TW479125B - Two dimensional displacement measurement method with conjugate optical paths - Google Patents
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479125 五、發明說明(l)【發明背景】 1 ·發明領域 本發明係提供一種共 別是一種對於光學元件間 射光栅間的對位誤差,具 =光路式二維位移量測方法,特 &,配精度,以及光學元件與繞 有N容許差之二維位移量測方法 2 ·發 對 量測模 光學尺LVDT ) 在中低 高精度 題,例 行度、 另外在 力的要 流動的 新 即直接 間相對 明背景 於二維運動位移量 組以正交方式組合 、磁性尺、電容式 、雷射干涉儀等, 精度的系統中是可 等級,正交架構的 如:兩軸間正交的 干涉儀的分光鏡/ 南精度需求下,正 求也提高許多,相 風險。 世代的作法是採用 將量測系統二維化 精度的問題,二維 的量測 成二維 感測器 都可以 行的, 做法就 精度、 反射鏡 交架構 對增加 ’傳統 的量測 、線性 依此方 但是當 會面臨 電容感 和光路 的做法 了教育 上是將 模組, 可變差 法組合 糸統的 愈來愈 測器感 之間的 對於使 訓練的 兩組 例如 維的 維的 動變壓器( 。這種做法 要求提高到 難克服的問 測面間的平 垂直度等, 用者技術能 成本和人才 目岫關於二維光學尺 t〇y〇 公司的us 5,204,524 積體式二維量測」的方法,亦 使用者不需要再去顧慮兩軸之 光學尺就是最好且最典型的例子 的相關技術已發表者有:Mitu — (1993) 、 Heidenhain 公司的us479125 V. Description of the invention (l) [Background of the invention] 1. Field of the invention The present invention provides a method for measuring the misalignment between the intersect gratings of optical elements. ;, With accuracy, and two-dimensional displacement measurement method of the tolerance between the optical element and N around it 2 · Send pair of measuring mode optical ruler LVDT) For low-to-medium accuracy problems, the degree of routine, and the flow of force The new method is to directly combine the relatively bright background with the two-dimensional motion displacement group in an orthogonal manner, magnetic ruler, capacitive type, laser interferometer, etc. The accuracy of the system is gradeable, and the orthogonal structure is as follows: The interferometer's beamsplitter / south precision requirements also increase the number of positive phase risks. The method of the generation is to use the problem of the two-dimensional accuracy of the measurement system. Two-dimensional measurement can be performed by two-dimensional sensors. The method is to increase the traditional measurement, linear dependence on the accuracy and the reflector architecture. This side, however, will face the practice of capacitive sensing and optical path. In education, the module and the variable-difference method are combined together. (. This method requires the level of verticality between the insurmountable measurement planes, etc., the technical cost of the user and the talents. About the two-dimensional optical rule t〇y〇 company's us 5,204,524 integrated two-dimensional measurement " This method, and the user does not need to worry about the two-axis optical ruler is the best and most typical example. Related technologies have been published by: Mitu — (1993), usid of Heidenhain Company
第4頁 479125 五、發明說明(2) 5,424, 833 (1995)、以及Optra 公司的US 5, 530,543 (1 99 6 )。 習用的二維光學尺,如專利US 5, 204, 524所述,採用 幾何式三光柵架構,其位移量測方法係利用當第一光栅和 其他元件發生相對運動時,光束受到光柵條紋的遮蔽作用 就會成為明暗相間的光訊號,經由光電檢測器的轉換可得 近似弦波的電訊號,再經解調電路的處理即可得知相對運 動的位移量,其在解析度和精度上由於幾何光學的諸多限 制,無法有效提昇至高精度等級。 如專利U S 5,4 2 4,8 3 3所述,採用雙光柵三次繞射式的 光路設計,光束經副光栅繞射之正負一階光束,再經主光 柵盤之反射及繞射作用,光束返回副光柵再經副光柵產生 一次繞射,經三次繞射後之光束可取出三個帶有兩光柵間 相對位移且相位各差一百二十度之訊號,此系統經過三次 光柵的繞射,對於光源的使用效率不佳,造成對系統組裝 精度及元件製作品質等級的要求相對提高。 如專利US 5, 5 3 0, 543所述,採用單光柵單光路繞射式 設計,光束經光栅盤繞射產生正負一階繞射光,利^光= 元件將正負一階繞射光重合,利用正負一階繞射光之干= 產生τ有位移訊號之干涉條紋’光電檢測器直接置、乂 負一階繞射光交會處,量測干涉訊號,該系統沒有於, 差的自我補償功能,致使系統對於光學元件和光、於誤 位精度要求甚高,不易得到穩定的輪出訊號。 