200930976 六、發明說明： 【發明所屬之技術領域】 本發明關於一種形狀測定方法，特別是關於一種具有圓 柱形狀或多角柱形狀的外周面及在與該等外周面垂直的平 面上之曲面的構造體的形狀測定方法。 【先前技術】 近幾年，在攜帶電話及數位相機等中所使用的非球面透 鏡，居多係將透鏡外形沿著圓筒狀的鏡筒作固定。因此爲了 〇 使商品的產率上升，在與透鏡插入鏡筒時相同的條件下，求 得以圓筒作爲基準時的透鏡光軸之傾斜及偏心量，已成爲光 學領域上的課題。 習知係以透鏡的外形作爲基準而算出透鏡光軸之傾斜 或偏心量。在特開2002-71344公報中所記載的方法中，在透 鏡的外周部使3個球狀物作接觸，由於通過各球狀物之中心 的圓之求得，求得透鏡外形。在透鏡的外周部係理想的圓筒 面（即圓柱形狀的外周面），且透鏡之底面爲平面的情況下， @ 具有以透鏡的外形及底面作爲基準而求得光軸的傾斜及偏 心量的可能。 在該形狀測定方法中所使用的形狀測定機中，使探針與 被測定物作接觸的狀態下在XY方向上作相對移動，求得在 探針追蹤被測定物的形狀而在Z方向上作移動時之在各χγ 座標位置的Z座標資料之列，根據該XYZ座標資料列進行 被測定面的形狀測定。在此XYZ係互相垂直之方向。 如係具有圓筒面與曲面的透鏡，設置成其w軸（在自圓 筒面略等距離之位置的中心軸）與測定機的Z軸平行，對探 -3- 200930976 針僅在Z方向上施加伺服（servo)。但是在此方法中’相對 XY平面的透鏡之測定部位的傾斜角度Θ變的越大伺服之追 蹤越困難，測定精度變差，而相對XY平面75度左右係可測 定之最大的傾斜角度0的界限。 這是因爲構成有探針的氣滑（airslide)在XY方向上的剛 性很高而僅可在 Z方向上移動，且因爲當施加例如 0.3111\( = 3〇11^〇之力時，探針前端的針尖之傾倒量係11111等級 之故。爲此，雖然至傾斜角度75度爲止可以nm等級之高精 Q 度作測定，但是由於圓筒面具90度的傾斜角，故以在Z方 向上之伺服無法進行追蹤，而無法進行測定。爲了消除此等 測定的限制，在上述之透鏡的外周部使3個球狀物作接觸的 測定方法已被提出。 特開2007- 1 55 628公報中記載的方法中，在具有3個球 狀部之測定用夾具中，設置用以測定非球面透鏡（具透鏡第1 面及透鏡第2面）之外周部的三次元形狀之測定空間。在該 夾具中保持非球面透鏡，由於探針對該透鏡第1面及透鏡第 @ 2面之表面形狀進行掃描而得到以3球狀部作爲基準之座標 的點列資料，此外由於探針對在透鏡的外周部之作爲基準的 圓筒面及3球狀部進行掃描，得到以3球狀部作爲基準之座 標的點群資料，藉由此等資料，求得圓筒面與透鏡第1面及 透鏡第2面的相對位置。 特許第3827493號公報中，揭示關於在端部具有轉寫面 的軸部在基座上豎立的透鏡模型之形狀測定方法。此方法 中’在別台已取得追溯性之測定機中預先測定3個球的各別 直徑’在軸部之圓筒面及底座之上面雙者與3球作接觸的狀 態下以探針追蹤3球及轉寫面而求得資料列，藉此求得通過 -4- 200930976 3球之頂點的圓，以基座之上面及軸部之圓筒面作爲基準， 求得轉寫面之光軸的傾斜及偏心量。 但是上述之特開2002-7 1 344公報中記載的方法，有在真 元度變形、在表面粗糙度係粗糙的情況下，只要與作爲定位 夾具之球狀物的透鏡外形作接觸之位置有些許差距，以透鏡 外形作爲基準之光軸的傾斜及偏心量的再現性將變差，而無 法滿足所望之精度的問題。例如，在透鏡之光軸的偏心量的 所望精度在1 μπι以下的情況，若透鏡外形的形狀精度或表面 > 粗糙度在1 μιη以上，則無法使用該測定方法。 且在特開2007- 1 55628公報中記載的方法，如上述，在 夾具中設置測定空間，雖對作爲基準之圓筒面的三次元形狀 作測定，但有與特開2002-7 1 344公報中記載的方法相同的問 題。且此方法中，在測定透鏡第1面時，雖然使用相對Ζ方 向之1方向而可測定之表面形狀測定裝置並從上方對透鏡第 1面及3球進行掃描，而在測定圓筒面時，雖然使用不管從 上方或橫方探針皆可抵觸之一般的三次元測定機而從側方 > 對圓筒面進行掃描及從上方對3球進行掃描，但是由於一般 的三次元測定機的精度爲μιη等級，因此有無法以在透鏡求 得之以0.1 μιη等級的精度作測定的問題。 此外，現況係雖然只要可對包括表面、背面及側面之全 方位的面以0.1 μιη等級的精度進行測定評估，即可大致上解 決關於透鏡形狀之精度評估的問題，但是由於測定機本身之 精度不足或探針等的測定方式的限制，而無法進行相關的測 定評估。 在特許第3827493號公報中所記載的方法，有在透鏡模 型之軸部的圓筒度及真圓度變形以及在表面粗糙度爲粗糙 -5- 200930976 的情況下，只要相對軸部的圓筒面之作爲定位夾具之球的接 觸位置有些許差距，就會使以軸部的圓筒面作爲基準之轉寫 面的光軸之傾斜及偏心量的再現性變差而無法滿足所望之 精度的問題。例如，轉寫面之光軸的偏心量之所望精度在 0.5 μιη以下的情況，如果軸部的形狀精度或表面粗糙度超過 0.5 μηι，則無法使用該測定方法。關於特開2002-7 1 344公報 中所記載的方法亦係與所述同樣的問題。一般而言，相較於 透鏡有對模型要求較高精度之傾向。 Q 【發明内容】 本發明係解決上述問題者，目的在於提供一種形狀測定 方法，可高精度地測定以插入有透鏡之鏡筒的圓筒面作爲基 準時之透鏡光軸的傾斜及偏心量。目的在於提供一種形狀測 定方法，關於不限制係透鏡的被測定物，例如關於在端部持 有轉寫面的軸部在基座上豎立之透鏡模型，可求得以基座的 上面以及軸部的圓筒面作爲基準時之轉寫面之光軸的傾斜 及偏心量。且，目的在於提供一種形狀測定方法，可對包括 〇 透鏡的表面、背面及側面之全方位的面以0.1 μιη等級的精度 進行測定評估。且，目的在於提供一種形狀測定方法，可算 出以透鏡的表面（或背面）之光軸作爲基準時之透鏡背面（或 表面）之光的傾斜及偏心量。 爲瞭解決上述之課題，本發明的形狀測定方法係藉由於 探針沿著被測定物的測定面上作掃描，根據透過該探針取得 之ΧΥΖ座標資料，測定該被測定物的三次元形狀的形狀測 定方法，其中該探針可在Ζ方向自由移動並且被保持在可 驅動於互相垂直之X及Υ軸方向之移動體上，其特徵在於： -6- 200930976 該被測物係具有圓柱形狀或多角柱形狀之外周面及與該外 周面垂直之平面上的曲面，且係具有與該外周面平行並通過 重心位置的中心軸的構造體，將該被測定物以同軸狀設置在 具有被測定物固定部及配置於固定部周圍的3個球狀部的夾 具內，將該被測定物及夾具傾斜成使該中心軸以相對沿著X 軸及Y軸方向之XY平面以既定的角度傾斜，使該傾斜之被 測定物及夾具以既定之相同角度在中心軸周圍迴轉，並在各 迴轉位置，由於探針在既定的經路上對該3個球狀部與被測 〇 定物的外周面及其片測面進行追蹤取得各球狀部的測定資 料及被測定物的測定資料群，自測定資料算出在各迴轉位置 上的該3個球狀部的中心位置声標値，由於以最小平方法加 以配適，將在全回全迴轉位置上的被測定物的測定資料群在 遍及該中心軸周圍全周上以該3個球狀部基準進行分佈，並 在該分佈後自測定資料群求得該被測定物的測定面之形 狀。被測定面的曲面可爲凸面、凹面或者凹凸複合面。夾具 的傾斜角度可爲15度~72度。 〇 在被測定物具有非球面的光軸時，自全迴轉位置之被測 定物的測定資料群中抽出外周面測定資料群，自該抽出的外 周面測定資料群，算出與夾具的被測定物固定部之固定平面 垂直且作爲與被測定物的外接面外接的外接圓筒面之基準 的中心軸。 在被測定物具有非球面的光軸時，自全迴轉位置之被測 定物的測定資料群中抽出外周面的片側之面的側定資料 群’將抽出的片側面測定資料群分離爲非球面資料群及邊緣 部資料群，自分離的邊緣部資料群求得邊緣部平面，自該抽 -7- 200930976 出之片側面測定資料群，算出該邊緣部平面垂直且作爲與被 測定物的外周面外接之外接圓筒面的基準之中心軸，並算出 以該外接圓筒面基準之中心軸作爲基準時的該非球面的光 軸之傾斜及偏心量。 在被測定物具有非球面的光軸時，自全迴轉位置之被測 定物的測定資料群中抽出外周面的片側之面的測定資料 群，將抽出的片側面測定資料群分離爲非球面資料群及邊緣 部資料群，以分離的非球面資料群及其設計式之差進行RMS 0 最小化的座標變換，求得在該被測定物之外周面或片側面上 的測定値之在3次元空間中的差距量及差距方向。 被測定物之重心的位置在連結夾具之3個球狀部的中心 i1 所成之三角形區域上。被測定固定部具有對被測定物進行空 氣吸著之吸著部。夾具的被測定物固定部係在吸著部的外周 側具有被測定物支援部。 在被測定物的外周面及夾具的被測定物固定部的側面 上設有定位用的記號。在被測定物固定部的上面的測定軌跡 〇 係圓狀。 關於被測定物的外周面及作爲其兩側的面之表面及背 面的界線A與B之間所包圍的區域，藉探針在XY方向上以 沿著界線A或界線B之測定軌跡進行追蹤。 被測定物，位於外周面兩側的位置之表面部及背面部， 各別由與該外周面垂直之平面及曲面組成，在該被測定物的 外周面及夾具的被測定物固定部的外周面上形成有定位用 記號，關於該被測定物的表面部，在使兩記號一致而在該夾 具的被測定物固定部上固定該被測定物的狀態下，以該被測 -8- 200930976 於定 關測 , 被 群之 料具 資夾 β該 測在 得而 取致 準一 基號 爲記 作兩 面使 平在 部， 面部 背面 及背 面的 周物 外定 的測 物被 定該 物固定部上固疋該被測定物的狀態下，以該被測定物的外周 面及表面不平面作爲基準取得測定資料群，結合雙方的測定 資料群，可取得自被測定物全方位所見之所有測定資料群。 【實施方式】 以下，關於本發明的實施形態，一面參照圖面一面作說 明。 Ο 第1圖係圖示本發明之形狀測定方法中所使用之形狀測 定機。在形狀測定機的XYZ座標系中，XY方向係在基座平 .，臺61之表面上垂直的兩個方向，Z方向係與XY方向垂直之 方向。XY台階69及70係被驅動朝向XY方向者，在χγ台 階69及70上安裝有平臺板63，在平臺板63上配置有作爲 長度之世界標準的發振頻率安定化He-Ne雷射71。而且在平 臺板63安裝有Z台階64，而在Z台階64安裝有探針65。 此外，具有奈米等級之高平面度的X基準鏡66、Y基準鏡 ® 67及Z基準鏡68係配置在既定的位置上。藉此，在X基準 鏡66、Y基準鏡67及Z基準鏡68反射來自雷射71之雷射 光，可對各種距離進行測長。 由於以使探針的前端位在X軸雷射測長62a、Y軸雷射 測長62b及Z軸雷射測長62c之延長的槪略位置而構成，就 算在進行測定中移動台有振動起伏，也可幾乎忽略其影f。 在考慮到探針之前端在X方向上移動Lx之情形，支持探針 的Z台階64及平臺板63在X方向上移動Lx，X軸雷射測長 62a亦有Lx之變化，此時之測長値具有奈米等級之測定精 -9- 200930976 度。在γ方向及z方向上亦可進行同樣的測定。由於此等情 形，可以奈米等級之超高精度測得XYZ座標。雖然未圖示， 但在此形狀測定機中具備有在控制各構件之驅動的同時，將 測得資料進行記憶演算的電腦。 在進行形狀測定時，使XY台階69及70相對被測定物 200作相對地移動，並藉由探針沿著被測物200的被測面S 作掃瞄。然後求得探針1因追蹤被測定面S的形狀而在Z方 向上移動時，在各XY座標位置上的Z座標資料列，根據該 〇 XYZ座標資料列測定被測定物200的三次元形狀。 以下根據第2圖一面參照第1圖及第3 ~ 20圖一面說明 以透鏡作爲被測定物200的形狀測定之流程。 [步驟S1] 第3圖（a)(b)係用以設置透鏡之夾具的平面圖及剖面圖。 夾具3 —般而言係圓盤狀，如第3圖（a)所示，在其上面 將具有相同直徑的三個球3 a~ 3c的位置以呈槪略正三角形的 方式配置，在其中心配置有圓筒狀的透鏡吸著部3d。透鏡吸 © 著部3d的上面，在圍繞吸著孔區的三個地方有透鏡3點支 持部3d2朝半徑方向延伸，在該透鏡3點支援部3d2的上面 以進行空氣吸著方式載置透鏡（未圖示）。 如第3圖（b)中所示，將該夾具3以使夾具的透鏡吸著部 3d朝向測定機χγζ座標系中的+Z方向的方式設置在台3j。 透鏡3點支持部3d2的上面與測定機XYZ座標系中之XY平 面呈槪略水準，且亦有球3a之中心3al與透鏡吸著部3d之 中心的連接直線與X軸呈平行。自-Y方向（測定機的作業者 側）可看見設置於透鏡吸著部3d之側面的記號m2。該記號 -10- 200930976 m2,將後述，在吸著透鏡時，用於該光軸周圍之位置的定位。 3e係設置在透鏡吸著部3d之背面側的夾具回動部，3h係空 氣管。 [步驟S2] 以第3圖中所示之狀態，對夾具3的球3 a〜3c及透鏡吸 著部3d的上面（平坦部）作測定。 由於透鏡吸著部3d呈如上述之圓筒狀，如模式地圖示， 以使測定資料7之位置在XY平面上呈複數個圓軌跡方式作 ❹ 測定。在此，將由球3a~3c之各個中心3al〜3cl所構成的平 面上之通過中心3al及3cl的Xs軸、與該平面及Xs軸垂直 之Zs軸以及與Xs軸及Zs軸垂直之Ys軸所構成之座標系定 義爲3球基準XsYsZs座標系。 此外，自透鏡吸著部3d上面突出之透鏡3點支持部3d2 的突出高度，因有必要使該高度係在測定透鏡吸著部3d上 面時之探針1前端的針尖半徑之一半以下，因而設計成如 此。理由係若以透鏡3點支持部3d2之突出高度爲h、以探 〇 針1前端的半徑爲Pr以及以在探針接觸下由低位元面升至 高位面之情形下的最大傾斜角度爲Θ時，平行階差之垂直方 向的階差會有以下方程式的關係之故。例如，Pr = 0.5 mm、θ = 60 度之情況時，h = 0.25mm»BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a shape measuring method, and more particularly to a configuration of a peripheral surface having a cylindrical shape or a polygonal column shape and a curved surface on a plane perpendicular to the outer circumferential surfaces. Method for determining the shape of a body. [Prior Art] In recent years, aspherical lenses used in mobile phones, digital cameras, and the like have mostly fixed the lens shape along a cylindrical lens barrel. Therefore, in order to increase the yield of the product, the tilting and eccentricity of the optical axis of the lens when the cylinder is used as a reference under the same conditions as when the lens is inserted into the lens barrel has become an issue in the field of optics. Conventionally, the tilt or eccentric amount of the optical axis of the lens is calculated based on the outer shape of the lens. In the method described in Japanese Laid-Open Patent Publication No. 2002-71344, three balls are brought into contact at the outer peripheral portion of the lens, and the lens shape is obtained by obtaining a circle passing through the center of each ball. When the outer peripheral portion of the lens is an ideal cylindrical surface (that is, an outer peripheral surface of a cylindrical shape) and the bottom surface of the lens is a flat surface, @ has an inclination and an eccentric amount of the optical axis based on the outer shape and the bottom surface of the lens. Possible. In the shape measuring machine used in the shape measuring method, the probe is moved in the XY direction while being in contact with the object to be measured, and the shape of the object to be measured is traced by the probe in the Z direction. The shape of the Z-coordinate data at each χ γ coordinate position during the movement is measured, and the shape of the surface to be measured is measured based on the XYZ coordinate data column. In this XYZ system is perpendicular to each other. For example, if it is a lens with a cylindrical surface and a curved surface, it is set such that its w axis (the central axis at a position equidistant from the cylindrical surface) is parallel to the Z axis of the measuring machine, and the probe -3-200930976 needle is only in the Z direction. Apply servo (servo). However, in this method, the larger the inclination angle of the measurement portion of the lens with respect to the XY plane, the more difficult the tracking of the servo is, and the measurement accuracy is deteriorated, and the maximum inclination angle of 0 which can be measured with respect to the XY plane is about 75 degrees. limit. This is because the airslide constituting the probe has a high rigidity in the XY direction and can only move in the Z direction, and because when a force such as 0.3111\(= 3〇11^〇 is applied, the probe The tilting amount of the tip of the tip is 11111. For this reason, although the angle of inclination to 75 degrees can be measured by the high precision Q of the nm level, since the cylinder mask has a tilt angle of 90 degrees, it is in the Z direction. The servo cannot be tracked and cannot be measured. In order to eliminate the limitation of these measurements, a measurement method in which three balls are brought into contact at the outer peripheral portion of the above-mentioned lens has been proposed. Japanese Patent Laid-Open Publication No. 2007- 1 55 628 In the method described above, a measurement space for measuring a three-dimensional shape of an outer surface of an aspherical lens (having a first surface of the lens and a second surface of the lens) is provided in the measurement jig having three spherical portions. The aspherical lens is held in the jig, and the probe scans the surface shape of the first