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《 光电系统噪声分析 》 Analysis of Noise in Opto-electrical Detection Systems

《 光电系统噪声分析 》 Analysis of Noise in Opto-electrical Detection Systems. 参考书 References ： 吴 杰， 《 光电信号检测 》 ，哈工大出版社， 1990 曾庆勇， 《 微弱信号检测 》 ，浙大出版社， 1986 陈佳圭， 《 微弱信号检测 》 ，中央广播电大出版社， 1987 罗先和等， 《 光电检测技术 》 ，北航出版社， 1995 R.M.Gagliardi 等著，陈根祥等译， 《 光通信技术与应

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《 光电系统噪声分析 》 Analysis of Noise in Opto-electrical Detection Systems

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  1. 《光电系统噪声分析》Analysis of Noise in Opto-electrical Detection Systems 参考书 References： 吴 杰，《光电信号检测》，哈工大出版社，1990 曾庆勇，《微弱信号检测》，浙大出版社，1986 陈佳圭，《微弱信号检测》，中央广播电大出版社， 1987 罗先和等，《光电检测技术》，北航出版社，1995 R.M.Gagliardi等著，陈根祥等译，《光通信技术与应 用》， 电子工业出版社，1998 下一页

  2. 绪 论 Introduction 一、意义 Importance： 1、光电信号检测在任何一个光电子系统中都是必不可少的部 分。PD is a necessary part for any photo-electric system. 2、光电信号检测水平高低对于光电子系统整体特性有十分重 要的影响。=>光电信号检测理论与技术是光电子技术的重要组 成部分。The level of PD has deciding influence to the propert. of the system, => the theory & techn. are an important part of photo-electronics techniques. 二、特点 Features： 光电信号多数比较微弱，需采用微弱信号检测手段。Most of the PD signals are feeble, => the techn. for feeble signal detec. should be used.

  3. 三、设课目的 The Aim of Offering This Course ： 1、系统地认识与理解光电信号检测理论； To understand systematically the theory of PE signals detection. 2、掌握光电信号检测的基本方法；为后续课程及将来工作 奠定基础。 To master the fundamental methods of PES; to be prepared for the continued courses and the job in the future. 四、主要内容 The Main Contents ： 光探测器工作原理与性能、光辐射的检测方法、光电 信号处理的一般方法等。 The principles & features of PD, the detection methods of optical radiation, the general approaches of PE signal processing, etc.

  4. 第一章 光探测器 Chapter 1 Light Detectors 引言 Introduction： 一、光辐射探测器是实现光电转换的关键元件，其性能如何直 接关系到整个系统性能好坏。 The PDs are the key components, whose characteristics will determine the performance of the systems. 二、分类 Classification：光子探测器 Photodetectors 热探测器 Thermodetectors 1 、光子探测器 Photodetectors ： <1> 原理：光子与物质相互作用引起的光电效应 The Photoelectric Effect describing the interaction between photon & material is the working principle of photodetectors.

  5. <2> 分类 Classification： （1）光电子发射探测器 Photon Detecting Diode: 真空/充气光电二极管 vacuum/gas filled photoelectric diode 光电倍增管 photomultiplier (tube): PMT （2）半导体光电探测器Semiconductor PD: 光导探测器 Photoconductive(PC)、光生伏特探测器 Photovoltaic(PV) <3> 特点 Features： （1）灵敏度高high sensitivity （2）响应速度快quick response （3）波长选择性敏感 sensitive to working wavelength （4）半导体光导探测器通常工作于低温work at low temperature

  6. 2、热探测器 Thermodetectors： <1> 原理：光辐射产生的热效应 Thermal Effect produced by O.R. <2> 分类：Classification （1）测辐射热电偶/热电堆 TE Couple（温差电效应）Thermoelectric effect （2）测辐射热敏电阻 Thermistor（体电阻温度敏感性）Temperature sensitivity （3）热释电探测器 TEED（热电晶体的热释电效应）Thermal Electron Emitting Effc. （4）高莱管 Golay Tube（气体受热辐射后力学参量改变）Dynamic Param. Change <3> 特点 Features： （1）灵敏度比光子探测器低1-2量级 Low sensitivity for 1-2 order （2）响应速度较慢Slow response speed （3）无波长选择性 No wavelength selectivity （4）工作于室温Working at room temperature

  7. 第一节、探测器的性能参数及测量Section 1 Parameters of PDs & their measurement 1.1 性能参数：测量和使用条件参数 Meas. & Appl. Conds. Params. 性能指标参数 Performance Target Params. 一、几何参数 Geometric Params. 1、探测器的面积 Area of PD 标称面积nominal：制造厂家提供的探测器的响应面积 选用面积used：实际使用（起作用）的面积 有效面积 effective：探测器整体响应度与最大响应度比值 The ratio of total responsibility over the maximum of the responsibility: （1.1.1）

