201017096 六、發明說明： 【發明所屬之技術領域】 本申請主張基於2008年10月29日申請之日本專利 申請第2008 - 2775 9 7號之優先權。該申請之全部內容藉 由參照援用於該說明書中。 本發明涉及利用3點法測量直線性之方法及測量直線 性之裝置。 【先前技術】 可由三點法進行測量對象物之表面直線性（專利文獻 1 )的測量。例如，利用3個位移計之基準點移動之軌跡 即仿效曲線之輪廓、測量對象物之表面輪廓、及3個位移 計之俯仰成分之輪廓來記述3個位移計之測量數據，藉由 將該記述式作爲聯立方程式解出，可決定表面輪廓。 專利文獻1 :日本專利公開2003-2 5 4747號公報 爲了基於藉由三點法測量之數據來分離位移計啓動之 軌跡即仿效曲線之輪廓、3個位移計移動時產生之俯仰成 分之輪廓、及測量對象物之表面輪廓，必須高精度調整3 個位移計之零點。例如，爲了測量平坦度爲幾V m之表面 之直線性，必須將3個位移計之零點從目標位置之偏移量 設爲幾十奈米〜幾奈米以下。 而且，雷射位移計等非接觸之位移計之零點根據測量 對象物之表面性狀，例如由砂輪引起之硏磨痕之狀態、粗 糙度、材質、反射率、透射率等變動。而且’零點之變動 -5- 201017096 量具有個體差。因此，難以事先高精度地進行位移計之零 點調整。 【發明內容】 本發明之目的在於，提供一種不必高精度進行3個位 移計之零點調整而可以計算測量對象物之表面輪廓之直線 性測量方法。 本發明之其他目的在於，提供一種運用上述方法測量 直線性之直線性測量裝置。 根據本發明之一觀點，提供一種直線性測量方法，該 方法，具有： 使排列在第1方向、相對位置被固定之3個位移計與 測量對象物相對，將該位移計及該測量對象物之一方之活 動物，相對於另一方之固定物一邊朝第1方向移動，一邊 測量從3個位移計到分別在測量對象物之表面沿著朝第1 方向延伸之測量對象線排列之3個被測量點之距離之步驟 » 根據上述3個位移計之測量結果計算對上述活動物之 相對位置被固定之基準點之軌跡即仿效曲線之輪廓之步驟 將上述仿效曲線計算出之輪廓之2次成分，基於事先 測量出之仿效曲線之輪廓之2次成分進行校正之步驟； 基於被校正之仿效曲線之輪廓，計算上述測量對象物 之表面輪廓之步驟。 -6- 201017096 根據本發明之另一觀點，提供一種直線性測量裝置， 其具有： 支撐測量對象物之工作臺； 感測器頭’包括測量到分別在該測量對象物之表面排 列於該第1方向之被測量點之距離之3個位移計； 導向機構’相對於另一方之固定物沿著上述第1方向 可移動地支撐上述感測器頭及上述工作臺之一方之活動物 :及 控制裝置’存儲有相對固定在上述活動物之基準點之 軌跡即仿效曲線之2次成分，基於由上述3個位移計測量 之測量數據，求出沿著平行於上述第1方向之測量對象線 之上述表面之輪廓， 上述控制裝置，執行： 一邊朝上述第1方向移動上述活動物，一邊藉由3個 位移計之每一個，測量到沿上述測量對象線之表面上之被 測量點之距離而取得測量數據之步驟； 基於上述3個位移計之測量結果，計算對上述活動物 之相對位置被固定之基準點之軌跡即仿效曲線之輪廓之步 驟； 將上述仿效曲線之計算出之輪廓之2次成分’基於被 存儲之仿效曲線之輪廓之2次成分進行校正之步驟；及 基於被校正之仿效曲線之輪廓’計算上述測量對象物 之表面輪廓之步驟。 藉由不受仿效曲線之輪廓變動之影響之方法事先測量 201017096 仿效曲線之輪廓之2次成分，即使在未進行位移計之零點 調整之情況下，也可確定仿效曲線之2次成分。由此’不 必進行精密之零點調整而能夠進行測量對象物之表面輪廓 的測量。 【實施方式】 於圖1A表示根據實施例之直線性測量裝置之槪要透 視透視圖。活動工作臺10藉由工作臺導向機構11被支撐 爲可朝一方向移動。定義將活動工作臺10之移動方向設 爲X軸、將垂直下方設爲Z軸之xyz直角坐標系。 導軌18在活動工作臺10之上方支撐硏磨頭15»硏磨 頭15可沿著導軌18在y軸方向移動。而且，硏磨頭15 也可相對於導軌18在z方向移動。即，硏磨頭15可相對 於活動工作臺10升降。在硏磨頭15之下端安裝有砂輪16 。砂輪16具有圓柱狀之外形，以其中心軸平行於y軸之 姿勢安裝在硏磨頭15。 於活動工作臺10上保持測量對象物（被硏磨物）20 。在使砂輪1 6接觸於測量對象物20之表面之狀態下’一 邊旋轉砂輪16，一邊藉由朝X方向移動活動工作臺1〇’ 從而可硏磨測量對象物20之表面。 控制裝置19控制活動工作臺10及硏磨頭15之移動 〇 如圖1B所示，在硏磨頭15之下端安裝有感測器頭 30。在感測器頭30，安裝有3個位移計31i、31j、31k。 -8 - 201017096 在位移計3 1 i、3 lj、3 1 k例如利用雷射位移計。位移計 3 li、3 lj、3 lk可分別測量從位移計到測量對象物20之表 面上之被測量點之距離。3個位移計3 1 i、3 lj、3 1 k排列 在y方向。而且，3個位移計3 1 i、3 lj、3 1 k之被測量點 也排列在y方向。因此，可測量沿著平行於y方向之測量 對象線之表面之高度。藉由一邊朝y方向移動硏磨頭15 一邊進行測量，可測量沿著測量對象物20表面之測量對 _ 象線之表面輪廓。測量數據從位移計31i、31j、31k輸入 Ό 到控制裝置1 9。 參照圖2對坐標系及各種函數進行說明。在圖2中， 將上方設爲ζ軸之正方向。因此，感測器頭30和測量對 象物20之上下關係與圖1Β所示之上下關係相反。位移計 3 1 i、3 1 j、3 1 k朝向y軸之負方向按該順序以等間隔Ρ配 置。將連接兩端之位移計31i、31k之零點之線段之中點 定義爲基準點。將從基準點到中央之位移計3 lj之零點之 φ 高度（零點誤差）設爲5。 將測量對象物20之表面、沿著測量對象線之輪廓設 爲W(y)。將朝y方向移動感測器頭30時基準點之軌跡 (仿效曲線）設爲h ( y )。理想地，仿效曲線h ( y )係 直線，但是實際上從理想的直線歪曲。 將連接兩端之位移計31i、31k之零點之直線從y軸 傾斜之角度設爲0 ( y )。理想地，傾斜角0 ( y ) =〇，但 是實際上隨著感測器頭30之移動而產生俯仰，由此傾斜 角0(y)與仿效曲線 h(y)之傾斜度爲獨立變動。位移 -9- 201017096 計31i之零點和基準點之高度之差、及位移計31k之零點 和基準點之高度之差可表示爲T(y)xP。此處，與俯仰 成分 T ( y) =sin ( 0 ( y))近似。若將位移計3 1i、3 1j 、3 1 k之測量値分別設爲i ( y ) 、j ( y ) 、k ( y )，則下 述式成立。 [數學式1] W(y + P) = h(y) + i(y) + T(y)xP ...(1) W(y) = h(y)+j(y) + 8 ... (2) W(y-P) = h(y) + k(y)-T(y)xP ...(3) 由於傾斜角0 ( y )非常小，因此，使cos ( 0 ( y ) )近似於1。 測量對象物20之形狀，例如係一邊之長度爲2m之正 方形，位移計之間隔P例如係1 〇〇mm。 若從式（1) 、（2) 、（3)消去 T(y)和 h(y)， 則可得到以下式。 [數學式3] W(y + P)-2W(y)+W(y-P) + 2S = i(y)-2j(y) + k(y)〜（4) 此處，假設用以下3次式（5)表示表面輪廓w(y) -10- 201017096 [數學式4] W(y) = ay3 + by2 + cy + d ...(5) 若將式（5 )代入到式（4 )，則得到以下式（6 ) » [數學式5] 6aP2y + 2bP2 + 25 = i(y)-2j(y) + k(y)...(6) ❿ 式（6)之右邊全部係測量數據，位移計之間隔P爲 已知。從而，左邊之未知數a可從右邊之變量y之1次成 分計算。但是，即使求出右邊之y之0次成分，左邊之零 點誤差6由於係未知，所以不能夠決定未知數b。即，可 決定表面輪廓W(y)之3次成分a，但不可決定2次成分 b。另外，也可與3次成分同樣地決定表面輪廓W(y)之 4次以上之成分。 φ 於實施例中，爲了彌補不可決定表面輪廓W(y)之 2次成分，事先測量好仿效曲線h(y)之2次成分。仿效 曲線h(y)之2次成分相當於導軌18之撓度，所以可認 定在每次測量時沒有大的變動。從而，事先測量好仿效曲 線h(y)之2次成分，則在每次進行測量對象物之表面輪 廓的測量時，不需要重新測量仿效曲線h ( y )之2次成分 。另外，可認定仿效曲線h(y)之3次以上之成分在每次 測量表面輪廓時（在感測器頭30每次移動時）不可預測 地變動。因此，即使事先測量好仿效曲線h(y)之3次以 -11 - 201017096 上之成分’也不可基於事先測量出之3次以上之成分來校 正實際之測量對象物之測量結果。 於圖3A作爲一例表示事先測量仿效曲線h(y)之2 次成分之方法之流程圖。如圖3B所示，在步驟S1中將測 量對象物20放置於活動工作臺1〇之上。沿著測量對象物 20之表面上之平行於y方向之任意直線移動傾斜儀35而 測量沿著該直線表面之傾斜之分布。根據該傾斜之分布計 算表面輪廓W(y)。由傾斜儀進行之測量不受導軌18之 歪斜之影響。 於步驟S2中，藉由利用位移計3 lj測量沿著與由傾 斜儀35測量傾斜分布之直線相同之直線之表面輪廓，從 而取得測量數據j ( y )。 於步驟S3中，計算仿效曲線h(y)之2次成分。以 下’對該計算方法進行說明。由位移計3 lj計測之表面輪 廓與根據由傾斜儀進行之計測求出之表面輪廓W(y)相 同。因此’在根據由傾斜儀進行之計測求出之表面輪廓W (y )和由位移計3 1 j測量之測量數據j ( y )之間，式（2 )之關係成立。由於零點誤差<5係常數，所以可根據表面 輪廓W(y)之2次成分和測量數據j(y)之2次成分計 算仿效曲線h(y)之2次成分。計算出之2次成分存儲在 控制裝置1 9。 仿效曲線h(y)之輪廓一般在每次朝y方向移動硏磨 頭15時變化，不限於每次成爲相同之輪廓。但是，可認 定仿效曲線h(y)之2次成分係決定仿效曲線之大致形狀 201017096 之低次成分且重現性高。即，可認定在每次測量時無大之 變動。 於圖4表示根據實施例之直線性測量方法之流程圖。 首先’將測量對象物2〇裝載於活動工作臺1〇。該測量對 象物20不需要與在圖3 a所示之步驟利用傾斜儀測量表面 輪廓之測量對象物20相同。 ❹ 於步驟SA1中’—邊朝y方向移動硏磨頭15及感測 器頭3 0，一邊由位移計3 i i、3丨j、3 i k測量到測量對象物 20表面之被測量點之距離i(y) 、j(y) 、k(y)。被測 量之數據輸入到控制裝置1 9。 於步驟SA2中，在測量數據i(y) 、j(y) 、k(y )運用低通濾波器而除去雜訊成分。爲了有效地使低通濾 波器作用，測量數據i ( y ) 、j ( y ) 、k ( y )以相對於位 移計之間隔P非常窄之刻度取得。例如，以0.0 5 mm之刻 度寬取得測量數據i(y) 、j(y) 、k(y)。 於步驟SA3中，對運用低通濾波器之後的測量數據i (y) ' j ( y ) 、k(y)進行採樣而生成步驟數據。採樣 之周期例如爲位移計之間隔P之一半，即5 0mm。 於步驟SA4中，基於步驟數據i(y) 、j(y) 、k( y)，利用遺傳算法導出仿效曲線h(y)和俯仰成分T(y 於圖5表示運用遺傳算法之步驟SA4之詳細流程圖。 在該遺傳算法中’將仿效曲線h(y)和俯仰成分T(y) 之羣組設爲1個個體。 -13- 201017096 於步驟SB1中生成初代個體群。例如，個體數爲200 。其中一例是將1個個體之仿效曲線h(y)和俯仰成分T (y)設爲0。其他之199個個體之仿效曲線h(y)和俯 仰成分T(y)根據隨機數決定。另外，在初始狀態中也 可將所有個體之仿效曲線h(y)及俯仰成分T(y)設定 爲0。 於步驟SB2中，由評估函數評估各個體，計算各個體 之適合度。根據表面輪廓W(y)設定評估函數。3個位 移計3 1 i、3 lj、3 1 k測量沿著同一測量對象物20表面之同 一測量對象線之輪廓，所以利用式（1 )〜式（3 )分別計 算之3個表面輪廓 Wi(y) 、W2(y) 、W3(y)應該一 致。 因此，首先求出Wi(y)和W2(y)之差量Wdy) -W2 ( y )、及 W2 ( y )和 W3 ( y )之差量 W2 ( y ) -W3 ( y )。用多項式表示表面輪廓W(y)時0次成分相當於測 量對象物20和感測器頭30之間隔，1次成分相當於測量 對象物20之姿勢。即，表面輪廓 W(y)之0次成分和1 次成分不直接關係到測量對象物20之表面輪廓。因此， 從差量Wdy) -W2(y)及差量W2(y) -W3(y)除去〇 次成分和1次成分。 計算除去0次成分和1次成分之差量W^y) -W2(y )及差量W2(y) -W3(y)之各分散。將這2個分散之和 設爲評估函數。可謂評估函數之値越小，適合度越高。根 據適合度排序所有個體。 201017096 於步驟SB3中，選擇成爲交叉對象之個體。作爲一例 ，越是適合度高的個體，選擇個體之槪率設定爲越高。基 於該選擇槪率，選擇由2個個體構成之10對。 於步驟SB4中，使選擇出之個體對之仿效曲線h(y )或俯仰成分T(y)之至少一方交叉，生成新的個體。 參照圖6說明交叉之方法。表示在這代個體中被選擇 爲交叉對象之2個個體Ua及Ub之仿效曲線h(y)及俯 i 仰成分之輪廓T(y)。更換（交叉）個體Ua之仿效曲線 h(y)之一部分和個體Ub之仿效曲線h(y)對應之部分 ，生成新的個體Uc及Ud。新的個體Uc及Ud之俯仰成分 之輪廓T(y)分別仍繼承原來個體Ua及Ub之俯仰成分 之輪廓T(y)。這樣，從2個個體新生成2個個體。在 步驟SB3中選擇10對個體，所以在步驟SB4中新生成10 對，即20個個體。 另外，也可交叉俯仰成分之輪廓T(y)，也可交叉 φ 仿效曲線h(y)和俯仰成分之輪廓T(y)之兩者。 若步驟SB4結束，則在步驟SB5中，選擇成爲突然 變異之對象之個體。作爲一例，適合度高的10個個體除 外，從剩餘之190個個體選擇80個。 於步驟SB6中，在選擇之個體上產生突然變異’生成 新的個體。 參照圖7對突然變異之方法進行說明。在圖7顯示在 步驟SB5中選擇之1個個體Ue。在個體Ue之仿效曲線 h(y)重疊任意幅度及高度之高斯曲線’生成新的個體 -15- 201017096The invention is based on the priority of Japanese Patent Application No. 2008-2775-9, filed on Oct. 29, 2008. The entire contents of this application are incorporated by reference in this specification. The present invention relates to a method of measuring linearity using a 3-point method and a device for measuring linearity. [Prior Art] The measurement of the surface linearity of the object to be measured (Patent Document 1) can be performed by the three-point method. For example, the measurement data of the three displacement meters is described by using the trajectory of the reference point movement of the three displacement meters, that is, the contour of the simulation curve, the surface contour of the measurement object, and the contour of the pitch components of the three displacement meters. The description is solved as a simultaneous equation, which determines the surface contour. Patent Document 1: Japanese Patent Laid-Open Publication No. 2003-2 5 4747, in order to separate the trajectory of the displacement meter, that is, the contour of the simulation curve, the contour of the pitch component generated when the three displacement gauges move, based on the data measured by the three-point method, And to measure the surface contour of the object, the zero point of the three displacement meters must be adjusted with high precision. For example, in order to measure the linearity of the surface having a flatness of several V m , it is necessary to set the offset of the zero point of the three displacement gauges from the target position to several tens of nanometers to several nanometers or less. Further, the zero point of the non-contact displacement meter such as a laser displacement meter varies depending on the surface properties of the object to be measured, for example, the state, roughness, material, reflectance, transmittance, and the like of the scratch caused by the grinding wheel. And the change in 'zero point' -5- 201017096 has an individual difference. Therefore, it is difficult to perform zero adjustment of the displacement gauge with high precision in advance. SUMMARY OF THE INVENTION An object of the present invention is to provide a linear measuring method capable of calculating a surface contour of a measuring object without performing zero adjustment of three shift meters with high precision. Another object of the present invention is to provide a linearity measuring apparatus for measuring linearity by the above method. According to one aspect of the present invention, there is provided a method for measuring a linearity, comprising: displacing three displacement meters arranged in a first direction and a relative position with an object to be measured, and the displacement meter and the object to be measured One of the moving objects moves in the first direction with respect to the other fixed object, and measures three rows from the three displacement meters to the measurement target line extending in the first direction on the surface of the measurement object. Step of measuring the distance of the measured point» Calculating the trajectory of the reference point to which the relative position of the movable object is fixed, i.e., the contour of the simulated curve, based on the measurement results of the above three displacement meters, and calculating the contour of the above imitating curve twice The step of correcting the component based on the secondary component of the profile of the imitative curve measured in advance; and calculating the surface profile of the object to be measured based on the contour of the corrected