JP2004286561A - Method and instrument for measuring 3-dimensional shape - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To precisely measure the whole face to be measured by dividing the face exceeding a measuring range of an interference shape measuring instrument into a plurality of faces to be measured, and by reducing connection errors generated when connecting them. <P>SOLUTION: The face is divided to have one reference face overlapped with any of the divided faces, and accumulation of the connection errors on the plurality of divided faces of the measured face is evaded by connecting the respective divided faces to the reference face. The whole face shape is precisely restored by eliminating tilting and defocusing in the reference face to connect the plurality of divided faces to the reference face. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

【０００６】
【０００７】
【数２】

【０００８】
に対して、最小二乗法を適用して（ｐ１，ａ１，ｂ１）および（ｐ２，ａ２，ｂ２）を算出する。得られた差分値（Δｐ，Δａ，Δｂ）に基づいて、例えば第１の測定データに「Δｐ＋Δａ・ｘｉ＋Δｂ・ｙｉ」を加算すれば、第１と第２の測定データがスムーズに接続できる。
【０００９】
【特許文献１】
特開平１０−２８１７３７号公報
【非特許文献１】
ＡＰＰＬＩＥＤ ＯＰＴＩＣＳ １３ Ｎｏ．１１ ２６９３〜２７０３
【００１０】
【発明が解決しようとする課題】
しかしながら、この方法ではあるいは球面レンズにおいては干渉計と球面レンズのアライメント誤差を含んだ状態で全面形状を復元してしまうといった問題点がある。
【００１１】
まず干渉計と被測定物のアライメント誤差を含んで全面形状を復元してしまう問題を図６を用いて説明する。図６は仮に被測定面が刃先のようなとがった形状の被測定面（図３（Ｂ）参照）に対して、被測定面全面を一括測定できるような干渉計があったとして、その干渉計を用いて被測定面を計測したときの干渉縞を表している。分割領域Ａ２〜Ｄ２のように被測定面を分割したとき、Ａ２の面形状からアライメント誤差であるティルト、デフォーカスを除去する必要がある。しかし、Ａ２の干渉縞のみからは、それが被測定物と干渉計とのアライメント誤差の１つであるティルト縞であるか面形状であるかの区別がつかない。従って、例えばＡ２に対してＢ２、Ｂ２に対してＣ２、Ｃ２に対してＤ２を接続していくと、Ａ２の姿勢に対してはＢ２、Ｃ２、Ｄ２を接続することは可能であるが、Ａ２のティルト、デフォーカス自体を除去することはできない。
【００１２】
そこで図７に示す、従来の技術の欄で説明したような分割方法が考えられた。図７において各分割領域Ａ１〜Ｅ１は隣接する領域と重複するように設けられている。たとえば領域Ａ１は隣接する領域Ｂ１およびＥ１とその一部が重複している。しかしながら図６のような分割方法で測定を行った場合、領域Ａ１からＥ１まで順に接続するため、接続誤差の二乗和平均の平方根がεであるとすると、領域Ａ１とＢ１はεという誤差で接続される。領域Ｃ１をＢ１に対して接続するときも同様にεの誤差で接続され、同様に領域Ｄ１、Ｅ１も接続される。領域Ａ１を基準に接続誤差の量を考えていくと、領域Ｂ１はε、Ｃ１は√２ε、Ｄ１は√３ε、Ｅ１は√４εと誤差の累積が起きてしまう。
【００１３】
本発明は上記従来例に鑑みてなされたもので、複数分割面を接続した復元形状において干渉計のアライメント誤差であるティルト、デフォーカスの影響を排除した状態で、複数の分割面を接続するときの接続誤差の累積を排除することができる３次元形状測定方法及び装置を提供することを目的とする。
【００１４】
【課題を解決するための手段】
本発明によれば、３次元形状を有する被測定面を複数の領域に分割して、該分割した複数の領域毎に前記被測定面の形状を干渉計を用いて測定し、各領域毎の測定値をつなぎ合わせる事で被測定面の形状を測定する３次元形状測定方法において、前記分割した複数の領域のうち少なくとも１つの領域は、他のすべての領域と重複するように設けられた基準面であり、前記基準面と前記他のすべての領域のそれぞれとの間のつなぎ合わせ誤差を補正する事で前記被測定面の形状を測定する３次元形状測定方法を提案している。
【００１５】
また本発明によれば、前記つなぎ合わせ誤差の補正は、前記基準面の測定値から前記干渉計のアライメント誤差であるティルトとデフォーカスを排除した値を用いて行われる３次元形状測定方法を提案している。
【００１６】
また本発明によれば、前記各領域毎の測定値をつなぎ合わせた後、更に各領域の重複回数に応じて平均化回数を変えて補正する３次元形状測定方法を提案している。
【００１７】
【発明の実施形態】
［第１の実施の形態］
まず、図面を参照しつつ球面レンズをフィゾー干渉計で測定する場合の第１の実施の形態を説明する。図１は球面レンズを分割測定するための測定装置１００の概要を示している。ｙ軸まわりに回転する回転ステージ３１、θｚ軸まわりに回転する回転ステージ３２、被測定物である球面レンズ３３を測定するためのフィゾー干渉計３４を有する。回転ステージ３１，３２は、駆動部３５によりそれぞれ指定された角度あるいは一定角度で回転される。そして測定時の各ステージの回転角度は、測定装置１００に接続された不図示のコンピュータにディジタルデータとして格納される。
【００１８】
測定時に得られる干渉像は、フィゾー干渉計３４内に設けられたＣＣＤ等の撮像デバイス上に結像され、ディジタル画像データとして同じくコンピュータに格納される。面形状は、このディジタル画像データに基づいて得られる。
【００１９】
＜被測定面の分割方法＞
