JP4171615B2 - Shape measurement method - Google Patents

Description

となり、特に被測定物２が球の時、

と表すことができる。
【００２６】
スタイラス１２の先端部に対する被測定面２ａの動摩擦係数μが大きい時、測定押圧が一定であれば、被測定面を上りながら測定する時のモーメントＭ₁ と、被測定面を下りながら測定する時のモーメントＭ₂ との差が式(3) より大きくなる。そして、モーメントの差が大きくなることにより、スタイラス１２の傾き量α、βの差が大きくなり、式(4) 、(5) よりＸ軸方向の誤差の差（ΔＸ₁ −ΔＸ₂ ）及びスタイラス１２の傾きの差（ｃｏｓα−ｃｏｓβ）が大きくなり、式(11)より（Ｚ_A1−Ｚ_A2）が大きくなる。さらに、測定点の傾きΦ_A が大きくなると、式(11)より（Ｚ_A1−Ｚ_A2）がさらに大きくなる。
【００２７】
例えば、球面上の測定において、スタイラス１２とスライド部１１の長さの和をＬ＝２０ｍｍとし、測定面の傾斜角度がΦ_A ＝６０°における、上りと下りのスタイラスの傾きを、それぞれα＝０．３°、β＝０．２°とすると、
Ｌ（ｃｏｓα−ｃｏｓβ）＝−０．１５２μｍ
ΔＸ₁ −ΔＸ₂ ＝３４．９０６μｍ
となり、Φ_A ＝６０°における

となる。
【００２８】
【発明が解決しようとする課題】
図１０は、横軸に被測定面の傾斜角度、縦軸に設計式Ｚ＝ｆ（Ｘ）と測定値との差Ｚｄ（μｍ）を表記し、球を測定したときの結果を示す。
【００２９】
図１０から明らかなように、ナノオーダーの測定においては、スタイラス１２の傾きの差が、微小角度であっても、傾斜が大きい被測定面では、測定値の誤差が無視できなくなるほど大きくなる。例えば、測定方向が上り場合と下りの場合ともに、被測定面の傾斜角度が３０°より大きくなると、測定値と設計値との差が大きくなる傾向が認められる。また、スタイラス１２に働く摩擦力は、測定方向で働く向きが異なり、動摩擦係数μが大きい面の測定では無視できない。このように、同じ測定点を測定しても、測定方向により測定値の誤差が大きくなる傾向にあり、この同じ測定点の測定値が測定方向により異なる現象（これを「ヒステリシス」と呼ぶ。）が生じることになる。
【００３０】
本発明は、上記従来の問題点に鑑み、ヒステリシスの影響を小さくすることができる形状測定方法を提供することを目的とする。
【００３２】
【課題を解決するための手段】
本発明の形状測定方法は、一端にスタイラスを他端にミラー面を設けたスライド部の前記スタイラスを被測定面に接触させ、第１の光源から照射した光が前記ミラー面で反射した反射光から前記被測定面の複数の位置における前記スライド部の軸芯方向の位置を測定する第１の測定工程と、第２の光源から照射した光が前記ミラー面で反射した反射光から前記スライド部と前記スライド部を支持するガイド部との相対位置を測定する第２の測定工程と、前記スライド部の軸芯方向と直交し、かつ互いに直交する２つの方向の位置を測定する第３の測定工程とを有し、前記第１の測定工程と第３の測定工程とで測定した前記被測定面の第１の測定位置における第１の測定値と前記第１の測定位置の１つ前の第２の測定位置における第２の測定値と前記第１の測定位置の１つ後の第３の測定位置における第３の測定値とに基づいて前記スタイラスが前記被測定面を走査する時の前記被測定面の傾斜角度と傾斜に対する測定方向を算出し、前記第２の測定工程で測定した前記スライド部と前記ガイド部との相対位置と前記算出した被測定面の傾斜角度と傾斜に対する測定方向とに基づいて前記スライド部と前記ガイド部の相対位置を調整して前記被測定面に対する前記スタイラスの押圧力を、下記の式（１）で表される測定方向が上りの時の押圧力Ｆｕと、下記の式（２）で表される下りの時の押圧力Ｆｄとで切り換えて変化させながら前記被測定面を測定することを特徴とするものである。
Ｆｕ＝Ｆ×（ｃｏｓΦ・ｓｉｎΦ−μｃｏｓΦ・ｃｏｓΦ）
但し ２０ [ ｍｇｆ ] ＜Ｆｕ＜５０ [ ｍｇｆ ] …式（１）
Ｆｄ＝Ｆ×（ｃｏｓΦ・ｓｉｎΦ＋μｃｏｓΦ・ｃｏｓΦ）
但し ２０ [ ｍｇｆ ] ＜Ｆｄ＜５０ [ ｍｇｆ ] …式（２）
ここで、Φは被測定面の傾き、μは被測定面の動摩擦係数、Ｆは一定値
本発明によると、任意の測定点において測定方向の違いにより生じる測定値の差（ヒステリシス）を小さくすることができる。
【００３３】
また、前記スライド部と前記ガイド部の間に弾性材が配置され、前記スライド部と前記ガイド部の相対位置を調整して前記弾性材の変位量を変化させることにより前記スタイラスの押圧力を変化させると、スタイラスの押圧力を自動制御できて好適である。
【００３４】
【発明の実施の形態】
以下、本発明の形状測定方法の一実施形態について、図１１〜図１９を参照して説明する。なお、形状測定装置の全体構成及び基本的な測定方法は、図１、図２を参照して説明した従来例と同一であり、その説明を援用し、主として相違点について説明する。
【００３５】
