JP2011033490A

JP2011033490A - Super-precision shape measuring method for rotation symmetrical shape and apparatus of the same

Info

Publication number: JP2011033490A
Application number: JP2009180408A
Authority: JP
Inventors: Katsuyoshi Endo; 勝義遠藤; Yasuo Azuma; 保男東
Original assignee: Osaka University NUC; High Energy Accelerator Research Organization
Current assignee: Osaka University NUC; High Energy Accelerator Research Organization
Priority date: 2009-08-03
Filing date: 2009-08-03
Publication date: 2011-02-17
Anticipated expiration: 2029-08-03
Also published as: JP5434345B2

Abstract

PROBLEM TO BE SOLVED: To provide a super-precision shape measuring method for rotation symmetrical shape, capable of measuring a rotation symmetrical shape and particularly, a shape of a surface of an object to be measured having a spherical surface or an aspherical surface approximate to the spherical surface and having a small curvature radius, with a shape precision of approximately 1 nm in a short time and capable of attaining cost reduction. SOLUTION: The normal vector tracking type super-precision shape measuring method determines a shape by reflecting measurement beam on a surface of an object to be measured, detecting the reflected beam with an optical detector and measuring a normal vector at a given measurement point of the surface. The optional detector 5 measures a displacement of reflection beam in a receiving surface. After an optical axis of an optical system 2 is made to meet a center line of the object to be measured and initial setting is made to overlap the measurement beam with the reflected beam, only one of a sample system 3 or an optical system 2 is driven with a set of two axes of goniometers 6, 7, a measurement range of the surface of the object to be measured is scanned with the measurement beam, and a normal vector at that point is calculated from an angular change in the reflected beam. COPYRIGHT: (C)2011,JPO&INPIT

Description

本発明は、回転対称形状の超精密形状測定方法及びその装置に係わり、更に詳しくは球面若しくは非球面の回転対称形の被測定物の表面形状を超精密に測定する方法及びその装置に関するものである。 The present invention relates to a rotationally symmetric ultra-precise shape measuring method and apparatus, and more particularly to a method and apparatus for measuring the surface shape of a spherical or aspheric rotationally symmetric object to be measured with high precision. is there.

Ｘ線自由電子レーザーや波長１３．５ｎｍの極紫外光を用いたリソグラフィー技術から要請される次世代高精度光学素子の製作には、非球面で形状誤差を１〜０．１ｎｍＲＭＳの精度で自由曲面の形状を計測することが不可欠である。また、大量に製造される民生用の種々の曲率を持つ非球面ミラー、レンズにも超精密形状計測が求められている。 For the production of next-generation high-precision optical elements required from lithography technology using X-ray free electron lasers and extreme ultraviolet light with a wavelength of 13.5 nm, free-form surfaces with an aspherical shape error of 1 to 0.1 nm RMS It is essential to measure the shape of Ultra-precision shape measurement is also required for aspherical mirrors and lenses with various curvatures for consumer use that are manufactured in large quantities.

従来、空間波長０．１ｍｍ以上の形状測定技術は、位相シフトフィゾー干渉計や三次元形状測定機、ＬＴＰ（Long Trace Profiler）がある。位相シフトフィゾー干渉計の場合は、参照面が不可欠である。原則測定対象が平面若しくは球面に限られ、非球面測定には測定対象物に合わせた特殊な工夫が必要である。また、曲率の大きな光学素子に対応ができず、原理的に絶対形状測定が不可能である。三次元形状測定機は、直線３軸の運動精度が測定精度を支配し、プローブが接触式であるため、光学素子表面に傷を残す。測定精度も接触式であるが故に、測定対象の形状に依存し、１０〜３００ｎｍが限界である。ＬＴＰは、５×１０^-7ｒａｄＲＭＳの測定精度（３ｎｍＲＭＳ）が得られているが、その測定範囲は±５ｍｒａｄ（１００ｍｍ）の長さで曲率半径が±５００ｍに限られており、直線上断面の二次元形状のみの測定である。 Conventionally, there are a phase shift Fizeau interferometer, a three-dimensional shape measuring machine, and an LTP (Long Trace Profiler) as a shape measuring technique with a spatial wavelength of 0.1 mm or more. In the case of a phase shift Fizeau interferometer, a reference plane is essential. In principle, the object to be measured is limited to a flat surface or a spherical surface, and a special device suitable for the object to be measured is required for aspherical measurement. Further, it cannot cope with an optical element having a large curvature, and in principle, absolute shape measurement is impossible. In the three-dimensional shape measuring machine, the motion accuracy of the three linear axes dominates the measurement accuracy, and the probe is a contact type, so that the surface of the optical element is damaged. Since the measurement accuracy is also a contact type, 10 to 300 nm is the limit depending on the shape of the measurement object. LTP has a measurement accuracy of 5 × 10 ⁻⁷ radRMS (3 nm RMS), but its measurement range is ± 5 mrad (100 mm) and the radius of curvature is limited to ± 500 m. It is a measurement of only two-dimensional shape.

このような従来の課題を解消する方法として、特許文献１に記載されるような自由曲面形状を計測する超精密形状測定方法が提案されている。この超精密形状測定方法の原理は、レーザーの直進性を活用し、水平垂直方向に回転する２軸のゴニオメータの回転中心から射出したレーザーは別の２軸ゴニオメータ上にセットされた光学素子（レンズ、ミラー）で反射されて、光源の位置にある検出器（４分割フォトダイオード；ＱＰＤ）の中心に戻るように２軸２組のゴニオメータを制御して、ミラーの任意測定点の法線ベクトルを０．１μｒａｄの精度で測定するものである。法線ベクトルは、これらのゴニオメータの回転角度のみで、測定座標点はゴニオメータの回転角度と測定試料の曲率半径から求めることが可能である。本計測法は基準面を用いないため、非球面、非回転対称面の形状を測定できる能力を持っている。形状の導出は、スロープ関数を補間・積分をおこなう傾斜角積分法や本発明者らが新しく開発したフーリエ級数で測定面形状を近似し、最小二乗法によって、その点での法線ベクトルの残差を最小にするフーリエ係数を求めて測定面形状を一意的に決定する「フーリエ級数展開最小二乗法」というアルゴリズムなどで絶対形状を求めるのである。 As a method for solving such a conventional problem, an ultra-precise shape measuring method for measuring a free-form surface shape as described in Patent Document 1 has been proposed. The principle of this ultra-precise shape measurement method uses the straightness of the laser, and the laser emitted from the center of rotation of a biaxial goniometer that rotates horizontally and vertically is an optical element (lens) set on another biaxial goniometer. , The two-axis two sets of goniometers to return to the center of the detector (quadrant photodiode; QPD) at the position of the light source, and the normal vector of the arbitrary measurement point of the mirror is The measurement is performed with an accuracy of 0.1 μrad. The normal vector is only the rotation angle of these goniometers, and the measurement coordinate point can be obtained from the rotation angle of the goniometer and the curvature radius of the measurement sample. Since this measurement method does not use a reference surface, it has the ability to measure the shape of an aspherical surface and a non-rotationally symmetric surface. The derivation of the shape is performed by approximating the measurement surface shape by the slope angle integration method that interpolates and integrates the slope function or the Fourier series newly developed by the present inventors, and the normal vector at that point is left by the least square method. The absolute shape is obtained by an algorithm such as an algorithm called “Fourier series expansion least square method” in which a Fourier coefficient that minimizes the difference is obtained to uniquely determine the shape of the measurement surface.

更に、本発明者らは、光源から出射されたレーザービームが光学素子に反射されて、光源の位置にある検出器（ＱＰＤ）の中心に戻るように２軸１組のゴニオメータを、また検出器と光学素子表面間の光路長Ｌを一定になるように光軸方向の１軸直進ステージを、それぞれの検出器の出力を直接駆動系に入力する３軸フルクローズドフィードバック制御することを提案している。このように、光学素子の法線ベクトルを追跡しながら、残りの２軸のゴニオメータで測定点座標を定値制御することで、計測時間の短縮化を図ることが可能な５軸制御形状測定法を提案している。 Furthermore, the present inventors have set a goniometer of two axes so that the laser beam emitted from the light source is reflected by the optical element and returns to the center of the detector (QPD) at the position of the light source. Proposed to perform three-axis full-closed feedback control for the uniaxial rectilinear stage in the optical axis direction so that the optical path length L between the optical element surface and the optical element surface becomes constant, and the output of each detector is directly input to the drive system. Yes. In this way, a 5-axis control shape measurement method that can shorten the measurement time by tracking the normal vector of the optical element and performing constant value control of the measurement point coordinates with the remaining two-axis goniometers. is suggesting.

