5(c). At this point, the non-normalized ${\text{CON}}_{\text{diff}}$ and ${\text{SNR}}_{\text{diff}}$ were 0.048 and 41.87, respectively. This indicates that $F1$-score can automatically balance ${\text{CON}}_{\text{diff}}$ and ${\text{SNR}}_{\text{diff}}$. The maximum $F1$-score naturally led to the optimal ${\text{λ}}_{\text{in}-\text{band}}$ and ${\text{λ}}_{\text{out}-\text{band}}$.

To investigate the impact of ΔTs on the selected ${\text{λ}}_{\text{in}-\text{band}}$ and ${\text{λ}}_{\text{out}-\text{band}}$, we calculate the ${\lambda }_{in-band}$ and ${\lambda }_{out-band}$ corresponding to the maximum $F1$-score at different ΔTs (1 K, 2 K, 3 K, 4 K, 5 K, 6 K, and 7 K), as shown in Figs. 5(e) and 5(f). We can see that although the maximum values of the F1-score are increased with the rising ΔTs (Fig. 5(e)), they derive the same ${\lambda }_{in-band}$ and ${\lambda }_{out-band}$, as shown in Fig. 5(f).

Therefore, the differential wavebands chosen by the maximum $F1$-score are only sensitive to the gas absorption and unaffected by the temperature differences between $T_B$ and $T_{gas}$.

3. ASPBF-based dual-band differential thermal imaging prototype

To demonstrate Archimedean spiral push-broom differential thermal imaging for detecting small gas leakages, we took C₂H₄ gas as an example and built a prototype with a four-zone dual-band A-disk. The components are shown in Fig. 6(a).

 

Fig. 6 (a) ASPBF-based dual-band differential thermal imaging prototype. (b) Four-zone dual-band A-disk with three circular holes and one slotted hole around the outer ring. (c) Schematic diagram of the frame synchronous pulses and rising edges of the readout signal. (d) Spectral characteristics for gas imaging, including the spectral radiance of the ambient background at 303 K (black curve), gas absorbance of C₂H₄ gas at the concentration length of 200 ppm·m (red curve), spectral transmittivity curves of the in-band (magenta) and out-band (blue) filtering zones, and normalized spectral response of the FPA (orange dotted curve).

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The $F_{\#}$-number of the infrared lens was designed to be 0.8 to ensure that a sufficient amount of radiation would reach the FPA. The lens’s back intercept (i.e., the distance between the last surface of the lens and the FPA) was increased to 23.31 mm in order to install the A-disk right between the infrared lens and FPA. Figure 6(b) shows the A-disk coated with alternating in-band and out-band filtering zones. The A-disk is a whole germanium (Ge) disk with diameter of 105 mm. A claw hole was designed in its center through which to connect a DC micromotor (2224U024SR, Faulhaber). To synchronize the filtering of the A-disk with the reading out of the electric signal of the FPA, a frame synchronization signal was required for each filtering zone. We designed three identical circular holes with a diameter of 2.2 mm and one larger slotted hole with a length of 4.2 mm and width of 2.2 mm around the A-disk’s outer ring. A synchronous signal generator was mounted beside the A-disk. When the A-disk rotated, three short rectangular pulses and one long rectangular pulse were generated to serve as the frame synchronization signal, as shown in Fig. 6(c). The rising edges of the pulses triggered the readout of the FPA frame by frame, while the widths of the pulses were used to identify the specific filtering zone. For example, Fig. 6(b) shows that one of the in-band filtering zones is identified by the long rectangular pulse. The output interfaces of the prototype included a BNC for the analog video and a Camera Link for 14-bit digital images captured by Camera Link frame grabbers (VCE-CLPCIe01).

Figure 6(d) shows the typical spectral characteristics for gas imaging, which include the spectral radiance of the ambient background at 303 K, the gas absorbance of the C₂H₄ gas, the spectral transmissivity curves of the in-band and out-band filtering zones (magenta and blue, respectively), and the normalized spectral response of the FPA.

The non-uniformity and stability of the output images directly reflected the performance of the prototype. We selected a uniform scene as the imaging target and calculated the non-uniformity with the raw 14-bit digital images. The calculated non-uniformities were 1.76% and 2.38% when the A-disk was stationary and rotating, respectively. Both values are of the same scale, so the A-disk does not lead to much non-uniformity. The stability tests were conducted under different blackbody temperatures. The stability of the output images was acquired by calculating the mean values of continuously captured images at different $T_B$ in the in-band and out-band, as shown in Fig. 7. The mean values of the in-band and out-band images were relatively stable at the same temperature and increased simultaneously with the rising temperature.