本実施形態においては、図１１に示すように、第１に測定時に任意の測定点の傾斜角度と、スタイラス１２が被測定面２ａの斜面を上りながらの測定か、下りながらの測定かといった測定方向を算出するための算出手段３３を設け、第２に算出手段３３により求められた測定点の傾斜角度や測定方向と、スタイラス１２の先端部に対する被測定面２ａの動摩擦係数に応じて、スタイラス１２が被測定面２ａに負荷する測定押圧を変えるように、サーボ回路２８に対して出力を指示する誤差信号を設定するように誤差信号発生部２７を構成している。なお、図１１において、３２はミラー面１３の位置を測定する位置測定手段であり、その測定結果が算出手段３３に入力されている。以下、上記算出手段３３における算出方法及び誤差信号発生部２７からの出力信号の設定方法について、順次説明する。
【００３６】
まず、被測定面２ａの任意の測定点における傾斜角度と測定方向を自動的に算出する測定手段３３の算出アルゴリズムを説明する。ここで、傾斜角度は測定点における法線とＺ軸がなす鋭角とする。なお、本発明の測定方法においては、連続面の測定に限定される。また、常に被測定面２ａの測定原点を決めてから測定を開始する。例えば、被測定物２が球であれば、球の頂点を原点として測定を開始し、また特公平７−６９１５８号公報に開示された方法により自動的に測定原点を求める機能を備えている。
【００３７】
図１２において、スタイラス１２は被測定面２ａの形状に追随しながら走査している。スタイラス１２の現在の測定位置における測定値をＡ₁(Ｘ_1,Ｚ₁)、ΔＸ離れた１つ前の測定値をＡ₀(Ｘ_0,Ｚ₀)、ΔＸ離れた次の測定値をＡ₂(Ｘ_2,Ｚ₂)とすると、ΔＸが非常に小さいとき、測定点Ａ₂(Ｘ_2,Ｚ₂)の傾斜角度と測定方向は次のように近似することができる。
【００３８】
傾斜角度Φ_A ＝ｔａｎ^-1｜（Ｚ₁ −Ｚ₀ ）／（Ｘ₁ −Ｘ₂ ）｜ (12)
また、被測定面２ａが設計式にほぼ一致する場合、被測定面２ａのＸ座標に対するＺの値を表す式をＺ＝ｆ（Ｘ）とすると、
傾斜角度Φ_A ＝ｔａｎ^-1｜ｄｆ（Ｘ）／ｄＸ｜ (13)
と表すことができる。
【００３９】
測定方向は、Ｚ₁ −Ｚ₀ ＞０のときは上り、Ｚ₁ −Ｚ₀ ＜０のときは下りとする。
【００４０】
次に、任意の測定点の、測定方向の違いにより生じるヒステリシスを小さくする測定押圧の設定方法について説明する。ヒステリシスを小さくするためには、任意の測定点を通過するときに、スタイラス１２先端が受ける曲げモーメントが、その任意の点において測定方向にかかわらず一定であれば良い。すなわち、測定方向と測定面の傾きに応じて、ある一定の法則で、スタイラス１２が測定面２ａに負荷する測定押圧を変えながら測定することで実現できる。
【００４１】
被測定面２ａの傾きがΦ_A2の任意の点Ａ₂(Ｘ_2,Ｚ₂)を、Ｚ₁ −Ｚ₀ ＞０の方向で測定する時と、Ｚ₁ −Ｚ₀ ＜０の方向で測定する時のスタイラス１２の先端部に働くモーメントは以下のようになる。
【００４２】
Ｚ₁ −Ｚ₀ ＞０の方向の測定で、測定押圧をＦu とすると、スタイラス１２の先端部には、

が働く。
【００４３】
同様に、Ｚ₁ −Ｚ₀ ＜０の方向の測定で、測定押圧をＦ_D とすると、スタイラス１２の先端部には、

が働く。ここで、Ｌはスタイラス１２とスライド部１１の長さの和である。
【００４４】
よって、ヒステリシスを無くすためには、
Ｍ_U ＝Ｌ×Ｆu （ｃｏｓΦ_A2・ｓｉｎΦ_A2＋μｃｏｓΦ_A2・ｃｏｓΦ_A2）
＝Ｍ_D ＝Ｌ×Ｆ_D （ｃｏｓΦ_A2・ｓｉｎΦ_A2−μｃｏｓΦ_A2・ｃｏｓΦ_A2）
であれば良い。その１つの実施例としては、
Ｚ₁ −Ｚ₀ ＞０の方向の測定時の測定押圧Ｆ_U は、
Ｆu ＝Ｆ×（ｃｏｓΦ_A2・ｓｉｎΦ_A2−μｃｏｓΦ_A2・ｃｏｓΦ_A2） (16)
Ｚ₁ −Ｚ₀ ＜０の方向の測定時の測定押圧Ｆ_D は、
Ｆ_D ＝Ｆ×（ｃｏｓΦ_A2・ｓｉｎΦ_A2＋μｃｏｓΦ_A2・ｃｏｓΦ_A2） (17)
というように、測定押圧を測定点の傾きΦ_A2と、動摩擦係数μによって切り換えることで、ヒステリシスを小さくすることができる。
【００４５】
さらに、プローブが被測定面２ａに追随し、被測定面２ａに傷を付けずに測定するために、Ｆu 、Ｆ_D ともに、以下の条件を満たすことが推奨される。
【００４６】
２０〔ｍｇｆ〕＜Ｆu ＜５０〔ｍｇｆ〕
２０〔ｍｇｆ〕＜Ｆ_D ＜５０〔ｍｇｆ〕 (18)
なお、式(16)、式(17)のＦは一定値とする。
【００４７】
図１３、図１４に、スタイラス１２の先端部に対する被測定面２ａの動摩擦係数がμ＝０．１、μ＝０．３のとき例について、ヒシテリシスを小さくするための測定押圧Ｆu 及びＦ_D の値を、測定点の傾きΦ_A をパラメータとして表している。なお、このときＦ＝８０〔ｍｇｆ〕として算出した。
【００４８】
次に、上記のようにスタイラス１２の測定押圧を制御するための構成について説明する。
【００４９】
図１５は、ミラー面１３で反射し、ピンホール２５ａ、２５ｂを通過し、２つの光検出器２６ａ、２６ｂに到達するレーザ光Ｇの光量を説明する図で、（ａ）はスライド部１１が上昇した時の、（ｂ）はスライド部１１が下降した時の状態を示す。（ａ）での光検出器２６ａ、２６ｂが受光する光量をＡ１、Ｂ１、（ｂ）での光検出器２６ａ、２６ｂが受光する光量をＡ２、Ｂ２とすると、（ａ）ではＡ１＜Ｂ１、（ｂ）ではＡ２＜Ｂ２となる。
【００５０】
２つの光検出器２６ａ、２６ｂの受光出力は、誤差信号発生部２７によりフォーカス誤差信号（ＦＥ〔Ｖ〕）として検出される。このＦＥ信号は、横軸に板ばね１４の変位量ΔＸ（μｍ）、縦軸にＦＥ信号を取り、かつスライド部１１、スタイラス１２、ミラー面１３から成る可動部の重量により伸びた自然状態におけるＦＥ信号の値を−１〔Ｖ〕とすると、図１６に示すようなＳ字形状の特性を示す。ただし、本実施形態では図１６の主に原点付近の範囲の信号を用いるため、図１７に示すように、ＦＥ信号と板ばね１４の変位量はほぼ比例関係にある。
