多光束激光外差超高精度测量金属线胀系数的方法.doc

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1、【精品文档】如有侵权，请联系网站删除，仅供学习与交流多光束激光外差超高精度测量金属线胀系数的方法.精品文档.基于振镜调制的多光束激光外差超高精度测量金属线膨胀系数的研究摘要: 提出了一种多光束激光外差测量金属线膨胀系数的方法。利用振镜把待测参数信息调制到多光束激光外差信号的频率差中，信号解调后可以同时得到多个待测参数值，对多个待测参数值加权平均，从而得到样品长度随温度的变化量。基于此方法，对不同温度情况下金属棒线膨胀系数进行了实验研究，结果表明：该方法测量金属棒线膨胀系数相对误差为0.6%。关键词: 线膨胀系数，多光束激光外差，激光多普勒技术，非接触式测量1. 引言物体的热膨胀性质反映了材料本

2、身的属性，通常将固体受热后在一维方向上长度的变化称为线膨胀1。测量材料的线膨胀系数，不仅对新材料的研制具有重要意义，而且也是选用材料的重要指标之一。在工程结构设计、机械和仪表的制造、材料的加工等过程中都必须考虑材料的热膨胀特性。否则，将影响结构的稳定性和仪表的精度。考虑失当，甚至会造成工程的损毁，仪表的失灵，以及加工焊接中的缺陷和失败等等。目前，对金属线膨胀系数的测定有光杠杆法、读数显微镜法、电热法和激光干涉法等测量方法。在用这些方法测量的过程中，由于需要直接测量的参数过多，操作较复杂，以至于实验的系统误差与偶然误差偏大，例如，用光杠杆法测金属线胀系数时，由于近似公式的采用与复杂的操作使其系统

3、误差偏大，同时，由于读数装置配备不合理引入的偶然误差也较大，以至于其相对误差达4.4%2.3；读数显微镜法4由于视觉引起的偶然误差和电热法5实际温度与传感器的延迟引起的系统误差等都极大的限制了其测量精度；激光干涉法由于该装置的干涉条纹锐细、分辨率高，同时实验操作简单，从而大大减小了实验误差，实现了金属线胀系数的精确测量，测量的相对误差可为2%6-9，但是这种方法在读取干涉条纹数时存在视觉引起的偶然误差，导致精度无法再提高，也不能满足目前超高精度测量的要求。而在光学测量法中，激光外差测量技术备受国内外学者关注，激光外差测量技术继承了激光外差技术和多普勒技术的诸多优点，是目前超高精度测量方法之一，

4、其测量的相对误差可达1%10-14。该方法具有高的空间和时间分辨率、测量速度快、精度高、线性度好、抗干扰能力强、动态响应快、重复性好和测量范围大等优点，已成为现代超精密检测及测量仪器的标志性技术之一，广泛应用于超精密测量、检测、加工设备、激光雷达系统等领域。传统的外差干涉均为双光束干涉，外差信号频谱只含单一频率信息，解调后得到单一的待测参数值。本文基于激光外差测量技术，在2m相干激光测风雷达系统平台基础上，设计了一套多光束激光外差测量金属线膨胀系数的实验装置，提出了一种提高外差测量精度的多光束激光外差测量法，即在光路中利用振镜对不同时刻的入射光进行频率调制，得到了多光束激光外差信号，其信号频谱

5、中同时包含多个频率值，每个频率值都包含待测参数信息，经过解调后可同时得到多个待测参数值，对得到的多个参数值加权平均，提高了待测参数的精度。文章对此方法进行了详细的理论分析，最后进行了实验验证，测量结果的相对误差仅为0.6%。The principle of traditional heterodyne detection are all dual-beam interference, the spectrum of the heterodyne signal contains only a single frequency information， can get a single value

6、 of parameter which is under test after demodulation. Based on laser heterodyne measurement techniques and 2m coherence wind-detecting lidar platform，designed a experimental device of multi-beam laser heterodyne measurement for linear expansion coefficient of metal, propose a scheme of multi-beam he