  8. 2、探测器的视场角和立体角 Ap`parent angle & Solid angle • （1）视场角：致冷型探测器响应元的中心对冷光阑的张角 • Apparent angle: the angle of the center of response element to diaphragm • （2）权重立体角 ：若来自（ ）方向的光辐射照射到探测的选用面积S上某点（x, y）处引起的响应度为 则探测器的有效权重立体角为 • （1.1.2） • 式中 是 的极大值。 • Weighted solid angle: If the responsibility at a certain point on the used area • S induced by the optical radiation from direction of ( ) is

  9. Then the Effective Weighted Solid Angle is given as where the is the maximum of the . 该公式的物理含义见下图 图1.1 权重立体角的物理含义 Fig.1 the physical meaning of the EWSA

  10. 解释: The explanations （1） 为探测器接受面积S上坐标为（x, y）的面元 对来自（ ）方向的光辐射的响应度 The is the responsibility of the area element with coordinates of (x, y) on the receiving area S of a detector induced by the optical radiation coming from the direction of ( ). （2） 为立体角元。 The is the solid angle element. （3） 乘 为（ ）方向的光辐射在法线N方向的投影， 因为响应度定义中要求以法线方向入射

  11. (4) 分子的物理含义：来自所有可能入射方向的光辐射换 • 算到法线入射后探测器的响应 • The meaning of the `numerator: The response of the detector after converting the optical radiation from all incident directions into that along the normal line direction. • (5) 分母的物理含义：全面积上的最大响应 • The meaning of the denominator: The maximum responsibility on the area. • (6) 分子除以分母后，仅余下立体角在法线方向的投影， • 故称为权重立体角 • Only the projection of the solid angle along the direction of normal line is left after dividing the numerator by the denominator.

  12. 二、电参数 The Electric Parameters 1、阻抗 Im`pedance （1）定义：探测器两端电压对瞬时电流的导数 其复表达式为 其中: 为直流电阻、为工作频率、 为探测器电容量、 分式为容抗 。 Def.: The derivative of the voltage between the two ends of a detector with respect to the instantaneous current: , the complex expression of which is , where is DC resistance, is working frequency, is capacity, the fraction is capacitive reactance of the detector.

  13. （2）依阻抗对探测器分类：Classification according to impedance 〈1〉低阻探测器： ，需用变压器等阻抗变换元件与 放大器连接 Detectors with low impedance, impedance transformation element such as transformer is needed when it is connected with an amplifier. 〈2〉中阻探测器： ，可直接与放大器耦合 Detectors with mid-impedance, can be coupled directly with an amplifier. 〈3〉高阻探测器： ，需与高输入阻抗放大器连用，热噪声与时间常数均较大。 Detectors with high impedance have higher thermal noise and time constant, should be used with an amplifier with high input impedance.

  14. 2、偏置条件 Bias conditions • （1）光伏探测器：反偏，以便与前放匹配 inverse biasing • （2）光电导或光敏电阻探测器：正偏 forward biasing • 三、其它参数 Other Parameters • （1）波长范围 wavelength range • （2）工作频率范围（调制频率范围）modulation freq. range • （3）放大器噪声带宽 noise bandwidth of amplifier • （4）探测器工作温度 working temperature of amplifier • 四、性能指标 Performance Target Parameters • 1、量子效率 Quantum effect 上一页 下一页

  15. （1）探测器工作的物理过程 • The working physical procedure of photodetectors • 探测器吸收辐射于其上的光子而产生光电子，光电子在探测器内及外加电路中形成光电流。光电流强度 与入射光功率 • 成正比。 • Detector produces photo-electrons after absorbing the photons impinged on its light sensitive area. The photo-electrons forms optical current inside the • detector and in the outside circuit. The current intensity is directly proportional • to the incident optical power: • （1.1.3） • （2 ）光电转换因子 : • The photon-electron transforming factor

  16. 上式中 称为光电转换因子 The in Form. (1.1.3) is called the photon-electron transforming factor. <1> 的微观含义 The microscopic meaning of : 由(1.1.3)可得 ,可知其微观含义为: 单位时间内,一个具有能量 的光子在探测器中产生的光电子电量（每个光电子电量为e），或: 一个具有能量 的光子在探测器中产生的电流强度。 From obtained from Eq.(1.1.3), one can see that the microscopic meaning of is the electric quantity of photo-electrons (e per photo-electron) produced in unit time interval by a photon with energy of .Or: The current intensity produced by a photon with energy inside the detector.

