JP4237530B2 - Wavefront evaluation method and apparatus using information entropy - Google Patents

Description

【００３５】
最後にこの確立分布Ｐ（ｘ，ｙ）を以下の式（４）に代入することで、情報エントロピーと呼ばれる一つの値（数値）εを得る（出力する）。（これは、図１中、デジタル信号処理装置４における、「情報エントロピーを計算する」という記載と対応している。）
【００３６】
【数２】

【００３７】
ただし、ここで、Ｐ（ｘ，ｙ）＝０の時には、−Ｐ（ｘ，ｙ）ｌｏｇＰ（ｘ，ｙ）＝０と定義し、対数の底は問わないものとする。
【００３８】
ここで、情報エントロピーとは、ある確率分布Ｐ（ｘ，ｙ）から式（４）によって得られる値をいう。上記のようにして得られる情報エントロピーεには、物理的なエントロピーと類似した以下のような特徴が知られている。つまり、確率分布Ｐ（ｘ，ｙ）の平坦度が高ければ高いほど情報エントロピーεの値は大きくなるのである。今、以下の式（５）で表されるような関係が成立する。
【００３９】
Ｐ（ｘ，ｙ）〜Ｃ（ｘ，ｙ）＝Ｗ（ｘ，ｙ）＆Ｗ（ｘ，ｙ） （５）
【００４０】
ただし、式（５）の左辺の記号〜は、Ｐ（ｘ，ｙ）の値がＣ（ｘ，ｙ）の値に比例することを表す。また、式（５）の右辺の記号＆は光電場Ｗ（ｘ，ｙ）の自己相関を表す。したがって、情報エントロピーεは被検波面Ｗ（ｘ，ｙ）の平坦度が高いほど大きな値を取ることになる。なお、この時、被検波面の強度成分は波面の位相構造に比べて十分に平らであり、空間的に十分な広がりを持つと仮定している。この特徴を示すために、幾つかの１次元波面の例と、そこからＷＩＥＭによって得られる１つの数値である情報エントロピーε（前記のような手順で波面Φ（ｘ，ｙ）により得られた情報エントロピーεをＷＩＥＭ値ともいう）を図２に示す。図２からも平坦な波面ほど情報エントロピー（ＷＩＥＭ値）εが大きくなることが見て取れる。
【００４１】
ＷＩＥＭの最大の利点は、図１の実施例で示したように、ＷＩＥＭに用いられる本発明の波面の平坦度評価装置（光学系、ＷＩＥＭシステム）が簡単な構成であることである。そのため、この波面の平坦度評価装置を、波面評価を必要とするような光学系（装置、システム）に簡単に「埋め込む」（適用する）事が出来る。このような光学系の実施例として、本発明者らは、上述のＷＩＥＭシステム及び波面補正用の可変鏡（薄膜可変鏡）２１が埋め込まれた共焦点顕微鏡装置１１を作成した（後述する図３参照）。
【００４２】
本発明者らは、この共焦点顕微鏡装置１１を用いて、１つの数値である情報エントロピー（ＷＩＥＭ値）εをコスト値とした最適化アルゴリズムにより、可変鏡２１形状の最適化を行い、試料（計測サンプル）２４（いずれも後述する図３参照）の手前に設置された屈折率不整合層（フューズドシリカ層、ガラス層）２５によって生じる（起因する）球面収差の補正を行った。最適化アルゴリズムの例として、本実施例では、遺伝的アルゴリズムを用いた。ここで、遺伝的アルゴリズムとは、複数の状態におけるコスト値を計算し、そのうち、より最適な値を持つ状態を複数採用し、不採用とした状態の代替として新たな状態を作成し、試行を行い、同様の試行を繰り返すことで、状態を最適化するようなアルゴリズムである。
【００４３】
なお、本実施例では最適化アルゴリズムの例として遺伝的アルゴリズムを用いたが、これに限られず、他の最適化アルゴリズム、例えば、シミュレーテッドアニーリング法（焼きなまし最適化アルゴリズム）や、トライ・アンド・エラー法(無作為な試行を行い、その誤差を前回の試行の誤差と比較し、そのうち誤差の小さいほうを採用し、さらに、その値を次なる無作為な試行と比較していくという行為を繰り返していく最適化アルゴリズム)を用いることも可能である。
【００４４】