a的對Page 4 479125 V. Description of the Invention (2) 5,424, 833 (1995), and US Pat. No. 5,530,543 (1 99 6). The conventional two-dimensional optical ruler, as described in the patent US 5, 204, 524, adopts a geometric three-grating structure. The displacement measurement method uses the light beam to be shielded by the grating stripes when the first grating and other components undergo relative movement. The effect will become a light signal between light and dark. The signal of an approximate sine wave can be obtained through the conversion of the photodetector. After processing by the demodulation circuit, the displacement of the relative motion can be obtained. Its resolution and accuracy are due to Many limitations of geometric optics cannot effectively improve to high precision levels. As described in US Pat. No. 5, 4 2 4, 8 3 3, a double-grating three-diffraction optical path design is adopted. The beam is diffracted by the positive and negative first-order beams diffracted by the sub-grating, and then reflected and diffracted by the main grating disk. The beam returns to the sub-grating and passes through the sub-grating to generate a diffraction. After three times of diffraction, the beam can take out three signals with a relative displacement between the two gratings and a phase difference of 120 degrees. Radiation, the use efficiency of the light source is not good, resulting in relatively higher requirements for system assembly accuracy and component production quality level. As described in the patent US 5, 530, 543, a single grating single optical path diffraction design is adopted, and the beam is diffracted by a grating disk to generate positive and negative first-order diffracted light. The interference of first-order diffraction light = generating interference fringes with τ displacement signal. The photodetector is placed directly at the intersection of the first-order diffraction light and the interference signal is measured. The system does not have the poor self-compensation function. Optical components and light have high requirements for misalignment accuracy, and it is not easy to obtain a stable wheel output signal. a's right
第5頁 479125 五、發明說明(3) 【發明目的] 旦 '則ΐ ΐ明之主要目的在於提供一種共轆光路式二 里測方法,該量測方法對於光學元件間的裝 70件與二維繞射光柵間的對位誤差,以及二:^ 身的光柵缺陷,具有高度的容許差。該量; 積體式二維量測法’大幅降低了量測系統對操作者 ^的依賴性’且@為具有高容許差的優&,對於旦 本身凡件的加工精度、元件間的組裝精度,以及二 兀件間的對位準度等,皆可大幅降低其 低r製造及組裝的成本,另-:面則 產口口的良率,達到產品普及化的目的。 如下有關本發明之詳細說明及技術内容,兹配合圖 【發明之詳細說明】 井/二第1圖』所示,係本發明之前段光路示意 m;係為一可發出近乎同調光之光源,其可 m偏振光或橢圓偏振光,該光源2 =一:亍化透鏡301後,形成-近乎平行化之第 =V _近乎入射點之法線方向入射在二 ϊ Λ入射點1011,該,射光栅1。1係經由 叶,使繞射光之能量集中在正負—階。 面心:次入射光901經二維繞:光柵101反射後 9111v個方位角產生四束正負-階的第-次 、913、914,亚和該第—次入射光9〇1間 維位移 、光學 光栅本 為採用 技術能 測糸統 對運動 如此, 可提南 式說明 圖 ,· - 為線偏 之光束 —次入 維繞射 適當設 ,在平 繞射光 具有相Page 5 479125 V. Description of the invention (3) [Objective of the invention] The main purpose of the invention is to provide a two-line optical measurement method with a common optical path. The misalignment between the diffraction gratings and the grating defects of the second and third bodies have a high tolerance. This quantity; the integrated two-dimensional measurement method 'significantly reduces the dependence of the measurement system on the operator ^', and @ is an excellent & with a high tolerance, for the accuracy of processing of various parts and assembly between components Accuracy and alignment between two components can greatly reduce its low-r manufacturing and assembly costs. In addition, the yield of the mouth is achieved to achieve the purpose of popularizing the product. The following detailed description and technical contents of the present invention are shown in the accompanying drawings [Detailed Description of the Invention] Well / 2 Figure 1 ", which is a schematic diagram