surface of the lens and the @@2 surface of the lens to obtain a dot-column data having coordinates of the three spherical portions as a reference, and further, since the probe pair is on the outer periphery of the lens Foundation Scanning the cylindrical surface and the three spherical portions to obtain the point group data with the coordinates of the three spherical portions as the reference, and obtaining the relative relationship between the cylindrical surface and the first surface of the lens and the second surface of the lens Japanese Patent No. 3827493 discloses a method for measuring a shape of a lens model in which a shaft portion having a transfer surface at an end is erected on a pedestal. In this method, 'in a measuring machine that has been traced in another stage, The respective diameters of the three balls are measured, and the data is obtained by tracking the three balls and the transfer surface with the probe in a state where the cylindrical surface of the shaft portion and the base are in contact with the three balls. The inclination and eccentricity of the optical axis of the transfer surface are obtained by the circle of the apex of the -4-200930976 3 ball, based on the upper surface of the pedestal and the cylindrical surface of the shaft portion. However, the above-mentioned special opening 2002-7 1 In the method described in the 344 publication, when the surface is rough and the surface roughness is rough, there is a slight difference in the position of the contact with the lens shape of the ball as the positioning jig, and the lens shape is used as a reference. The tilt of the optical axis and the reproducibility of the amount of eccentricity will change For example, when the accuracy of the eccentricity of the optical axis of the lens is less than 1 μπι, if the shape accuracy of the lens shape or the surface roughness is 1 μm or more, it cannot be used. In the method described in Japanese Laid-Open Patent Publication No. H2007-155628, as described above, the measurement space is provided in the jig, and the cubic shape of the cylindrical surface as the reference is measured. However, there is a special opening 2002- The same problem as the method described in the Japanese Patent Publication No. 7 344. In this method, when measuring the first surface of the lens, the surface shape measuring device measurable with respect to one direction of the Ζ direction is used, and the first surface of the lens is 3 balls are scanned, and when the cylindrical surface is measured, the cylindrical surface is scanned from the side > using a general three-dimensional measuring machine that can be prevented from the upper or lateral probes. The ball is scanned, but since the accuracy of the general three-dimensional measuring machine is μμη level, there is a problem that it cannot be measured with an accuracy of 0.1 μm in the lens. In addition, the current situation is that as long as the surface including the surface, the back surface and the side surface can be measured and evaluated with an accuracy of 0.1 μm, the accuracy evaluation of the lens shape can be roughly solved, but the accuracy of the measuring machine itself is Insufficient or limited measurement methods such as probes, and the relevant measurement evaluation cannot be performed. In the method described in Japanese Patent No. 3,294, 493, there is a cylindricality and a roundness deformation of a shaft portion of a lens model, and a case where the surface roughness is rough - 5 - 200930976, as long as the cylinder is opposed to the shaft portion. When there is a slight difference in the contact position of the ball as the positioning jig, the inclination of the optical axis and the reproducibility of the eccentric amount of the transfer surface based on the cylindrical surface of the shaft portion are deteriorated, and the desired precision cannot be satisfied. problem. For example, when the accuracy of the eccentricity of the optical axis of the transfer surface is 0.5 μm or less, the measurement method cannot be used if the shape accuracy or the surface roughness of the shaft portion exceeds 0.5 μm. The method described in Japanese Laid-Open Patent Publication No. 2002-7 1344 is also the same as the above. In general, there is a tendency for the lens to require higher precision than the lens. The present invention has been made in view of the above problems, and an object of the invention is to provide a shape measuring method capable of accurately measuring the tilt and eccentric amount of a lens optical axis when a cylindrical surface of a lens barrel into which a lens is inserted is used as a reference. It is an object of the present invention to provide a method for measuring a shape, for example, a lens model in which a shaft portion having a transfer surface at an end portion is erected on a susceptor, and the upper surface of the pedestal and the shaft portion can be obtained. The cylindrical surface serves as the reference for the tilt and eccentricity of the optical axis of the transfer surface. Further, it is an object of the invention to provide a method for measuring a shape which can be measured and evaluated with an accuracy of 0.1 μm on the surface including the surface, the back surface and the side surface of the 透镜 lens. Further, it is an object of the invention to provide a shape measuring method capable of calculating the inclination and eccentricity of light on the back surface (or surface) of the lens when the optical axis of the surface (or the back surface) of the lens is used as a reference. In order to solve the above problems, the shape measuring method of the present invention measures the three-dimensional shape of the object to be measured by scanning the probe along the measurement surface of the object to be measured based on the coordinate data obtained by the probe. The shape measuring method, wherein the probe is freely movable in the x-direction and is held on a moving body that is drivable in mutually perpendicular X and x-axis directions, and is characterized in that: -6- 200930976 the measured object has a cylinder a curved surface on a plane other than the shape and the polygonal column shape and a plane perpendicular to the outer peripheral surface, and a structure having a central axis parallel to the outer peripheral surface and passing through the center of gravity, and the object to be measured is coaxially provided The object to be measured and the jigs of the three spherical portions disposed around the fixing portion are inclined such that the central axis is predetermined with respect to the XY plane along the X-axis and the Y-axis direction. The angle is inclined so that the inclined object to be measured and the jig are rotated around the central axis at a predetermined same angle, and at each rotation position, the probe is on the predetermined spherical path to the three spherical portions. The measurement of each spherical portion and the measurement data group of the object to be measured are performed by tracking the outer peripheral surface of the measured object and the measurement surface thereof, and the three spherical portions at the respective rotation positions are calculated from the measurement data. The center position sound mark 値 is distributed by the least square method, and the measurement data group of the object to be measured at the full-return position is distributed over the entire circumference around the central axis by the three spherical portions. And, after the distribution, the shape of the measurement surface of the object to be measured is obtained from the measurement data group. The curved surface of the surface to be measured may be a convex surface, a concave surface or a concave-convex composite surface. The tilt angle of the fixture can be from 15 degrees to 72 degrees. When the object to be measured has an aspherical optical axis, the outer peripheral surface measurement data group is extracted from the measurement data group of the object to be measured at the full rotation position, and the data group is measured from the extracted outer circumferential surface, and the object to be measured is calculated. The fixing shaft has a fixed plane perpendicular to the center axis of the reference of the external cylindrical surface circumscribing the external surface of the object to be measured. When the object to be measured has an aspherical optical axis, the side data group of the surface on the side of the outer peripheral surface is extracted from the measurement data group of the object to be measured at the full-rotation position, and the extracted side surface measurement data group is separated into an aspherical surface. For the data group and the edge data group, the edge portion plane is obtained from the separated edge portion data group, and the data group is measured from the side surface of the sample taken from -7-200930976, and the edge portion plane is calculated to be perpendicular to the periphery of the object to be measured. The center axis of the reference surface of the cylindrical surface is externally connected to the surface, and the inclination and eccentric amount of the optical axis of the aspherical surface when the central axis of the circumscribed cylindrical surface is used as a reference is calculated. When the object to be measured has an optical axis of an aspherical surface, the measurement data group of the surface on the side of the outer peripheral surface is