特許第３５９８９８３号公報Japanese Patent No. 3598983

新しい５軸制御形状測定法の開発によって、各計測点座標での法線ベクトルの計測を素早く行うことができ、被測定物の表面形状の測定が短時間で行えるようになり、また大型の被測定物でも精密に形状を測定することができるようになったが、それでも計測には長時間を要する。また、５軸制御であれば、形状測定装置のコストが高くなる。大量に製造される民生用の光学素子を短時間・低コストで高精度に形状計測できる方法の出現が望まれている。 With the development of a new 5-axis control shape measurement method, the normal vector at each measurement point coordinate can be measured quickly, the surface shape of the object to be measured can be measured in a short time, and a large object can be measured. Although it has become possible to accurately measure the shape of a measurement object, it still takes a long time to measure. Moreover, if it is 5-axis control, the cost of a shape measuring apparatus will become high. The emergence of a method capable of measuring the shape of consumer optical elements manufactured in large quantities with high accuracy in a short time and at low cost is desired.

そこで、本発明が前述の状況に鑑み、解決しようとするところは、回転対称形状であり、主に球面若しくは球面に近似できる非球面の形状で、曲率半径が小さな被測定物の表面の形状を、短時間で１ｎｍ程度の形状精度で測定することが可能であり、しかも低コスト化を図ることが可能な回転対称形状の超精密形状測定方法及びその装置を提供する点にある。 Therefore, in view of the above situation, the present invention is intended to solve a rotationally symmetric shape, mainly a spherical surface or an aspherical shape that can be approximated to a spherical surface, and the shape of the surface of the object to be measured having a small curvature radius. The object is to provide a rotationally symmetric ultra-precise shape measuring method and apparatus capable of measuring with a shape accuracy of about 1 nm in a short time and reducing the cost.

本発明は、前述の課題解決のために、光源と光検出器を設けた光学系と被測定物を保持した試料系とを備え、光源から出射された計測ビームが被測定物表面で反射され、その反射ビームを光検出器で検出して被測定物表面の任意計測点の法線ベクトルを計測することから形状を求める法線ベクトル追跡型超精密形状測定方法において、前記被測定物の表面が回転対称形状で、主に球面若しくは球面に近似できる非球面の形状であり、前記光検出器が受光面における反射ビームの変位を計測可能であり、前記光学系の光軸と被測定物の中心線を一致させて計測ビームと反射ビームとが重なるように初期設定した後、試料系又は光学系の一方のみを２軸１組のゴニオメータで駆動して計測ビームで被測定物表面の測定範囲を走査し、反射ビームの角度変化からその点での法線ベクトルを算出することを特徴とする回転対称形状の超精密形状測定方法を構成した（請求項１）。 In order to solve the above-described problems, the present invention includes an optical system provided with a light source and a photodetector and a sample system holding the object to be measured, and a measurement beam emitted from the light source is reflected on the surface of the object to be measured. In the normal vector tracking type ultra-precise shape measuring method for obtaining the shape by detecting the reflected beam with a photodetector and measuring the normal vector at an arbitrary measurement point on the surface of the object, the surface of the object to be measured Is a rotationally symmetric shape, mainly a spherical surface or an aspherical shape that can approximate a spherical surface, and the photodetector can measure the displacement of the reflected beam on the light receiving surface, and the optical axis of the optical system and the object to be measured After initial setting so that the measurement beam and reflected beam overlap with the center line coincident, only one of the sample system or the optical system is driven by a pair of goniometers with two axes, and the measurement range of the surface of the object to be measured with the measurement beam Of the reflected beam It was constructed ultra-precision shape measurement method of rotationally symmetrical shape from degrees change and calculates the normal vector at that point (claim 1).

ここで、光検出器として、４分割フォトダイオード（ＱＰＤ）を用いることが好ましい（請求項２）。あるいは、光検出器として、ＣＣＤイメージセンサ又はＣＭＯＳイメージセンサを用いることも好ましい（請求項３）。 Here, a quadrant photodiode (QPD) is preferably used as the photodetector. Alternatively, it is also preferable to use a CCD image sensor or a CMOS image sensor as the photodetector.

また、前記被測定物が凸面である場合には、試料系の２軸１組のゴニオメータで駆動する可動部に被測定物を保持し、２軸１組のゴニオメータのＢ軸に被測定物の中心線を一致させるとともに、ゴニオメータのＣ軸が被測定物の中心線上の曲率中心を通るように所期設定するのである（請求項４）。 When the object to be measured is a convex surface, the object to be measured is held on a movable part that is driven by a pair of two goniometers of the sample system, and the object to be measured is placed on the B axis of the pair of two goniometers. The center line is made coincident and the goniometer C axis is set so as to pass through the center of curvature on the center line of the object to be measured.

また、前記被測定物が凹面である場合には、光学系の２軸１組のゴニオメータで駆動する可動部に光源と光検出器を設け且つ２軸１組のゴニオメータのＡ軸とＣ軸が光検出器の受光面中心を通るように設定するとともに、光検出器の受光面中心が被測定物の中心線上の曲率中心を通るように所期設定するのである（請求項５）。 When the object to be measured is a concave surface, a light source and a light detector are provided in a movable part driven by a pair of goniometers of a two-axis optical system, and the A-axis and the C-axis of a pair of two-axis goniometers It is set so that it passes through the center of the light receiving surface of the photodetector and the center of the light receiving surface of the photodetector passes through the center of curvature on the center line of the object to be measured.

そして、本発明は、光源と受光面における入射ビームの変位を計測可能な光検出器を設けた光学系と、表面が球面若しくは球面に近似した非球面の回転対称形凸面の被測定物を、２軸１組のゴニオメータで駆動する可動部に、該ゴニオメータのＢ軸に被測定物の中心線を一致させるとともに、ゴニオメータのＣ軸が被測定物の中心線上の曲率中心を通るように保持した試料系と、前記光学系の光軸と被測定物の中心線及びゴニオメータのＢ軸を一致させて、光源から出射された計測ビームと被測定物表面で反射された反射ビームとが重なるように初期設定するアライメント手段と、前記試料系を２軸１組のゴニオメータで駆動して計測ビームで被測定物表面の測定範囲を走査し、前記光検出器の受光面に当たる反射ビームの位置を検出し、該反射ビームの角度変化からその点での法線ベクトルを算出し、被測定物表面の任意計測点の法線ベクトルから表面形状を導出する制御・演算手段と、を備えたことを特徴とする回転対称形状の超精密形状測定装置を構成した（請求項６）。 Then, the present invention provides an optical system provided with a light source and a photodetector capable of measuring the displacement of the incident beam at the light receiving surface, and a measurement object having a rotationally symmetric convex surface having a spherical surface or an aspheric surface whose surface is approximated to a spherical surface. The movable part driven by a pair of two goniometers is made to have the center line of the object to be measured coincident with the B axis of the goniometer, and the C axis of the goniometer is held so as to pass through the center of curvature on the center line of the object to be measured. The sample system and the optical axis of the optical system coincide with the center line of the object to be measured and the B axis of the goniometer so that the measurement beam emitted from the light source and the reflected beam reflected from the surface of the object to be measured overlap. Alignment means for initial setting and the sample system are driven by a pair of two goniometers to scan the measurement range of the surface of the object to be measured with the measurement beam, and detect the position of the reflected beam that hits the light receiving surface of the photodetector. The Rotation characterized by comprising control and calculation means for calculating a normal vector at that point from the angle change of the incident beam and deriving the surface shape from the normal vector of the arbitrary measurement point on the surface of the object to be measured A symmetrical ultra-precise shape measuring apparatus was constructed.