図３は、本実施例の共焦点顕微鏡装置１１の模式的な構成図である。つまり、図３は、上述したように、可変鏡２１とＷＩＥＭシステムとを組み込んだ共焦点顕微鏡装置１１の構成図を示している。共焦点顕微鏡装置１１は、光源１２と、偏光子１４と、光源１２からの光を集光・拡大するピンホール１６及びレンズ１５、１７、２６（レンズ２６はフーリエ変換レンズである）と、光線束を分離する偏光ビームスプリッタ１９及びビームスプリッタ１８と、光の利用効率を上げるために用いられる１／２波長板２０と、可変鏡２１と、対物レンズ２２と、走査ステージ２３と、ディテクターであるＣＣＤカメラ２７と、コントロールユニット（制御装置）２８とデジタル信号処理装置２９と、を含んで構成される。
【００４５】
本発明の特徴としては、レンズ２６とＣＣＤカメラ２７とからなる光学系と、デジタル信号処理装置２９とが、本実施例の共焦点顕微鏡装置１１に備えられる（埋め込まれた）本発明の波面の平坦度評価装置１ａ、つまり、ＷＩＥＭシステムを構成していることである。レンズ２６は、既に述べたようにフーリエ変換レンズであり、焦点距離は２００ｍｍである。この波面の平坦度評価装置１ａを構成する、レンズ２６、ＣＣＤカメラ２７、及びデジタル信号処理装置２９は、図１で示した波面の平坦度評価装置１を構成するフーリエ変換レンズ２、ＣＣＤカメラ３、及びデジタル信号処理装置４にそれぞれ対応する。
【００４６】
共焦点顕微鏡装置１１の光源１２としては、例えば、単色光源である波長λが６３２．８ｎｍのＨｅ−Ｎｅレーザーが用いられる。コントロールユニット２８は、走査ステージ２３、可変鏡２１、及びＣＣＤカメラ２７に接続されており、それぞれを制御する。走査ステージ２３は、コントロールユニット２８に制御されて、例えばピエゾ素子により矢印ａで示されるようにＺ軸方向（紙面上下方向）に移動可能である。
【００４７】
本発明に係る共焦点顕微鏡装置１１では、可変鏡２１に任意のデフォーカス（受像面の移動）を与えることにより、機械的な走査を行うことなく光軸方向の走査が可能である。
【００４８】
つまり、本発明の共焦点顕微鏡装置１１の原理では、対物レンズ２２のデフォーカスを、本発明の共焦点顕微鏡装置１１中に設置させた可変鏡２１の形状をコントロールユニット２８により変化させ、３種類もしくはそれ以上の可変鏡（補償鏡）２１の形状で取得された共焦点強度の値から試料（計測物体）２４の高さを計測している。
【００４９】
次に、図１を参照しつつ、本発明の共焦点顕微鏡装置１１の作用について説明する。光源１２からのレーザー光ｈａは、偏光子１４を経て、レンズ１５とピンホール１６で拡大され、コリメートされた後、レンズ１７、ビームスプリッタ１８、偏光ビームスプリッタ１９、及び１／２波長板（半波長板）２０を通過し、図３中左に位置する可変鏡（薄膜可変鏡）２１で反射される。そして、偏光ビームスプリッタ１９を経て対物レンズ２２により走査ステージ２３上に載置された試料２４の表面に集光する。この際、対物レンズ２２と試料２４との間には、例えば厚さ３．４ｍｍの屈折率不整合層であるフューズドシリカ層２５が存在し、それにより球面収差が発生している。
【００５０】
試料（サンプル）２４により反射された光ｈｂは、再び偏光ビームスプリッタ１９及び１／２波長板２０を経て、再び可変鏡（変形鏡、補償鏡）２１で反射された後、偏光ビームスプリッタ１９、ビームスプリッタ１８を経て、レンズ２６を通過する。レンズ２６はフーリエ変換レンズであり、入射した光の被計測波面Φ（ｘ，ｙ）をフーリエ変換する。そして、ＣＣＤカメラ２７の受像面上に共焦点スポットを形成する。
【００５１】
この時、可変鏡（補正鏡）２１によって収差がキャンセルされていれば、可変鏡（補正鏡）２１を２回通過した後の光の波面は平坦になっているはずである。そこで、この共焦点顕微鏡装置（システム）１１では、ＣＣＤカメラ２７で得られた共焦点画像から面Ｓにおける波面の情報エントロピー（ＷＩＥＭ値）εをＣＣＤカメラ２７に接続されるデジタル信号処理装置２９により計算処理する。つまり、上述した波面の平坦度評価方法に基づき、１つの数値である情報エントロピー（ＷＩＥＭ値）εを算出（出力）する。そして、さらに、このデジタル信号処理装置２９において、図３に示すように、その値、つまり情報エントロピー（ＷＩＥＭ値）εをコスト値として用いた遺伝的アルゴリズムを用いて計算処理することで可変鏡（変形鏡）２１の形状の最適化を行う。