【００５１】
従って、今、板ばね１４のばね定数を２００〔ｍｇｆ／ｍｍ〕とし、横軸にＦＥ信号〔Ｖ〕、縦軸に被測定物２の被測定面２ａに負荷される測定押圧〔ｍｇｆ〕をとると、図１８に示すような関係になる。
【００５２】
かくして、スタイラス１２の先端部に対する被測定面２ａの動摩擦係数がμ＝０．１の場合には、測定点の傾きΦ_A に応じて、図１３に示したような測定押圧を負荷して、測定方向の違いによるヒステリシスを小さくするため、誤差信号発生部２７から、測定点の傾きΦ_A に応じて、図１９に示すようなＦＥ_U 信号、ＦＥ_D 信号を出力し、これらＦＥ_U 信号、ＦＥ_D 信号に基づいてサーボ回路２８にてリニアモータ２９を制御するように構成されている。
【００５３】
このようにＦＥ信号の目標値を受けて、スライド部１１とガイド部１５の相対位置を制御し、被測定面２ａに対するスタイラス１２の測定押圧を変えながら測定することで、被測定面２ａの傾きが大きい場合にも、測定方向の違いによるヒステリシスが小さい状態で高精度の測定を行うことができる。
【００５４】
【発明の効果】
本発明の形状測定方法によれば、従来よりはるかに高精度で、より傾きの大きな面形状を非常に広範囲に測定することができる。
【図面の簡単な説明】
【図１】本発明及び従来例の形状測定装置の一構成例を示す全体概略斜視図。
【図２】従来例の形状測定装置におけるオートフォーカス制御部の構成図。
【図３】被測定面上の任意点の傾きの説明図。
【図４】被測定物からスタイラスが受ける抗力の説明図。
【図５】（ａ）は測定方向が上り時に被測定物とスタイラスとの間に働く摩擦力の説明図、（ｂ）は測定方向が下り時に被測定物とスタイラスとの間に働く摩擦力の説明図。
【図６】（ａ）は測定方向が上り時にスタイラスが受けるトータルの力の説明図、（ｂ）は測定方向が下り時にスタイラスが受けるトータルの力の説明図。
【図７】（ａ）は測定方向が上り時にスタイラスに働くＸ方向の分力の説明図、（ｂ）は測定方向が下り時にスタイラスに働くＸ方向の分力の説明図。
【図８】スタイラスの傾きを表す模式図。
【図９】スタイラスの傾きを表す別の模式図。
【図１０】球を測定した時の測定結果を示すグラフ。
【図１１】本実施形態の形状測定装置における測定押圧制御部の構成図。
【図１２】測定面上の任意点の傾斜角度と測定方向の算出方法の説明図。
【図１３】動摩擦係数がμ＝０．１の時にヒステリシスを小さくする測定押圧の特性図。
【図１４】動摩擦係数がμ＝０．３の時にヒステリシスを小さくする測定押圧の特性図。
【図１５】（ａ）はスライド部が上昇した時に光検出器に到達するレーザ光の光量の説明図、（ｂ）はスライド部が上昇した時の光検出器に到達するレーザ光の光量の説明図。
【図１６】フォーカス誤差信号と板ばねの変位量の関係を示す図。
【図１７】図１６の原点付近の拡大図。
【図１８】測定押圧とフォーカス誤差信号の関係を示す図。
【図１９】ヒステリシスを小さくするためのフォーカス誤差信号の値の説明図。
【符号の説明】
２ 被測定物
２ａ 被測定面
４ レーザ測長光学系
５ 原子間力プローブ
１１ スライド部
１２ スタイラス
１３ ミラー面
１４ 板ばね（弾性材）
１５ ガイド部
２７ 誤差信号発生部（相対位置測定手段）
２８ サーボ回路（位置調整手段）
２９ リニアモータ（位置調整手段）
３１ エア軸受
３２ 位置測定手段
３３ 算出手段[0001]
BACKGROUND OF THE INVENTION
The present invention, the surface shape measurement, the shape measurement of the free-form surface, such as aspherical lenses, Ru can be performed two-dimensional or three-dimensional shape measurement, such as surface roughness or stepped shape measurements with high accuracy and at a low measurement pressure it relates shape measuring method.
[0002]
[Prior art]
Japanese Patent Application Laid-Open No. 4-2992064 discloses an ultra-high-precision three-dimensional measuring machine capable of measuring surface shape measurement, free-form surface shape measurement such as an aspheric lens, and surface roughness measurement with high accuracy of about submicron (nonameter). This is disclosed in Japanese Patent Laid-Open No. 10-170243.
