The research on infrared radiation affected by smoke or fog in different environmental temperatures
Construction of the experimental platform
This experimental platform is designed to investigate the impact of smoke or fog environments on infrared thermal imaging at varying temperatures. The key equipment employed in this experiment includes an ultrasonic fog machine, smoke cakes, a fan, a ceramic heater, a heatsink, an infrared thermal imaging camera, a laser transmitter, a photoelectric power meter, temperature sensors, an MCU, MOS tubes, and other essential components. The layout of the experimental platform is illustrated in Fig. 2.
Layout of infrared thermal imaging lab bench.
The structural framework of the entire testing setup is crafted from acrylic boards, creating a confined space measuring 400mm × 300mm × 300mm. This space is enclosed in thermal insulation cotton to shield the internal temperature from external influences. Corresponding apertures and positions are integrated into the outer wall of the experimental platform for tasks such as capturing images, conducting data measurements, and arranging power cords.
Fog is generated using the ultrasonic fog machine and dispersed throughout the entire experimental platform by the fan. The size and consistency of the fog are meticulously controlled by evaluating the attenuation of the 405nm laser emitted from the laser transmitter. This evaluation is conducted through the optoelectronic power meter, ensuring the stability and uniformity of the fog across the entire testing platform. Figures 3a depict the ultrasonic fog machine.
The experimental apparatus. (a) Ultrasonic atomizer. (b) Smoke cartridges. (c) Heating device. (d) Temperature sensor. (e) Target. (f) MOS transistor.
Smoke is generated by igniting the smoke cake and then propelled throughout the space by a fan. The visibility of the smoke is quantified using an optoelectronic power meter equipped with a laser emitter. Figure 3b provides a visual representation of the smoke cake used in the experiment.
The heating apparatus comprises four sets of ceramic heating pads, heat sinks, and fans. Utilizing fans and heat sinks, the heat generated from the ceramic heating pads is evenly distributed throughout the interior of the experimental platform. Temperature sensors are strategically positioned near the target, and their data are employed to regulate the heating device, ensuring the stability of the temperature within the experimental platform. Figure 3c depicts the heating device, while Fig. 3d illustrates the temperature sensor.
Due to the elevated external environmental temperature, which fails to meet the experiment’s low-temperature requirements, the internal environmental temperature within the experimental platform is meticulously regulated. This is achieved by incorporating a DC small fan and ice. The cold air generated by the ice is disseminated throughout the entire experimental platform via the fan. Simultaneously, the temperature inside the platform is closely monitored by temperature sensors, influencing the rotational speed of the fan to maintain temperature stability.
The target consists of a ceramic heating pad and a temperature sensor. To secure both components together, black electrical insulating tape is employed. The temperature sensor governs the heating power of the ceramic heating pad, ensuring the constancy of the target temperature. Figure 3e is the target.
To guarantee the stability of the target temperature within the experimental platform, a STC89C516R + microcontroller and MOS tubes are employed. These components utilize an incremental PID algorithm for precise control. The control equation for the PID algorithm 23 is illustrated in Eq. (1). The image of the MOS transistor is shown in Fig. 3f.
$$ \left\{ {\begin{array}{*{20}l} {\Delta {\text{u}}_{{\text{k}}} {\text{ = K}}_{{\text{p}}} \times \left( {{\text{e}} – {\text{e}}_{1} } \right){\text{ + K}}_{{\text{i}}} \times {\text{e + K}}_{{\text{d}}} \times \left( {{\text{e}} – {2} \times {\text{e}}_{{1}} {\text{ + e}}_{{2}} } \right)} \hfill \\ {{\text{u}}_{{\text{k}}} { = }\Delta {\text{u}}_{{\text{k}}} {\text{ + u}}_{{{\text{k1}}}} } \hfill \\ \end{array} } \right. $$
(1)
where \({\text{e}}\) is the current deviation value variable,\({\text{e}}_{1}\) is the subsequent deviation value variable,\({\text{e}}_{2}\) is the further deviation value variable,\({\text{K}}_{\text{p}}\) is the proportionality coefficient,\({\text{K}}_{\text{i}}\) is the integration coefficient,\({\text{K}}_{\text{d}}\) is the differentiation coefficient,\({\text{u}}_{\text{k}}\) is the total current deviation value variable,\({\text{u}}_{\text{k}1}\) is the total subsequent deviation value variable and \({\Delta \text{u}}_{\text{k}}\) is the total deviation value variable.