profile curve. -6- 201017096 According to another aspect of the present invention, there is provided a linearity measuring apparatus having: a table supporting a measuring object; the sensor head 'including measuring to be arranged on the surface of the measuring object, respectively Three displacement meters of the distance of the measured point in one direction; the guiding mechanism 'movably supports the movable body of the sensor head and one of the working tables along the first direction with respect to the other fixed object: and The control device 'stores a secondary component that is a trajectory that is fixed to a reference point of the movable object, that is, a simulation curve, and obtains a measurement target line parallel to the first direction based on measurement data measured by the three displacement meters. In the outline of the surface, the control device performs: measuring the distance to the measured point along the surface of the measurement target line by moving each of the three movable meters while moving the movable object in the first direction And obtaining the measurement data; calculating a trajectory of the reference point to which the relative position of the movable object is fixed based on the measurement results of the three displacement meters a step of emulating the contour of the curve; a step of correcting the second component of the contour of the calculated curve of the above imitation curve based on the second component of the contour of the stored imitative curve; and calculating the above based on the contour of the corrected emulation curve The step of measuring the surface profile of the object. By measuring the secondary component of the contour of the 201017096 emulation curve in advance without affecting the contour of the emulation curve, the second component of the emulation curve can be determined even if the zero adjustment of the displacement gauge is not performed. Therefore, it is not necessary to perform precise zero adjustment to measure the surface contour of the object to be measured. [Embodiment] Fig. 1A shows a perspective view through a perspective view of a linear measuring device according to an embodiment. The movable table 10 is supported by the table guiding mechanism 11 so as to be movable in one direction. The xyz rectangular coordinate system in which the moving direction of the movable table 10 is set to the X axis and the vertical lower direction is set to the Z axis is defined. The guide rail 18 supports the honing head 15 from above the movable table 10. The honing head 15 is movable along the guide rail 18 in the y-axis direction. Moreover, the honing head 15 can also move in the z direction relative to the guide rail 18. That is, the honing head 15 can be raised and lowered with respect to the movable table 10. A grinding wheel 16 is mounted at the lower end of the honing head 15. The grinding wheel 16 has a cylindrical outer shape and is attached to the honing head 15 with its central axis parallel to the y-axis. The object to be measured (the object to be honed) is held on the movable table 10. When the grinding wheel 16 is brought into contact with the surface of the object 20 to be measured, the grinding wheel 16 is rotated, and the surface of the measuring object 20 can be sharpened by moving the movable table 1' in the X direction. The control unit 19 controls the movement of the movable table 10 and the honing head 15. As shown in Fig. 1B, the sensor head 30 is mounted at the lower end of the honing head 15. In the sensor head 30, three displacement meters 31i, 31j, and 31k are mounted. -8 - 201017096 In the displacement meters 3 1 i, 3 lj, 3 1 k, for example, a laser displacement meter is used. The displacement meters 3 li, 3 lj, and 3 lk can measure the distances from the displacement gauge to the measured points on the surface of the object 20 to be measured, respectively. Three displacement meters 3 1 i, 3 lj, and 3 1 k are arranged in the y direction. Further, the measured points of the three displacement meters 3 1 i, 3 lj, and 3 1 k are also arranged in the y direction. Therefore, the height of the surface of the measuring object line parallel to the y direction can be measured. By measuring while moving the honing head 15 in the y direction, the surface profile of the measurement target line along the surface of the object 20 can be measured. The measurement data is input from the displacement meters 31i, 31j, 31k to the control device 19. The coordinate system and various functions will be described with reference to Fig. 2 . In Fig. 2, the upper direction is set to the positive direction of the x-axis. Therefore, the upper and lower relationship of the sensor head 30 and the measuring object 20 is opposite to the above-described relationship shown in Fig. 1A. The displacement