of the optical path in the previous section of the present invention; it is a light source that can emit nearly the same light. It can be m-polarized light or elliptically polarized light. The light source 2 = one: after the lens 301 is formed, the-near-parallelized = V _ near the normal direction of the incident point is incident on the second Λ incident point 1011, The diffraction grating 1.1 passes through the leaves, so that the energy of the diffracted light is concentrated in the positive and negative-order. Face center: The secondary incident light 901 is two-dimensionally wound: after the grating 101 reflects 9111v azimuths, four positive-negative-order first-orders, 913, and 914 are generated, and the first-order incident light has a dimensional shift of 901, The optical grating is originally a technology that can measure the motion of the system. So we can refer to the South-style explanatory diagram. ··············································································································· ············
第6頁 479125 五、發明說明(4) 同的第一階繞射角,其在X —Y平面上的分量分別指向(丨,J ) 、(—I丨)、(―丨,—D、(丨,—1)四個方向,當該二維繞射光 柵101和光源201之間產生X-Y平面上的二維相對運動時, 由於都卜勒頻移效應(The Doppler Effect),該第一次繞 射光9 1 1、9 1 2、9 1 3、9 1 4將分別載有和二維運動位移量相 關的相位偏移訊號。 取其中的兩道第一次繞射光9 1 1和9 1 3,經由兩組利用 平行化透鏡311、313與平面反射鏡401、403所組成之波前 重建光學組件,循原光徑反射形成第二次入射光911,和91 3 ’ ’入射於該二維繞射光柵1 〇1之入射點丨〇丨丨。 該兩組波前重建光學組件的配置方法,係將平行化透 鏡3 1 1、3 1 3之光軸置於第一次繞射光9 1 1和9 1 3之光徑上, 該平面反射鏡401、403則垂直於該光軸,並使入射點ιοί 1 和平面反射鏡4 0 1、4 0 3的反射點4 0 1 1、4 0 3 1皆在該光軸上 ,並分別位於該平行化透鏡3 11、3 1 3之前焦點和後焦點上 ’此配置法應用了重建光學原理’使光束在第一次繞射時 形成的像差,在第二次繞射時由於經過兩次傅立葉轉換而 發生自我補償作用,讓第二次繞射光的光波波前回復至與 原來入射光具有同樣特性之平行波前,此一具波前重建特 性之光學設計方法可以有效提昇系統的偏位容忍度。 如『第2圖』所示,係本發明之後段光路示意圖,該 兩道第二次入射光911 ’和91 3 ’經二維繞射光柵1 〇 1反射後 ,在平面點對稱的四個方位角產生四束正負一階的第二次 繞射光921、922、923、924,該第二次繞射光921、922、Page 6 479125 V. Description of the invention (4) The same first-order diffraction angle, whose components on the X-Y plane point to (丨, J), (-I 丨), (-丨, -D, (丨, -1) In four directions, when a two-dimensional relative motion on the XY plane is generated between the two-dimensional diffraction grating 101 and the light source 201, the first Doppler effect is caused by the Doppler effect. The secondary diffracted lights 9 1 1, 9 1 2, 9 1 3, 9 1 4 will respectively carry phase shift signals related to the two-dimensional motion displacement. Take two of the first diffracted lights 9 1 1 and 9 1 3. Through two sets of wavefront reconstruction optical components composed of parallelizing lenses 311, 313 and plane mirrors 401, 403, reflecting the original optical path to form a second incident light 911, and 91 3 '' incident in the The incident point of the two-dimensional diffraction grating 1 〇1 丨 〇 丨 丨. The two sets of wavefront reconstruction optical components are arranged by placing the optical axes of the parallelizing lenses 3 1 1 and 3 1 3 on the first diffracted light. On the optical paths of 9 1 1 and 9 1 3, the plane mirrors 401 and 403 are perpendicular to the optical axis and make the incident points ι 1 and the plane mirrors 4 0 1, 4 0 3 The reflection points 4 0 1 1 and 4 0 3 1 are all on the optical axis and are respectively located at the front focus and the back focus of the parallelizing lens 3 11 and 3 1 3 'This configuration method applies the principle of reconstruction optics' to make the beam at The aberrations formed during the first diffraction are self-compensated due to two Fourier transforms during the second diffraction, so that the