また、本発明は、２軸１組のゴニオメータで駆動する可動部に、光源と受光面における入射ビームの変位を計測可能な光検出器を設け且つゴニオメータのＡ軸とＣ軸が光検出器の受光面中心を通るように設定した光学系と、表面が回転対称形状で、主に球面若しくは球面に近似できる非球面の凹面の被測定物を保持した試料系と、光検出器の受光面中心が被測定物の中心線上の曲率中心を通るように設定し、前記光学系の光軸と被測定物の中心線を一致させて、光源から出射された計測ビームと被測定物表面で反射された反射ビームとが重なるように初期設定するアライメント手段と、前記光学系を２軸１組のゴニオメータで駆動して計測ビームで被測定物表面の測定範囲を走査し、前記光検出器の受光面に当たる反射ビームの位置を検出し、該反射ビームの角度変化からその点での法線ベクトルを算出し、被測定物表面の任意計測点の法線ベクトルから表面形状を導出する制御・演算手段と、を備えたことを特徴とする回転対称形状の超精密形状測定装置を構成した（請求項７）。 The present invention also provides a light source and a light detector capable of measuring the displacement of the incident beam on the light receiving surface in a movable part driven by a pair of goniometers, and the A axis and the C axis of the goniometer are the light detectors. An optical system set to pass through the center of the light receiving surface, a sample system having a rotationally symmetric surface and holding a measured object that is mainly a spherical surface or an aspherical concave surface that can be approximated to a spherical surface, and the center of the light receiving surface of the photodetector Is set so that it passes through the center of curvature on the center line of the object to be measured, and the optical axis of the optical system is aligned with the center line of the object to be measured, and is reflected by the measurement beam emitted from the light source and the surface of the object to be measured. Alignment means for initial setting so that the reflected beam overlaps, and the optical system is driven by a pair of two goniometers to scan the measurement range of the surface of the object to be measured with the measurement beam, and the light receiving surface of the photodetector The position of the reflected beam that hits Control / calculating means for calculating a normal vector at the point from the angle change of the reflected beam and deriving the surface shape from the normal vector at an arbitrary measurement point on the surface of the object to be measured. A rotationally symmetric ultra-precise shape measuring apparatus was constructed.

ここで、超精密形状測定装置においても、光検出器として、４分割フォトダイオード（ＱＰＤ）を用いることが好ましい（請求項８）。あるいは、光検出器として、ＣＣＤイメージセンサ又はＣＭＯＳイメージセンサを用いることも好ましい（請求項９）。 Here, also in the ultra-precise shape measuring apparatus, it is preferable to use a quadrant photodiode (QPD) as the photodetector (claim 8). Alternatively, it is also preferable to use a CCD image sensor or a CMOS image sensor as the photodetector.

以上にしてなる本発明の回転対称形状の超精密形状測定方法及びその装置は、法線ベクトルの計測に２軸１組のゴニオメータのみを用いるため、簡便な構造になり、表面が回転対称形状で、主に球面若しくは球面に近似できる非球面の被測定物の形状測定を短時間で行うことができる。また、光学系の調整も簡単で、高速化も容易であり、装置コストも下げることができる。現在、民生用の光学素子として需要の多い曲率半径Ｒ＝１０ｍｍ程度の小径レンズ又はその成形金型の形状測定を１ｎｍ程度の形状精度で測定することが可能であり、民生用の光学素子の製造現場で使用することが可能になる。 The rotationally symmetric ultra-precise shape measuring method and apparatus according to the present invention as described above have a simple structure because only a two-axis goniometer is used for normal vector measurement, and the surface has a rotationally symmetric shape. The shape measurement of an object to be measured which is mainly spherical or can be approximated to a spherical surface can be performed in a short time. Further, the adjustment of the optical system is simple, the speed can be easily increased, and the apparatus cost can be reduced. Currently, it is possible to measure the shape of a small-diameter lens having a radius of curvature R of about 10 mm or its molding die, which is in great demand as a consumer optical element, with a shape accuracy of about 1 nm. It can be used in the field.

本発明の超精密形状測定装置の概念図である。It is a conceptual diagram of the ultraprecision shape measuring apparatus of this invention. 凸面の被測定物を測定する第１実施形態の測定装置の簡略配置図である。It is a simplified arrangement view of the measuring apparatus of the first embodiment for measuring a convex object to be measured. 凹面の被測定物を測定する第２実施形態の測定装置の簡略配置図である。It is a simplified arrangement view of a measuring apparatus according to a second embodiment for measuring a concave object to be measured. ＱＰＤの簡略説明図である。It is a simplified explanatory diagram of QPD. ＱＰＤと入射光の水平方向位置を相対移動させた場合の変移量とＱＰＤの出力電圧の関係を示すグラフである。It is a graph which shows the relationship between the variation | change_quantity when the horizontal direction position of QPD and incident light is moved, and the output voltage of QPD. 曲率半径Ｒ＝２５ｍｍの試料に座標誤差を与えた場合の形状誤差のシミュレーション結果を示し、（ａ）は座標誤差の標準偏差がσ＝５０ｎｍのグラフ、（ｂ）は座標誤差の標準偏差がσ＝５００ｎｍのグラフである。The simulation result of the shape error when a coordinate error is given to a sample with a curvature radius R = 25 mm is shown, (a) is a graph in which the standard deviation of the coordinate error is σ = 50 nm, and (b) is the standard deviation of the coordinate error is σ. = 500 nm graph. 曲率半径Ｒ＝４００ｍｍの試料に座標誤差を与えた場合の形状誤差のシミュレーション結果を示し、（ａ）は座標誤差の標準偏差がσ＝５０ｎｍのグラフ、（ｂ）は座標誤差の標準偏差がσ＝５００ｎｍのグラフである。The simulation result of the shape error when a coordinate error is given to a sample with a curvature radius R = 400 mm is shown, (a) is a graph in which the standard deviation of the coordinate error is σ = 50 nm, and (b) is the standard deviation of the coordinate error is σ. = 500 nm graph. 試料に法線ベクトルの誤差として標準偏差σ＝０．０５μｒａｄ、０．５μｒａｄ、５μｒａｄを与えた場合の形状誤差のシミュレーション結果を示すグラフである。It is a graph which shows the simulation result of the shape error at the time of giving standard deviation (sigma) = 0.05 microrad, 0.5 microrad, and 5 microrad as a normal vector error to a sample. Ｒ＝２５ｍｍスチールボールの同じ位置の法線測定を複数回行った場合のＱＰＤの出力信号を示すグラフである。It is a graph which shows the output signal of QPD at the time of performing normal measurement of the same position of R = 25mm steel ball in multiple times.

次に、添付図面に示した実施形態に基づき、本発明を更に詳細に説明する。図１及び図２は、本発明の第１実施形態を示し、光の直進性を利用して被測定物１の表面上における各点の法線ベクトルを測定するのである。本発明における形状測定対象は、表面が回転対称形状で、主に球面若しくは球面に近似できる非球面の被測定物１であり、曲率半径が小さな比較的小さいものである。具体的な被測定物１は、レンズやミラー等の光学素子であり、更にはレンズやミラーの成形金型である。 Next, the present invention will be described in more detail based on the embodiments shown in the accompanying drawings. 1 and 2 show a first embodiment of the present invention, in which the normal vector of each point on the surface of the DUT 1 is measured using the straightness of light. The shape measurement object in the present invention is a measurement object 1 having a rotationally symmetric surface and mainly an aspherical surface that can be approximated to a spherical surface or a spherical surface, and has a relatively small curvature radius. A specific object to be measured 1 is an optical element such as a lens or a mirror, and further a molding die for the lens or mirror.

本発明の形状測定原理は、光源４と光検出器５を設けた光学系２と被測定物１を保持した試料系３とを備え、光源４から出射された計測ビームＢ１が被測定物１の表面で反射され、その反射ビームＢ２を光検出器５で検出して被測定物表面の任意計測点の法線ベクトルを計測することから形状を求める法線ベクトル追跡型超精密形状測定方法である。 The shape measurement principle of the present invention includes an optical system 2 provided with a light source 4 and a light detector 5 and a sample system 3 holding a device under test 1, and a measurement beam B 1 emitted from the light source 4 is measured under the device under test 1. A normal vector tracking type ultra-precise shape measuring method for obtaining a shape by detecting the reflected beam B2 with a photodetector 5 and measuring a normal vector at an arbitrary measurement point on the surface of the object to be measured. is there.