gauges 3 1 i, 3 1 j, and 3 1 k are arranged at equal intervals in the negative direction of the y-axis in this order. The midpoint of the line segment connecting the zero points of the displacement meters 31i and 31k at both ends is defined as a reference point. The φ height (zero point error) of the zero point of the displacement meter 3 lj from the reference point to the center is set to 5. The surface of the object 20 to be measured and the contour of the line to be measured are set to W(y). The trajectory (imitation curve) of the reference point when moving the sensor head 30 in the y direction is set to h ( y ). Ideally, the emulation curve h ( y ) is a straight line, but actually distort from the ideal straight line. The angle at which the straight line connecting the zero points of the displacement gauges 31i and 31k at both ends is inclined from the y-axis is set to 0 (y). Ideally, the tilt angle 0 (y) = 〇, but actually the pitch is generated as the sensor head 30 moves, whereby the tilt angle 0(y) and the slope of the emulation curve h(y) are independently varied. Displacement -9- 201017096 The difference between the height of the zero point of the 31i and the reference point, and the difference between the zero point of the displacement meter 31k and the height of the reference point can be expressed as T(y)xP. Here, it is similar to the pitch component T ( y) = sin ( 0 ( y)). When the measurement 値 of the displacement meters 3 1i, 3 1j , and 3 1 k are set to i ( y ) , j ( y ) , and k ( y ), respectively, the following equation holds. [Math 1] W(y + P) = h(y) + i(y) + T(y)xP (1) W(y) = h(y)+j(y) + 8 . .. (2) W(yP) = h(y) + k(y)-T(y)xP (3) Since the tilt angle 0 ( y ) is very small, so make cos ( 0 ( y ) ) is approximately 1. The shape of the object 20 to be measured is, for example, a square having a length of 2 m on one side, and the interval P of the displacement meter is, for example, 1 〇〇 mm. If T(y) and h(y) are eliminated from equations (1), (2), and (3), the following equation can be obtained. [Math 3] W(y + P)-2W(y)+W(yP) + 2S = i(y)-2j(y) + k(y)~(4) Here, assume the following 3 times Equation (5) represents the surface profile w(y) -10- 201017096 [Math 4] W(y) = ay3 + by2 + cy + d (5) If equation (5) is substituted into equation (4) , then the following formula (6) is obtained » [Math 5] 6aP2y + 2bP2 + 25 = i(y)-2j(y) + k(y)...(6) 全部 All the measurements on the right side of equation (6) The data, the interval P of the displacement meter is known. Thus, the unknown number a on the left can be calculated from the first component of the variable y on the right. However, even if the zeroth component of y on the right side is obtained, the zero error 6 on the left side is unknown because the unknown number b cannot be determined. That is, the third component a of the surface profile W(y) can be determined, but the secondary component b cannot be determined. Further, the component of the surface profile W(y) of four or more times may be determined in the same manner as the third component. φ In the embodiment, in order to compensate for the secondary component of the undeterminable surface profile W(y), the secondary component of the simulation curve h(y) is measured in advance. The second component of the emulation curve h(y) corresponds to the deflection of the guide rail 18, so that it is determined that there is no large variation in each measurement. Therefore, when the secondary component of the emulation curve h(y) is measured in advance, it is not necessary to re-measure the secondary component of the emulation curve h (y) every time the measurement of the surface profile of the object to be measured is performed. Further, it can be considered that the components of the simulation curve h(y) three or more times are unpredictably changed each time the surface profile is measured (when the sensor head 30 moves each time). Therefore, even if the component i of the simulation curve h(y) is measured in advance to the component on -11 - 201017096, the measurement result of the actual measurement object can not be corrected based on the component measured three times or more in advance. Fig. 3A is a flow chart showing a method of measuring the secondary component of the emulation curve h(y) in advance as an example. As shown in Fig. 3B, the measuring object 20 is placed on the movable table 1 in step S1. The inclination of the slope along the straight surface is measured by moving the inclinometer 35 along an arbitrary line parallel to the y direction on the surface of the measuring object 20. The surface profile W(y) is calculated from the distribution of the inclination. The measurement by the inclinometer is not affected by the skew of the guide rail 18. In step S2, the measurement data j ( y ) is obtained by measuring the surface profile along the same