All-solid-state temperature sensing device and system based on optical fiber concave surface high-reflection optical film
The all-solid-state temperature sensing device formed by the concave high-reflection optical film of the optical fiber is solved by using the optical microcavity of the high-reflection film and the solid-state thermal expansion material to solve the problem of insufficient sensitivity of the existing temperature sensor at room temperature, and realizes a high sensitivity and simplified temperature measurement process.
Patent Information
- Application Number
- CN202510446342.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-10
- Publication Date
- 2025-07-11
- Estimated Expiration
- 2045-04-10
AI Technical Summary
The existing temperature sensors have limited sensitivity at room temperature, and when measuring temperature, all wavelengths need to be scanned to calculate the central wavelength of the transmission spectrum, with a large delay.
The all-solid-state temperature sensing device formed by a concave high-reflection optical film of the optical fiber is simplified by calculating the temperature by real-time transmittance or thermal transmission coefficient.
It realizes high sensitivity temperature measurement at room temperature, simplifies the temperature calculation process, improves real-time and sensitivity, and is simple and easy to integrate, and has low cost. It is suitable for micro-scale equipment.
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Figure CN120293342A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a temperature sensor, and particularly to an all-solid-state temperature sensing device and system based on an optical fiber concave high-reflection optical film. Background Art
[0002] Temperature, as a fundamental physical parameter, plays an important role in scientific research, industrial production, and daily life. High-sensitivity temperature measurement technology is crucial for fields such as nanoscale thermal imaging and sensing, integrated circuits, energy harvesting, environmental monitoring, biomedicine, etc. In particular, integrating high-sensitivity temperature sensors in microscale devices is of great significance for applications and research in measuring local temperature changes. Currently, various methods have been developed to improve the sensitivity of temperature measurement, including nanoscale temperature sensors based on superconducting quantum interference devices, with a diameter less than 50 nm and a sensitivity of up to 870 nK / Hz. -1 / 2 However, this temperature sensor needs to work at low temperatures and has limited sensitivity. To achieve higher-sensitivity temperature measurement at room temperature, researchers have developed temperature sensors using an F-P cavity. By filling the F-P cavity with a liquid, the change in the cavity length of the F-P cavity caused by the expansion of the liquid at different temperatures leads to the drift of the central wavelength of the transmission spectrum, thereby realizing temperature sensing, such as in 201910454405.5, 201720373255, and 202110310914.8, etc. However, the sensitivity of this technology still needs to be further improved, and when measuring temperature, all wavelengths need to be scanned, and then the central wavelength of the transmission spectrum is calculated, and then the temperature is calculated based on the relationship between the central wavelength of the transmission spectrum and temperature, resulting in a large time delay. Summary of the Invention
[0003] Aiming at the problems existing in the prior art, the purpose of the present invention is to provide an all-solid-state temperature sensing device based on an optical fiber concave high-reflection optical film with higher sensitivity.
[0004] To achieve the above-mentioned invention purpose, the present invention provides the following technical solutions:
[0005] A fully solid-state temperature sensing device based on a fiber-optic concave highly reflective optical film, comprising a laser, a fiber-optic attenuator, a fiber-optic microcavity, a fiber-optic coupler, a first photodetector, and a second photodetector. The fiber-optic microcavity is composed of a first fiber-optic concave mirror and a second fiber-optic concave mirror. Both the first fiber-optic concave mirror and the second fiber-optic concave mirror are formed by plating a highly reflective optical film on the concave surface prepared from the fiber-optic end face. The concave surfaces of the first fiber-optic concave mirror and the second fiber-optic concave mirror face each other, and a solid thermal expansion material is filled between the first fiber-optic concave mirror and the second fiber-optic concave mirror. The laser emits laser light that enters the fiber-optic coupler through the fiber-optic attenuator. The fiber-optic coupler divides the laser beam output by the laser into a first beam and a second beam. The first beam enters the first photodetector through the fiber-optic microcavity, and the second beam directly enters the second photodetector.
[0006] Further, the fiber-optic coupler divides the laser into a first beam and a second beam with a splitting ratio of 90:10.