図１に示すように、本発明の第１実施形態の超精密形状測定装置は、光源４と受光面における入射ビームの変位を計測可能な光検出器５を設けた光学系２と、表面が回転対称形状で、主に球面若しくは球面に近似できる非球面の凸面の被測定物１を、２軸１組のゴニオメータ６，７で駆動する可動部８に、該ゴニオメータ７のＢ軸に被測定物１の中心線を一致させるとともに、ゴニオメータ６のＣ軸が被測定物１の中心線上の曲率中心を通るように保持した試料系３と、前記光学系２の光軸Ｒと被測定物１の中心線ＣＬ及びゴニオメータ７のＢ軸を一致させて、光源４から出射された計測ビームＢ１と被測定物表面で反射された反射ビームＢ２とが重なるように初期設定するアライメント手段（図示せず）と、前記試料系３を２軸１組のゴニオメータ６，７で駆動して計測ビームＢ１で被測定物１表面の測定範囲を走査し、前記光検出器５の受光面に当たる反射ビームＢ２の位置を検出し、該反射ビームＢ２の角度変化からその点での法線ベクトルを算出し、被測定物表面の任意計測点の法線ベクトルから表面形状を導出する制御・演算手段（図示せず）とを備えている。 As shown in FIG. 1, the ultra-precision shape measuring apparatus according to the first embodiment of the present invention includes an optical system 2 provided with a light source 4 and a photodetector 5 capable of measuring the displacement of an incident beam on a light receiving surface, and a surface thereof. A to-be-measured object 1 having a rotationally symmetric shape and mainly an aspherical convex surface that can be approximated to a spherical surface or a spherical surface is measured on the B axis of the goniometer 7 on the movable unit 8 driven by a pair of goniometers 6 and 7 of two axes. The sample system 3 is held such that the center line of the object 1 coincides and the C axis of the goniometer 6 passes through the center of curvature on the center line of the object 1 to be measured, and the optical axis R of the optical system 2 and the object 1 to be measured 1 Alignment means (not shown) for initializing the measurement beam B1 emitted from the light source 4 and the reflected beam B2 reflected from the surface of the object to be measured so that the center line CL of the goniometer 7 and the B axis of the goniometer 7 coincide with each other. ) And the sample system 3 in a pair of two shafts The measurement beam B1 is driven by the meters 6 and 7 to scan the measurement range on the surface of the DUT 1, the position of the reflected beam B2 that strikes the light receiving surface of the photodetector 5 is detected, and the angle change of the reflected beam B2 is detected. Control / calculation means (not shown) for calculating a normal vector at that point and deriving the surface shape from the normal vector of an arbitrary measurement point on the surface of the object to be measured is provided.

更に詳しくは、前記光学系２は、光源４が直径１μｍ以下の光ファイバーであり、図示しないレーザーから導かれ先端から射出された光をＦ５とＦ５０の二枚のコリメータレンズ９を通した後、偏光ビームスプリッター１０を通して４５°向きを変え、１／４波長板１１とＦ１００の対物レンズ１２を通して被測定物１の表面を照射する計測ビームＢ１系と、被測定物１の表面の表面で反射した光を対物レンズ１２と１／４波長板１１を通して
前記偏光ビームスプリッター１０を直進し、減光フィルター１３を通して光検出器５に入射する反射ビームＢ２系を有している。本実施形態では、前記被測定物１の表面でのスポット径を０．５ｍｍに設定している。ここで、光源４から出射された計測ビームＢ１と被測定物表面で反射された反射ビームＢ２とが重なるとは、その光軸が重なることを意味している。図２は、図１を簡略化して示した装置の概念図である。 More specifically, in the optical system 2, the light source 4 is an optical fiber having a diameter of 1 μm or less, and light guided from a laser (not shown) and emitted from the tip is passed through two collimator lenses 9 of F5 and F50, and then polarized. A measurement beam B1 system that changes the direction of 45 ° through the beam splitter 10 and irradiates the surface of the object 1 to be measured through the quarter-wave plate 11 and the objective lens 12 of F100, and light reflected by the surface of the object 1 to be measured. Through the objective lens 12 and the quarter-wave plate 11, the polarization beam splitter 10 travels straight, and a reflected beam B 2 system that enters the photodetector 5 through the neutral density filter 13 is provided. In this embodiment, the spot diameter on the surface of the DUT 1 is set to 0.5 mm. Here, the measurement beam B1 emitted from the light source 4 and the reflected beam B2 reflected by the surface of the object to be measured mean that their optical axes overlap. FIG. 2 is a conceptual diagram of the apparatus shown in simplified form in FIG.

図３に示した本発明の第２実施形態の超精密形状測定装置は、２軸１組のゴニオメータで駆動する可動部に、光源（図示せず）と受光面における入射ビームの変位を計測可能な光検出器５を設け且つゴニオメータ１４，１５のＡ軸とＣ軸が光検出器５の受光面中心を通るように設定した光学系２と、表面が回転対称形状で、主に球面若しくは球面に近似できる非球面の凹面の被測定物１を保持した試料系３と、光検出器５の受光面中心が被測定物１の中心線上の曲率中心を通るように設定し、前記光学系２の光軸と被測定物の中心線を一致させて、光源から出射された計測ビームＢ１と被測定物表面で反射された反射ビームとが重なるように初期設定するアライメント手段（図示せず）と、前記光学系２を２軸１組のゴニオメータ１４，１５で駆動して計測ビームＢ１で被測定物表面の測定範囲を走査し、前記光検出器５の受光面に当たる反射ビームの位置を検出し、該反射ビームの角度変化からその点での法線ベクトルを算出し、被測定物表面の任意計測点の法線ベクトルから表面形状を導出する制御・演算手段（図示せず）とを備えている。 The ultra-precision shape measuring apparatus according to the second embodiment of the present invention shown in FIG. 3 can measure the displacement of an incident beam on a light source (not shown) and a light receiving surface on a movable part driven by a pair of two goniometers. An optical system 2 provided with an optical detector 5 and set so that the A-axis and C-axis of the goniometers 14 and 15 pass through the center of the light-receiving surface of the photodetector 5, and the surface is rotationally symmetric, mainly spherical or spherical The sample system 3 holding the measured object 1 having an aspherical concave surface that can be approximated to the optical system 2 and the center of the light receiving surface of the photodetector 5 are set so as to pass through the center of curvature on the center line of the measured object 1. Alignment means (not shown) for initially setting the measurement beam B1 emitted from the light source and the reflected beam reflected by the surface of the object to be measured so that the optical axis of the object coincides with the center line of the object to be measured. The optical system 2 is made up of a pair of goniometers 14 and 15 of two axes. The measurement beam B1 is driven to scan the measurement range of the surface of the object to be measured, the position of the reflected beam hitting the light receiving surface of the photodetector 5 is detected, and the normal vector at that point is determined from the angle change of the reflected beam. Control / calculation means (not shown) for calculating and deriving the surface shape from the normal vector of an arbitrary measurement point on the surface of the object to be measured is provided.

第２実施形態では、光学系２を２軸１組のゴニオメータで回転駆動したが、これは凹面の被測定物１を保持した試料系３を２軸１組のゴニオメータで曲率中心を中心として回転駆動することが幾何学的に困難なためである。しかし、第１実施形態のように試料系３をＢ軸とＣ軸を有する２軸１組のゴニオメータで回転駆動する構造とし、凹面からなる被測定物１の中心線をゴニオメータのＢ軸に一致させるとともに、ゴニオメータのＣ軸が被測定物１の中心線上の曲率中心を通るように保持できるようなホルダーを介して取付けることができれば、装置構成は第１実施形態と同じにすることは可能である。 In the second embodiment, the optical system 2 is rotationally driven by a pair of goniometers with two axes. This is because the sample system 3 holding the object 1 having a concave surface is rotated around the center of curvature by a pair of goniometers with two axes. This is because it is geometrically difficult to drive. However, as in the first embodiment, the sample system 3 is rotationally driven by a pair of two goniometers having a B axis and a C axis, and the center line of the object to be measured 1 made of a concave surface coincides with the B axis of the goniometer. In addition, the apparatus configuration can be made the same as that of the first embodiment if it can be attached via a holder that can hold the goniometer C axis so that it passes through the center of curvature on the center line of the DUT 1. is there.