7、terodyne measurement in this article, that is, modulate the frequency of different time incident light by the oscillating mirror in the optical path, and get the multi-beam laser heterodyne signal, whose spectrum of signal contains multiple frequencies, each frequency contains information of paramet

8、er under test, and can get multiple values of parameter which is under test after signal demodulation simultaneously, processing multiple values of parameter by the weighted-average, increase the accuracy of parameter which is under test. A detailed theoretical analysis of this method is taken in th

9、is article, theres an experimental verification at last, and the relative error is just 0.6%.2. 测量原理2.1线胀系数测量原理假设温度为T1时金属的长度为l1，温度为T2时金属的长度为l2，当温度变化范围不大时，金属的伸长量l(l = l2-l1)与温度变化量T (T =T2-T1)及金属的原长l0成正比5，即 (1)式中, 即为金属的线胀系数。于是可得： (2)因此，只要测出T1，T2间隔内金属棒长度的变化量l即可求出金属的线胀系数。2.2多光束激光干涉原理如图1所示，由于光束在薄玻璃板和平面反射

10、镜之间会不断地反射和折射，而这种反射和折射对于反射光和透射光在无穷远处或透镜焦平面上的干涉都有贡献，所以在讨论干涉现象时，必须考虑多次反射和折射效应，即应讨论多光束激光干涉。图1 多光束激光干涉原理示意图在不考虑薄玻璃板自身厚度的情况下，当激光以入射角0斜入射时，设入射光场为E(t)=Eexp(i0t)，多普勒振镜的振动方程和速度方程分别是x(t)=a(t2/2)和v(t)= at。由于振镜的运动，反射光的频率变为=0(1+ at/c)，式中0为激光角频率，a为振动加速度，c为光速。则t-l/c 时刻到达薄玻璃板表面的光场为： (3)而经薄玻璃板透射的光在不同时刻被平面反射镜2多次反射，其反射

11、光的表达式可以分别写成如下形式： (4)其中，1=r，2= r，m= r(2m-3)，r为光从周围介质射入薄玻璃板时的反射率，透射率为，r 为平面反射镜2的反射率，薄玻璃板和平面反射镜2之间反射光射出薄玻璃板时的透射率为，d为薄玻璃板和平面反射镜2之间的距离。这样，探测器接收到的总光场可以表示为： (5)则探测器输出的光电流可以表示为： (6)其中，e为电子电量，Z为探测器表面介质的本征阻抗，为量子效率，D为探测器光敏面的面积，h为普朗克常数，v为激光频率。由于直流项经过低通滤波器后可以滤除，因此，这里只考虑交流项，此交流项通常称为中频电流，整理可得中频电流为： (7)将(3)式和(4)式代入

12、(7)式，通过软件计算积分结果为： (8)忽略1/c3的小项之后可以简化为： (9)(9)式可记为： (10)其中： (11) (12)这里，p取自然数。通过(10)式可以看到，多光束外差测量法获得的中频项频率差以及相位差中都有薄玻璃板和平面反射镜2之间距离d的信息。主要针对中频项中频率差进行分析，因为采用傅里叶变换很容易实现频率测量。此时，根据(11)式，可以把干涉信号的频率记为： (13)根据（13）式可知，干涉信号的频率与待测距离成正比，比例系数为： (14)与光源角频率0、薄玻璃板和平面反射镜2之间介质的折射率n、折射角以及振镜常数a有关。应当说明的是，通过(10)式和(14)式可以看

13、出，探测器输出的光电流是由不同谐波组成的，每一项分别对应着频率的自然倍数，也就是说相邻频率差为固定值，经傅里叶变换之后在频谱上可以看到不同谐波频率波峰，通过测量不同谐波频率，就可以测出薄玻璃板和平面反射镜2之间的距离d，当d改变时，就可以根据(13)式测出对应d的变化量d，然后d对测量值加权平均，这样处理之后就可以提高d的测量精度，知道了d就可以根据(2)式计算得到待测样品线膨胀系数。2. Measurement principle2.1 Principle of linear expansion coefficient measurement Suppose that, the length

