热红外遥感器温度灵敏度提升手段简析

热红外遥感器温度灵敏度提升手段简析 Analysis of the means to improve the temperature sensitivity of thermal IR remote sensing system 1 2 first-author 李晓曼，1981年生，女，高级工程师，研究方向为空间红外遥感技术。E-mail： lixiaoman_bisme@163.com 李晓曼，1981年生，女，高级工程师，研究方向为空间红外遥感技术。E-mail： lixiaoman_bisme@163.com lixiaoman_bisme@163.com 1 2 1 2 北京空间机电研究所, 北京 100094 北京空间机电研究所, 北京 100094 Beijing Institute of Space Mechanics & Electricity, Beijing 100094, China Beijing Institute of Space Mechanics & Electricity, Beijing 100094, China 先进光学遥感技术北京市重点实验室, 北京 100094 先进光学遥感技术北京市重点实验室, 北京 100094 Key Laboratory for Space Based Target Monitoring Technology of CAST, Beijing 100094, China Key Laboratory for Space Based Target Monitoring Technology of CAST, Beijing 100094, China 热红外遥感器主要使用遥感手段感应地物热红外辐射信息，可用于识别地物和反演地表温度参数。由于热红外遥感器在夜间的工作工作能力优于可见光，且环境适应性好，已广泛应用于资源调查、生态环境监测、灾害评估以及军事目标探测识别等领域。随着工程应用及科学研究的不断深入，提升热红外遥感器的探测灵敏度需求日益迫切。热红外遥感器的温度灵敏度与遥感器自身收集目标能量的能力和遥感器系统噪声特性相关。其中，遥感器系统噪声由光子噪声（景物辐射和遥感器本体背景辐射共同到达焦平面处的光子的波动）、探测器组件噪声、电路噪声共同组成。在成像谱段、积分时间、探测器及视频电路参数固定的条件下，光学系统降温能够减小其自身背景辐射，降低光子噪声，提升系统的温度灵敏度。本文通过仿真分析量化了光学系统辐射与光路设计、光学系统工作温度以及探测器冷屏设置的关系，并以某热红外遥感器为例验证了光学系统温度对热红外遥感器温度灵敏度的影响。文中的仿真分析方法和验证情况对于热红外遥感器的设计研制有参考意义。 TIR remote sensing systems mainly use remote sensing means to sense the thermal infrared radiation difference of ground objects, which can be used to identify ground objects and retrieve surface temperature parameters. TIR remote sensing detecting technology has been widely used in resource investigation, ecological environment monitoring, disaster assessment and military target detection and recognition because of its excellent working ability in bad weather and night. With the deepening of engineering application and scientific research, it is urgent to improve the thermal sensitivity of infrared remote sensors. In the design of TIR remote sensing system, for the application needs of detection capability, the target, background need to consider the three main factors of the system. Noise Equivalent Temperature Difference (NETD) is an important indicator of representing the temperature sensitivity of the remote sensing system. NETD could be affected by the optical system radiation on the TIR remote sensing system.The influence of NETD by optical system radiation could be analyzed by the method of the number of noise electron or by the method of D* of the detector. The noise of the remote sensor system consists of photon noise (scene radiation and the fluctuation of the main background radiation reaching the focal plane), detector assembly noise and circuit noise. Under the condition of fixed imaging spectrum, integral time, detector and video circuit parameters, the cryogenic optical system can reduce its own radiation, reduce the photon noise, and improve the temperature sensitivity of the system. This paper quantified the relationship between optical system radiation and optical path design, operating temperature and the temperature sensitivity of thermal infrared remote sensing camera. The simulation method uses the software TracePro to conduct light tracing, analyzes the irradiance distribution of the optical system and the optical machine structure at the respective working temperature, and finally accumulates all the components to obtain the total radiation amount on the detector. The working temperature of optical system will affect the temperature sensitivity of the system. When the optical system radiation drops to lower than 1/10 of the target signal radiation, it could be regarded as a background-limiting detecting system, where the optical system radiation impact on the temperature sensitivity of the thermal infrared remote sensor can be ignored. In the load design, when the detector type is fixed, the sensitivity of load detection can be improved by reducing the optical system temperature. In order to verify the