これまで、法線ベクトルを測定するために、光検出器として４分割フォトダイオード（ＱＰＤ）を用い、２軸２組のゴニオメータと１軸のリニアステージからなる５軸駆動系を制御し、検出器と被測定物の両方を変化させて法線ベクトルを追跡する零位法を用いていた。それに対して本発明では、光検出器又は試料を固定して、光検出器の出力から法線ベクトルの方向を測定するようにした。つまり、本発明では、被測定物１の表面の任意点での法線ベクトルを計測する際に、計測ビームを走査するために駆動する軸を最小の２軸にし、計測時間を短縮することに最大のポイントを置いている。そのため、測定対象は回転対称形状に限られるものの、ＱＰＤの受光面における反射ビームの変位を検出することによりその点での法線ベクトルを素早く計測できるのである。このとき、光検出器出力の直線性が保障されていなければならない。つまり、完全球面の場合は、球面の各点から反射した反射ビームは、常にＱＰＤの受光面の中心に当り、ＱＰＤの出力に変化は生じないが、部分的に完全球面からずれた面や非球面の場合には、完全球面からのずれ具合に応じて反射ビームがＱＰＤの受光面の中心から偏心した位置に当たることになり、ＱＰＤの出力に変化が生じる。本発明では、光検出器５が受光面における反射ビームの変位を計測可能であることが重要であり、しかも反射ビームの偏心する距離に応じて出力が直線的に変化することが必要である。反射ビームの変位が小さければ、ＱＰＤは本発明において光検出器５として使用することができる。また、反射ビームの変位が大きければ、光検出器５として、ＱＰＤの代わりに一般的な固体撮像素子を用いることが可能であり、具体的はＣＣＤイメージセンサ又はＣＭＯＳイメージセンサを用いることが可能である。従って、原理的には被測定物１の形状が球面から大きくずれていても、光学系２により反射ビームを光検出器５に導くことができれば形状計測は可能である。 Up to now, in order to measure the normal vector, a quadrant photodiode (QPD) is used as a photodetector, and a 5-axis drive system comprising a 2-axis, 2-set goniometer and a 1-axis linear stage is controlled. The null method is used to track the normal vector by changing both the measured object and the measured object. On the other hand, in the present invention, the photodetector or the sample is fixed, and the direction of the normal vector is measured from the output of the photodetector. That is, in the present invention, when measuring a normal vector at an arbitrary point on the surface of the DUT 1, the axes driven to scan the measurement beam are set to the minimum two axes, thereby shortening the measurement time. The biggest point is placed. Therefore, although the object to be measured is limited to a rotationally symmetric shape, the normal vector at that point can be quickly measured by detecting the displacement of the reflected beam on the light receiving surface of the QPD. At this time, the linearity of the photodetector output must be ensured. In other words, in the case of a perfect sphere, the reflected beam reflected from each point on the sphere always hits the center of the light receiving surface of the QPD, and there is no change in the output of the QPD. In the case of a spherical surface, the reflected beam hits a position decentered from the center of the light receiving surface of the QPD according to the degree of deviation from the perfect spherical surface, and the output of the QPD changes. In the present invention, it is important that the photodetector 5 can measure the displacement of the reflected beam on the light receiving surface, and the output needs to change linearly according to the distance that the reflected beam is decentered. If the displacement of the reflected beam is small, the QPD can be used as the photodetector 5 in the present invention. If the displacement of the reflected beam is large, a general solid-state imaging device can be used as the photodetector 5 in place of the QPD. Specifically, a CCD image sensor or a CMOS image sensor can be used. is there. Therefore, in principle, even if the shape of the DUT 1 is greatly deviated from the spherical surface, the shape can be measured if the reflected beam can be guided to the photodetector 5 by the optical system 2.

凸面を測定する場合は、光検出器を固定して、被測定物を２軸ゴニオメータに設置する。測定開始時には、光検出器が光学的に同じ位置にあるレーザー光源からの入射光が被測定物表面に反射し、光検出器の中心に反射光が戻るように調整する。このとき、Ｂ軸ゴニオメータを回転しても光検出器の中心に反射光が戻るように調整することで、光学系の光軸と被測定物、ゴニオメータの軸合わせができる。その後、被測定物の２軸を回転したときの法線ベクトルの方向を光検出器の出力から求め、測定座標と合わせて形状を求める。尚、凹面の場合は、幾何学的な制約から試料を固定して光検出器を２軸ゴニオメータに搭載する。 When measuring a convex surface, the photodetector is fixed and the object to be measured is placed on a biaxial goniometer. At the start of measurement, adjustment is made so that incident light from a laser light source in which the photodetector is optically in the same position is reflected on the surface of the object to be measured and the reflected light returns to the center of the photodetector. At this time, by adjusting the reflected light to return to the center of the photodetector even if the B-axis goniometer is rotated, the optical axis of the optical system can be aligned with the object to be measured and the goniometer. Thereafter, the direction of the normal vector when the two axes of the object to be measured are rotated is obtained from the output of the photodetector, and the shape is obtained together with the measurement coordinates. In the case of a concave surface, the sample is fixed due to geometric restrictions, and the photodetector is mounted on the biaxial goniometer.

光検出器５は、図４に示すように、４分割フォトダイオード（ＱＰＤ）で構成されＸ，Ｚ座標の各象限に分割セル５Ａ〜５Ｄを配置している。被測定面の法線ベクトルが変化すると光てこの原理によって光検出器５上のピンホール像の位置が変位する。ピンホール像のＸ，Ｚ方向の変位量に応じて各分割セル５Ａ〜５Ｄ毎に出力変化Ｖ_A，Ｖ_B，Ｖ_C，Ｖ_Dとして現れ、それぞれの加減算により水平、垂直方向の位置変化量としてＶ₁＝（Ｖ_A＋Ｖ_B）−（Ｖ_C＋Ｖ_D）、Ｖ₂＝（Ｖ_A＋Ｖ_D）−（Ｖ_B＋Ｖ_C）が得られる。法線ベクトルの変化量と光検出器５上の位置変位量の関係は一意的に決定される。 As shown in FIG. 4, the photodetector 5 includes a four-division photodiode (QPD), and the divided cells 5 A to 5 D are arranged in each quadrant of the X and Z coordinates. When the normal vector of the surface to be measured changes, the position of the pinhole image on the photodetector 5 is displaced by the light lever principle. Depending on the amount of displacement of the pinhole image in the X and Z directions, output changes V _A , V _B , V _C , and V _D appear for each of the divided cells 5A to 5D. As a result, V ₁ = (V _A + V _B ) − (V _C + V _D ) and V ₂ = (V _A + V _D ) − (V _B + V _C ) are obtained. The relationship between the amount of change in the normal vector and the amount of positional displacement on the photodetector 5 is uniquely determined.

図５は、変位に対するＱＰＤの出力の応答性を調べるために行った実験結果を示している。ＱＰＤの受光面を垂直に配置し、水平方向からレーザースポット光を受光面の中心に照射し、ＱＰＤを、容量型変位計を備えたピエゾ駆動装置で水平方向に往復変化させた。図５のグラフの横軸は時間／ｓｅｃであり、下側の波形はＱＰＤの水平移動量／ｎｍ、上側の波形はＱＰＤの出力電圧／Ｖである。この二つの波形は形状と位相が略一致しており、それによりＱＰＤの水平移動量に応じて略直線的に出力電圧が変化していることが分かる。 FIG. 5 shows the results of experiments conducted to examine the response of the QPD output to displacement. The light receiving surface of the QPD was arranged vertically, the laser spot light was irradiated from the horizontal direction to the center of the light receiving surface, and the QPD was reciprocated in the horizontal direction by a piezo drive device equipped with a capacitive displacement meter. The horizontal axis of the graph of FIG. 5 is time / sec, the lower waveform is the horizontal movement amount / nm of QPD, and the upper waveform is the output voltage / V of QPD. It can be seen that the two waveforms have substantially the same shape and phase, and the output voltage changes approximately linearly in accordance with the amount of horizontal movement of the QPD.

