JP4011902B2 - Birefringence measuring apparatus and method considering wavelength dependence - Google Patents

Description

の関係を満たすように波形解析で周波数情報と位相情報との和として求めるデータ処理手段を備える。
【００１６】
前記データ処理手段は、本発明の好適な例として、前記光信号の光強度分布を示す波形データのフーリエ解析で得られる周波数の振幅スペクトルの内のスペクトル分布の頂点の周波数、及びそのスペクトル分布の開始点の周波数をそれぞれｆ_ｐ、及びｆ_ｓとし、前記光信号の光強度分布を示す波形データのフーリエ解析で得られる位相、前記波数ｋの最小値、及び最大値をそれぞれφ_（ｋ）、ｋ_ｍｉｎ、ｋ_ｍａｘとしたとき、前記波長依存性を考慮した複屈折位相差Δ（ｋ）を、
【数７】

の関係を満たすように波形解析で求める手段である。
【００１７】
前記データ処理手段は、本発明の好適な例として、前記光信号の光強度分布を示す波形データのフーリエ解析で得られる周波数の振幅スペクトルの内のスペクトル分布の開始点の周波数をｆ_Ｓとし、前記光信号の光強度分布を示す波形データのフーリエ解析で得られる位相、前記波数ｋの最小値、及び最大値をそれぞれφ’_（ｋ）、ｋ_ｍｉｎ、ｋ_ｍａｘとしたとき、前記波長依存性を考慮して複屈折位相差Δ（ｋ）を、
【数８】

の関係を満たすように波形解析で求める手段である。
【００１８】
前記データ処理手段は、本発明の好適な例として、前記光信号の光強度分布を示す波形データのフーリエ解析で得られる周波数の振幅スペクトルの内のスペクトル分布の開始点の周波数をｆ_Ｓとし、前記光信号の光強度分布を示す波形データのフーリエ解析で得られる位相、前記波数ｋの最小値、及び最大値をそれぞれφ’_（ｋ）、ｋ_ｍｉｎ、ｋ_ｍａｘとしたとき、前記複屈折位相差Δ（ｋ）を、
【数９】

の関係を満たすように波形解析で求める手段である。
【００１９】
前記データ処理手段は、本発明の好適な例として、前記光信号の光強度分布を示す波形データのフーリエ解析で得られる周波数の振幅スペクトルの内のスペクトル分布の頂点の周波数をｆ_Ｐとし、前記光信号の光強度分布を示す波形データのフーリエ解析で得られる位相、前記波数ｋの最小値、及び最大値をそれぞれφ’_（ｋ）、ｋ_ｍｉｎ、ｋ_ｍａｘとしたとき、前記複屈折位相差Δ（ｋ）を、
【数１０】

の関係を満たすように波形解析で求める手段である。
【００２０】
本発明に係る波長依存性を考慮した複屈折測定方法は、測定対象の複屈折に関する情報を担う光信号の光強度分布を示す波形データから高次複屈折の次数を含む周波数成分及び波長依存性を担う位相成分を解析し、その解析データから前記高次複屈折に加え、前記波長依存性を示す複屈折をキャリア成分項と分散項とに分けて求めることを特徴とする。
【００２１】
【発明の実施の形態】
以下、本発明に係る波長依存性を考慮した複屈折測定装置及び方法の実施の形態を添付図面を参照して具体的に説明する。
【００２２】
最初に、本発明における波長依存性を考慮した複屈折計測の基本測定原理図１及び図２に基づいてを説明する。ここでは、点計測の適用例を詳細に説明するが、この基本測定原理は、後述するように２次元測定にも拡張できるものである。
【００２３】
図１に示す点計測用の複屈折測定装置１は、白色ランプを用いた白色光源１０及びその出射系（光ファイバケーブル１１ａ、コリメータレンズ１１ｂ）と、その白色光源１０から出射される白色光の光路上で、サンプルＳａ（測定試料）を挟んで対向する位置に並設される１対の偏光子１２及び検光子１３と、その出射光の光路上に配置される分光器１４（回折格子（又はプリズム）１４ａ、リニアＣＣＤ（受光素子アレイ）１４ｂ）及びその入射系（集光レンズ１５ａ、光ファイバケーブル１５ｂ）と、分光器１４の出力側に接続され、本発明の測定原理に基づく解析アルゴリズムを実行する解析装置（コンピュータ）として用いるＰＣ（パーソナルコンピュータ）１６とを備えている。
【００２４】
この構成によれば、白色光源１０からの出射光がその出射系１１ａ、１１ｂを介して方位４５度の偏光子１２、サンプルＳａ、及び方位４５度の検光子１３を順次透過し、そのサンプルＳａの複屈折情報を持った透過光の光信号として、分光器１４にその入射系１５ａ、１５ｂを介し入力される。そして、この光信号は、分光器１４内部の回折格子１４ａを介しそのリニアＣＣＤ１４ｂにより各波長λにおける光強度Ｉ_（λ）として測定され、ＰＣ１６に送られる。
【００２５】
上記で得られる透過光の光強度Ｉ_（λ）は、図１中（中段）に示すように、次の（１）式で表される。
【００２６】
【数１１】

この（１）式において、Ｉ_ＤＣはバイアス成分（直流成分）、Ｓ_（λ）はシステムの透過特性（システム依存係数、波長透過率特性）、φは偏光子１２とサンプルＳａの主軸方位の差、ΔはサンプルＳａの複屈折位相差をそれぞれ示す。
【００２７】
この内、サンプルＳａの複屈折位相差Δは、図１中（中段）に示すように、次の（２）式で表される。
【００２８】
【数１２】

この（２）式において、λは波長、δ_ｎはサンプルＳａのもつ複屈折、ｄはサンプルＳａの厚さ、ｋは波数（ｋ＝１／λ）をそれぞれ示す。
【００２９】
上記（２）式のようにサンプルＳａの複屈折位相差Δを波数ｋを用いて表すことができるため、上記（１）式の光強度Ｉ_（λ）は、図１中（下段）に示すように波数ｋに対し余弦状に変化する波形として実測される。
【００３０】
そこで、このように波数ｋに対し余弦状に変化する波形分布を示す光強度Ｉ_（λ）に対し、ＰＣ１６の処理により、最大エントロピー法を用いて高分解な周波数解析を行い、この解析で得られる周波数スペクトルの中心周波数を読むことにより、サンプルＳａのもつ複屈折δ_ｎ（複屈折位相差Δ及び主軸方位φ）の計測が行われる。ここまでの複屈折計測の原理は、特開２００１−１４１６０２号公報で提案されているものと同様である。
【００３１】
上記の原理では、図１に示すように波数ｋに対し余弦状に変化する光強度Ｉ_（λ）の成分がどの波数ｋに対しても周期が変わらず、すなわち単一周期で構成されるものとして解析を行っているが、実際には、図１中（下段）に示すように、光強度Ｉ_（λ）の成分が波数ｋによって周期が僅かに変化している。これは、複屈折が波長依存性を示すためである。
【００３２】
そこで、本発明では、上記原理に加え、多くのサンプルＳａが示す複屈折の波長依存性を考慮して、光強度Ｉ_（λ）が波長λ（又は波数ｋ）によって周期が異なることに着目し、その波長依存性を含めた複屈折計測を実現することをその主眼とするものである。このことを図２を参照して説明する。
【００３３】
図２中（上段）に示すように、まず、上記（２）式は、複屈折位相差Δの波長依存性を考慮すると、複屈折δ_ｎをキャリア成分項δ_ｎ０及び分散項δ_λに分けて考えることができるため、δ_ｎ＝δ_ｎ０＋δ_λを代入して両項δ_ｎ０、δ_λにそれぞれ展開して整理すると、次の（３）式が得られる。
【００３４】
【数１３】

この（３）式において、φ_（ｋ）は位相情報を示す。
【００３５】
この（３）式及び図２中（上段）に示すように、波長依存性を含む複屈折位相差Δ（ｋ）は、複屈折の次数に対応して位相差が２π、４π、６π、…と大きく変化する次数項としての「周波数情報」と、複屈折の波長依存性により位相差が僅かに変化する分散項としての「位相情報」とをそれぞれ計算し、両者の和として求めることができる。
【００３６】
そこで、図２中（中段）に示すように、「周波数情報」及び「位相情報」は、上記のように得られた分光光強度信号、すなわち波数ｋに対し余弦状に変化する光強度Ｉ_（λ）の成分に対して、ＦＦＴ（高速フーリエ変換法）を用いて求めることができる。具体的には、透過光の光強度分布（波数ｋに対する光強度Ｉ_（λ）の分布）に対しＦＦＴによるフーリエ変換を行い、そのスペクトル分布に所定の窓関数を掛け、そのスペクトルをゼロ次にシフトした後、フーリエ逆変換を行うことにより「位相情報」を求めると共に、フーリエ変換によって取り除かれるキャリア周波数成分である「周波数情報」を振幅スペクトル分布の半値幅等から求める（詳細は後述参照）。
【００３７】
図２中（中段）の例は、透過光の光強度分布のフーリエ解析で得られる振幅スペクトルの広がりから「周波数情報」を、またフーリエ逆変換で得られる位相から「位相情報」をそれぞれ求める場合を説明するものである。
【００３８】
ここで、図２中（中段左側）に示す「周波数情報」において、ｆ_ｐは、振幅スペクトルの中心周波数、ｆ_ｓは、ｆ_ｐの１／ｅ^２（ｆ_ｓ＝ｆ_ｐ×１／ｅ^２）の周波数をそれぞれ示す。ここでのｆ_ｓの取り方の基準は、あくまで便宜的なものであり、スペクトルの半値を用いても良く、要するに、スペクトルの幅を決める位置と、その周波数の関係とが求められれば、どの位置を選択しても構わない。また、図２中（中段右側）に示す「位相情報」において、Ｋ_ｍｉｎ及びＫ_ｍａｘは、それぞれ計測される波数ｋの最小値及び最大値を示す。
【００３９】
以上の周波数解析を元に得られる「周波数情報」と「位相情報」を上記（３）式中に入れて整理すると、次の（４）式が得られる。
【００４０】
【数１４】

この（４）式を元に「周波数情報」と「位相情報」を計算すれば、サンプルＳａの波長依存性を考慮した複屈折位相差Δ（ｋ）が求まることになる。
【００４１】
以上の測定原理に基づく解析アルゴリズムは、予めＰＣ１６上のプロセッサ（ＣＰＵ）がその動作時に実行可能なプログラムとして、そのプロセッサに接続される半導体メモリ（可搬型のＩＣカード等も含む）、ハードディスク、リムーバブルメディア（フロッピーディスク、光磁気ディスク（ＭＯ）、ＣＤ−ＲＯＭ、ＣＤ−Ｒ、ＣＤ−ＲＷ、ＤＶＤ−ＲＯＭ等）等の記録媒体に記録され、測定時にそのプロセッサにより実行される。
【００４２】
すなわち、ＰＣ１６のプロセッサによるプログラム処理により、以上の測定原理に基づく解析アルゴリズムが実行され、上記（４）式に従ってサンプルＳａの波長依存性を考慮した複屈折位相差Δが求められる。
【００４３】
なお、上記の波形解析では、フーリエ変換で得られたスペクトルから「周波数情報」及び「位相情報」を求める処理方法として、スペクトルをゼロ次にシフトする方法を説明しているが、本発明はこれに限らず、後述するように種々の手法が採用できる。
【００４４】
また、上記の波形解析では、代表的な周波数解析方法であるＦＦＴを用いているが、本発明はこれに限らず、波数ｋに対し余弦状に変化する光強度Ｉ_（λ）（分光光強度信号）の周波数、強度、及び位相が計算できる手法であれば、いずれの波形解析方法でも適用可能である。
【００４５】
また、上記の光強度Ｉ_（λ）を表す（１）式は、１対の偏光子１２及び検光子１３が互いに「平行ニコル」となるように配置された場合の式であるが、両者１２、１３が互いに「直交ニコル」となるように配置された場合は、上記（１）式に代えて、次の（１ａ）式で表される（これは、特開２００１−１４１６０２号公報で記載されているものと同様である）。
【００４６】
【数１５】

