CN107462165A - High optical fine dual-frequency grating interferometer based on bigrating structures - Google Patents
High optical fine dual-frequency grating interferometer based on bigrating structures Download PDFInfo
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Abstract
本发明公开一种基于双光栅结构的高光学细分双频光栅干涉仪,该光栅干涉仪包括了双频正交激光器、非偏振分束镜、偏振分束镜、四分之一波片、反射镜、标尺光栅、指示光栅、偏振片、光电探测器、数据采集与处理单元等元器件。根据多普勒效应,激光非垂直入射在移动的测量光栅时,衍射光会携有多普勒频移项,该干涉仪利用激光多次在标尺光栅与指示光栅之间衍射,测量光携带多倍频移分量,因此该光栅干涉仪具有高光学细分结构。为提高测量光束信号强度,降低环境噪声的影响,标尺光栅与指示光栅皆为‑1级次高衍射效率反射式光栅。该发明在提高光栅干涉仪的分辨率与稳定性等测量领域都有重要价值。
The invention discloses a high optical subdivision dual-frequency grating interferometer based on a double-grating structure. The grating interferometer includes a dual-frequency orthogonal laser, a non-polarizing beam splitter, a polarizing beam splitter, a quarter-wave plate, Reflectors, scale gratings, index gratings, polarizers, photodetectors, data acquisition and processing units and other components. According to the Doppler effect, when the laser beam is non-perpendicularly incident on the moving measuring grating, the diffracted light will carry the Doppler frequency shift item. Doubling the frequency-shifted component, so the grating interferometer has a high optical subdivision structure. In order to improve the signal strength of the measurement beam and reduce the influence of environmental noise, both the scale grating and the indicator grating are ‑1 order high diffraction efficiency reflective gratings. The invention has great value in measurement fields such as improving the resolution and stability of the grating interferometer.
Description
技术领域technical field
本发明属于高精密度位移测量领域,特点是基于双光栅结构的高光学细分双频光栅干涉仪。The invention belongs to the field of high-precision displacement measurement, and is characterized by a high optical subdivision double-frequency grating interferometer based on a double-grating structure.
背景技术Background technique
随着高精度制造业向着微型化,便携式方向发展,对于微纳米级高精度定位和测量技术的需求在不断提高,特别是在加工和测量系统中的精确定位和测量。目前主要有两类系统用于测量微纳米精度位移,一类是激光干涉仪,另一类是光栅干涉仪。激光干涉仪被广泛应用于各种测量系统中。激光干涉仪具有高分辨率、高精度、大量程等优势,但其生产成本高,装置复杂,且由于激光干涉仪是以激光波长作为测量基准,易受到环境因素的影响,导致随机测量误差大,因此激光干涉仪的使用受到了一定限制。光栅干涉仪较好的弥补了这一缺陷,由于光栅干涉仪测量基准是光栅周期,因此光栅干涉仪的对于环境干扰因素的抵抗性强,故光栅干涉仪被广泛使用。With the development of high-precision manufacturing in the direction of miniaturization and portability, the demand for high-precision positioning and measurement technology at the micro-nano level is constantly increasing, especially in processing and measurement systems. At present, there are mainly two types of systems used to measure displacement with micronano precision, one is laser interferometer, and the other is grating interferometer. Laser interferometers are widely used in various measurement systems. The laser interferometer has the advantages of high resolution, high precision, and large range, but its production cost is high and the device is complicated, and because the laser interferometer uses the laser wavelength as the measurement reference, it is easily affected by environmental factors, resulting in large random measurement errors , so the use of laser interferometers is limited. The grating interferometer better makes up for this defect. Since the measurement basis of the grating interferometer is the grating period, the grating interferometer has strong resistance to environmental interference factors, so the grating interferometer is widely used.