[0003]
A configuration example of the ultra-high accuracy coordinate measuring machine will be described with reference to FIG. In FIG. 1, the tip of an atomic force probe 5 attached to a moving body 3 is made to follow a measurement surface 2a of a measurement object 2 such as a lens installed on a stone surface plate 1 to measure the measurement surface 2a. It is comprised so that the surface shape of may be measured.
[0004]
Specifically, an X reference mirror 6, a Y reference mirror 7, and a Z reference mirror 8 are arranged on a stone surface plate 1 on which the device under test 2 is mounted via a support portion. The movable body 3 provided with the atomic force probe 5 is disposed on the stone surface plate 1 via the X stage 9 and the Y stage 10, and the surface shape of the measurement surface 2 a of the measurement object 2. Following this, the moving body 3 and the atomic force probe 5 can be scanned in the X-axis direction and the Y-axis direction.
[0005]
The moving body 3 is provided with a laser length measuring optical system 4, and the X coordinate of the atomic force probe 5 based on the X reference mirror 6 and the atoms based on the Y reference mirror 7 by a known optical interference method. The Y coordinate of the atomic force probe 5 and the Z coordinate of the atomic force probe 5 based on the Z reference mirror 8 can be measured.
[0006]
Next, as an example of a configuration in which the atomic force probe 5 and the atomic force probe 5 are subjected to autofocus control, those described in Japanese Patent Nos. 2638157 and 3000819 are referred to FIG. To explain.
[0007]
The atomic force probe 5 includes a slide part 11 supported by a guide part 15 via an air bearing 31 so as to be movable in the Z coordinate direction, and a stylus 12 attached to an end of the slide part 11 in the −Z direction. A position measuring means for measuring the Z coordinate of the slide portion 11 is provided. This position measuring means is configured to use the other end of the slide portion 11 as a mirror surface 13, irradiate the mirror surface 13 with a laser beam Fz, and measure the position of the mirror surface 13 from the reflected light.
[0008]
The weight of the movable part composed of the slide part 11, the stylus 12, and the mirror surface 13 is supported by an elastic material that elastically restricts movement in the Z direction, specifically, a leaf spring 14, and the slide part 11 and the stylus 12 are plate. It moves up and down following the surface to be measured 2 a while being suspended by the spring 14. In addition, the slide portion 11 is highly rigid in the XY direction by the air bearing 31 and is configured to move freely in the Z direction, and the slide portion 11 can be made simple and light in weight, so that a measured object with a large inclination can be obtained. Since the lateral displacement due to the measurement pressure can be reduced with respect to the surface 2a, and the measurement pressure can also be reduced, the surface 2a to be measured can be measured with high accuracy without scratching.
[0009]
Furthermore, the relative position measuring means for measuring the relative position between the slide part 11 and the guide part 15 and the guide part 15 so that the relative position between the slide part 11 and the guide part 15 obtained from the relative position measuring means is substantially constant. There is provided auto-focusing control means for driving in the Z direction. By the autofocusing control means, the relative position in the Z direction with respect to the guide portion 15 of the slide portion 11 is restricted to a predetermined position, so that the measurement is always performed with a constant measurement pressure on the measured surface 2a.
[0010]
The relative position measuring means and the autofocusing control means are disposed on the probe body 16 to which the guide portion 15 is connected and movable in the Z direction. Explaining the configuration, the laser light G emitted from the semiconductor laser 17 passes through the collimating lens 18, the polarizing beam splitter 19, and the λ / 4 wavelength plate 20, is reflected by the dichroic mirror 21, and is slid by the objective lens 22. The light is condensed on the mirror surface 13 of the part 11.
[0011]
The reflected light of the laser beam G that has returned to the objective lens 22 is totally reflected by the dichroic mirror 21 and the polarization beam splitter 19, collected by the lens 23, and separated into two by the half mirror 24. , 25b and received by the two photodetectors 26a, 26b.
[0012]
Detection outputs from the two photodetectors 26 a and 26 b are input to the error signal generator 27. A focus error signal is output from the error signal generator 27 to the servo circuit 28, and the linear motor 29 is driven and controlled by the servo circuit 28, and the position of the probe body 16 is focused to a position where a predetermined measuring force can be obtained. The weight of the Z moving part including the probe main body 16 is supported by the spring 30.
[0013]
Next, the force that the stylus 12 attached to the atomic force probe 5 receives during measurement will be described. Hereinafter, in order to simplify the description, the object 2 to be measured is a sphere, and as shown in FIG. 3, the slope Φ of an arbitrary point on the surface 2a to be measured is the normal to the arbitrary point on the surface 2a to be measured and Z The acute angle formed by the axis. Now consider the force acting on the two-dimensional surface of the XZ plane. A similar force is considered to work on the YZ plane. Note that Φ> 0 when X> 0, and Φ <0 when X <0.
[0014]
FIG. 4 is a diagram for explaining the drag that the stylus 12 receives from the DUT 2. At the time of measurement, the stylus 12 applies a measurement pressure to the measured surface 2a with a constant force F in the -Z direction. The stylus 12 receives a drag force FcosΦ from the surface to be measured 2a in the normal direction to the surface. Therefore, the drag acting on the stylus 12 becomes smaller as the inclination of the measured surface 2a becomes larger (the inclination Φ becomes larger).
[0015]
FIG. 5A is a diagram for explaining the frictional force acting between the DUT 2 and the stylus 12 when the measurement direction is up, and FIG. 5B is a diagram illustrating the DUT 2 when the measurement direction is down. It is a figure explaining the frictional force which acts between the stylus. The stylus 12 always receives a frictional force μFcosΦ from the surface 2a to be measured in a tangential direction to the surface. Here, μ represents the dynamic friction coefficient of the surface 2a to be measured with respect to the tip of the stylus 12. Therefore, the greater the inclination of the measured surface 2a (the greater the inclination Φ), the smaller the frictional force acting between the measured surface 2a and the stylus 12. This frictional force always acts on the stylus 12 in the direction opposite to the measurement direction.
