CN100480622C - Method for measuring distance between wave source point and roughcast centre point in concave grating production light path - Google Patents

Method for measuring distance between wave source point and roughcast centre point in concave grating production light path Download PDF

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CN100480622C
CN100480622C CNB2006100169015A CN200610016901A CN100480622C CN 100480622 C CN100480622 C CN 100480622C CN B2006100169015 A CNB2006100169015 A CN B2006100169015A CN 200610016901 A CN200610016901 A CN 200610016901A CN 100480622 C CN100480622 C CN 100480622C
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pinhole filter
distance
blank
grating
plane mirror
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CN101082480A (en
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李文昊
齐向东
巴音贺希格
李英海
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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Abstract

凹面光栅制作光路中测量波源点与毛坯中心点距离的方法，属于光谱技术领域中涉及的一种测量波源点与光栅毛坯中心点距离的方法。要解决的技术问题是：提供一种凹面全息光栅制作光路中测量波源点与凹面全息光栅毛坯中心点距离的方法。技术方案为：第一步，建立一套凹面全息光栅曝光装置。第二步，制备一套测量凹面全息光栅制作光路中波源点与毛坯中心点之间距离的装置。第三步，利用第一步建立的凹面全息光栅曝光装置的光路。第四步，调整第二步中建立的测距装置在干涉场中的位置。第五步，确定针孔滤波器的位置。针孔滤波器的针孔位置到凹面全息光栅毛坯中心点的距离就是所测的波源点到凹面全息光栅毛坯中心点的距离。The invention relates to a method for measuring the distance between a wave source point and a blank center point in an optical path for making a concave grating, which belongs to a method for measuring the distance between a wave source point and a grating blank center point in the field of spectrum technology. The technical problem to be solved is: to provide a method for measuring the distance between the wave source point and the center point of the concave holographic grating blank in the light path for making the concave holographic grating. The technical solution is as follows: the first step is to establish a set of concave holographic grating exposure device. The second step is to prepare a set of devices for measuring the distance between the wave source point and the center point of the blank in the optical path of the concave holographic grating. The third step is to use the optical path of the concave holographic grating exposure device established in the first step. The fourth step is to adjust the position of the ranging device established in the second step in the interference field. The fifth step is to determine the position of the pinhole filter. The distance from the pinhole position of the pinhole filter to the center point of the concave holographic grating blank is the measured distance from the wave source point to the center point of the concave holographic grating blank.

Description

凹面光栅制作光路中测量波源点与毛坯中心点距离的方法 Method for Measuring the Distance Between the Wave Source Point and the Blank Center Point in the Optical Path of Concave Grating Manufacturing

一.技术领域 1. Technical field

本发明属于光谱技术领域中涉及的凹面全息光栅制作光路中测量波源点与凹面全息光栅毛坯中心点距离的方法。The invention belongs to the field of spectrum technology and relates to a method for measuring the distance between a wave source point and a center point of a concave holographic grating blank in an optical path for manufacturing a concave holographic grating.

二.背景技术 2. Background technology

凹面全息光栅是用于可见、紫外区的多波段分光器件，使用它可以缩小光谱仪器的尺寸，减少组成的零部件数量，消除光学系统的像散，提高光学仪器的成像质量、分辨本领和测试精度。The concave holographic grating is a multi-band spectroscopic device used in the visible and ultraviolet regions. Using it can reduce the size of the spectroscopic instrument, reduce the number of components, eliminate the astigmatism of the optical system, and improve the imaging quality, resolution and testing of the optical instrument. precision.

