Calculation Method for Response Band Magnitude of Aerospace Sensors
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摘要: 精确的恒星星等信息是开展导航星表建立、航天器定姿、红外相机定标等工作的基础，现有公开星表涵盖测光波段不全且带宽普遍较窄，难以找到与任务传感器响应波段相匹配的星等信息。为此提出了一种基于恒星辐射光谱的传感器响应波段星等计算方法。该方法利用公开星表数据信息，建立星表测光波段与传感器响应波段星等差值模型，对星表星等与传感器响应波段星等差值进行估算；将色指数计算的恒星近似表面温度作为先验信息，在传感器响应波段区间进行普朗克方程求解，进而推算恒星在传感器响应波段的星等。星表数据计算验证表明，该方法具有较好的稳健性和适应性，对传感器响应波段星等推导精度为0.066等 （1δ），93.3%恒星推算误差优于0.2等，可满足导航星表建立、航天器定姿、红外相机定标等应用需求。Abstract: Accurate stellar magnitude information is the foundation for conducting navigation star catalog establishment, spacecraft attitude determination, infrared camera calibration, and other work. The existing public star catalogs do not cover all the photometry bands and the bandwidth is generally narrow, making it difficult to find magnitude information that matches the response bands of the mission sensors. A method for calculating the magnitude of sensor response bands based on stellar radiation spectra is proposed. This method utilizes publicly available catalog data information to establish a model for the magnitude difference between the photometry band of the catalog and the sensor response band, and estimates the magnitude difference between the catalog magnitude and the sensor response band. Using the approximate surface temperature of the star calculated by the color index as prior information, the Planck equation is solved in the sensor response band range to calculate the magnitude of the star in the sensor response band. The verification of star catalog data calculation shows that the method has good robustness and adaptability, and the star magnitude derivation accuracy of sensor response band is 0.066 magnitude (1δ), 93.3% of the star estimation error is better than 0.2 magnitude, which can meet the needs of navigation star catalog establishment, spacecraft attitude determination, infrared camera calibration, and other applications.
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Key words:
- Magnitude /
- Color index /
- Sensors /
- Response band /
- Black-body radiation /
- Radiation flux
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图 3 星表测光波段与传感器响应波段星等差值
Figure 3. Difference in magnitude between the photometry band of the star catalog and the sensor response band
图 4 恒星传感器响应波段星等计算流程
Figure 4. Flow chart of star sensor response band magnitude calculation
图 5 星表星等差值统计
Figure 5. Statistical chart of star magnitude difference in different star catalogue
图 6 黑体辐射推算星等误差统计
Figure 6. Statistical diagram of magnitude error in blackbody radiation estimation
表 1 Johnson测光系统部分参数
Table 1. Partial parameters of Johnson photometry system
测光波段 U B V R I J H K 有效波长/μm 0.366 0.438 0.545 0.641 0.798 1.22 1.63 2.19 半波带宽/μm 0.066 0.094 0.088 0.138 0.149 0.213 0.307 0.390 0星等辐流量/（10–14 W·cm–2·μm–1） 417.5 632 363.1 217.7 112.6 31.47 11.38 3.961 
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表 2 同一恒星不同波段星等差异
Table 2. Different band magnitudes of the same star
恒星HIP编号 测光波段 B V R I J H 21479 7.32 5.87 5.06 4.39 –2.62 –3.73 32349 –1.46 –1.46 –1.46 –1.43 –1.36 –1.33 34444 2.69 1.91 1.43 1.05 0.77 0.54 78265 2.66 2.83 2.91 3.08 3.47 3.5 91262 0.03 0.03 0.07 0.10 –0.18 –0.03
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表 3 部分星表测光波段数据
Table 3. Partial photometric band data of open star catalog
星表 滤光片 有效波长/μm 半波带宽/μm Hipparcos Hp 0.550 0.225 Tycho BT 0.420 0.075 VT 0.510 0.100 SDSS u 0.352 0.063 g 0.480 0.141 r 0.625 0.139 i 0.769 0.154 z 0.911 0.141 PAN-STARRS Ps1 g 0.484 0.105 Ps1 r 0.620 0.125 Ps1 w 0.629 0.256 Ps1 open 0.694 0.398 Ps1 i 0.753 0.121 Ps1 z 0.868 0.099 Ps1 y 0.963 0.064 2 MASS J 1.236 0.162 H 1.662 0.251 K 2.159 0.262 GAIA Gbp 0.504 0.233 G 0.585 0.420 Grp 0.769 0.284 WISE W1 3.353 0.663 W2 4.603 1.042 W3 11.561 5.506 W4 22.088 4.102 IRAS IRAS 12 μm 10.164 6.067 IRAS 25 μm 21.735 10.018 IRAS 60 μm 52.137 30.516 IRAS 100 μm 95.484 33.265
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表 4 星表对应波段星等差值统计
Table 4. Magnitude differences of star catalogue for corresponding bands
星等差值|Δmag| 0.05 0.05～0.1 0.1～0.2 0.2～0.3 <0.5 均值 方差 Hp与VT 62.7% 30.2% 4.3% 1.2% 99.7% 0.05 0.08 G与R 21.8% 16.6% 18.1% 36.9% 98.3% 0.16 0.15
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