extracted from the measurement data group of the object to be measured at the full-rotation position, and the extracted side measurement data group is separated into aspherical data. The group and the edge data group are subjected to the coordinate transformation of the RMS 0 minimization by the difference between the separated aspheric data group and the design formula, and the measurement on the outer surface or the sheet side of the object to be measured is obtained in the third dimension. The amount of gaps in the space and the direction of the gap. The position of the center of gravity of the object to be measured is on a triangular area formed by the center i1 of the three spherical portions of the connection jig. The fixed portion to be measured has a absorbing portion that vacates the object to be measured. The object fixing portion of the jig has an object support portion on the outer peripheral side of the absorbing portion. A mark for positioning is provided on the outer peripheral surface of the object to be measured and the side surface of the workpiece fixing portion of the jig. The measurement track on the upper surface of the object-fixing portion is rounded. The area surrounded by the boundary between the outer peripheral surface of the object to be measured and the surface and the back surface of the surface on both sides of the object is traced by the probe in the XY direction along the measurement trajectory along the boundary line A or the boundary line B. . The surface of the object to be measured and the back surface portion at the positions on both sides of the outer peripheral surface are each composed of a plane and a curved surface perpendicular to the outer peripheral surface, and the outer peripheral surface of the object to be measured and the outer periphery of the object-fixing portion of the jig The surface of the object to be measured is placed on the surface of the object to be measured, and the object to be measured is fixed to the surface of the object to be measured. In the Dingguan test, the group of materials with the folder β is measured and obtained. The base number is recorded as two sides to make the flat part, and the object on the back and back of the face is determined to be fixed. In the state in which the object to be measured is fixed, the measurement data group is obtained based on the outer peripheral surface and the surface non-plane of the object to be measured, and the measurement data group is combined with each other to obtain all the measurements seen from all sides of the object to be measured. Data group. [Embodiment] Hereinafter, embodiments of the present invention will be described with reference to the drawings. Ο Fig. 1 is a view showing a shape measuring machine used in the shape measuring method of the present invention. In the XYZ coordinate system of the shape measuring machine, the XY direction is flat on the susceptor, and the two directions are perpendicular to the surface of the stage 61, and the Z direction is perpendicular to the XY direction. The XY steps 69 and 70 are driven in the XY direction, the platform plate 63 is attached to the χγ steps 69 and 70, and the vibration frequency stabilized He-Ne laser 71 as the world standard of the length is placed on the platform plate 63. . Further, a Z-step 64 is attached to the platen 63, and a probe 65 is attached to the Z-step 64. Further, the X reference mirror 66, the Y reference mirror ® 67, and the Z reference mirror 68 having a high flatness of the nanometer level are disposed at predetermined positions. Thereby, the X-ray mirror 66, the Y-reference mirror 67, and the Z-reference mirror 68 reflect the laser light from the laser 71, and the length can be measured for various distances. Since the front end position of the probe is formed by the extended position of the X-axis laser length 62a, the Y-axis laser length 62b, and the Z-axis laser length 62c, the mobile station vibrates even in the measurement. Ups and downs can also almost ignore the shadow f. Considering the case where the front end of the probe moves Lx in the X direction, the Z step 64 of the support probe and the platform plate 63 move Lx in the X direction, and the X-axis laser length 62a also has a change of Lx. The long sputum has a nanometer level of fine -9- 200930976 degrees. The same measurement can be performed in the γ direction and the z direction. Due to these circumstances, the XYZ coordinates can be measured with ultra-high precision of the nanometer level. Although not shown, the shape measuring machine includes a computer that controls the measurement of each member and performs memory calculation on the measured data. When the shape measurement is performed, the XY steps 69 and 70 are relatively moved with respect to the object to be measured 200, and the probe is scanned along the measured surface S of the object 200 by the probe. Then, when the probe 1 moves in the Z direction by tracking the shape of the surface to be measured S, the Z coordinate data column at each XY coordinate position is determined, and the three-dimensional shape of the object 200 is measured based on the 〇XYZ coordinate data column. . Hereinafter, the flow of measuring the shape of the object to be measured 200 using a lens will be described with reference to Fig. 1 and Fig. 3 to Fig. 3 to Fig. 2 . [Step S1] Fig. 3 (a) and (b) are a plan view and a cross-sectional view of a jig for arranging a lens. The jig 3 is generally disc-shaped, as shown in Fig. 3(a), on which the positions of the three balls 3a to 3c having the same diameter are arranged in a slightly equilateral triangle shape. A cylindrical lens absorbing portion 3d is disposed at the center. The lens suctions the upper portion of the portion 3d, and the three-point support portion 3d2 extends in the radial direction at three places around the suction hole region, and the lens is placed on the upper surface of the lens three-point support portion 3d2 by air suction. (not shown). As shown in Fig. 3(b), the jig 3 is placed on the stage 3j such that the lens suction portion 3d of the jig faces the +Z direction of the measuring machine χ ζ coordinate system. The upper surface of the lens three-point support portion 3d2 is slightly horizontal to the XY plane in the coordinate system XYZ coordinate system, and the connection line between the center 3al of the ball 3a and the center of the lens absorbing portion 3d is parallel to the X-axis. The mark m2 provided on the side surface of the lens absorbing portion 3d is visible from the -Y direction (the operator side of the measuring machine). This symbol -10-200930976 m2, which will be described later, is used for positioning the position around the optical axis when the lens is sucked. 3e is a jig returning portion provided on the back side of the lens absorbing portion 3d, and 3h is an air tube. [Step S2] The balls 3a to 3c of the jig 3 and the upper surface (flat portion) of the lens suction portion 3d are measured in the state shown in Fig. 3. Since the lens absorbing portion 3d has a cylindrical shape as described above, as shown in the figure, the position of the measurement data 7 is measured in a plurality of circular trajectories on the XY plane. Here, the Xs axis passing through the centers 3al and 3cl, the Zs axis perpendicular to the plane and the Xs axis, and the Ys axis perpendicular to the Xs axis and the Zs axis on the plane formed by the centers 3a to 3cl of the balls 3a to 3c The coordinate system is defined as a 3-ball reference XsYsZs coordinate system. Further, the protruding height of the lens three-point support portion 3d2 protruding from the upper surface of the lens absorbing portion 3d is required to be such that the height is one-half or less of the tip radius of the tip end of the probe 1 when measuring the lens absorbing portion 3d. Designed to be like this. The reason is that the projection height of the lens 3 point support portion 3d2 is h, the radius of the tip end of the probe needle 1 is Pr, and the maximum inclination angle in the case where the probe unit is raised from the low-order surface to the high-level surface is Θ When the step of the vertical direction of the parallel step has the relationship of the following equation. For example, when Pr = 0.5 mm and θ = 60 degrees, h = 0.25 mm »
