JPH10221053A - Method for measuring radius of curvature of spherical face - Google Patents
Method for measuring radius of curvature of spherical faceInfo
- Publication number
- JPH10221053A JPH10221053A JP9038342A JP3834297A JPH10221053A JP H10221053 A JPH10221053 A JP H10221053A JP 9038342 A JP9038342 A JP 9038342A JP 3834297 A JP3834297 A JP 3834297A JP H10221053 A JPH10221053 A JP H10221053A
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- Prior art keywords
- curvature
- measuring
- radius
- spherical
- shape
- Prior art date
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- Length Measuring Devices With Unspecified Measuring Means (AREA)
- A Measuring Device Byusing Mechanical Method (AREA)
Abstract
Description
【０００１】[0001]
【発明の属する技術分野】この発明は、三次元座標測定
機や断面形状測定装置の中でも、高い精度が要求される
各種の形状測定装置を校正する際における、当該装置の
測定針の球面形状を測定する方法に関するものである。BACKGROUND OF THE INVENTION The present invention relates to a method for correcting the spherical shape of a measuring needle of a three-dimensional coordinate measuring machine or a cross-sectional shape measuring device when calibrating various shape measuring devices requiring high accuracy. It relates to a method of measuring.
【０００２】[0002]
【従来の技術】近年、機械部品の形状評価のみならず、
光学要素のひとつである非球面光学素子の形状評価用と
しても、三次元座標測定機に代表される形状測定装置は
幅広く用いられている。それは、従来の光学素子が球面
や平面等の幾何形状で構成されていたのに対し、非球面
光学素子は三次元的な自由曲面を有するために、従来の
干渉測定等の光学的な手法による形状測定が困難になっ
たためである。2. Description of the Related Art In recent years, not only the evaluation of the shape of mechanical parts,
A shape measuring device represented by a three-dimensional coordinate measuring machine is also widely used for evaluating the shape of an aspherical optical element, which is one of the optical elements. That is, while the conventional optical element is configured with a geometrical shape such as a spherical surface or a plane, the aspherical optical element has a three-dimensional free-form surface. This is because the shape measurement became difficult.
【０００３】しかしながら、非球面光学素子の形状評価
に三次元座標測定機を使用しようとした場合、従来の機
械部品に要求されていた精度の１桁から２桁以上の高い
精度が要求される。そこで、形状測定装置そのものの高
精度化は言うに及ばず、この測定装置の校正についても
従来の方法を見直す必要が生じてきた。なかでも、通
常、この形状測定装置の測定針には先端部が球形をした
ものを使用するが、この測定針先端が有する曲率半径の
校正は非常に重要な課題となっている。なぜなら、測定
針半径に誤差があった場合、その誤差が測定面の法線方
向の誤差となってしまい、光学素子で重要なパラメータ
のひとつである曲率半径に誤差が生じてしまうからであ
る。However, when an attempt is made to use a three-dimensional coordinate measuring machine to evaluate the shape of an aspherical optical element, a high precision of one to two or more orders of magnitude required for conventional mechanical parts is required. Therefore, it goes without saying that it is necessary to review the conventional method for calibrating the shape measuring device itself, not to mention improving the accuracy of the shape measuring device itself. Above all, usually, a measuring needle of this shape measuring device has a spherical tip, and calibration of the radius of curvature of the tip of the measuring needle is a very important issue. This is because, if there is an error in the radius of the measurement needle, the error becomes an error in the normal direction of the measurement surface, and an error occurs in the radius of curvature, which is one of the important parameters in the optical element.