influence of changing the temperature of the optical system on the temperature sensitivity of the thermal infrared remote sensor, an airborne infrared remote sensor was designed and developed. The working temperature of the optical lens of the infrared remote sensor was changed form 313 K to 293 K, and NETD was tested. With the decrease of optical system temperature, the temperature sensitivity is improved. So the performance improvement was verified by the NETD testing. With the limitation of atmospheric temperature of airborne thermal infrared remote sensor below the dew point, this test did not carry out the performance verification of the temperature below 293 K. NETD test of the remote sensor with the lower temperature work on the deep low temperature working in the vacuum tank will be done in future. The development of this study is important for the design and development of cryogenic optical TIR remote sensing systems. 遥感 热红外遥感器 探测能力 测试 温度灵敏度 remote sensing FIR remote sensing system detection capability performance testing Noise Equivalent Temperature Difference （NETD） 1　引言 1 热红外遥感器主要收集热红外辐射信息，可用于识别地物和反演地表温度参数，由于其夜间的工作工作能力优于可见光且环境适应性好，已广泛应用于资源调查、生态环境监测、灾害评估以及军事目标探测识别等领域。在工程应用及科学研究中，提升热红外遥感器的探测灵敏度具有非常重要的意义（ 周桃勇 等，2020 周桃勇 等，2020 ）。 热红外遥感器温度灵敏度越高，对所观测目标的温差细节信号获取能力越强（ Sobrino 等，2004 Sobrino 等，2004 ），甚至能分辨目标内结构微小温度差异（ 李俊山 等，2014 李俊山 等，2014 ），更高灵敏度的热红外成像技术将广泛应用于军民多个领域。噪声等效温差NETD（Noise Equivalent Temperature Difference）是表征遥感器温度灵敏度的重要指标（赵利民 等，2010）。在远距离探测的热红外遥感器设计时，针对探测能力应用需求，需综合考虑目标、背景和探测系统3方面的因素，对遥感器的探测能力制定评估模型。对特定探测环境下的遥感器探测能力的估算是进行系统优化设计和研制的基础（马文坡，2011； 吴骅 等，2021 吴骅 等，2021 ； 段四波 等，2021 段四波 等，2021 ）。 热红外遥感器的光学系统辐射的降低有助于提升系统探测灵敏度，美国和欧洲等国从20世纪80年代开始已将低温光学技术成功应用在多个遥感器中。在红外天文卫星IRAS（Infrared Astronomical Satellite）卫星热红外相机、宇宙背景探测卫星COBE（Cosmic Background Explorer）热红外相机、空间红外望远镜SIRTF（Space Infrared Telescope Facility）等空间红外探测遥感器的研制中，借助辐射制冷、机械制冷或者固态/液态工质制冷的方式，对遥感器的光学系统进行降温，以实现高灵敏度探测（ Collaudin等，2000 Collaudin等，2000 ）。 中国正逐步开展低温光学技术研究及工程实施工作，目前缺乏对光学系统辐射与热红外遥感器灵敏度定量关系分析，且常规的通过光学系统镜片发射率等效计算光机辐射的分析方法不具有普适性（ 李春来 等，2006 李春来 等，2006 ）。本文对光学系统辐射定量化分析方法进行了分析，并结合某遥感器研制测试实例介绍了光学系统温度对热红外遥感器灵敏度的影响。 2　光学系统辐射对系统NETD的影响 1 光学系统辐射对热红外遥感器NETD的影响可通过对噪声等效电子数的影响或者通过对探测器比探测率的影响（ 吴立民 等，2010 吴立民 等，2010 ）进行分析。 2.1　对噪声等效电子数的影响分析 2 在工程测试中，热红外遥感器对黑体辐射源产生两个不同温度点的辐射进行观测，基于两个温度点观测的信号数据计算信号差及噪声，然后由 式（1） 式（1） 计算得到NETD。 <math display="block" id="M1"><mi mathvariant="normal">N</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">T</mi><mi mathvariant="normal">D</mi><mo>=</mo><mfrac><mrow><mfenced separators="|"><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn 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48.09066391 11.59933376 式中， <math id="M2"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19637946&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19637943&type= 3.21733332 3.72533321 为高温点； <math id="M3"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19637955&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19637950&type= 3.21733332 3.72533321 为低温点； <math id="M4"><msub><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19637965&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19637961&type= 9.48266602 4.23333359 为遥感器对 T 2 温度点黑体产生的信号电子数； <math id="M5"><msub><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19637974&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19637970&type= 9.48266602 4.23333359 为遥感器对 T 1 温度点黑体产生的信号电子数； <math id="M6"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19637983&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19637977&type= 6.68866634 3.72533321 为遥感器对 T 1 温度点黑体成像时产生的噪声电子数（ 刘兆军 等，2006 刘兆军 等，2006 ）。 