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Abstract
Highly emissive spaceborne blackbody radiation sources are important devices for infrared value traceability by providing accurate infrared radiation to calibrate infrared load. To meet the needs of the radiation calibration accuracy needed for infrared remote sensing, this paper proposes a highly emissive blackbody that uses cubic reflection and an absorption method based on light capture. An emissivity simulation based on ray tracing was carried out. The influences of specular reflection (SR), near specular reflection (NSR), and diffuse reflection (DR) on the emissivity of the blackbody were analyzed. Two blackbodies with NSR and DR were fabricated, simulated, and tested experimentally; the experimental and simulation results were consistent.
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1. Introduction
Infrared remote sensing has been widely used in weather forecasting [1–3], national defense [4], climate change monitoring [5,6], and disaster prevention and mitigation [7–9]. With the development of infrared remote sensing technology [10–13], a high detection accuracy is required for infrared remote sensing loads. For example, when measuring climate change, the sea surface temperature needs to meet the measurement accuracy of 0.1 K and stability of 0.04 K decade-1 [14,15]. Since the onboard calibration source of the infrared remote sensing load is a spaceborne blackbody, its accuracy determines the calibration capability of the load.
Emissivity is an important indicator of the reference blackbody. It increases if the structure of the blackbody supports it and if there is a high emissivity coating. The Cross-track Infrared Sounder (CrIS) [16–19] and Infrared Atmospheric Sounding Interferometer (IASI) [20,21] are currently the infrared remote sensing loads that have a high quantitative level on the orbit. The internal calibration source of the CrIS is a spectral trap blackbody with an emissivity of 0.995 without a heater. The internal reference blackbody of the IASI is a cavity blackbody with an emissivity not less than 0.996. The spaceborne blackbody for the infrared hyperspectral atmospheric detector of the Fengyun-3E satellite is also a cavity blackbody and its emissivity can extend beyond 0.996 [22].
The sum of reflectivity, absorptivity, and transmissivity is a constant, 1. According to Kirchhoff ‘s law, absorptivity is equal to emissivity. Spraying a high emissivity coating or making a microstructure array is a way to improve surface emissivity [23–25]. Practically, cylindrical structures are also used to obtain high emissivity [26,27]. However, they require a large aspect ratio [28]. To meet the high emissivity requirements of blackbodies, the reflection of light can be reduced to improve the emissivity. The optical properties of the surface of blackbodies are designed to ensure that the falling light is reflected several times. Most of the energy is absorbed and a small part of it is reflected in each reflection. Finally, only a small part of the energy is reflected out of the blackbody.
In this study, research on a highly emissive spaceborne blackbody based on light capture (BBLC) was carried out to meet the needs of radiation calibration accuracy, such as that required by the Fengyun-4 series satellites. The mechanism behind the blackbody achieving high emissivity through multiple reflections and absorptions was determined, and simulations and experiments were carried out.
2. Optical transmission model of the BBLC
The ideal optical path transmission model for the BBLC after three absorptions and reflections is shown in Fig. 1. The light ray “1” represents the incident ray. The light ray “2” and “3” represent the reflected rays. The light ray “4” represents the emergent ray. It was assumed that the inner surface of the blackbody had high emissivity and that the reflection component was specular reflection (SR). The angle between the inner surfaces A and B of the blackbody is 45°. The incident light was first absorbed and then reflected by the surface A. Most of the energy was absorbed, and a small part of the reflected energy was absorbed and then reflected by planes B and A. After that, the reflected light returned along the original path of the incident light. This model realized the capture ability of incident light and obtained a high emissivity by absorbing and reflecting the incident light three times.
If the emissivity of surfaces A and B is ε, the specular reflectivity is (1-ε), and there is no diffuse reflection (DR) and near specular reflection (NSR); the normal emissivity of the blackbody εnormal can be achieved [29]:
where n is the number of reflections; n is 3 for the BBLC with three reflections and absorptions. When the emissivity of surfaces A and B was 0.9 and the SR component was 0.1, the normal emissivity of the blackbody was 0.999.It was difficult for surfaces A and B to achieve high emissivity, and the reflected part was mirror reflection. Therefore, it was necessary to analyze the influence of different types of reflection characteristics on the emissivity of the blackbody through theoretical simulation.