【０００４】この課題に対して、従来の方法では、図２
に示すように、高精度ミラー１の上に校正用基準球２が
載せられ、この基準球２が押え部材３により転がらない
ように設置されている。そして、この設置状態で、測定
針４の球状部４ａを、高精度ミラー１のＺ方向の位置Ｚ
１、Ｚ３及び校正用基準球２の頂点の位置Ｚ２に当接さ
せて、それらの位置Ｚ１，Ｚ２，Ｚ３を測定する。得ら
れたＺ１、Ｚ３の平均値とＺ２との差を求めることによ
り、測定針４の球状部４ａの曲率半径Ｒｐが分からなく
ても、校正用基準球２の直径Ｄが明らかとなる。一方、
同一のセッティングのもとに、測定針４の球状部４ａを
校正用基準球２の周面に沿わせて摺動させることによ
り、この校正用基準球２の形状を測定し、得られた測定
針４の中心を通る面の曲率半径Ｒ３から先に得られてい
る校正用基準球２の半径（Ｄ／２）を引けば、測定針４
の球状部４ａの曲率半径Ｒｐを求めることができる。こ
の測定値に基づいて、測定針４の球状部４ａを校正し、
適正な形状として、高精度の形状測定装置が提供できる
ようにしている。[0004] In order to solve this problem, the conventional method employs FIG.
As shown in FIG. 1, a calibration reference sphere 2 is placed on a high-precision mirror 1, and the reference sphere 2 is set so as not to be rolled by a pressing member 3. Then, in this installation state, the spherical portion 4a of the measuring needle 4 is moved to the position Z in the Z direction of the high-precision mirror 1.
1, Z3 and the vertex position Z2 of the calibration reference sphere 2 are brought into contact with each other, and the positions Z1, Z2, Z3 are measured. By calculating the difference between the obtained average value of Z1 and Z3 and Z2, the diameter D of the calibration reference sphere 2 becomes clear even if the radius of curvature Rp of the spherical portion 4a of the measurement needle 4 is unknown. on the other hand,
Under the same setting, the shape of the calibration reference sphere 2 is measured by sliding the spherical portion 4a of the measuring needle 4 along the peripheral surface of the calibration reference sphere 2, and the obtained measurement is performed. By subtracting the radius (D / 2) of the calibration reference sphere 2 obtained earlier from the radius of curvature R3 of the plane passing through the center of the needle 4, the measurement needle 4
Of the spherical portion 4a can be obtained. Based on the measured value, the spherical portion 4a of the measuring needle 4 is calibrated,
As an appropriate shape, a highly accurate shape measuring device can be provided.
【０００５】[0005]
【発明が解決しようとする課題】しかしながら、先の従
来の方法では以下の問題があった。However, the above conventional method has the following problems.
【０００６】第一に校正用基準球２の真球度である。こ
の手法で使用する基準球２は、あらゆる方向に対して真
球度が数十nmオーダで保証されている必要があるが、そ
のような真球を入手することは非常に難しい。また、他
の測定手法を用いて真球度を校正して使用することも考
えられるが、実施にあたっては手間が非常にかかってし
まい現実的ではない。First, the sphericity of the calibration reference sphere 2 is described. The reference sphere 2 used in this method needs to have a sphericity in every direction on the order of several tens of nm, but it is very difficult to obtain such a sphere. It is also conceivable to calibrate and use the sphericity by using another measurement method, but this is not realistic because it takes much time and effort to implement.
【０００７】第二に校正用基準球２の固定方法および、
その変形である。この手法では、校正用基準球２を高精
度ミラー１に接触させ、なおかつ校正用基準球２が動か
ないように押さえ部材３で固定する必要がある。しか
し、このように校正用基準球２を固定するのは、校正用
基準球２が押さえ部材３により浮き上がってしまった
り、又、校正用基準球２と押さえ部材３との間でガタ付
きが生じたりして極めて難しいと共に、校正用基準球２
は高精度ミラー１に微小な１点でのみ接触しているた
め、校正用基準球２は固定方法によって簡単に接触点が
変形してしまい、校正用基準球２の直径測定の際に誤差
が生じてしまう。Second, a method of fixing the calibration reference sphere 2 and
It is a variant. In this method, it is necessary to bring the calibration reference sphere 2 into contact with the high-precision mirror 1 and to fix the calibration reference sphere 2 with the holding member 3 so as not to move. However, fixing the calibration reference sphere 2 in this manner may cause the calibration reference sphere 2 to be lifted up by the pressing member 3 or cause looseness between the calibration reference sphere 2 and the pressing member 3. Is extremely difficult and the reference sphere for calibration 2
Is in contact with only one minute point on the high-precision mirror 1, the contact point of the calibration sphere 2 is easily deformed by the fixing method, and an error occurs when the diameter of the calibration sphere 2 is measured. Will happen.