【００５２】
従来の共焦点顕微鏡装置等の光学系では、計測装置としてピンホールと点ディテクターを用いるのに対し、本実施例の共焦点顕微鏡装置１１では、ＣＣＤカメラ２７を用い、ＣＣＤカメラ２７の撮像素子上のある範囲のピクセル（画素）上の光強度を計測することで共焦点計測を行う。つまり、本実施例の共焦点顕微鏡装置１１では、従来の共焦点顕微鏡装置に用いられているピンホールと点ディテクターに代えてＣＣＤカメラ２７に置き換えて用いることにより、容易に本発明に係る波面の平坦度評価装置１ａ、つまり、ＷＩＥＭ光学系（ＷＩＥＭシステム）を埋め込むことが可能なのである。
【００５３】
（実験例）
ここでは実際に、デジタル信号処理装置２９において、ＷＩＥＭ値εをコスト値とし遺伝的アルゴリズムを用いて計算処理することで、コントロールユニット２８を介して可変鏡（補償鏡）２１の形状を最適化し、収差の除去を試みた。遺伝的アルゴリズムにおいては、可変鏡（補償鏡）２１の各駆動電極（図示せず）に印可する電圧値を遺伝子とした個体を３０個体用い、最大７０世代まで世代交代を行っている。世代交代においては、各世代の内、ＷＩＥＭ値εの大きいものから順に２１個体を次世代の両親としてランダム交配、さらに適宜突然変異を与えている。また、屈折率不整合層（図３に示す実施例では屈折率不整合層としてフューズドシリカ層２５が置かれている）の下に置かれる計測物体（図３の実施例では試料２４を配置）としては、参考のために試料２４の代わりに通常の平面鏡を用いている。
【００５４】
このようにして最適化された後の共焦点（コンフォーカル）軸応答を図４に示す。つまり、図４は、共焦点顕微鏡の軸応答を示すグラフである。図４のそれぞれの軸応答は、異なったコスト値を用いた遺伝的アルゴリズムで最適化された可変鏡２１を用いて計測されている。この計測ではＣＣＤカメラ２７の１ピクセル(１ピクセルは１１μｍ×１１μｍ)を共焦点ピンホールと見なして、これらの軸応答を計測している。図中のＡで示す線は最適化前の共焦点軸応答を、Ｄで示す線はＷＩＥＭによって最適化された後の軸応答を示している。これより、ＷＩＥＭと遺伝的アルゴリズムの組合わせにより、球面収差が補正され、軸応答の強度が増強されていることが判る。
【００５５】
なお、図中のＣで示す線は、ＷＩＥＭを用いずに、ピンホール出力値を最大化するように最適化を行った場合である。つまり、Ｃで示す線は、１１μｍ×１１μｍの正方形ピンホールからの出力を用いて可変鏡２１の形状を最適化している。この方法でも収差が補正され信号強度が増大している事が判る。この方法はピンホールの位置の決定に極めて敏感（センシティブ）である。実際に最適化の際のピンホールの位置が横方向それぞれに１ピクセルづつずれていた場合の結果が、Ｂで示す線で示されている。つまり、Ｂで示す線は、縦横に１ピクセルづつシフトした正方形ピンホールからの出力を用いて可変鏡２１の形状を最適化している。しかし、ここでは、信号強度はある程度増強されているものの、信号右側の矢印ｇで示された箇所の非対称が解消されておらず、収差も補償されていないものと思われる。
【００５６】
この理由を説明するために、球面収差、及びデフォーカスを持った波面の情報エントロピー（ＷＩＥＭ値）ε、理想的な位置のピンホール出力（図５のピンホール（ａ）参照）、及び、ピンホールがＣＣＤカメラの受光面内の縦、横各方向にそれぞれ１１μｍずれた場合の（位置エラーである）ピンホール（図５のピンホール（ｂ）参照）出力の特性を考えてみる。図３の共焦点顕微鏡装置１１の場合と同様に、焦点距離２００ｍｍのレンズを用いて共焦点スポットを得ていると仮定した場合のそれらの値の様子を図５（ａ）’（ｂ）’（ｃ）に示す。ここで、（ａ）’（ｂ）’（ｃ）中、それぞれ横（水平）軸は被検波面の球面収差係数、縦（垂直）軸はデフォーカス（焦点ずれ）係数である。