line as the straight line measuring the oblique distribution by the inclinometer 35 by using the displacement meter 3 lj . In step S3, the secondary component of the emulation curve h(y) is calculated. The calculation method will be described below. The surface profile measured by the displacement gauge 3 lj is the same as the surface profile W(y) obtained from the measurement by the inclinometer. Therefore, the relationship of the equation (2) holds between the surface contour W (y ) obtained by the measurement by the tilt meter and the measurement data j ( y ) measured by the displacement meter 3 1 j. Since the zero point error <5 series constant, the second component of the emulation curve h(y) can be calculated from the second component of the surface profile W(y) and the second component of the measurement data j(y). The calculated secondary component is stored in the control device 19. The outline of the emulation curve h(y) generally changes each time the honing head 15 is moved in the y direction, and is not limited to being the same contour each time. However, it can be determined that the second component of the emulation curve h(y) determines the general shape of the emulation curve and the low-order component of 201017096 is highly reproducible. That is, it can be considered that there is no major change in each measurement. A flow chart of the linearity measuring method according to the embodiment is shown in FIG. First, the object 2 to be measured is loaded on the movable table 1〇. The measuring object 20 does not need to be the same as the measuring object 20 which measures the surface contour by the inclinometer in the step shown in Fig. 3a. ' In step SA1, the distance between the measured point on the surface of the object 20 is measured by the displacement meter 3 ii, 3丨j, 3 ik while moving the honing head 15 and the sensor head 30 in the y direction. i(y) , j(y) , k(y). The measured data is input to the control unit 19. In step SA2, a low-pass filter is applied to the measurement data i(y), j(y), and k(y) to remove the noise component. In order to effectively act on the low-pass filter, the measurement data i ( y ) , j ( y ) , k ( y ) are obtained on a very narrow scale with respect to the interval P of the displacement. For example, the measurement data i(y), j(y), k(y) are obtained with a width of 0.05 mm. In step SA3, the measurement data i (y) ' j ( y ) and k (y) after the low-pass filter is used are sampled to generate step data. The sampling period is, for example, one half of the interval P of the displacement meter, that is, 50 mm. In step SA4, based on the step data i(y), j(y), k(y), the simulation curve h(y) and the pitch component T (y are derived by the genetic algorithm are shown in Fig. 5, which shows the step SA4 using the genetic algorithm. Detailed flowchart. In the genetic algorithm, the group of the emulation curve h(y) and the pitch component T(y) is set to one individual. -13- 201017096 The first generation individual group is generated in step SB1. For example, the number of individuals It is 200. One of them is to set the emulation curve h(y) and the pitch component T(y) of one individual to 0. The other imitation curves h(y) and the pitch component T(y) of 199 individuals are based on random numbers. In addition, in the initial state, the emulation curve h(y) and the pitch component T(y) of all individuals can also be set to 0. In step SB2, each body is evaluated by the evaluation function, and the fitness of each body is calculated. The evaluation function is set according to the surface contour W(y). The three displacement meters 3 1 i, 3 lj, and 3 1 k measure the contour of the same measurement target line along the surface of the same measurement object 20, so the equation (1) is used. (3) The three surface profiles Wi(y), W2(y), and W3(y) calculated separately should be consistent. Therefore, first find Wi(y) and W2(y) Difference Wdy) -W2 (y), and W2 (y) and W3 (y) of the difference W2 (y) -W3 (y). When the surface contour W(y) is expressed by a polynomial, the zero-order component corresponds to the interval between the measurement object 20 and the sensor head 30, and the primary component corresponds to the posture of the measurement object 20. That is, the 0th order component and the 1st order component of the surface profile W(y) are not directly related to the surface profile of the measuring object 20. Therefore, the 〇 component and the priming component are removed from the difference Wdy) - W2 (y) and the difference W2 (y) - W3 (y). The dispersion of the difference W^y) - W2 (y ) and the difference W2 (y) - W3 (y) of the zero-order component and the primary component was calculated. The sum of these two dispersions is set as an evaluation function. It can be said that the smaller the evaluation function, the higher the fitness. Sort all individuals according to fitness. 