【０００８】そこで、この発明は、球に比べて比較的容
易に高精度なものが製作可能なものを基準とし、また基
準とする部材が設置時に変形することなく、高精度に測
定針の曲率半径が校正できる方法を提供することを課題
としている。Accordingly, the present invention is based on the object that can be manufactured relatively easily with high precision as compared with a sphere. In addition, the reference member does not deform at the time of installation and the curvature of the measuring needle can be accurately determined. It is an object to provide a method capable of calibrating a radius.
【０００９】[0009]
【課題を解決するための手段】かかる課題を達成するた
めに、請求項１に記載の発明は、測定針の先端部が球面
形状を呈する形状測定装置の該球面形状を測定する方法
において、曲率半径が一致または曲率半径の差が既知
で、一方が凸、他方が凹の球面形状を有する部材の、二
つの球面の形状に対し、曲率半径が未知で球面形状の測
定針を用いて前記２つの球面形状を測定し、その結果得
られた測定針の中心座標列が構成する球面の曲率半径を
演算でそれぞれ求め、前記２つの曲率半径の差から測定
針の曲率半径を求める球面曲率半径測定方法としたこと
を特徴としている。According to a first aspect of the present invention, there is provided a method for measuring a spherical shape of a shape measuring apparatus in which a tip of a measuring needle has a spherical shape. For a member having a spherical shape in which the radii match or the radius of curvature is known and one of which is convex and the other is concave, the two spheres are measured using a spherical measuring needle having an unknown radius of curvature. Spherical radii measured by measuring two spherical shapes, calculating the radii of curvature of the spheres formed by the resulting central coordinate sequence of the measuring needle, and calculating the radius of curvature of the measuring needle from the difference between the two radii of curvature. Method.
【００１０】請求項２に記載の発明は、請求項１に記載
の構成に加え、前記測定針の中心座標列から球面の曲率
半径を求める際に、計算上得られる球面と測定値との差
の二乗和が最小となるように最小自乗法を用いて計算す
ることを特徴とする。According to a second aspect of the present invention, in addition to the configuration of the first aspect, when calculating the radius of curvature of the spherical surface from the center coordinate sequence of the measuring needle, the difference between the spherical surface obtained by calculation and the measured value is obtained. Is calculated using the least squares method so that the sum of squares of
【００１１】[0011]
【発明の実施の形態】以下、この発明の実施の形態につ
いて説明する。Embodiments of the present invention will be described below.
【００１２】図１には、この発明の実施の形態を示す。FIG. 1 shows an embodiment of the present invention.
【００１３】この実施の形態は、図１の（ａ）に示す球
面形状の凸面１１ａを有する凸レンズ１１及び図１の
（ｂ）に示す球面形状の凹面１２ａを有する凹レンズ１
２を使用して測定針４の球状部４ａの曲率半径Ｒｐを測
定して校正を行うようにしている。In this embodiment, a convex lens 11 having a spherical convex surface 11a shown in FIG. 1A and a concave lens 1 having a spherical concave surface 12a shown in FIG.
2, the radius of curvature Rp of the spherical portion 4a of the measuring needle 4 is measured and calibration is performed.