wavefront of the second diffraction light has the same characteristics as the original incident light. Parallel wavefront, this optical design method with wavefront reconstruction characteristics can effectively improve the system's tolerance for misalignment. As shown in "Figure 2", it is a schematic diagram of the optical path in the latter stage of the present invention, and the two incident light After 911 'and 91 3' are reflected by the two-dimensional diffraction grating 1 〇1, four positive and negative first-order diffracted lights 921, 922, 923, and 924 are generated at four azimuth angles symmetrical to the plane point. Secondary diffracted light 921, 922,
第7頁 479125 五、發明說明(5) 9 23、924和第一次入射光9〇1間的夾角皆相等,其在X-Y平 面上的分量分別指向(丨,〇 )、( 〇,1 )、( — 1,〇 )、( 〇,- 1 )四個 方向。 當二維繞射光柵101和其餘光學組件間產生X-Y平面上 的二維相對運動時,該第二次繞射光921、922、923、924 即載有和該二維運動位移量相關的相位偏移訊號,其中的 第二次繞射光921、923分別經平面反射鏡411、413形成反 射光束931、93 3,再經由偏極分光鏡501將該反射光束931 、9 33重合成載有干涉訊號的干涉光941 ;第二次繞射光92 2、924則分別經平面反射鏡412、414形成反射光束932、 9 34 ’再經由偏極分光鏡5〇2將該反射光束932、934重合成 載有干涉訊號的干涉光9 4 2。 最後將該干涉光9 4 1、9 4 2,經一般光干涉解相技術處 理後’即可同時得到該二維運動中兩個線性獨立方向上的 位移量。 以一柵距4mm、振輻高度〇.2111111的二維弦波光柵為例, 其在X-Y平面方向上的轉換函數可以近似地表示為·· [exp (i2 7rkx) + exp( ~12 π kx)] x [exp(i2 ;rky) + exp( —i2 7Γ ky)],其中k為傳播常數。 當第一次入射光9 〇 1垂直入射在二維繞射光柵丨〇 1的入 射點1 0 11 ’並經該二維繞射光柵1 〇 1反射後,其所產生的 第一次繞射光911、912、913、914在X-Y平面方向上的分 *可以分別表示為:exp(i27rk(x+y))、exp(i27rk(~x + y))、exp(i2 7rk(—χ—y))、exp(i2 7rk(x—y))。Page 7 479125 V. Description of the invention (5) 9 23, 924 and the first incident light 901 are equal in angle, and their components on the XY plane point to (丨, 〇), (〇, 1), respectively. , (— 1, 〇), (〇, -1) four directions. When a two-dimensional relative motion on the XY plane occurs between the two-dimensional diffraction grating 101 and the other optical components, the second diffraction light 921, 922, 923, 924 carries a phase deviation related to the two-dimensional motion displacement amount. Shift signal, the second diffracted light 921 and 923 form reflected light beams 931 and 93 3 through the plane mirrors 411 and 413 respectively, and then the reflected light beams 931 and 9 33 are recombined with the interference signal through the polarizing beam splitter 501 Interfering light 941; the second diffracted light 92 2 and 924 form reflected light beams 932 and 9 34 through the plane mirrors 412 and 414 respectively, and then the reflected light beams 932 and 934 are recombined by the polarizing beam splitter 502. Interference light 9 4 2 with interference signal. Finally, after the interference light 9 4 1 and 9 4 2 are processed by a general optical interference phase separation technique, the displacements in two linear independent directions in the two-dimensional movement can be obtained at the same time. Taking a two-dimensional sine wave grating with a grid pitch of 4mm and a height of 0.211111 as an example, its conversion function in the XY plane direction can be approximately expressed as ... [exp (i2 7rkx) + exp (~ 12 π kx )] x [exp (i2; rky) + exp (—i2 7Γ ky)], where k is the propagation constant. When the first incident light 9 〇1 is perpendicularly incident on the two-dimensional diffraction grating 1 0 11 ′ and reflected by the two-dimensional diffraction grating 1 〇 1, the first diffracted light generated by the first incident light 9 〇 1 The points of 911, 912, 913, and 914 in the XY plane direction can be expressed as: exp (i27rk (x + y)), exp (i27rk (~ x + y)), exp (i2 7rk (-χ-y )), Exp (i2 7rk (x-y)).