[0016]
FIG. 6A is a diagram for explaining the total force that the stylus 12 receives when measuring the measured surface 2a in the measuring direction up, and FIG. 6B shows the measured surface 2a in the measuring direction down. It is a figure explaining the total force which stylus 12 receives when measuring. The stylus 12 receives a drag force FcosΦ in the normal direction + Zφ direction of the measured surface 2a and a frictional force μFcosΦ acting between the measured surface 2a and the tangential direction Xφ of the measured surface 2a. This frictional force always acts on the stylus 12 in the direction opposite to the measurement direction.
[0017]
FIG. 7A is a diagram that considers the component force in the X-axis direction of the force acting on the stylus 12 when the measurement direction goes up, and FIG. 7B shows the force acting on the stylus 12 when going down the measurement direction. It is the figure which considered the component force of the axial direction. When the measurement is performed while ascending the surface to be measured 2a, the drag X-axis direction component force FcosΦ · sinΦ and the frictional force X-axis direction component force μFcosΦ · cosΦ act on the stylus 12 in the same direction. When measuring while descending the measured surface 2a, the X-axis direction component force FcosΦ · sinΦ of the drag force and the X-axis direction component force μFcosΦ · cosΦ of the friction force act on the stylus 12 in opposite directions. .
[0018]
From the above, when the measurement is performed while ascending the surface to be measured 2a, the moment M _U acting on the tip of the stylus 12 is
M _U = L × (FcosΦ · sinΦ + μFcosΦ · cosΦ) (1)
When measuring while down the measurement surface 2a, the moment M _D acting on the tip portion of the stylus 12,
M _D = L × (FcosΦ · sinΦ−μFcosΦ · cosΦ) (2)
Will each work. Here, the moment is positive in the counterclockwise direction. L represents the sum of the lengths of the stylus 12 and the slide portion 11, and is 17 mm to 22 mm in a specific configuration example.
[0019]
From the above, the moment to the left when measuring while going up the measured surface 2a and when measuring while going down the measured surface 2a is M _U −M _D = 2 × L × μFcosΦ from the equations (1) and (2).・ CosΦ (3)
If the measurement pressure F is constant, the moment M _U when measuring while moving up the measured surface 2a from the equation (3) as the dynamic friction coefficient μ of the measured surface 2a with respect to the tip of the stylus 12 increases, the difference between the moment M _D at the time of measurement, while down the surface to be measured 2a can not be ignored.
[0020]
FIG. 8 shows the inclination of the stylus 12 when passing through the measurement point A (X _A , Z _A ) of the measured surface 2a when the dynamic friction coefficient μ of the measured surface 2a relative to the tip of the stylus 12 is large. Reference numeral 12 a represents an ideal state where no drag force and friction force are acting on the stylus 12. Reference numeral 12b denotes a stylus when measuring while going up the measured surface 2a, and 12c denotes a stylus when measuring while going down the measured surface 2a. Further, the difference in the X-axis direction between the contact A (X _A , Z _A ) between the stylus 12a and the measured surface 2a and the contact B (X _B , Z _B ) between the stylus 12b and the measured surface 2a is expressed as ΔX _1. The difference in the Z-axis direction is ΔZ ₁ . Similarly, the difference in the X-axis direction between A (X _A , Z _A ) and the contact C (X _C , Z _C ) between the stylus 12c and the measured surface 2a is ΔX ₂ , and the difference in the Z-axis direction is ΔZ _2. And
[0021]
Now, in order to represent the a [Delta] Z ₁ and [Delta] Z _2, respectively [Delta] X ₁ and [Delta] X _2, consider the model of Figure 9. 12a ′ and 12b ′ represent central axes of the stylus 12a and stylus 12b, respectively. Further, if the angle formed by 12a ′ and 12b ′ is α, and the angle formed by 12a ′ and 12c ′ is β, ΔX ₁ and ΔX ₂ can be expressed as follows.
[0022]
ΔX ₁ = Lcosα (4)
ΔX ₂ = Lcosβ (5)
Further, when a design formula representing a value of Z with respect to the X coordinate of the surface to be measured 2a is Z = f (X),
ΔZ ₁ = L (1-cos α) + f (X _A ) −f (X _A + ΔX ₁ ) (6)
ΔZ ₂ = L (1-cosβ) + f (X _A ) −f (X _A + ΔX ₂ ) (7)
It becomes. Note that | ΔX ₁ |> | ΔX ₂ | and α> β.
[0023]
Therefore, the measurement value Z _{A at} the measurement point A (X _A , Z _A ) includes the errors of the equations (6) and (7). When measuring while going up the measured surface 2a,
Z _A1 = Z _A −ΔZ ₁ = −L (1−cos α) + f (X _A + ΔX ₁ ) (8)
It can be expressed as.
[0024]
Similarly, when measuring while descending the measured surface 2a,
Z _A2 = Z _A −ΔZ ₂ = −L (1−cos β) + f (X _A + ΔX ₂ ) (9)
It becomes.
[0025]
From the above, the difference between the measurement values at the measurement point A (X _A , Z _A ) when measuring while going up the measured surface 2a and when going down while measuring the measured surface 2a is the equation (8), 9) From

Especially when the DUT 2 is a sphere,

It can be expressed as.