【００１４】すなわち、その凸レンズ１１と凹レンズ１
２とは、凸面１１ａの曲率半径Ｒｃｖと凹面１２ａの曲
率半径Ｒｃｃとが一致しているか、あるいは両曲率半径
Ｒｃｖ，Ｒｃｃの差が明らかであるものを使用する。ま
た、その凸レンズ１１と凹レンズ１２とは、熱変形の影
響の度合いが等しくなるように、同一素材を使用するこ
とが望ましい。この凸レンズ１１と凹レンズ１２との曲
率半径Ｒｃｖ，Ｒｃｃを一致させること、あるいは、曲
率半径Ｒｃｖ，Ｒｃｃの差を測定することは、通常のガ
ラスレンズ製作において行われる様に球面の凹、凸を重
ね合わせて生じるニュートン縞を観察して加工、測定す
る行うことにより、サブミクロンオーダを越えて簡便に
実現することができる。このとき、それぞれのレンズ１
１，１２の曲率半径Ｒｃｖ，Ｒｃｃの値は、リングスフ
ェロメータ等で測定可能であるが、本発明で目的として
いる測定精度とくらべ非常に低いため、レンズ１１，１
２の曲率半径Ｒｃｖ，Ｒｃｃの値は未知なものとして扱
う。なお、凸レンズ１１と凹レンズ１２は設置の容易さ
から底が平らな形状が望ましいが、測定面に変形が生じ
ないのであれば、取付けの容易な治工具に接着等で固定
してもかまわない。That is, the convex lens 11 and the concave lens 1
A value of 2 means that the radius of curvature Rcv of the convex surface 11a matches the radius of curvature Rcc of the concave surface 12a, or that the difference between the two radii of curvature Rcv and Rcc is clear. It is desirable that the convex lens 11 and the concave lens 12 be made of the same material so that the degree of the influence of thermal deformation is equal. Matching the radii of curvature Rcv and Rcc between the convex lens 11 and the concave lens 12 or measuring the difference between the radii of curvature Rcv and Rcc is performed by overlapping concave and convex spherical surfaces as is performed in normal glass lens manufacturing. By observing and processing and measuring the Newtonian fringes generated together, it is possible to easily realize the processing beyond the submicron order. At this time, each lens 1
The values of the radii of curvature Rcv and Rcc of the lenses 1 and 12 can be measured by a ring spherometer or the like, but are very low compared to the measurement accuracy aimed at in the present invention.
The values of the curvature radii Rcv and Rcc of 2 are treated as unknown. The convex lens 11 and the concave lens 12 preferably have flat bottoms for ease of installation. However, if the measurement surface does not deform, the convex lens 11 and the concave lens 12 may be fixed to a jig or tool which can be easily attached by bonding or the like.
【００１５】また、図１（ａ）（ｂ）には図示していな
いが、測定針４と凸レンズ１１,凹レンズ１２とは駆動
機構によりＸ、Ｙ、Ｚ方向に相対的に移動可能であると
共に、測定針４が両レンズ１１，１２の凹凸面１１ａ，
１２ａに接触したことを検出してその時のＸ、Ｙ、Ｚ座
標値を演算装置に取り込むことができるようになってい
る。Although not shown in FIGS. 1A and 1B, the measuring needle 4 and the convex lens 11 and the concave lens 12 can be relatively moved in the X, Y, and Z directions by a driving mechanism. The measuring needle 4 is provided with the uneven surfaces 11a of the two lenses 11 and 12,
The X, Y, and Z coordinate values at that time can be taken into an arithmetic unit by detecting that the contact has come into contact with 12a.
【００１６】図１（ａ）において、測定針４は少なくと
も凸レンズ１１の形状が認識できる回数を凸レンズ１１
の凸面１１ａに接触させて形状測定する。演算処理時に
平均化の効果を高めるため、接触回数は多いほどよい。
接触時に得られたＸ、Ｙ、Ｚ座標値は、凸レンズ１１の
凸面１１ａの曲率半径Ｒｃｖに測定針４の球状部４ａの
曲率半径Ｒｐを加えた値、すなわち測定針４の中心座標
値を示す。これらの測定点座標で構成されている曲面の
曲率半径Ｒ１は（１）式で表現できる。In FIG. 1A, the measuring needle 4 determines at least how many times the shape of the convex lens 11 can be recognized.
The shape is measured by contacting the convex surface 11a. In order to increase the effect of averaging during arithmetic processing, it is better to increase the number of contacts.
The X, Y, and Z coordinate values obtained at the time of contact indicate the value obtained by adding the radius of curvature Rcv of the convex portion 11a of the convex lens 11 to the radius of curvature Rp of the spherical portion 4a of the measuring needle 4, that is, the central coordinate value of the measuring needle 4. . The radius of curvature R1 of the curved surface constituted by these measurement point coordinates can be expressed by equation (1).