【００４７】
また、上記の例では、回折格子（又はプリズム）及びリニアＣＣＤ（受光素子アレイ）を有する分光器（マルチチャンネル型の分光器）を例示してあるが、本発明はこれに限らず、例えば、回折格子やプリズムを回転させて回折角の異なる波長を次々に出射スリットに導く構造をもつ波長走査型や波長選択型の分光器等であってもよい。
【００４８】
次に、サンプルＳの主軸方位φの計測・解析方法を図３に基づいて説明する。この例では、位相シフト法を用いた場合を例示している。
【００４９】
まず、図３中（上段）に示すように、前述した複屈折測定装置１において、１対の偏光子１２及び検光子１３が互いに平行ニコル（直交ニコルでも構わない）の状態となるようにセッティングされ、その間にサンプルＳａが置かれる。この状態で、検光子１３からの出射光の光強度Ｉ_（λ）が前述した分光器１４にて測定される。この光強度Ｉ_（λ）は、図３中（中段）に示すように前述した（１）式で表現でき、これを展開すると、次の（５）式のように表現できる。
【００５０】
【数１６】

【００５１】
この（５）式より、位相シフト法を用いてサンプルＳａの主軸方位φを求めることができる。すなわち、この位相シフト法では、図３中に示すように、１対の偏光子１２と検光子１３を一緒に回転させて上記（５）式中のシフト量θを与えることにより、主軸方位φが次の（６）式で計算できる。
【００５２】
【数１７】

【００５３】
この（６）式において、Ｉ_１、Ｉ_２、Ｉ_３、及びＩ_４は、偏光子１２と検光子１３を同時に２２．５度ずつ回転させたときのシフト量θがそれぞれ０度、２２．５度、４５度、及び６７．５度の位置における光強度を示す。
【００５４】
なお、上記の主軸方位φの計測・解析には、位相シフト法を用いた場合を例示してあるが、偏光子と検光子を回転することによって得られる光強度の変化（余弦波状に変化する）の初期位相が得られれば、どの様な手法（例えば、ＦＦＴ）を使っても構わない。
【００５５】
従って、上述した本発明の基本測定原理によれば、従来例では測定できなかったサンプルＳａの波長依存性を考慮した複屈折δ_ｎ、すなわち複屈折位相差Δについて、前述した通り、フーリエ解析により得られるスペクトルの「周波数情報」から高次複屈折の次数を含めた絶対値を、また「位相情報」から複屈折δ_ｎの波長依存性を示す相対値をそれぞれ求めることができる。さらに、サンプルＳａの主軸方位φを例えば位相シフト法を用いて求めることができる。
【００５６】
以上の例は、本発明の基本測定原理を点計測に適用した場合であるが、次に２次元計測に適用した例を説明する。
【００５７】
図４は、２次元計測用の複屈折測定装置２の構成例を示す。この例では、複屈折測定装置２は、ハロゲンランプ（白色光源）２０及びその出射系（光ファイバケーブル２１ａ、コリメータレンズ２１ｂ）と、そのハロゲンランプ２０から出射される白色光の光路上に配置される光学系、すなわちＡＯＴＦ（Ａｃｏｕｓｔｏ−Ｏｐｔｉｃ Ｔｕｎａｂｌｅ Ｆｉｌｔｅｒ：音響光学チューナブルフィルタ（音響光学素子））２２、ビームエキスパンダ（レンズ系）２３、サンプルＳａを挟む１対の偏光子２４及び検光子２５、集束光学系（レンズ系）２６、及びＣＣＤカメラ２７と、このＣＣＤカメラ２７の出力側に接続され、本発明の測定原理に基づく解析アルゴリズムを実行する解析及び制御装置として用いるＰＣ２８と、このＰＣ２８からの指令を受けてＡＯＴＦ２２の動作を制御するＡＯＴＦコントローラ２９とを備えている。
【００５８】
この内、ＡＯＴＦ２２は、ＡＯＴＦコントローラ２９からの電気的な制御により、入射される白色光のバンド帯域の中心波長を変化させることにより、特定の波長を取り出すバンドパスフィルタとして機能する。
【００５９】
上記の構成によれば、まず、ハロゲンランプ２０から出射される白色光が光ファイバケーブル２１ａを通りコリメータレンズ２１ｂからＡＯＴＦ２２に照射される。この照射光は、ＡＯＴＦ２２により特定の波長λ（波数ｋ）をもつ光として出射され、その出射光がレンズ系２３でコリメートされ、サンプルＳａを挟む方位４５度の１対の偏光子２４及び検光子２５に入射される。そして、この検光子２５からの出射光は、サンプルＳａのもつ複屈折の情報を担う光として、レンズ系２６を透過した後、ＣＣＤカメラ２７により計測画像として撮り込まれ、ＰＣ２８に送られる。
【００６０】
図５は、上記で取り込まれる計測画像の例を示す。この例に示すように、計測画像は、例えば１２８枚の画像（画素数の例：２５６（縦方向）×５１２（横方向））から構成される。この各画像は、波長λが４５０〜６１０［ｎｍ］の範囲内で波数ｋの値が順次変化して異なるようにＡＯＴＦ２２で制御された出射光による計測画像にそれぞれ対応するものである（図中の例ではｋ＝ｋ_１、ｋ_２、…、ｋ_ｎ：ｎ＝１２８）。このときのＡＯＴＦ２２の制御は、ＰＣ２８からの指令によりＡＯＴＦコントローラ２９を介して行われる。
【００６１】
なお、取り込む画像は、この例の１２８枚に限らず、その後に行われるフーリエ解析を効率良く利用できるものであれば、いずれの枚数でもよい。また、画像を取り込む枚数を増やす程、高次の複屈折が測定できるため、その点も考慮に入れて画像枚数を決めることが望ましい。
【００６２】
図６は、上記のように取り込まれる計測画像を元にＰＣ２８の処理で実行される２次元解析の手順を説明するものである。
【００６３】
まず、図６中（上段）に示すように、上記で得られた例えば１２８枚の波数ｋ（ｋ＝ｋ_１、ｋ_２、…、ｋ_ｎ：ｎ＝１２８）毎の計測画像（画素数の例：２５６（縦方向）×５１２（横方向））は、それぞれ同一座標位置の画素Ｐ_ｃａｌ毎に、波数ｋ（ｋ_１、ｋ_２、…、ｋ_ｎ：ｎ＝１２８）に対する光強度Ｉ_（λ）の変化を表す光強度分布（横軸：波数ｋ、縦軸：光強度Ｉ_（λ））のデータとして変換される。
【００６４】
ここで、各画素毎に得られる各波数ｋに対する光強度Ｉ_（λ）は、前述の（１）式に従って変化するため、これから後の処理は、各画素毎に前述の点計測の場合と同様のフーリエ変換及びその後の解析アルゴリズムを用いることが出来る。具体的には、各画素毎に変換された光強度分布のデータに適当な窓関数を掛けてフーリエ変換を行い、これで得られたスペクトルをゼロ次にシフトしてフーリエ逆変換を行う。
【００６５】
このフーリエ解析により、図６中（中段左側）に示すように、計測画像の画素毎に前述と同様の「周波数情報」と「位相情報」が得られる（（４）式参照）。ここでの「周波数情報」の計算に際しては、スペクトルデータを補間し、キャリア周波数を求め、また、「位相情報」の計算に際しては、ＦＦＴによるフーリエ逆変換で得られるデータ列中に２πを越える部分が生じた場合にはアンラッピング法（後述参照）を用いて、連続した位相となるように修正する。
【００６６】
次いで、以上の波形解析で求まる「周波数情報」と「位相情報」を元に、図６中（中段右側）に示すように、前述した（４）式に従って波長依存性を考慮した複屈折、すなわち波数ｋに対する複屈折位相差Δの分布が求まる。
【００６７】
以上の一連の解析処理は、計測画像上の全画素で実行され、これで得られた波数ｋに対する複屈折位相差Δの分布データが一定の波長λ（λ_１、λ_２、…、λ_ｎ：ｎ＝１２８）毎の複数画像に変換され、図６中（下段）に示すように、波長λ毎の複屈折の２次元分布を示す画像が得られる。なお、サンプルＳａの主軸方位φについては、上記と同様に位相シフト法やＦＦＴ等の方法を用いて計測することができる。
【００６８】
ここで、上記で計測される複屈折の２次元分布の実測例を説明する。この実測例で測定対象としたサンプル（被測定試料）Ｓａは、ポリマーフィルム（位相フィルム）と水晶板の２試料である。
【００６９】
（ポリマーフィルムの計測結果）
まず、ポリマーフィルムの計測結果を図７〜図１０に基づいて説明する。この例では、被測定試料としてアクリル基板上に階段状に積層させたポリマーフィルムを用いて、前述した波長依存性を考慮した２次元複屈折分布を計測している。
【００７０】
図７（ａ）は、この計測で使用されたポリマーフィルムの外観（写真）、図７（ｂ）は、図７（ａ）中のＸ−Ｘ’線に沿ったポリマーフィルムの断面、図７（ｃ）は、この計測で撮影されたポリマーフィルムの原画像（撮影範囲：２８（縦）［ｍｍ］×２８（横）［ｍｍ］、画素数：１２８×１２８）をそれぞれ示す。図７（ｂ）に示すように、ポリマーフィルムの１枚当たりの厚さは６０［μｍ］で、その複屈折位相差Δは、波長５５０［ｎｍ］のときに２π［ｒａｄ］である。また、図７（ｃ）に示す原画像では、ポリマーフィルムの内、フィルム枚数が１１枚、１０枚、及び９枚の各積層部分（１１層、１０層、及び９層）の各境界位置が分かる部分が図中の左側から右側に順に撮影されている。
【００７１】
図８は、上記のポリマーフィルムに対し、波長λ＝４６０、５００、５３２、５５０、及び６０８［ｎｍ］の各条件で計測及び解析された波長λ毎の複屈折分布を表す画像を示す。この複屈折分布を示す複屈折位相差Δの大きさは、Δ＝５０〜１００［ｒａｄ］の範囲内で変化しており、その分布の様子が画像を見て容易に分かるように、例えばグレイスケール（例えば、Δ＝５０〜１００が黒色〜白色に変化）を用いて表示しているが、これに限らず、カラースケール（例えば、Δ＝５０〜１００が紫色〜青色〜緑色〜黄緑色〜黄色〜赤色に順次変化）を用いてカラー表示してもよい。
【００７２】
図８に示すように、波長λの異なる各画像のどの画像を見ても、ポリマーフィルム上でフィルム枚数が１１層、１０層、及び９層と変化するに従って（各画像中の左右方向）、複屈折位相差Δがその境界部で変化していること、また、波長λの異なる各画像を比較すると、波長λが長くなるにつれて、複屈折位相差Δが小さくなっていることが、それぞれ明瞭に確認された。
【００７３】
図９は、波長λ＝５５０［ｎｍ］の条件で計測及び解析された複屈折分布を表す画像上のＡ−Ａ’線（図７（ｃ）参照）に沿った断面位置に対するポリマーフィルムの複屈折位相差Δの変化を示す。図９に示す結果では、複屈折位相差Δは、Ａ−Ａ’線断面位置上におけるポリマーフィルム上のフィルム枚数が１１層から１０層に変化する位置と１０層から９層に変化する位置の２個所で、それぞれ約２π［ｒａｄ］の段差が明瞭に確認された。この結果は、本発明の基本測定原理に基づく手法により定量的な複屈折計測が行われていることを実証するものである。これは、従来例の単色光を用いた偏光計測では、計測できなかったものである。
【００７４】
図１０は、波長λ＝５３２［ｎｍ］の条件で計測及び解析されたポリマーフィルムの主軸方位φの２次元分布を示す画像で、図中の例では主軸方位φの方向をグレイスケール（φ＝−３０［度］〜３０［度］）による画像表示及びその画像上で格子状に配列された測定点でのベクトルの向きでそれぞれ示している。図１０に示す結果では、ポリマーフィルムの主軸方位φは、どの位置でもほぼ１方向に揃っており、約０度を示していることが確認された。
【００７５】
（水晶板の計測結果）
次に、水晶板の計測結果を図１０〜図１２に基づいて説明する。この例では、被測定対象としてくさび型にカットされた水晶板を用いて、その２次元複屈折位相差分布を計測している。
【００７６】
図１１（ａ）は、この計測で使用された水晶板の外観（写真）、図１１（ｂ）は、Ｘ−Ｘ’線に沿った水晶板の断面、図１１（ｃ）は、この計測で撮影された原画像をそれぞれ示す。図１１（ｂ）に示すように、水晶板はその厚さが連続して変化しており、図１１（ｃ）に示す原画像上では、図中の上側（Ａ−Ａ’線のＡ側）が厚い部分に相当し、そこから下側（Ａ−Ａ’線のＡ’側）に向って順次薄くなっている。
【００７７】
図１２は、上記と同様の波長λ（λ＝４６０、５００、５３２、５５０、及び６０８［ｎｍ］）の条件で計測及び解析された波長λ毎の２次元複屈折分布を表す画像を示す。図１２に示すように、解析された水晶板の複屈折分布を示す複屈折位相差Δの大きさは、大きいところで２５０［ｒａｄ］、小さいところで１００［ｒａｄ］という結果となり、どの波長λの画像も水晶板の厚さ方向に複屈折位相差Δが変化している様子が良く確認された。また、波長λの異なる各画像を比較すると、上記と同様に、波長λが長くなるにつれて、複屈折位相差Δが小さくなっていることが確認された（なお、図１２中で観察される画像中のムラは、水晶板の製造時に生じた研磨ムラであると考えられる）。
【００７８】
図１３は、波長λ＝５６７［ｎｍ］の条件で計測及び解析された２次元複屈折分布を表す画像上のＡ−Ａ’線（図７（ｃ）参照）に沿った断面位置に対する水晶板の複屈折位相差Δの変化を示す。図１３に示す結果では、複屈折位相差Δが直線的に変化している様子が示され、信頼性の高い測定値を表していることが確認された。
【００７９】
図１４は、波長λ＝５３２［ｎｍ］の条件で計測及び解析された水晶板の主軸方位φの２次元複屈折分布を示す画像で、上記と同様に、主軸方位φの方向をグレイスケール及びベクトルでそれぞれ示している。図１４に示す結果では、水晶板の主軸方位φは、各測定点でのベクトルの向きで見ると、ほぼ同じ方向を向いているが、グレイスケールで見ると、画像は均一となっておらず、縞状の分布が観察される。本来、水晶の結晶の方位はこのような縞状の分布を示すことはないため、これは測定誤差と考えられる。この誤差発生の原因は、複屈折位相差Δがπ／２、３π／２、及び５π／２と変化しているところで、前述した（６）式から位相シフト法が使用できない特異点が存在しているためと考えられる。
【００８０】
次に、上記のポリマーフィルム及び水晶板で計測及び解析された各複屈折位相差Δ（複屈折δ_ｎ）の波長依存性における計測結果を説明する。
【００８１】
図１５（ａ）は、波長λに対する複屈折位相差Δの変化（縦軸：複屈折位相差Δ［ｒａｄ］、横軸：波長λ［ｎｍ］）を、図１５（ｂ）は、波長λに対する複屈折δ_ｎの変化（縦軸：複屈折位相差Δ［ｒａｄ］、横軸：波長λ［ｎｍ］）をそれぞれ示す。図１５（ａ）及び（ｂ）において、実線で示す曲線はポリマーフィルムの測定結果、点線で示す曲線は水晶板の測定結果、三角印（△）で示す点は公知文献（理科年表）から計算で求めた複屈折値、ひし形印（◇）示す点は所定のメーカから公表されているカタログ値（図１５（ａ）のみ）をそれぞれ示す。
【００８２】
図１５（ａ）及び（ｂ）に示すポリマーフィルム及び水晶板の各測定結果は、いずれも、理科年表の複屈折値及びメーカのカタログ値とほぼ一致する傾向が確認され、これにより、本発明による複屈折計測の手法を用いた波長依存性の計測の有効性が確認された。なお、図１５（ａ）に示す結果では、ポリマーフィルムの測定結果による複屈折位相差がカタログ値よりも若干大きめの傾向を示しているが、この原因はサンプルを光学系にセットするときに光軸に対し多少傾いていた為であると考えられる。この場合でも、ポリマーフィルムの測定結果及びカタログ値における複屈折位相差の波長依存性の傾向は、ほぼ同じとなっている。
【００８３】
従って、本実施の形態による複屈折計測によれば、点計測に限らず２次元計測でも、従来例では測定できなかった複屈折の波長依存性を含めた測定を精度良く実現することができる。
【００８４】
なお、上記の波長依存性を考慮した２次元複屈折計測では、白色光の中から特定の波長を取り出す方法として、ＡＯＴＦ（Ａｃｏｕｓｔｏ−Ｏｐｔｉｃ Ｔｕｎａｂｌｅ Ｆｉｌｔｅｒ：音響光学チューナブルフィルタ）を用いた例を説明しているが、本発明はこれに限らず、例えば、干渉フィルタを複数枚並べて順次提示する方法、複屈折性のバンドパスフィルタ（これはフィルタを光軸に対して傾斜させることで、透過光の中心波長を変化させることが出来る）等であってもよい。
【００８５】
また、上記の波数に対し余弦状に変化する分光データ（光強度分布）のフーリエ解析で得られるスペクトルから「位相情報」及び「周波数情報」を求めるための処理方法については、図２中（中段及び下段）に示す手法に限らず、その他、種々の手法が適用できる。以下、この各手法の適用例を図１６〜図１９に基づいて説明する。
【００８６】
図１６は、前述した（４）式の計算例を含む解析手順の概要を示す。図１６に示す解析手順では、前述した本発明の基本測定原理に従って、分光データ（光強度分布データ）を取得し（ステップＳｔ１）、この分光データに適用な窓関数を掛け（ステップＳｔ２）、フーリエ解析によりスペクトルを求め（ステップＳｔ３）、このスペクトルから「周波数情報」と「位相情報」を求め（ステップＳｔ４）、これで得られた「位相情報」から複屈折の波長依存性を示す相対値を、また「周波数情報」から高次複屈折の次数を含めた絶対値をそれぞれ求めるものである（ステップＳｔ５）。
【００８７】
まず、ステップＳｔ１にて、取得される分光データは、図１６中（上段）に示すように、フーリエ変換により波数ｋに対し余弦状に変化する光強度Ｉ_（λ）の式（前述の（１）式）で表される。この式は、複屈折位相差Δが波長依存性をもつΔ_（λ）と考えると、図１６中の（１）´式に置き換えることができる。そして、この複屈折位相差Δ又はΔ_（λ）は、前述で説明した通り、（２）式から（３）式に展開して「周波数情報」と「位相情報」の計算から求めることができる。
【００８８】
そのため、ステップＳｔ２にて、光強度Ｉ_（λ）の式で表される分光データに窓関数を掛ける演算を行う。この演算式は、例えば次の式（７）式で表される。
【００８９】
【数１８】