[0026]
When the dynamic friction coefficient μ of the measured surface 2a with respect to the tip of the stylus 12 is large, if the measurement pressure is constant, the moment M ₁ when measuring while ascending the measured surface and when measuring while descending the measured surface The difference from the moment M ₂ is larger than that in the equation (3). As the difference in moment increases, the difference between the inclination amounts α and β of the stylus 12 increases, and the difference in error in the X-axis direction (ΔX ₁ −ΔX ₂ ) and the stylus are determined from the equations (4) and (5). The difference in the inclination of 12 (cos α−cos β) is increased, and (Z _A1 −Z _A2 ) is increased from the equation (11). Further, when the inclination Φ _{A of the} measurement point increases, (Z _A1 −Z _A2 ) further increases from Equation (11).
[0027]
For example, in the measurement on the spherical surface, the sum of the lengths of the stylus 12 and the slide portion 11 is L = 20 mm, and the inclination of the up and down styluss when the inclination angle of the measurement surface is Φ _A = 60 ° is α = If 0.3 ° and β = 0.2 °,
L (cos α-cos β) = − 0.152 μm
ΔX ₁ −ΔX ₂ = 34.906 μm
At Φ _A = 60 °

It becomes.
[0028]
[Problems to be solved by the invention]
FIG. 10 shows the result of measuring a sphere with the horizontal axis representing the tilt angle of the surface to be measured and the vertical axis representing the design formula Z = f (X) and the difference Zd (μm) between the measured values.
[0029]
As is apparent from FIG. 10, in the nano-order measurement, even if the difference in the inclination of the stylus 12 is a minute angle, the measured value error becomes large on the measurement surface with a large inclination so that the measurement value error cannot be ignored. For example, it is recognized that the difference between the measured value and the design value tends to increase when the inclination angle of the surface to be measured is larger than 30 ° both when the measurement direction is up and down. Further, the friction force acting on the stylus 12 is different in the direction of working in the measurement direction, and cannot be ignored in the measurement of a surface having a large dynamic friction coefficient μ. As described above, even if the same measurement point is measured, the measurement value error tends to increase depending on the measurement direction, and a phenomenon in which the measurement value at the same measurement point varies depending on the measurement direction (this is referred to as “hysteresis”). Will occur.
[0030]
The present invention aims at providing the light of the conventional problems, shape measurement method that can be reduced the effect of the hysteresis.
[0032]
[Means for Solving the Problems]
In the shape measuring method of the present invention, the stylus of the slide portion having the stylus at one end and the mirror surface at the other end is brought into contact with the surface to be measured, and the light irradiated from the first light source is reflected by the mirror surface. From the first measurement step of measuring the position of the slide portion in the axial direction at a plurality of positions on the surface to be measured, and the slide portion from the reflected light reflected from the mirror surface by the light emitted from the second light source And a second measurement step for measuring the relative position between the slide portion and the guide portion supporting the slide portion, and a third measurement for measuring positions in two directions perpendicular to the axial direction of the slide portion and perpendicular to each other A first measurement value at the first measurement position of the surface to be measured measured in the first measurement process and the third measurement process, and one previous to the first measurement position. Second measurement value at the second measurement position An inclination angle of the surface to be measured and a measurement direction with respect to the inclination when the stylus scans the surface to be measured based on a third measurement value at a third measurement position immediately after the first measurement position. And the slide portion and the guide portion based on the relative position between the slide portion and the guide portion measured in the second measurement step, the calculated inclination angle of the measured surface, and the measurement direction relative to the inclination. The pressing force of the stylus against the surface to be measured by adjusting the relative position is expressed by the pressing force Fu when the measurement direction represented by the following formula (1) is up and the following formula (2). Ru der those characterized by measuring the measurement surface while switching by changing in the pressing force Fd when the downlink that.
Fu = F × (cosΦ · sinΦ−μcosΦ · cosΦ)
However, 20 [ mgf ] <Fu <50 [ mgf ] ... Formula (1)
Fd = F × (cosΦ · sinΦ + μcosΦ · cosΦ)
However, 20 [ mgf ] <Fd <50 [ mgf ] ... Formula (2)
Where Φ is the inclination of the surface to be measured, μ is the coefficient of dynamic friction of the surface to be measured, and F is a constant value
According to the present invention, it is possible to reduce a difference (hysteresis) in measurement values caused by a difference in measurement direction at an arbitrary measurement point.
[0033]
The front the kiss riding portion guide portion is disposed elastic material between, press the stylus by adjusting the relative position of the guide portion and the sliding portion to vary the displacement amount of the elastic member It is preferable to change the pressure because the pressing force of the stylus can be automatically controlled.
[0034]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, an embodiment of a shape measuring method of the present invention will be described with reference to FIGS. 11 to 19. Note that the overall configuration and basic measurement method of the shape measuring apparatus are the same as those of the conventional example described with reference to FIGS. 1 and 2, and the differences will be mainly described with reference to the description.
[0035]
In the present embodiment, as shown in FIG. 11, firstly, the measurement is performed such as the inclination angle of an arbitrary measurement point at the time of measurement and whether the stylus 12 is measured while going up or down the measured surface 2a. Calculation means 33 for calculating the direction is provided, and secondly, the stylus according to the inclination angle and measurement direction of the measurement point obtained by the calculation means 33 and the dynamic friction coefficient of the measured surface 2a with respect to the tip of the stylus 12 The error signal generator 27 is configured to set an error signal for instructing the servo circuit 28 to output so that 12 changes the measurement pressure applied to the surface 2a to be measured. In FIG. 11, reference numeral 32 denotes position measuring means for measuring the position of the mirror surface 13, and the measurement result is input to the calculating means 33. Hereinafter, the calculation method in the calculation means 33 and the method for setting the output signal from the error signal generator 27 will be sequentially described.