201017096 In step SB3, the individual who becomes the intersection object is selected. As an example, the higher the suitability of the individual, the higher the rate of selecting the individual. Based on the selection rate, 10 pairs of 2 individuals were selected. In step SB4, the selected individual crosses at least one of the emulation curve h(y) or the pitch component T(y) to generate a new individual. The method of intersection will be described with reference to FIG. The contour curve h(y) and the contour T(y) of the two components Ua and Ub selected as the intersecting objects in this generation are shown. A new individual Uc and Ud is generated by replacing (crossing) the part of the i-effect curve h(y) of the individual Ua with the part of the individual Ub's emulation curve h(y). The contour T(y) of the pitch components of the new individuals Uc and Ud still inherits the contour T(y) of the pitch components of the original individuals Ua and Ub, respectively. In this way, two individuals are newly generated from two individuals. Ten pairs of individuals are selected in step SB3, so 10 pairs, that is, 20 individuals, are newly generated in step SB4. Alternatively, the contour T(y) of the pitch component may be crossed, or both the contour curve h(y) and the contour T(y) of the pitch component may be crossed. When the step SB4 is ended, in step SB5, the individual who is the subject of the sudden mutation is selected. As an example, in addition to the 10 individuals with high suitability, 80 are selected from the remaining 190 individuals. In step SB6, a sudden mutation is generated on the selected individual to generate a new individual. The method of sudden variation will be described with reference to FIG. An individual Ue selected in step SB5 is shown in Fig. 7. In the individual Ue, the emulation curve h(y) overlaps the Gaussian curve of arbitrary amplitude and height to generate a new individual -15- 201017096
Uf。另外，也可在個體Ue之俯仰成分之輪廓T(y)重叠 高斯曲線，也可在仿效曲線h(y)和俯仰成分之輪廓 T (y)之兩方重疊高斯曲線。由於在步驟SB5中選擇了 80 個個體，因此在步驟SB6，新生成80個個體。 於步驟SB7中，淘汰適合度低的個體。具體而言，在 當這代200個個體中用新生成之100個體替換適合度低的 1〇〇個個體。由此，決定新的一代200個個體。 於步驟SB8中，評估新一代200個個體而求出適合度 。另外，對未在步驟SB7淘汰之上一代100個個體已計算 適合度，所以沒有必要重新計算適合度。根據適合度排序 新一代200個個體。 於步驟SB9中，判定世代數是否達到目標値，在未達 到目標値時返回步驟 SB3。在達到目標値時，在步驟 SB 10中，將最新一代個體中適合度最高的個體之仿效曲 線h(y)及俯仰成分之輪廓 T(y)作爲最佳解。 於圖8表示評估値之位移。橫軸表示世代數，縱軸表 示在當這代個體中適合度最高的個體之評估函數之値（評 估値）。可知隨著世代演變，評估値下降（適合度上升） 。在2000代，評估函數之値下降到大約0.4 μιη2。可知標 準偏差成爲〇_63μπι，得到充分之精度。而且，在5〇〇代 左右，評估値收斂到90%程度，其後，根據最佳解之探索 緩慢演變之情況，認爲遺傳算法之各參數之設定也適當。 於圖9Α表示適合度最高的個體之仿效曲線h(y)及 俯仰成分之輪廓 T(y)。縱軸表示h(y)及T(y)之 201017096 値，h ( y )之單位係[μηι]，Τ ( y )之單位係[lOprad]。橫 軸以單位[mm]表示y方向之位置。另外，仿效曲線h(y) 及俯仰成分之輪廓T(y)之0次成分和1次成分與表面輪 廓無關，所以在圖8A除去0次成分;和1次成分而表示。 於圖9B表示由位移計31i、31j、31k測量之測量數 據i(y) 、j(y) 、k(y)。橫軸以單位[mm]表示y方向 之位置，縱軸以單位[μ®]表示測量數據之値。另外’除去 〇次成分及1次成分。 於圖9C表示將仿效曲線h(y)及俯仰成分之輪廓Τ (y)之最佳解代入到式（1)〜（3)而求出之表面輪廓 Wi ( y ) 、W2 ( y ) ' W3 ( y )。可知根據最佳解計算之3 個表面輪廓與在圖9B所示之3個測量數據相比差小。 如此，藉由利用遺傳算法，不必直接解出包括3個未 知函數之聯立方程式，可求出仿效曲線h(y)、俯仰成分 之輪廓T(y)、及表面輪廓W(y)之最佳解。 於上述遺傳算法中，由仿效曲線h(y)和俯仰成分之 輪廓T(y)定義遺傳算法之候選解，根據表面輪廓W(y )定義評估函數。此外，也可以由仿效曲線h(y)、俯仰 成分之輪廓T(y)、表面輪廓W(y)中2個輪廓定義候 選解，也可由剩餘之1個輪廓定義評估函數。 於圖4之步驟SA5中，進行仿效曲線h(y)之2次 成分之校正。如式（6)所示，不能夠從聯立方程式（1) 〜（3)確定仿效曲線h(y)之2次成分。因此，由遺傳 算法求出之仿效曲線h(y)之最佳解之2次成分沒有意義 -17- 201017096 。從而，從藉由遺傳算法得到之仿效曲線h(y)之最佳解 除去2次成分而求出僅包含3次以上之成分之仿效曲線h (y) 。在僅包含該3次以上之成分之仿效曲線h(y)上 ，使在圖3A之步驟S2計算出之仿效曲線h(y)之2次 成分重疊。由此，求出包含有意義之2次成分之仿效曲線 h ( y ) ° 於步驟SA6中，藉由將在步驟SA5校正2次成分之 仿效曲線h ( y )、及位移計3 1 j之測量數據j ( y )代入到 式（2)，從而求出表面輪廓W(y)之2次以上之成分。 另外，由於零點誤差<5係常數，所以，即使零點誤差<5未 知，也能夠確定表面輪廓W(y)之2次以上之成分。 朝X方向偏離活動工作臺1〇，藉由重複從圖4之步驟 S A 1到S A 6之步驟，從而可測量測量對象物2 0整面之表 面輪廓。即使朝X方向偏離活動工作臺10，可認定仿效曲 線h(y)之2次成分也不變化。因此，在每朝著x方向偏 離活動工作臺10時，不需要再執行由圖3A所示之傾斜儀 進行之測量。而且，即使更換測量對象物20，也不需要再 執行由傾斜儀進行之測量。 由傾斜儀測量表面輪廓需要很多之功夫和時間，難以 自動化。在根據實施例之方法中，藉由利用容易自動化之 位移計之測量，可容易地測量測量對象物20之表面輪廓。 於上述實施例中’在零點誤差δ殘留時也可確定表面 輪廓W(y)之2次成分。因此，沒有必要進行精密的零 點調整。 -18 · 201017096 於上述實施例中，相對測量對象物20移動了位移計 3 1i、31j、3 1k，但相反也可相對位移計31i、3 1j、31k移 動測量對象物2 0。例如，在圖1A中，朝x方向排列位移 計31i、3 lj、31k，一邊朝X方向移動測量對象物20 —邊 進行測量，從而可測量沿著測量對象物20表面之平行於X 方向之測量對象線之表面輪廓。將圖1B所示之感測器頭 3〇以平行於z軸之旋轉軸爲中心旋轉90°，從而可以使位 移計3 li、3 lj、3 1k排列在X方向。也可以在感測器頭30 設置這種旋轉機構。 藉由重疊沿著平行於y方向之多個測量對象線之表面 輪廓、和沿著平行於X方向之多個測量對象線之表面輪廓 ’可得到測量對象物20表面之2維表面輪廓資訊。 根據以上實施例說明了本發明，但本發明不限於這些 。熟悉本案技術之人士當然理解例如可進行各種變更、改 良、組合等。 【圖式簡單說明】 圖1之（1 A )係根據實施例之直線性測量裝置之透視 圖，（1B)係感測器頭部分之槪略圖。 圖2係表示測量對象物之表面輪廓w ( y )、位移計 之測量數據i(y) 、j(y) 、k(y)、仿效曲線h(y)、 及俯仰成分T(y)之定義之線圖。 圖3之（3A)係表示事先測量仿效曲線之2次成分之 方法之流程圖’ 3(B)係表示由傾斜儀測量表面輪廓之樣 -19- 201017096 子之槪略圖。 圖4係根據實施例之直線性測量方法之流程圖。 圖5係根據實施例之直線性測量方法中採用之遺傳算 法之流程圖。 圖6係用於說明由遺傳算法進行之交叉之圖。 圖7係用於說明由遺傳算法進行之突然變異之圖。 圖8係表示藉由遺傳算法，評估値隨著世代增加而減 小（適合度變高）之情況之圖表。 圖9之（9A)係表示由遺傳算法求出之仿效曲線h( Θ y)及俯仰成分T(y)之最佳解之圖表，（9B)係表示3 個位移計之測量數據之圖表，（9C)係表示運用藉由遺傳 算法求出之最佳解時表面輪廓之圖表。 