この（７）式において、Ｉ_ω（ｋ）は窓関数をかけた光強度Ｉ_（λ）、Ｉ_０は窓関数を掛ける前の光強度Ｉ_（λ）、Ａ−Ｂ・ｃｏｓ（２πｋ／ｋ_０）は窓関数、Ａ、Ｂは定数（任意）、ｋ_０はデータサンプリング数をそれぞれ示す。
【００９０】
この処理によって、図１６中（中段）に示すように、光強度Ｉ_（λ）分布のスペクトルの中心が測定波数領域の中心と一致するようになる。ここで、Ａ、Ｂの値の仮定は任意であるが、スペクトル解析による周波数ｆのスペクトル上のｆ_ｓの位置を決定するためのスペクトル強度に相関があるため、実際にＡ、Ｂを決める際は、この点を考慮する必要がある。
【００９１】
次いで、ステップＳｔ３にて、上記で窓関数をかけた光強度Ｉ_（λ）からフーリエ解析により周波数ｆのスペクトルを求める。この周波数ｆのスペクトルは、図１６中（下段）に示すように、周波数ｆ＝０（ゼロ次）からシフトした位置にピークをもっている。
【００９２】
そこで、ステップＳｔ４にて、上記の周波数ｆのスペクトルから「周波数情報」と「位相情報」を求めるが、このときの処理方法は、１）スペクトルをゼロ（０）次にシフト（スペクトルのピークであるｆ_ｐの位置をｆ＝０の位置にシフト）して逆変換を行う方法（前述の基本測定原理で説明する方法で、図２及び（４）式参照）、２）スペクトルを０次にシフトしないでフーリエ逆変換を行う方法（後述の図１７参照）、３）スペクトルをｆ_ｓ（ｆ_１）分だけシフト（スペクトルのｆ_ｓの位置をｆ＝０の位置にシフト）してフーリエ逆変換を行う方法（後述の図１８参照）、４）スペクトルのｆ_ｐをそのまま用いてフーリエ逆変換を行う方法（後述の図１９参照）等、いずれの方法でも適用可能である。
【００９３】
図１７は、上記ステップＳｔ４における、２）スペクトルを０次にシフトしないでフーリエ逆変換を行う方法を説明するものである。この方法によれば、上記で得られる周波数ｆのスペクトル（図中の最上段参照）に対し０次にシフトしないでフーリエ逆変換を行い、そのフーリエ逆変換後の波数ｋ（１／λ）に対する位相φ_（ｋ）のデータ（図中の上から二段目参照）に対しアンラッピングを施し、そのアンラッピング後の波数ｋに対する位相φ’_（ｋ）のデータ（図中の上から三段目参照）に対しｆ_ｓ分のオフセットβを加える（図中の下から二段目参照）。従って、この方法で得られる複屈折位相差Δ（ｋ）は、次の（８）式で表される。
【００９４】
【数１９】