无论是激光干涉仪还是光栅干涉仪,提高分辨率,都可对电子细分和光学细分进行提高。电子细分是在光学细分的基础上对于信号的识别。因此通过光路改进提高光学细分对于提高分辨率至关重要。现在市场广泛应用的德国的海德汉、英国的雷尼绍等光栅干涉仪一般采用一次衍射二倍光学细分,或二次衍射四倍光学细分。如海德汉的专利US5574558,美国IBM公司的专利US5442172。我国有专利发明采用高倍数光学细分如CN104729411A,CN104729402B,CN104613865A。本发明相较于以上发明,采用结构更为紧凑的不同周期双光栅自准直结构,制作工艺简单,成本低,安装公差小。本发明使用双光栅结构,旨在提高光学细分以及降低安装误差,最终提高光栅干涉仪的分辨率与精确性,若光栅制作精良,负一级衍射效率极高,达到90%及其以上,则理论上光学细分可以提高到三十二细分及其以上。Whether it is a laser interferometer or a grating interferometer, increasing the resolution can improve the electronic subdivision and optical subdivision. Electronic subdivision is the identification of signals based on optical subdivision. Therefore, it is very important to improve the optical subdivision by improving the optical path to improve the resolution. The grating interferometers such as Heidenhain in Germany and Renishaw in Britain, which are widely used in the market now, generally use the first-order diffraction double optical subdivision, or the second-order diffraction four-fold optical subdivision. Such as the patent US5574558 of Heidenhain, the patent US5442172 of IBM Corporation of the United States. There are patented inventions in my country that use high-magnification optical subdivision, such as CN104729411A, CN104729402B, and CN104613865A. Compared with the above inventions, the present invention adopts a more compact self-collimation structure of double gratings with different periods, simple manufacturing process, low cost and small installation tolerance. The present invention uses a double grating structure to improve optical subdivision and reduce installation errors, and finally improve the resolution and accuracy of the grating interferometer. If the grating is well-made, the negative first-order diffraction efficiency is extremely high, reaching 90% and above. Theoretically, the optical subdivision can be increased to thirty-two subdivisions and above.
发明内容Contents of the invention
本发明为基于双光栅的高光学细分双频光栅干涉仪,旨在解决现在市场广泛应用的光栅干涉仪光学细分倍数低的问题。本发明采用双光栅结构,一个标尺光栅,另一个为指示光栅,双光栅都为负一级高衍射效率光栅。利用测量光束以近似利特罗角入射标尺光栅,负一级光束出射至指示光栅,选取适合的指示光栅周期,使得负一级光束再次以近似利特罗角入射标尺光栅,再次发生高效率负一级衍射。测量光束在双光栅结构中来回衍射,最终以利特罗角入射指示光栅,光束沿原路返回。测量光束多次于移动的标尺光栅上进行负一级衍射,故光栅干涉仪光学细分得到提高。The invention is a dual-grating-based high optical subdivision dual-frequency grating interferometer, which aims to solve the problem of low optical subdivision multiples of the grating interferometer widely used in the market. The invention adopts a double grating structure, one is a scale grating and the other is an indicating grating, both of which are minus-order high diffraction efficiency gratings. The measurement beam is incident on the scale grating at an approximate Littrow angle, and the negative first-order beam is emitted to the index grating. A suitable period of the index grating is selected so that the negative first-stage beam enters the scale grating at an approximate Littrow angle again, and high-efficiency negative first order diffraction. The measuring beam is diffracted back and forth in the double grating structure, and finally enters the indicating grating at the Littrow angle, and the beam returns along the original path. The measuring beam is diffracted on the moving scale grating multiple times, so the optical subdivision of the grating interferometer is improved.
本发明的技术解决方案:Technical solution of the present invention:
一种基于双光栅结构的高光学细分双频光栅干涉仪,其特点在于,包括双频正交线偏振激光光源、非偏振分束器、偏振分束器、第一四分之一波片、第二四分之一波片、第一反射镜、第二反射镜、标尺光栅、指示光栅,以及由与双频正交偏振光成45°的第一检偏器和与之对应的第一光电探测器,与双频正交偏振光成45°的第二检偏器和与之对应第二光电探测器和数据采集与处理控制单元共同构成的解调相位单元;A highly optically subdivided dual-frequency grating interferometer based on a dual-grating structure, which is characterized in that it includes a dual-frequency orthogonal linearly polarized laser source, a non-polarizing beam splitter, a polarizing beam splitter, and a first quarter-wave plate , the second quarter-wave plate, the first reflector, the second reflector, the scale grating, the index grating, and the first analyzer with a 45° angle to the dual-frequency orthogonally polarized light and the corresponding first polarizer A photodetector, a second analyzer that is 45° to the dual-frequency orthogonally polarized light, and a demodulation phase unit that is jointly formed by the corresponding second photodetector and the data acquisition and processing control unit;
