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1、附 录附录1一种基于带有特别的过滤和偏移调制的光栅投影的位移传感器胡建明，曾爱军，王向朝，中国摘要由美国A-B公司生产的ControlLogix系列可编程序逻辑控制器(PLC)提供了多种接口类型：如以太网、ControlNet、DeviceNet、RS-232等等。ControlLogix以太网连接模块“1756-ENET”使用了EtherNet/IP、ControlNet等协议，并采用了专业的服务代码封装于以太网协议包中。针对“实验性物理和工业控制系统”(EPICS)开发的驱动程序使用了EtherNet/IP协议，从而使得控制器可以运行vxWorks RTOS、Win32和Unix/Linu
2、x的测试程序。现在来分析一下这个接口的特点和使用场合。1 正文一种基于石油光栅空间滤波和偏振调制的位置传感器被提出。它是一种光栅投射到被测物体上要通过4倍的空间滤波器光学系统。经被测物体反射的光栅投影通过另一个4倍光学系统成像形成莫尔条纹。莫尔极化信号获取被测物体的位置信息。在位置传感器，不同的莫尔正弦信号对应不同的对象的位置。测量是用独立的光栅投影强度和对象的反射率来衡量。在实验中，位置传感器的效力得到证明，并且均方根（RMS）的每个测量位置误差小于13纳米。位置的测量已在许多领域发挥了重要作用，例如制造，生物物理学，和自动控制领域。在位置的测量方法，光学方法让人更有兴趣，因为它具有高度的准
3、确性并且是非接触式测量。在普通光学方法，诸如图像测量，干涉仪，使用位置灵敏探测器（PDS）的直线位移测量，测量光束方向是垂直于被测物体表面的。当有物体阻挡在对象的垂直方向时，普通光学方法就不在适用。要解决这个问题,本文提出一种新的基于临界入射的位移光栅传感器。这种位置传感器是如图-1所示。一个投射光栅被平行激光束照亮,投置到前面的焦面镜L1。焦距透镜组L1和L2组成4倍焦系统1。在这个4倍焦系统中，频率平面有一个孔径。投影光栅被投射到被测物体投影光栅通过这个临界入射的4倍焦系统1 被检测。由镜头L3和L4组成的4倍焦系统2同系统1有相同的光学参数。这个传感光栅呈现在L4的背面焦点平面。经物体反
4、射后,这个投影光栅的影像通过4倍焦系统2 投影到传感光栅上。由于检测光栅和投影光栅的影像重叠产生莫尔条纹。莫尔条纹输出信号随物体的方位变化由一个探测器通过透镜L5探测到。一个起偏镜和镀板在L4和检测光栅之间。形成投影光栅图像的光线通过偏光系统成为线性偏振光。通过镀板，线性偏振光被分成两个垂直极化相互交叉的光线。一个分析仪安置在检测光栅和L5之间。当分析仪是围绕在4倍焦系统2的光轴线周围，偏光器板和分析形成偏振调制器。随着极化调制，莫尔信号对在光栅投影上光的强度的变化是不敏感的。因此，该被测物体的位置，通过检测调制能够准确的测量。图-1位置传感器示意图在图-1中，位于4倍焦系统中的光轴定义为z轴
5、。投影光栅平面上,垂直、平行于投影光栅槽的方向分别被定义为x0和y0轴。同样，定义x2，y2轴和x3，y3轴。在4倍焦系统1的频平面上的x1，y1轴分别平行于光栅投影平面x0，y0轴。光栅投影中心放置在x0轴的起点。该光栅投影空间的比例为1:1。光栅投影的周期和宽度分别为D和B。通过光栅投影振幅分布表示为：（-1）公式（-1）中I1是在光栅投影强度。随着透镜L1傅立叶变换，在4焦距系统的频平面上的频率分布情况为：（-2）式中是激光波长和f是L1的焦距。在频平面上，孔径作为空间滤波器，其过滤的功能如下所示：（-3）因此，只有0， 1衍射角的光能通过孔径，通过孔径的频率分布写为：（-4）经L2傅里
6、叶变换，在L2的回焦平面上振幅E(x2) 分布如下式：（-5）因此，在光栅投影图像的光强分布表示为：（-6）被测物放在靠近L2 的背焦点的地方。L3的前焦点与L2的背焦点是重叠，4倍焦系统的1和2在纵向是对称的。经过对象反射，投影通过4倍焦系统成像与检测光栅上。L3的前焦点所在水平面被定义为位移传感器的零平面。如果在被测物与传感器的零平面之间存在一距离x，检测光栅投影光栅在检测光栅上的图像将随着位置的改变而变化：（-7）式中是入射光角度。关于检测光栅投影光栅在检测光栅上的图像的光强分布表示为：（-8）式中R表示被测物的反射率。起偏器的传播轴线与检测光栅槽间的夹角为45 。镀板包括两块相互正交的
7、双折射板。它将形成投影光栅的图像光线分成正交极化、相互交叉的两条线，即常规的和特殊的光射线。因此，投影光栅的被称作常和特殊的两个图像在检测光栅上成像。两图像间的距离是d/2。常规和特殊的图像强度分布表示为：（-9）（-10）两式中，B/2x32x sinB/2。检测光栅有同投影光栅一样的周期和占空比，而且有平行的槽。检测光栅放在距离轴X3的起点d/4的地方。两个莫尔信号表示如下：（-11）（-12）如果检偏镜透线与检测光栅槽间的角度是，那么这两个通过检偏镜的莫尔信号表示如下：，（-13）（-14）检测器通过检偏镜检测光通量，探测器上的光强度由下式给出：（-15）当检偏镜绕4倍焦系统2的光轴转动
8、角度为时，莫尔信号的极化调制得以实现，它在检测器上表示为：（-16）此时，光强度信号被检测器转化为包含直流分量IDC和交变电流分量IAC的电信号。电力信号由放大器放大，其直流和交流成分被滤波电路分开。被测物的位移表示如下：（-17）x的范围：（-18）在(17)中，IAC和IDC有相同的因子I1和R，因此，位移x与初始强度I1和反射率R无关。那么，激光输出强度和不同被测物的反射率将不会影响位移传感器。按光路图-1所示，进行了实验。用一束波长为785nm的平行激光照射投影光栅。投影光栅的周长为0.1mm，占空比为1:1。透镜L1的焦距为120 mm。4倍焦系统1的频率板上的孔径为3.5 mm。被
9、测物放在一个能提供做上下线性运动的地方。4倍焦系统1的光轴线与正规物体间的夹角为84.5。4倍焦系统2和4倍焦系统1有相同的光学参数，检测光栅和投影光栅有相同的光学参数。起偏器和检偏器是格伦泰勒棱镜。镀板由两个相同的光束位移差0.05 mm的石英棱镜组成。检偏镜放置在一移动的装置上，通过旋转调制莫尔信号。 图-2 当垂直移动对象时IAC/IDC（a）和均方根误差（b）测量结果试验中，通过移动装置在50um的范围内按2.5um的步进一步步移动被测物。在每个位置对被测物高度测量100次。实验结果显示在图-2。图-2(a)显示IACIDC与被测物高度的关系。IACIDC随高度做正弦变化。至此，该位置
10、传感器测量原理得以验证。图-2（b）显示了均方根（RMS）21位置测量误差的均方根（RMS），其值小于13 nm。因此，被测物象的高度被位移传感器高精度测量。最后，我们提出了一种基于带有特别的过滤和偏移调制的光栅投影的位移传感器。这种位移传感器适用于垂直被测物方向有障碍物的测量。莫尔信号随物体位移变化而产生的正弦曲线由位移传感器得到。这种位置传感器是基于不敏感的光源和物体极化调制反射率的差异而在输出发生变化。试验中，该方法的可行性得以验证。 附录2A position sensor based on grating projection with spatial filtering and p
11、olarization modulationJianmlng Hu(胡建明)12，Aijun Zeng(曾爱军)1，and Xiangzhao Wang(王向朝)Shanghai Institute of Optics and Fine Mechanics，Chinese Academy of Sciences，Shanghai 201800 Graduate School of the Chinese Academy of Sciences, Beijing 100039Received April 262005A position sensor based oil grating proj