本発明の第１実施形態の超精密形状測定装置は、２軸のゴニオメータの回転角度と反射光を受ける４分割フォトダイオード（ＱＰＤ）の電気信号で被測定物表面の法線ベクトルを測定することが可能である。次に、この高速形状計測装置を用いて、曲率半径２５ｍｍの被測定物を所望の精度で測定するために必要な装置精度を、シミュレーションを行うことによって導出する。 The ultraprecision shape measuring apparatus according to the first embodiment of the present invention measures the normal vector of the surface of the object to be measured by the rotation angle of the biaxial goniometer and the electric signal of the quadrant photodiode (QPD) that receives the reflected light. Is possible. Next, by using this high-speed shape measuring apparatus, the apparatus accuracy necessary for measuring an object having a curvature radius of 25 mm with a desired accuracy is derived by performing a simulation.

本発明の計測装置で得ることができるパラメータは被測定物表面の座標及びその各点での法線ベクトルである。その２つのパラメータに誤差を与え、後述の「フーリエ級数展開最小二乗法」によって形状導出し、１ｎｍの精度で形状導出できる許容誤差を確認した。座標に与える誤差は平均０、標準偏差σ＝５０ｎｍ、５００ｎｍの２種類の正規分布乱数であり、法線ベクトルに与える誤差は平均０、標準偏差σ＝０．０５μｒａｄ、０．５μｒａｄ、５μｒａｄの３種類である。この座標誤差と法線ベクトル誤差を、それぞれ平面、Ｒ＝４００ｍｍ、曲率半径Ｒ＝２５ｍｍのサンプル試料の測定範囲±１０ｍｍの範囲の測定点１００１点のデータに与えて形状導出し、理想形状との差を見た。先ず始めに各種試料に対し、座標誤差を与えて導出した形状誤差を見たのが図６及び図７である。平面の場合、座標誤差による形状導出誤差は０なので省略するが、図６はＲ＝２５ｍｍの表面の場合であり、座標誤差の標準偏差がσ＝５０ｎｍの場合ＰＶ１．２ｎｍ（図６（ａ）参照）、σ＝５００ｎｍの場合ＰＶ４．１１ｎｍ（図６（ｂ）参照）である。図７はＲ＝４００ｍｍの表面の場合であり、座標誤差の標準偏差がσ＝５０ｎｍの場合ＰＶ０．０７ｎｍ（図７（ａ）参照）、σ＝５００ｎｍの場合ＰＶ０．２４ｎｍ（図７（ｂ）参照）であることが分かった。つまり、座標誤差による形状誤差は、測定面の曲率半径に反比例することが実証され、Ｒ＝２５ｍｍの試料を測定範囲±１０ｍｍまでで１ｎｍ程度の形状精度で測定するには座標精度が１００ｎｍ程度必要なことが示された。 The parameters that can be obtained with the measuring apparatus of the present invention are the coordinates of the surface of the object to be measured and the normal vector at each point. An error was given to these two parameters, and a shape was derived by “Fourier series expansion least square method” described later, and an allowable error capable of deriving the shape with an accuracy of 1 nm was confirmed. The errors given to the coordinates are two types of normal distribution random numbers with an average of 0, standard deviation σ = 50 nm, and 500 nm, and the errors given to the normal vectors are 3 with an average of 0, standard deviation σ = 0.05 μrad, 0.5 μrad, 5 μrad, and 5 μrad. It is a kind. The coordinate error and the normal vector error are given to the data of 1001 measurement points in the range of ± 10 mm in the measurement range of the sample specimen having a plane, R = 400 mm, and radius of curvature R = 25 mm, respectively, and the shape is derived. I saw the difference. First, FIG. 6 and FIG. 7 show the shape errors derived by giving coordinate errors to various samples. In the case of a flat surface, the shape derivation error due to the coordinate error is 0 and is omitted, but FIG. 6 is for the surface of R = 25 mm, and PV1.2 nm when the standard deviation of the coordinate error is σ = 50 nm (FIG. 6A). Reference), when σ = 500 nm, PV 4.11 nm (see FIG. 6B). FIG. 7 shows the surface of R = 400 mm. When the standard deviation of the coordinate error is σ = 50 nm, PV is 0.07 nm (see FIG. 7A), and when σ = 500 nm, PV is 0.24 nm (FIG. 7B). It was found that In other words, it is proved that the shape error due to the coordinate error is inversely proportional to the radius of curvature of the measurement surface, and a coordinate accuracy of about 100 nm is required to measure a sample with R = 25 mm with a shape accuracy of about 1 nm up to a measurement range of ± 10 mm. It was shown.

次にシミュレーションを行ったのが、法線ベクトル誤差による形状誤差の見積りである。データに与える法線ベクトル誤差は、平面、曲率半径Ｒ＝４００ｍｍ，Ｒ＝２５ｍｍのサンプル試料のそれぞれに平均０、標準偏差σ＝０．０５μｒａｄ、０．５μｒａｄ、５μｒａｄの３種類である。サンプル試料の測定範囲±１０ｍｍの範囲の測定点１００１点のデータで形状導出し、理想形状に対する形状誤差を示したのが図８である。全てのサンプル試料に対し、形状誤差は図８の通りに導出され、具体的な値としてはσ＝０．０５μｒａｄの場合ＰＶ０．０４ｎｍ、０．５μｒａｄの場合ＰＶ０．４ｎｍ、５μｒａｄの場合ＰＶ４ｎｍとなり、法線ベクトル誤差による形状誤差は、測定面の曲率半径には依存せず、法線ベクトル誤差の絶対量に比例する。Ｒ＝２５ｍｍの試料を１ｎｍ程度の形状精度で測定するには法線ベクトルの測定精度が１μｒａｄ程度必要なことが示された。 Next, the simulation was performed to estimate the shape error due to the normal vector error. There are three types of normal vector errors given to the data: average 0, standard deviation σ = 0.05 μrad, 0.5 μrad, 5 μrad for each of the sample samples having a plane and curvature radii R = 400 mm and R = 25 mm. FIG. 8 shows the shape error with respect to the ideal shape, which is derived from the data of 1001 measurement points within the measurement range of the sample specimen ± 10 mm. For all the sample specimens, the shape error is derived as shown in FIG. 8, and concrete values are PV 0.04 nm for σ = 0.05 μrad, PV 0.4 nm for 0.5 μrad, PV 4 nm for 5 μrad, The shape error due to the normal vector error does not depend on the radius of curvature of the measurement surface, and is proportional to the absolute amount of the normal vector error. In order to measure a sample with R = 25 mm with a shape accuracy of about 1 nm, it has been shown that a normal vector measurement accuracy of about 1 μrad is required.

以上のシミュレーション結果を踏まえて、Ｒ＝２５ｍｍのスチールボールを高速且つ高精度に測定するための実験を行った。２軸のゴニオメータでスチールボールを回転させ、反射光をＱＰＤで受け、測定試料表面の法線ベクトルを測定することが可能である。１０ｎｍ以上の精度でこのスチールボールを測定するには、計測装置のセットアップ環境の精度が上記のシミュレーションでの精度を満たす必要がある。そこで、アライメント手段による本セットアップ環境の精度を確認する実験を行った。確認事項は（１）Ｂ軸心ずれ精度、（２）Ｃ軸心ずれ精度、（３）法線ベクトル感度、（４）ＱＰＤの位置感度の４つである。 Based on the above simulation results, an experiment for measuring a steel ball of R = 25 mm at high speed and with high accuracy was performed. It is possible to measure a normal vector on the surface of a measurement sample by rotating a steel ball with a biaxial goniometer and receiving reflected light with a QPD. In order to measure this steel ball with an accuracy of 10 nm or more, the accuracy of the setup environment of the measuring device needs to satisfy the accuracy in the above simulation. Therefore, an experiment was conducted to confirm the accuracy of the setup environment by the alignment means. There are four confirmation items: (1) B-axis misalignment accuracy, (2) C-axis misalignment accuracy, (3) normal vector sensitivity, and (4) QPD position sensitivity.