【主要元件符號說明】 1 0 :活動工作臺 1 1 :工作臺導向機構 1 5 :硏磨頭 ® 1 6 :砂輪 18 :導軌 1 9 :控制裝置 2 0 :測量對象物 3 0 :感測器頭 3Ii、31j、31k:位移計 3 5 :傾斜儀 -20-Uf. Alternatively, the Gaussian curve may be superimposed on the contour T(y) of the pitch component of the individual Ue, or the Gaussian curve may be superimposed on both the emulation curve h(y) and the contour T(y) of the pitch component. Since 80 individuals are selected in step SB5, 80 individuals are newly generated in step SB6. In step SB7, individuals with low fitness are eliminated. Specifically, 1 individual individuals with low fitness were replaced with 100 newly generated individuals in this generation of 200 individuals. Thus, a new generation of 200 individuals is determined. In step SB8, a new generation of 200 individuals is evaluated to determine the fitness. In addition, the fitness has been calculated for the elimination of the previous generation of 100 individuals who have not been eliminated in step SB7, so it is not necessary to recalculate the fitness. Sorted by fitness A new generation of 200 individuals. In step SB9, it is judged whether or not the generation number has reached the target 値, and when the target 値 has not been reached, the flow returns to step SB3. When the target 値 is reached, in step SB 10, the emulation curve h(y) of the most suitable individual among the latest generation individuals and the contour T(y) of the pitch component are taken as the optimal solution. Figure 8 shows the displacement of the evaluation 値. The horizontal axis represents the number of generations, and the vertical axis represents the evaluation function of the most appropriate individual in this generation (evaluation). It can be seen that as the generation evolves, the assessment 値 decreases (the fitness rises). In the 2000s, the evaluation function dropped to approximately 0.4 μηη2. It can be seen that the standard deviation becomes 〇_63μπι, and sufficient accuracy is obtained. Moreover, in the 5th generation, the evaluation 値 converges to 90%, and then, according to the slow evolution of the exploration of the best solution, it is considered that the parameters of the genetic algorithm are also set appropriately. Fig. 9A shows the emulation curve h(y) of the most suitable individual and the contour T(y) of the pitch component. The vertical axis represents h(y) and T(y) of 201017096 値, the unit of h ( y ) is [μηι], and the unit of Τ ( y ) is [lOprad]. The horizontal axis indicates the position in the y direction in units of [mm]. Further, the zero-order component and the primary component of the contour curve h(y) and the contour T(y) of the pitch component are not related to the surface profile, so that the component 0 is removed in Fig. 8A; and the component is represented by the first component. The measurement data i(y), j(y), k(y) measured by the displacement meters 31i, 31j, 31k are shown in Fig. 9B. The horizontal axis represents the position in the y direction in units of [mm], and the vertical axis represents the measurement data in units of [μ®]. In addition, the fractional component and the primary component are removed. Fig. 9C shows the surface contours Wi ( y ) and W2 ( y ) ' obtained by substituting the optimal solution of the contour curve h(y) and the contour Τ (y) of the pitch component into the equations (1) to (3). W3 ( y ). It can be seen that the three surface profiles calculated from the optimal solution are small compared to the three measurement data shown in Fig. 9B. Thus, by using the genetic algorithm, it is not necessary to directly solve the simultaneous equations including the three unknown functions, and the simulation curve h(y), the pitch component T(y), and the surface contour W(y) can be found. Good solution. In the above genetic algorithm, the candidate solution of the genetic algorithm is defined by the emulation curve h(y) and the contour T(y) of the pitch component, and the evaluation function is defined according to the surface contour W(y). Further, a candidate solution may be defined by two contours in the contour curve h(y), the contour T(y) of the pitch component, and the surface contour W(y), or the evaluation function may be defined by the remaining one contour. In step SA5 of Fig. 4, the correction of the second component of the simulation curve h(y) is performed. As shown in the equation (6), the secondary component of the emulation curve h(y) cannot be determined from the simultaneous equations (1) to (3). Therefore, the second component of the optimal solution of the simulation curve h(y) obtained by the genetic algorithm has no meaning -17- 201017096. Therefore, the secondary component is removed from the optimal solution of the simulation curve h(y) obtained by the genetic algorithm, and the simulation curve h (y) containing only three or more components is obtained. On the emulation curve h(y) including only the three or more components, the second component of the emulation curve