  17. <2> 的宏观含义: The macroscopic meaning of 将(1.1.3)改写为 ,可知其宏观含义为: 单位入射 光功率可产生的光电流强度。 Rewriting Eq.(1.1.3) as , one can obtain the macroscopic meaning of : The optical current intensity produced by unit incident optical power. <3>量子效率 : The quantum effect 由(1.1.3)移项得量子效率的定义式: Transposing Eq.(1.1.3), we have (1.1.4)

  18. 分子：单位时间内由吸收的光子激励产生的光电子数 The numerator is the number of photo-electrons produced by the photons absorbed in unit time interval. 分母：单位时间内入射到探测器表面的光子数 The denominator is the number of the photons impinged on the surface of the detector in unit time interval. 量子效率 ：单位时间内入射到探测器上的每个光子能产生 的光电子数量。 Quantum effect : The number of photo-electrons produced by each photon impinged on the surface of the detector in unit time interval. 理想情形： for ideal cases、实际情形： for practical ones。

  19. 2、响应度R : Responsibility R (1) 定义：Definition 一般定义：探测器输出电压或电流与入射到探测器上的辐射功 率之比 Thegeneral definition:The ratio of the output voltage or current of detector over the incident optical power is defined as the responsibility of PD. 确切定义：在入射辐射垂直投射到探测器响应平面的条件下， 探测器输出的基频信号开路电压的方均根值或基频信号短路电流的方均根值与入射辐射功率中基频功率的方均根值之比。 (1.1.5-1)

  20. 或 (1.1.5-2) The exact definition: The ratio of the rms value of the open circuit output voltage or the short circuit output current of the basic frequency signal over the rms value of the basic frequency component of the incident optical power. （2）影响R的因素: The Factors affecting R 入射光波长The wavelength of incident light、调制频率The modulation frequency、探测偏置条件 The bias conditions of detector、 工作温度 The working temperature及测量R所用的放大器的噪声带宽 and the noise bandwidth of the amplifier used to measure R of detectors. （3）电子带宽与噪声等效带宽： Electronic bandwidth & Noise bandwidth

  21. <1> 电子带宽 ：Electronic bandwidth 放大器的电压增益或电流增益下降到其峰值增益的一半 (-3dB)时的频率间隔。The freq. Interval corresponding to the points where the gain of the V or I declines to the half of the peak value. <2> 噪声等效带宽 ：Noise equivalent bandwidth a. 一般情形：General cases 将实际功率增益对频率变化曲线下的面积化为等面积的矩 形功率增益曲线时的频率间隔。The freq. Interval corresponding to the points where the area of the rectangle equals to that under the practical p~f curve.

  22. b. 白噪声情形： White noise cases • whereis the gain of the amplifier, is the peak gain of the amplifier • working at the peak frequency , is the peak frequency at which • the amplifier has the maximum gain. • 3 、 噪声等效光功率NEP（最小可探测光功率） • N. Equivalent P. (Minimum value of the detectable optical power) • （1）探测器的探测能力由响应度和自身噪声电平决定The detection • ability is determined by the responsibility & the noise level of the detector.

  23. （2）NEP的物理含义： 考虑到探测器自身噪声电平后探测器的最小可探测光功率。 Phys. Meaning: The minimum value of detectable optical power after considering the noise level of detectors themselves. （3）定义：使输出方均根电压或电流与无入射时探测器的方均根 噪声电压或电流等值的入射光功率称为噪声等效光功率。 Definition: The incident optical power of PD, which makes the output rms V (or I) equal to the noise rms V (or I) without incident optical power, is called the Noise Equivalent Power. （4）定义的数学表达式： The mathematical expression of the definition:

  24. 依定义，将公式（1.1.5-1）中分子与分母分别用噪声依定义，将公式（1.1.5-1）中分子与分母分别用噪声 电压与噪声等效光功率代替有: Substituting the numerator and denominator by noise voltage and NEP, we have 将上式移项得: Transposing it one can obtain: (1.1.6-1) or (1.1.6-2) （5）相关因素：Relative factors 入射光波长incident wavelength、探测器偏置条件bias conditions of PD、工作温度working temperature、探测器面积area of PD、调制频率modulation frequency、放大器噪声带宽noise bandwidth of PD

  25. （6）物理含义：Phys. meaning NEP越小探测能力越强，或灵敏度越高。 The less the NEP, the stronger the detection ability, or the higher the sensitivity. 4、探测度D Detectivity (1) 探测度D Detectivity <1> 定义：噪声等效光功率的倒数称为探测度D (1.1.7) Def.: The re`ciprocal of NEP is defined as the detectivity.

  26. <2> 物理含义: 单位入射光功率时探测器的电压信噪比。 Phys. Meaning: The signal noise (voltages) ratio (SNR) of the PD with unit incident optical power. <3> 推论: 将(1.1.7)移项得 Inference: Transposing Eq. (1.1.7), we obtain (1.1.8) 表明: 探测度一定时,输出电压信噪比与入射光功率成正比。 which shows that the output SNR is directly proportional to the incident optical power when the detectivity of the PD has a certain value. (2) 归一化探测度 Normalized detectivity <1> 为何引入 Why the normalized detectivity should be introduced?