Pr(l-cos^) = h [步驟S3] 算出透鏡3點支持部3 d2的上面之3球基準XsYsZs座 標系的平面方程式。 爲此首先，便於思考，在3球基準XsYsZs座標系之XsYs -11- 200930976 平面中，使球3a的中心3al與藉由球3a的中心3&1~球3c 的中心3cl所求得之重心位置之連接直線Xs’與測定機的X 軸一致，且對透鏡吸著部3d上的測定資料7進行座標變換’ 使得Zs軸與Z軸一致。此時之座標變換量，由於仍在之後 之步驟中所使用，因此保存於電腦中。 接著，從在透鏡吸著部3d上的測定資料7,抽出透鏡3 點支持部3d3上的測定資料，亦即抽出只有高出h之階差高 度的測定資料。藉由抽出之透鏡3點支持部3 d2上的測定資 〇 料，利用最小平方法算出平面方程式。 在此情況下，可得到以下方程式所示之透鏡3點支持部 的法線向量。 „ 藉由決定符合此平面方程式之代表點a(Xa，Ya，Za)，其 與透鏡吸著部3d上之任一點P(X，Y，Z)之間，有以下關係式 成立。 ηρ · {,Χ — Χα, Υ — Υα, Ζ — Ζά) = 0 此即3球基準XsYsZs座標系（對測定機ΧΥΖ座標系進 行座標轉換後）之藉由透鏡吸著部3d上的測定資料7所算出 之透鏡3點支持部 3 <12上之平面的方程式7a。將此關係圖 示於第4圖。 然而，不必要以透鏡3點支援部3 d2之上面爲平面，亦 可以3個球構成。例如，將3個具相同直徑的球嵌入透鏡吸 著部3d上面，計測3個球的各頂點之3次元座標値，將自 該3頂點的3次元座標値算出之平面方程式作爲透鏡吸著部 -12- 200930976 3d上面的平面方程式亦可。 [步驟S4] 如第5圖（a)(b)中所示，在夾具3之中心的透鏡吸著部 3d對透鏡4作空氣吸著，將夾具3傾斜成透鏡4的中心軸（w 軸）相對測定機XY平面有θ( 15〜72度）之傾斜角度。 透鏡4係具有第6圖（a)中所示之形狀的構造體，具有原 筒面4a、與其垂直之面4al以及突出其上方的曲面4b。將 在自該圓筒面4a爲槪略等距離之中心軸上的w軸、以該w Ο 軸及曲面4b之交點爲原點下，在垂直W軸的方向上延伸的 U軸以及V軸定義爲測定物UVW座標系。 將該透鏡4在夾具3上設置碎如第6圖（b)中放大所示， 使w軸與透鏡吸著部3d的中心軸一致，且使設置於圓筒面 4a上之記號ml與透鏡吸著部3d上的記號m2 —致。接著將 該夾具3設置在傾斜台3i，該傾斜台3i設計成使夾具相對 測定機XYZ座標系之XY平面有Θ爲15度〜72度之傾斜角 度。圖中之eLT表示相對在透鏡頂點之Z軸的傾斜角度，0LY-¥ 表示相對在透鏡有效半徑位置的X軸之傾斜角度。 將說明使夾具傾斜角度Θ爲15度~72度的理由。第7 圖係求得在測定透鏡4之圓筒面時的Z軸與圓筒面法線方向 的夾角0之槪念圖。第7圖（a)係圖示測定物uvw座標系的 w軸與測定機XYZ座標系的XY平面平行（夾具傾斜角度θ = 0) 的情形，第7圖（b)則圖示測定物uvw座標系的w軸相對測 定機XYZ座標系的XY平面作傾斜（夾具傾斜角度Θ夫0)的情 形。 探針1之軸方向的法線向量ns表示於下面的方程式。 -13- = < 0 ^ 0' 200930976 > 1 .> 關於探針接觸面的法線向量nt(夾具傾斜角度θ = 0)以及 探針接觸面的法線向量nu(夾具傾斜角度Θ矣0)，如第7圖有 以下關係式的成立。 Ο nt= 0 cosφΑ -sin在4 0 sin ^ cos^4 ns cos0 0 sin0 •nt 0 cos^ -sin在4 0 sin^ cos φΑ 0 1 0 -sin 0 0 cos 0 cos0 0 sin0 0 1 0 -sin0 0 cos0 探針1之軸方向的法線向量ns與探針接觸面的法線向 量nu(夾具傾斜角Θ# 0)之夾角0係相對XY平面之圓筒面的 最大傾斜角度。關於夾具傾斜角度0，只要將作爲相對χγ 平面之圓筒面的最大傾斜角度之法線向量ns與nu的夾角0 以及在透鏡頂點的傾斜角度eLT之每一者，皆設定成在相對 使用於本發明中之測定裝置的XY平面的最大傾斜角度75 度以內即可。 此外，透鏡4的記號ml (參照第6圖（b))係相對圓筒面 4a呈中空狀，且呈毛邊等不會飛出的加工形狀。這是因爲如 果只要記號ml的一部份在圓筒面4a的外周側突出，在將透 -14- 200930976 鏡4插入透鏡鏡筒（未圖示）時，會因爲記號mi的毛邊等而 在透鏡4產生偏心差距之故。 在固定透鏡4方.面，除了上述的空氣吸著以外，亦考慮 到將透鏡外周部的圓筒面4a使用黏土或者蠟作3點固定的 方法，或者使用彈簧作三點固定等方法。在此情形下，不將 突出於比透鏡4之圓筒面4a較外側的黏土等之區域作爲測 定資料而取得》將在之後敘述藉由計算依據原筒面4a的測 定資料求得外接圓筒的方法，因爲在計算時，由於黏土等造 €> 成原筒面4a部分比原來的形狀較膨脹之原因，而有與原本 透鏡形狀不同的算出結果。 [，步驟S 5 ] 對以上述方式設置之夾具3中的球3 a〜3 c及對透鏡4之 圓筒面4a與表面的一部份進行測定。 再次參照第5圖及第6圖。首先，在球3a上使探針1 以執行焦點伺服而定位中心之方式找出暫定的頂點，進行X 軸及Y軸測定。之後，利用最小平方法將測定資料及球3a ® 的之設計値於XYZ方向作配適，藉此之XYZ座標變換量而 算出正確的頂點位置。藉由事先在別台已取得追溯性之厚度 測定機中測得直徑，可從先前所算出之正確頂點位置算出中 心位置座標値（Xa，Ya，Za)。以別的方法而言，藉由以測定機 的標準裝備的半徑基準球進行測定，先將探針前端半徑的値 校正至〇.〇1 μπι等級，利用該探針半徑値，並藉由以使上述 測定球3a時的測定資料與將設計半徑作變化的最佳配適R 之RMS成爲最小之方式算出最佳配適R，進而算出球3a的 正確半徑。若測定結束，則使探針1停止在球3a的聚焦並 -15- 200930976 退避至Z上方。由於對於球3b，球3c進行同樣方法，可算 出中心位置的座標値（Xb，Yb，Zb)及（Xc，Yc，Zc)。 對於透鏡的表面，透鏡4之圓筒面的中心軸…軸），即 在透鏡吸著部3d之中心軸的周圍進行迴轉之方向上，在χγ 方向上藉由探針1進行掃描。藉此，探針1沿著透鏡表面的 形狀在Z方向上作追蹤，而可取得測定資料。圖中的2a係 測定區域，0A表示中心軸（w軸）周圍的圓筒面測定角度。 在第8圖中，擴大圖示透鏡4的測定軌跡。自中心軸方 © 向所見頂點時之以0A角度所夾之區域係測定區域。自+Z方 向看透鏡4時，在該圓筒面4a與透鏡表面的界線4e，以及 圓筒面4a與透鏡背面的界線所包圍的區域，以使該區域成 爲沿著界線4e或者界線4f的測定軌跡2(即沿著圓筒面4a 的圓周方向的測定軌跡（側面側）2’）方式，在XY方向上藉由 探針作追蹤。以上接著，以使面向界線4e時在右側的透鏡 表面區域成爲測定軌跡（透鏡面側）2”方式，在XY方向上作 掃描。這些自Z方向而視的測定軌跡（側面側）2 ’及測定軌跡 © 的（透鏡面側）2”之各條線皆爲橢圓的一部份，全體爲槪略線 形狀。如此在XY方向上做追蹤期間，探針1沿著透鏡4的 形狀在Z方向上做追蹤，而取得測定資料。 [步驟S6] 使夾具3在透鏡4的圓筒面中心軸（w軸）周圍僅進行迴 轉角度0之迴轉，並重複步驟S5的動作。第9圖（a) (aJ及 (b) (b')係圖示，透鏡4的圓筒面中心軸^軸）周圍的迴轉角 度0與圓筒面測定角度0a的關係。呈0A=±6O度（120度測 定）。藉由三次的迴轉所得的夾具迴轉角度0之0〇。、012〇。、 -16- 200930976 0240°而可得到全周的測定資料。 在此情況下，就算每次以120度作迴轉，由於因球3a〜3c 的位置會依順序替換，而使自+Z方向而視之球3 a〜3c與透 鏡之關係不變，使探針1與測定時的球3a〜3c及透鏡4的接 觸皆爲相同即可。在測定球3a〜3c或者透鏡4中之任一者 時，探針1與除了在測定時點的測定對象物以外者不會有干 涉。 如第9圖中所示之令圓筒面測定角度0Α=±6〇度（120 © 度測定）的情況 (a) 夾具傾斜角度θ=15度時， 作爲在透鏡圓筒面的最大傾斜角度之！^與nu的 夾角0 = 61.1度，在透鏡頂點的最大傾斜角度eLT = 75度。 (b) 夾具傾斜角度θ = 58度時， 作爲在透鏡圓筒面的最大傾斜角度之！^與㈣的 夾角0 = 74.6度，在透鏡頂點的最大傾斜角度0lt = 32 ❹ 度。 亦即’夾具傾斜角度在15度〜5 8度的範圍內係測定可能 的。 在第10圖（a)(a’）以及（b)(b’）中，圖示在透鏡4之圓筒 面中心軸（w軸）周圍的迴轉角度0及圓筒面測定角度0八之 間的關係。呈0a= ±30度（60度測定）。夾具迴轉角度0，以 0 0°、060。、012G°、018〇°、024Q°、03GG。之六次的迴轉而可 得到全周的測定資料。與先前第9圖中的夾具3相較下，將 透鏡吸著部3d的中心軸與球3a〜3c的間隔取大，不管在夾 -17- 200930976 具迴轉角度0係何者時，從+Z方向所見之情況下，透鏡4 與球3a〜3c不會重疊。 此第10圖中的夾具3與第9圖中之夾具3相同，在測 定球3 a〜3 c或者透鏡4中之任一者時，探針1與除了在測定 時點的測定對象物以外者不會有干涉。另一方面，與第9圖 中的夾具3不同的係由於只要每迴轉60度，自+Z方向看過 去時之球3 a〜3 c之配置皆會有變化，因此有將至球3 a〜3 c之 探針1的接觸位置一起作變化之必要。 〇 如第10圖中所示之將圓筒面測定角度0A= ±30(60度測 定）之情況 (a) 夾具傾斜角度θ=15度時 作爲在透鏡圓筒面的最大傾斜角度之ns與nu 的夾角0 = 33.2度，在透鏡頂點的傾斜角度0lt = 75 度。 (b) 夾具傾斜角度θ = 72度時 作爲在透鏡圓筒面的最大傾斜角度之ns與nu的 〇 夾角0 = 7 4.5度，在透鏡頂點的傾斜角度eLT= 18度。 亦即，夾具傾斜角度在1 5度〜72度的範圍內係測定可 能的。 若使角度比圓筒面測定角度0a = ±3O(6O度測定）更小 時，因爲測定回數增多而使測定時間增加，所以還是不要採 用如此之角度係被期望的。 以下，取圓筒面測定角度0A爲±60度（120度測定）的情 況（參照第9圖）作爲例示作說明。 [步驟S7] -18- 200930976 如第1 1圖（a)(b)所示’將在步驟S6中所測定之所有測 定資料結合使3球的中心位置爲一致下，取得透鏡4之圓筒 面中心軸（w軸）周圍之3 60度全周的圓筒面4a及表面的資 料。 具體而言，將在上述的0 0。、0 ] 2 〇。、0 2 4 G。之各迴轉角度 的透鏡4之測定資料以3球基準XsYsZs座標系作爲基準而 作配置。藉此’透鏡4的圓筒面4a及表面的測定資料在遍 及3 60度全周作結合。2b係圖示測定資料結合區域。 G 在此時點上’使在步驟S3中所求之直線XS，（即在3球 基準XsYsZs座標系中的XSYS平面上之自球3a的中心3al 連接至重心位置的連接直線Xs’）與測定機的X軸一致。此 外’使用在爲了使Zs軸成爲與Z軸一致而將透鏡吸著部3d 上的測定資料7作座標變換時的座標變換量，對在此得到之 360全周的透鏡4之圓筒面4a及表面的測定資料作座標變 換》 [步驟S8] © 如模式地在第12圖（a)〜（d)中所圖示，藉由在步驟 S7 得到的透鏡4之圓筒面4a與表面的合成資料而抽出圓筒面 資料群8，算出外接圓筒A6，而以使作爲其中心軸的Zg軸 成爲與設計上的Z軸一致方式對測定資料作座標變換。 在第12圖（a)中，圖示在步驟S7中得到的透鏡4之圓 筒面4a與表面之合成資料的分佈。以圓筒面測定資料群8 與在+Z方向上可見到之表面測定資料群9而構成。關於圓 筒面測定資料群8，圓周方向之資料的排列上，有考慮到藉 由後述之最小平方法之計算處理而使其爲充分的許多資料 -19- 200930976 數之必要。例如，相對圓周1周之一刻度程度，亦即，取得 1周360度分割程度的資料係被期望的。 第12圖（b)係在第12圖（a)之合成資料的分佈中自·γ方 向所見的圖。不僅有圓筒面測定資料群8及表面測定資料群 9,亦圖示在步驟S3中求得之透鏡3點支持部3d2的平面式 7a。此時之平面式以下面的方程式表示。 ηρ·{Χ-Χα,Υ -Υα,Ζ-Ζά) = 0 〇 對第12圖（b)的合成資料，如第12圖（C)中所示，爲了 使透鏡3點支持部3d2的平面式7a與測定機XYZ座標系中 的XY平面（即，Z = 0的平面）一致而作座標變換。此時之平 面式7al以下面的方程式表示。藉此，以透鏡3點支持部爲 基準而處理透鏡4的合成資料成爲可能。 Z = 0,np\ - (0,0,1) 如此般從已座標變換之合成資料，抽出圓筒面測定資料 © 群8。決定適切的R1値，由於選擇了在滿足下式時的測定 資料（Χ，Υ，Ζ)，而可抽出圓筒面測定資料群8。 4(X - Xa\f +(Υ- Υα\)2 > R, 然而R1選擇比在表面測定資料群9之邊緣部（平面部） 上的最外周之圓狀資料的半徑大，比圓筒面測定資料8的半 徑小之値。在邊緣部（平面部）上之最外周的圓資料的槪略半 徑，藉由在第6圖中所示之透鏡4的中心軸傾斜eLT時之測 定軌跡2的NC情報而可作計算。且圓筒面部之資料料的槪 -20- 200930976 略半徑可藉由透鏡圓筒面的設計値而作計算。 第12圖（d)係以+Z方向看在第12圖（c)中所抽出之圓筒 面測定資料群8的圖。藉由使用此圓筒面測定資料群8之最 小平方法而算出圓，選擇自算出之圓方離至外側的點以大至 小排序的前三個，而求得該三個點Al、A2及A3的重心Ga 的位置’並以重心Ga爲中心求得通過點a 1、A2及A3的外 接圓A5。將外接圓A5在Z軸上延伸者定義爲外接圓筒A6, 其中心軸定義爲Zg軸’對上述的合成資料以使此Zg軸成爲 Q 測定機xyz座標系的z軸一致方式作座標變換。 第13圖係自-Y所見第12圖（d)中所座標變換的合成資 料；^分佈的圖。使透鏡3點支持部3d2上的平面式7al與測 定機XYZ座標系中的XY平面（即Z = 〇的平面）—致，且使中 心軸（Zg軸）與測定機XYZ座標系中的Z軸一致。1 2係表示 設計上的透鏡形狀。 根據以上步驟S1-S8，以透鏡3點支持部3d2及透鏡4 的圓筒面4a爲基準，在3次元空間的X、γ及z並進方向 〇 與《( X軸周圍）、β(Υ軸周圍）、γ(Ζ軸周圍）的回轉 方向之6自由度之中，使X、Υ、ζ、α、β之5自由度做變 動而根據最小平方法加以配適。關於γ，藉由設定成使透鏡 4之記號ml與夾具3之透鏡吸著部3d的記號m2 —致，誤 差値在±1度以內係充分可能的。結果，可決定全部之3次 元空間的定位所必要的6自由度。 在步驟S1-S8中所說明之方法的優點，就算在透鏡4的 圓筒面4a有歪曲，由於考慮並加以決定根據圓筒面4a的測 定資料而算出的外接圓筒A6在與鏡筒接觸下進行定位，有 -21- 200930976 實現具良好再現性的透鏡4之定位的利點j。 此外’就算測定時在透鏡4的圓筒面4a上附著塵埃， 關於以塵埃爲原因而發生之在測定資料中有許多雜訊，由於 有作業者大多可認識該等雜訊之情況，藉由消除雜訊，可取 得比實際形狀更接近的測定資料。 [步驟S9] 如第14圖（a) (b)中所示，自在步驟S8中進行座標變換 的合成資料中抽出表面測定資料群9,將該表面資料群9分 Ο 離爲透鏡面部資料群9a及邊緣部資料群9b，並僅抽出透鏡 面部資料群9a。爲此例如’對於合成資料（χ，γ，ζ)，決定適 切的Ζ1値’並由於選擇在Ζ2Ζ1時的資料，而可抽出透鏡 面部資料群9a。然而對於Ζ1，相對透鏡的邊緣部（平面部） 之表面與背面的厚度設計値d，取Z1 = d + Δ(1之値。 在決定Ad方面，設定成在第14圖（a)之Ζ1以下的表面 測定資料群9之中的邊緣部的資料9b確實地落入範圍內。 作爲設定之範例，將控制測定機的電腦在顯示器中表示，使 © 其可被使用者所設定亦可。 [步驟s 1 〇] 如第1 5圖中所示，在測定機XYZ座標系中，進行座標 轉換而使先前在步驟S9中所抽出的透鏡面部資料群9a與設 計上的透鏡形狀1 2之間的RMS成爲最小》 亦即，雖然在步驟S9中透鏡3點支持部3 d2上有原點， 爲了便於思考，將原點轉移至設計上的透鏡形狀12的頂點 部。若進行座標變換而使RMS成爲最小，如圖示，透鏡面 部資料群9a以該中心軸Zp傾斜座標變換量β (或α)方式 -22- 200930976 '作迴轉移動，此外以並進座標變換量dX(或dY)及dZ做並進 移動。使此轉移量在電腦中保存而在之後的計算作處理》 [步驟S11] 如第16圖中所示，將在先前的步驟S10中求得之座標 變換量施加-1，求得自設計値的偏心dX(或dY)、高度差距 dZ及傾斜β(或〇〇。根據以上的步驟S1〜S11，可算出以透鏡 吸著部3d之透鏡支持部3 d2的上面之平坦部（對應透鏡背面 側的邊緣部）與透鏡4的外周部之圓筒面4a爲基準之透鏡表 〇 面之光軸Zp的傾斜量、偏心量dX(或dY)及高度差距dZ。 關於透鏡背面亦，即，設置透鏡4使其面向爲可從+Z 方向看見其背面且使其記號ml與透鏡吸著部的m2 —致， 並根據經過步驟S1~S11，而可算出以透鏡吸著部3d之透鏡 支持部3d2的上面之平坦部（對應透鏡表面側的邊緣部）與透 鏡4的外周部之圓筒面4a爲基準時之透鏡背面的光軸之傾 斜量、偏心量以及高度差距。 然而，以上的步驟S1〜S 11雖以透鏡4的外周部爲圓筒 © 面4a爲前提，在外周部爲多角柱狀之情況，亦同樣地根據 側面的測定資料求得外接圓，而可算出透鏡表面及背面的光 軸之傾斜量以及偏心量。透鏡4之圓筒面4a或透鏡表面（以 及透鏡背面）之全資料的差距量，亦可根據以與設計式之差 進行RMS最小化的座標變換而求得。 接著，參照第18圖〜第20圖，根據第17圖對求得自透 鏡全方位所見之所有面的形狀之流程作說明。 [步驟S12〜S15] 對於透鏡背面，藉由實施上述的步驟S1~S7，如第18 -23- 200930976 圖（a)中所示，在中心軸周圍作成360度全周之圓筒面測定資 料群1〇與背面測定資料群11所構成的合成資料（步驟 S12)。接著，根據實施上述的步驟S8及S9，如第18圖（1)) 中所示（自-Y方向看第18圖（a))，算出背面測定資料群u 的透鏡邊緣部之平面式1 lbl(步驟S13)。 接著，如第18圖（c)中所示，對透鏡邊緣部之平面式llbl 進行座標變換而使其與測定機XYZ座標系中的χγ平面 (即，Z = 0的平面）一致。此時之平面式1 lb2係Z = 0(步驟S14)。 Ο 在此狀態下’將合成資料分離爲圓筒面測定資料群10 及背面測定資料群11’並抽出圓筒面測定資料群10。爲此 例如，在測定資料（X，Y，Z)中決定適切的ri値，選擇p足以 下式的測定資料，而可抽出圓筒面測定資料群10。 V(X - Xa\)2 +(Y- Ya\f > Rx 選擇R1比背面測定資料群11之邊緣部（平面部）上的最 外周之圓狀資料的半徑大，比圓筒面測定資料群10之半徑 ® 小的値。邊緣部（平面部）之最外周的圓狀資料的槪略半徑可 根據在第6圖中所示之透鏡4之中心軸傾斜eLT時的測定軌 跡2之NC情報而計算。且圓筒面部的資料的槪略半徑係可 根據透鏡圓筒面的設計値而計算。 接著，如第1 8圖（d)中所示，求得抽出之圓筒面測定資 料群10的外接圓筒B6(自+Z方向所見），對作爲其中心軸的 zg軸進行座標變換而使其與測定機XYZ座標系中的Z軸一 致。此時，根據圓筒面測定資料群10藉由最小平方法算出 圓，選出以大至小排序之前三個的自該圓向外側分離的點， -24- t 200930976 求得三個點B1〜B3的重心位置Gb，藉由描繪以重心Gb爲 中心且通過點B1〜B3的圓而求得外接圓B5,將此外接圓B5 在Z軸上延伸成爲外接圓筒B6，而使其中心軸爲Zg軸（步 驟 S15)。 [步驟S16] 第19(a)圖係自-Y方向所見之在步驟S15中進行座標變 換之透鏡背面側資料的分佈的圖。使透鏡邊緣部（對應透鏡3 點支持部3 d2上的平面）的式11 b2與測定機XYZ座標系中的 〇 XY平面（Z = 〇)—致，而使中心軸（Zg軸）與測定機XYZ座標 系中的Z軸一致。 將此透鏡背面測的資料，如第19圖（b)中所示，進行180 回轉移動而使透鏡背面面向-Z方向，且使透鏡的記號ml(參 照第6圖）一致。此時之迴轉中心，爲了使其在就算記號ml 作180度迴轉下也不會有變化，有使與測定物uvw座標系中 的v軸平行的軸作爲回轉中心軸之必要。在此，在與v軸同 方向的Y軸周圍作180度迴轉移動，藉此自測定物uvw座 ® 標系進行座標變換爲測定機XYZ座標系。透鏡邊緣部的式 Ilb3係呈與測定機XYZ座標系中的χγ平面（z = 0)—致。 [步驟S 1 7] 第20圖（a)係圖示在上述的步驟S8中得到的透鏡表側 的資料。圓筒面測定資料群9及表面測定資料群9係呈透鏡 3點支持部上的平面式7al與Z = 0 —致，並以Z軸爲基準。 第20圖（b)係圖示在上述步驟S16中得到的透鏡背側的資 料。圓筒面測定資料群10及背面測定資料群11係呈透鏡3 點支持部1 lb3與Z = 0 —致的狀態，亦即，使透鏡邊緣部與 -25- 200930976 透鏡3點支持部上的平面式7a 1(Z = 0)—致的狀態，且呈以z 軸爲基準。 將這些透鏡表側的資料與透鏡背的資料，如第20(c)中 所示般作接合。亦即，以透鏡背面的邊緣部（透鏡3點支持 部上的平面式7al，透鏡邊緣部的平面式llb3)與透鏡之外 周的圓筒面（圓筒面測定資料群8，圓筒面測定資料群1〇)爲 基準作結合。 如以上，藉由進一步經過步驟S12〜S17，而可在各處全 〇 方位地求得透鏡4之所有面的形狀。 接著，一邊參照第22圖，一邊對根據第21圖中之在以 透鏡表側的光軸爲華準時之透鏡背側的光軸偏心dX(或 dY)、高度差距dZ以及傾斜β(或α)的流程圖做說明。 [步驟S1 8] 在先前的步驟S17中求得之全部的資料中，如第22(a) 圖所示，對於背面測定資料群11，僅抽出透鏡邊緣部資料以 外的透鏡面部資料。 © 爲此，如步驟S9，對於測定資料（χ，γ，ζ)，決定適切的 Ζ1値’藉由選擇在ZSZ1時的測定資料，而可僅抽出背面 測定資料群1 1內的透鏡面部資料。在此情況下，由於透鏡3 點支持部上的平面式7al(即透鏡邊緣部的平面式llb3)爲 Z = 0，決定Z1之値爲接近〇的負數即可。 [步驟S19] 如第22圖（b)中所示，進行座標變換使在步驟S18中得 到的透鏡背側的透鏡面部資料與設計式之間的RMS爲最 小。與步驟S10同樣的方法。 -26- 200930976 [步驟S20] 在步驟S19的座標變換量施加-1，而算出自設計値得偏 心dX(或dY)、高度差距（dZ)以及傾斜β(或α)。與步驟S11 相同之方法。 [步驟S21] 以在步驟S11中求得之自透鏡表側的設計値之任一者 爲基準’對在步驟S20中求得之自透鏡背側的設計値之差距 作微分，而算出在以透鏡表側之非球面的光軸16a爲基準時 © 的透鏡背側之非球面光軸16b的偏心dX(或dY)、高度差距 (dZ)以及傾斜β(或α)。19係中心厚度，Z〇係中心厚度的設 計値>，dZ則表示自該設計値ZG的差距量。 如以上，藉由進一部經過步驟S18-S21，可求得在以透 鏡的表面側的光軸16a爲基準時的背側之光軸16b的偏心 dX(或dY)、高度差距（dZ)及傾斜β(或〇〇。同樣地，可算出 在以背面側的光軸1 6b爲基準時的表側之光軸1 6a的偏心 dX(或dY)、高度差距dZ及傾斜；3 (或α )。 © 亦可藉由步驟S1~S11，以圖示之透鏡模型101作爲對 象代替透鏡4，在以底座101a之上面與軸部101b之圓筒面 爲基準時，算出轉寫面l〇lc之光軸的傾斜量，偏心量及高 度差距。 如以上說明，根據本發明的形狀測定方法，在使用具有 接觸式或非接觸式探針的3次元形狀測定機下，以對應鏡筒 的透鏡外周部作爲基準求得透鏡面之光軸的傾斜量及偏心 量；以透鏡外周部之圓筒面作爲基準涉及全方位地求得透鏡 的所有面（表面、背面及側面）的形狀；以透鏡之表側（或背側） -27- 200930976 的光軸作爲基準，而具有算出透鏡背側（或表側）之光軸的偏 心、高度差距及傾斜的可能。因此，對於在攜帶電話或數位 相機等中所使用的非球面透鏡的形狀測定特別地有用。關於 不限於透鏡的被測定物，亦可以透鏡面等之外周面作爲基 準，具有進行同樣地形狀測定的可能。 【圖式簡單說明】 第1圖係圖示使用於本發明中的形狀測定機之槪略構成 的斜視圖， Ο 第2圖係說明本發明之透鏡之形狀測定的流程圖， 第3圖係圖示同形狀測定方法之步驟S1〜S2的圖， 第4圖係圖示同形狀測定方法之步驟S3的圖， 第5圖係圖示同形狀測定方法之步驟S4〜S5的圖， 第6圖係圖示第5圖一部分的擴大圖， 第7圖係同形狀測定方法之步驟S4的槪念圖， 第8圖係同形狀測定方法之步驟S5的槪念圖， 第9圖係圖示同形狀測定方法之步驟S6的圖， ® 第10圖係圖示同形狀測定方法之步驟S6之其他的圖， 第1 1係圖示同形狀測定方法之步驟S7的圖， 第12圖係圖示同形狀測定方法之步驟S8的圖， 第13圖係圖示同形狀測定方法之步驟S8之其他的圖， 第14圖係圖示同形狀測定方法之步驟S 9的圖， 第15圖係圖示同形狀測定方法之步驟S10的圖， 第16圖係圖示同形狀測定方法之步驟S11的圖， 第17圖係圖示同形狀測定方法之第1圖之接續的流程 圖， -28- 200930976 第18圖係圖示同形狀測定方法之步驟S12~S 15的圖’ 第19圖係圖示同形狀測定方法之步驟S16的圖’ 第20圖係圖示同形狀測定方法之步驟S17的圖’ 第21圖係圖示同形狀測定方法之步驟之第14圖的接續 之流程圖， 第22圖係圖示同形狀測定方法之步驟S18~S21的圖， 第23圖係圖示藉本發明而進行形狀測定之透鏡模型的 圖。 