被測定面の分割方法について示す。まず被測定面である球面レンズ３３の中心とフィゾー干渉計３４の光軸が一致するようにしたときの測定範囲を基準面とする。すなわち、被測定物である球面レンズ３３の光軸をθｚ軸と一致するように回転ステージ３２に載置しておき、回転ステージ３１によるｙ軸の回転角を０度（ｙ軸の回転角度は、θｚ軸が干渉計３４の光軸と平行となる角度を０度とする。）として、球面レンズ３３を測定する。この場合に測定される範囲が基準面となる。
【００２０】
次に、この基準面と重複するように分割測定面（分割領域とも呼ぶことがある。）を測定する。分割測定面の数は任意でよいが、本実施形態では分割面数は４面とする。基準面および４面の各分割面で被測定面全面（すなわち球面レンズ３３の被測定面）を測定することを考慮すると、被測定面外周と分割面外周が交わる２つの交点それぞれと被測定面の中心とを結ぶ線分のなす角が９０度以上である必要がある。なお４分割以外の数に分割測定する場合でも、望ましい角度は均等に分割した場合の角度となる。たとえば、３分割であれは前記角度はおおむね１２０度程度であり、５分割であればおおむね７２度程度が望ましい。なお、本実施形態においては、「分割」という用語を、互いに重複する部分を有する領域に分けることを含めて用いている。
【００２１】
また、ｙ軸まわりに回転する回転ステージ３１を用いて被測定面を傾けることを考慮すると、傾ける角度が小さいほど傾きによる被測定面の重力変形が小さいので、なるべく基準面の中心と分割面の中心との距離が短いことが好ましい。そのためには、互いに隣接する分割領域の交差する２つの交点のうちの測定対象レンズ外周側の交点（以下、外周側交点と呼ぶ。）が、ほぼレンズ外周上あるいはそのやや外側にあることが望ましい。もしも外周側交点がレンズ外周よりの内側にあれば、測定されない領域が被測定面上に残ってしまい、一方外周側交点がレンズ外周よりの外側にあれば、測定されない領域が残ることは防止できるものの、基準面の中心と分割面の中心との距離をなるべく短くするという条件を満たせなくなるためである。したがって、回転ステージ３１のｙ軸周りの回転角は、上記条件が満たされるように決定される。
【００２２】
図２は、被測定面を、上記の条件を考慮して４つの領域に分割した例を示した図である。領域Ｂと被測定面のそれぞれ外周の交点をＫ１，Ｋ２として、被測定面の中心をＡ０、領域Ｂの中心をＢ０としたときに、∠Ｋ１Ａ０Ｋ２が９０度以上の条件の下で、Ａ０とＢ０との距離はなるべく短くなるように分割してある。領域Ｃ，Ｄ，Ｅについても同様である。
【００２３】
図中、分割領域Ａ，Ｂ，Ｃ，Ｄ，Ｅについて測定し、基準面である領域Ａの測定結果に、分割領域Ｂ、Ｃ、Ｄ、Ｅの測定結果を接続して被測定面全体についての測定結果を求める手順を説明する。
【００２４】
あらかじめ、フィゾー干渉計における参照面の面形状（ｄａｔａ＿Ｒとする）を求めて（具体的な方法としてはＡＰＰＬＩＥＤ ＯＰＴＩＣＳ １３ Ｎｏ．１１ ２６９３〜２７０３を参照。）参照面の形状としてコンピュータに記憶しておく。コンピュータには参照面の面形状は正方行列として保存される。なお、これ以降に記す面形状は特に断りがないかぎり正方行列形式である。
【００２５】
その後、領域Ａの範囲の形状を測定する。つぎに領域Ｂの範囲を測定するためにｙ軸回りに回転する回転ステージ３１を用いて必要な角度だけ球面レンズを傾ける。この場合の必要な角度は、たとえば、上述したように、互いに隣接する分割領域の交差する２つの交点のうちの測定対象レンズ外周側の交点が、ほぼレンズ外周上あるいはそのやや外側となるような角度が選ばれる。
【００２６】
この状態で領域Ａの範囲を計測したときと同じ要領で形状計測する。領域Ｃの範囲を測定するときはレンズを傾けたまま、θｚ軸まわりに回転する回転ステージ３２を用いてレンズを回転させ計測する。本例では４つの領域に分割されているので、最初に領域Ｂについて計測した状態から、θｚ軸周りに回転ステージ３２を９０度一定の方向に回転させて、領域Ａと同じ要領で領域Ｃの範囲について計測する。同様に領域Ｄ、Ｅの範囲についても計測する。このようにして得られた領域Ａの範囲の測定データ（測定された面形状）をｄａｔａ＿Ａ、領域Ｂの範囲をｄａｔａ＿Ｂ、以下ｄａｔａ＿Ｃ、ｄａｔａ＿Ｄ、ｄａｔａ＿Ｅと表記することにする。
【００２７】
まず、測定データｄａｔａ＿Ａ、ｄａｔａ＿Ｂ、ｄａｔａ＿Ｃ、ｄａｔａ＿Ｄ、ｄａｔａ＿Ｅから参照面の測定データｄａｔａ＿Ｒを差し引き、それぞれをｄａｔａ＿ＡＲ、ｄａｔａ＿ＢＲ、ｄａｔａ＿ＣＲ、ｄａｔａ＿ＤＲ、ｄａｔａ＿ＥＲと表記する。この結果、ｄａｔａ＿ＡＲ、ｄａｔａ＿ＢＲ、ｄａｔａ＿ＣＲ、ｄａｔａ＿ＤＲ、ｄａｔａ＿ＥＲは、それぞれ参照面の形状誤差が補正された値となる。
【００２８】
次に、干渉測定の際に生じるｄａｔａ＿ＡＲのアライメント誤差を除去し、基準面である領域Ａの面形状を得る。次に領域Ａと領域Ｂの重複する領域のデータを、領域Ａ、領域Ｂそれぞれについて抽出し、領域Ａの面形状を基にｄａｔａ＿ＢＲのアライメント誤差を算出する。さらに、算出したｄａｔａ＿ＢＲのアライメント誤差を用いてｄａｔａ＿ＢＲ全体のアライメント誤差を減算する。測定データｄａｔａ＿ＣＲ、ｄａｔａ＿ＤＲ、ｄａｔａ＿ＥＲも同様にアライメント誤差を減算する。すべての分割面の測定データから参照面の形状とアライメント誤差を除去した面形状を基に被測定物の全面の面形状を出力する。
【００２９】
＜アラインメント誤差の補正＞
測定データからアライメント誤差を除去する方法の１例を以下に示す。１つの方法としてはゼルニケ多項式を用いて分離する方法が知られている。
【００３０】
ゼルニケ多項式とは数式３に示すとおりである。
【００３１】
【数３】

【００３２】
ただし、ｎ、ｍ は整数、ｉ は虚数単位、ρおよびθは極座標系での動径成分（０≦ρ≦１）、角度成分である。実用上、ｍが正のときｅｘｐ（ｉｍθ）＝ｃｏｓ（ｍθ）、ｍが負のときｅｘｐ（ｉｍθ）＝ｓｉｎ（ｍθ）とする。
【００３３】
さらにゼルニケ多項式を結合すると（数式３中のｎの和は理論上∞であるが説明の都合上ｎ＝１５までの和としてある）、数式４のようになる。
【００３４】
【数４】

【００３５】
ただし、Ｗ（ρ，θ）は波面を示している。Ｃｎ，ｍをゼルニケ係数と呼ぶことにする。数式４のようにゼルニケ多項式を結合させることにより任意の波面、すなわち干渉計においては形状情報を表現することができる。
【００３６】
このゼルニケ多項式のうち、球面レンズのアライメント誤差として、Ｚ（０，０，ρ，θ）＝１、Ｚ（１，１，ρ，θ）＝ρｃｏｓ（θ），Ｚ（１，−１，ρ，θ）＝ρｓｉｎ（θ）、Ｚ（２，０，ρ，θ）＝２ρ２−１が、それぞれＤＣ成分を意味するピストン成分、ＸおよびＹティルト成分、デフォーカス成分を表している。