12、ection with spatial filtering and polarization modulation is presentedA grating is projected onto the object to be measured through a 4f optical system with a spatial filterAfter reflected by the object the grating projection is imaged on a detection grating through another 4f optical system to form
13、 moir fringes. The polarization modulated moire signal is detected to obtain the position information of the objectIn the position sensor，the moire signal varies sinusoidally with the position of object. The measurement is independent of the incident intensity on the projection grating and the refle
14、ctivity of the object to be measuredIn experiments，the effectiveness of the position sensor is proved，and the root mean square(RMS) error at each measurement position is less than 13 nmPosition measurements have been playing an important role in many fields such as fabrication, biophysics, and auto
15、controlIn methods of position measurement，optical method holds more interest because of its high accuracy and non-contact measurement. In the common optical methods such as image measurement, interferometer ,and direct position detection using position sensitive detector (PDS),the measuring beam is
16、in the direction perpendicular to the surface of the object to be measured. When there exists a block in the direction perpendicular to the object，the common optical methods cannot be applied. To solve the problem，a new position sensor based on grating projection with grazing incidence is presented
17、in this paper.The position sensor is schematically shown in Fig. -1.A proiection grating is illuminated by a collimated laser beam and placed in the front focal plane of lens L1Lenses L1 and L2 form 4f system 1In this 4f system，an aperture is placed in the frequency planeThe projection grating is pr
18、ojected onto the object to be measured through the 4f system 1 with grazing incidenceThe 4f system 2 composed of lenses L3 and L4 Jams the same optical parameters with 4f system 1The detection grating is placed in the back focal plane of L4After reflected by the object，the image of the projection gr
19、ating is imaged onto the detection grating through the 4f system 2Due to tile overlapping of the detection grating and the image of the projection grating, the moire fringes are produced. The moir signal varying with tile position of the object is detected by a detector through lens L5A polarizer an
20、d a Savant plate are plated between L4 and the detection gratingThe rays forming the image of the projection grating become linearly polarized light through the polarizerPassing the Savant plate, the linearly polarized light is split into two orthogonally polarized and mutually sheared beamsAn analy
21、zer is placed between the detection grating and L5When the analyzer is rotated around the optical axis of 4f system 2，the polarizer Savant plate and analyzer form a polarization modulatorWith the polarization modulation，the moir signal is insensitive to the change of light intensity on the projectio