【００１７】 Ｒ１＝Ｒｃｖ＋Ｒｐ （１ ） 曲率半径Ｒ１は、測定点座標に対して最小自乗法を用い
て球面形状をフィッティングして容易に演算で求めるこ
とができる。R1 = Rcv + Rp (1) The radius of curvature R1 can be easily calculated by fitting the spherical shape to the measurement point coordinates using the least square method.
【００１８】一方、図１（ｂ）においては、凹レンズ１
２を図１（ａ）と同様な方法で測定する。このとき、凸
レンズ１２の測定とできるだけ同じ条件が得られるよ
う、凹レンズ１２を凸レンズ１１を測定した位置に合わ
せた方が望ましい。得られた測定点座標で構成されてい
る曲面の曲率半径Ｒ２は（２）式で表現できる。On the other hand, in FIG.
2 is measured in the same manner as in FIG. At this time, it is preferable that the concave lens 12 is set at the position where the convex lens 11 is measured so that the same condition as that of the measurement of the convex lens 12 is obtained as much as possible. The radius of curvature R2 of the curved surface constituted by the obtained measurement point coordinates can be expressed by equation (2).
【００１９】 Ｒ２＝Ｒｃｃ−Ｒｐ （２ ） また、ＲｃｖとＲｃｃとは、あらかじめ等しくなるよう
に製作されているので Ｒｃｖ＝Ｒｃｃ （３ ） である。そこで、（４）式、（５）式より、未知数Ｒｃ
ｖ（＝Ｒｃｃ）および、Ｒｐを求めることができる。R2 = Rcc−Rp (2) Further, since Rcv and Rcc are previously manufactured to be equal, Rcv = Rcc (3). Therefore, from the equations (4) and (5), the unknown Rc
v (= Rcc) and Rp can be obtained.
【００２０】 （Ｒ１＋Ｒ２）／２＝｛（ Ｒｃｖ＋Ｒｐ）＋（Ｒｃｃ−Ｒｐ）｝／２ ＝Ｒｃｖ （４ ） （Ｒ１−Ｒ２）／２＝｛（ Ｒｃｖ＋Ｒｐ）−（Ｒｃｃ−Ｒｐ）｝／２ ＝Ｒｐ （５ ） なお、ＲｃｖとＲｃｃに誤差がある場合も、ニュートン
縞を観測することにより容易にその量ｅが把握できるの
で、得られた誤差量ｅでＲ１またはＲ２を補正すればＲ
ｃｖ、Ｒｐを求めることは可能である。(R1 + R2) / 2 = {(Rcv + Rp) + (Rcc-Rp)} / 2 = Rcv (4) (R1-R2) / 2 = {(Rcv + Rp)-(Rcc-Rp)} / 2 = Rp (5) Even when there is an error between Rcv and Rcc, the amount e can be easily grasped by observing Newton's fringes. If R1 or R2 is corrected using the obtained error amount e, R
It is possible to obtain cv and Rp.
【００２１】すなわち、上記（３）式は、ＲｃｖとＲｃ
ｃとは、誤差量ｅがあるので Ｒｃｖ＝Ｒｃｃ＋ｅ （３）´ とする。また、上記（４）式、（５）式は、 （Ｒ１＋Ｒ２）／２＝｛（ Ｒｃｖ＋Ｒｐ）＋（Ｒｃｃ−Ｒｐ）｝／２ ＝｛（ Ｒｃｃ＋ｅ＋Ｒｐ）＋（Ｒｃｃ−Ｒｐ）｝／２ ＝Ｒｃｃ＋ｅ／２ （４）´ （Ｒ１−Ｒ２）／２＝｛（ Ｒｃｖ＋Ｒｐ）−（Ｒｃｃ−Ｒｐ）｝／２ ＝｛（ Ｒｃｃ＋ｅ＋Ｒｐ）−（Ｒｃｃ−Ｒｐ）｝／２ ＝Ｒｐ＋ｅ／２ （５）´ となり、誤差量ｅは既知であることから、未知数Ｒｃ
ｖ,Ｒｃｃおよび、Ｒｐを求めることができる。That is, the above equation (3) shows that Rcv and Rc
Since c has an error amount e, Rcv = Rcc + e (3) ′. Equations (4) and (5) are as follows: (R1 + R2) / 2 = {(Rcv + Rp) + (Rcc-Rp)} / 2 = {(Rcc + e + Rp) + (Rcc-Rp)} / 2 = Rcc + e / 2 (4) ′ (R1−R2) / 2 = {(Rcv + Rp) − (Rcc−Rp)} / 2 = {(Rcc + e + Rp) − (Rcc−Rp)} / 2 = Rp + e / 2 (5) ′, Since the error amount e is known, the unknown number Rc
v, Rcc and Rp can be obtained.