【００３７】
次にｄａｔａ＿ＡＲからゼルニケ多項式を用いてアライメント誤差であるピストン、ティルト、デフォーカス成分を除去する方法について示す。ｄａｔａ＿ＡＲの正方行列データのアドレスを表す行列をＩ，Ｊと表記する。正方行列データの中心のアドレスｃｅｎｔＸ，ｃｅｎｔＹを次のように定義する。
【００３８】
【数５】

【００３９】
ただし、［ ］は整数への丸めを意味している。数式５のｃｅｎｔＸおよびｃｅｎｔＹを用いて、
Ｉ１＝Ｉ−ｃｅｎｔＸ，Ｊ１＝Ｊ−ｃｅｎｔＹ …（数６）
とアドレスを表すベクトル変換をする。上式の如く各データのアドレスを表すベクトル変換後、Ｒ１を
Ｒ１＝Ｉ１．２＋Ｊ１．２ …（数７）
とする。行列の直後の”．”（ドット）は行列の要素についての演算を意味する。
Ｒ１の最大値をＭＡＸＲとする。ＭＡＸＲとＩ１、Ｊ１を用いて数式８の要領で座標Ｘ，Ｙを求める。
Ｘ＝Ｉ１／ＭＡＸＲ，Ｙ＝Ｊ１／ＭＡＸＲ …（数８）
この座標ＸおよびＹから数式３および数式４においてのρ、θを求める。
Ｒ＝√（Ｘ．２＋Ｙ．２），Ｔ＝ｔａｎ−１Ｙ．／Ｘ …（数９）
ここでＲがρに、Ｔがθに相当している。
【００４０】
Ｒ、ＴおよびＺを列ベクトルに変換し、変換したものをＲｖ、Ｔｖと表記する。以降記号の語尾にｖをつけたものはベクトルを意味する。また、ｄａｔａ＿ＡＲをベクトル化したものをＺＡｖとする。数式４はゼルニケ多項式の線形結合であるので、ベクトルＲｖ、Ｔｖを用いて次のように表せる。
Ｗｖ＝ＣＡ …（数１０）
ただし
Ｃ＝［Ｃ０，０ Ｃ１，−１ Ｃ１，０ ・・・ Ｃ１５，１４］ｔ
Ａ＝［Ｚ（０，０，Ｒｖ，Ｔｖ） Ｚ（１，−１，Ｒｖ，Ｔｖ） Ｚ（１，０，Ｒｖ，Ｔｖ） ・・・ Ｚ（１５，１４，Ｒｖ，Ｔｖ） ］
Ｗｖは波面である。よって、各ゼルニケ係数Ｃは、
Ｃ＝Ａ−１ＺＡｖ …（数１１）
により算出できる。
【００４１】
最後にＺＡｖからアライメント誤差であるピストン、ティルト、デフォーカスを差し引いた値ＺｆＡｖを得るには、
ＺｆＡｖ＝ＺＡｖ−Ｃ’Ｂ …（数１２）
ただし
Ｃ’＝［Ｃ０，０ Ｃ１，−１ Ｃ１，１ Ｃ２，０］ｔ
Ｂ＝［Ｚ（０，０，Ｒ，Ｔ） Ｚ（１，−１，Ｒ，Ｔ） Ｚ（１，０，Ｒ，Ｔ） ・・・ Ｚ（１５，１４，Ｒ，Ｔ） ］
とする。すなわちＢはアラインメント誤差を、Ｃ’はそのゼルニケ係数を表す。
【００４２】
ベクトルＺｆＡｖがアライメント誤差を除去したＡの範囲の形状情報でありｄａｔａ＿ＡＲｆと表記する。
【００４３】
次にｄａｔａ＿ＢＲからアライメント誤差を除去する手順について説明する。図３は球面レンズを傾けたときにデータピッチが変化することについて示したものである。球面レンズ６１は回転前の状態を、球面レンズ６２は回転後の状態をそれぞれ表している。回転前の座標系を（Ｘ１，Ｙ１）とし、回転後の座標系を（Ｘ２，Ｙ２）とする。（Ｘ２，Ｙ２）は（Ｘ１，Ｙ１）の座標系を回転させたものと等しい。データピッチは（Ｘ１，Ｙ１），（Ｘ２，Ｙ２）上においては等しい。しかし、球面レンズ全体の形状を例えば（Ｘ１，Ｙ１）座標系で評価しようとすると、回転前のデータピッチと回転後のデータピッチは一致しないことは明らかである。
【００４４】
そこでｄａｔａ＿ＢＲのデータピッチをｄａｔａ＿ＡＲのデータピッチに合わせるため、線形補間によりデータ補間を行う。ｄａｔａ＿ＢＲを線形補間してｄａｔａ＿ＡＲのデータピッチに合わせたものをｄａｔａ＿ＢＲｓと表記する。ｄａｔａ＿ＢＲｓの面形状をＺＢｓとする。ＺＢｓのアドレスからＸＹ座標に変換するにはＺＢｓのアドレスの中でＴＳ光軸中心に相当するアドレスｘ＿ｃｅｎｔ、ｙ＿ｃｅｎｔを求める。このｘ＿ｃｅｎｔ、ｙ＿ｃｅｎｔは球面レンズの傾け角から計算することができる。
Ｉ２＝Ｉ−ｘ＿ｃｅｎｔ，Ｊ２＝Ｊ−ｙ＿ｃｅｎｔ …（数１３）
Ｉ２およびＪ２からＸＹ座標に変換するには数式５、数式６に示した計算を実行すればよい。
【００４５】
ｄａｔａ＿ＢＲｓとｄａｔａ＿ＡＲｆとが重複している範囲のデータをそれぞれ抽出してｄａｔａ＿ＢＲｓＵ，ｄａｔａ＿ＡＲｆＵとする。ｄａｔａ＿ＢＲｓＵには形状情報とアライメント誤差が含まれている。また、ｄａｔａ＿ＡＲｆＵは形状情報のみであるので、ｄａｔａ＿ＢＲｓＵからｄａｔａ＿ＡＲｆＵを差し引いたデータ（ｄａｔａ＿ＳＢとする）は、アライメント誤差であるピストン、ティルト、デフォーカス成分のみから構成されている。これらアライメント誤差からピストン、ティルト、デフォーカスを成分ごとに分離するにはｄａｔａ＿ＢＲｓＵのＸＹ座標とｄａｔａ＿ＳＢのデータＺＳＢｖから数式１０の行列Ｂを生成して、
Ｃ’＝Ｂ−１ＺＳＢｖ …（数１４）
とすればよい。ここで求めたゼルニケ係数Ｃ’とｄａｔａ＿ＢＲｓのＸＹ座標について数式１２の行列Ｂを生成して、数式１２の如くｄａｔａ＿ＢＲｓのアライメント誤差のみを除去する。ここでｄａｔａ＿ＢＲｓの面形状はＺＢｓで表されるから下記の数式１５により誤差が除去される。
ＺｆＢｖ＝ＺＢｓｖ−Ｃ’Ｂ …（数１５）
ＺｆＢｖがＢの範囲の面形状であり、アライメント誤差を排除したＡの範囲のデータに対してＢの範囲の面形状が接続されたことになる。
【００４６】
領域Ｃ、Ｄ、Ｅの範囲においてもＢの範囲でＺｆＢｖを求めた手順でそれぞれＺｆＣｖ 、ＺｆＤｖ 、ＺｆＥｖを求めることができる。これによりすべてアライメント誤差を排除したＡの範囲の面形状に対して領域Ｂ、Ｃ、Ｄ、Ｅとすべての分割面の面形状が接続されている。
【００４７】
図２のように被測定面を基準面を含めて５つにの領域に分割して測定した場合、重複のない部分から５つの領域全てが重なる部分まで、５通りの重複状態の部分が存在する。図４にその重複状態を示す。図中、部分αはただひとつの分割領域のみによりカバーされて重複のない部分、部分βは二つの分割領域が重複した部分、部分γは三つの分割領域が重複した部分、部分δは四つの分割領域が重複した部分、部分εは五つの分割領域が重複した部分である。斜線部は被測定面外の部分である。
【００４８】
そこで、各領域を接続して被測定面全体の面形状を求める際に、ＺｆＡｖ〜ＺｆＥｖをすべて足し合わせて、図４にあるように部分によって重複した領域数が違うので、重複した領域数に応じて平均化回数を変えることによって全面形状を復元する。例えば、５重に重複した部分については、ＺｆＡｖ〜ＺｆＥｖすべてにデータが含まれているために、それら全てを加算して、重複した領域数である５で平均する。これは他の部分についても同様である。
【００４９】
重なる領域の数は各面のＸＹ座標を基に導く。すなわち面形状ＺｆＡｖ〜ＺｆＥｖと面形状の座標（Ｘ，Ｙ）について、同じ座標値をもつ点が複数あれば、その座標値における面形状をすべて足し合わせて、足し合わせた回数により平均化する。このことで、ステージの運動誤差等により干渉計の測定点がずれたとしても、分割面が重複する領域ではその影響は平均化により緩和されるので全面形状を精度よく復元することができる。