This infrared thermal imaging camera is sensitive to wavelengths within the range of 8-14μm and has a temperature detection span from − 20 to + 400 °C. Within this range, the camera’s error is ± 2 °C. Since the measured temperatures primarily fall between 20 °C and 50 °C, the infrared thermal imaging camera ‘s operational range is chosen to be − 20 to 120 °C. Within this range, the camera’s error is ± 0.667 °C. The field of view angle of this infrared thermal imaging camera is 30 ° x 22.5 ° Notably, the infrared thermal imaging camera allows for the correction of deviations directly at its terminals. The image of the infrared thermal imaging camera is shown in Fig. 4.
The Infrared thermal imaging camera.
The theoretical analysis of experiments
The theoretical analysis of the visibility of smoke or fog
The attenuation of the laser’s intensity \({\text{I}}_{0}\) after transmission over a distance L mainly depends on the transmittance of the laser beam T24,25,26, as described in Eq. (2).
$$ {\text{T = I/I}}_{{\text{0}}} {\text{ = exp}}\left( { – \int\limits_{{\text{0}}}^{{\text{L}}} {\upbeta {\text{dl}}} } \right) $$
(2)
where I is the light intensity after the transmission distance L, and \(\upbeta \) is the atmospheric attenuation coefficient.
The ultrasonic fog machine produces fog particles with an average diameter of 0.4μm 27, while the combustion of the smoke cake yields smoke particles with an average diameter of 160 nm 26. Given that the laser’s wavelength is 405 nm, the Mie scattering principle is applicable. The attenuation formula for laser light is expressed in Eqs. (3) and (4) 28.
$$ \upbeta {\text{ = (3}}{\text{.912/V)}} \times {\text{(0}}{\text{.55/}}\uplambda {\text{)}}^{{\text{q}}} $$
(3)
$$ {\text{q = }}\left\{ {\begin{array}{*{20}l} {0} \hfill & {{\text{(D < 0}}{.5}\;{\text{km)}}} \hfill \\ {{\text{D}} – 0.5} \hfill & {{(0}{\text{.5}}\;{\text{km < D < 1}}\;{\text{km)}}} \hfill \\ {{0}{\text{.16D}}\;{ + }\;{ 0}{\text{.34}}} \hfill & {{(1}\;{\text{km < D < 6}}\;{\text{km)}}} \hfill \\ {{1}{\text{.3}}} \hfill & {{(6}\;{\text{km < D < 50}}\;{\text{km)}}} \hfill \\ {1.6} \hfill & {{\text{(D > 50}}\;{\text{km)}}} \hfill \\ \end{array} } \right. $$
(4)
where V is the meteorological visibility,\(\uplambda \) is the wavelength of the laser, D is the measurement distance.
After the collation of formula (2) (4), the meteorological visibility formula is obtained as Eq. (5).
$$ {\text{V = }}\frac{ – 3.912}{{{\text{ln}}\frac{{\text{I}}}{{{\text{I}}_{{0}} }}}}\left( {\frac{{{0}{\text{.55}}}}{{\uplambda }}} \right)^{{\text{q}}} {\text{L}} $$
(5)
The theoretical analysis of infrared thermography affected by smoke or fog
Infrared thermal imaging is influenced by atmospheric conditions, wherein the infrared radiation emitted by the target undergoes alterations as it interacts with smoke or fog before reaching the infrared thermal imaging camera. This process is intricate, involving the absorption and scattering of infrared radiation. Relevant theories such as the Lambert–Beer law, Mie scattering, Rayleigh scattering, and others are integral components in understanding this phenomenon.