【００９５】
この（８）式では、前述した１）スペクトルを０次にシフトする方法に比べ、得られる式が簡単になる。
【００９６】
図１８は、上記ステップＳｔ４における、３）スペクトルをｆ_ｓ分だけシフト（スペクトルのｆ_ｓの位置をｆ＝０の位置にシフト）してフーリエ逆変換を行う方法を説明するものである。この方法によれば、上記で得られる周波数ｆのスペクトルに対し、図中の最上段に示すように、ｆ_ｓ分シフトしてフーリエ逆変換を行い、そのフーリエ逆変換後の波数ｋ（１／λ）に対する位相φ_（ｋ）のデータ（図中の上から二段目参照）に対しアンラッピングを施し、そのアンラッピング後の波数ｋに対する位相φ’_（ｋ）のデータ（図中の上から三段目参照）に対しｆ_ｓ分のオフセットβを加える（図中の下から二段目参照）。従って、この方法で得られる複屈折位相差Δ（ｋ）は、次の（９）式で表される。
【００９７】
【数２０】

【００９８】
この（９）式でも、（８）式と同様に、前述した１）スペクトルを０次にシフトする方法に比べ、得られる式が簡単になる。
【００９９】
図１９は、ステップＳｔ４における、４）スペクトルのｆ_ｐをそのまま用いてフーリエ逆変換を行う方法を説明するものである。この方法によれば、上記で得られる周波数ｆのスペクトル（図中の最上段参照）に対しそのｆ_ｐを用いてフーリエ逆変換を行い、そのフーリエ逆変換後の波数ｋ（１／λ）に対する位相φ_（ｋ）のデータ（図中の上から二段目参照）に対しアンラッピングを施し、そのアンラッピング後の波数ｋに対する位相φ’_（ｋ）のデータ（図中の上から三段目参照）に対しｆ_ｐ分のオフセットを加える（図中の下から二段目参照）。従って、この方法で得られる複屈折位相差Δ（ｋ）は、次の（１０）式で表される。
【０１００】
【数２１】

【０１０１】
この（１０）式でも、（８）式及び（９）式と同様に、前述した１）スペクトルを０次にシフトする方法に比べ、得られる式が簡単になる。
【０１０２】
ここで、図１６に戻り、ステップＳｔ５にて、以上の処理で得られた位相情報から、複屈折の波長依存性を示す相対値が、また周波数情報から、高次複屈折の次数を含めた絶対値が求められる。
【０１０３】
なお、上記の例において、振幅スペクトル内のスペクトル分布の頂点の周波数ｆ_ｐとそのスペクトル分布の開始点の周波数ｆ_ｓを精度良く求める為には、次のような処理を行うことが望ましい。通常のフーリエ解析で得られるスペクトル分布は、波数ｋに対する光強度の測定点数に応じて離散的に得られる。例えば、図２の中段左に示すものや、図６の中段に示す周波数情報に示されるように、得られるデータはとびとびの値になる。ｆ_ｐとｆ_ｓとを精度良く求めるためには、このスペクトル分布の形状をフィッティング等の処理を用いて、離散データを内挿する必要がある。このために利用される手法は，例えば、１）分布形状をガウス分布や二項分布などの関数に近似する方法、２）部分的な領域を取り出し、隣り合う数点のデータを元にして、その領域内を多項式近似し、内挿領域を逐次移動し全体の分布形状を近似する方法、等を例示できる。
【０１０４】
なお、上記の例では、解析装置としてＰＣを例示したが、本発明はこれに限らず、本発明の測定原理に基づく解析アルゴリズムを実行するコンピュータの機能を有するものであれば、例えばネットワーク接続された専用ワークステーション等、いずれの装置（マシン、モジュール、ユニット等）でも適用可能である。
【０１０５】
なお、本発明は、代表的に例示した上述の実施形態及び適用例に限定されるものではなく、当業者であれば、特許請求の範囲の記載内容に基づき、その要旨を逸脱しない範囲内で種々の態様に変形、変更することができ、それらも本発明の権利範囲に属するものである。
【０１０６】
【発明の効果】
以上説明したように、本発明によれば、高次複屈折に加え、複屈折の波長依存性を考慮した高精度の複屈折計測を実現できる。この複屈折計測では、点計測のみならず、２次元計測に適用でき、より拡張性及び実用度の高いものとなっている。
【図面の簡単な説明】
【図１】本発明の実施形態に係る波長依存性を考慮した複屈折測定装置及び方法の基本測定原理の前提部分を説明する図。
【図２】本発明の実施形態に係る波長依存性を考慮した複屈折測定装置及び方法の基本測定原理の骨子部分を説明する図。
【図３】位相シフト法を用いた主軸方位計測を説明する図。
【図４】２次元計測に適用した場合の複屈折測定装置の構成例を示す図。
【図５】図４に示す複屈折測定装置で取り込まれる画像を説明する図。
【図６】２次元計測に適用した場合の解析手順を説明する図。
【図７】複屈折計測で実測されたポリマーフィルムを示す図で、（ａ）は外観図（写真）、（ｂ）は（ａ）中のＸ−Ｘ’線に沿った断面図、（ｃ）は原画像を示す図。
【図８】ポリマーフィルム（位相フィルム）の複屈折位相差の解析結果を示す図。
【図９】図７（ｃ）中のＡ−Ａ’線に沿って計測された複屈折位相差を示す図。
【図１０】ポリマーフィルムの主軸方位の解析結果を示す図。
【図１１】複屈折計測で実測された水晶板を示す図で、（ａ）は外観図（写真）、（ｂ）は（ａ）中のＸ−Ｘ’線に沿った断面図、（ｃ）は原画像を示す図。
【図１２】水晶板の複屈折位相差の解析結果を示す図。
【図１３】図１１（ｃ）中のＡ−Ａ’線に沿って計測された複屈折位相差を示す図。
【図１４】水晶板の主軸方位の解析結果を示す図。
【図１５】ポリマーフィルム及び水晶板の計測値の精度を外部資料（理科年表、カタログ値）と比較して説明する図で、（ａ）は波長に対する複屈折位相差の変化を示すグラフ、（ｂ）は波長に対する複屈折の変化を示すグラフ。
【図１６】本発明の基本測定原理に基づく解析手順を説明する図。
【図１７】図１６に示す解析手順の内、スペクトルをゼロ次にシフトしないでフーリエ逆変換を行う方法を説明する図。
【図１８】図１６に示す解析手順の内、スペクトルをｆｓ分シフトしてフーリエ逆変換を行う方法を説明する図。
【図１９】図１６に示す解析手順の内、ｆｐを用いてフーリエ逆変換を行う方法を説明する図。
【符号の説明】
１ 複屈折測定装置（点計測用）
２ 複屈折測定装置（２次元計測用）
１０ 白色光源
１１ａ 光ファイバケーブル
１１ｂ コリメータレンズ
１２ 偏光子
１３ 検光子
１４ 分光器
１４ａ 回折格子
１４ｂ リニアＣＣＤ
１５ａ 集光レンズ
１５ｂ 光ファイバケーブル
１６ ＰＣ（パーソナルコンピュータ）
２０ ハロゲンランプ
２１ａ 光ファイバケーブル
２１ｂ コリメータレンズ
２２ 音響光学チューナブルフィルタ（ＡＯＴＦ）
２３ ビームエキスパンダ（レンズ系）
２４ 偏光子
２５ 検光子
２６ 集束光学系（レンズ系）
２７ ＣＣＤカメラ（２次元撮像素子）
２８ ＰＣ（パーソナルコンピュータ）
２９ ＡＯＴＦコントローラ
Ｓａ サンプル（被測定試料）[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a birefringence measuring apparatus and method considering wavelength dependency.
[0002]
[Prior art]
With the development of optoelectronics in recent years, in the engineering field, demands for injection molded products, optical discs, thin film products, optical elements using crystals, polymer films, liquid crystals, and the like are rapidly increasing. Accordingly, birefringence measurement is attracting attention as one of quantitative evaluation methods for quantitatively evaluating the quality of such products.
[0003]
In particular, polymer materials and crystals are known to have very strong wavelength dependence of birefringence and high-order birefringence. Therefore, such birefringence wavelength dependence and higher-order birefringence are known. There is a request for measurement. In material evaluation in the engineering field, birefringence measurement considering wavelength dependence is desired.
[0004]
[Problems to be solved by the invention]
However, the conventional polarization measurement method using monochromatic light cannot measure high-order birefringence due to the fact that the phase is folded at 2π [rad] as well as the wavelength dependence of birefringence. there were.
[0005]
As an example of a related technology, spectroscopic polarimetry using white light has been proposed. Especially in the field of spectroscopic ellipsometry, Stokes parameters are obtained using a channel spectrum consisting of three sinusoidal components. (For example, “K. Oka et al: Opt. Lett. 24, 21, pp 1475 (1999)”). This research is limited to point measurement, cannot be applied to two-dimensional measurement, and has the birefringence distribution and the wavelength dependence of birefringence (hereinafter sometimes referred to as “birefringence dispersion” if necessary). It cannot be used for simultaneous measurement or measurement of higher-order birefringence.
[0006]
Separately from this, a method of birefringence measurement by the inventors of the present application (Japanese Patent Laid-Open No. 2001-141602) has been proposed in which higher-order birefringence is quantitatively evaluated using polarized light spectral interference. In this birefringence measurement method, focusing on the fact that the light intensity changes in a cosine shape with respect to the wave number due to the influence of the birefringence of the sample (measurement object), a high-resolution maximum entropy method (MEM: Maximum Entropy Method). By analyzing the frequency using and reading the center frequency of the spectrum obtained by this, it is possible to obtain higher-order birefringence larger than one wavelength of the optical signal used for birefringence measurement.
[0007]
However, this method can certainly measure higher-order birefringence using spectroscopic measurement and frequency analysis, but is not particularly aware of the wavelength dependence of birefringence and therefore cannot be used for the measurement.
[0008]
The present invention has been made against the background of such a conventional situation, and a main object thereof is to realize birefringence measurement in consideration of wavelength dependence of birefringence in addition to high-order birefringence.
[0009]
In addition to the main object described above, the present invention has a further object to enable not only point measurement but also birefringence measurement with high expansibility and practicality applicable to two-dimensional measurement.
[0010]
[Means for Solving the Problems]
In the present invention, in order to achieve the above object, the wavelength of the birefringence is further increased while utilizing the advantages of the high-order birefringence measurement method using the spectroscopic measurement and the frequency analysis method previously proposed by the present inventors. We propose a birefringence measurement method that takes into account the dependence.
[0011]
In this method, a formula for calculating the birefringence phase difference Δ proposed in the above-described high-order birefringence measurement method (Δ = δn · d · k, δn is birefringence, d is the thickness of the sample, and k is the wave number. ) In consideration of the wavelength dependence of the birefringence δn, “frequency information” (order term corresponding to the order of higher-order birefringence) and “phase information” (dispersion term including birefringence wavelength dependence) In addition to the absolute value of high-order birefringence, the “frequency information” and “phase information” are calculated and calculated using the Fast Fourier Transform (FFT). This enables birefringence measurement in which a relative value indicating wavelength dependency is measured (see “Basic measurement principle of the present invention” described later).
[0012]
The birefringence measuring apparatus considering wavelength dependency according to the present invention includes a birefringence measuring optical system that acquires an optical signal that bears information on the birefringence of a measurement target, and the optical signal acquired by the birefringence measuring optical system. The frequency component including the order of higher-order birefringence and the phase component responsible for wavelength dependency are analyzed from the waveform data indicating the light intensity distribution of the light, and the birefringence indicating the wavelength dependency is added to the higher-order birefringence from the analysis data. Refraction Divided into frequency component terms and dispersion terms And an analyzing device to be obtained.
[0013]
As one aspect of the present invention, the birefringence measurement optical system includes a white light source, a pair of polarizers and an analyzer disposed at a position sandwiching the measurement target on an optical path of an optical signal from the white light source, It comprises a point measurement optical system having a spectroscope that splits an optical signal carrying information relating to the birefringence of the measurement object emitted from the analyzer for each wavelength and outputs it to the analysis device.
[0014]
As another aspect of the present invention, the birefringence measuring optical system includes a white light source, an acoustooptic element that variably extracts a specific wavelength component from an optical signal from the white light source, and light extracted by the acoustooptic element. A pair of polarizers and analyzers arranged at positions sandwiching the measurement object on the optical path of the signal, and an optical device that takes information about the birefringence of the measurement object emitted from the analyzer and captures the optical signal And a two-dimensional measurement optical system having an image pickup device that outputs the image.
[0015]
As a preferred example of the present invention, the analysis device sets the wave number of the optical signal to k, and sets the birefringence, birefringence phase difference, thickness, and principal axis direction of the measurement target to δ, respectively. _n , Δ (k), d, and φ, and the birefringence δ _n The frequency component term, dispersion term, and phase information of _n0 , Δ _λ , Φ _(K) Said, Includes wavelength dependence Birefringence phase difference Δ (k)
[Formula 6]