479125 五、發明說明(6) 一 备一維繞射光柵1 〇 1和光源2 〇 1之間產生X _ γ平面上的 二維相對運動時,其相位偏移量可以分別表示為:+ φχ + φγ、- d)X+(Dy、一 φχ-φγ、+ Φχ—Φ” 取第一次繞射光9 1 1、9 1 3,分別經相對應之波前重建 光學組件,循原光徑折回入射於二維繞射光柵1〇1的入射 點1011,並經該二維繞射光柵1〇1反射後,產生四束第二 次繞射光921、9 22、923、9 24。 一479125 V. Description of the invention (6) When a two-dimensional relative movement on the X _ γ plane is generated between a prepared one-dimensional diffraction grating 1 〇1 and a light source 2 〇1, the phase shifts can be expressed as: + φχ + φγ,-d) X + (Dy, a φχ-φγ, + Φχ—Φ ”Take the first diffracted light 9 1 1, 9 1 3, respectively, and reconstruct the optical components through the corresponding wavefronts, and retrace the original optical path. After incident on the incident point 1011 of the two-dimensional diffraction grating 101 and reflected by the two-dimensional diffraction grating 101, four second-diffraction light beams 921, 9 22, 923, and 9 24 are generated.
该第二次繞射光921、923,係分別由原分量為ex〆土 2 /rk(—x—y))、exp(l2;rk(x+y))之第一次繞射光913、 911 ,經相對應之波前重建光學組件折回入射於該二維繞 射光栅1 0 1的入射點1 0 11 ’並經該二維繞射光柵丨〇 1反射後 所形成’其分別載有一 2 (Dy、+ 2 〇y的相位偏移訊號,經 由相對應之平面反射鏡411和4 1 3 ’以及偏極分光鏡5 〇 1的 作用,將其重合形成載有干涉訊號的干涉光94 i ,最後經 光干涉解相技術處理後,即可解讀出二維運動中γ方向上 的位移量。同理可由第二次繞射光922、924,經由相對應 之平面反射鏡412和414 ’以及偏極分光鏡502的作用,形 成載有一 2 Φ X、+ 2 Φ X干涉訊號的干涉光9 4 2,解讀出二 維運動中X方向上的位移量。The second diffracted lights 921 and 923 are the first diffracted lights 913 and 911, respectively, whose original components are ex 〆 2 / rk (—x—y)) and exp (l2; rk (x + y)). , Formed by the corresponding wavefront reconstruction optical component reentering the incident point 1 0 11 incident on the two-dimensional diffraction grating 1 0 1 and formed by reflection of the two-dimensional diffraction grating 丨 〇1, which respectively contain a 2 (The phase shift signals of Dy and + 2 0y are superimposed to form interference light carrying an interference signal by the action of the corresponding plane mirrors 411 and 4 1 3 'and the polarizing beam splitter 5 01. Finally, after the optical interference phase-separation technology is processed, the displacement in the γ direction in the two-dimensional motion can be interpreted. Similarly, the second diffraction light 922 and 924 can be passed through the corresponding plane mirrors 412 and 414 ′ and The function of the polarizing beam splitter 502 forms an interference light 9 4 2 carrying an interference signal of 2 Φ X, + 2 Φ X, and interprets the amount of displacement in the X direction in a two-dimensional motion.