G 【主要元件符號說明】 1 探針 2 測定軌跡 2， 測定軌跡（側面側） 2” 測定軌跡（透鏡面側） 2a 測定區域 3 夾具 3 a，3 b，3 c 球 3 a，3 b，3 c 3al，3bl，3cl 中心 3 a 1，3 b 1，3 c 1 3d 透鏡吸著部 3d2 透鏡3點支持部 3 e 夾具回動部 3h 空氣管 3i 傾斜台 3j 台 4 透鏡 4 a 圓筒面 -29- 200930976 4al 4b 4e，4f 7 7a，7al，1 lbl，1lb2,1lb3 8 9 9 a 〇 9b 10 11 12 16a 16b 19 6 1 ❹ 62a 62b 62c 63 64 65 66 67 68 面 曲面 界線 測定資料 平面式 圓筒面測定資料群 表面測定資料群 透鏡面部資料群 邊緣部資料群 圓筒面測定資料群 背面測定資料群 設計上的透鏡形狀 透鏡表側之非球面的光軸 透鏡背側之非球面光軸 中心厚度 基座平臺 X軸雷射測長 Y軸雷射測長 Z軸雷射測長 平臺板 Z台階 探針 X基準鏡 Y基準鏡 Z基準鏡 -30-Pr(l-cos^) = h [Step S3] The plane equation of the three-ball reference XsYsZs coordinate system of the upper surface of the lens three-point support portion 3d2 is calculated. For this reason, first of all, it is easy to think, in the XsYs -11-200930976 plane of the 3-ball reference XsYsZs coordinate system, the center 3al of the ball 3a and the center of gravity obtained by the center 3cl of the center 3&1~ball 3c of the ball 3a The position connecting line Xs' coincides with the X axis of the measuring machine, and coordinates the measurement data 7 on the lens absorbing portion 3d so that the Zs axis coincides with the Z axis. The coordinate conversion amount at this time is stored in the computer since it is still used in the subsequent steps. Then, from the measurement data 7 on the lens absorbing portion 3d, the measurement data on the lens 3 point support portion 3d3 is extracted, that is, the measurement data having only the height difference of h is extracted. The plane equation is calculated by the least squares method by extracting the measurement information on the three-point support portion 3 d2 of the lens. In this case, the normal vector of the lens 3-point support shown in the following equation can be obtained. „ By determining the representative point a(Xa, Ya, Za) that conforms to this plane equation, it has the following relationship with any point P(X, Y, Z) on the lens absorbing portion 3d. ηρ · {, Χ — Χα, Υ — Υα, Ζ — Ζά) = 0 This is the 3-ball reference XsYsZs coordinate system (after coordinate conversion of the coordinate system of the measuring machine) by the measurement data 7 on the lens absorbing part 3d Equation 7a of the plane on the three-point support portion 3 <12 of the lens is calculated. This relationship is shown in Fig. 4. However, it is not necessary to use the lens 3 point support portion 3 d2 as a plane or three balls. For example, three balls having the same diameter are embedded in the lens absorbing portion 3d, and the ordinate coordinates of the vertices of the three balls are measured, and the plane equation calculated from the ternary coordinates of the three vertices is taken as a lens. The plane equation of the above section -12- 200930976 3d may also be used. [Step S4] As shown in Fig. 5 (a) (b), the lens absorbing portion 3d at the center of the jig 3 is absorbing air to the lens 4. , tilting the jig 3 so that the central axis (w axis) of the lens 4 has a tilt angle of θ (15 to 72 degrees) with respect to the XY plane of the measuring machine The lens 4 has a structure having the shape shown in Fig. 6(a), and has a original cylindrical surface 4a, a surface 4a perpendicular thereto, and a curved surface 4b projecting upward. The cylindrical surface 4a is 槪. The w-axis on the central axis of the equidistant distance, the intersection of the w Ο axis and the curved surface 4b as the origin, and the U-axis and the V-axis extending in the direction of the vertical W-axis are defined as the UVW coordinate system of the measuring object. The lens 4 is provided on the jig 3 as shown in an enlarged view in Fig. 6(b), so that the w-axis coincides with the central axis of the lens absorbing portion 3d, and the mark ml and the lens provided on the cylindrical surface 4a are attracted. The symbol m2 on the portion 3d is fixed. Next, the jig 3 is placed on the tilting table 3i, and the tilting table 3i is designed such that the jig has an inclination angle of 15 to 72 degrees with respect to the XY plane of the coordinate system XYZ coordinate system. The eLT indicates the tilt angle with respect to the Z axis of the apex of the lens, and 0LY-¥ indicates the tilt angle with respect to the X axis at the effective radius position of the lens. The reason why the tilt angle of the jig is 15 degrees to 72 degrees will be explained. The figure is a view of the angle between the Z-axis and the normal direction of the cylindrical surface when measuring the cylindrical surface of the lens 4. 7 (a) shows the case where the w-axis of the measurement object uvw coordinate system is parallel to the XY plane of the measuring machine XYZ coordinate system (the jig tilt angle θ = 0), and the figure 7 (b) shows the measurement object uvw coordinates. The w-axis of the system is inclined with respect to the XY plane of the XYZ coordinate system of the measuring machine (the tilt angle of the clamp is 0.) The normal vector ns of the axial direction of the probe 1 is expressed by the following equation. -13- = < 0 ^ 0' 200930976 > 1 .> The normal vector nt (clamp tilt angle θ = 0) of the probe contact surface and the normal vector nu (clamp tilt angle Θ矣0) of the probe contact surface, as in the seventh The diagram has the following relationship established. Ο nt= 0 cosφΑ -sin at 4 0 sin ^ cos^4 ns cos0 0 sin0 •nt 0 cos^ -sin at 4 0 sin^ cos φΑ 0 1 0 -sin 0 0 cos 0 cos0 0 sin0 0 1 0 -sin0 0 cos0 The angle between the normal vector ns in the axial direction of the probe 1 and the normal vector nu (clamp tilt angle Θ# 0) of the probe contact surface is the maximum inclination angle of the cylindrical surface with respect to the XY plane. Regarding the tilt angle 0 of the jig, each of the angles θ of the normal vector ns and nu as the maximum tilt angle of the cylindrical surface relative to the χ γ plane and the tilt angle eLT at the apex of the lens are set to be used in relative use. In the measuring device of the present invention, the maximum inclination angle of the XY plane may be within 75 degrees. Further, the symbol ml (see Fig. 6(b)) of the lens 4 is hollow in shape with respect to the cylindrical surface 4a, and has a processed shape in which burrs or the like do not fly out. This is because if only a part of the mark ml protrudes on the outer peripheral side of the cylindrical surface 4a, when the mirror 14 of the through--14-200930976 is inserted into the lens barrel (not shown), it may be caused by the burrs of the mark mi or the like. The lens 4 produces an eccentricity gap. In addition to the above-described air absorbing, the fixed surface of the fixed lens 4 is also considered to have a method of fixing the cylindrical surface 4a of the outer peripheral portion of the lens by three points using clay or wax, or a three-point fixing using a spring. In this case, the area of the clay or the like which is protruded from the outer side of the cylindrical surface 4a of the lens 4 is not obtained as measurement data, and the circumscribed cylinder is obtained by calculation based on the measurement data of the original cylinder surface 4a. In the calculation, the calculation results are different from the original lens shape due to the fact that the portion of the original cylindrical surface 4a is expanded more than the original shape due to the clay or the like. [Step S5] The balls 3a to 3c in the jig 3 set as described above and a portion of the cylindrical surface 4a of the lens 4 and the surface are measured. Referring again to Figures 5 and 6. First, the probe 1 is positioned on the ball 3a to perform a focus servo to locate the center, and the X-axis and Y-axis are measured. After that, the measurement data and the design of the ball 3a ® are adjusted in the XYZ direction by the least square method, and the correct vertex position is calculated by the XYZ coordinate transformation amount. The center position coordinate 値 (Xa, Ya, Za) can be calculated from the previously calculated correct vertex position by measuring the diameter in the thickness measuring machine which has been traced in advance. In another method, by measuring the radius reference sphere equipped with the standard of the measuring machine, the 値 of the radius of the front end of the probe is first corrected to a level of 〇.