22、n gratingThus the position of the object can be measured accurately by detecting the modulated signalFig. -1.Schematic diagram of the position sensorIn Fig -1the optical axes of the 4f systems are defined as z axisIn the projection grating plane，the directions perpendicular and parallel to the groov
23、e of the projection grating are defined as directions of x0 mid y0 axes respectivelySimilarly, x2 ,y2 axes and x3，y3 axes are defined on the image planes of the projection gratingIn the frequency plane of the 4f system 1，x1，y1 axes are parallel to x0, y0 axes in the projection grating plane，respecti
24、velyThe center of the projection grating is placed at the origin of x0 axes. The line-to-space ratio of the projection grating is 1:1The period and width of the projection grating are represented by D and B, respectivelyThe amplitude distribution through the projection grating is expressed as（-1）Whe
25、re I1 is the intensity on the projection gratingWith Fourier transform of lens L1, the frequency distribution in the frequency plane of the 4f system 1 is given as （-2）where is the wavelength of the laser and f is the focal length of L1In the frequency plane，the aperture is used as a spatial filter
26、and its filtering function is written as （-3）Hence only 0, 1 diffraction orders pass the aperture and the frequency distribution through the aperture is written as （-4） With Fourier transform of L2，the amplitude distribution E(x2) in the back focal plane of L2 is given by（-5）Thus the intensity distr
27、ibution I(x2) of the image of projection grating is expressed as（-6）The object to be measured is placed near the back focus of L2The front focus of L3 is superposed with the back focus of L2 and 4f systems 1 and 2 are laid symmetrically relative to tile vertical. After reflected by the object，the pr
28、ojection is imaged on the detection grating through the 4f system 2The horizontal plane where the front focus of L3 is placed is defined as the zero plane of the position sensorIf there exists a distance x between the object and the sensors zero plane, the image of the projection grating on the dete
29、ction grating will be moved with displacement（-7）whereis the angle of grazing incidenceThe intensity distribution of the image of the projection grating on the detection grating is expressed as （-8） where R is the reflectivity of the object to be measured. The angle between the polarizers transmissi
30、on axis and the groove direction of the detection grating is 45The Savant plate comprises two birefringence plates whose optic axes are orthogonal mutuallyIt splits the rays that form the image of the projection grating into two orthogonally polarized and mutually sheared rays，namely ordinary and ex
31、traordinary rays. Thus two images of the projection grating called ordinary and extraordinary images are formed on the detection grating. The distance between the two images is d2The intensity distribution of the ordinary and extraordinary images are expressed as（-9） （-10）respectively，where B2x32x s
32、inB2The detection grating has the same period and line-to-space ratio as the projection grating and its groove is parallel to the groove of the projection gratingThe detection grating is placed with d4 offset relative to the origin of axis x3The two moir signals are written as（-11）（-12）If the angle