在凹面全息光栅的制作过程中，一个非常关键的工艺流程就是将涂有光致抗蚀剂的凹面光栅毛坯放在由两束球面波相干后确定的干涉场中，由光致抗蚀剂记录干涉场中的干涉条纹。将Fermat原理应用到Seya-Namioka成像系统中去，使用光程展开法修正光学系统的像差，通过计算可以得出两束记录球面波波源点与凹面全息光栅毛坯中心的距离以及这两束球面波主光线与凹面全息光栅毛坯法线的夹角，理论分析和计算结果表明，通过改变球面波波源点的位置可以改变像差的大小，进而达到消除光学系统中的像散和彗差的目的。可见，精确地确定这两束球面波的波源点与凹面全息光栅毛坯中心的距离对于制作凹面全息光栅有着非常重要的意义。In the production process of concave holographic gratings, a very critical process is to place the concave grating blank coated with photoresist in the interference field determined by the coherence of two beams of spherical waves, and the interference field is recorded by the photoresist interference fringes in . Apply the Fermat principle to the Seya-Namioka imaging system, use the optical path expansion method to correct the aberration of the optical system, and calculate the distance between the source point of the two beams of recorded spherical waves and the center of the concave holographic grating blank and the distance between the two beams of spherical waves Theoretical analysis and calculation results show that the included angle between the chief ray of the wave and the normal line of the concave holographic grating blank can change the size of the aberration by changing the position of the spherical wave source point, thereby achieving the purpose of eliminating astigmatism and coma in the optical system . It can be seen that it is very important to accurately determine the distance between the source point of the two beams of spherical waves and the center of the blank holographic grating for the production of the concave holographic grating.

传统测量长度的方法主要有：利用光栅莫尔条纹现象的光栅尺；利用电磁原理工作的磁栅式传感器、感应同步器；利用激光干涉原理的激光测距仪等。这几种方法可以用于很多场合的长度或距离测量，但是在凹面全息光栅制作光路中用于测量球面波波源点与凹面全息光栅毛坯中心点的距离却不是很实用。光栅尺和利用电磁原理工作的长度测量仪器多用于测量运动物体的位移；利用激光测距仪时，其中一点必须位于仪器的出光位置，这是很难达到。可见传统测量长度或距离的方法都不适用于测量凹面全息光栅制作光路中波源点与毛坯中心点的距离。The traditional methods of measuring length mainly include: grating ruler using grating Moiré fringe phenomenon; magnetic grating sensor and inductive synchronizer using electromagnetic principle; laser rangefinder using laser interference principle, etc. These methods can be used to measure the length or distance in many occasions, but it is not very practical to measure the distance between the source point of the spherical wave and the center point of the blank of the concave holographic grating in the optical path of the concave holographic grating. Grating rulers and length measuring instruments that use electromagnetic principles are mostly used to measure the displacement of moving objects; when using a laser rangefinder, one of the points must be located at the light output position of the instrument, which is difficult to achieve. It can be seen that the traditional methods of measuring length or distance are not suitable for measuring the distance between the wave source point and the blank center point in the optical path of concave holographic grating manufacturing.

三.发明内容 3. Contents of the invention

为了克服上述已有技术存在的缺陷，本发明的目的在于提出了一种新颖的、低成本的、易于实现的用于凹面全息光栅制作光路中测量波源点与凹面全息光栅毛坯中心点距离的方法。In order to overcome the defects in the above prior art, the object of the present invention is to propose a novel, low-cost, easy-to-implement method for measuring the distance between the wave source point and the center point of the concave holographic grating blank in the optical path of concave holographic grating production .