〇1 μπι, and the radius of the probe is used, and by The optimum fit R is calculated so that the measurement data at the time of measuring the ball 3a and the RMS of the optimum fit R for changing the design radius are minimized, and the correct radius of the ball 3a is calculated. When the measurement is completed, the probe 1 is stopped at the focus of the ball 3a and -15-200930976 is retracted above Z. Since the ball 3c is subjected to the same method for the ball 3b, the coordinates 値 (Xb, Yb, Zb) and (Xc, Yc, Zc) at the center position can be calculated. The surface of the lens, the central axis of the cylindrical surface of the lens 4, the axis, i.e., the direction in which the central axis of the lens absorbing portion 3d is rotated, is scanned by the probe 1 in the χγ direction. Thereby, the probe 1 is tracked in the Z direction along the shape of the lens surface, and measurement data can be obtained. In the figure, 2a is a measurement area, and 0A represents a cylindrical surface measurement angle around the central axis (w axis). In Fig. 8, the measurement trajectory of the illustrated lens 4 is enlarged. From the center axis side The area sandwiched by the 0A angle to the apex seen is the measurement area. When the lens 4 is viewed from the +Z direction, the boundary between the cylindrical surface 4a and the lens surface 4e, and the boundary between the cylindrical surface 4a and the back surface of the lens, so that the region becomes along the boundary 4e or the boundary 4f The trajectory 2 (that is, the measurement trajectory (side surface side 2' along the circumferential direction of the cylindrical surface 4a) is measured, and is traced by the probe in the XY direction. In the above, the lens surface region on the right side when facing the boundary line 4e is scanned in the XY direction by the measurement trajectory (lens surface side). These measurement trajectories (side surface side) 2' from the Z direction are Each line of the "lens side" 2" of the measurement track © is a part of an ellipse, and the whole is a slightly line shape. Thus, during the tracking in the XY direction, the probe 1 traces in the Z direction along the shape of the lens 4 to obtain measurement data. [Step S6] The jig 3 is rotated only around the central axis (w axis) of the cylindrical surface of the lens 4, and the operation of the step S5 is repeated. Fig. 9(a) (aJ and (b) and (b') are diagrams showing the relationship between the angle of rotation 0 around the cylindrical surface axis axis of the lens 4 and the cylindrical surface measurement angle 0a. It is 0A = ±60 degrees (measured at 120 degrees). The angle of rotation of the jig obtained by three revolutions is 0 〇. 012〇. , -16- 200930976 0240 ° can get the measurement data for the whole week. In this case, even if the rotation is performed at 120 degrees each time, since the positions of the balls 3a to 3c are sequentially replaced, the relationship between the balls 3a to 3c and the lens from the +Z direction is not changed. The needle 1 may be the same as the contacts of the balls 3a to 3c and the lens 4 at the time of measurement. When either of the balls 3a to 3c or the lens 4 is measured, the probe 1 does not interfere with the measurement object other than the measurement target at the time of measurement. As shown in Fig. 9, when the cylindrical surface is measured at an angle of 0 Α = ± 6 〇 (120 © degree measurement) (a) When the clamp inclination angle θ = 15 degrees, the maximum inclination angle at the cylindrical surface of the lens It! ^ The angle with nu is 0 = 61.1 degrees, and the maximum tilt angle at the apex of the lens is eLT = 75 degrees. (b) When the jig tilt angle θ = 58 degrees, it is the maximum tilt angle on the cylindrical surface of the lens! The angle between ^ and (4) is 0 = 74.6 degrees, and the maximum tilt angle at the apex of the lens is 0 lt = 32 ❹. That is, it is possible to measure the tilt angle of the jig in the range of 15 to 58 degrees. In Figs. 10(a)(a) and (b)(b'), the angle of rotation 0 around the central axis (w axis) of the cylindrical surface of the lens 4 and the angle of measurement of the cylindrical surface are shown. Relationship between. It is 0a = ±30 degrees (measured at 60 degrees). The jig rotation angle is 0, 0 0 °, 060. , 012G°, 018〇°, 024Q°, 03GG. The measurement data of the whole week can be obtained by the six rotations. Compared with the jig 3 in the previous FIG. 9, the interval between the central axis of the lens absorbing portion 3d and the balls 3a to 3c is made larger, regardless of whether the yaw angle of the -17-200930976 has a rotation angle of 0, from +Z In the case where the direction is seen, the lens 4 and the balls 3a to 3c do not overlap. The jig 3 in Fig. 10 is the same as the jig 3 in Fig. 9, and when the ball 3 a to 3 c or the lens 4 is measured, the probe 1 and the measurement object other than the measurement point are measured. There will be no interference. On the other hand, unlike the jig 3 in Fig. 9, since the configuration of the balls 3 a to 3 c is changed from the +Z direction as long as the rotation is 60 degrees, there is a change to the ball 3 a The contact position of the probe 1 of ~3 c is necessary for change. For example, as shown in Fig. 10, the cylindrical surface is measured at an angle of 0A = ±30 (measured at 60 degrees). (a) When the tilt angle of the clamp is θ = 15 degrees, the maximum tilt angle of the cylindrical surface of the lens is ns and The angle of nu is 0 = 33.2 degrees, and the angle of inclination at the apex of the lens is 0 lt = 75 degrees. (b) When the jig tilt angle θ = 72 degrees The angle ns between ns and nu at the maximum tilt angle of the cylindrical surface of the lens is 0 = 7 4.5 degrees, and the inclination angle eLT at the apex of the lens is 18 degrees. That is, it is possible to measure the tilt angle of the jig in the range of 15 to 72 degrees. If the angle is smaller than the cylindrical surface measurement angle 0a = ±3O (measured at 60 degrees), the measurement time is increased because the number of measurement returns is increased, so it is not desirable to adopt such an angle. Hereinafter, the case where the cylindrical surface measurement angle 0A is ±60 degrees (measured at 120 degrees) (see Fig. 9) will be described as an example. [Step S7] -18- 200930976 As shown in Fig. 1 (a) and (b), the cylinder of the lens 4 is obtained by combining all the measurement data measured in the step S6 so that the center positions of the three balls are identical. The information of the cylindrical surface 4a and the surface of the full circumference of 3 60 degrees around the central axis (w axis) of the surface. Specifically, it will be at 0 0 above. , 0 ] 2 〇. , 0 2 4 G. The measurement data of the lens 4 at each rotation angle is arranged based on the three-ball reference XsYsZs coordinate system. Thereby, the measurement data of the cylindrical surface 4a and the surface of the lens 4 are combined over the entire circumference of 3 60 degrees. 2b shows the measurement data binding area. G At this point, 'the straight line XS obtained in step S3, that is, the connecting line Xs' connected to the center of gravity 3z from the center 3al of the ball 3a on the XSYS plane in the 3-ball reference XsYsZs coordinate system) The X axis of the machine is the same. In addition, the coordinate conversion amount when the measurement data 7 on the lens absorbing portion 3d is coordinate-converted in order to make the Zs axis coincide with the Z axis is used, and the cylindrical surface 4a of the lens 4 obtained 360 times here is used. And the measurement data of the surface is used as a coordinate conversion. [Step S8] © as shown in Fig. 12 (a) to (d), by the cylindrical surface 4a of the lens 4 obtained at step S7 and the surface The cylindrical surface data group 8 is extracted by synthesizing the data, and the external cylinder A6 is calculated, and the measurement data is coordinate-converted so that the Zg axis as the central axis thereof coincides with the designed Z-axis. In Fig. 12(a), the distribution of the synthesized data of the cylindrical surface 4a of the lens 4 obtained in the step S7 and the surface is shown. The data set 8 is measured by the cylindrical surface and the surface measurement data group 9 visible in the +Z direction. Regarding the cylindrical surface measurement data group 8, the arrangement of the data in the circumferential direction is necessary in consideration of the calculation processing by the least square method described later to make it sufficient for many data -19-200930976. For example, a degree of one-degree scale with respect to one circumference of the circumference, that is, a degree of 360 degree division of one week is expected. Fig. 12(b) is a view seen from the γ direction in the distribution of the synthesized data in Fig. 12(a). The cylindrical surface measurement data group 8 and the surface measurement data group 9 are also shown in Fig. 9 in the plane pattern 7a of the lens three-point support portion 3d2 obtained in the step S3. The plane type at this time is expressed by the following equation. Ηρ·{Χ-Χα, Υ -Υα, Ζ-Ζά) = 0 〇 For the synthetic data of Fig. 12(b), as shown in Fig. 12(C), in order to make the plane of the lens 3 point support portion 3d2 Equation 7a is coordinate-converted in accordance with the XY plane (i.e., the plane of Z = 0) in the XYZ coordinate system of the measuring machine. The flat type 7al at this time is expressed by the following equation. Thereby, it is possible to process the synthesized data of the lens 4 with reference to the lens 3-point support portion. Z = 0, np\ - (0,0,1) Extract the cylindrical surface measurement data from the synthesized data of the coordinate transformation as such. When the appropriate R1値 is determined, the cylindrical surface measurement data group 8 can be extracted by selecting the measurement data (Χ, Υ, Ζ) when the following formula is satisfied. 