由激光光源射出的双频正交偏振光经过非偏振分束器分为反射光和透射光两部分,其中,反射光作为参考量进入与双频正交偏振光成45°的第一检偏器,第一光电探测器探测到作为双频外差干涉术的参考光的干涉信号,并传输至数据采集与处理控制单元;The dual-frequency orthogonally polarized light emitted by the laser light source is divided into reflected light and transmitted light through a non-polarizing beam splitter. The reflected light enters the first analyzer at 45° to the dual-frequency orthogonally polarized light as a reference quantity. device, the first photodetector detects the interference signal as the reference light of the dual-frequency heterodyne interferometry, and transmits it to the data acquisition and processing control unit;
透射光作为测量信号经过偏振分束器分为两束,一束为偏振态与入射面平行的P光,另一束为偏振态与入射面垂直的S光,S光经过第一四分之一波片变成左旋圆偏光,经第一反射镜反射后进入标尺光栅,经标尺光栅的-1级衍射光进入指示光栅,经指示光栅的-1级衍射光再次入射标尺光栅,依次左旋圆偏光在标尺光栅与指示光栅之间来回衍射,最终以利特罗角入射指示光栅,并依照原路返回经第一反射镜再次进入第一四分之一波片变为P光;由所述偏振分束器出射的P光经过第二四分之一波片变成右旋圆偏光,经第二反射镜镜反射后进入标尺光栅,经标尺光栅的-1级衍射光进入指示光栅,经指示光栅的-1级衍射光再次入射标尺光栅,依次右旋圆偏光在标尺光栅与指示光栅之间来回衍射,最终以利特罗角入射指示光栅,右旋圆偏光依照原路返回经第二反射镜再次进入第二四分之一波片变为S光;所述的原路返回的P光透过偏振分束镜和所述的原路返回的S光经偏振分束镜反射重合在同一光路上,共同入射到所述的第二检偏器形成干涉信号,由所述的第二探测器接收后作为双频外差干涉术的测量信号传输至数据采集和处理及控制单元。The transmitted light as the measurement signal is divided into two beams by a polarization beam splitter, one beam is P light whose polarization state is parallel to the incident plane, and the other beam is S light whose polarization state is perpendicular to the incident plane, and the S light passes through the first quarter A wave plate becomes left-handed circularly polarized light, which enters the scale grating after being reflected by the first mirror, and the -1 order diffracted light passing through the scale grating enters the indicating grating, and the -1 order diffracted light passing through the indicating grating enters the scale grating again, and turns left-handed circularly The polarized light diffracts back and forth between the scale grating and the index grating, and finally enters the index grating at the Littrow angle, and returns according to the original path, passes through the first reflector and enters the first quarter-wave plate again to become P light; The P light emitted by the polarizing beam splitter becomes right-handed circularly polarized light through the second quarter-wave plate, and enters the scale grating after being mirror-reflected by the second mirror, and the -1 order diffracted light through the scale grating enters the indicating grating, and passes through the The -1st-order diffracted light of the index grating enters the scale grating again, and the right-handed circularly polarized light diffracts back and forth between the scale grating and the index grating in turn, and finally enters the index grating at the Littrow angle, and the right-handed circularly polarized light returns through the second The reflector enters the second quarter-wave plate again to become S light; the P light returned by the original path passes through the polarizing beam splitter and the S light returned by the original path is reflected by the polarizing beam splitter and overlapped at On the same optical path, they are jointly incident on the second analyzer to form an interference signal, which is received by the second detector and transmitted to the data acquisition, processing and control unit as a measurement signal of dual-frequency heterodyne interferometry.
与现有技术相比,本发明的技术效果:Compared with prior art, technical effect of the present invention:
采用紧凑的不同周期双光栅自准直结构,使得测量光束在双光栅结构不断以近似利特罗角进行来回负一级衍射。由于多普勒效应,测量光束每次在测量光栅进行负一级衍射就会携带一个多普勒频移分量。最终测量光束以利特罗角入射光栅,并沿原路返回,此时频移分量加倍,两束测量光干涉与偏振分束器。A compact self-collimating structure of double gratings with different periods is adopted, so that the measurement beam continuously undergoes negative first-order diffraction back and forth at the approximate Littrow angle in the double grating structure. Due to the Doppler effect, each time the measurement beam undergoes negative order diffraction on the measurement grating, it will carry a Doppler frequency shift component. Finally, the measurement beam enters the grating at the Littrow angle and returns along the original path. At this time, the frequency shift component is doubled, and the two measurement beams interfere with the polarization beam splitter.