[0007] Further, the fiber-optic microcavity is an F-P cavity. Further, the first fiber-optic concave mirror is connected to the fiber-optic coupler through a fiber, and the second fiber-optic concave mirror is connected to the first photodetector through a fiber.
[0008] Further, the highly reflective optical film is a dielectric film with a reflectivity of 99.9%.
[0009] A fully solid-state temperature sensing system based on a fiber-optic concave highly reflective optical film, comprising the above fully solid-state temperature sensing device and a temperature calculation module. The temperature calculation module is used to calculate the transmission spectrum of the fiber-optic microcavity according to the optical powers detected by the first photodetector and the second photodetector when the laser scans within a preset wavelength range, and substitute the central wavelength of the transmission spectrum into the pre-stored relationship curve between the central wavelength of the transmission spectrum and temperature to calculate the current real-time temperature.
[0010] Further, the temperature calculation module specifically includes:
[0011] A relationship curve storage unit for storing the relationship curve between the central wavelength of the transmission spectrum and temperature of the current fully solid-state temperature sensing device;
[0012] A real-time transmission spectrum calculation unit for obtaining the optical powers detected by the first photodetector and the second photodetector when the laser scans within a preset wavelength range, calculating the ratio of the optical powers detected by the first photodetector and the second photodetector at each wavelength as the transmittance at each wavelength, and forming a transmission spectrum;
[0013] A real-time central wavelength calculation unit for obtaining the wavelength at which the transmittance peak is located in the transmission spectrum as the real-time transmission spectrum central wavelength;
[0014] A real-time temperature calculation unit is configured to substitute the central wavelength of the transmission spectrum into the relationship curve between the central wavelength of the transmission spectrum and temperature to find the real-time temperature.
[0015] A fully solid-state temperature sensing system based on an optical fiber concave high-reflection optical film includes the above-mentioned fully solid-state temperature sensing device and a temperature calculation module. The temperature calculation module is configured to calculate the real-time transmittance of the optical fiber microcavity according to the optical powers detected by the first photodetector and the second photodetector, calculate the real-time thermal transmittance coefficient according to the real-time transmittance, substitute the real-time thermal transmittance coefficient into the relationship curve between the thermal transmittance coefficient and temperature, and calculate the current real-time temperature.
[0016] Further, the temperature calculation module specifically includes:
[0017] A relationship curve storage unit is configured to store the relationship curve between the thermal transmittance coefficient and temperature of the current fully solid-state temperature sensing device;
[0018] A real-time transmittance calculation unit is configured to calculate the ratio of the optical powers detected by the first photodetector and the second photodetector as the real-time transmittance;
[0019] A real-time thermal transmittance coefficient calculation unit is configured to calculate the real-time thermal transmittance coefficient according to the real-time transmittance by the following formula:
[0020]
[0021] In the formula, k represents the real-time thermal transmittance coefficient, S represents the real-time transmittance, and T represents the temperature;
[0022] A real-time temperature calculation unit is configured to substitute the real-time thermal transmittance coefficient into the relationship curve between the thermal transmittance coefficient and temperature to find the real-time temperature.
[0023] Further, the relationship curve between the thermal transmittance coefficient and temperature is obtained by the following method:
[0024] Place the optical fiber microcavity in a heating device and set the heating temperature to any normal temperature value;
[0025] At the current normal temperature, set the laser to scan at different wavelengths, and calculate the transmittance at different wavelengths at the current normal temperature according to the optical powers detected by the first photodetector and the second photodetector, that is, the transmission spectrum at the current normal temperature;
[0026] Derive the transmission spectrum at the current normal temperature to obtain the relationship between the transmittance and the wavelength;
[0027] Set the heating temperature of the heating device to other different values, so as to obtain the transmission spectra at different temperature values, extract the central wavelengths of the transmission spectra, and establish the relationship between the central wavelength and the temperature change;
[0028] Multiply the relationship between transmittance and wavelength, the relationship between the central wavelength and temperature change, and the negative first power of the transmittance to obtain the relationship curve between the thermal transmittance coefficient and temperature.
[0029] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0030] (1) The present invention uses an optical microcavity formed by a first fiber concave mirror and a second fiber concave mirror coated with a high-reflection film to achieve temperature sensing. Compared with the optical microcavities of the prior art, the interference effect of the present invention is better, the quality is higher, and the sensitivity is higher.