【００５０】
＜測定処理のコンピュータによる実行＞
上記手順は、測定装置１００に接続されたコンピュータにより実行される。ここでコンピュータにより上記手順を実行するためには、コンピュータの有するメモリやプロセッサというハードウエア資源を上記処理のため、特に測定されるデータの格納、計算手順を記録したプログラムおよび計算結果データの格納のために割り当て、処理を実行することになる。
【００５１】
コンピュータを接続した測定装置の概略構成は図８のようになる。測定装置１００内において、レーザ光源８０５から出射した光はレンズ８０４により広げられ、ビームスプリッタ８０３で反射されレンズ８０２を介して平行光に変換されレンズ８０１に入射する。レンズ８０１の最終面８００はある曲率半径を有する球面形状であり、最終面８００の反射光を参照光、透過光を被検光とする。被検光は、制御可能な回転ステージ３１，３２に載置された被測定物の球面レンズ３３の表面で反射して再びレンズ８０１を通り平行光に変換される。参照光と被検光はビームスプリッタ８０３、レンズ８０６を通り撮像系８０７で干渉縞を形成する。撮像系８０７で形成された干渉縞はコンピュータ８０８に読み込まれて、以下に説明する手順で、上述した補正や変換、接続処理が施されて、被測定面の形状情報が得られる。コンピュータ８０８に読み込まれる干渉縞は、公知の方法により上述した形状情報に加工される。また、参照面８００の形状データは上述したようにあらかじめ測定されてコンピュータ８０８に格納されている。
【００５２】
なお、図８には示していないが、図１に示す測定部の回転ステージの制御をコンピュータにより行うこともできる。その場合には、各ステージはパルスモータ等により回転駆動され、コンピュータによりそのパルスモータの駆動量を制御することで、ステージの回転角が制御される。
【００５３】
図９はコンピュータ８０８における形状情報の処理手順を示すフローチャートである。なお、図９の例では、図２に示すように基準領域Ａと４つの分割領域Ｂ〜Ｅとに分けて、被測定面を測定した場合の例を示す。
【００５４】
まずステップＳ９０１において、基準領域および各分割領域について測定を行い、得られた干渉縞の画像に基づき、正方行列で示される形状データｄａｔａ＿Ａ、ｄａｔａ＿Ｂ、ｄａｔａ＿Ｃ、ｄａｔａ＿Ｄ、ｄａｔａ＿Ｅを生成する。この形状データは公知の手順により得ることができる。
【００５５】
次にあらかじめ得ておいた参照面の形状データを、各分割領域の形状データから差し引くことで参照面の形状誤差を補正したｄａｔａ＿ＡＲ、ｄａｔａ＿ＢＲ、ｄａｔａ＿ＣＲ、ｄａｔａ＿ＤＲ、ｄａｔａ＿ＥＲを求める（ステップＳ９０２）。
【００５６】
次に基準領域Ａについて、数式１２を実行してアラインメント誤差を補正した基準領域Ａの形状データＺｆＡｖを算出する（ステップＳ９０３）。
【００５７】
次に、基準領域Ａの形状データを基に、分割領域の各々に注目して、注目分割領域について数式１３および数式５，６を計算して、注目分割領域測定時の測定ピッチを基準領域Ａにおける測定ピッチに合わせて補間する。なお狭いピッチに合わせてデータを補間する代わりに、広い方のピッチに合わせて、対応しないデータを廃棄する方法もある。補間後の形状データに基づいて、数式１０，１４，１５を実行してアラインメント誤差を補正した形状データＺｆＸｖを算出する（ステップＳ９０４）。ここで、添え字のＸは、注目領域Ｂ〜Ｅいずれかを示す。
【００５８】
ステップＳ９０４を、注目分割領域を順次代えつつ全ての分割領域について実行し、全領域についてアラインメント誤差を補正する（ステップＳ９０６）。
【００５９】
それが終了したなら、ＺｆＡｖ〜ＺｆＥｖについて、同じ座標値を持つ点が複数あれば、それらデータをすべて足し合わせて、加算した回数で除算して平均化する（ステップＳ９０６）。求められた値は、被測定面の形状データとして格納される（Ｓ９０７）。以上のようにして、測定結果から誤差補正された形状データが得られる。
【００６０】
このように本発明によれば、分割面（分割領域）の接続の累積誤差が乗ることなく、ティルト、デフォーカスを精度よく排除した状態ですべての分割面を接続することが可能になり、被測定面全面の形状を精度よく復元することができる。
【００６１】
また、被測定面を復元する際に分割面同士で重複する面での形状データはそれぞれ足し合わせて平均化することにより、重複面では測定点ずれの影響が緩和され被測定面全面を精度よく復元することができる。
【００６２】
【発明の効果】
本発明の効果により分割面の接続の累積誤差が乗ることなく、ティルト、デフォーカスを精度よく排除した状態ですべての分割面を接続することが可能になり、被測定面全面を精度よく復元することができた。
【００６３】
また、被測定面を復元する際に分割面同士で重複する面での形状データはそれぞれ足し合わせて平均化することにより、重複面では測定点ずれの影響が緩和され被測定面全面を精度よく復元することができる。
【図面の簡単な説明】
【図１】本発明にかかる形状測定装置の概略図
【図２】被測定面の分割した状態を示す図
【図３】球面レンズを傾けたときにデータピッチが変化することについて示した図
【図４】重複している回数が違う領域の状態を示した図
【図５】従来の形状測定装置の概略図
【図６】従来の被測定面の分割した状態を示す図
【図７】従来の被測定面の分割した状態を示す図
【図８】実施形態に係る、コンピュータを接続した形状測定装置全体の構成図
【図９】実施形態に係る、測定された形状データから被測定面全面の形状データを生成する手順のフローチャート
【符号の説明】
１１ 干渉計
１２ 被測定物
１３ 平行移動可能なステージ
３１ ｙ軸まわりに回転する回転ステージ
３２ θｚ軸まわりに回転する回転ステージ
３３ 被測定物である球面レンズ
３４ フィゾー干渉計[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a three-dimensional shape measurement of a spherical lens or the like mounted on a semiconductor exposure apparatus or the like, and more particularly, to a three-dimensional shape measurement method and apparatus capable of measuring with an accuracy on the order of nanometers.