With waveform analysis to satisfy As the sum of frequency information and phase information The required data processing means is provided.
[0016]
As a preferred example of the present invention, the data processing means, as a preferred example of the present invention, the frequency of the peak of the spectrum distribution in the amplitude spectrum of the frequency obtained by Fourier analysis of the waveform data indicating the light intensity distribution of the optical signal, and the spectrum distribution Set the starting point frequency to f _p And f _s And the phase obtained by Fourier analysis of the waveform data indicating the light intensity distribution of the optical signal, the minimum value and the maximum value of the wave number k are φ _(K) , K _min , K _max When said Considering wavelength dependence Birefringence phase difference Δ (k)
[Expression 7]

This is a means for obtaining by waveform analysis so as to satisfy the relationship.
[0017]
As a preferred example of the present invention, the data processing means sets the frequency of the starting point of the spectrum distribution in the amplitude spectrum of the frequency obtained by Fourier analysis of the waveform data indicating the light intensity distribution of the optical signal as f. _S And the phase obtained by Fourier analysis of the waveform data indicating the light intensity distribution of the optical signal, the minimum value and the maximum value of the wave number k are φ ′ _(K) , K _min , K _max When said Considering wavelength dependence Birefringence phase difference Δ (k)
[Equation 8]

This is a means for obtaining by waveform analysis so as to satisfy the relationship.
[0018]
As a preferred example of the present invention, the data processing means sets the frequency of the starting point of the spectrum distribution in the amplitude spectrum of the frequency obtained by Fourier analysis of the waveform data indicating the light intensity distribution of the optical signal as f. _S And the phase obtained by Fourier analysis of the waveform data indicating the light intensity distribution of the optical signal, the minimum value and the maximum value of the wave number k are φ ′, respectively. _(K) , K _min , K _max Where the birefringence phase difference Δ (k) is
[Equation 9]

This is a means for obtaining by waveform analysis so as to satisfy the relationship.
[0019]
As a preferred example of the present invention, the data processing means sets the frequency of the peak of the spectrum distribution in the amplitude spectrum of the frequency obtained by Fourier analysis of the waveform data indicating the light intensity distribution of the optical signal as f. _P And the phase obtained by Fourier analysis of the waveform data indicating the light intensity distribution of the optical signal, the minimum value and the maximum value of the wave number k are φ ′, respectively. _(K) , K _min , K _max Where the birefringence phase difference Δ (k) is
[Expression 10]

This is a means for obtaining by waveform analysis so as to satisfy the relationship.
[0020]
The birefringence measurement method considering wavelength dependence according to the present invention is a frequency component including the order of high-order birefringence and wavelength dependence from waveform data indicating the light intensity distribution of an optical signal carrying information on the birefringence of the measurement target. In addition to the higher-order birefringence, the birefringence showing the wavelength dependence is analyzed from the analysis data. Dividing into carrier component term and dispersion term It is characterized by seeking.
[0021]
DETAILED DESCRIPTION OF THE INVENTION
DESCRIPTION OF EMBODIMENTS Hereinafter, embodiments of a birefringence measuring apparatus and method considering wavelength dependency according to the present invention will be specifically described with reference to the accompanying drawings.
[0022]
First, the basic measurement principle of birefringence measurement in consideration of wavelength dependency in the present invention will be described based on FIGS. 1 and 2. Here, an application example of point measurement will be described in detail, but this basic measurement principle can be extended to two-dimensional measurement as described later.
[0023]
The birefringence measuring apparatus 1 for point measurement shown in FIG. 1 includes a white light source 10 using a white lamp and its emission system (optical fiber cable 11a, collimator lens 11b), and white light emitted from the white light source 10. On the optical path, a pair of polarizers 12 and analyzers 13 arranged in parallel at positions facing each other across the sample Sa (measurement sample), and a spectroscope 14 (diffraction grating ( Or prism) 14a, linear CCD (light receiving element array) 14b) and its incident system (condensing lens 15a, optical fiber cable 15b), and an analysis algorithm based on the measurement principle of the present invention, connected to the output side of the spectrometer 14. PC (personal computer) 16 used as an analysis apparatus (computer) for executing the above.
[0024]
According to this configuration, the light emitted from the white light source 10 sequentially passes through the polarizer 12 having the azimuth of 45 degrees, the sample Sa, and the analyzer 13 having the azimuth of 45 degrees through the output systems 11a and 11b, and the sample Sa. Is transmitted to the spectroscope 14 through its incident systems 15a and 15b. This optical signal is transmitted through the diffraction grating 14a inside the spectroscope 14 by the linear CCD 14b, and the light intensity I at each wavelength λ. _(Λ) And sent to the PC 16.
[0025]
Light intensity I of the transmitted light obtained above _(Λ) Is represented by the following expression (1) as shown in FIG.
[0026]
[Expression 11]

In this formula (1), I _DC Is the bias component (DC component), S _(Λ) Is the transmission characteristic of the system (system dependence coefficient, wavelength transmittance characteristic), φ is the difference in principal axis orientation between the polarizer 12 and the sample Sa, and Δ is the birefringence phase difference of the sample Sa.
[0027]
Among these, the birefringence phase difference Δ of the sample Sa is expressed by the following equation (2) as shown in FIG. 1 (middle stage).
[0028]
[Expression 12]

In this equation (2), λ is the wavelength, δ _n Represents the birefringence of the sample Sa, d represents the thickness of the sample Sa, and k represents the wave number (k = 1 / λ).
[0029]
Since the birefringence phase difference Δ of the sample Sa can be expressed using the wave number k as in the above equation (2), the light intensity I in the above equation (1). _(Λ) Is actually measured as a waveform that changes in a cosine with respect to the wave number k as shown in FIG.
[0030]
Therefore, the light intensity I indicating the waveform distribution that changes in a cosine manner with respect to the wave number k in this way. _(Λ) On the other hand, the processing of the PC 16 performs a high resolution frequency analysis using the maximum entropy method, and reads the center frequency of the frequency spectrum obtained by this analysis, whereby the birefringence δ of the sample Sa _n Measurement of (birefringence phase difference Δ and main axis direction φ) is performed. The principle of birefringence measurement so far is the same as that proposed in Japanese Patent Laid-Open No. 2001-141602.
[0031]
In the above principle, as shown in FIG. 1, the light intensity I changes in a cosine shape with respect to the wave number k. _(Λ) However, in practice, as shown in FIG. 1 (bottom), the light intensity I is not changed. _(Λ) The period of this component slightly changes depending on the wave number k. This is because birefringence shows wavelength dependence.
[0032]
Therefore, in the present invention, in addition to the above principle, the light intensity I is considered in consideration of the wavelength dependence of birefringence exhibited by many samples Sa. _(Λ) However, focusing on the fact that the period varies depending on the wavelength λ (or wave number k), the main purpose is to realize birefringence measurement including the wavelength dependence. This will be described with reference to FIG.
[0033]
As shown in FIG. 2 (upper), first, the above equation (2) is obtained by taking into account the wavelength dependence of the birefringence phase difference Δ. _n Is the carrier component term δ _n0 And the dispersion term δ _λ Can be divided into _n = Δ _n0 + Δ _λ Substituting _n0 , Δ _λ Then, the following expression (3) is obtained.
[0034]
[Formula 13]

In this equation (3), φ _(K) Indicates phase information.
[0035]
As shown in the equation (3) and in FIG. 2 (upper stage), the birefringence phase difference Δ (k) including wavelength dependence has a phase difference of 2π, 4π, 6π,... Corresponding to the order of birefringence. "Frequency information" as the order term that changes greatly and "Phase information" as the dispersion term whose phase difference slightly changes due to the wavelength dependence of birefringence can be calculated and obtained as the sum of both. .
[0036]
Therefore, as shown in FIG. 2 (middle stage), the “frequency information” and the “phase information” are the spectral intensity signals obtained as described above, that is, the light intensity I that changes in a cosine with respect to the wave number k. _(Λ) Can be obtained using FFT (Fast Fourier Transform). Specifically, the light intensity distribution of transmitted light (light intensity I with respect to wave number k) _(Λ) (Frequency distribution) is subjected to Fourier transform by FFT, the spectrum distribution is multiplied by a predetermined window function, the spectrum is shifted to zero order, and Fourier inverse transform is performed to obtain “phase information” and Fourier transform. The “frequency information” that is the carrier frequency component removed by the above is obtained from the half-value width of the amplitude spectrum distribution or the like (see below for details).
[0037]
In the example in FIG. 2 (middle stage), “frequency information” is obtained from the spread of the amplitude spectrum obtained by Fourier analysis of the light intensity distribution of transmitted light, and “phase information” is obtained from the phase obtained by inverse Fourier transform. Is described.
[0038]
Here, in the “frequency information” shown in FIG. _p Is the center frequency of the amplitude spectrum, f _s Is f _p 1 / e of ² (F _s = F _p × 1 / e ² ) Are shown respectively. F here _s However, the half value of the spectrum may be used. In short, if the position that determines the width of the spectrum and the relationship between the frequencies are determined, which position should be selected. It doesn't matter. Further, in the “phase information” shown in FIG. _min And K _max Indicates the minimum value and the maximum value of the wave number k to be measured, respectively.
[0039]
When “frequency information” and “phase information” obtained based on the above frequency analysis are put into the above equation (3) and arranged, the following equation (4) is obtained.
[0040]
[Expression 14]