33、between the analyzers transmission axis and groove direction of the detection grating is ，the two moir signals through the analyzer are written as（-13）（-14）The detector detects the light flux through the analyzer，and the intensity on the detector is given by（-15）When the analyzer is rotated with ang
34、le (t) around the optical axis of the 4f system 2，polarization modulation of the moir signal is realize and the modulated intensity on the detector is expressed as（-16）The intensity is converted by the detector into electric signal which includes a direct current component IDC and an alternating cur
35、rent component IACThe electric signal is amplified by an amplifier and its direct and alternating current components are separated by a filter circuitThe position of the object is given by（-17）with the variation range（-18）In Eq(17)，IAC and IDC have common factors I1 and R，so the distance is independ
36、ent of the initial intensity I1 and the reflectivity RThe influence of the output variation of the laser and the reflectivity difference in different objects to be measured can be eliminated in the position sensorUsing the light path shown in Fig. -1, the experiment was carried outA projection grati
37、ng was illuminated by a collimated laser beam whose wavelength was 785nmThe period of projection grating was 0.1 mmThe fine-to-space ratio of projection grating is 1：1The focal length of lens L1 was 120 mmThe diameter of the aperture in the frequency plane of the 4f system 1 was 3.5 mm. The object t
38、o be measured was placed on a manual linear stage supplying updown movementThe angle between the axis of 4 f system 1 and the normal of the object was 84.5The 4f system 2 and the detection grating had same optical parameter as the 4f system 1 and the projection grating，respectivelyThe polarizer and
39、the analyzer were Glen-Taylor prismsThe Savant plate Was made of two same quartz prisms whose beam displacement was 0.05 mmThe analyzer was placed in a rotation mount and was rotated to modulate the moir signal Fig -2IACIDC (a) and RMS error(b)measurement results when vertically moving the objectIn
40、the experiment，the position of the object was changed by moving the manual linear stage step by step with 2.5-um step size within 50-um rangeAt each position，the height of the object was measured 100 timesThe experiment results are shown in Fig. -2Figure- 2(a) shows the relation between the IACIDC a
41、nd the height of the objectIACIDC varies sinusoidally with the heightTherefore the measuring principle of the position sensor is verifiedFigure- 2(b)shows the root mean square(RMS) errors at 21 measurement positions，the RMS errors are less than 13 nmSo the height of object can be measured by the pos
42、ition sensor with high precisionIn conclusion，we have proposed a position sensor based on grating projection with spatial filtering and polarization modulationThe position sensor can be applied when there is a block in the direction perpendicular to the object to be measured .The moire signal varying sinusoidally with the position of the object is obtained in the position sensorThe position sensor is insensitive to the output variation of light source and the reflectivity difference in object with the polarization modulationIn experimentsThe feasibility of the method was verified