[0036]
First, the calculation algorithm of the measuring means 33 for automatically calculating the inclination angle and the measurement direction at an arbitrary measurement point on the measurement surface 2a will be described. Here, the inclination angle is an acute angle formed by the normal line at the measurement point and the Z axis. In addition, in the measuring method of this invention, it is limited to the measurement of a continuous surface. Further, the measurement is always started after the measurement origin of the measured surface 2a is determined. For example, if the DUT 2 is a sphere, the measurement is started with the top of the sphere as the origin, and the measurement origin is automatically obtained by the method disclosed in Japanese Patent Publication No. 7-69158.
[0037]
In FIG. 12, the stylus 12 is scanned while following the shape of the surface 2a to be measured. The measurement value at the current measurement position of the stylus 12 is A ₁ (X _1, Z ₁ ), the previous measurement value separated by ΔX is A ₀ (X _0, Z ₀ ), and the next measurement value separated by ΔX is A Assuming ₂ (X _2, Z ₂ ), when ΔX is very small, the inclination angle and measurement direction of the measurement point A ₂ (X _2, Z ₂ ) can be approximated as follows.
[0038]
Inclination angle Φ _A = tan ⁻¹ | (Z ₁ −Z ₀ ) / (X ₁ −X ₂ ) | (12)
In addition, when the surface to be measured 2a substantially matches the design formula, if the equation representing the value of Z with respect to the X coordinate of the surface to be measured 2a is Z = f (X),
Inclination angle Φ _A = tan ⁻¹ | df (X) / dX | (13)
It can be expressed as.
[0039]
The measurement direction is up when Z ₁ −Z ₀ > 0, and down when Z ₁ −Z ₀ <0.
[0040]
Next, a measurement pressing setting method for reducing hysteresis caused by a difference in measurement direction at an arbitrary measurement point will be described. In order to reduce the hysteresis, the bending moment received by the tip of the stylus 12 when passing through an arbitrary measurement point may be constant regardless of the measurement direction at the arbitrary point. In other words, the measurement can be realized by changing the measurement pressure applied to the measurement surface 2a by the stylus 12 according to a certain law according to the measurement direction and the inclination of the measurement surface.
[0041]
When measuring an arbitrary point A ₂ (X _2, Z ₂ ) where the inclination of the measured surface 2a is Φ _A2 in the direction of Z ₁ -Z ₀ > 0, and in the direction of Z ₁ -Z ₀ <0 The moment acting on the tip of the stylus 12 at the time is as follows.
[0042]
When measuring in the direction of Z ₁ −Z ₀ > 0 and the measurement pressure is Fu, the tip of the stylus 12 is

Work.
[0043]
Similarly, in the measurement in the direction of Z ₁ −Z ₀ <0, when the measurement pressure is F _D , the tip of the stylus 12 is

Work. Here, L is the sum of the lengths of the stylus 12 and the slide portion 11.
[0044]
Therefore, to eliminate hysteresis,
_{M U = L × Fu (cosΦ} A2 · sinΦ A2 + μcosΦ A2 · cosΦ A2)
_{= M D = L × F D} (cosΦ A2 · sinΦ A2 -μcosΦ A2 · cosΦ A2)
If it is good. One example is as follows:
The measurement pressure F _U when measuring in the direction of Z ₁ −Z ₀ > 0 is
Fu = F × (cos Φ A ₂ · sin Φ _A2 −μ cos Φ A ₂ , cos Φ _A2 ) (16)
The measurement pressure F _D at the time of measurement in the direction of Z ₁ −Z ₀ <0 is
_{F D = F × (cosΦ A2} · sinΦ A2 + μcosΦ A2 · cosΦ A2) (17)
As described above, the hysteresis can be reduced by switching the measurement pressure according to the inclination Φ _{A2 of the} measurement point and the dynamic friction coefficient μ.
[0045]
Further, the probe to follow the measurement surface 2a, in order to measure without scratching the surface to be measured 2a, Fu, F _D together is recommended that the following conditions are satisfied.
[0046]
20 [mgf] <Fu <50 [mgf]
20 [mgf] <F _D <50 [mgf] (18)
Note that F in equations (16) and (17) is a constant value.
[0047]
13, 14, the dynamic friction coefficient mu = 0.1 of the sample surface 2a against the tip portion of the stylus 12, for example when mu = 0.3, measuring the pressing Fu and F _D for reducing the hysteresis The value is expressed using the inclination Φ _{A of the} measurement point as a parameter. At this time, F = 80 [mgf] was calculated.
[0048]
Next, a configuration for controlling the measurement press of the stylus 12 as described above will be described.
[0049]
FIG. 15 is a diagram for explaining the light quantity of the laser light G that is reflected by the mirror surface 13, passes through the pinholes 25a and 25b, and reaches the two photodetectors 26a and 26b. (B) when it raises shows the state when the slide part 11 descend | falls. When the light amounts received by the photodetectors 26a and 26b in (a) are A1 and B1, and the light amounts received by the photodetectors 26a and 26b in (b) are A2 and B2, in FIG. In (b), A2 <B2.
[0050]
The light reception outputs of the two photodetectors 26a and 26b are detected as a focus error signal (FE [V]) by the error signal generator 27. This FE signal takes the displacement amount ΔX (μm) of the leaf spring 14 on the horizontal axis, the FE signal on the vertical axis, and in a natural state extended by the weight of the movable part including the slide part 11, the stylus 12, and the mirror surface 13. When the value of the FE signal is -1 [V], an S-shaped characteristic as shown in FIG. 16 is shown. However, in the present embodiment, since signals in the vicinity of the origin in FIG. 16 are mainly used, as shown in FIG. 17, the displacement of the FE signal and the leaf spring 14 is substantially proportional.
[0051]
Therefore, the spring constant of the leaf spring 14 is now set to 200 [mgf / mm], the horizontal axis represents the FE signal [V], and the vertical axis represents the measurement pressure [mgf] applied to the measurement surface 2a of the DUT 2. If it takes, it will become a relationship as shown in FIG.