If “frequency information” and “phase information” are calculated based on the equation (4), the birefringence phase difference Δ (k) considering the wavelength dependence of the sample Sa can be obtained.
[0041]
The analysis algorithm based on the above measurement principle is a program that can be executed in advance by the processor (CPU) on the PC 16 during its operation, such as a semiconductor memory (including a portable IC card) connected to the processor, a hard disk, and a removable device. It is recorded on a recording medium such as a medium (floppy disk, magneto-optical disk (MO), CD-ROM, CD-R, CD-RW, DVD-ROM, etc.) and executed by the processor at the time of measurement.
[0042]
That is, the analysis algorithm based on the above measurement principle is executed by the program processing by the processor of the PC 16, and the birefringence phase difference Δ considering the wavelength dependence of the sample Sa is obtained according to the above equation (4).
[0043]
In the above waveform analysis, a method of shifting the spectrum to zero order is described as a processing method for obtaining “frequency information” and “phase information” from the spectrum obtained by Fourier transform. Not limited to this, various methods can be adopted as will be described later.
[0044]
In the above-described waveform analysis, FFT, which is a typical frequency analysis method, is used. However, the present invention is not limited to this, and the light intensity I that changes in a cosine shape with respect to the wave number k is used. _(Λ) Any waveform analysis method can be applied as long as it can calculate the frequency, intensity, and phase of (spectral light intensity signal).
[0045]
In addition, the above light intensity I _(Λ) (1) is a formula when a pair of polarizers 12 and an analyzer 13 are arranged so as to be “parallel Nicols”, but both 12 and 13 are “orthogonal Nicols”. In this case, the following expression (1a) is used instead of the above expression (1) (this is the same as that described in JP-A-2001-141602).
[0046]
[Expression 15]

[0047]
In the above example, a spectroscope (multichannel spectroscope) having a diffraction grating (or prism) and a linear CCD (light receiving element array) is illustrated, but the present invention is not limited to this. It may be a wavelength scanning type or wavelength selective type spectroscope having a structure in which the diffraction grating or the prism is rotated to guide the wavelengths having different diffraction angles to the exit slit one after another.
[0048]
Next, a method for measuring and analyzing the main axis direction φ of the sample S will be described with reference to FIG. In this example, the case where the phase shift method is used is illustrated.
[0049]
First, as shown in FIG. 3 (upper), in the birefringence measuring apparatus 1 described above, the pair of polarizers 12 and the analyzer 13 are set in a state of parallel Nicols (or crossed Nicols). Sample Sa is placed between them. In this state, the light intensity I of the emitted light from the analyzer 13 _(Λ) Is measured by the spectroscope 14 described above. This light intensity I _(Λ) Can be expressed by the above-described equation (1) as shown in FIG. 3 (middle), and can be expressed by the following equation (5) when expanded.
[0050]
[Expression 16]

[0051]
From this equation (5), the principal axis azimuth φ of the sample Sa can be obtained using the phase shift method. That is, in this phase shift method, as shown in FIG. 3, by rotating the pair of polarizers 12 and the analyzer 13 together to give the shift amount θ in the above equation (5), the main axis direction φ Can be calculated by the following equation (6).
[0052]
[Expression 17]

[0053]
In this equation (6), I ₁ , I ₂ , I ₃ And I ₄ Indicates the light intensities at positions where the shift amounts θ are 0 degree, 22.5 degrees, 45 degrees, and 67.5 degrees, respectively, when the polarizer 12 and the analyzer 13 are simultaneously rotated by 22.5 degrees.
[0054]
In addition, although the case where the phase shift method is used is illustrated in the measurement and analysis of the main axis azimuth, the change in light intensity obtained by rotating the polarizer and the analyzer (changes in a cosine wave shape). Any method (for example, FFT) may be used as long as the initial phase is obtained.
[0055]
Therefore, according to the basic measurement principle of the present invention described above, the birefringence δ in consideration of the wavelength dependence of the sample Sa that could not be measured in the conventional example. _n That is, with respect to the birefringence phase difference Δ, as described above, the absolute value including the order of higher-order birefringence from the “frequency information” of the spectrum obtained by Fourier analysis, and the birefringence δ from the “phase information”. _n Relative values indicating the wavelength dependence of each can be obtained. Furthermore, the principal axis direction φ of the sample Sa can be obtained by using, for example, a phase shift method.
[0056]
The above example is a case where the basic measurement principle of the present invention is applied to point measurement. Next, an example of application to two-dimensional measurement will be described.
[0057]
FIG. 4 shows a configuration example of the birefringence measuring apparatus 2 for two-dimensional measurement. In this example, the birefringence measuring apparatus 2 is disposed on the halogen lamp (white light source) 20 and its emission system (optical fiber cable 21a, collimator lens 21b) and on the optical path of white light emitted from the halogen lamp 20. An optical system, that is, an AOTF (Acousto-Optic Tunable Filter (acousto-optic tunable filter)) 22, a beam expander (lens system) 23, a pair of polarizers 24 and an analyzer 25 sandwiching the sample Sa, A focusing optical system (lens system) 26, a CCD camera 27, a PC 28 connected to the output side of the CCD camera 27 and used as an analysis and control device for executing an analysis algorithm based on the measurement principle of the present invention, and the PC 28 AOTF controller that controls the operation of AOTF22 in response to the command And a roller 29.
[0058]
Among these, the AOTF 22 functions as a band-pass filter that extracts a specific wavelength by changing the center wavelength of the band band of the incident white light by electrical control from the AOTF controller 29.
[0059]
According to the above configuration, first, white light emitted from the halogen lamp 20 is irradiated to the AOTF 22 from the collimator lens 21b through the optical fiber cable 21a. This irradiated light is emitted as light having a specific wavelength λ (wave number k) by the AOTF 22, and the emitted light is collimated by the lens system 23, and a pair of polarizers 24 and an analyzer having an azimuth of 45 degrees sandwiching the sample Sa. 25 is incident. The emitted light from the analyzer 25 passes through the lens system 26 as light that bears information on the birefringence of the sample Sa, is taken as a measurement image by the CCD camera 27, and is sent to the PC.
[0060]
FIG. 5 shows an example of the measurement image captured as described above. As shown in this example, the measurement image includes, for example, 128 images (example of the number of pixels: 256 (vertical direction) × 512 (horizontal direction)). Each of the images corresponds to a measurement image by the emitted light controlled by the AOTF 22 so that the value of the wave number k is sequentially changed within the wavelength λ range of 450 to 610 [nm] (in the drawing). In the example, k = k ₁ , K ₂ ..., k _n : N = 128). At this time, the control of the AOTF 22 is performed via the AOTF controller 29 in response to a command from the PC 28.
[0061]
The number of images to be captured is not limited to 128 in this example, and any number may be used as long as Fourier analysis performed thereafter can be used efficiently. Further, since the higher-order birefringence can be measured as the number of images to be captured is increased, it is desirable to determine the number of images in consideration of this point.
[0062]
FIG. 6 explains the procedure of two-dimensional analysis executed by the processing of the PC 28 based on the measurement image captured as described above.
[0063]
First, as shown in FIG. 6 (upper stage), for example, 128 wave numbers k (k = k) obtained as described above. ₁ , K ₂ ..., k _n : N = 128) for each measurement image (example of the number of pixels: 256 (vertical direction) × 512 (horizontal direction)), each pixel P at the same coordinate position _cal Wave number k (k ₁ , K ₂ ..., k _n : Light intensity I for n = 128) _(Λ) Intensity distribution representing the change of light (horizontal axis: wave number k, vertical axis: light intensity I _(Λ) ) Data.
[0064]
Here, the light intensity I for each wave number k obtained for each pixel. _(Λ) Changes in accordance with the above-described equation (1), and the subsequent processing can use the same Fourier transform and the subsequent analysis algorithm as in the above-described point measurement for each pixel. Specifically, the Fourier transform is performed by multiplying the data of the light intensity distribution converted for each pixel by an appropriate window function, and shifting the spectrum obtained thereby to zero order to perform the Fourier inverse transform.
[0065]
By this Fourier analysis, as shown in FIG. 6 (left side of the middle stage), “frequency information” and “phase information” similar to those described above are obtained for each pixel of the measurement image (see equation (4)). In calculating the “frequency information” here, the spectrum data is interpolated to obtain the carrier frequency, and in calculating the “phase information”, a portion exceeding 2π in the data string obtained by the inverse Fourier transform using FFT. If this occurs, the unwrapping method (see later) is used to correct the phase to be continuous.
[0066]
Next, based on the “frequency information” and “phase information” obtained by the above waveform analysis, as shown in FIG. 6 (right side of the middle stage), birefringence considering wavelength dependency according to the above-described equation (4), that is, The distribution of the birefringence phase difference Δ with respect to the wave number k is obtained.
[0067]
The above-described series of analysis processing is executed for all the pixels on the measurement image, and the distribution data of the birefringence phase difference Δ with respect to the wave number k thus obtained is a constant wavelength λ (λ ₁ , Λ ₂ , ..., λ _n : N = 128), and an image showing a two-dimensional distribution of birefringence for each wavelength λ is obtained as shown in FIG. Note that the principal axis direction φ of the sample Sa can be measured using a method such as a phase shift method or FFT in the same manner as described above.
[0068]
Here, an actual measurement example of the two-dimensional distribution of birefringence measured above will be described. Samples (samples to be measured) Sa to be measured in this actual measurement example are two samples of a polymer film (phase film) and a quartz plate.
[0069]
(Measurement result of polymer film)
First, the measurement result of a polymer film is demonstrated based on FIGS. In this example, a two-dimensional birefringence distribution considering the above-described wavelength dependency is measured using a polymer film laminated stepwise on an acrylic substrate as a sample to be measured.
[0070]
7A shows the appearance (photograph) of the polymer film used in this measurement, FIG. 7B shows the cross section of the polymer film along the line XX ′ in FIG. 7A, and FIG. (C) shows an original image (photographing range: 28 (vertical) [mm] × 28 (horizontal) [mm], number of pixels: 128 × 128) of the polymer film photographed by this measurement. As shown in FIG. 7B, the thickness of one polymer film is 60 [μm], and the birefringence phase difference Δ is 2π [rad] at a wavelength of 550 [nm]. Further, in the original image shown in FIG. 7C, each boundary position of each of the laminated portions (11 layers, 10 layers, and 9 layers) of 11 films, 10 films, and 9 films among the polymer films is shown. The parts to be understood are taken in order from the left side to the right side in the figure.
[0071]
FIG. 8 shows an image representing the birefringence distribution for each wavelength λ measured and analyzed under the conditions of wavelengths λ = 460, 500, 532, 550, and 608 [nm] for the polymer film. The magnitude of the birefringence phase difference Δ indicating the birefringence distribution changes within a range of Δ = 50 to 100 [rad]. For example, the gray state can be easily seen by looking at the image. Although the display is performed using a scale (for example, Δ = 50 to 100 is changed from black to white), the present invention is not limited to this, and a color scale (for example, Δ = 50 to 100 is purple to blue to green to yellowish green to yellow). A color display may be performed using a sequence of yellow to red.
[0072]
As shown in FIG. 8, in any image of each image having a different wavelength λ, as the number of films changes on the polymer film as 11 layers, 10 layers, and 9 layers (left and right direction in each image), It is clear that the birefringence phase difference Δ changes at the boundary, and that when the images having different wavelengths λ are compared, the birefringence phase difference Δ decreases as the wavelength λ increases. Was confirmed.
[0073]
FIG. 9 shows the state of the polymer film with respect to the cross-sectional position along the line AA ′ (see FIG. 7C) on the image representing the birefringence distribution measured and analyzed under the condition of wavelength λ = 550 [nm]. The change of the refractive phase difference Δ is shown. In the results shown in FIG. 9, the birefringence phase difference Δ is a position where the number of films on the polymer film on the AA ′ line cross-sectional position changes from 11 layers to 10 layers and a position where the number of layers changes from 10 layers to 9 layers. Steps of about 2π [rad] were clearly confirmed at two locations. This result demonstrates that quantitative birefringence measurement is performed by a method based on the basic measurement principle of the present invention. This cannot be measured by the polarization measurement using the monochromatic light of the conventional example.
[0074]
FIG. 10 is an image showing a two-dimensional distribution of the principal axis azimuth φ of the polymer film measured and analyzed under the condition of wavelength λ = 532 [nm]. In the example in the figure, the direction of the principal axis azimuth φ is expressed in gray scale (φ = -30 [degrees] to 30 [degrees]), and the orientation of the vectors at the measurement points arranged in a grid on the image. In the results shown in FIG. 10, it was confirmed that the principal axis direction φ of the polymer film was almost uniform in one direction at any position, indicating about 0 degrees.
[0075]
(Measurement result of quartz plate)
Next, the measurement result of the quartz plate will be described with reference to FIGS. In this example, a two-dimensional birefringence phase difference distribution is measured using a wedge-cut quartz plate as a measurement target.
[0076]
11A shows the appearance (photograph) of the quartz plate used in this measurement, FIG. 11B shows the cross section of the quartz plate along the line XX ′, and FIG. 11C shows this measurement. The original images taken in are shown respectively. As shown in FIG. 11 (b), the thickness of the quartz plate changes continuously. On the original image shown in FIG. 11 (c), the upper side (A side of the line AA 'in the figure). ) Corresponds to a thick portion, and gradually decreases from there toward the lower side (A ′ side of the AA ′ line).
[0077]
FIG. 12 shows an image representing a two-dimensional birefringence distribution for each wavelength λ measured and analyzed under the conditions of the same wavelength λ (λ = 460, 500, 532, 550, and 608 [nm]) as described above. As shown in FIG. 12, the magnitude of the birefringence phase difference Δ indicating the birefringence distribution of the analyzed quartz plate is 250 [rad] at a large value and 100 [rad] at a small value. Also, it was well confirmed that the birefringence phase difference Δ changed in the thickness direction of the quartz plate. Further, when the images having different wavelengths λ were compared, it was confirmed that the birefringence phase difference Δ was decreased as the wavelength λ was increased as described above (the image observed in FIG. 12). The unevenness inside is considered to be polishing unevenness generated during the production of the quartz plate).
[0078]
FIG. 13 shows a crystal plate with respect to the cross-sectional position along the line AA ′ (see FIG. 7C) on the image representing the two-dimensional birefringence distribution measured and analyzed under the condition of wavelength λ = 567 [nm]. The change in the birefringence phase difference Δ is shown. The result shown in FIG. 13 shows that the birefringence phase difference Δ is linearly changed, and it has been confirmed that the measurement value is highly reliable.
[0079]
FIG. 14 is an image showing the two-dimensional birefringence distribution of the principal axis direction φ of the quartz plate measured and analyzed under the condition of wavelength λ = 532 [nm]. Similar to the above, the direction of the main axis direction φ is expressed in gray scale and Each is shown as a vector. In the results shown in FIG. 14, the principal axis direction φ of the quartz plate is almost the same when viewed in the direction of the vector at each measurement point, but the image is not uniform when viewed in gray scale. A striped distribution is observed. Originally, the crystal orientation does not show such a striped distribution, so this is considered a measurement error. The cause of this error is that the birefringence phase difference Δ changes to π / 2, 3π / 2, and 5π / 2, and there is a singular point where the phase shift method cannot be used from the above equation (6). It is thought that it is because.
[0080]
Next, each birefringence phase difference Δ (birefringence δ) measured and analyzed with the polymer film and the quartz plate described above. _n The measurement result in the wavelength dependence of) will be described.
[0081]
15A shows the change of the birefringence phase difference Δ with respect to the wavelength λ (vertical axis: birefringence phase difference Δ [rad], horizontal axis: wavelength λ [nm]), and FIG. 15B shows the wavelength λ. Birefringence for δ _n (Vertical axis: birefringence phase difference Δ [rad], horizontal axis: wavelength λ [nm]). 15 (a) and 15 (b), the curve indicated by the solid line is the measurement result of the polymer film, the curve indicated by the dotted line is the measurement result of the quartz plate, and the point indicated by the triangle (Δ) is from the known literature (Science Chronology). The birefringence values obtained by calculation and the points indicated by rhombuses (示 す) indicate the catalog values (only FIG. 15A) published by a predetermined manufacturer.
[0082]
Each of the measurement results of the polymer film and the quartz plate shown in FIGS. 15 (a) and 15 (b) has a tendency to almost coincide with the birefringence value of the scientific chronology and the catalog value of the manufacturer. The effectiveness of wavelength-dependent measurement using the birefringence measurement technique according to the invention was confirmed. The result shown in FIG. 15A shows that the birefringence phase difference due to the measurement result of the polymer film tends to be slightly larger than the catalog value. This is because the light is emitted when the sample is set in the optical system. This is thought to be due to a slight inclination with respect to the axis. Even in this case, the tendency of the wavelength dependence of the birefringence phase difference in the measurement result and catalog value of the polymer film is almost the same.
[0083]
Therefore, according to the birefringence measurement according to the present embodiment, the measurement including the wavelength dependence of the birefringence that cannot be measured by the conventional example can be realized with high accuracy not only by the point measurement but also by the two-dimensional measurement.
[0084]
In the two-dimensional birefringence measurement considering the wavelength dependency, an example using an AOTF (Acousto-Optic Tunable Filter) as a method for extracting a specific wavelength from white light will be described. However, the present invention is not limited to this. For example, a method of arranging a plurality of interference filters in order and presenting them sequentially, a birefringent bandpass filter (this is because transmitted light is inclined by tilting the filter with respect to the optical axis). Or the like.
[0085]
Further, a processing method for obtaining “phase information” and “frequency information” from a spectrum obtained by Fourier analysis of spectral data (light intensity distribution) that changes in a cosine shape with respect to the wave number is shown in FIG. In addition, the present invention is not limited to the method shown in FIG. Hereinafter, application examples of each method will be described with reference to FIGS.
[0086]
FIG. 16 shows an outline of an analysis procedure including a calculation example of the above-described equation (4). In the analysis procedure shown in FIG. 16, in accordance with the basic measurement principle of the present invention described above, spectral data (light intensity distribution data) is acquired (step St1), this spectral data is multiplied by a window function (step St2), and Fourier is obtained. A spectrum is obtained by analysis (step St3), "frequency information" and "phase information" are obtained from this spectrum (step St4), and a relative value indicating the wavelength dependence of birefringence is obtained from the obtained "phase information". Also, absolute values including the order of higher-order birefringence are obtained from “frequency information” (step St5).
[0087]
First, as shown in FIG. 16 (upper stage), the spectral data acquired in step St1 is a light intensity I that changes in a cosine with respect to the wave number k by Fourier transform. _(Λ) (Expression (1) described above). This equation shows that the birefringence phase difference Δ has a wavelength dependency Δ _(Λ) Therefore, it can be replaced with the expression (1) ′ in FIG. And this birefringence phase difference Δ or Δ _(Λ) Can be obtained from the calculation of “frequency information” and “phase information” by expanding from equation (2) to equation (3) as described above.
[0088]
Therefore, in step St2, the light intensity I _(Λ) An operation is performed to multiply the spectral data represented by the following formula by a window function. This arithmetic expression is expressed by, for example, the following expression (7).
[0089]
[Expression 18]