本发明要解决的技术问题是：提供一种凹面全息光栅制作光路中测量波源点与凹面全息光栅毛坯中心点距离的方法。解决技术问题的技术方案为：第一步，建立一套凹面全息光栅曝光装置。如图1所示，包括Kr+激光器1、第一平面反射镜2、半反半透镜3、第二平面反射镜4和第三平面反射镜5、第一针孔滤波器6和第二针孔滤波器7、干涉场8和光栅毛坯9。在Kr+激光器1的激光束传播方向的光轴上置有第一平面反射镜2，第一平面反射镜2与光轴成45°角；在第一平面反射镜2的反射光的光路上置有半反半透镜3，它的半反半透面与光轴成45°角；分别在半反半透镜3的反射面和透射面出射光的光轴上置有第二平面反射镜4和第三平面反射镜5；分别在第二平面反射镜4和第三平面反射镜5的反射光线的光轴上置有第一针孔滤波器6和第二针孔滤波器7；第一针孔滤波器6和第二针孔滤波器7发射光线的交汇区域形成了干涉场8；在干涉场8内置有光栅毛坯9，光栅毛坯9的中心点位于干涉场8的中心位置。本发明要测量的是经过第一针孔滤波器6和第二针孔滤波器7发出的球面波波源点与光栅毛坯9的中心点之间的距离，也就是针孔位置与毛坯中心点之间的距离。第二步，制备一套测量凹面全息光栅制作光路中波源点与毛坯中心点之间距离的装置。如图2所示，包括带有刻度的滑轨10、带有刻度的游标11、转接杆12、夹具13、千分表右探头14、千分表左探头15和千分表16。带有刻度的游标11安装在带有刻度的滑轨10上，两者之间滑动接触，两者的结合相当于游标卡尺，固定在转接杆12的下端，并与转接杆12垂直，夹具13在转接杆12的上端，固定在转接杆12的腔内，千分表16和它的左、右探头是一体件，千分表右探头14水平地穿过夹具13，伸向夹具13的右方，千分表16的左探头15和右探头14在同一水平轴线上。第三步，利用第一步建立的凹面全息光栅曝光装置的光路，如图3所示，光路中没有摆放第一针孔滤波器6和第二针孔滤波器7，而第二平面反射镜4、第三平面反射镜5和光栅毛坯9的位置已经确定，激光束正好打在光栅毛坯9的中心位置O，用虚线画出的第一针孔滤波器6和第二针孔滤波器7表示需要放入光路中的位置，它们的具体位置要根据具体数值和测距装置来确定。第四步，调整第二步中建立的测距装置在干涉场中的位置，使千分表的两个探头即千分表右探头14和千分表左探头15与激光的主光轴重合。第五步，根据球面波波源点与凹面全息光栅毛坯中心点的具体数值，结合游标卡尺、千分表和高度尺的刻度值，确定第一针孔滤波器6和第二针孔滤波器7的位置。第一针孔滤波器6和第二针孔滤波器7的针孔位置到凹面全息光栅毛坯中心点的距离就是所测的波源点到凹面全息光栅毛坯中心点的距离。The technical problem to be solved by the present invention is to provide a method for measuring the distance between the wave source point and the center point of the concave holographic grating blank in the optical path for the production of the concave holographic grating. The technical solution to solve the technical problem is as follows: the first step is to establish a set of concave holographic grating exposure device. As shown in Figure 1, it includes a Kr + laser 1, a first plane mirror 2, a half mirror 3, a second plane mirror 4 and a third plane mirror 5, a first pinhole filter 6 and a second needle Aperture filter 7 , interference field 8 and grating blank 9 . On the optical axis of the laser beam propagation direction of the Kr + laser 1, a first plane reflector 2 is placed, and the first plane reflector 2 forms an angle of 45° with the optical axis; on the optical path of the reflected light of the first plane reflector 2 A half-mirror 3 is provided, and its half-reflective surface forms an angle of 45° with the optical axis; a second flat reflector 4 is placed on the optical axis of the light emitted from the reflective surface and the transmissive surface of the half-reflective mirror 3 respectively and the third plane reflector 5; the first pinhole filter 6 and the second pinhole filter 7 are placed on the optical axis of the reflected light of the second plane reflector 4 and the third plane reflector 5 respectively; The intersecting area of the light emitted by the pinhole filter 6 and the second pinhole filter 7 forms an interference field 8; a grating blank 9 is built in the interference field 8, and the center point of the grating blank 9 is located at the center of the interference field 8. What the present invention is to measure is the distance between the source point of the spherical wave emitted by the first pinhole filter 6 and the second pinhole filter 7 and the center point of the grating blank 9, that is, the distance between the pinhole position and the center point of the blank. distance between. The second step is to prepare a set of devices for measuring the distance between the wave source point and the center point of the blank in the optical path of the concave holographic grating. As shown in FIG. 2 , it includes a slide rail 10 with a scale, a vernier 11 with a scale, an adapter rod 12 , a fixture 13 , a dial gauge right probe 14 , a dial gauge left probe 15 and a dial gauge 16 . The vernier 11 with scale is installed on the slide rail 10 with scale, and the two are in sliding contact. The combination of the two is equivalent to a vernier caliper, fixed on the lower end of the transfer rod 12, and perpendicular to the transfer rod 12, the clamp 13 is fixed on the upper end of the adapter rod 12 in the cavity of the adapter rod 12, the dial indicator 16 and its left and right probes are one piece, and the right probe 14 of the dial indicator passes through the clamp 13 horizontally and extends to the clamp On the right side of 13, the left probe 15 and the right probe 14 of dial gauge 16 are on the same horizontal axis. The third step is to use the optical path of the concave holographic grating exposure device established in the first step, as shown in Figure 3, the first pinhole filter 6 and the second pinhole filter 7 are not placed in the optical path, and the second plane reflection The positions of the mirror 4, the third plane mirror 5 and the grating blank 9 have been determined, and the laser beam hits the center position O of the grating blank 9, and the first pinhole filter 6 and the second pinhole filter drawn with dotted lines 7 represents the positions that need to be placed in the optical path, and their specific positions will be determined according to specific values and distance measuring devices. The fourth step is to adjust the position of the distance measuring device established in the second step in the interference field, so that the two probes of the dial gauge, namely the right probe 14 of the dial gauge and the left probe 15 of the dial gauge, coincide with the main optical axis of the laser . The fifth step is to determine the first pinhole filter 6 and the second pinhole filter 7 according to the specific values of the spherical wave source point and the center point of the concave holographic grating blank, combined with the scale values of the vernier caliper, dial indicator and height gauge. Location. The distance from the pinhole position of the first pinhole filter 6 and the second pinhole filter 7 to the center point of the concave holographic grating blank is the measured distance from the wave source point to the center point of the concave holographic grating blank.