[0031] (2) When calculating the temperature in the present invention, according to the measured transmittance and based on the relationship among transmittance - thermal transmittance coefficient - temperature, the real-time temperature is obtained without scanning all wavelengths, and the real-time performance is high. In addition, by utilizing the high sensitivity of the thermal transmittance coefficient to temperature change, the present invention realizes the effective amplification of small temperature changes and further improves the sensitivity.
[0032] (3) The device of the present invention is simple, easy to integrate, low in cost, small in size, and large in dynamic range, and has better commercial value compared with existing high-sensitivity temperature sensors.
[0033] (4) The detection method is simple and can be detected using a photodetector and a computer.
[0034] (5) The materials of the system are simple and easy to obtain, and the system is easy to implement. BRIEF DESCRIPTION OF THE DRAWINGS
[0035] Figure 1 is a schematic structural diagram of a fully solid-state temperature sensing device based on a fiber concave high-reflection optical film provided by an embodiment of the present invention;
[0036] Figure 2 is a schematic structural diagram of a fully solid-state temperature sensing system based on a fiber concave high-reflection optical film provided by an embodiment of the present invention;
[0037] Figure 3 is a schematic diagram of the placement position of the heating device;
[0038] Figure 4 is a graph showing the relationship between the central wavelength of the transmission spectrum and temperature of the present invention;
[0039] Figure 5 is a graph showing the variation of the sensitivity of a fully solid-state temperature sensing system based on a fiber concave high-reflection optical film provided by the present invention with frequency;
[0040] Figure 6 is a graph showing the relationship between the thermal transmittance coefficient and temperature of the present invention;
[0041] Figure 7It is a graph showing the variation of the sensitivity of another all-solid-state temperature sensing system based on an optical fiber concave high-reflection optical film provided by the present invention with frequency. Specific Embodiments
[0042] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention.
[0043] Embodiment 1
[0044] The embodiment of the present invention provides an all-solid-state temperature sensing device based on an optical fiber concave high-reflection optical film, as Figure 1 shown, which includes a laser 1, an optical fiber attenuator 2, an optical fiber coupler 3, an optical fiber microcavity (composed of a first optical fiber concave mirror 4 and a second optical fiber concave mirror 5, and a solid thermal expansion material 6, such as ultraviolet glue, is filled between the first optical fiber concave mirror 4 and the second optical fiber concave mirror 5), a first photodetector 7, and a second photodetector 8.
[0045] The laser 1, the optical fiber attenuator 2, and the optical fiber coupler 3 form Region I to achieve laser modulation. The laser 1 is a tunable continuous laser for emitting continuous laser, and the laser scanning range is 1500nm - 1600nm. The power of the light beam is adjusted to an appropriate size through the optical fiber attenuator 2. Subsequently, the light beam enters the optical fiber coupler 3, and the optical fiber coupler 3 divides the incident light into a first light beam and a second light beam according to a ratio of 90:10. 90% of the first light beam enters the optical fiber microcavity, and 10% of the second light beam is used for detection.
[0046] The optical fiber microcavity constitutes Region II. Among them, the optical fiber microcavity is an F-P cavity, which is composed of a first optical fiber concave mirror 4 and a second optical fiber concave mirror 5. The first optical fiber concave mirror 4 and the second optical fiber concave mirror 5 are specifically formed by plating a high-reflection optical film after the end face of the optical fiber is burned by a CO2 laser to form a concave surface. The high-reflection optical film is a dielectric film with a reflectivity of 99.9%. The first optical fiber concave mirror 5 is connected to the optical fiber coupler 3 through an optical fiber, and the second optical fiber concave mirror 5 is connected to the first photodetector 7 through an optical fiber. In this embodiment, the cavity length of the optical fiber microcavity is 16μm, the finesse F value is 2730, and the quality factor Q value is 154918. The optical fiber microcavity is filled and encapsulated with a solid thermal expansion material 6. The solid thermal expansion material 6 filled in the optical fiber microcavity has a high thermal expansion property. When the surrounding environment temperature changes, the thermally induced deformation of the solid thermal expansion material 6 causes the transmittance and the transmission spectrum to change. According to the relationship between the transmittance or the center wavelength of the transmission spectrum and the temperature, the temperature can be obtained.