本发明为增强光栅干涉系统的环境抗性,采用对称结构,若单路测量光束在测量光栅进行N=3次负一级衍射,则该结构进行了12次光学细分。In order to enhance the environmental resistance of the grating interference system, the present invention adopts a symmetrical structure. If a single measuring beam performs N=3 times of negative first-order diffraction on the measuring grating, the structure performs 12 optical subdivisions.
附图说明Description of drawings
图1是本发明基于双光栅结构的高光学细分双频光栅干涉仪的结构示意图Fig. 1 is the structural representation of the high optical subdivision dual-frequency grating interferometer based on the double grating structure of the present invention
图2是单侧二倍光学细分双光栅示意图Figure 2 is a schematic diagram of double optical subdivision double grating on one side
图3是单侧四倍光学细分双光栅示意图Figure 3 is a schematic diagram of a four-fold optical subdivision double grating on one side
图4是单侧六倍光学细分双光栅示意图Figure 4 is a schematic diagram of a single-side six-fold optical subdivision double grating
具体实施方式detailed description
下面结合实施例和附图对本发明作进一步说明,但不应以此限制本发明的保护范围。The present invention will be further described below in conjunction with the embodiments and accompanying drawings, but the protection scope of the present invention should not be limited thereby.
图1是本发明基于双光栅结构的高光学细分双频光栅干涉仪的结构示意图,如图所示,双频正交线偏振激光光源9发出正交双频偏振光束经非偏振分束器8分为两束,一束射入第一检偏器10形成干涉信号,由第一探测器12接收后作为双频外差干涉术的参考信号传输至数据采集和处理及控制单元14,另一束经偏振分束器7分为透射的P光和反射的S光。由偏振分束器7出来的所述的S光经第一四分之一波片5变为左旋圆偏光,经第一反射镜3入射到高密度标尺光栅1,经标尺光栅1衍射的-1级次衍射光打到指示光栅2,经指示光栅2进行-1级衍射再次入射到高密度标尺光栅1,依此左旋圆偏光在标尺光栅1和指示光栅2之间来回衍射,并最终以利特罗角入射到指示光栅2上,左旋圆偏光沿原光路返回经第一反射镜3,经第一四分之一波片5变为P光。由偏振分束器7出来的所述的P光经第二四分之一波片6变为右旋圆偏光,经第二反射镜4入射到高密度标尺光栅1,经标尺光栅1衍射的-1级次衍射光打到指示光栅2,经指示光栅2的-1衍射光再次入射到高密度标尺光栅1,依此右旋圆偏光在标尺光栅1和指示光栅2之间来回衍射,并最终以利特罗角入射指示光栅2,右旋圆偏光沿原光路返回经第二反射镜4,经第二四分之一波片变6为S光。原路返回的S光透过偏振分光镜和原路返回的P光经偏振分光镜7反射重合在同一光路上,共同经入射到第二检偏器11形成干涉信号,由第二探测器13接收后作为双频外差干涉术的测量信号传输至数据采集和处理及控制单元14。通过分析参考信号和测量信号即可获得标尺光栅1的位移。Fig. 1 is a structural schematic diagram of a high optical subdivision dual-frequency grating interferometer based on a dual-grating structure in the present invention. As shown in the figure, a dual-frequency orthogonal linearly polarized laser light source 9 emits an orthogonal dual-frequency polarized beam through a non-polarizing beam splitter 8 is divided into two beams, one beam is injected into the first analyzer 10 to form an interference signal, and after being received by the first detector 12, it is transmitted to the data acquisition, processing and control unit 14 as a reference signal of dual-frequency heterodyne interferometry, and the other One beam is split into transmitted P light and reflected S light by a polarizing beam splitter 7 . The S light coming out of the polarizing beam splitter 7 is transformed into left-handed circularly polarized light through the first quarter-wave plate 5, and enters the high-density scale grating 1 through the first reflector 3, and the diffracted by the scale grating 1- The 1st-order diffracted light hits the index grating 2, undergoes -1-order diffraction through the index grating 2, and then enters the high-density scale grating 1, and then the left-handed circularly polarized light diffracts back and forth between the scale grating 1 and the index grating 2, and finally forms a The Littrow angle is incident on the index grating 2, and the left-handed circularly polarized light returns along the original optical path through the first mirror 3, and becomes P light through the first quarter-wave plate 5. The P light coming out of the polarizing beam splitter 7 is transformed into right-handed circularly polarized light through the second quarter-wave plate 6, enters the high-density scale grating 1 through the second reflector 4, and is diffracted by the scale grating 1 The -1 order diffracted light hits the index grating 2, and the -1 diffracted light of the index grating 2 enters the high-density scale grating 1 again, and accordingly the right-handed circularly polarized light diffracts back and forth between the scale grating 1 and the index grating 2, and Finally, the index grating 2 is incident at the Littrow angle, and the right-handed circularly polarized light returns along the original optical path through the second mirror 4, and becomes S light through the second quarter-wave plate. The S light returning from the original path passes through the polarizing beam splitter and the P light returning from the original path is reflected by the polarizing beam splitter 7 and overlapped on the same optical path, and they are incident on the second analyzer 11 to form an interference signal, which is detected by the second detector 13 After receiving, it is transmitted to the data acquisition and processing and control unit 14 as a measurement signal of dual-frequency heterodyne interferometry. The displacement of the scale grating 1 can be obtained by analyzing the reference signal and the measurement signal.