The reflections can be divided into SR, NSR, and DR. θi and θs are the incident and reflection angles, respectively. The included angle between the NSR light and SR light is θns, as shown in Fig. 2(a). SR follows the law of reflection, under which the incident angle is equal to the reflection angle. The power distribution of the NSR usually follows the cosine scattering model, Gaussian scattering, and the user-defined method. In the Gaussian scattering model, the NSR power distribution [30] is:
3. Emissivity simulation of the BBLC
3.1 Emissivity simulation model
According to Kirchhoff's law, the relationship between reflectivity, emissivity, and transmissivity is shown in Eq. (3):
where r is the reflectivity. ε is the emissivity, and τ is the transmissivity, where τ=0 since the surface is opaque.The reflectivity can be further expressed as Eq. (4):
where rspecular, rnear_specular, and rdiffuse are SR, NSR, and DR, respectively.By substituting Eq. (4) into Eq. (3), the emissivity of the blackbody can be obtained, as shown in Eq. (5):
where the optical paths of the three reflections depend on the type of reflection. The incident beam is a parallel beam perpendicular to the aperture of the blackbody. In SR, the light returns to the initial position after three reflections, so the power distribution of the reflected light is as uniform as that of the incident light. In NSR, the extreme center of the power of the reflected light is below the inclined plane. In DR, the closer the light is to the bottom of the cavity, the more difficult it is for it to be reflected after repeated reflections and absorptions. Therefore, the extreme center of the power of the reflected light tends to be above the inclined plane. The optical path diagram and received power distribution of the reflected light for the above three reflection types are shown in Fig. 3.To quantify the influence of the reflection characteristics of the inner surface of the blackbody on its emissivity, a mechanical structure model of the blackbody was built. The diameter of the aperture and cavity depth of the blackbody are each 100 mm. All the internal surfaces have the same reflection characteristics, as shown in Fig. 4(a). The emissivity at different positions of the aperture of the blackbody was simulated. The center point; and the circular test area, with a diameter of 8 mm; were evenly selected at 20 and 40 mm away from the center, as shown in Fig. 4(b).
The central normal emissivity of the blackbody with different surface proportions of DR, the normal emissivity of the blackbody at different positions, and the directional emissivity of the blackbody with a small angle were simulated and calculated with software LightTools. Firstly, the model of the blackbody, light source, and receiving surface were constructed. The parameters included: the structural size of the blackbody; model surface parameters; the position, size, and angle of the light source; and the position and size of the receiving surface, as shown in Fig. 5(a). Then, the basic parameters of ray tracing were set, which included the number of rays, direction of the incident light, and minimum power threshold, as shown in Fig. 5(b), and ray tracing was performed. Finally, the total powers of the incident light and hemispherical reflected light were calculated; the power distributions of these lights on the receiving surface are shown in Fig. 5(c) and Fig. 5(d), respectively.
The simulation parameter settings of the blackbody are shown in Table 1.
Table 1. Emissivity simulation settings of the blackbody
3.2 Simulation results
3.2.1 Central normal emissivity of the blackbody with different reflection types
Due to the different ray paths of the three kinds of reflected light, the influence of the proportion of each kind on the emissivity of the BBLC needed to be considered. Therefore, the simulation of different combinations of SR, NSR, and DR in different proportions was carried out. The simulation results are shown in Fig. 6.
For the same surface reflection setting—when the proportion of the DR, NSR, and SR remained unchanged—the greater the surface absorptivity of the blackbody was, the higher the central normal emissivity of the blackbody was. When the surface absorptivity remained unchanged, the central normal emissivity of the blackbody was the highest at 100% SR. The smaller the proportion of the DR and the larger the proportion of the NSR were, the higher the central normal emissivity of the blackbody was. This indicated that the central normal emissivity of the blackbody could be improved by promoting the surface emissivity and reducing the DR proportion of the surface.
3.2.2 Normal emissivity of the blackbody at different positions
The better the emissivity uniformity of the blackbody was, the better its performance was. Emissivity simulation was carried out at different positions of the blackbody. The surface settings are shown in Table 2 and the simulation results of three typical surface settings are shown in Figs. 7(a–c).