【００２２】このようなものにあっては、凸レンズ１１
や凹レンズ１２は、凹、凸を重ね合わせて生じるニュー
トン縞を観察して加工等を行うことができるため、従来
のような校正用基準球２より、比較的容易に高精度のも
のが成形できることから、測定精度も向上することとな
る。また、かかる凸レンズ１１及び凹レンズ１２を用い
ることにより、従来の校正用基準球２と異なり、単に各
レンズ１１，１２の平面部をステージに載置するだけで
簡単に固定できると共に、従来の校正用基準球２と異な
り、変形する虞が少ないため、高精度の測定ができる。In such a case, the convex lens 11
Since the concave lens 12 can be processed by observing Newton's fringes generated by superimposing concave and convex, it can be relatively easily formed with higher precision than the conventional calibration sphere 2. Therefore, the measurement accuracy is also improved. Further, by using the convex lens 11 and the concave lens 12, unlike the conventional calibration sphere 2, the flat portions of the lenses 11 and 12 can be easily fixed simply by being placed on the stage, and the conventional calibration sphere 2 can be used. Unlike the reference sphere 2, since there is little possibility of deformation, high-precision measurement can be performed.
【００２３】[0023]
【発明の効果】以上説明してきたように、各請求項に記
載された発明によれば、凸、凹の球面形状を有する部材
は、凸凹を重ね合わせて生じるニュートン縞を観察して
加工等を行うことができるため、従来のような校正用基
準球２より、比較的容易に高精度のものが成形できるこ
とから、測定精度を向上させることができる。また、か
かる凸、凹の球面形状を有する部材を用いることによ
り、従来の校正用基準球２と異なり、単に各部材の平面
部をステージに載置するだけで簡単に固定できると共
に、従来の校正用基準球２と異なり、その凸、凹の球面
形状は変形する虞が少ないため、高精度の測定ができ
る。また、測定針の曲率半径が未知であっても、球面形
状の曲率半径の正確な値を測定することができる。As described above, according to the invention described in the claims, a member having a convex or concave spherical shape can be processed by observing Newton's fringes generated by superimposing the concave and convex. Since it can be performed, a high-precision one can be formed relatively easily from the calibration reference sphere 2 as in the related art, so that the measurement accuracy can be improved. In addition, unlike the conventional calibration reference sphere 2, the use of the member having such a convex or concave spherical shape makes it possible to simply fix the flat portion of each member on the stage and easily fix the conventional calibration sphere. Unlike the reference sphere 2, the convex and concave spherical shapes are less likely to be deformed, so that highly accurate measurement can be performed. Further, even if the radius of curvature of the measuring needle is unknown, an accurate value of the radius of curvature of the spherical shape can be measured.
【図１】この発明の実施の形態に係る測定針の曲率半径
の測定状態を示す説明図である。FIG. 1 is an explanatory diagram showing a measurement state of a radius of curvature of a measurement needle according to an embodiment of the present invention.
【図２】従来例に係る測定針の曲率半径の測定状態を示
す説明図である。FIG. 2 is an explanatory diagram showing a measurement state of a radius of curvature of a measuring needle according to a conventional example.