[0002]
[Prior art]
Conventionally, an aperture synthesis method has been known as a measurement method when the surface to be measured is larger than the measurement range of the interferometer. In this method, the surface to be measured cannot be measured at one time, so that the measurement is performed in two or more steps, and the entire shape of the surface to be measured is restored by connecting the surface shapes.
[0003]
A conventional aperture synthesis method will be described with reference to FIG. FIG. 5 is an outline of a configuration for performing aperture synthesis that has been conventionally performed. A method in which the surface to be measured is divided by a method in which the interferometer 11 is fixed and the object 12 is moved by using the stage 13 which can be translated, or a method in which the interferometer 11 is moved and the object 12 is fixed. The surface shape is obtained for the region. At this time, the measurement of the adjacent area is always performed so that a part thereof is overlapped. Then, by applying the least squares method or the like to the measurement data of the overlapped portion and matching them, the connection between the divided surfaces is performed (for details of the specific connection method, see Patent Document 1. Further, the interferometer The measurement method when a Fizeau interferometer is used as 11 is described in Non-Patent Document 1.)
[0004]
According to this method, the divided measurement data of the two overlapping planes are respectively referred to as first measurement data, and the respective measurement data overlapping as the second measurement data are represented by (xi, yi, zij) and (xm, yn). , Zmn),
[0005]
(Equation 1)

[0006]
[0007]
(Equation 2)

[0008]
, The least squares method is applied to calculate (p1, a1, b1) and (p2, a2, b2). If, for example, “Δp + Δa · xi + Δb · yi” is added to the first measurement data based on the obtained difference values (Δp, Δa, Δb), the first and second measurement data can be smoothly connected.
[0009]
[Patent Document 1]
JP-A-10-281737
[Non-patent document 1]
APPLIED OPTICS 13 No. 11 2693-2703
[0010]
[Problems to be solved by the invention]
However, this method or the spherical lens has a problem that the entire shape is restored in a state where the alignment error between the interferometer and the spherical lens is included.
[0011]
First, the problem of restoring the entire shape including the alignment error between the interferometer and the DUT will be described with reference to FIG. FIG. 6 shows an example in which an interferometer capable of collectively measuring the entire surface of the measured surface with respect to the measured surface having a pointed shape such as a cutting edge (see FIG. 3B) is assumed. 7 shows interference fringes when a surface to be measured is measured using a meter. When the surface to be measured is divided as in the divided regions A2 to D2, it is necessary to remove tilt and defocus, which are alignment errors, from the surface shape of A2. However, from the interference fringe A2 alone, it cannot be distinguished whether it is a tilt fringe, which is one of the alignment errors between the object to be measured and the interferometer, or a surface shape. Therefore, for example, if B2 is connected to A2, C2 is connected to B2, and D2 is connected to C2, it is possible to connect B2, C2, and D2 to the posture of A2, but A2 Tilt and defocus itself cannot be removed.
[0012]
Therefore, a dividing method as described in the section of the prior art shown in FIG. 7 has been considered. In FIG. 7, each of the divided areas A1 to E1 is provided so as to overlap with an adjacent area. For example, the area A1 partially overlaps the adjacent areas B1 and E1. However, when the measurement is performed by the division method as shown in FIG. 6, since the regions A1 to E1 are connected in order, if the square root of the root mean square of the connection error is ε, the regions A1 and B1 are connected with an error of ε. Is done. Similarly, when the area C1 is connected to the area B1, the area C1 is connected with an error of ε, and the areas D1 and E1 are also connected. When the amount of connection error is considered based on the area A1, the error accumulates as follows: ε for the area B1, √2ε for the C1, 、 3ε for the D1, and √4ε for the E1.
[0013]
The present invention has been made in view of the above conventional example, and when connecting a plurality of divided planes in a state where the influence of tilt and defocus which are alignment errors of an interferometer in a restored shape in which a plurality of divided planes are connected is eliminated. It is an object of the present invention to provide a method and an apparatus for measuring a three-dimensional shape, which can eliminate the accumulation of connection errors.
[0014]
[Means for Solving the Problems]
According to the present invention, the surface to be measured having a three-dimensional shape is divided into a plurality of regions, and the shape of the surface to be measured is measured using an interferometer for each of the plurality of divided regions. In a three-dimensional shape measuring method for measuring the shape of a surface to be measured by joining measured values, at least one of the plurality of divided regions is provided with a reference provided so as to overlap with all other regions. And proposes a three-dimensional shape measuring method for measuring the shape of the surface to be measured by correcting a joining error between the reference surface and each of the other regions.
[0015]
Further, according to the present invention, there is proposed a three-dimensional shape measuring method in which the joint error is corrected using a value obtained by excluding a tilt and a defocus, which are alignment errors of the interferometer, from the measured values of the reference plane. are doing.
[0016]
Further, according to the present invention, a three-dimensional shape measuring method is proposed in which the measured values of the respective regions are connected, and then the correction is performed by changing the number of times of averaging in accordance with the number of overlaps of each region.
[0017]
DETAILED DESCRIPTION OF THE INVENTION
[First Embodiment]
First, a first embodiment in the case of measuring a spherical lens with a Fizeau interferometer will be described with reference to the drawings. FIG. 1 shows an outline of a measuring apparatus 100 for split measurement of a spherical lens. It has a rotating stage 31 rotating around the y-axis, a rotating stage 32 rotating around the θz-axis, and a Fizeau interferometer 34 for measuring a spherical lens 33 as an object to be measured. The rotation stages 31 and 32 are rotated at an angle designated by the drive unit 35 or at a fixed angle, respectively. The rotation angle of each stage at the time of measurement is stored as digital data in a computer (not shown) connected to the measuring device 100.