如『第3圖』所示,係本發明替代實施例之前段光路 不意圖’ """"^光源201所發出之光束經過^—平行化透鏡3 〇 1後 ,形成一近乎平行化之第一次入射光9 0 1 ,然後以近乎入 射點之法線方向入射在二維繞射光柵1 0 1的入射點丨〇丨丨, 經二維繞射光柵1 0 1反射後,在平面點對稱的四個方位角As shown in "Fig. 3", the optical path before the alternative embodiment of the present invention is not intended. &Quot; " " " ^ The light beam emitted by the light source 201 passes through the ^ -parallelizing lens 301, and forms an almost The first parallel incident light 9 0 1 is parallelized, and then incident on the two-dimensional diffraction grating 1 0 1 at an incidence point near the normal direction of the incident point, and reflected by the two-dimensional diffraction grating 1 0 1. , Four azimuths that are point-symmetric in the plane
第9頁 479125 五、發明說明(7) 產生四束正負一階的第一次繞射光9 π、9 1 2、9 1 3、9 1 4,, 並和該第一次入射光9 0 1間具有相同的第一階繞射角,其 在X-Y平面上的分量分別指向(1,1 )、(-1,1)、(―丨,—丨)、 · (1,-1)四個方向,當該二維繞射光栅1〇1和光源2〇1之間產 生X-Y平面上的二維相對運動時,由於都卜勒頻移效應, 該第一次繞射光91 1、912、913、914將分別载有和二維運 動位移量相關的相位偏移訊號。 該第一次繞射光9 11、9 1 2、9 1 3、9 1 4,經由四組利用 平行化透鏡311、312、313、314與平面反射鏡401、402、 4 0 3、4 0 4所組成之波前重建光學組件,循原光徑反射形成 第二次入射光911,、912,、913,、914,,入射於該二維繞 春 射光栅1 0 1之入射點1 0 1 1。 : 該四組波前重建光學組件的配置方法,係將平行化透 -鏡311、312、313、314之光軸置於第一次繞射光911、912 、913、914之光徑上,該平面反射鏡401、402、40 3、404 ‘ 則垂直於該光軸,並使入射點1 〇 11和平面反射鏡4 0 1、4 0 2 ^ 、4 0 3、404的反射點4011、4021、403 1、404 1皆在該光軸 上’並分別位於該平行化透鏡311、312、313、314之前焦 _ 點和後焦點上,此配置法應用了重建光學原理,使光束在 、 第一次繞射時形成的像差,在第二次繞射時由於經過兩次 傅立葉轉換而發生自我補償作用,讓第二次繞射光的光波 鲁 波前回復至與原來入射光具有同樣特性之平行波前,此一 具波前重建特性之光學設計方法可以有效提昇系統的偏位 容忍度。Page 9 479125 V. Description of the invention (7) Generate four first-order diffracted light beams 9 π, 9 1 2, 9 1 3, 9 1 4, and the first incident light 9 0 1 Have the same first-order diffraction angle between them, and their components on the XY plane point to (1,1), (-1,1), (― 丨, — 丨), and (1, -1) respectively Direction, when a two-dimensional relative motion on the XY plane occurs between the two-dimensional diffraction grating 100 and the light source 201, the first diffraction light 91 1, 912, 913 is due to the Doppler frequency shift effect. , 914 will carry phase shift signals related to two-dimensional motion displacement, respectively. The first diffracted light 9 11, 9 1 2, 9 1 3, 9 1 4 passes through four groups using the parallelizing lenses 311, 312, 313, and 314 and the flat mirror 401, 402, 4 0 3, 4 0 4 The formed wavefront reconstruction optical component reflects the original light path to form the second incident light 911, 912, 913, and 914, and is incident on the incident point 1 0 1 of the two-dimensional spring beam grating 1 0 1 1. : The configuration method of the four sets of wavefront reconstruction optical components is to set the optical axes of the parallelized trans-mirrors 311, 312, 313, and 314 on the optical paths of the first diffraction light 911, 912, 913, and 914. The plane mirrors 401, 402, 40 3, and 404 'are perpendicular to the optical axis, and the reflection points 4011 and 4021 of the plane reflection mirrors 401, 4 0 2 ^, 4 0 3, and 404 are made. , 403 1, 404 1 are all on the optical axis' and are located on the front focus point and the back focus of the parallelizing lenses 311, 312, 313, and 314, respectively. This configuration method applies the principle of reconstruction optics, so that the beam The aberrations formed during the first diffraction are self-compensated due to the two Fourier transforms during the second diffraction, so that the light wave front of the second diffraction light has the same characteristics as the original incident light. For parallel wavefronts, this optical design method with wavefront reconstruction characteristics can effectively improve the system's offset tolerance.