実験の結果、（１）Ｂ軸心ずれ精度＝２．５μｍ、（２）Ｃ軸心ずれ精度＝２μｍ、（３）法線ベクトル感度＝１μｒａｄ、（４）ＱＰＤの位置感度＝１μｍであり、形状精度１０ｎｍでこのスチールボールを測定するのに十分な初期セットアップ環境であることが確認された。 As a result of the experiment, (1) B-axis misalignment accuracy = 2.5 μm, (2) C-axis misalignment accuracy = 2 μm, (3) Normal vector sensitivity = 1 μrad, (4) QPD position sensitivity = 1 μm, It was confirmed that the initial setup environment was sufficient to measure this steel ball with a shape accuracy of 10 nm.

次に、この測定装置を用いて、計測の安定性を確かめるために、Ｒ＝２５ｍｍスチールボールの同じ位置の法線ベクトル測定を複数回行ってＱＰＤの出力信号の変化を見た。Ｃ軸ゴニオメータを駆動して±２０°の測定範囲を１回測定し、翌日に続いて３回測定した。図９に、これら４回の法線ベクトルの測定データであるＱＰＤの信号の値をプロットして示している。Ｃ軸ゴニオメータは０．２°／ｓｅｃの回転速度で駆動し、図９のグラフの横軸は約２００ｓｅｃ（＝４０degree）の計測時間に相当する。図９より、４回の計測でＱＰＤの信号が略重なって各信号が分別不能であることが分かり、非常に再現性良く試料表面の法線ベクトルを測定することが可能であることが実証された。 Next, in order to confirm the stability of the measurement using this measuring apparatus, normal vector measurement at the same position of the R = 25 mm steel ball was performed a plurality of times, and changes in the output signal of the QPD were observed. The C-axis goniometer was driven and the measurement range of ± 20 ° was measured once, followed by three measurements following the next day. FIG. 9 plots the values of QPD signals, which are measurement data of these four normal vectors. The C-axis goniometer is driven at a rotational speed of 0.2 ° / sec, and the horizontal axis of the graph of FIG. 9 corresponds to a measurement time of about 200 sec (= 40 degrees). From FIG. 9, it can be seen that the QPD signals are substantially overlapped in four measurements and the signals cannot be distinguished, and it is demonstrated that the normal vector of the sample surface can be measured with very good reproducibility. It was.

以上により、本発明の測定装置を用いて小型で曲率半径が小さい試料を１０ｎｍ以上という高精度で高速に測定することができることが分かった。また、本発明の測定方法で１ｎｍという高精度で測定するために必要な条件をシミュレーションから明らかにした。また、法線ベクトル計測にあたって初期セットアップ精度が十分であることを確認し、法線ベクトルの計測を再現性良く行うことができることが分かった。 From the above, it was found that a small sample with a small radius of curvature can be measured at high speed with high accuracy of 10 nm or more using the measuring apparatus of the present invention. In addition, the conditions necessary for measuring with a high accuracy of 1 nm by the measurement method of the present invention were clarified from simulation. In addition, it was confirmed that the initial setup accuracy was sufficient for normal vector measurement, and it was found that normal vector measurement can be performed with good reproducibility.

最後に、座標（ｘ、ｙ）と法線ベクトルから表面形状を導出するための「フーリエ級数展開最小二乗法」について簡単に説明する。一般的な三次元形状は、数１のように表される。 Finally, the “Fourier series expansion least square method” for deriving the surface shape from the coordinates (x, y) and the normal vector will be briefly described. A general three-dimensional shape is expressed as Equation 1.

次の数２に一般的な三次元形状を複素数表現による指数関数でｘ，ｙの交差項（クロスターム）を入れて表現したフーリエ級数形式形状関数を示している。 The following Formula 2 shows a general three-dimensional shape, which is a Fourier series form function that expresses a cross term of x and y by an exponential function in complex number expression.

ここで、ａ_nmはフーリエ係数、ｅは自然対数の底、ｎ，ｍはフーリエ級数の次数であり、ｋは波数で測定範囲Range（周期境界条件）を用いて２π／Rangeで表される。数２において第３項が交差項である。また、実数条件により、フーリエ係数に次の数３が要求される。 Here, a _nm is the Fourier coefficient, e is the base of the natural logarithm, n and m are the orders of the Fourier series, k is the wave number, and is expressed by 2π / Range using the measurement range Range (periodic boundary condition). In Equation 2, the third term is a cross term. Further, the following number 3 is required for the Fourier coefficient depending on the real number condition.

そして、ｚ（ｘ、ｙ）のｘとｙの微分形（ｘ方向の傾きとｙ方向の傾き）は、次の数４になる。 The differential form of x (y, y) and y (the inclination in the x direction and the inclination in the y direction) is given by the following equation (4).

ここで、実数条件により、フーリエ係数に次の数５が要求される。 Here, the following number 5 is required for the Fourier coefficient according to the real number condition.

そして、実測した法線ベクトルから求めた傾きを一般的にｇ（ｘ_p，ｙ_p）と表すと、数４を用いて次のスロープ残差εが最小になるように最小二乗法を適用する。

Then, when the slope obtained from the measured normal vector is generally expressed as g (x _p , y _p ), the least square method is applied using Equation 4 so that the next slope residual ε is minimized. .

そして、被測定物表面の導出形状をフーリエ級数展開で表したフーリエ級数形式形状関数とその微分形のスロープ関数と、被測定物表面の理想形状関数を用いて算出した理想データを用い、最小二乗法により形状残差とスロープ残差が最小になる条件でフーリエ係数を決定し、形状残差とスロープ残差が共に要求精度よりも小さくなるまで次数ｎ、ｍを増やして繰り返し計算することにより次数ｎ、ｍを決定した後、この決定した次数ｎ、ｍで表した前記スロープ関数と、実測で得た計測座標データと計測法線ベクトルから算出した計測スロープデータを用い、最小二乗法によりスロープ残差が最小になる条件でフーリエ係数を決定し、被測定物表面の導出形状をフーリエ級数展開形形式で表すのである。 Then, using the ideal data calculated using the Fourier series form function expressed by Fourier series expansion of the derived shape of the surface of the object to be measured and its differential slope function and the ideal shape function of the surface of the object to be measured, The Fourier coefficient is determined under the condition that the shape residual and slope residual are minimized by multiplication, and the order is calculated by repeatedly increasing the orders n and m until both the shape residual and slope residual become smaller than the required accuracy. After n and m are determined, the slope function represented by the determined orders n and m and the measured slope data calculated from the measured coordinate data and the measured normal vector are used to determine the remaining slope by the least square method. The Fourier coefficient is determined under the condition that the difference is minimized, and the derived shape of the surface of the object to be measured is expressed in a Fourier series expansion form.

１被測定物、
２光学系、
３試料系、
４光源、
５光検出器、
６ゴニオメータ（Ｃ軸）、
７ゴニオメータ（Ｂ軸）、
８可動部、
９コリメータレンズ、
１０偏光ビームスプリッター、
１１１／４波長板、
１２対物レンズ、
１３減光フィルター、
１４ゴニオメータ（Ｃ軸）、
１５ゴニオメータ（Ａ軸）。
1 DUT,
2 optical system,
3 Sample system,
4 Light source,
5 photodetectors,
6 Goniometer (C axis),
7 Goniometer (B axis),
8 moving parts,
9 Collimator lens,
10 Polarizing beam splitter,
11 1/4 wave plate,
12 Objective lens,
13 neutral density filter,
14 Goniometer (C axis),
15 Goniometer (A axis).