[0018]
The interference image obtained at the time of the measurement is formed on an imaging device such as a CCD provided in the Fizeau interferometer 34, and stored in the computer as digital image data. The surface shape is obtained based on the digital image data.
[0019]
<Method of dividing the surface to be measured>
A method of dividing the surface to be measured will be described. First, a measurement range when the optical axis of the Fizeau interferometer 34 coincides with the center of the spherical lens 33 that is the surface to be measured is set as a reference surface. That is, the optical axis of the spherical lens 33 to be measured is mounted on the rotary stage 32 so as to coincide with the θz axis, and the rotation angle of the y axis by the rotary stage 31 is 0 degree (the rotation angle of the y axis is , The angle at which the θz axis is parallel to the optical axis of the interferometer 34 is set to 0 °), and the spherical lens 33 is measured. The range measured in this case is the reference plane.
[0020]
Next, a divided measurement plane (also referred to as a divided area) is measured so as to overlap with the reference plane. Although the number of divided measurement surfaces may be arbitrary, the number of divided surfaces is four in the present embodiment. Considering that the entire surface to be measured (that is, the surface to be measured of the spherical lens 33) is measured on each of the reference surface and the four divided surfaces, each of two intersections where the outer periphery of the measured surface and the outer periphery of the divided surface intersect, and the surface to be measured The angle formed by the line segment connecting the center of the image and the center must be 90 degrees or more. Note that, even when the measurement is performed by dividing the number into divisions other than four, the desired angle is the angle when the division is performed equally. For example, in the case of three divisions, the angle is approximately 120 degrees, and in the case of five divisions, approximately 72 degrees is desirable. Note that in the present embodiment, the term “division” is used including division into regions having mutually overlapping portions.
[0021]
Also, considering that the surface to be measured is tilted using the rotating stage 31 that rotates around the y axis, the smaller the angle of tilt, the smaller the gravitational deformation of the surface to be measured due to the tilt. Preferably, the distance from the center is short. For this purpose, it is desirable that an intersection (hereinafter, referred to as an outer peripheral side intersection) on the outer peripheral side of the lens to be measured, of the two intersecting points of the divided regions adjacent to each other, is substantially on or slightly outside the outer periphery of the lens. . If the outer intersection is located inside the outer periphery of the lens, an unmeasured region remains on the surface to be measured.On the other hand, if the outer intersection is located outside the outer periphery of the lens, the unmeasured region can be prevented from remaining. However, this is because the condition that the distance between the center of the reference plane and the center of the division plane is made as short as possible cannot be satisfied. Therefore, the rotation angle of the rotation stage 31 around the y-axis is determined so that the above condition is satisfied.
[0022]
FIG. 2 is a diagram showing an example in which the surface to be measured is divided into four regions in consideration of the above conditions. When K1 and K2 are the intersections of the outer periphery of the area B and the measured surface, and the center of the measured surface is A0 and the center of the area B is B0, A0 and A0 are determined under the condition that ∠K1A0K2 is 90 degrees or more. The distance from B0 is divided so as to be as short as possible. The same applies to the areas C, D, and E.
[0023]
In the figure, the measurement is performed for the divided areas A, B, C, D, and E, and the measurement result of the divided areas B, C, D, and E is connected to the measurement result of the area A that is the reference plane. The procedure for obtaining the measurement results of the above will be described.
[0024]
The surface shape (referred to as data_R) of the reference surface in the Fizeau interferometer is obtained in advance (refer to APPLIED OPTICS 13 No. 11 2693-2703 for a specific method) and stored in the computer as the shape of the reference surface. . The computer stores the surface shape of the reference surface as a square matrix. The surface shapes described hereinafter are in the form of a square matrix unless otherwise specified.
[0025]
Then, the shape of the area A is measured. Next, in order to measure the range of the region B, the spherical lens is tilted by a necessary angle using the rotating stage 31 that rotates around the y-axis. The required angle in this case is, for example, as described above, such that the intersection on the outer peripheral side of the lens to be measured, of the two intersecting intersections of the divided regions adjacent to each other, is almost on or slightly outside the outer periphery of the lens. The angle is chosen.
[0026]
In this state, the shape is measured in the same manner as when the range of the area A is measured. When measuring the range of the region C, the lens is rotated using the rotation stage 32 that rotates around the θz axis while the lens is tilted, and the measurement is performed. In this example, since the area is divided into four areas, the rotation stage 32 is rotated around the θz axis in a fixed direction by 90 degrees from the state measured first for the area B, and the area C is rotated in the same manner as the area A. Measure over the range. Similarly, the measurement is performed for the ranges of the regions D and E. The measurement data (measured surface shape) of the range of the region A obtained in this manner is referred to as data_A, the range of the region B is referred to as data_B, and hereinafter data_C, data_D, and data_E.
[0027]
First, the measurement data data_R of the reference surface is subtracted from the measurement data data_A, data_B, data_C, data_D, and data_E, and these are respectively described as data_AR, data_BR, data_CR, data_DR, and data_ER. As a result, data_AR, data_BR, data_CR, data_DR, and data_ER are values in which the shape error of the reference surface has been corrected.
[0028]
Next, the alignment error of data_AR generated at the time of the interference measurement is removed, and the surface shape of the region A as the reference surface is obtained. Next, data of an overlapping area of the area A and the area B is extracted for each of the area A and the area B, and an alignment error of data_BR is calculated based on the surface shape of the area A. Further, the alignment error of the entire data_BR is subtracted using the calculated alignment error of data_BR. The measurement data data_CR, data_DR, and data_ER also subtract the alignment error in the same manner. The surface shape of the whole object to be measured is output based on the surface shape obtained by removing the shape of the reference surface and the alignment error from the measurement data of all the divided surfaces.
[0029]
<Correction of alignment error>
An example of a method for removing an alignment error from measurement data will be described below. As one method, a separation method using a Zernike polynomial is known.
[0030]
The Zernike polynomial is as shown in Expression 3.
[0031]
[Equation 3]

[0032]
Here, n and m are integers, i is an imaginary unit, ρ and θ are radial components (0 ≦ ρ ≦ 1) and angle components in a polar coordinate system. For practical use, when m is positive, exp (imθ) = cos (mθ), and when m is negative, exp (imθ) = sin (mθ).
[0033]
When the Zernike polynomials are further combined (the sum of n in Equation 3 is theoretically ∞, but for the sake of explanation, it is a sum up to n = 15), and Equation 4 is obtained.
[0034]
(Equation 4)

[0035]
Here, W (ρ, θ) indicates a wavefront. Let Cn, m be called the Zernike coefficient. By combining Zernike polynomials as in Expression 4, an arbitrary wavefront, that is, shape information can be expressed in an interferometer.