热红外遥感器的噪声 <math id="M7"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638316&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638312&type= 6.68866634 3.72533321 主要由光子噪声 <math id="M8"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638008&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638000&type= 7.87400007 3.72533321 、探测器读出噪声 <math id="M9"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638020&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638014&type= 8.46666718 3.72533321 、暗电流噪声 <math id="M10"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">k</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638031&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638025&type= 6.18066692 3.72533321 、电路噪声 <math id="M11"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638042&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638037&type= 5.84200001 3.72533321 组成，即 <math display="block" id="M12"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi></mrow></msub><mo>=</mo><mroot><mrow><msup><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">t</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">k</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638052&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638047&type= 63.58466721 5.33400011 式中，光子噪声 <math id="M13"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638065&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638060&type= 7.87400007 3.72533321 是到达探测器处的光子数随机起伏，使得光生电子也随机起伏而产生的噪声。注入到探测器的辐射功率越大，产生的光子噪声也就越大。 <math display="block" id="M14"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>=</mo><mroot><mrow><mfenced separators="|"><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">b</mi><mi mathvariant="normal">j</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">t</mi></mrow></msub><mo>+</mo><msub><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">s</mi></mrow></msub></mrow></mfenced></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638076&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638067&type= 36.91466904 6.51933336 式中， <math id="M15"><msub><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">b</mi><mi mathvariant="normal">j</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638083&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638079&type= 6.77333355 3.72533321 为景物到达探测器处产生的光生电子数， <math id="M16"><msub><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638310&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638307&type= 6.60400009 3.72533321 为光学系统辐射到达探测器处产生的光生电子数。光学系统温度影响其辐射，因此也影响了到达探测器处产生的光生电子数 <math id="M17"><msub><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638310&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638307&type= 6.60400009 3.72533321 ，可直接影响系统光子噪声 <math id="M18"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638110&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638105&type= 7.87400007 3.72533321 ，从而影响热红外遥感器NETD。 2.2　对探测器比探测率影响分析 2 NETD还可用 式（4） 式（4） 的方法进行估算。 <math display="block" id="M19"><mi mathvariant="normal">N</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">T</mi><mi mathvariant="normal">D</mi><mo>=</mo><mfrac><mrow><mn mathvariant="normal">4</mn><mo>·</mo><mroot><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi mathvariant="normal">d</mi></mrow></msub></mrow><mrow/></mroot><mo>·</mo><mroot><mrow><mfrac><mrow><mi mathvariant="normal">π</mi></mrow><mrow><mn mathvariant="normal">2</mn><mo>·</mo><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi></mrow></msub></mrow></mfrac></mrow><mrow/></mroot></mrow><mrow><msub><mrow><mfenced separators="|"><mrow><mfrac><mrow><mi mathvariant="normal">d</mi><mi>M</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi>T</mi></mrow></mfrac></mrow></mfenced></mrow><mrow><mi>T</mi><mo>=</mo><mi mathvariant="normal">探</mi><mi mathvariant="normal">测</mi><mi mathvariant="normal">景</mi><mi mathvariant="normal">物</mi><mi mathvariant="normal">等</mi><mi mathvariant="normal">效</mi><mi mathvariant="normal">黑</mi><mi mathvariant="normal">体</mi><mi mathvariant="normal">温</mi><mi