 

Fig. 7 Mean values of continuously captured images at different $T_B$ in the in-band and out-band.

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The frame rate of the prototype was tested and reached up to 8 fps (Visualization 1), which is eight times higher than the 1 fps of Second Sight. This demonstrates that the mode of optically filtering the present row and electronically reading out the previous row can effectively avoid FPA idleness during filter switching and increase the frame rate. Table 1 lists the input and designed parameter values and the real performance of our prototype.

Table 1. Input and designed parameter values & the real performance of our prototype

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4. Results and discussion

We performed C₂H₄ gas detection experiments using our ASPBF-based dual-band differential thermal imaging prototype in a controlled laboratory environment and uncontrolled open field.

4.1. Laboratory experiments

The experimental setup is shown in Fig. 8. The C₂H₄ gas flowed out from its bottle through a plastic tube with an internal diameter of 6 mm to simulate gas leakage. An extended blackbody (DCN 1000 H4) with an area of 10 cm × 10 cm was placed as a background behind the tube outlet. The tube was 3.5 m long. Therefore, the temperature of the leaking gas was approximately equal to the ambient temperature of 300 K. The gas flow rate was precisely controlled by a Bronkhorst mass flow meter and controller (EL-FLOW) with a flow rate range of 0–50 ml/min. The prototype was placed 2.1 m away from the blackbody. The lab test imaging results of C₂H₄ gas leakage with the prototype are shown in Fig. 9.

 

Fig. 8 Experimental setup in the laboratory. C₂H₄ gas comes out of the plastic tube and is observed against the background of the extended blackbody. The gas flow rate is precisely controlled by EL-FlOW. The ASPBF-based dual-band differential thermal imaging prototype is placed 2.1 meters’ away from the blackbody. (Visualization 2)

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Fig. 9 Lab test imaging results of C₂H₄ gas leakage with the prototype at the leak rate of 20 ml/min and ΔT of 3 K (Visualization 3). (a) in-band image. (b) out-band image. (c) differential image calculated by Eq. (14). (d) “differential + in-band” image. (e) Gray-value along the 121^th line of the in-band image (blue solid curve) and “differential + in-band” image (red dotted curve). The gas region is encircled by a purple ellipse. Another lab test at higher leak rate of 35ml/min and higher ΔT of 10 K is also conducted (Visualization 4).

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Figures 9(a) and 9(b) show the in-band and out-band images of the C₂H₄ gas leakage when the extended blackbody temperature was set to 301 K, the gas flow rate is controlled at 20ml/min and the ΔT is 3 K. Figure 9(c) shows the differential image which is calculated as Eq. (14):

In Fig. 9(c), the differential image presents a gray value scale that different from the in-band and out-band images. The whole image turns gray, but the gas cloud is popped out effectively and the background clutter is partly decreased. Figure 9(d) is the result of adding the in-band image to the differential image of Fig. 9(c). The background information is recovered and the gas cloud is still distinct.

Figure 9(e) shows the gray values along the 121^th line of the in-band (blue dotted curve) and the “differential + in-band” image (red solid curve). The mean value of the gas region (encircled by a purple ellipse) in the in-band image is 5.53% lower than the background’s. In contrast, the mean value of the gas region in the “differential + in-band” image is 11.07% lower than the background’s. This quantitatively illustrates the effects of the differential method on the gas contrast enhancement.

Figures 10(a) and 10(b) show the gas contrast enhancement at different gas flow rates and background temperatures. The theoretical values [32] of $CO{N}_{diff}$ were calculated according to Eq. (10). The $CO{N}_{diff}$ values generally increased with the rising flow rate and background temperature. In particular, the gas could be hardly observed when the flow rate was less than 10 ml/min at $\Delta T=3 ℃$. Therefore, we took 11 ml/min as the detection limit. As shown in Fig. 10(b), $CO{N}_{diff}$ decreased when the gas temperature was close to the ambient temperature. However, when $T_B$ was equal to ambient temperature, a singular value appeared because the difference between the gas and background was very small, which made the gas difficult to distinguish from the background.

 

Fig. 10 (a) Gas contrast of the differential image ($CO{N}_{\text{diff}}$) at different gas flow rates when the blackbody temperature $T_B$ was 303 K and gas temperature was 300 K. (b) $CO{N}_{\text{diff}}$ at different blackbody temperatures when the gas flow rate was 25 ml/min and gas temperature was 300 K. Red dots: experimental results; solid blue line: theoretical simulation curve.