本发明工作原理说明：采用游标卡尺、千分表和高度尺相结合的方法，将凹面全息光栅制作光路中不容易测量到的波源点与凹面全息光栅毛坯中心点之间的距离精确地测量出来。步骤一，建立一套凹面全息光栅曝光装置。步骤二，将制备的测量波源点到凹面全息光栅毛坯中心点距离的装置置于曝光装置的光路中，并且调整测距装置的位置，保持千分表探头与激光的主光轴重合。调整测距装置的位置，使激光束主光轴直射到千分表左探头15的中心，在滑轨上移动游标11，保持千分表右探头14和千分表左探头15与激光的主光轴重合，将游标11移动到千分表右探头14刚刚接触到光栅毛坯9的中心点。步骤三，确定第一针孔滤波器6和第二针孔滤波器7的位置。这里只讲述如何确定第一针孔滤波器6的位置，第二针孔滤波器7类同。①理论上计算出第一针孔滤波器6的针孔位置与光栅毛坯9的中心位置之间距离，用L表示；②用游标卡尺测量千分表两探头即右探头14与左探头15之间的距离，记为L1；③在千分表右探头14刚刚接触到光栅毛坯9的中心位置时记下滑轨10的刻度，向激光束方向移动游标，使其运行适当的距离L2，此时千分表左探头15与光栅毛坯9的中心点的距离为L1+L2，并且使L1+L2稍稍大于L；④将第一针孔滤波器6放置在光路中，并且距离千分表左探头15的位置很近，调节用于摆放第一针孔滤波器6的光具座上的前后调节螺丝，使第一针孔滤波器6向千分表左探头15方向移动直至接触，同时读取千分表16的刻度变化，将变化的数值记为L3，当L3＝L1+L2—L时停止调节，此时的位置就是理论计算出的第一针孔滤波器6的位置了。步骤四，记录测量出的具体数值，计算出激光光路中两点的距离。此时球面波波源点与凹面全息光栅毛坯中心点的距离就是L＝L1+L2—L3。Description of the working principle of the invention: the method of combining vernier calipers, dial indicators and height gauges is used to accurately measure the distance between the wave source point and the center point of the concave holographic grating blank, which is not easy to measure in the optical path of concave holographic grating production. Step 1, establishing a set of concave holographic grating exposure device. Step 2: Place the prepared device for measuring the distance from the wave source point to the center point of the concave holographic grating blank in the optical path of the exposure device, and adjust the position of the distance measuring device to keep the dial gauge probe coincident with the main optical axis of the laser. Adjust the position of the distance measuring device so that the main optical axis of the laser beam directly hits the center of the left probe 15 of the dial gauge, move the cursor 11 on the slide rail, and keep the right probe 14 of the dial gauge and the left probe 15 of the dial gauge in line with the main laser beam. The optical axes are coincident, and the vernier 11 is moved to the center point where the right probe 14 of the dial indicator just touches the grating blank 9 . Step 3, determining the positions of the first pinhole filter 6 and the second pinhole filter 7 . Only how to determine the position of the first pinhole filter 6 is described here, and the second pinhole filter 7 is similar. ① theoretically calculate the distance between the pinhole position of the first pinhole filter 6 and the center position of the grating blank 9, expressed by L; ② use a vernier caliper to measure the distance between the two probes of the dial gauge, namely the right probe 14 and the left probe 15 ③ When the right probe 14 of the dial indicator just touches the center position of the grating blank 9, write down the scale of the slide rail 10 , and move the cursor to the direction of the laser beam to make it run for an appropriate distance L 2 . The distance between the left probe 15 of the dial gauge and the center point of the grating blank 9 is L 1 +L 2 , and make L 1 +L 2 slightly larger than L; ④ Place the first pinhole filter 6 in the optical path, and the distance The position of the left probe 15 of the dial indicator is very close, adjust the front and rear adjustment screws on the optical bench for placing the first pinhole filter 6, so that the first pinhole filter 6 moves in the direction of the left probe 15 of the dial gauge Read the scale change of the dial gauge 16 at the same time, record the changed value as L 3 , stop adjusting when L 3 =L 1 +L 2 —L, the position at this time is the theoretically calculated first needle Aperture filter 6 is positioned. Step 4, record the measured specific values, and calculate the distance between two points in the laser light path. At this time, the distance between the spherical wave source point and the center point of the concave holographic grating blank is L=L 1 +L 2 −L 3 .