[0047] The first photodetector 7 and the second photodetector 8 constitute Region III, and their function is to receive the output signal and process it. The temperature is calculated according to the optical signal power detected by the first photodetector 7 and the second photodetector 8.
[0048] The optical microcavity of the embodiment of the present invention is composed of a first fiber concave mirror 4 and a second fiber concave mirror 5. Compared with the optical microcavities in the prior art, it has better interference effect, higher quality, and higher sensitivity.
[0049] Embodiment 2
[0050] The embodiment of the present invention provides a fully solid-state temperature sensing system based on a fiber concave high-reflection optical film, as Figure 2 shown, including the fully solid-state temperature sensing device of Embodiment 1 and a temperature calculation module. The temperature calculation module is used to calculate the transmission spectrum of the fiber microcavity according to the optical powers detected by the first photodetector and the second photodetector when the laser scans within a preset wavelength range, substitute the central wavelength of the transmission spectrum into the pre-stored relationship curve between the central wavelength of the transmission spectrum and temperature, and calculate the current real-time temperature.
[0051] Among them, the temperature calculation module specifically includes:
[0052] A relationship curve storage unit for storing the relationship curve between the central wavelength of the transmission spectrum and temperature of the current fully solid-state temperature sensing device;
[0053] A real-time transmission spectrum calculation unit for obtaining the optical powers detected by the first photodetector and the second photodetector when the laser scans within a preset wavelength range, calculating the ratio of the optical powers detected by the first photodetector and the second photodetector at each wavelength as the transmittance at each wavelength, and forming a transmission spectrum;
[0054] A real-time central wavelength calculation unit for obtaining the wavelength at which the transmittance peak is located in the transmission spectrum as the real-time transmission spectrum central wavelength;
[0055] A real-time temperature calculation unit for substituting the central wavelength of the transmission spectrum into the relationship curve between the central wavelength of the transmission spectrum and temperature to find the real-time temperature.
[0056] Among them, the relationship curve between the central wavelength of the transmission spectrum and temperature can be obtained through the following method: Place a heating device 9 under the fiber microcavity, as Figure 3 shown, set the heating temperature to any value, scan the laser wavelength, obtain the transmission spectrum at this temperature, extract the central wavelength of the transmission spectrum resonator through the Lorentz fitting function, then set the heating temperature to different values, obtain the central wavelengths of the transmission spectra at different temperatures, and establish the relationship between the central wavelength drift amount and the temperature change. Figure 4 It is the change of the central wavelength of the fiber F-P microcavity transmission spectrum with the surrounding ambient temperature. Figure 4 It shows that as the surrounding ambient temperature rises, the central wavelength of the transmission spectrum drifts towards the long wavelength, and the dynamic range is 22°C - 27°C. And this temperature sensor has good linearity and realizes a responsivity of 0.45 nm / °C. Figure 5It represents the sensitivity of the temperature sensor obtained by using the variation relationship between the central wavelength of the transmission spectrum and temperature. The specific operation is to fix the ambient temperature around the fiber optic F-P microcavity at 24 °C, measure the change of the central wavelength of the transmission spectrum within 1 s, and use the power spectral density calculation method to obtain the sensitivity of the temperature sensor. The result shows that the present invention achieves a sensitivity of 1 μK / Hz -1 / 2 The temperature sensor measured by this method has the advantages of a large dynamic range and high sensitivity.
[0057] Embodiment III
[0058] The embodiment of the present invention provides a fully solid-state temperature sensing system based on a fiber optic concave high-reflection optical film, as Figure 2 shown, which includes the fully solid-state temperature sensing device of Embodiment I and a temperature calculation module. The temperature calculation module is used to calculate the real-time transmittance of the fiber optic microcavity according to the optical powers detected by the first photodetector and the second photodetector, calculate the real-time thermal transmittance coefficient according to the real-time transmittance, substitute the real-time thermal transmittance coefficient into the relationship curve between the thermal transmittance coefficient and temperature, and calculate the current real-time temperature.