mathvariant="normal">度</mi></mrow></msub><mo>·</mo><mi>Ω</mi><mo>·</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>·</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi>o</mi></mrow></msub><mo>·</mo><msup><mrow><mi>D</mi></mrow><mrow><mi>*</mi></mrow></msup><mo>·</mo><mi>δ</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638121&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638115&type= 68.66466522 21.50533485 式中， Ω 为瞬时视场立体角； A d 为探测器面积； <math id="M20"><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638129&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638126&type= 3.30200005 3.72533321 为积分时间； <math id="M21"><msub><mrow><mi>D</mi></mrow><mrow><mi>O</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638138&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638133&type= 3.97933316 3.72533321 为光学系统口径；τ o 为光学系统效率； <math id="M22"><msup><mrow><mi>D</mi></mrow><mrow><mi>*</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638151&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638144&type= 3.55599999 2.96333337 为探测器比探测率； <math id="M23"><mi>δ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638159&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638156&type= 1.60866666 2.62466669 为过程因子； <math id="M24"><msub><mrow><mfenced separators="|"><mrow><mfrac><mrow><mi mathvariant="normal">d</mi><mi>M</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi>T</mi></mrow></mfrac></mrow></mfenced></mrow><mrow><mi>T</mi><mo>=</mo><mi mathvariant="normal">探</mi><mi mathvariant="normal">测</mi><mi mathvariant="normal">景</mi><mi mathvariant="normal">物</mi><mi mathvariant="normal">等</mi><mi mathvariant="normal">效</mi><mi mathvariant="normal">黑</mi><mi mathvariant="normal">体</mi><mi mathvariant="normal">温</mi><mi mathvariant="normal">度</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638170&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638165&type= 31.83466530 9.82133293 ：对于温度为 T （景物温度）的黑体，单位温度变化引起的发射辐照度变化，由普朗克函数对温度求导而来。 <math display="block" id="M25"><msub><mrow><mfenced separators="|"><mrow><mfrac><mrow><mi mathvariant="normal">d</mi><mi>M</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi>T</mi></mrow></mfrac></mrow></mfenced></mrow><mrow><mi>T</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>C</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>·</mo><msup><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac><msubsup><mo>∫</mo><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mrow><mi>M</mi><mfenced separators="|"><mrow><mi>λ</mi><mo>,</mo><mi>T</mi></mrow></mfenced><mi mathvariant="normal">d</mi><mi mathvariant="normal">λ</mi></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638180&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638176&type= 45.12733078 9.82133293 式中， M （ λ ， T ）为光谱辐射出射度，λ为波长， T 为黑体温度，λ m 为中心波长，和λ 1 和λ 2 分别为谱段的下限和上限， c 2 为第二辐射常数， c 2 =1.4388 cm·K。 热红外探测器的比探测率定义为探测器对单位入射功率的探测能力（ 曾戈虹 等，2012 曾戈虹 等，2012 ），红外探测器比探测率与探测器背景限探测率 <math id="M26"><msubsup><mrow><mi>D</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>*</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638197&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638194&type= 3.64066648 4.06400013 和 G 因子相关，其中 <math id="M27"><msubsup><mrow><mi>D</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>*</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638197&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638194&type= 3.64066648 4.06400013 可以表示为 <math display="block" id="M28"><msubsup><mrow><mi>D</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo>=</mo><mfrac><mrow><mi>λ</mi></mrow><mrow><mi>h</mi><mo>·</mo><mi mathvariant="normal">c</mi></mrow></mfrac><mroot><mrow><mfrac><mrow><mi>η</mi></mrow><mrow><mn mathvariant="normal">2</mn><mo>·</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>q</mi><mo>,</mo><mi