本发明的积极效果：本发明的方法是新型的、低成本的、易于实现的，可以准确快速地确定凹面全息光栅制作光路中球面波波源点与凹面全息光栅毛坯中心点的距离，在准确的位置放置球面波波源。这样就能制作出高质量的凹面全息光栅，该种光栅在光学系统中的应用能够减少系统的零部件，消除光学系统的象散和彗差。Positive effects of the present invention: the method of the present invention is novel, low-cost, and easy to implement, and can accurately and quickly determine the distance between the source point of the spherical wave and the center point of the concave holographic grating blank in the optical path for the production of the concave holographic grating. position to place the spherical wave source. In this way, a high-quality concave holographic grating can be produced. The application of this kind of grating in the optical system can reduce the components of the system and eliminate the astigmatism and coma of the optical system.

四、附图说明 4. Description of drawings

图1是本发明方法第一步建立的凹面全息光栅曝光装置光路结构示意图。图2是本发明方法第二步制备的测量光路波源点与凹面全息光栅毛坯中心点距离的装置的结构示意图。图3是本发明方法第三步利用第一步建立的凹面全息光栅曝光装置的光路未放入针孔滤波器时的光路结构示意图。Fig. 1 is a schematic diagram of the optical path structure of the concave holographic grating exposure device established in the first step of the method of the present invention. Fig. 2 is a structural schematic diagram of the device for measuring the distance between the wave source point of the optical path and the center point of the concave holographic grating blank prepared in the second step of the method of the present invention. Fig. 3 is a schematic view of the optical path structure when the optical path of the concave holographic grating exposure device established in the first step is used in the third step of the method of the present invention without a pinhole filter.

五、具体实施方式 5. Specific implementation

本发明按所建立的第一、第二、第三、第四、第五步方法实施。其中，第一步、建立的凹面全息光栅曝光装置中，光源1采用Kr+激光器，波长为413.1nm；第一平面反射镜2、第二平面反射镜4和第三平面反射镜5为玻璃基底镀铝反射镜；半反半透镜3为双胶合玻璃棱镜；第一针孔滤波器6和第二针孔滤波器7由显微物镜和针孔组成；光栅毛坯9采用K9光学玻璃，K9光学玻璃上涂敷的光致抗蚀剂为日本产的Shipley 1805型光致抗蚀剂；第二步、制备的测量光路波源点与凹面全息光栅毛坯中心点距离的装置中，滑轨10与游标11由高度尺组成；转接杆12与夹具13是机械加工的；千分表16是由哈尔滨量具刃具厂生产的，其精度为微米级；千分表右探头14和千分表左探头15是千分表16上自带的。The present invention implements according to the first, second, third, fourth and fifth step methods established. Among them, in the first step, in the concave holographic grating exposure device established, the light source 1 uses a Kr + laser with a wavelength of 413.1nm; the first plane mirror 2, the second plane mirror 4 and the third plane mirror 5 are glass substrates Aluminum-coated reflector; half mirror 3 is a double-glued glass prism; the first pinhole filter 6 and the second pinhole filter 7 are composed of a microscopic objective lens and a pinhole; the grating blank 9 is made of K9 optical glass, K9 optical glass The photoresist coated on the glass is the Shipley 1805 photoresist produced in Japan; in the second step, in the prepared device for measuring the distance between the wave source point of the optical path and the center point of the concave holographic grating blank, the slide rail 10 and the vernier 11 is composed of a height gauge; the adapter rod 12 and the fixture 13 are machined; the dial indicator 16 is produced by Harbin Measuring Tool and Cutting Tool Factory, and its accuracy is micron; the dial gauge right probe 14 and the dial gauge left probe 15 It comes with dial gauge 16.