4(X - Xa\f +(Υ- Υα\)2 > R, however, the radius of R1 is larger than the radius of the outermost rounded data on the edge portion (planar portion) of the surface measurement data group 9 The radius of the cylindrical surface measurement data 8 is small. The radius of the circle data of the outermost circumference on the edge portion (planar portion) is measured by tilting the eLT of the central axis of the lens 4 shown in Fig. 6 The NC information of Track 2 can be calculated. The radius of the cylindrical surface material 槪-20- 200930976 can be calculated by the design of the cylindrical surface of the lens. Figure 12 (d) is in the +Z direction. Looking at the map of the cylindrical surface measurement data group 8 extracted in Fig. 12(c), the circle is calculated by using the least square method of the cylindrical surface measurement data group 8, and the circle from the calculation is selected to the outside. Find the position of the center of gravity Ga of the three points Al, A2, and A3 by the top three, and find the circumcircle A5 through the points a 1 , A2 , and A3 centered on the center of gravity Ga The extension of the circumscribed circle A5 on the Z axis is defined as the circumscribed cylinder A6, and the central axis thereof is defined as the Zg axis 'to the above synthetic data so that the Zg axis becomes the Q measuring machine xy The z-axis coincidence mode of the z coordinate system is used for coordinate transformation. Fig. 13 is a composite data of the coordinate transformation in Fig. 12 (d) seen from -Y; the map of the distribution is made to make the lens 3 point on the support portion 3d2 7al is aligned with the XY plane in the XYZ coordinate system of the measuring machine (ie, the plane of Z = 〇), and the central axis (Zg axis) is aligned with the Z axis in the coordinate system XYZ coordinate system. The 1 2 system represents the design lens. According to the above steps S1-S8, X, γ, and z in the 3-dimensional space are parallel to "(X-axis around), β (in terms of the lens 3 point support portion 3d2 and the cylindrical surface 4a of the lens 4). Among the six degrees of freedom in the direction of rotation around Υ (around the Υ axis), the five degrees of freedom of X, Υ, ζ, α, and β are varied and adapted according to the least squares method. It is set such that the symbol ml of the lens 4 coincides with the symbol m2 of the lens absorbing portion 3d of the jig 3, and the error 値 is sufficiently within ±1 degrees. As a result, it is necessary to determine the positioning of all the three dimensional spaces. 6 degrees of freedom. The advantages of the method described in steps S1-S8, even if the cylindrical surface 4a of the lens 4 is distorted, due to The external cylinder A6 calculated based on the measurement data of the cylindrical surface 4a is positioned in contact with the lens barrel, and has a point j of the positioning of the lens 4 having good reproducibility from 21 to 200930976. Even if dust adheres to the cylindrical surface 4a of the lens 4 at the time of measurement, there is a lot of noise in the measurement data which occurs due to dust, and many operators can recognize the noise, and eliminate impurities. It is possible to obtain measurement data closer to the actual shape. [Step S9] As shown in Fig. 14 (a) and (b), the surface measurement data group 9 is extracted from the synthesized data subjected to the coordinate transformation in step S8. The surface data group 9 is divided into a lens face data group 9a and an edge portion data group 9b, and only the lens face data group 9a is extracted. For this purpose, for example, for the synthetic data (χ, γ, ζ), the appropriate Ζ1値' is determined and the lens face data group 9a can be extracted due to the selection of the data at Ζ2Ζ1. However, for Ζ1, 値d is designed for the thickness of the surface and the back surface of the edge portion (planar portion) of the lens, and Z1 = d + Δ(1). In determining Ad, set it to Ζ1 in Fig. 14(a) The data 9b at the edge portion of the surface measurement data group 9 below is surely within the range. As an example of setting, the computer that controls the measuring machine is displayed on the display so that it can be set by the user. [Step s 1 〇] As shown in Fig. 15, in the measuring machine XYZ coordinate system, coordinate conversion is performed so that the lens face data group 9a previously extracted in step S9 and the design lens shape 1 2 are In the step S9, the origin of the lens 3 point support portion 3 d2 has an origin, and for the sake of consideration, the origin is shifted to the apex portion of the designed lens shape 12. If coordinate conversion is performed The RMS is minimized. As shown, the lens face data group 9a is rotated by the coordinate transformation amount β (or α) mode -22-200930976' with the central axis Zp, and the parallel coordinate conversion amount dX (or dY) and dZ do the parallel move. Make this transfer amount in the computer The calculation is performed after the calculation. [Step S11] As shown in Fig. 16, the coordinate value dX (or dY) of the design 値 is obtained by applying -1 to the coordinate transformation amount obtained in the previous step S10. The height difference dZ and the inclination β (or 〇〇. According to the above steps S1 to S11, the flat portion on the upper surface of the lens supporting portion 3 d2 of the lens absorbing portion 3d (corresponding to the edge portion on the back side of the lens) and the lens can be calculated. The cylindrical surface 4a of the outer peripheral portion of the lens 4 is the tilt amount, the eccentric amount dX (or dY), and the height difference dZ of the optical axis Zp of the reference lens surface. The lens rear surface is also provided with the lens 4 facing The back surface can be seen from the +Z direction, and the mark ml is matched with the m2 of the lens absorbing portion, and the flat portion of the upper surface of the lens supporting portion 3d2 of the lens absorbing portion 3d can be calculated based on the steps S1 to S11. (corresponding to the edge portion on the lens surface side) and the cylindrical surface 4a of the outer peripheral portion of the lens 4 as the reference, the tilt amount, the eccentric amount, and the height difference of the optical axis of the lens back surface. However, the above steps S1 to S11 are The outer peripheral portion of the lens 4 is premised on the cylindrical surface 4a, and is on the outer peripheral portion. In the case of a prismatic shape, the circumscribed circle is obtained from the side measurement data, and the amount of tilt and the amount of eccentricity of the optical axis of the lens surface and the back surface can be calculated. The cylindrical surface 4a of the lens 4 or the lens surface (and the lens back surface) The amount of the total data gap can also be obtained by the coordinate transformation which minimizes the RMS with the difference between the design formulas. Next, referring to Fig. 18 to Fig. 20, the angle of the lens is obtained from the perspective of Fig. 17 The flow of the shape of all the faces is explained. [Steps S12 to S15] For the back surface of the lens, by performing the above-described steps S1 to S7, as shown in the drawing (a) of 18-23-200930976, the circumference is made around the central axis. The synthetic data composed of the cylindrical surface measurement data group 1 of 360 degrees and the back surface measurement data group 11 (step S12). Next, according to the above-described steps S8 and S9, as shown in Fig. 18 (1)) (see Fig. 18 (a) from the -Y direction), the plane 1 of the lens edge portion of the back side measurement data group u is calculated. Lbl (step S13). Next, as shown in Fig. 18(c), the plane type llb1 of the lens edge portion is coordinate-converted to coincide with the χγ plane (i.e., the plane of Z = 0) in the coordinate system XYZ coordinate system. At this time, the plane type 1 lb2 is Z = 0 (step S14). Ο In this state, the synthetic data is separated into the cylindrical measurement data group 10 and the back measurement data group 11', and the cylindrical measurement data group 10 is extracted. For this purpose, for example, in the measurement data (X, Y, Z), the appropriate ri 决定 is determined, and the measurement data sufficient for the following formula is selected, and the cylindrical measurement data group 10 can be extracted. V(X - Xa\)2 + (Y- Ya\f > Rx selects R1 to be larger than the radius of the outermost circumference of the edge portion (planar portion) of the back side measurement data group 11 and is larger than the cylindrical surface The radius of the data group 10 is small. The radius of the outermost rounded data of the edge portion (planar portion) can be determined according to the measurement trajectory 2 when the eLT is tilted from the central axis of the lens 4 shown in Fig. 6. Calculated by NC information, and the radius of the data of the cylindrical surface can be calculated according to the design of the cylindrical surface of the lens. Next, as shown in Fig. 18 (d), the cylindrical surface is extracted. The circumscribed cylinder B6 of the data group 10 (as seen from the +Z direction) coordinates the zg axis as its central axis to match the Z axis in the coordinate system XYZ coordinate system. The data group 10 calculates the circle by the least square method, and selects the points separated from the circle to the outside by the top three in the order of large to small, -24-t 200930976 finds the center of gravity Gb of the three points B1 to B3, by The circle B5 is drawn around the center of gravity Gb and passes through the circles of points B1 to B3, and the additional circle B5 is extended on the Z axis. The cylinder B6 is circumscribed so that its central axis is the Zg axis (step S15). [Step S16] Figure 19(a) shows the distribution of the back side data of the lens which is coordinate-converted in step S15 as seen from the -Y direction. Fig. 11 b2 of the lens edge portion (corresponding to the plane on the lens 3 point support portion 3 d2) and the 〇XY plane (Z = 〇) in the coordinate system XYZ coordinate system, and