[0059] Among them, the temperature calculation module specifically includes:
[0060] A relationship curve storage unit for storing the relationship curve between the thermal transmittance coefficient and temperature of the current fully solid-state temperature sensing device;
[0061] A real-time transmittance calculation unit for calculating the ratio of the optical powers detected by the first photodetector and the second photodetector as the real-time transmittance;
[0062] A real-time thermal transmittance coefficient calculation unit for calculating the real-time thermal transmittance coefficient according to the real-time transmittance according to the following formula:
[0063]
[0064] In the formula, k represents the real-time thermal transmittance coefficient, S represents the real-time transmittance, and T represents the temperature;
[0065] A real-time temperature calculation unit for substituting the real-time thermal transmittance coefficient into the relationship curve between the thermal transmittance coefficient and temperature to find the real-time temperature.
[0066] Among them, the relationship curve between the thermal transmittance coefficient and temperature is obtained by the following method:
[0067] Place the fiber optic microcavity under a heating device 9 and set the heating temperature to any normal temperature value, such as 22 °C;
[0068] At the current normal temperature, the laser is set to scan at different wavelengths (1500 nm - 1600 nm). According to the optical powers detected by the first photodetector and the second photodetector, the transmittance S at different wavelengths λ at the current normal temperature is calculated, that is, the transmission spectrum at the current normal temperature;
[0069] The derivative of the transmission spectrum at the current normal temperature is taken to obtain the relationship between the transmittance S and the wavelength λ
[0070] The heating temperature of the heating device 9 is set to other different values (for example, from 22 °C to 27 °C), so as to obtain the transmission spectra at different temperature values. By using the Lorentz fitting function to fit the peak values of the transmission spectra, the central wavelength of the transmission spectra is extracted, and the relationship between the central wavelength λ and the temperature T change is established
[0071] Multiply the relationship between the transmittance and the wavelength, the relationship between the central wavelength and the temperature change, and the negative first power of the transmittance, that is The relationship curve between the thermal transmission coefficient k and the temperature T is obtained.
[0072] In this embodiment, the relationship curve between the thermal transmission coefficient k and the temperature T is as Figure 6 shown, and the maximum thermal transmission coefficient k max > 50 K -1 . To determine the sensitivity of the sensing device, the wavelength and temperature are fixed at the maximum transmission coefficient, the change of the transmittance within 1 s is measured, and the power spectral density calculation method is used to represent the temperature fluctuation here, and the sensitivity <1 nk Hz -1 / 2 , as Figure 7 shown. It can be seen that the temperature sensing device of the present invention has extremely high sensitivity.
[0073] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations.
[0074] It should be understood that the above embodiments and the descriptions in the specification are only the principles, main features and advantages of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the protection scope of the present invention.
Claims
1. A fully solid-state temperature sensing device based on an optical fiber concave high-reflection optical film, characterized in that, It includes a laser, an optical fiber attenuator, an optical fiber microcavity, an optical fiber coupler, a first photodetector and a second photodetector. The optical fiber microcavity is composed of a first optical fiber concave mirror and a second optical fiber concave mirror. Both the first optical fiber concave mirror and the second optical fiber concave mirror are formed by preparing the end face of the optical fiber into a concave surface and then coating a high-reflection optical film. The concave surfaces of the first optical fiber concave mirror and the second optical fiber concave mirror face each other, and a solid thermal expansion material is filled between the first optical fiber concave mirror and the second optical fiber concave mirror. The laser emits laser light, which enters the optical fiber coupler through the optical fiber attenuator. The optical fiber coupler divides the light beam output by the laser into a first light beam and a second light beam. The first light beam enters the first photodetector through the optical fiber microcavity, and the second light beam directly enters the second photodetector.
2. The all-solid-state temperature sensing device based on the fiber-optic concave highly reflective optical film according to claim 1, characterized in that: The optical fiber coupler divides the laser into a first light beam and a second light beam with a splitting ratio of 90:
10.
3. The all-solid-state temperature sensing device based on the optical fiber concave high-reflection optical film according to claim 1, characterized in that: The optical fiber microcavity is a Fabry-Pérot (F-P) cavity.
4. The all-solid-state temperature sensing device based on the optical fiber concave high-reflection optical film according to claim 1, characterized in that: The first optical fiber concave mirror is connected to the optical fiber coupler through an optical fiber, and the second optical fiber concave mirror is connected to the first photodetector through an optical fiber.