14、 of metal is l1 in the temperature T1, the length of metal is l2 in the temperature T2, when the temperature varies little, the elongation of the metal l(l = l2-l1) is in direct proportion to temperature variation T (T =T2-T1) and metal original length l05, given by: (1)In this expression, stand for

15、 represents the linear expansion coefficient of metal rod. Then: (2)Therefore, measuring variation in length of metal rodl between T1, T2 can find the linear expansion coefficient of metal.Fig. 2. Multi-beam interference principle2.2 Principle of multi-beam laser interferenceAccording to the scheme,

16、 because of the beam reflect and refract continuously from thin glass plate and mirror which is shown in Figure 2, and the reflection and refraction have a contribution to the interference between reflected and transmitted light in the infinite distance or the focal plane of the lens, so when discus

17、sing interference, must consider multiple reflection and refraction effects, which should discuss the multi-beam laser interference. Compared with the distance between thin glass plate and mirror2, the thickness of thin glass plate can be ignored, so the reflected light from the back surface of thin

18、 glass plate can be ignored, either. When the beam makes an oblique incidence in the incident angle 0, suppose incident field is E(t)=Eexp(i0t). The motion equation and rate equationof the oscillating mirror are x(t)=a(t2/2) and v(t)=at. As the movement of oscillating mirror, frequency of reflected

19、lightchange into =0(1+at/c). In this expression, 0 stand for angular frequency of laser, a is vibration acceleration, c is light speed. So optical field arrive the surface of thin glass plate at t-l/c time is: (3)The beam goes though the thin glass plate reflected by mirror 2 repeatedly in different

20、 moment, the reflect light can be described as the following form: (4)Which, 1=r，2= r, m= r(2m-3), r is the reflectivity of thin glass plate, is the transmissivity, r is the reflectivity of mirror 2, is the transmissivitywhen the reflect between thin glass plate and mirror 2 go out from the thin gla

21、ss plate, d is the distance between thin glass plate and mirror 2.So the total optical field received by the photodetector is: (5)Then the outputphotocurrent of the photodetector is: (6)Which, e is electronic charge, Z intrinsic impedanceof the medium in the surfaceof detector, is quantum efficiency

22、, D is photosensitive surfacearea of detector, h is Planck constant and v is laser frequency. As the DC component can be filtered after went through the low-pass filter, therefore, consider AC component only, call this AC component as intermediate frequency current, coordinating and obtain the inter

23、mediate frequency current as: (7)Substitute the equation (3) and the equation (4) into the equation (7), calculate integral by software and get the results as: (8)After ignore the minor termof 1/c3 equation (8) can be simplified as: (9)The equation (9) can be written as: (10)Where, (11) (12)Which, p

24、 is defined as positive integer.By (10), it can be seen that there are information of the distance d between thin glass plate and mirror 2 in frequency difference of intermediate frequency component andphase retardation obtained by the multi-beam heterodyne measurement. Analyze frequency difference

25、of intermediate frequency component primarily, since the use of Fast-Fourier Transform (FFT) is easy to implement frequency measurement. According to (11), the frequency of interference signal can be recorded as: (13)According to (13), the frequency of interference signal is in direct proportion to

26、the distance which is under test, the scale factors is: (14)Depend on angular frequency of light source0, refraction index of the medium between thin glass plate and mirror2 n, refraction angle and vibration acceleration a. It should be noted that through (10) and (14), we can infer that the outputp

27、hotocurrent of detector is composed of different harmonics, each of them is corresponding to the positive integer multiple of the frequency, it means that adjacent frequency difference of arrivalis a fixed value, after Fourier transform, wave peak of different harmonic frequencies can be seen on the