In this equation (7), I _{ω (k)} Is the light intensity I multiplied by the window function I _(Λ) , I ₀ Is the light intensity I before being multiplied by the window function _(Λ) , AB · cos (2πk / k ₀ ) Is a window function, A and B are constants (arbitrary), k ₀ Indicates the number of data sampling.
[0090]
By this processing, as shown in FIG. 16 (middle), the light intensity I _(Λ) The center of the distribution spectrum coincides with the center of the measured wavenumber region. Here, the assumptions of the values of A and B are arbitrary, but f on the spectrum of the frequency f by spectral analysis. _s Since there is a correlation in the spectrum intensity for determining the position of A, it is necessary to consider this point when actually determining A and B.
[0091]
Next, in step St3, the light intensity I multiplied by the window function as described above. _(Λ) The spectrum of the frequency f is obtained by Fourier analysis. The spectrum of the frequency f has a peak at a position shifted from the frequency f = 0 (zero order) as shown in FIG. 16 (lower).
[0092]
Therefore, in step St4, “frequency information” and “phase information” are obtained from the spectrum of the frequency f. The processing method at this time is as follows: 1) Shift the spectrum to zero (0) and then shift it at the peak of the spectrum. F _p The method of performing the inverse transformation by shifting the position of f to the position of f = 0 (refer to the equations shown in FIGS. 2 and 4 in the method described in the basic measurement principle described above), and 2) without shifting the spectrum to the zero order. Method for performing inverse Fourier transform (see FIG. 17 described later), 3) spectrum f _s (F ₁ ) Shift (the spectrum f _s And the inverse Fourier transform (see FIG. 18 to be described later). 4) Spectrum f _p Any method can be applied, such as a method of performing inverse Fourier transform using the above as it is (see FIG. 19 described later).
[0093]
FIG. 17 illustrates a method of performing inverse Fourier transform 2) without shifting the spectrum to the zero order in step St4. According to this method, the spectrum of the frequency f obtained above (refer to the uppermost stage in the figure) is subjected to inverse Fourier transform without shifting to the zero order, and the wave number k (1 / λ) after the inverse Fourier transform is obtained. Phase φ _(K) Is unwrapped (see the second stage from the top in the figure), and the phase φ ′ with respect to the wave number k after the unwrapping _(K) F (see the third row from the top in the figure) _s Add the minute offset β (see the second row from the bottom in the figure). Therefore, the birefringence phase difference Δ (k) obtained by this method is expressed by the following equation (8).
[0094]
[Equation 19]

[0095]
In this equation (8), the obtained equation becomes simpler than the above-described method 1) shifting the spectrum to the zero order.
[0096]
FIG. 18 shows 3) the spectrum f in step St4. _s Shift by (f of the spectrum _s This is a method for performing the inverse Fourier transform by shifting the position of (1) to the position of f = 0). According to this method, with respect to the spectrum of the frequency f obtained above, as shown in the uppermost part of the figure, f _s The phase φ with respect to the wave number k (1 / λ) after the inverse Fourier transform is performed by performing a minute shift. _(K) Is unwrapped (see the second stage from the top in the figure), and the phase φ ′ with respect to the wave number k after the unwrapping _(K) F (see the third row from the top in the figure) _s Add the minute offset β (see the second row from the bottom in the figure). Therefore, the birefringence phase difference Δ (k) obtained by this method is expressed by the following equation (9).
[0097]
[Expression 20]