h(y) calculated in step S2 of Fig. 3A is superposed. Thus, the simulation curve h ( y ) ° including the meaningful secondary component is obtained. In step SA6, the simulation curve h ( y ) for correcting the secondary component in step SA5 and the measurement of the displacement gauge 3 1 j are obtained. The data j ( y ) is substituted into the equation (2) to obtain a component of the surface contour W(y) twice or more. Further, since the zero point error <5 series constant, even if the zero point error <5 is unknown, the component of the surface contour W(y) twice or more can be identified. Deviating from the movable table 1 in the X direction, by repeating the steps from steps S A 1 to S A 6 of Fig. 4, the surface profile of the entire surface of the measuring object 20 can be measured. Even if the moving table 10 is deviated in the X direction, it can be considered that the secondary component of the emulation curve h(y) does not change. Therefore, it is not necessary to perform the measurement by the inclinometer shown in Fig. 3A every time the movable table 10 is deviated in the x direction. Moreover, even if the object 20 to be measured is replaced, it is not necessary to perform the measurement by the inclinometer. Measuring the surface contour by the inclinometer requires a lot of effort and time and is difficult to automate. In the method according to the embodiment, the surface profile of the measuring object 20 can be easily measured by using the measurement of the displacement meter which is easy to automate. In the above embodiment, the secondary component of the surface profile W(y) can also be determined when the zero point error δ remains. Therefore, there is no need to make precise zero adjustments. -18 · 201017096 In the above embodiment, the displacement meters 3 1i, 31j, and 3 1k are moved relative to the object 20 to be measured, but the object 20 to be measured may be moved relative to the displacement meters 31i, 31j, 31k. For example, in FIG. 1A, the displacement meters 31i, 3 lj, and 31k are arranged in the x direction, and the measurement object 20 is moved while moving in the X direction, so that the surface along the measurement object 20 can be measured parallel to the X direction. Measure the surface contour of the object line. The sensor head 3 shown in Fig. 1B is rotated by 90° about the axis of rotation parallel to the z-axis, so that the shift meters 3 li, 3 lj, and 3 1k can be arranged in the X direction. This rotating mechanism can also be provided at the sensor head 30. The two-dimensional surface contour information of the surface of the measuring object 20 can be obtained by overlapping the surface contours of the plurality of measuring object lines parallel to the y direction and the surface contours of the plurality of measuring object lines parallel to the X direction. The present invention has been described based on the above embodiments, but the present invention is not limited to these. Those skilled in the art will understand, for example, that various changes, modifications, combinations, and the like can be made. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 (1 A) is a perspective view of a linear measuring device according to an embodiment, and (1B) is a schematic view of a head portion of a sensor. 2 is a view showing a surface profile w ( y ) of a measurement object, measurement data i(y), j(y), k(y), a simulation curve h(y), and a pitch component T(y) of the displacement meter. A line graph of the definition. Fig. 3 (3A) is a flow chart showing a method of measuring the secondary component of the emulation curve in advance. '3(B) is a schematic diagram showing the measurement of the surface profile by the inclinometer -19-201017096. 4 is a flow chart of a linear measurement method according to an embodiment. Fig. 5 is a flow chart of the genetic algorithm employed in the linearity measuring method according to the embodiment. Figure 6 is a diagram for explaining the intersection of genetic algorithms. Figure 7 is a diagram for explaining the sudden variation by the genetic algorithm. Fig. 8 is a graph showing the case where the genetic algorithm is used to estimate the decrease (the fitness becomes higher) as the generation increases. Fig. 9 (9A) is a graph showing the best solution of the simulation curve h( Θ y) and the pitch component T(y) obtained by the genetic algorithm, and (9B) is a graph showing the measurement data of the three displacement meters. (9C) shows a graph using the surface contour of the optimal solution obtained by genetic algorithm. [Description of main component symbols] 1 0 : movable table 1 1 : table guide mechanism 1 5 : honing head ® 1 6 : grinding wheel 18 : guide rail 1 9 : control device 2 0 : measuring object 3 0 : sensor Head 3Ii, 31j, 31k: Displacement meter 3 5: Inclinometer-20-