【００５７】
これより、ＷＩＥＭ値ε、及び理想的な位置のピンホール出力共に、球面収差及びデフォーカスが共に０の点にただ一つのピークＰａを持っていることがわかる（図５（ａ）’（ｃ）参照）。つまり、これらのどちらの値をコスト値としても波面の最適化が可能であるということである。しかし、ピンホールの位置がずれた場合（図５（ｂ）参照）には、大きくその様相が異る。位置ずれを伴ったピンホール出力は球面収差-デフォーカス平面上に４つのピークＰ１、Ｐ２、Ｐ３、Ｐ４を持ち、そのどれもが最適解を示していない（図５（ｂ）’参照）。例えば、先ほどの図４の場合においては、最適化アルゴリズムがデフォーカス０の線上に存在する、球面収差が打ち消されていない解を発見したものと思われる。
【００５８】
この問題は、数学的探索の問題ではなく、物理状態を数値に変換する際に発生する問題である。そのため、最適化アルゴリズムそのものの改良によって解消することは不可能である。一方、情報エントロピー（ＷＩＥＭ値）εを計算するためには、式（４）からも判るように、位置の情報は用いられておらず、共焦点形状における強度のヒストグラムのみが用いられている。そのため、ＷＩＥＭにおいては光軸の決定などの任意性を排除することが可能になるのである。
【００５９】
また、ＷＩＥＭ値はラテラルな（横方向の）共焦点スポット形状全てを反映しているのに対し、ピンホール出力は局所的な光強度しか反映していない。コスト値を計算するためのコスト関数が大域的であれば、最適化アルゴリズムに要求される探索の大域性は減少し、既に述べたシミュレートアニーリング（ｓｉｍｕｌａｔｅｄ ａｎｎｅａｌｉｎｇ）法等のような、より単純で計算量、探索量の少ないアルゴリズムでの最適化が可能になる。今回のような応用においては、一回の試行が物理的な計測を伴うため、探索量の減少により最適化に要する時間を劇的に減少させることができる。
【００６０】
また、コスト値そのものがグローバルな情報を反映していれば、最適化の途中で局所解に収束する危険性も小さくなる。このことからも、情報エントロピー（ＷＩＥＭ値）εはピンホール出力よりもよりコスト値として適していると考えられる。
【００６１】
次に、図３に示したコントロールユニット２８を介して、球面収差だけでなく、デフォーカスも同時に補正した場合の共焦点軸応答を図６に示す。つまり、図６は、２つの異なったコスト値を用いて最適化された共焦点軸応答を示す図である。（ａ）はＷＩＥＭを用いた場合、（ｂ）は１１μｍ×１１μｍのピンホール出力を用いた場合である。ＥからＨで示されるそれぞれの線は、最適化過程における異なった世代の共焦点軸応答を示している。図６では、遺伝的アルゴリズムにおける世代交代に従って、軸応答が改善されていく様子がＥ〜Ｈの線で示されている。Ｆで示される線は遺伝的アルゴリズムの第１４世代を、Gで示される線は第２８世代を、Hで示される線は第７０世代を示す。また、Eで示される線は最適化前の共焦点軸応答を表している。ここで、図６（ａ）に示すように、ＷＩＥＭを用いた場合は各世代で正しくデフォーカスが補正されているのに対し、図６（ｂ）で示すように、ピンホールを用いた場合にはデフォーカスの位置の補正にふらつきがあることが判る。これは、ピンホール（ＣＣＤカメラのピクセル位置の選択)が完全ではなかったため、最適化アルゴリズムが、図５（ｂ）’で示されるように、デフォーカスが非０の解に集束したためだと考えられる。
【００６２】
以下にまとめると、本発明者らは、情報エントロピーを用いた波面評価方法、即ち、波面の平坦度評価方法（Wavefront Correlation Information Entropy Method、ＷＩＥＭ）及び、この方法を用いる波面の平坦度評価装置を発明した。そして、本発明の方法を用いる波面の平坦度評価装置は、極めて単純（シンプル）な光学系及びデジタル信号処理装置の組み合わせにより実現されるので、容易に様々な光学系（装置）に埋め込むことが可能である。そして、上記波面の平坦度評価装置が埋め込まれた光学系の収差を容易に補正することができる。