mathvariant="normal">b</mi></mrow></msub></mrow></mfrac></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638210&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638204&type= 28.10933495 10.07533360 式中， <math id="M29"><mi>η</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638219&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638215&type= 2.20133328 3.38666677 为探测器的量子效率； h 为普朗克常数，6.63×10 -34 J/s；c为光速，取为3×10 8 m/s； <math id="M30"><msub><mrow><mi>E</mi></mrow><mrow><mi>q</mi><mo>,</mo><mi mathvariant="normal">b</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638229&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638224&type= 5.33400011 3.72533321 为探测器背景辐照度值，ph·s -1 ·cm -2 。 探测器背景辐射噪声的极限允许值是影响探测器性能的因素之一（ 王世涛 等，2012 王世涛 等，2012 ），背景辐射噪声 <math id="M31"><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">b</mi><mi mathvariant="normal">k</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638239&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638233&type= 4.48733330 3.72533321 可由下式得到： <math display="block" id="M32"><msub><mrow><mi>E</mi></mrow><mrow><mi mathvariant="normal">b</mi><mi mathvariant="normal">k</mi></mrow></msub><mo>=</mo><mfrac><mrow><mi>h</mi><mo>·</mo><mi mathvariant="normal">c</mi></mrow><mrow><mi>λ</mi></mrow></mfrac><msub><mrow><mi>E</mi></mrow><mrow><mi>q</mi><mo>,</mo><mi mathvariant="normal">b</mi></mrow></msub><mo stretchy="false">(</mo><mi>W</mi><mo>/</mo><msup><mrow><mi>m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638251&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638245&type= 31.32666588 7.70466709 综上可见，在成像谱段、积分时间、探测器及视频电路参数确定的条件下，光学系统背景辐射影响探测器背景限探测率，从而影响热红外遥感器NETD。 2.3　光学系统背景辐射估算方法 2 光学系统背景辐射源为暴露在光路中的所有光学和机械元件，背景辐射分析包含两部分：视场内的光学镜片辐射到达像面的部分、光机结构表面产生的杂散辐射到达像面的部分（马文坡，2011）。 在光学系统设计完成后，应用TracePro等仿真软件进行光线追迹，逐一分析光学系统和光机结构在各自工作温度下的辐射在到达遥感器像面的辐照度分布，最终将所有分量累加得到探测器上的总辐射量。 为达到最佳灵敏度，大多数制冷型红外探测器都有冷屏结构，探测器从视场角“观看”目标辐射。很明显，目标辐射越能很好地覆盖探测器的整个视场角，有用辐射与干扰辐射之比就越大。为了抑制成像系统的背景辐射，提高辐射分辨率并增大成像动态范围，一般要求红外光学系统的出瞳与探测器杜瓦的冷屏匹配。 对于冷屏严格匹配的成像系统，可以近似认为光机结构表面产生的杂散辐射可以忽略不计。此时，相机光机结构的自身辐射与光学系统的透过率 <math id="M33"><msub><mrow><mi>τ</mi></mrow><mrow><mi>o</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638261&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638256&type= 2.87866688 3.72533321 相关，相机光机等效发射率可以表示为 <math display="block" id="M34"><msub><mrow><mi>ε</mi></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi>o</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638269&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638265&type= 16.51000023 3.72533321 其辐射可以表示为 <math display="block" id="M35"><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><mi mathvariant="normal">q</mi></mrow></msub><mo>=</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>o</mi></mrow></msub><mo>·</mo><msubsup><mo>∫</mo><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msub><mfenced separators="|"><mrow><mi>λ</mi><mo>,</mo><mi mathvariant="normal">T</mi></mrow></mfenced></mrow><mi mathvariant="normal">d</mi><mi>λ</mi><mo>·</mo><mi>Ω</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638275&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638271&type= 37.76133347 6.85799980 式中， <math id="M36"><msub><mrow><mi>ε</mi></mrow><mrow><mi>o</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638284&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638280&type= 3.04800010 3.72533321 为光机等效发射率； <math id="M37"><msub><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msub><mfenced separators="|"><mrow><mi>λ</mi><mo>,</mo><mi mathvariant="normal">T</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638293&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638291&type= 12.36133385 4.14866638 为利用普朗克定律计算的光谱辐亮度， T 为光学系统和光机结构的温度； <math id="M38"><mi>Ω</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638304&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638299&type= 2.62466669 2.79399991 为立体角。 