由于两束测量光对称入射双光栅结构,故对单侧结构进行分析。Since the two beams of measuring light are symmetrically incident on the double-grating structure, the single-side structure is analyzed.
如图二所示,光束从偏振分光镜7出射后,经过四分之一波片6,入射第二反射镜(4),反射进入双光栅结构。第二反射镜4与标尺光栅1的夹角为:As shown in Figure 2, after the light beam emerges from the polarizing beam splitter 7, it passes through the quarter-wave plate 6, enters the second mirror (4), and is reflected into the double grating structure. The angle between the second mirror 4 and the scale grating 1 is:
η为第二反射镜4与标尺光栅1的夹角,in为光线第一次入射标尺光栅的入射角。光线由第二反射镜4进入标尺光栅和指示光栅,进入标尺光栅的入射角分别为in,in-1,in-2…i3,i2,i1,标尺光栅上的衍射角依次为θn,θn-1,θn-2…θ3,θ2,θ1,光线由标尺光栅衍射后,进入指示光栅,入射角依次为i'n,i'n-1,i'n-2…i'3,i'2,i1'.指示光栅的衍射角为αn,αn-1,αn-2…α3,α2,α1。η is the angle between the second reflector 4 and the scale grating 1, and in is the incident angle of the light incident on the scale grating for the first time. The light enters the scale grating and the index grating from the second reflector 4, and the incident angles entering the scale grating are i n , i n-1 , i n-2 ... i 3 , i 2 , i 1 , and the diffraction angles on the scale grating θ n , θ n-1 , θ n-2 ... θ 3 , θ 2 , θ 1 , the light is diffracted by the scale grating and then enters the index grating, and the incident angles are i' n , i' n-1 , i ' n-2 ...i' 3 , i' 2 , i 1 '. Indicates that the diffraction angles of the grating are α n , α n-1 , α n-2 ... α 3 , α 2 , α 1 .
在测量光栅上,入射角in和衍射角θn满足光栅方程:On the measurement grating, the incident angle i n and the diffraction angle θ n satisfy the grating equation:
d1*(sin in+sinθn)=mλ (1)d 1 *(sin i n +sinθ n )=mλ (1)
式中d1为标尺光栅的周期,λ为激光波长,m为衍射级次,在此专利中m=-1In the formula, d 1 is the period of the scale grating, λ is the laser wavelength, and m is the diffraction order. In this patent, m=-1
在标尺光栅上,入射角i'n和衍射角αn同样满足光栅方程:On the scale grating, the incident angle i' n and the diffraction angle α n also satisfy the grating equation:
d2*sin(i'n+αn)=mλ (2)d 2 *sin(i' n +α n )=mλ (2)
式中d2为测量光栅周期,λ为激光波长,m为衍射级次,在此专利中m=-1In the formula, d 2 is the measurement grating period, λ is the laser wavelength, m is the diffraction order, and m=-1 in this patent
且满足如下的角度关系:And satisfy the following angle relationship:
θn=i'n (3)θ n =i' n (3)
αn=in-1 (4)α n =i n-1 (4)
i'1=α1 (5)i' 1 =α 1 (5)
当确定d1、d2以及测量光束衍射次数n时,可通过以上5个方程确定在标尺光栅和指示光栅上的光路,以及第二反射镜4的安装角度。When determining d 1 , d 2 and the diffraction number n of the measuring beam, the optical path on the scale grating and indicating grating and the installation angle of the second reflector 4 can be determined through the above five equations.