Claims

光源と光検出器を設けた光学系と被測定物を保持した試料系とを備え、光源から出射された計測ビームが被測定物表面で反射され、その反射ビームを光検出器で検出して被測定物表面の任意計測点の法線ベクトルを計測することから形状を求める法線ベクトル追跡型超精密形状測定方法において、前記被測定物の表面が回転対称形状で、主に球面若しくは球面に近似できる非球面であり、前記光検出器が受光面における反射ビームの変位を計測可能であり、前記光学系の光軸と被測定物の中心線を一致させて計測ビームと反射ビームとが重なるように初期設定した後、試料系又は光学系の一方のみを２軸１組のゴニオメータで駆動して計測ビームで被測定物表面の測定範囲を走査し、反射ビームの角度変化からその点での法線ベクトルを算出することを特徴とする回転対称形状の超精密形状測定方法。 An optical system with a light source and a light detector and a sample system that holds the object to be measured are provided. The measurement beam emitted from the light source is reflected on the surface of the object to be measured, and the reflected beam is detected by the light detector. In a normal vector tracking type ultra-precise shape measuring method for obtaining a shape by measuring a normal vector at an arbitrary measurement point on the surface of the object to be measured, the surface of the object to be measured has a rotationally symmetric shape, mainly a spherical surface or a spherical surface. Aspherical surface that can be approximated, the optical detector can measure the displacement of the reflected beam on the light receiving surface, and the optical beam of the optical system coincides with the center line of the object to be measured so that the measurement beam and the reflected beam overlap. After the initial setting as described above, only one of the sample system and the optical system is driven by a two-axis set of goniometers, and the measurement range of the surface of the object to be measured is scanned with the measurement beam. Calculate normal vector Ultra-precision shape measuring method of rotationally symmetric shape wherein Rukoto.

光検出器として、４分割フォトダイオード（ＱＰＤ）を用いる請求項１記載の回転対称形状の超精密形状測定方法。 2. The rotationally symmetric ultra-precise shape measuring method according to claim 1, wherein a quadrant photodiode (QPD) is used as the photodetector.

光検出器として、ＣＣＤイメージセンサ又はＣＭＯＳイメージセンサを用いる請求項１記載の回転対称形状の超精密形状測定方法。 2. The rotationally symmetric ultra-precise shape measuring method according to claim 1, wherein a CCD image sensor or a CMOS image sensor is used as the photodetector.

前記被測定物が凸面であり、試料系の２軸１組のゴニオメータで駆動する可動部に被測定物を保持し、２軸１組のゴニオメータのＢ軸に被測定物の中心線を一致させるとともに、ゴニオメータのＣ軸が被測定物の中心線上の曲率中心を通るように所期設定してなる請求項１〜３何れかに記載の回転対称形状の超精密形状測定方法。 The object to be measured is a convex surface, the object to be measured is held on a movable part driven by a pair of two goniometers of the sample system, and the center line of the object to be measured is aligned with the B axis of the pair of two goniometers. In addition, the rotationally symmetric ultra-precise shape measuring method according to any one of claims 1 to 3, wherein the goniometer is set so that the C axis passes through the center of curvature on the center line of the object to be measured.

前記被測定物が凹面であり、光学系の２軸１組のゴニオメータで駆動する可動部に光源と光検出器を設け且つ２軸１組のゴニオメータのＡ軸とＣ軸が光検出器の受光面中心を通るように設定するとともに、光検出器の受光面中心が被測定物の中心線上の曲率中心を通るように所期設定してなる請求項１〜３何れかに記載の回転対称形状の超精密形状測定方法。 The object to be measured is a concave surface, and a light source and a light detector are provided in a movable portion driven by a pair of goniometers of a two-axis optical system, and the A axis and the C axis of a pair of two-axis goniometers receive light from the light detector. The rotationally symmetric shape according to any one of claims 1 to 3, wherein the rotationally symmetric shape is set so as to pass through the center of the surface and so that the center of the light receiving surface of the photodetector passes through the center of curvature on the center line of the object to be measured. Ultra-precision shape measurement method.

光源と受光面における入射ビームの変位を計測可能な光検出器を設けた光学系と、
表面が回転対称形状で、主に球面若しくは球面に近似できる非球面の凸面の被測定物を、２軸１組のゴニオメータで駆動する可動部に、該ゴニオメータのＢ軸に被測定物の中心線を一致させるとともに、ゴニオメータのＣ軸が被測定物の中心線上の曲率中心を通るように保持した試料系と、
前記光学系の光軸と被測定物の中心線及びゴニオメータのＢ軸を一致させて、光源から出射された計測ビームと被測定物表面で反射された反射ビームとが重なるように初期設定するアライメント手段と、
前記試料系を２軸１組のゴニオメータで駆動して計測ビームで被測定物表面の測定範囲を走査し、前記光検出器の受光面に当たる反射ビームの位置を検出し、該反射ビームの角度変化からその点での法線ベクトルを算出し、被測定物表面の任意計測点の法線ベクトルから表面形状を導出する制御・演算手段と、
を備えたことを特徴とする回転対称形状の超精密形状測定装置。 An optical system provided with a light source and a photodetector capable of measuring the displacement of the incident beam at the light receiving surface;
The object to be measured, which has a rotationally symmetrical surface and is mainly a spherical surface or an aspherical convex surface that can be approximated to a spherical surface, is moved to a movable part that is driven by a pair of two goniometers, and the center line of the object to be measured is placed on the B axis of the goniometer A sample system in which the C axis of the goniometer passes through the center of curvature on the center line of the object to be measured;
Alignment in which the optical axis of the optical system coincides with the center line of the object to be measured and the B axis of the goniometer so that the measurement beam emitted from the light source and the reflected beam reflected by the surface of the object to be measured overlap. Means,
The sample system is driven by a pair of two goniometers, the measurement range of the surface of the object to be measured is scanned with the measurement beam, the position of the reflected beam hitting the light receiving surface of the photodetector is detected, and the angle change of the reflected beam A control / calculation means for calculating a normal vector at that point from the surface, and deriving a surface shape from a normal vector at an arbitrary measurement point on the surface of the object to be measured;
An ultra-precise shape measuring device having a rotationally symmetric shape.

２軸１組のゴニオメータで駆動する可動部に、光源と受光面における入射ビームの変位を計測可能な光検出器を設け且つゴニオメータのＡ軸とＣ軸が光検出器の受光面中心を通るように設定した光学系と、
表面が回転対称形状で、主に球面若しくは球面に近似できる非球面の回転対称形凹面の被測定物を保持した試料系と、
光検出器の受光面中心が被測定物の中心線上の曲率中心を通るように設定し、前記光学系の光軸と被測定物の中心線を一致させて、光源から出射された計測ビームと被測定物表面で反射された反射ビームとが重なるように初期設定するアライメント手段と、
前記光学系を２軸１組のゴニオメータで駆動して計測ビームで被測定物表面の測定範囲を走査し、前記光検出器の受光面に当たる反射ビームの位置を検出し、該反射ビームの角度変化からその点での法線ベクトルを算出し、被測定物表面の任意計測点の法線ベクトルから表面形状を導出する制御・演算手段と、
を備えたことを特徴とする回転対称形状の超精密形状測定装置。 A light detector capable of measuring the displacement of the incident beam on the light source and the light receiving surface is provided in a movable part driven by a pair of two goniometers, and the A axis and C axis of the goniometer pass through the center of the light receiving surface of the light detector. An optical system set to
A sample system having a rotationally symmetric shape and holding an object to be measured which is mainly a spherical surface or an aspherical rotationally symmetric concave surface that can be approximated to a spherical surface;
The light receiving surface center of the photodetector is set so as to pass through the center of curvature on the center line of the object to be measured, the optical axis of the optical system is aligned with the center line of the object to be measured, and the measurement beam emitted from the light source Alignment means for initial setting so that the reflected beam reflected from the surface of the object to be measured overlaps,
The optical system is driven by a pair of two goniometers, the measurement range of the surface of the object to be measured is scanned with the measurement beam, the position of the reflected beam hitting the light receiving surface of the photodetector is detected, and the angle change of the reflected beam A control / calculation means for calculating a normal vector at that point from the surface, and deriving a surface shape from a normal vector at an arbitrary measurement point on the surface of the object to be measured;
An ultra-precise shape measuring device having a rotationally symmetric shape.

光検出器として、４分割フォトダイオード（ＱＰＤ）を用いる請求項６又は７記載の回転対称形状の超精密形状測定装置。 The ultra-precision shape measuring apparatus having a rotationally symmetric shape according to claim 6 or 7, wherein a quadrant photodiode (QPD) is used as the photodetector.

光検出器として、ＣＣＤイメージセンサ又はＣＭＯＳイメージセンサを用いる請求項６又は７記載の回転対称形状の超精密形状測定装置。
The rotationally symmetric ultraprecision shape measuring apparatus according to claim 6 or 7, wherein a CCD image sensor or a CMOS image sensor is used as the photodetector.