the central axis (Zg axis) Consistent with the Z axis in the XYZ coordinate system of the measuring machine. The data measured on the back side of the lens, as shown in Fig. 19(b), is rotated 180 degrees so that the back side of the lens faces the -Z direction, and the mark of the lens is made ml. (Refer to Fig. 6). The center of rotation at this time is not changed as long as the symbol ml is rotated 180 degrees, and the axis parallel to the v-axis in the coordinate system of the measuring object uvw is used as the center of rotation. It is necessary for the axis. Here, a 180-degree swivel movement around the Y-axis in the same direction as the v-axis is performed, and coordinates are converted from the uvw seat® standard to the XYZ coordinate system of the measuring machine. The Ilb3 of the lens edge portion is It is in accordance with the χγ plane (z = 0) in the coordinate system of the XYZ of the measuring machine. [Step S 1 7] Figure 20 (a) shows the data on the lens front side obtained in the above-described step S8. The cylindrical surface measurement data group 9 and the surface measurement data group 9 are in the form of a plane 7al and Z = 0 on the three-point support portion of the lens. The figure is based on the Z axis. Fig. 20(b) shows the data on the back side of the lens obtained in the above step S16. The cylindrical surface measurement data group 10 and the back measurement data group 11 are lens 3 point support portions. 1 lb3 and Z = 0, that is, the state of the edge of the lens and the plane 7a 1 (Z = 0) on the 3-point support of the -25-200930976 lens, and the z-axis is Benchmark. The data on the front side of these lenses and the data on the back of the lens are joined as shown in Fig. 20(c). In other words, the edge portion of the lens back surface (the flat pattern 7a on the lens 3 point support portion, the plane pattern 11b3 at the lens edge portion) and the cylindrical surface on the outer circumference of the lens (the cylindrical surface measurement data group 8 and the cylindrical surface measurement) The data group 1〇) is combined as a benchmark. As described above, by further performing steps S12 to S17, the shapes of all the faces of the lens 4 can be obtained in all directions. Next, while referring to Fig. 22, the optical axis eccentricity dX (or dY), the height difference dZ, and the inclination β (or α) on the back side of the lens on the optical axis of the lens side in Fig. 21 are used. The flow chart is explained. [Step S1 8] In all the data obtained in the previous step S17, as shown in Fig. 22(a), only the lens face data other than the lens edge portion data is extracted for the back side measurement data group 11. © For this purpose, in step S9, for the measurement data (χ, γ, ζ), determine the appropriate Ζ1値' by selecting the measurement data at ZSZ1, and extracting only the lens surface data in the back measurement data group 1 1 . In this case, since the plane type 7al (i.e., the plane type llb3 of the lens edge portion) on the lens 3 point support portion is Z = 0, it is determined that the Z of Z1 is a negative number close to 〇. [Step S19] As shown in Fig. 22(b), the coordinate transformation is performed so that the RMS between the lens face data on the back side of the lens obtained in step S18 and the design is minimized. The same method as step S10. -26- 200930976 [Step S20] A -1 is applied to the coordinate conversion amount in the step S19, and the eccentricity dX (or dY), the height difference (dZ), and the inclination β (or α) are calculated from the design. The same method as step S11. [Step S21] The difference between the design 自 from the back side of the lens obtained in step S20 is determined by using any one of the design 値 from the lens side obtained in step S11 as a reference, and the lens is calculated. The aspherical optical axis 16a on the front side is the eccentricity dX (or dY), height difference (dZ), and inclination β (or α) of the aspherical optical axis 16b on the back side of the lens at the time of reference. The thickness of the center of the 19 series, the design of the thickness of the center of the Z 〇 >, and dZ indicate the amount of the difference from the design 値ZG. As described above, by further performing the steps S18-S21, the eccentricity dX (or dY) and the height difference (dZ) of the optical axis 16b on the back side when the optical axis 16a on the surface side of the lens is used as a reference can be obtained. The inclination β (or 〇〇). Similarly, the eccentricity dX (or dY), the height difference dZ, and the inclination of the optical axis 16a on the front side when the optical axis 16b on the back side is used as a reference can be calculated; 3 (or α) © Steps S1 to S11, the lens model 101 is used as an object instead of the lens 4, and when the upper surface of the base 101a and the cylindrical surface of the shaft portion 101b are used as a reference, the transfer surface l〇lc is calculated. The amount of tilt of the optical axis, the amount of eccentricity, and the height difference. As described above, the shape measuring method according to the present invention uses the lens outer circumference of the corresponding lens barrel under the use of a three-dimensional shape measuring machine having a contact or non-contact probe. The amount of inclination and the amount of eccentricity of the optical axis of the lens surface are obtained as a reference, and the shape of all surfaces (surface, back surface, and side surface) of the lens is determined in all directions using the cylindrical surface of the outer peripheral portion of the lens as a reference; The optical axis of the front side (or back side) -27- 200930976 is used as a reference, and There is a possibility of calculating the eccentricity, height difference, and inclination of the optical axis on the back side (or the front side) of the lens. Therefore, it is particularly useful for measuring the shape of an aspherical lens used in a cellular phone, a digital camera, etc. The object to be measured may have the same shape measurement as the reference on the outer peripheral surface such as the lens surface. [Simplified Description of the Drawings] Fig. 1 is a schematic diagram showing the configuration of the shape measuring machine used in the present invention. FIG. 2 is a flow chart for measuring the shape of the lens of the present invention, FIG. 3 is a view showing steps S1 to S2 of the same shape measuring method, and FIG. 4 is a view showing the same shape measuring method. Fig. 5 is a view showing a step S4 to S5 of the same shape measuring method, Fig. 6 is an enlarged view showing a part of Fig. 5, and Fig. 7 is a step S4 of the same shape measuring method. Fig. 8 is a view of the step S5 of the same shape measuring method, Fig. 9 is a view showing the step S6 of the same shape measuring method, and Fig. 10 is a view showing the step S6 of the same shape measuring method. Other figures, number 1 1 is a view showing a step S7 of the same shape measuring method, FIG. 12 is a view showing a step S8 of the same shape measuring method, and FIG. 13 is a view showing another step S8 of the same shape measuring method, Fig. 14 is a view showing a step S9 of the same shape measuring method, Fig. 15 is a view showing a step S10 of the same shape measuring method, and Fig. 16 is a view showing a step S11 of the same shape measuring method, the 17th FIG. 18 is a flowchart showing the steps S12 to S15 of the same shape measuring method. FIG. Fig. 20 is a diagram showing the step S17 of the same shape measuring method. Fig. 21 is a flowchart showing the continuation of Fig. 14 of the step of the same shape measuring method, Fig. 22 is a diagram Fig. 19 is a view showing a step S18 to S21 of the same shape measuring method, and Fig. 23 is a view showing a lens model for performing shape measurement by the present invention. G [Description of main component symbols] 1 Probe 2 Measurement trace 2, measurement trace (side surface side) 2" Measurement trace (lens surface side) 2a Measurement area 3 Fixture 3 a, 3 b, 3 c Ball 3 a, 3 b, 3 c 3al,3bl,3cl center 3 a 1,3 b 1,3 c 1 3d lens absorbing part 3d2 lens 3 point support part 3 e clamp return part 3h air tube 3i tilting stage 3j stage 4 lens 4 a cylinder面-29- 200930976 4al 4b 4e,4f 7 7a,7al,1 lbl,1lb2,1lb3 8 9 9 a 〇9b 10 11 12 16a 16b 19 6 1 ❹ 62a 62b 62c 63 64 65 66 67 68 Surface boundary measurement data Planar cylindrical surface measurement data group surface measurement data group lens face data group edge portion data group cylindrical surface measurement data group back measurement data group design lens shape lens surface side aspherical optical axis lens back side aspheric surface light Shaft Center Thickness Base Platform X-Axis Laser Measurement Length Y-Axis Laser Measurement Length Z-Axis Laser Measurement Platform Plate Z-Step Probe X Reference Mirror Y Reference Mirror Z Reference -30-
200930976 69,70 7 1 101 101a 101b 101c 200 α，β，θ，0, 0a，Qly，Qlt A 1, A2，A3 ,B 1，B2, B3 d200930976 69,70 7 1 101 101a 101b 101c 200 α,β,θ,0, 0a,Qly,Qlt A 1, A2,A3 ,B 1,B2, B3 d
d，dX，dY，dZ ml, m2 S u，v，w，X，Y，Z,Zg,Zp,Xs，Ys，Zs np，nr，nrl ,nr2，ns，ntin-u XY台階 雷射 透鏡模型 底座 軸部 轉寫面 被測定物 角度 點 距離量 記號 被測面 軸 向量d, dX, dY, dZ ml, m2 S u, v, w, X, Y, Z, Zg, Zp, Xs, Ys, Zs np, nr, nrl, nr2, ns, ntin-u XY step laser lens Model base shaft part transfer surface measured object angle point distance quantity mark measured surface axis vector
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