  27. 当探测器的噪声等效带宽不太大时,多数探测器的NEP与探当探测器的噪声等效带宽不太大时,多数探测器的NEP与探 测器的面积的平方根成正比，与噪声等效带宽的平方根成正比， 为消除上述二因素的影响，需引入 。 When the noise equivalent bandwidth of is not too great, the NEP of most of PDs is directly proportional to the square root of the area and the square root of the noise equivalent bandwidth of the PD. Therefore, the should be introduced to eliminate the Influences of these two factors. <2> 定义式：Definition formula Since , define normalized NEP as , Taking the reciprocals of both sides of the equality, we have (1.1.9)

  28. <3> 用途：用于同类型不同面积探测器间性能比较 Applications: To compare the performances of the same kind PDs with different areas. （3） : Double `asterisked D 致冷型探测器的探测度还与视场角有关，为消除视场角 的影响，还需引入 。 The detectivity of a cold-typed detector is relative to the apparent angle. To eliminate this influence, the should be introduced. <1> 定义 definition： (1.1.10) Where is the given apparent angle.

  29. <2> 物理含义： 是给定视场角条件下的 , 是 时 的归一化探测度 。 Phys. Meaning: is the working at a given apparent angle, or say, is the normalized detectivity when . 5、光谱响应 Spectrum Response (1) 定义： 当入射光功率、调制频率和偏置条件固定时，探测器的响 应度或归一化响应度对波长的依赖关系称为探测器的光谱响应。 Definition :The dependence of the normalized responsibility on the working wavelength is called the Spectrum Response of a detector when the incident optical power, the modulation frequency & the bias conditions are fixed.

  30. (2) 物理含义：对探测器针对不同波长入射光的响应能力的度量。 The measurement of the response ability of a detector to the incident light with different working wavelength, respectively. (3) 表示法：Expressions <1> 绝对光谱响应曲线：纵轴为 或 Absolute spectrum response curve: The vertical axis represents or . <2> 相对光谱响应曲线：纵轴为 Relative spectrum response curve: The vertical axis represents . (4) 特征量：Characteristic values <1> 热探测器：无波长选择性，其光谱响应为一直线。

  31. Thermal Detectors: The spectrum response curve is a straight line, because they are not sensitive to the working wavelength. <2> 光子探测器: <i> 响应曲线的极大值称为峰值响应, 记为 。 The maximum of the response curve is called the Peak Response which is denoted as . <ii> 相应的波长称为峰值响应波长,记为 。 The corresponding wavelength is called the Peak Response wave-length, which is denoted as . <iii> 光谱响应降至峰值响应一半时对应的波长称为截止波长， 它决定探测器的光谱响应范围。The corresponding wavelength when the response declines to the half of the is called the Cutoff Wavelength, which determines the response range of the detector.

  32. 6 频率响应与时间常数 Frequency Response & Time Constant (1) 定义：探测器响应度随调制频率的变化称为探测器的频率 响应。 Def.:The relation between the responsibility & frequency of a detector is defined as the Frequency Response of the detector. (2) 相关因素：Relative factors <1> 半导体光子探测器：光生载流子寿命限制响应速度 Semiconductor PD: The life of the light generated carrier affects the response speed. <2> 热探测器：响应元的热容大小影响响应速度 Thermal Detector: The quantity of the thermal capacity of the response element affects the response speed.

  33. (3) 表达式Expression：若无调制信号时的响应度为 ，则在调 制频率为 时的响应度与调制频率 的关系为 If the responsibility without modulation signals is , then the relation between the responsibility and the modulation frequency , when the modulation frequency is , is expressed as (1.1.11) (4) 响应时间：Response time (Time constant) <1> 上式中的 称为探测器的响应时间或时间常数，它是探 测器将入射光转变为电信号所需要的时间，是对探测器响应速度 的度量。

  34. The in above formula is called the Response Time or Time Constant of the detectors. It is the time needed by the detector to transform the incident light into electrical signals, which is the measurement of the response speed of the detectors. <2> 记使响应度下降到最大值的 时的调制频率为 ， 则时间常数在数值上等于 。 Denoting the frequency making responsibility decline to of its maximum as , then the value of the time constant is given by .

  35. (5) 脉冲时间常数：Pulse time constant 对矩形脉冲信号而言，探测信号电压或电流上升至其渐进值 的 或使信号电压或电流下降至渐进值的 倍所需的时间。 For pulse signals, the needed time when the signal V (or I) rises to the or declines to the times of the progressive value is defined the Pulse Time Constant. 1.2 探测器性能参数的测量 (自学) The measurement of detector’s parameters. See: Reference book 1：p66-67

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