第10頁 479125Page 10 479125
如『第4圖』所示,係本發明替代實施例之後段光 示意圖,該第二次入射光911’ 、91 2,、913,、914,經二維 繞射光拇101反射後,在平面點對稱的四個方位角產生四 束正負一階的第二次繞射光9 2 1、9 2 2、9 2 3、9 2 4,該第一 次繞射光921、9 22、9 23、924和第一次入射光9〇][間 角皆相等’其在X-Y平面上的分量分別指向(1,〇)、(〇 $ 、(-1,0)、(0,-1)四個方向。 ’As shown in "Fig. 4", it is a schematic diagram of the light after the alternative embodiment of the present invention. The second incident light 911 ', 91 2, 913, and 914 are reflected by the two-dimensional diffracted light thumb 101 and are on a plane. The four azimuths with point symmetry generate four second-order diffracted light beams of the first and second order 9 2 1, 9, 2 2, 9 2 3, 9 2 4, the first diffracted lights 921, 9 22, 9 23, 924 And the first incident light 9〇] [the angles are all equal ', and their components on the XY plane point in four directions (1, 0), (〇 $, (-1, 0), (0, -1), respectively) ... '
當二維繞射光柵1 01和其餘光學組件間發生义—丫平面上 的二維相對運動時,該第二次繞射光921、922、923、9Μ 即載有和該二維運動位移量相關的光干涉訊號。 表後將该第一次繞射光9 2 1、9 2 2、9 2 3、9 2 4,經—般 光干涉解相技術處理後,即可同時得到該二維運動中個 線性獨立方向上的位移量。 Λ 以一柵距4mm、振輻高度〇· 2mm的二維弦波光栅為例, 其在X-Y平面方向上的轉換函數可以近似地表示為:[αρ (i2 7rkx) + exp( —i2 7rkx)] x [exp(i2 7rky) + exp( _·〇 7Γ ky )],其中k為傳播常數。When the two-dimensional relative motion on the sense-y plane occurs between the two-dimensional diffraction grating 101 and the other optical components, the second diffraction light 921, 922, 923, 9M is loaded with the two-dimensional motion displacement. Light interference signal. After the table, the first diffracted light 9 2 1, 9, 2 2, 9 2 3, 9 2 4 is processed by the ordinary light interference phase separation technology, and the linear independent directions in the two-dimensional movement can be obtained at the same time. The amount of displacement. Λ Taking a two-dimensional sine wave grating with a grid pitch of 4 mm and a height of 0.2 mm as an example, its transfer function in the XY plane direction can be approximately expressed as: [αρ (i2 7rkx) + exp (—i2 7rkx) ] x [exp (i2 7rky) + exp (_ · 〇7Γ ky)], where k is the propagation constant.
當第一次入射光9 〇 1垂直入射在二維繞射光柵丨〇 1的入 射,1011後,並經該二維繞射光柵1〇1反射後,其所產生 的^一次繞射光911、912、913、914在X-Y平面方向上的 刀里可以分別表示為:exp(i2vk(x+y))、exp(i2^( — y)) exP(i27rk(—χ—y))、eXp(i27rk(x—y))。When the first incident light 901 is perpendicularly incident on the two-dimensional diffraction grating 101, and after 1011, it is reflected by the two-dimensional diffraction grating 101, and the generated primary diffraction light 911, The blades of 912, 913, and 914 in the XY plane direction can be expressed as: exp (i2vk (x + y)), exp (i2 ^ (— y)) exP (i27rk (—χ—y)), eXp ( i27rk (x-y)).