5. The all-solid-state temperature sensing device based on the fiber optic concave high-reflection optical film according to claim 1, characterized in that: The high-reflection optical film is a dielectric film with a reflectivity of 99.9%.
6. A fully solid-state temperature sensing system based on an optical film with a concave high-reflection fiber optic, characterized in that, It includes the all-solid-state temperature sensing device described in claim 1 and a temperature calculation module. The temperature calculation module is used to calculate the transmission spectrum of the optical fiber microcavity according to the optical powers detected by the first photodetector and the second photodetector when the laser scans within a preset wavelength range, substitute the central wavelength of the transmission spectrum into the pre-stored relationship curve between the central wavelength of the transmission spectrum and temperature, and calculate the current real-time temperature.
7. The all-solid-state temperature sensing system based on the fiber-optic concave highly reflective optical film according to claim 6, characterized in that, The temperature calculation module specifically includes: A relationship curve storage unit for storing the relationship curve between the central wavelength of the transmission spectrum and temperature of the current all-solid-state temperature sensing device; A real-time transmission spectrum calculation unit for obtaining the optical powers detected by the first photodetector and the second photodetector when the laser scans within a preset wavelength range, calculating the ratio of the optical powers detected by the first photodetector and the second photodetector at each wavelength as the transmittance at each wavelength, and forming a transmission spectrum; A real-time central wavelength calculation unit for obtaining the wavelength at which the transmittance peak is located in the transmission spectrum as the real-time transmission spectrum central wavelength; A real-time temperature calculation unit for substituting the central wavelength of the transmission spectrum into the relationship curve between the central wavelength of the transmission spectrum and temperature to find the real-time temperature.
8. A fully solid-state temperature sensing system based on an optical fiber concave highly reflective optical film, characterized in that, It includes the all-solid-state temperature sensing device described in claim 1 and a temperature calculation module. The temperature calculation module is used to calculate the real-time transmittance of the optical fiber microcavity according to the optical powers detected by the first photodetector and the second photodetector, calculate the real-time thermal transmission coefficient according to the real-time transmittance, and substitute the real-time thermal transmission coefficient into the relationship curve between the thermal transmission coefficient and temperature to calculate the current real-time temperature.
9. The all-solid-state temperature sensing system based on the fiber optic concave highly reflective optical film according to claim 8, characterized in that: The temperature calculation module specifically includes: A relationship curve storage unit for storing the relationship curve between the thermal transmission coefficient and temperature of the current all-solid-state temperature sensing device; A real-time transmittance calculation unit for calculating the ratio of the optical powers detected by the first photodetector and the second photodetector as the real-time transmittance; A real-time heat transmission coefficient calculation unit, which is used to calculate the real-time heat transmission coefficient according to the real-time transmittance according to the following formula: In the formula, k represents the real-time heat transmission coefficient, S represents the real-time transmittance, and T represents the temperature; A real-time temperature calculation unit, which is used to substitute the real-time heat transmission coefficient into the relationship curve between the heat transmission coefficient and the temperature, and find the real-time temperature.
10. The all-solid-state temperature sensing system based on the fiber optic concave high-reflection optical film according to claim 8, characterized in that: The relationship curve between the heat transmission coefficient and the temperature is obtained through the following method: Place the fiber optic microcavity in a heating device and set the heating temperature to any normal temperature value; At the current normal temperature, set the laser to scan at different wavelengths, and calculate the transmittance at different wavelengths at the current normal temperature according to the optical powers detected by the first photodetector and the second photodetector, that is, the transmission spectrum at the current normal temperature; Derive the transmission spectrum at the current normal temperature to obtain the relationship between the transmittance and the wavelength; Set the heating temperature of the heating device to other different values, so as to obtain the transmission spectra at different temperature values, extract the central wavelengths of the transmission spectra, and establish the relationship between the central wavelength and the temperature change; Multiply the relationship between the transmittance and the wavelength, the relationship between the central wavelength and the temperature change, and the negative first power of the transmittance to obtain the relationship curve between the heat transmission coefficient and the temperature.
Citation Information
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