28、 frequency spectrum, the distance d between thin glass plate and mirror 2 can be measured by measuring the different harmonic frequencies. When d changed, the variation d of d can be measured according to (13), and then weighted averageto d, so that the measurement accuracy of measuring d is improve

29、d. According to equation (2), linear expansion coefficient of sample under testcan be calculated when d is known.3. 实验结果与误差分析3.1 实验装置多光束激光外差测量金属线膨胀系数的装置如图2所示，主要由加热系统与干涉测量系统组成。加热系统部分主要由数显温控仪、测温探头以及给待测金属杆加热的电热炉组成。数显温控仪的测温探头通过铂热电阻，取得代表温度的信号；而温度设定值使用“设定旋钮”调节，两个信号经选择开关和A/D转换器，可在数码管上分别显示测量温度和设定温度。电热炉对待测样品

30、均匀加热接近设定温度，通过继电器自动断开加热电路；在测量状态，显示当前探测到的温度。干涉测量系统部分主要由多光束外差干涉装置(该装置由H0固体激光器、全反射镜、四分之一波片、振镜、平面反射镜1、分束镜BS1、会聚透镜、薄玻璃板、平面反射镜2、光电探测器组成)和信号处理系统（该装置由滤波器、前置放大器、A/D和DSP组成）组成。平面反射镜1胶合在振镜前表面上，振镜在驱动电源作用下带动平面反射镜1一起做匀加速直线振动，加入振镜的好处是可以对不同时刻入射到平面反射镜1表面的激光进行频率调制。图2 多光束激光外差测量金属线膨胀系数的装置打开激光器，使线偏振光依次经过平面反射镜3、分束镜BS1和四分之一

31、波片后照射到胶合在振镜前表面的平面反射镜1上，而不同时刻被振镜调制的反射光又经过四分之一波片后透过分束镜BS1斜入射到薄玻璃板上，经薄玻璃板透射的光被平面反射镜2反射后与经过薄玻璃板前表面反射的光一起被凸透镜会聚到探测器光敏面上，最后经探测器光电转换后的电信号经过放大器、A/D转换器和数字信号处理器DSP后得到待测的参数信息。需要说明的是：用该装置进行测量时，要保证带有平面反射镜2的电炉对待测金属棒均匀加热，同时将薄玻璃板置于平面反射镜2前面1520mm处，仔细调节是薄玻璃板和平面反射镜平行、等高。之后，利用温度控制仪监测电炉内部的温度，读取并记录温度显示值T和信号处理后得到的l值。其中，l的

32、大小恰好等于薄玻璃板和平面反射镜2之间距离的变化量d，就可以通过记录薄玻璃板和平面反射镜2之间距离的变化量d来获得l的数值。3. Experimental results and error analysis3.1 Experimental deviceScheme of multi-beam laser heterodynes measurement for linear expansion coefficient of metal shown in Figure 1. The scheme mainly consists of heating system and the interfer

33、ometric system. Heating system consists of Digital Temperature Controller, temperature probe, and electric furnace which heating the metal rod under test. Temperature probeof Digital temperature controller obtains the temperature signal through the platinum resistance thermometer sensor. While the s

34、etting value of temperature is adjusted by setting knob, the two signals go through the selector switch and the A/D converter, measured temperature and setting temperature can be shown in the digitron. Heating the sample uniformly to the setting temperature, auto shut downthe heater circuit by the r

35、elays. In the measuring condition, displays the current detected temperature. Interferometric system mainly consists of the multi-beam interference device, which consists of holmium solid-state laser, quarter-wave plate, mirror, oscillating mirror, mirror1, beam split mirror BS1, quarter wave plate,

36、 lens, thin glass plate and mirror 2, and the signal processing system, which consists of the filter, preamplifier, A/D converter and Digital Signal Processor (DSP). Mirror 1 is agglutinate on the front surface of the oscillating mirror, the oscillating mirror drives the mirror1 move as vibration to