一 當二維繞射光栅101和光源2〇1之間產生X-Y平面上的 一維相對運動時,其相位偏移量可以分別表示為:+❿X-When a one-dimensional relative motion on the X-Y plane occurs between the two-dimensional diffraction grating 101 and the light source 201, the phase shifts can be expressed as: + ❿X
第11頁 479125 五、發明說明(9) + 〇y、-Φχ + cDy、- φχ—φγ、+ φχ_φγ。 该第一次繞射光9 1 1、9 1 2、9 1 3、9 1 4,分別經相對應 之波刖重建光學組件,循原光徑折回入射於二維繞射光柵 1 0 1的入射點1 〇1丨,並經該二維繞射光柵丨〇 i反射後,產生 四束第二次繞射光921、922、923、924。 該第二次繞射光921,係由原分量為exp(i2 rk( — X + yD'expl^Trkl:—x~y))之第一次繞射光912、&13,分 別經相對應之波前重建光學組件折回入射於該二維繞射光 21 0 1的入射點1 〇 1 1,並經該二維繞射光柵1 〇 1反射後所組 口而成’其載有+ 2 Φ y和一2 Φ y的相位偏移訊號,經光干 f解相技術處理後,可解讀出二維運動中Y方向上的位移 里’ 4第二次繞射光9 2 2則載有+ 2 Φ X和一2 φ X的相位偏 移Λ號’經光干涉解相技術處理後,可解讀出二維運動中 X方向上的位移量,如此即可同時得到該二維運動中兩個 ^性獨立方向上的位移量。同理第二次繞射光9 2 3、9 2 4, 經光干涉解相技術處理後,亦可同時得到該二維運動中兩 個線性獨立方向Υ、X上的位移量。Page 11 479125 V. Description of the invention (9) + 〇y, -Φχ + cDy,-φχ—φγ, + φχ_φγ. The first diffracted light 9 1 1, 9 1 2, 9 1 3, 9 1 4 are respectively reconstructed through the corresponding wave chirps to rebuild the optical components, and the incident light incident on the two-dimensional diffraction grating 1 0 1 is turned back along the original optical path. After the point 1 〇1 丨 is reflected by the two-dimensional diffraction grating 丨 0i, four second diffracted lights 921, 922, 923, and 924 are generated. The second diffraction light 921 is composed of the first diffraction light 912 and & 13 whose original components are exp (i2 rk (— X + yD'expl ^ Trkl: —x ~ y)). The wavefront reconstruction optical component reenters the incident point 1 〇1 1 incident on the two-dimensional diffracted light 21 0 1 and is reflected by the two-dimensional diffractive grating 1 〇1 to form a port, which contains + 2 Φ y And a phase shift signal of 2 Φ y, which can be interpreted in the displacement in the Y direction in 2D motion after being processed by the photo-drying f phase-resolving technology. 4 The second diffraction light 9 2 2 contains + 2 Φ After the phase shift Λ 'of X and a 2 φ X is processed by the optical interference phase-separation technology, the displacement in the X direction in the two-dimensional motion can be interpreted, so that the two properties in the two-dimensional motion can be obtained at the same time. Amount of displacement in independent directions. Similarly, the second diffracted light 9 2 3 and 9 2 4 can also be obtained simultaneously by two optically independent directions Υ and X in the two-dimensional motion after being processed by the optical interference phase separation technology.
479125 圖式簡單說明 1 ·圖式之簡要說明 第1圖係本發明之前段光路示意圖。 第2圖係本發明之後段光路示意圖。 第3圖係本發明替代實施例之前段光路示意圖 第4圖係本發明替代實施例之後段光路示意圖 2 ·圖號之簡要說明 二維繞射光柵.....101 入射點........1011 光源.........2 01 平行化透鏡······ 3 0 1 平面反射鏡......401 411 反射點........4011 偏極分光鏡......501 第一次入射光.....901 第一次繞射光.....911 第二次入射光.....9 1 Γ 第二次繞射光· · · · · 9 21 反射光束.......931 干涉光........941 311 402 412 、40 2 1 502 312 403 413 313 404 414 314 4031 、 4041 912 、 913 、 914 、912’、913’、914’ 922 、 923 、 924 932 ^ 933 > 934 942479125 Brief description of the drawings 1 · Brief description of the drawings Figure 1 is a schematic diagram of the optical path in the previous stage of the present invention. Fig. 2 is a schematic diagram of the optical path at the later stage of the present invention. Figure 3 is a schematic diagram of the optical path before the alternative embodiment of the present invention. Figure 4 is a schematic diagram of the optical path after the alternative embodiment of the present invention. 2 Brief description of the drawing number. Two-dimensional diffraction grating. ... 1011 Light source ......... 2 01 Parallel lens ... 3 0 1 Flat mirror ... 401 411 Reflection point ... 4011 Polarizing Beamsplitter ... 501 First Incident Light ......... 901 First Diffraction Light ......... 911 Second Incident Light ... 9 1 Γ Second Diffractive light 9 21 Reflected light ... 931 Interfering light ......... 941 311 402 412, 40 2 1 502 312 403 413 313 404 414 314 4031, 4041 912, 913, 914, 912 ', 913', 914 '922, 923, 924 932 ^ 933 > 934 942
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