【００６３】
そのようなＷＩＥＭ（ＷＩＥＭを用いる平坦度評価装置）を埋め込んだ装置の実施例として、本発明者らは収差補正能力をもった図３に示すような共焦点顕微鏡装置１１を作成した。この共焦点顕微鏡装置１１では、試料２４と対物レンズ２２との間の屈折率不整合層であるフューズドシリカ層２５に起因する球面収差を補正するために、可変鏡（薄膜可変鏡）２１が組み込まれている。
【００６４】
この共焦点顕微鏡装置１１中の波面の平坦度を、共焦点顕微鏡装置（システム）１１中に埋め込まれた本発明の波面の平坦度評価装置１ａを用いて、ＷＩＥＭにより評価し、その値を元にして遺伝的アルゴリズムによって可変鏡２１の形状の最適化を行った。その結果、この共焦点顕微鏡装置１１により、本発明者らは、厚さ３．４ｍｍのフューズドシリカ層２５によって発生した球面収差を補正することに成功した。
【００６５】
以上、本発明に係る情報エントロピーを用いた波面評価方法等の実施形態を実施例に基づいて説明したが、本発明は特にこのような実施例に限定されることなく、特許請求の範囲記載の技術的事項の範囲内でいろいろな実施例があることはいうまでもない。
【００６６】
【発明の効果】
以上の構成から成る本発明によると、簡単なシステムで、容易に様々な光学系に適用することができ、波面の平坦度を定量的に評価して、容易かつ確実に共焦点顕微鏡等の光学系における収差の補正を行うことができる。
【図面の簡単な説明】
【図１】本発明の実施例に係る波面の平坦度評価方法（ＷＩＥＭ）を実施するための波面の平坦度評価装置（光学系）の模式的な構成図である。
【図２】幾つかの種類の波面の例と、その自己相関の形状と、ＷＩＥＭ値を示す図である。
【図３】本実施例の共焦点顕微鏡装置１１の模式的な構成図である。
【図４】共焦点顕微鏡の共焦点（コンフォーカル）軸応答を示すグラフである。
【図５】球面収差及びデフォーカスを持った波面のＷＩＥＭ値、ピンホール出力、及びピンホールがＣＣＤカメラ２７の受光面内の縦、横各方向にそれぞれ１１μｍずれた場合のピンホール出力の特性を示す図である。ただし、強度は規格化されている。
【図６】２つの異なったコスト値を用いて最適化された共焦点軸応答を示す図である。（ａ）はＷＩＥＭを用いた場合、（ｂ）は１１μｍ×１１μｍのピンホール出力を用いた場合である。
【符号の説明】
１ 波面の平坦度評価装置
２、２６ フーリエ変換レンズ
３、２７ ＣＣＤカメラ
４、２９ デジタル信号処理装置
１１ 共焦点顕微鏡装置
１２ 光源
１４ 偏光子
１５、１７、２６ レンズ
１６ ピンホール
１８ ビームスプリッタ
１９ 偏光ビームスプリッタ
２０ １／２波長板
２１ 可変鏡（薄膜可変鏡）
２２ 対物レンズ
２３ 走査ステージ
２４ 試料
２５ 屈折率不整合層（フューズドシリカ層）
２８ コントロールユニット
３０ 共焦点スポット[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a wavefront evaluation method, a wavefront evaluation method using information entropy that can be used as a wavefront monitor in an adaptive optical system, a wavefront flatness evaluation device, and an optical device such as a confocal microscope using the same, And an aberration correction method of the optical device.