在实例中,如图二所示,n=1,d1=1000nm、d2=1500nm、λ=632.8nm,标尺光栅上的入射角为i1=24.9525°,衍射角为θ1=12.1771°,指示光栅上的入射角为i′1=12.1771°,衍射角为α1=12.1771°。反射镜与标尺光栅的夹角为79.9788°,假设光栅负一级衍射效率为95%,原路返回光强为入射光强的85.7375%,即入射标尺光栅结构的探测光功率为20mw,原路返回到达偏振分束器的光功率为19mw,可达到光电探测器阈值功率。In the example, as shown in Figure 2, n=1, d 1 =1000nm, d 2 =1500nm, λ=632.8nm, the incident angle on the scale grating is i 1 =24.9525°, and the diffraction angle is θ 1 =12.1771° , indicating that the incident angle on the grating is i′ 1 =12.1771°, and the diffraction angle is α 1 =12.1771°. The included angle between the reflector and the scale grating is 79.9788°, assuming that the negative first-order diffraction efficiency of the grating is 95%, the return light intensity of the original path is 85.7375% of the incident light intensity, that is, the detection light power of the incident scale grating structure is 20mw, and the original path The optical power returned to the polarization beam splitter is 19mw, which can reach the threshold power of the photodetector.
如图三所示,n=2,d1=1000nm、d2=1300nm、λ=632.8nm,标尺光栅上的入射角依次为i1=22.9181°,i2=32.3741°,衍射角依次为θ1=14.0864°,θ2=5.5868°,指示光栅上的入射角依次为i′1=14.0864°,i'2=5.5868°,衍射角依次为α1=14.0864°,α2=22.9181°。反射镜与标尺光栅的夹角为83.6871°,假设光栅负一级衍射效率为95%,原路返回光强为入射光强的69.8337%,即入射标尺光栅结构的探测光功率为20mw,原路返回到达偏振分束器的光功率为13.96674mw,可达到光电探测器阈值功率。As shown in Figure 3, n=2, d 1 =1000nm, d 2 =1300nm, λ=632.8nm, the incident angle on the scale grating is i 1 =22.9181°, i 2 =32.3741°, and the diffraction angle is θ 1 =14.0864°, θ 2 =5.5868°, indicating that the incident angles on the grating are i′ 1 =14.0864°, i′ 2 =5.5868°, and the diffraction angles are α 1 =14.0864°, α 2 =22.9181°. The included angle between the reflector and the scale grating is 83.6871°, assuming that the negative first-order diffraction efficiency of the grating is 95%, the return light intensity of the original path is 69.8337% of the incident light intensity, that is, the detection light power of the incident scale grating structure is 20mw, and the original path The light power returned to the polarization beam splitter is 13.96674mw, which can reach the threshold power of the photodetector.
如图四所示,n=3,d1=1000nm、d2=1100nm、λ=632.8nm,标尺光栅上的入射角依次为i1=20.1918°,i2=23.7645°,i3=27.4012°,衍射角依次为θ1=16.7165°,θ2=13.3035°,θ3=9.9380°。指示光栅上的入射角依次为i′1=16.7165°,i'2=13.3035°,i'3=9.9380°,衍射角依次为,α1=16.7165°,α2=20.1918°,α3=23.7465°。反射镜与标尺光栅的夹角为81.2006°。假设光栅负一级衍射效率为95%,原路返回光强为入射光强的56.88%,即入射标尺光栅结构的探测光功率为20mw,原路返回到达偏振分束器的光功率为11.376mw可达到光电探测器阈值功率。三种衍射情况如表1所示。As shown in Figure 4, n=3, d 1 =1000nm, d 2 =1100nm, λ=632.8nm, and the incident angles on the scale grating are i 1 =20.1918°, i 2 =23.7645°, i 3 =27.4012° , the diffraction angles are θ 1 =16.7165°, θ 2 =13.3035°, θ 3 =9.9380° in turn. The incident angles on the indicating grating are i′ 1 =16.7165°, i’ 2 =13.3035°, i’ 3 =9.9380°, and the diffraction angles are, α 1 =16.7165°, α 2 =20.1918°, α 3 =23.7465 °. The included angle between the mirror and the scale grating is 81.2006°. Assuming that the grating’s negative first-order diffraction efficiency is 95%, the original return light intensity is 56.88% of the incident light intensity, that is, the detection light power of the incident scale grating structure is 20mw, and the original return light power reaching the polarization beam splitter is 11.376mw Achievable photodetector threshold power. The three diffraction situations are shown in Table 1.
表1Table 1
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