[0036]
Among the Zernike polynomials, Z (0,0, ρ, θ) = 1, Z (1,1, ρ, θ) = ρcos (θ), Z (1, −1, ρ) , Θ) = ρ sin (θ) and Z (2, 0, ρ, θ) = 2ρ 2-1 represent a piston component, a X and Y tilt component, and a defocus component, respectively, which mean a DC component.
[0037]
Next, a method for removing the piston, tilt, and defocus components, which are alignment errors, from data_AR using Zernike polynomials will be described. Matrices representing the addresses of the square matrix data of data_AR are denoted by I and J. The center addresses centX and centY of the square matrix data are defined as follows.
[0038]
(Equation 5)

[0039]
However, [] means rounding to an integer. Using centX and centY of Equation 5,
I1 = I-centX, J1 = J-centY (Equation 6)
And a vector conversion representing the address. After the vector conversion representing the address of each data as in the above equation, R1 is
R1 = I1.2 + J1.2 (Equation 7)
And "." (Dot) immediately after the matrix means an operation on elements of the matrix.
The maximum value of R1 is MAXR. Using MAXR, I1, and J1, coordinates X and Y are obtained in the manner of Expression 8.
X = I1 / MAXR, Y = J1 / MAXR (Equation 8)
From these coordinates X and Y, ρ and θ in Expressions 3 and 4 are obtained.
R = √ (X.2 + Y.2), T = tan-1Y. / X (Equation 9)
Here, R corresponds to ρ and T corresponds to θ.
[0040]
R, T and Z are converted into column vectors, and the converted ones are denoted as Rv and Tv. Hereafter, the suffix “v” means a vector. A vectorized version of data_AR is defined as ZAv. Since Equation 4 is a linear combination of Zernike polynomials, it can be expressed as follows using the vectors Rv and Tv.
Wv = CA (Equation 10)
However
C = [C0,0 C1, -1 C1,0 ... C15,14] t
A = [Z (0,0, Rv, Tv) Z (1, -1, Rv, Tv) Z (1,0, Rv, Tv) ... Z (15,14, Rv, Tv)]
Wv is the wavefront. Therefore, each Zernike coefficient C is
C = A-1ZAv (Equation 11)
Can be calculated by
[0041]
Finally, to obtain a value ZfAv obtained by subtracting the piston, tilt, and defocus, which are alignment errors, from ZAv:
ZfAv = ZAv−C′B (Equation 12)
However
C ′ = [C0,0 C1, −1 C1,1 C2,0] t
B = [Z (0,0, R, T) Z (1, -1, R, T) Z (1,0, R, T)... Z (15,14, R, T)]
And That is, B represents the alignment error, and C ′ represents its Zernike coefficient.
[0042]
The vector ZfAv is the shape information of the range A from which the alignment error has been removed, and is expressed as data_ARf.
[0043]
Next, a procedure for removing an alignment error from data_BR will be described. FIG. 3 shows that the data pitch changes when the spherical lens is tilted. The spherical lens 61 shows a state before rotation, and the spherical lens 62 shows a state after rotation. The coordinate system before rotation is (X1, Y1), and the coordinate system after rotation is (X2, Y2). (X2, Y2) is equivalent to a rotated coordinate system of (X1, Y1). The data pitch is equal on (X1, Y1) and (X2, Y2). However, when trying to evaluate the entire shape of the spherical lens in, for example, the (X1, Y1) coordinate system, it is clear that the data pitch before rotation does not match the data pitch after rotation.
[0044]
Therefore, in order to match the data pitch of data_BR with the data pitch of data_AR, data interpolation is performed by linear interpolation. Data_BRs obtained by linearly interpolating data_BR to the data pitch of data_AR are referred to as data_BRs. The surface shape of data_BRs is ZBs. To convert the ZBs address into the XY coordinates, the addresses x_cent and y_cent corresponding to the center of the TS optical axis are obtained from the ZBs address. X_cent and y_cent can be calculated from the tilt angle of the spherical lens.
I2 = Ix_cent, J2 = Jy_cent (Expression 13)
In order to convert I2 and J2 into XY coordinates, the calculations shown in Expressions 5 and 6 may be performed.
[0045]
Data in a range where data_BRs and data_ARf overlap each other are extracted as data_BRsU and data_ARfU. data_BRsU includes shape information and an alignment error. Since data_ARfU is only shape information, data (data_SB) obtained by subtracting data_ARfU from data_BRsU includes only piston, tilt, and defocus components, which are alignment errors. To separate the piston, tilt, and defocus for each component from these alignment errors, a matrix B of Expression 10 is generated from the XY coordinates of data_BRsU and the data ZSBv of data_SB,
C ′ = B−1ZSBv (Equation 14)
And it is sufficient. A matrix B of Expression 12 is generated for the Zernike coefficients C ′ and the XY coordinates of data_BRs obtained here, and only the alignment error of data_BRs is removed as in Expression 12. Here, since the surface shape of data_BRs is represented by ZBs, an error is removed by the following equation (15).
ZfBv = ZBsv−C′B (Equation 15)
ZfBv is the surface shape in the range B, and the surface shape in the range B is connected to the data in the range A excluding the alignment error.
[0046]
ZfCv, ZfDv, and ZfEv can be obtained by the procedure for obtaining ZfBv in the range B even in the ranges C, D, and E. As a result, the areas B, C, D, and E and the surface shapes of all the divided surfaces are connected to the surface shape in the range A where all the alignment errors are eliminated.
[0047]
When the surface to be measured is divided into five regions including the reference surface as shown in FIG. 2, there are five overlapping portions from a non-overlapping portion to a portion where all five regions overlap. I do. FIG. 4 shows the overlapping state. In the figure, the portion α is a portion that is covered by only one divided region and does not overlap, the portion β is a portion where two divided regions overlap, a portion γ is a portion where three divided regions overlap, and a portion δ is four portions. The portion where the divided regions overlap, the portion ε is a portion where the five divided regions overlap. The hatched portion is a portion outside the surface to be measured.
[0048]
Therefore, when connecting the respective regions to obtain the surface shape of the entire surface to be measured, ZfAv to ZfEv are all added up, and as shown in FIG. The entire shape is restored by changing the number of times of averaging accordingly. For example, for a quintuple overlapping portion, since data is included in all of ZfAv to ZfEv, all of them are added and averaged by 5 which is the number of overlapping regions. This is the same for the other parts.
[0049]
The number of overlapping regions is derived based on the XY coordinates of each surface. That is, if there are a plurality of points having the same coordinate value for the surface shapes ZfAv to ZfEv and the coordinates (X, Y) of the surface shape, all the surface shapes at the coordinate values are added up and averaged by the number of additions. As a result, even if the measurement point of the interferometer is shifted due to a stage motion error or the like, in a region where the divided planes overlap, the effect is reduced by averaging, so that the entire shape can be accurately restored.
[0050]
<Execution of measurement processing by computer>
The above procedure is executed by a computer connected to the measuring device 100. Here, in order to execute the above procedure by a computer, hardware resources such as a memory and a processor of the computer are used for the above processing, especially for storing measured data, a program recording a calculation procedure, and storing calculation result data. And execute the processing.