Table 2. Surface settings of the simulation
For the same reflection setting—when the proportion of the DR, NSR, and SR remained unchanged, the normal emissivity of the blackbody was low in the middle and high at both ends along the horizontal direction of the center from left to right. In the vertical direction of the center, the normal emissivity of the blackbody decreased from the bottom to the top and from the bottom left to the top right. According to the three different DR and NSR proportions, the higher the DR proportion was, the worse the normal emissivity uniformity and the lower the overall emissivity were. The emissivity uniformity of the blackbody with 100% NSR was the smallest. Based on the above results, the higher the NSR proportion of the surface or the lower the DR proportion was, the higher the overall normal emissivity of the blackbody was and the better the normal emissivity uniformity was.
3.2.2 Central directional emissivity at small angles
To ensure the calibration performance of the blackbody, the normal emissivity and directional emissivity in a certain range of small angles should only undergo minimal changes or remain unchanged. For the BBLC, directional emissivity was simulated at small angles for the three kinds of surface settings, as shown in Table 2. The simulated small angles were ±1, ±3, and ±5° at the horizontal and vertical directions with the normal direction of the aperture. The simulation results are shown in Fig. 8.
For the three surface reflection settings, the directional emissivity uniformity was smallest with the 100% NSR. Under the same surface reflection setting, the directional emissivity varied greatly with the angle of the pitch direction and minimally with the angle of the horizontal direction.
4. Experiments on emissivity
4.1 Structure of the blackbodies
Two blackbodies with a cavity structure, based on light capture, were fabricated with different surface treatments, corresponding to NSR and DR. The cavity depth was 110 mm and the diameter of the aperture was 100 mm. The blackbodies were heated at equal powers. Heating sheets were pasted to ensure the uniformity of the temperature field in the cavity of the blackbody, and a thermal insulation interlayer was pasted on the surface of the blackbody. The blackbodies under the irradiation of the front light source are shown in Fig. 9(a). The blackbodies with the pasted heating sheet and thermal insulation compartment are shown in Fig. 9(b). The inner surfaces of the blackbody can be described as follows.
- (1) Blackbody A: The internal surface was oxidized and blackened after polishing, and the surface reflection was approximately NSR.
- (2) Blackbody B: The internal surface was oxidized and blackened after polishing, and it was coated with high emissivity paint Nextel 811-21. The surface reflection was mainly DR.
4.2 Waveband emissivity measurement under atmosphere
4.2.1 Experimental results
The waveband emissivity of the two blackbodies, ranging from 8 to 14 µm, was measured with the emissivity measurement device based on a method wherein the surrounding radiation was controlled [31,32].
(I) Normal emissivity of the blackbody at different positions
The normal emissivity of the blackbodies A and B were measured. The test results of normal emissivity at different positions of the blackbodies A and B are shown in Figs. 10(a) and (b).
For blackbody A, the central emissivity is 0.9988, the emissivity uniformity is 0.0016, and the normal emissivity shows small fluctuations in the normal emissivity, as shown in Fig. 10(a). For blackbody B, the central emissivity is 0.9947, the emissivity uniformity is 0.0088, and the normal emissivity fluctuates slightly from the left to the right in the horizontal direction, and there are obvious gradient changes from the bottom to the top and from the lower left to the top right. The normal emissivity near the bottom of the cavity is higher than that near the aperture, as shown in Fig. 10(b). By comparison, the central emissivity of blackbody A is higher than that of blackbody B and its emissivity uniformity is smaller than that of blackbody B.
(II) Central directional emissivity at small angles
The central directional emissivity of blackbodies A and B at small angles were measured. The measured small angles were ±1 and ±3 ° in the horizontal direction and vertical direction, respectively, with the normal direction of the aperture. The test results of the measurements are shown in Fig. 11.
The directional emissivity uniformities of blackbodies A and B within their small angle range were 0.0004 and 0.0002, respectively. The above measurement results revealed that the directional emissivity of the blackbodies A and B changed minimally within the small angle range.