[0052]
Thus, when the dynamic friction coefficient of the surface 2a to be measured with respect to the tip of the stylus 12 is μ = 0.1, a measurement pressure as shown in FIG. 13 is applied according to the inclination Φ _{A of the} measurement point, In order to reduce the hysteresis due to the difference in the measurement direction, the error signal generator 27 outputs FE _U signals and FE _D signals as shown in FIG. 19 according to the inclination Φ _{A of the} measurement point, and these FE _U signals, It is configured to control the linear motor 29 by the servo circuit 28 based on the FE _D signal.
[0053]
In this way, receiving the target value of the FE signal, the relative position between the slide portion 11 and the guide portion 15 is controlled, and the measurement is performed while changing the measurement pressure of the stylus 12 with respect to the measurement surface 2a, whereby the inclination of the measurement surface 2a is measured. Even when is large, highly accurate measurement can be performed in a state where hysteresis due to a difference in measurement direction is small.
[0054]
【The invention's effect】
According to shape measuring method of the present invention, with much higher precision than the conventional, more large surface shape of the gradient can be quite extensive measurements.
[Brief description of the drawings]
FIG. 1 is an overall schematic perspective view showing a configuration example of a shape measuring apparatus according to the present invention and a conventional example.
FIG. 2 is a configuration diagram of an autofocus control unit in a conventional shape measuring apparatus.
FIG. 3 is an explanatory diagram of an inclination of an arbitrary point on a surface to be measured.
FIG. 4 is an explanatory diagram of a drag force received by a stylus from an object to be measured.
5A is an explanatory diagram of a friction force acting between the object to be measured and the stylus when the measurement direction is ascending, and FIG. 5B is a friction force acting between the object to be measured and the stylus when the measurement direction is descending. FIG.
6A is an explanatory diagram of the total force received by the stylus when the measuring direction is up, and FIG. 6B is an explanatory diagram of the total force received by the stylus when the measuring direction is down.
7A is an explanatory diagram of a component force in the X direction acting on the stylus when the measurement direction is up, and FIG. 7B is an explanatory diagram of a component force in the X direction acting on the stylus when the measurement direction is down.
FIG. 8 is a schematic diagram showing the inclination of a stylus.
FIG. 9 is another schematic diagram showing the inclination of the stylus.
FIG. 10 is a graph showing a measurement result when a sphere is measured.
FIG. 11 is a configuration diagram of a measurement pressing control unit in the shape measuring apparatus according to the present embodiment.
FIG. 12 is an explanatory diagram of a method of calculating an inclination angle of an arbitrary point on a measurement surface and a measurement direction.
FIG. 13 is a characteristic diagram of measurement pressing that reduces the hysteresis when the dynamic friction coefficient is μ = 0.1.
FIG. 14 is a characteristic diagram of measurement pressing for reducing the hysteresis when the dynamic friction coefficient is μ = 0.3.
15A is an explanatory diagram of the amount of laser light reaching the photodetector when the slide portion is raised, and FIG. 15B is the amount of laser light reaching the photodetector when the slide portion is raised. Illustration.
FIG. 16 is a diagram illustrating a relationship between a focus error signal and a displacement amount of a leaf spring.
17 is an enlarged view near the origin of FIG.
FIG. 18 is a diagram illustrating a relationship between measurement pressing and a focus error signal.
FIG. 19 is an explanatory diagram of the value of a focus error signal for reducing hysteresis.
[Explanation of symbols]
2 Measurement object 2a Measurement surface 4 Laser length measurement optical system 5 Atomic force probe 11 Slide portion 12 Stylus 13 Mirror surface 14 Leaf spring (elastic material)
15 Guide part 27 Error signal generation part (relative position measuring means)
28 Servo circuit (Position adjustment means)
29 Linear motor (position adjustment means)
31 air bearing 32 position measuring means 33 calculating means

Claims (2)

The stylus of the slide portion having a stylus at one end and a mirror surface at the other end is brought into contact with the surface to be measured, and a plurality of light beams emitted from the first light source are reflected from the reflected light from the mirror surface. A first measurement step for measuring the position of the slide part in the axial direction at a position, and a guide for supporting the slide part and the slide part from the reflected light reflected by the mirror surface by the light emitted from the second light source A second measuring step for measuring a relative position with respect to the portion, and a third measuring step for measuring a position in two directions orthogonal to the axial direction of the slide portion and orthogonal to each other, A first measurement value at a first measurement position on the surface to be measured measured in one measurement step and a third measurement step, and a second measurement position at a second measurement position immediately before the first measurement position. Of the measured value and 1 of the first measurement position Based on a third measurement value at a later third measurement position, an inclination angle of the measurement surface and a measurement direction with respect to the inclination when the stylus scans the measurement surface are calculated, and the second measurement is performed. The relative position between the slide part and the guide part is adjusted by adjusting the relative position between the slide part and the guide part based on the relative position between the slide part and the guide part measured in the process, the calculated inclination angle of the measured surface and the measurement direction relative to the inclination. The pressing force of the stylus on the measurement surface is expressed by the pressing force Fu when the measurement direction represented by the following formula (1) is up, and the pressing force Fd when the measurement direction is represented by the following formula (2). A shape measuring method, characterized in that the surface to be measured is measured while being changed by changing the position.
Fu = F × (cosΦ · sinΦ−μcosΦ · cosΦ)
However, 20 [ mgf ] <Fu <50 [ mgf ] ... Formula (1)
Fd = F × (cosΦ · sinΦ + μcosΦ · cosΦ)
However, 20 [ mgf ] <Fd <50 [ mgf ] ... Formula (2)
Where Φ is the inclination of the surface to be measured, μ is the coefficient of dynamic friction of the surface to be measured, and F is a constant value   An elastic material is disposed between the slide portion and the guide portion, and the pressing force of the stylus is changed by changing a displacement amount of the elastic material by adjusting a relative position between the slide portion and the guide portion. The shape measuring method according to claim 1.

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