Claims (1)

1, concave grating is made the method for measuring wave source point and blank central point distance in the light path, it is characterized in that: the first step, set up a cover concave holographic grating exposure device; Comprise Kr+ laser instrument (1), first plane mirror (2), half-reflecting half mirror (3), second plane mirror (4) and the 3rd plane mirror (5), first pinhole filter (6) and second pinhole filter (7), interference field (8) and grating blank (9); On the optical axis of the laser beam direction of propagation of Kr+ laser instrument (1), be equipped with first plane mirror (2), first plane mirror (2) and optical axis angle at 45; On the catoptrical light path of first plane mirror (2), be equipped with half-reflecting half mirror (3), its half-reflection and half-transmission face and optical axis angle at 45; On the optical axis of the reflecting surface of half-reflecting half mirror (3) and transmission plane emergent light, be equipped with second plane mirror (4) and the 3rd plane mirror (5) respectively; On the optical axis of the reflection ray of second plane mirror (4) and the 3rd plane mirror (5), be equipped with first pinhole filter (6) and second pinhole filter (7) respectively; The intersectional region of first pinhole filter (6) and second pinhole filter (7) emission light has formed interference field (8); Be built-in with grating blank (9) at interference field (8), the central point of grating blank (9) is positioned at the center of interference field (8); The present invention will measure is distance between the central point of the spherical wave wave source point that sends through first pinhole filter (6) and second pinhole filter (7) and grating blank (9), just the distance between pin hole position and the blank central point; In second step, preparation one cover is measured the device of distance between concave surface holographic grating production light path medium wave source point and the blank central point; Comprise the slide rail (10) that has scale, the vernier (11) that has scale, adapting rod (12), anchor clamps (13), the right probe of clock gauge (14), a clock gauge left side probe (15) and clock gauge (16); The vernier (11) that has scale is installed on the slide rail (10) that has scale, sliding contact between the two, both combinations are equivalent to vernier caliper, be fixed on the lower end of adapting rod (12), and it is vertical with adapting rod (12), anchor clamps (13) are in the upper end of adapting rod (12), be fixed in the chamber of adapting rod (12), clock gauge (16) and its left and right probe are integral pieces, the right probe of clock gauge (14) flatly passes anchor clamps (13), stretch to the right-hand of anchor clamps (13), the left side probe (15) of clock gauge (16) and right probe (14) are on same horizontal axis; The 3rd step, utilize the light path of the concave holographic grating exposure device of first step foundation, do not put first pinhole filter (6) and second pinhole filter (7) in the light path, and the position of second plane mirror (4), the 3rd plane mirror (5) and grating blank (9) has been determined, laser beam is just in time beaten the center O at grating blank (9), first pinhole filter (6) that with dashed lines draws and second pinhole filter (7) expression need be put into the position of light path, and their particular location will be determined according to concrete numerical value and distance measuring equipment; The 4th step, adjust the position of distance measuring equipment in interference field of setting up in second step, two probes that make clock gauge are that right probe of clock gauge (14) and clock gauge left side probe (15) overlap with the primary optical axis of laser; In the 5th step,,, determine the position of first pinhole filter (6) and second pinhole filter (7) in conjunction with the scale value of vernier caliper, clock gauge and height gauge according to the concrete numerical value of spherical wave wave source point with concave holographic grating blank central point; The pin hole position of first pinhole filter (6) and second pinhole filter (7) is exactly the distance that the wave source surveyed is put concave holographic grating blank central point to the distance of concave holographic grating blank central point.
CNB2006100169015A 2006-06-02 2006-06-02 Method for measuring distance between wave source point and roughcast centre point in concave grating production light path Expired - Fee Related CN100480622C (en)

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