The theoretical analysis of attenuation in normal and fog environment
The infrared thermal imaging temperature measurement calculation formula is shown in Eq. (6) 29.
$$ {\text{T}}_{{\text{0}}} {\text{ = }}\left\{ {\frac{{\text{1}}}{\upvarepsilon }\left[ {\frac{{\text{1}}}{{\uptau _{{\text{a}}} }}{\text{T}}_{{\text{r}}}^{{\text{n}}} – {\text{(1}} – \upvarepsilon {\text{)T}}_{{\text{u}}}^{{\text{n}}} – \left( {\frac{{\text{1}}}{{\uptau _{{\text{a}}} }} – {\text{1}}} \right){\text{T}}_{{\text{a}}}^{{\text{n}}} } \right]} \right\}^{{{\text{1/n}}}} $$
(6)
where \({\text{T}}_{0}\) is the true temperature of the object to be measured, ε is the emissivity of the object to be measured, \({\uptau }_{{\text{a}}}\) is the atmospheric transmittance,\({\text{T}}_{{\text{r}}}\) is the temperature measured by the infrared thermal imaging, \({\text{T}}_{{\text{u}}}\) is the environmental temperature, \({\text{T}}_{{\text{a}}}\) is the atmospheric temperature, and n is a constant related to the wavelength of the infrared thermal imaging. n is 9.2554 when the wavelength is 3–5 μm, and n is 3.9889 when the wavelength is 8–12 μm 30.
Atmospheric attenuation of infrared radiation is mainly related to four phenomena; (1) absorption of water vapour; (2) absorption of carbon dioxide; (3) scattering of molecules, aerosols and particles in the atmosphere; (4) attenuation of meteorological conditions. Therefore, the transmittance of infrared radiation to the atmosphere is also composed of four parts, as shown in Eq. (7).
$$ \uptau _{{\text{a}}} {\text{ = }}\uptau _{{{\text{H}}_{{\text{2}}} {\text{O}}}} \times \uptau _{{{\text{CO}}_{{\text{2}}} }} \times \uptau _{{\text{p}}} \times \uptau _{{\text{R}}} $$
(7)
where \({\uptau }_{{{\text{H}}_{{2}} {\text{O}}}}\) is the infrared radiation transmittance after absorption by water vapour, \({\uptau }_{{{\text{CO}}_{{2}} }}\) is the infrared radiation transmittance after absorption by carbon dioxide, \({\uptau }_{{\text{p}}}\) is the infrared radiation transmittance after scattering, and \({\uptau }_{{\text{R}}}\) is the infrared radiation transmittance after attenuation by rain, snow and so on.
In the experiment, there is no rain, snow and other weather phenomena, so this experiment don’t consider \({\uptau }_{{\text{R}}}\).
(1) Calculation of water vapour attenuation.
The determination of \({\uptau }_{{{\text{H}}_{{2}} {\text{O}}}}\) needs to refer to the concept of “the content of water vapour after a certain distance of transmission in the sea level \({\upomega }\)“, the value of \({\upomega }\) is calculated according to the formula (8).
$$ \upomega {\text{ = H}}_{{\text{r}}} \times {\text{H}}_{{\text{a}}} \times {\text{D}} $$
(8)
where \({\text{H}}_{\text{a}}\) represents the content of saturated water vapor, The relative humidity \({\text{H}}_{\text{r}}\) is 27% in normal conditions, 100% in foggy environments, and the transmission distance D is 0.3 m.
Based on the calculated value of ω and the detection band of the infrared thermal imaging, the water vapour transmission rate for the band can be found in the relevant sources 31.
(2) Calculation of carbon dioxide attenuation.
According to relevant studies, the density of carbon dioxide remains practically constant in the atmosphere in the surface layer. Therefore \({\uptau }_{{{\text{CO}}_{{2}} }}\) is related to the distance through which the radiation passes, and the value of \({\uptau }_{{{\text{CO}}_{{2}} }}\) is also given in the relevant sources, which can be consulted directly 32.