3　光学系统降温对提升系统温度灵敏度的效果仿真 1 某热红外遥感器采用 B 1 （10.3 μm—11.3 μm）、 B 2 （10.4 μm—12.5 μm）两个长波红外谱段对300 K地面景物进行探测。采用含有3片透镜的透射式光学系统，光学系统孔径为100 mm，F/#为1，单片透镜的透过率均为0.94，发射率为0.06；采用长波红外探测器，探测器像元尺寸大小为23.5 μm×23.5 μm，读出噪声为500 e - ，电路噪声420 e - ，暗电流噪声在两个谱段分别为63 e - 和79 e - ，积分时间为0.2 ms。采用仿真分析软件TracePro结合计算软件Matlab编程，利用 式（1） 式（1） — 式（3） 式（3） 进行NETD仿真，得到仿真结果见表 1 1 、 2 2 所示，在光学系统温度从313 K降低至253 K的过程中， <math id="M39"><msub><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638310&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638307&type= 6.60400009 3.72533321 不断降低， <math id="M40"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638316&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638312&type= 6.68866634 3.72533321 降低，温度灵敏度提高。对于该系统，温度从313 K降低至253 K， B 1 、 B 2 谱段NETD降幅分别达到9.8%和9.0%。 2 参数 4 光学系统温度/K 313 293 273 253 <math id="M41"><msub><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mo>,</mo><mn>302</mn><mi mathvariant="normal">K</mi></mrow></msub><mo>-</mo><msub><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mo>,</mo><mn>298</mn><mi mathvariant="normal">K</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638327&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638319&type= 21.50533485 2.87866688 /e - 4.73e 5 4.73e 5 4.73e 5 4.73e 5 <math id="M42"><msub><mrow><mi>S</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638416&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638415&type= 5.07999992 2.87866688 /e - 3.07e 6 2.28e 6 1.63e 6 1.10e 6 <math id="M43"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638347&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638342&type= 6.01133299 2.87866688 /e - 3354 3234 3132 3046 <math id="M44"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638357&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638352&type= 6.43466663 2.87866688 /e - 500 500 500 500 <math id="M45"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">k</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638368&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638361&type= 4.65666676 2.87866688 /e - 63 63 63 63 <math id="M46"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638454&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638451&type= 4.48733330 2.87866688 /e - 420 420 420 420 <math id="M47"><msub><mrow><mi>N</mi></mrow><mrow><mi mathvariant="normal">n</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19638387&type= 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为了验证改变光学系统温度对热红外遥感器温度灵敏度的影响，设计并研制了机载热红外遥感器，遥感器由长波红外镜头、红外探测器、滤光片组件、结构支撑件及电子学组成。系统光学链路示意图如 图1 图1 所示。热红外遥感器光学系统指标参数见 表3 表3 。光学系统布局如 图2 图2 所示。在探测器前放置滤光片组件，实现所需谱段的获取（Xiong等，2003）。定制了长波红外探测器，主要技术指标见 表4 表4 。 参数 单位 数值 工作谱段 μm 10.3—12.5 焦距 mm 100 F/# — 1.0 MTF平均值（@21lp/mm） — 0.35 透过率 % 84 参数 单位 数值 像元规模 像元 640×512 探测元中心间距 μm 23.5×23.5 光谱响应范围 μm 8—14 典型NETD mK 优于50 在光学镜头外壳上粘贴了加热片和测温热敏电阻，通过温度控制电路实现加热片加热功率调节，实现对光学镜头的温度调节。测试过程由遥感器入光口处放置大规模面源黑体，在300 K附近选取两个温度点，分别测试了遥感器对两个温度黑体的输出，计算得到NETD（ 龙亮 等，2013 龙亮 等，2013 ）。测试结果如 表5 表5 所示，可以看出，随着光学系统的温度降低，温度灵敏度有提升，性能变化情况与 表1 表1 、 表2 表2 中的仿真的变化趋势一致，变化百分比接近。 谱段 光学系统温度/K NETD/mK B 1 （10.3—11.3 μm） 293 59.2 B 1 （10.3—11.3 μm） 313 61.5 B 2 （11.4—12.5 μm） 293 64.4 B 2 （11.4—12.5 μm） 313 66.8 5　结论 1 在热红外遥感器设计中，红外探测器、光学系统选型确定后，随着光学系统的降温，光学系统及光机结构的杂散辐射降低，热红外遥感器的温度灵敏度有所提升。当光学系统辐射降至比目标信号辐射低一个数量级时，可视为背景限探测，此时光学系统辐射对热红外遥感器温度灵敏度影响可以忽略。为验证光学系统降温对热红外遥感器温度灵敏度的影响，设计并研制了某机载红外遥感器，通过镜头加热控温装置改变红外遥感器的光学镜头不同工作温度并实测NETD，验证了理论仿真结果。由于机载热红外遥感器在大气中使用温度不能低于露点的限制，本次试验未开展293 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National Remote Sensing Bulletin， 25（8）：1655-1660 Li X M，Zhao Y H and Ma W P. 2021. Analysis of the means to improve the temperature sensitivity of thermal IR remote sensing system. National Remote Sensing Bulletin， 25（8）：1655-1660 2021-04-25 2021-08-07 2021-09-09 2021-07-02 遥感学报 8 25