４ 測定針 4a 球状部（先端部） 11 凸レンズ（凸の球面形状を有する部材） 11a 凸面（凸の球面形状） 12 凹レンズ（凹の球面形状を有する部材） 12a 凹面（凹の球面形状） 4 Measuring needle 4a Spherical part (tip) 11 Convex lens (member with convex spherical shape) 11a Convex surface (convex spherical shape) 12 Concave lens (member with concave spherical shape) 12a Concave surface (concave spherical shape)
Claims (2)
測定装置の該球面形状を測定する方法において、 曲率半径が一致または曲率半径の差が既知で、一方が
凸、他方が凹の球面形状を有する部材の、二つの球面の
形状に対し、曲率半径が未知で球面形状の測定針を用い
て前記２つの球面形状を測定し、その結果得られた測定
針の中心座標列が構成する球面の曲率半径を演算でそれ
ぞれ求め、前記２つの曲率半径の差から測定針の曲率半
径を求めることを特徴とする球面曲率半径測定方法。1. A method for measuring a spherical shape of a shape measuring device in which a tip portion of a measuring needle has a spherical shape, wherein a radius of curvature coincides or a difference in radius of curvature is known, one of which is convex and the other is concave is spherical. For the two spherical shapes of the member having the shape, the two spherical shapes are measured using a spherically shaped measuring needle whose radius of curvature is unknown, and the resulting central coordinate sequence of the measuring needles is formed. A method of measuring a radius of curvature of a spherical surface, wherein a radius of curvature of a spherical surface is obtained by calculation, and a radius of curvature of a measuring needle is obtained from a difference between the two radiuses of curvature.
において、 前記測定針の中心座標列から球面の曲率半径を求める際
に、計算上得られる球面と測定値との差の二乗和が最小
となるように最小自乗法を用いて計算することを特徴と
する球面曲率半径測定方法。2. The spherical radius of curvature measuring method according to claim 1, wherein when calculating the radius of curvature of the spherical surface from the central coordinate sequence of the measuring needle, the sum of squares of the difference between the spherical surface and the measured value obtained by calculation is calculated. A method of measuring a radius of curvature of a spherical surface, wherein calculation is performed using a least square method so as to minimize the radius.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP9038342A JPH10221053A (en) | 1997-02-06 | 1997-02-06 | Method for measuring radius of curvature of spherical face |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP9038342A JPH10221053A (en) | 1997-02-06 | 1997-02-06 | Method for measuring radius of curvature of spherical face |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| JPH10221053A true JPH10221053A (en) | 1998-08-21 |
Family
ID=12522624
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP9038342A Pending JPH10221053A (en) | 1997-02-06 | 1997-02-06 | Method for measuring radius of curvature of spherical face |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPH10221053A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2006349411A (en) * | 2005-06-14 | 2006-12-28 | Toshiba Mach Co Ltd | Calibration gauge |
| CN108917689A (en) * | 2018-08-01 | 2018-11-30 | 京东方科技集团股份有限公司 | Radius of curvature measurement equipment and its measurement method |
| CN112964211A (en) * | 2021-01-22 | 2021-06-15 | 大连理工大学 | Method and device for detecting thickness and surface shape of spherical shell part |
-
1997
- 1997-02-06 JP JP9038342A patent/JPH10221053A/en active Pending
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2006349411A (en) * | 2005-06-14 | 2006-12-28 | Toshiba Mach Co Ltd | Calibration gauge |
| CN108917689A (en) * | 2018-08-01 | 2018-11-30 | 京东方科技集团股份有限公司 | Radius of curvature measurement equipment and its measurement method |
| WO2020024694A1 (en) * | 2018-08-01 | 2020-02-06 | 京东方科技集团股份有限公司 | Curvature radius measurement device and measurement method thereof |
| CN108917689B (en) * | 2018-08-01 | 2021-01-22 | 京东方科技集团股份有限公司 | Curvature radius measuring apparatus and measuring method thereof |
| CN112964211A (en) * | 2021-01-22 | 2021-06-15 | 大连理工大学 | Method and device for detecting thickness and surface shape of spherical shell part |
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