(3) Calculation of scattering by molecules and particles in the atmosphere.
In the process of infrared radiation, it will be refracted by molecules and particles in the atmosphere, etc. The attenuation coefficient of the infrared radiation after attenuation by atmospheric molecules and particles can be calculated according to Eq. (4). From the attenuation coefficient can be based on the Lambert–Beer law to derive the corresponding wavelength of the atmospheric transmittance as shown in Eq. (9).
$$ \uptau _{{\text{P}}} {\text{ = exp(}} – \beta {\text{D}}) $$
(9)
where \(\upbeta \) is the attenuation factor, which can be obtained by formula (4) , the distance D between the target object and the infrared thermal imager is 0.3 m, and e is a constant.
The theoretical analysis of attenuation in smoke environment
In smoke environment, the atmospheric transmittance of infrared radiation is mainly composed of two components, absorption and scattering, and the scattering rate is shown in Eq. (10) 33.
$$ \uptau _{{\text{a}}} {\text{ = }}\uptau _{\alpha } \times {\text{ }}\uptau _{\beta } $$
(10)
The attenuation due to absorption obeys Beer’s law as shown in Eq. (11).
$$ {\uptau }_{{\upalpha }} {\text{ = exp(}} – {\upsigma }_{{\text{a}}} {\text{cD)}} $$
(11)
where D represents the distance from the infrared thermal imager to the target object, the absorption extinction coefficient \({\upsigma }_{{\text{a}}}\) of smoke is \({1}{\text{.5}}\;{\text{g/m}}^{{2}}\), and the mass concentration c of smoke is \({0}{\text{.885}}\;{\text{g/m}}^{{3}}\).The attenuation due to scattering is shown in Eq. (12).
$$ {\uptau }_{{\upbeta }} {\text{ = exp(}} – {\text{k}}_{{\text{s}}} {\text{ND)}} $$
(12)
where \({\text{k}}_{\text{s}}\) is the scattering attenuation cross section, which can be obtained from the following Eq. (13).
$$ {\text{k}}_{{\text{s}}} {\text{ = N}}\uppi {\text{r}}^{{\text{2}}} {\text{Q}}_{{{\text{sca}}}} $$
(13)
where D represents the distance from the infrared thermal imager to the target object, the number density N of scattering particles in smoke is \({5}{\text{.9}} \times {10}^{{{14}}} { }\;{\text{particles/m}}^{{3}}\), the radius r of smoke particles is 180 nm, and \({\text{Q}}_{\text{sca}}\) is the scattering efficiency factor.
To describe the problem intuitively, a size factor x is introduced as shown in Eq. (14).
$$ {\text{x = 2}}\uppi {\text{r/}}\uplambda $$
(14)
where the wavelength λ of the incident light is 8–14 µm.
When the size of the smoke screen particles is small, usually referred to as x < 0.3, the scattering obeys Rayleigh’s law 34. It is known from the electromagnetic field theory of light that the scattering intensity currently is inversely proportional to the fourth power of the wavelength of the incident laser. The scattering efficiency factor is shown in Eq. (15).
$$ {\text{Q}}_{{{\text{sca}}}} {\text{ = }}\frac{{{\text{128}}\uppi ^{{\text{4}}} {\text{r}}^{{\text{4}}} }}{{{\text{3}}\uplambda ^{{\text{4}}} }}\left( {\frac{{{\text{m}}^{{\text{2}}} – {\text{1}}}}{{{\text{m}}^{{\text{2}}} {\text{ + 1}}}}} \right)^{{\text{2}}} $$
(15)
If expressed in terms of the size parameter x, it is shown in Eq. (16).
$$ {\text{Q}}_{{{\text{sca}}}} { = }\frac{{8}}{{3}}{\text{x}}^{{4}} \left( {\frac{{{\text{m}}^{{2}} – {1}}}{{{\text{m}}^{{2}} { + 1}}}} \right)^{{2}} $$
(16)
where the refractive index m of smoke particles is 1.4.
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