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Table 2 compares the C₂H₄ gas detection performances of two uncooled systems: a gas cloud imager (GCI) from Hagen et al. [33], and our prototype. The minimum detectable volumetric flow rate (MDVFR) of our prototype was 11 ml/min, which is an order of magnitude lower than that of the GCI at 127.5 ml/min. The dual-band differential imaging employed by our prototype can detect the small gas leakage more easily.

Table 2. Comparison of C₂H₄ Gas Detection.

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4.2. Field experiments

Field experiments were conducted under cloudy weather conditions with a subtle breeze. The prototype was placed 2.5 m away from the C₂H₄ gas bottle. The background in the field of view was an asphalt pavement. The gas flow rate was approximately 30 ml/min. The in-band, out-band, differential and “differential + in-band” images are shown in Figs. 11(a)–11(d), respectively. Figure 11(e) shows the gray value along the 133th line of the in-band and the “differential + in-band” image. The mean values of the gas region are 2.26% and 4.90% lower than their corresponding background’s in in-band and “differential + in-band” images, respectively. The visual effect of the gas cloud in Figs. 11(c) and 11(d) and the quantitative results in Fig. 11(c) all demonstrate the capability of our prototype to effectively detect the leaking gas.

 

Fig. 11 Field test imaging results of C₂H₄ gas leakage with the prototype at the leak rate of 30 ml/min and ΔT of 15 K (Visualization 5). (a) in-band image. (b) out-band image. (c) differential image calculated by Eq. (14). (d) “differential + in-band” image. (e) Gray-value along the 133th line of the in-band image (blue solid curve) and “differential + in-band” image (red dotted curve). The gas region is encircled by a purple ellipse.

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It is necessary to note that we enhance the image contrast of the in-band and out-band images in order to show readers high-contrast images. From Visualization 3, Visualization 4, and Visualization 5 we can see that the gas leakage is also visible in the out-band image. The reason is that the transmitted spectrum of the out-band covers a fraction of the absorption spectrum of ethylene gas. Thus, the gas leakage will be visible in the out-band image under conditions of high leak rate of gas, high temperature difference between the gas and the background, or the image is enhanced with image enhancement algorithms.

5. Conclusions

In an attempt to improve the frame rate of an uncooled infrared FPA-based multiband OGI system using the division of time for detecting small gas leakages, we report the first Archimedean spiral push-broom differential thermal imaging system. Our system employs the operating mode of optically filtering the present row and electronically reading out the previous row to guarantee that the FPA is filtered row by row without FPA idleness to increase the frame rate. In particular, the mismatch between the optical filtering and electronic readout of each pixel of the FPA is used to establish a mathematical model of ASPBF. By minimizing the mismatch, the optimal values for the Archimedean spiral parameter, rotational angular velocity of the A-disk, and position of the FPA are derived.

Differential imaging among wideband longwave-pass filters is applied to promote gas detection sensitivity. One of the filtering zones of the A-disk serves as the out-band filter to handle the transparent spectra of the gas. The remaining filtering zones act as in-band filters to cover the strong absorption peaks of the gases. In particular, the gas absorption peaks are located at the non-overlapping spectral regions of the in-band and out-band filtering zones. To improve the contrast of the gas plume while maintaining a high $\text{SNR}$, we propose an $\text{F}1$-score factor that can automatically balance the effects of the contrast and $\text{SNR}$ on the differential image. We also propose a practical way of maximizing the $\text{F}1$-score factor to select optimal differential wavebands for gas leakage detection.

An ASPBF-based dual-band differential thermal imaging prototype with an uncooled VOx infrared FPA was developed for detecting C₂H₄ gas leakage. The frame rate reached 8 fps, which is eight times higher than the 1 fps of Second Sight. In the laboratory, the MDVFR was 11 ml/min at $\Delta T=3 ℃$. Our results are superior to those of GCI with an uncooled LWIR FPA at $\Delta T>2 ℃$ (127.5 ml/min). The prototype was also applied in the field test where the gas leakage flow rate was approximately 30 ml/min.

Overall, ASPBF-based differential thermal imaging opens a new way to build an imaging system for small gas plumes with a considerably high frame rate, sensitivity, and cost efficiency. However, this system requires precisely installation and time-consuming calibration to ensure the match between the optical filtering and electronic readout of each pixel of the FPA. In future work, we will work on developing ASPBF-based multiband differential thermal imaging to detect a variety of gases. We are also working on recognizing gas species in mixed gases. Our ASPBF mode can also be extended to polarization imaging to increase the frame rate when acquiring polarimetric images with different angles of polarization.