37、gether under the action ofthe power, and the advantage of the oscillating mirror is that the laser incidence on the surface of mirror 1 in different moment can be modulated in frequency.Fig.1. Designing of the schemeof multiple-beam interference to measure metal linear expansion coefficientTurn on t

38、he laser, make the linearly polarized beams go through mirror 3, beam split mirror BS1 and quarter-wave plate, then reach the mirror 1 which agglutinate on the front surface of the oscillating mirror, therefore, the reflected ray in different moment modulated by the oscillating mirror go through the

39、 beam split mirror BS1 and quarter-wave plate oblique incidenceat the thin glass plate, some chaotic light spots can be seen in the thin glass plate, by adjusting the screw of the bench of thin glass plate, can turn them into a sharp pyramidal spot, careful adjustment to make it to be light spot, he

40、re, make thin glass plate and mirror 2 parallel approximately, interference device has been adjusted well; the light transmission through the thin glass plate was reflected by mirror 2 and the light reflected by the front surface of the thin glass plate were assembled on photosensitive surface by th

41、e convex lens together, finally, electrical signal converted by the photodetector go through the preamplifier, A/D converter and DSP, and get the parameter under test. It should be noted that: measuring by this device, make sure that the rod is heated uniformly by the electric furnace with mirror 2.

42、 at the same time, then put the thin glass plate in front of mirror 2 at 1520mm, fine tuning to make mirror 2 parallel and in the same height with thin glass plate; then, monitoring the internal temperature of the electric furnace by Digital Temperature Controller, read and record the temperature di

43、splayed T and signal processing value l,. In which the value of l is just equal to d, the variation of the distance between thin glass plate and mirror 2, so that the value of l can be obtained by recording the variation d of the distance between thin glass plate and mirror 2.3.2 理论仿真基于图2所搭建的多光束激光外差

44、测量系统，测量了长150mm，直径为18.00mm的黄铜金属棒材料线膨胀系数，并验证多光束激光外差测量方法的可行性。测量中所配置的温度控制仪器为XMT型数字显示温度调节仪；所使用的Ho固体激光器波长=2050nm，此激光对人眼安全；通常情况下平面反射镜2和薄玻璃板之间介质的折射率取n =1；探测器的光敏面孔径为D=1mm，探测器灵敏度为1A/W；振镜的振动加速度a= 4.02106m/s2。根据(10)式仿真可以看到，当金属棒处于室温15oC时，经信号处理得到的多光束激光外差信号的傅里叶变换频谱如图3所示，其中实线为室温15oC且激光斜入射情况下，测量金属棒长度变化量l时对应多光束激光外差信号

45、的傅里叶变换频谱；虚线为室温15oC且激光正入射情况下，测量金属棒长度变化量l时对应多光束激光外差信号的傅里叶变换频谱。图3 15oC情况下多光束激光外差信号的傅里叶变换频谱图从图3中实线可以看出，多光束激光外差信号的频谱分布，其频谱是等间隔分布的，与前面理论分析是相符的。同时，从图3中还可以看到，实验中给出了正入射的情况下的理论曲线，目的是：在多光束激光外差信号频谱图中，可以同时得到斜入射时多光束激光外差信号频谱第一个主峰的中心频率和正入射时理论曲线的中心频率的数值，这样，很容易得到的两个中心频率的比值： (15)在得到中心频率的情况下，通过（15）式可以算出激光经薄玻璃板后折射角的大小，进而根据折射定律可以获得入射角0的大小，最后通过(14)式求的Kp的数值，最终获得薄玻璃板和平面反射镜2之间距离变化量d的值，由于d=l，从而根据(2)式可以计算出任意入射角情况下金属棒的线膨胀系数。Based on fig2, establish multi-beam laser heterodyne measurement system to measure linear expansion coefficient of the brass rod, whose length is 150mm, diameter is 18mm, and veri