4.2.2 Discussion on experimental and simulation results
The simulation and experimental results showed that the high emissivity of the spaceborne BBLC depended on the emissivity, reflection type, and proportion of the inner surface of the blackbody. In case the structures of the blackbody were similar, the higher the emissivity of the inner surfaces were, the higher the emissivity would be. In case the structures of the blackbody were similar and they had similar surface emissivity, the higher the proportion of the NSR was, the higher the emissivity and the better the emissivity uniformity would be. Combined with the surface characteristic parameters of blackbodies A and B [33,34], a waveband emissivity of 8∼14 µm was simulated and compared with the experimental results. The comparison is shown in Table 3. The overall difference between the experimental and simulation results was less than 0.007; the results were consistent. Although the inner surface emissivity of blackbody A was lower than that of blackbody B, the former still had a higher emissivity and better emissivity uniformity than the latter did. Regarding the central directional emissivity of the blackbodies at small angles, the experimental and simulation results showed that the emissivity of the blackbodies changed minimally.
Table 3. Comparison between experimental and simulation results for central normal emissivity, normal emissivity uniformity, and directional emissivity uniformity at small angles for blackbodies A and B
In addition, the simulation and experimental results revealed that the emissivity of the blackbody was low near its aperture and high near its bottom. When the light source was near the aperture, the light emitted by the light source reflected out of the blackbody after a few reflections, rather than after multiple absorptions, showing that the blackbody had a low emissivity here. Near the bottom of the blackbody, the light emitted by the light source was reflected out of the blackbody after multiple reflections and absorptions, showing that it had a high emissivity here.
4.3 Spectral emissivity measurement under vacuum
4.3.1 Experimental results
The spectral emissivities of blackbodies A and B were measured based on the vacuum radiance-temperature standard facility (VRTSF) [35,36]. A spectral emissivity in the range of 4∼16 µm was measured by the MCT and INSB detector for blackbodies A and B, which is shown in Fig. 12(a) and (b).
The average emissivity of blackbody A was 0.9989 in the range of 7∼16 µm, its normal emissivity fluctuated greatly in the range of 4∼7 µm, and its lowest was 0.9431 near 5.4 µm. In the range of 8∼14,. The emissivity of blackbody B fluctuated between 0.94 and 0.98 in the range of 4∼16 µm, with an average emissivity of 0.9965. In the range of 8∼14 µm, the average emissivity of blackbodies A and B are 0.9990 and 0.9963.
4.3.2 Discussion on spectral emissivity results
The surface characteristic parameters of blackbodies A and B [33,34] were used to simulate the normal emissivity at the wavelengths of 5.4, 8, 12, and 14 µm. The comparison between the experimental and simulation results for the blackbodies is shown in Table 4. The results were consistent, and the overall difference was within 0.004. According to the spectral emissivity curve of blackbody A, the emissivity was low at 5.4 µm, which was mainly due to the low emissivity of the inner surface of the blackbody radiation source at this wavelength. Even after repeated absorptions and reflections, it was difficult to achieve a high emissivity.
Table 4. Comparison of experimental and simulation results for normal emissivities of blackbodies A and B at different wavelengths
5. Conclusions
Space reference blackbodies use accurate infrared radiation to calibrate the infrared load, which supports their wide use in fields such as weather prediction and infrared remote sensing. Improving emissivity is an important means to improve the accuracy of blackbodies. In this study, a highly emissive spaceborne blackbody was designed based on light capture, and a simulation experiment based on the ray tracing method was carried out. The simulation results showed that the higher the proportion of SR and NSR were, the higher the normal emissivity and the better the emissivity uniformity of the blackbodies would be. A highly emissive BBLC with an oxidized black surface and mainly NSR, and a highly emissive blackbody coated with high emissivity paint and mainly DR were fabricated. The experimental and simulation results showed that the blackbody whose surface reflection component was NSR had a better light capture ability in the range of 8∼14 µm, and it could achieve a higher emissivity and lower uniformity. The emissivity of the BBLC can reach 0.999 both in simulation and experiment, which can meet the application requirements. For future study, the emissivity of the blackbody in mid-wave infrared band could also be improved based on the principle of the BBLC. The surface coating material selection and surface treatment are reminded as are reminded as our future works.
Funding
National Natural Science Foundation of China (12075229, 62031018); National Key Research and Development Program of China (2018YFB0504700, 2018YFB0504702).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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