[0051]
FIG. 8 shows a schematic configuration of a measuring device to which a computer is connected. In the measurement apparatus 100, light emitted from the laser light source 805 is spread by a lens 804, reflected by a beam splitter 803, converted into parallel light via a lens 802, and incident on a lens 801. The final surface 800 of the lens 801 has a spherical shape with a certain radius of curvature, and the reflected light of the final surface 800 is used as reference light and the transmitted light is used as test light. The test light is reflected by the surface of the spherical lens 33 of the object placed on the controllable rotating stages 31 and 32, passes through the lens 801 again, and is converted into parallel light. The reference light and the test light pass through the beam splitter 803 and the lens 806 to form an interference fringe in the imaging system 807. The interference fringes formed by the imaging system 807 are read into the computer 808, and are subjected to the above-described correction, conversion, and connection processing in the procedure described below to obtain shape information of the surface to be measured. The interference fringes read into the computer 808 are processed into the above-described shape information by a known method. The shape data of the reference plane 800 is measured in advance and stored in the computer 808 as described above.
[0052]
Although not shown in FIG. 8, the control of the rotary stage of the measuring unit shown in FIG. 1 can be performed by a computer. In that case, each stage is driven to rotate by a pulse motor or the like, and the rotation amount of the stage is controlled by controlling the drive amount of the pulse motor by a computer.
[0053]
FIG. 9 is a flowchart showing a processing procedure of the shape information in the computer 808. Note that the example of FIG. 9 shows an example in which the surface to be measured is measured in the reference region A and the four divided regions B to E as shown in FIG.
[0054]
First, in step S901, measurement is performed on the reference region and each divided region, and based on the obtained interference fringe images, shape data data_A, data_B, data_C, data_D, and data_E represented by a square matrix are generated. This shape data can be obtained by a known procedure.
[0055]
Next, data_AR, data_BR, data_CR, data_DR, and data_ER in which the shape error of the reference surface has been corrected by subtracting the shape data of the reference surface obtained in advance from the shape data of each divided region are obtained (step S902).
[0056]
Next, for the reference region A, the shape data ZfAv of the reference region A in which the alignment error is corrected by executing Expression 12 is calculated (step S903).
[0057]
Next, based on the shape data of the reference area A, focusing on each of the divided areas, Expressions 13 and 5 and 6 are calculated for the noticed divided area, and the measurement pitch at the time of measurement of the noticed divided area is set as Is interpolated according to the measurement pitch in. Instead of interpolating data according to a narrow pitch, there is also a method of discarding uncorresponding data according to a wider pitch. Based on the interpolated shape data, formulas 10, 14, and 15 are executed to calculate shape data ZfXv in which an alignment error has been corrected (step S904). Here, the suffix X indicates one of the attention areas B to E.
[0058]
Step S904 is performed for all the divided regions while sequentially changing the divided region of interest, and the alignment error is corrected for all the regions (step S906).
[0059]
When the processing is completed, if there are a plurality of points having the same coordinate value for ZfAv to ZfEv, those data are all added, divided by the number of additions, and averaged (step S906). The obtained value is stored as shape data of the surface to be measured (S907). As described above, error-corrected shape data is obtained from the measurement result.
[0060]
As described above, according to the present invention, it is possible to connect all the divided planes while eliminating tilt and defocus with high accuracy without accumulating errors in the connection of the divided planes (divided areas). The shape of the entire measurement surface can be accurately restored.
[0061]
In addition, when restoring the surface to be measured, the shape data on the surfaces that overlap each other on the divided surfaces are added together and averaged, so that the influence of the measurement point shift is reduced on the overlapping surface, and the entire surface to be measured can be accurately measured. Can be restored.
[0062]
【The invention's effect】
According to the effects of the present invention, it is possible to connect all the divided surfaces without tilting and defocusing accurately without accumulating accumulated errors in the connection of the divided surfaces, and to accurately restore the entire surface to be measured. I was able to.
[0063]
In addition, when restoring the surface to be measured, the shape data on the surfaces that overlap each other on the divided surfaces are added together and averaged, so that the influence of the measurement point shift is reduced on the overlapping surface, and the entire surface to be measured can be accurately measured. Can be restored.
[Brief description of the drawings]
FIG. 1 is a schematic diagram of a shape measuring apparatus according to the present invention.
FIG. 2 is a view showing a state where a surface to be measured is divided;
FIG. 3 is a diagram showing that a data pitch changes when a spherical lens is tilted.
FIG. 4 is a diagram showing a state of an area where the number of times of overlap is different;
FIG. 5 is a schematic view of a conventional shape measuring device.
FIG. 6 is a diagram showing a conventional state where a surface to be measured is divided.
FIG. 7 is a diagram showing a state where a surface to be measured is divided according to the related art.
FIG. 8 is a configuration diagram of an entire shape measuring apparatus connected to a computer according to the embodiment;
FIG. 9 is a flowchart of a procedure for generating shape data of the entire surface to be measured from measured shape data according to the embodiment;
[Explanation of symbols]
11 Interferometer
12 DUT
13 Parallel movable stage
31 Rotary stage rotating around y-axis
32 Rotary stage rotating around θz axis
33 Spherical lens to be measured
34 Fizeau Interferometer

Claims (5)

A three-dimensional measuring method for measuring a shape of a surface to be measured,
The surface to be measured is divided into a plurality of divided regions including a reference region having at least one overlapping portion with all others, and the shape data of each divided region is measured by an interferometer,
Correct the error of the shape data of the reference area,
A method of measuring a three-dimensional shape, wherein the plurality of divided regions are connected based on corrected shape data of the reference region in the overlapping portion. Dividing the surface to be measured having a three-dimensional shape into a plurality of regions, measuring the shape of the measurement surface using an interferometer for each of the plurality of divided regions, and joining the measured values for each region A three-dimensional shape measuring method for measuring the shape of the surface to be measured with
At least one of the plurality of divided regions is a reference plane provided so as to overlap with all other regions, and is a joint between the reference region surface and each of the other regions. A three-dimensional shape measuring method, wherein the shape of the surface to be measured is measured by correcting an error. 3. The three-dimensional structure according to claim 1, wherein the correction of the joining error is performed using a value obtained by excluding a tilt and a focus, which are alignment errors of the interferometer, from a measured value of the reference plane. 4. Shape measurement method. The three-dimensional shape measurement method according to claim 1, further comprising, after joining the measured values of the respective regions, further changing the number of times of averaging in accordance with the number of overlaps of each region. A three-dimensional measuring device for measuring a shape of a surface to be measured,
The surface to be measured is divided into a plurality of divided regions including a reference region having at least one overlapping portion with all others, and an interferometer for measuring the shape data of each divided region,
Correction means for correcting an error in the shape data of the reference area,
A connection unit that connects the plurality of divided regions based on the corrected shape data of the reference region in the overlapping portion, and a connection unit that connects the plurality of divided regions.

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