[0098]
Also in this equation (9), as in the equation (8), the obtained equation becomes simpler than the above-described 1) method of shifting the spectrum to the zero order.
[0099]
FIG. 19 shows 4) spectrum f in step St4. _p A method for performing inverse Fourier transform using the above as it is will be described. According to this method, the spectrum of the frequency f obtained above (see the uppermost stage in the figure) _p Is used to perform the inverse Fourier transform, and the phase φ with respect to the wave number k (1 / λ) after the inverse Fourier transform _(K) Is unwrapped (see the second stage from the top in the figure), and the phase φ ′ with respect to the wave number k after the unwrapping _(K) F (see the third row from the top in the figure) _p Add the minute offset (see the second row from the bottom in the figure). Therefore, the birefringence phase difference Δ (k) obtained by this method is expressed by the following equation (10).
[0100]
[Expression 21]

[0101]
Also in this formula (10), the formula obtained is simpler than the above-described method 1) shifting the spectrum to the zero order, similarly to formulas (8) and (9).
[0102]
Here, returning to FIG. 16, in Step St5, the relative value indicating the wavelength dependence of birefringence is included from the phase information obtained by the above processing, and the order of higher-order birefringence is included from the frequency information. An absolute value is obtained.
[0103]
In the above example, the peak frequency f of the spectrum distribution in the amplitude spectrum is used. _p And the frequency f of the starting point of the spectrum distribution _s It is desirable to perform the following processing in order to obtain the value accurately. The spectral distribution obtained by ordinary Fourier analysis is obtained discretely according to the number of measurement points of the light intensity with respect to the wave number k. For example, as shown in the middle left of FIG. 2 and the frequency information shown in the middle of FIG. 6, the obtained data has discrete values. f _p And f _s Therefore, it is necessary to interpolate discrete data using a process such as fitting the shape of the spectrum distribution. The methods used for this are, for example, 1) a method of approximating the distribution shape to a function such as a Gaussian distribution or a binomial distribution, 2) taking out a partial region, and based on data of several adjacent points, For example, a method of approximating the inside of the region by polynomial approximation, sequentially moving the interpolation region to approximate the entire distribution shape, and the like can be exemplified.
[0104]
In the above example, a PC is illustrated as an analysis device. However, the present invention is not limited to this, and any computer having a computer function for executing an analysis algorithm based on the measurement principle of the present invention may be connected to a network, for example. Any device (machine, module, unit, etc.) such as a dedicated workstation can be applied.
[0105]
It should be noted that the present invention is not limited to the above-described exemplary embodiments and application examples that are exemplarily illustrated, and those skilled in the art will be within the scope of the gist of the present invention based on the content of the claims. Various modifications and changes can be made and these are also within the scope of the present invention.
[0106]
【The invention's effect】
As described above, according to the present invention, in addition to high-order birefringence, high-precision birefringence measurement in consideration of the wavelength dependence of birefringence can be realized. This birefringence measurement can be applied not only to point measurement but also to two-dimensional measurement, and is more scalable and practical.
[Brief description of the drawings]
FIG. 1 is a diagram for explaining a premise part of a basic measurement principle of a birefringence measuring apparatus and method considering wavelength dependency according to an embodiment of the present invention.
FIG. 2 is a view for explaining the essence of the basic measurement principle of a birefringence measuring apparatus and method considering wavelength dependence according to an embodiment of the present invention.
FIG. 3 is a diagram for explaining spindle direction measurement using a phase shift method.
FIG. 4 is a diagram showing a configuration example of a birefringence measuring apparatus when applied to two-dimensional measurement.
FIG. 5 is a view for explaining an image captured by the birefringence measuring apparatus shown in FIG. 4;
FIG. 6 is a diagram illustrating an analysis procedure when applied to two-dimensional measurement.
7A and 7B are diagrams showing a polymer film actually measured by birefringence measurement, where FIG. 7A is an external view (photograph), FIG. 7B is a cross-sectional view taken along line XX ′ in FIG. ) Is a diagram showing an original image.
FIG. 8 is a view showing an analysis result of a birefringence phase difference of a polymer film (phase film).
9 is a diagram showing a birefringence phase difference measured along the line AA ′ in FIG. 7C. FIG.
FIG. 10 is a diagram showing the analysis result of the principal axis orientation of a polymer film.
11A and 11B are diagrams showing a crystal plate actually measured by birefringence measurement, in which FIG. 11A is an external view (photograph), FIG. 11B is a cross-sectional view taken along line XX ′ in FIG. ) Is a diagram showing an original image.
FIG. 12 is a diagram showing an analysis result of a birefringence phase difference of a crystal plate.
13 is a diagram showing a birefringence phase difference measured along the line AA ′ in FIG.
FIG. 14 is a diagram showing an analysis result of a principal axis orientation of a crystal plate.
FIG. 15 is a diagram for explaining the accuracy of measurement values of a polymer film and a quartz plate in comparison with external data (science chronology, catalog values), (a) is a graph showing a change in birefringence phase difference with respect to wavelength; (B) is a graph which shows the change of the birefringence with respect to a wavelength.
FIG. 16 is a diagram illustrating an analysis procedure based on the basic measurement principle of the present invention.
FIG. 17 is a diagram for explaining a method for performing inverse Fourier transform without shifting the spectrum to zero order in the analysis procedure shown in FIG. 16;
18 is a diagram for explaining a method of performing inverse Fourier transform by shifting the spectrum by fs in the analysis procedure shown in FIG. 16;
19 is a diagram for explaining a method of performing inverse Fourier transform using fp in the analysis procedure shown in FIG. 16;
[Explanation of symbols]
1 Birefringence measurement device (for point measurement)
2 Birefringence measuring device (for 2D measurement)
10 White light source
11a optical fiber cable
11b Collimator lens
12 Polarizer
13 Analyzer
14 Spectrometer
14a Diffraction grating
14b linear CCD
15a condenser lens
15b optical fiber cable
16 PC (personal computer)
20 Halogen lamp
21a optical fiber cable
21b Collimator lens
22 Acousto-optic tunable filter (AOTF)
23 Beam expander (lens system)
24 Polarizer
25 analyzer
26 Focusing optical system (lens system)
27 CCD camera (two-dimensional image sensor)
28 PC (personal computer)
29 AOTF controller
Sa sample (sample to be measured)

Claims (9)

A birefringence measuring optical system for acquiring an optical signal carrying information on the birefringence of the measurement target;
From the waveform data indicating the light intensity distribution of the optical signal acquired by the birefringence measuring optical system, the frequency component including the order of high-order birefringence and the phase component responsible for wavelength dependence are analyzed, and the high-frequency component is analyzed from the analysis data A birefringence measuring apparatus in consideration of wavelength dependence, comprising: an analyzer for obtaining birefringence exhibiting the wavelength dependence separately for a carrier component term and a dispersion term in addition to the second birefringence.   The birefringence measuring optical system includes a white light source, a pair of polarizers and an analyzer disposed at a position sandwiching the measurement target on the optical path of an optical signal from the white light source, and the light emitted from the analyzer. 2. A wavelength-dependent optical system according to claim 1, further comprising: a point measuring optical system having a spectroscope that splits an optical signal carrying information related to the birefringence of a measurement target for each wavelength and outputs the spectral signal to the analyzer. Birefringence measurement device that takes into account the characteristics.   The birefringence measuring optical system includes a white light source, an acoustooptic element that variably extracts a specific wavelength component from the optical signal from the white light source, and the measurement target on the optical path of the optical signal extracted by the acoustooptic element. A pair of polarizers and analyzers disposed at positions sandwiching the image sensor, and an image sensor that captures an optical signal carrying information related to the birefringence of the measurement object emitted from the analyzer and outputs the optical signal to the analysis device. 2. The birefringence measuring apparatus considering wavelength dependency according to claim 1, comprising a two-dimensional measuring optical system. The analysis apparatus sets the wave number of the optical signal to k, and sets the birefringence, birefringence phase difference, thickness, and principal axis direction of the measurement target to δ _n , Δ (k), d, and φ, respectively. When the frequency component term, the dispersion term, and the phase information of refraction δ _n are expressed as δ _n0 , δ _λ , and φ _(k) , respectively, the birefringence phase difference Δ (k) in consideration of the wavelength dependency is expressed as follows:

2. The birefringence measuring apparatus considering wavelength dependency according to claim 1, further comprising data processing means for obtaining the sum of frequency information and phase information by waveform analysis so as to satisfy the above relationship. The data processing means sets the frequency at the apex of the spectrum distribution in the amplitude spectrum of the frequency obtained by Fourier analysis of the waveform data indicating the light intensity distribution of the optical signal, and the frequency at the start point of the spectrum distribution as f _p. , And f _s ,
Said optical signal of the light intensity distribution obtained by Fourier analysis of the waveform data indicating the phase, the minimum value of the wave number k, and the maximum value, respectively φ _{(k), k min,} when the k _max, the wavelength dependence Considering the birefringence phase difference Δ (k),

5. The birefringence measuring apparatus considering wavelength dependence according to claim 4, wherein the means is obtained by waveform analysis so as to satisfy the above relationship. The data processing means indicates the light intensity distribution of the optical signal, where fS is the frequency of the start point of the spectrum distribution in the amplitude spectrum of the frequency obtained by Fourier analysis of the waveform data indicating the light intensity distribution of the optical signal. phase obtained by Fourier analysis of the waveform data, the minimum value of the wave number k, and the maximum value, respectively φ '(k), k min , k when the _max, birefringence phase difference in consideration of the wavelength dependence delta ( k)

5. The birefringence measuring apparatus considering wavelength dependence according to claim 4, wherein the means is obtained by waveform analysis so as to satisfy the above relationship. The data processing means sets f _{S as} the frequency of the start point of the spectrum distribution in the amplitude spectrum of the frequency obtained by Fourier analysis of the waveform data indicating the light intensity distribution of the optical signal, and determines the light intensity distribution of the optical signal. obtained by Fourier analysis of the waveform data indicating the phase, the minimum value of the wave number k, and the maximum value, respectively _{φ '(k), k min} , when the k _max, the birefringence phase difference Δ a (k),

5. The birefringence measuring apparatus considering wavelength dependence according to claim 4, wherein the means is obtained by waveform analysis so as to satisfy the above relationship. The data processing means uses fP as the frequency of the peak of the spectrum distribution in the amplitude spectrum of the frequency obtained by Fourier analysis of the waveform data indicating the light intensity distribution of the optical signal, and the waveform indicating the light intensity distribution of the optical signal. phase obtained by Fourier analysis of the data, the minimum value of the wave number k, and the maximum value, respectively _{φ '(k), k min} , when the _{k max,} the birefringence phase difference Δ a (k),

5. The birefringence measuring apparatus considering wavelength dependence according to claim 4, wherein the means is obtained by waveform analysis so as to satisfy the above relationship. From the waveform data indicating the light intensity distribution of the optical signal that bears information on the birefringence of the measurement target, the frequency component including the order of higher-order birefringence and the phase component responsible for wavelength dependence are analyzed, and the higher-order birefringence is analyzed from the analysis data. In addition to refraction, the birefringence exhibiting the wavelength dependency is obtained separately for a carrier component term and a dispersion term .

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