[0002]
[Prior art]
For example, in the precision machinery industry and other industrial fields that require precise processing of objects, a system capable of quantitatively measuring (microscopically measuring) the surface shape of processed objects with high accuracy is required. The In such industrial microscopic measurement, it is often necessary to measure the shape of the object surface located under the thick refractive index mismatching layer.
[0003]
In the microscopic measurement of a living body (biological microscopic measurement), the measurement sample itself functions as a refractive index mismatching layer. In optical measurement under such conditions, it is an important issue to correct spherical aberration generated by the refractive index mismatch layer.
[0004]
In response to this problem, a wavefront correction method using an adaptive mirror (also referred to as a variable mirror, a deformable mirror, a compensation mirror, or a correction mirror) is widely used. In this wavefront correction method, one of the methods for finding a variable mirror (adaptive mirror) for wavefront correction is a simulated annealing method (simulated annealing), and the evolution of organisms. The shape of the variable mirror (adaptive mirror) is determined by using an optimization algorithm such as a genetic algorithm, which is an operational framework in which the process is extremely simplified from an engineering viewpoint. These optimization algorithms express the degree of optimization quantitatively using a single numerical value called a “cost value” and maximize or minimize the value to optimize the state of the entire system. Optimization is performed (see, for example, Non-Patent Document 1).
In the simulated annealing method, the cost value of one condition is obtained in one trial, the cost value is compared with the cost value of the previous trial, and optimization is performed to minimize the cost value. In the case of optimization that maximizes the cost value with a smaller cost value, the trial condition with the larger cost value is adopted and the trial process is repeated to optimize the trial condition. It is an algorithm like this.
[0005]
In living body microscopic measurement, a confocal microscope in a fluorescence mode is widely used. A confocal microscope (confocal scanning microscope) is one of the means for measuring the shape of an object. It scans with a point probe (measurement) to produce a three-dimensional image with very high contrast. Etc. using a microscope. In the measurement using the confocal microscope in the fluorescence mode, the aberration of the entire confocal microscope apparatus (system, system) is corrected, and the fluorescence intensity increases as the concentration of the three-dimensional light in the sample increases. The confocal signal strength also increases. Therefore, the confocal output intensity of the fluorescence itself can be used as a cost value for aberration correction.
[0006]
On the other hand, in a linear confocal microscope that does not use non-linear phenomena such as fluorescence, the confocal output intensity, that is, the intensity of light passing through the detection pinhole provided in the confocal microscope, is optimal as a cost value. Absent. Therefore, normally, a wavefront sensor called a Shack Hartmann wavefront sensor or a wavefront measurement method such as an interferometry is used to detect the state of the wavefront in the system and correct the aberration based on the detected state. Yes.
[0007]
[Non-Patent Document 1]
Lijun Zhu, Pang-Chen Sun, Dirk-Uwe Bartsch, William R. Freeman, Yeshaiahu Fainman, “Adaptive Control of a Micromachined Continuous-Membrane Deformable Mirror for Aberration Compensation,” Appl. Opt., 38, 168-176 (1999)
[0008]
[Problems to be solved by the invention]
However, the above method has the following problems. First, since an additional wavefront measurement system is required in addition to the original system (apparatus, system) configuration, the entire system becomes complicated. Furthermore, there is a problem that a part of the energy of the signal light is consumed for monitoring the wavefront. In addition, these wavefront measurement methods require a large amount of calculation power (calculation time) in order to reconstruct the wavefront from the measured focal position shift and interference fringes.
[0009]
Furthermore, this wavefront measurement method obtains a “physical state” of the shape of the wavefront itself and not a single “value” that can be used as a cost value. In other words, in order to obtain the cost value for the optimization algorithm, the question “how to calculate a single“ number ”of the degree of optimization from the physical state of“ wavefront ”” remains unresolved. .
[0010]
In view of the above, the present invention can be easily applied to various optical systems with a simple system, can quantitatively evaluate the flatness of the wavefront, and can easily and reliably use a confocal microscope or the like. It is an object to realize a wavefront evaluation method using information entropy, a wavefront flatness evaluation apparatus, a confocal microscope apparatus incorporating the same, and an aberration correction method for the confocal microscope apparatus capable of correcting aberrations in an optical system It is what.
[0011]
[Means for Solving the Problems]
In order to solve the above-mentioned problem, the present invention performs Fourier transform on the wavefront to be measured of incident light, images the spot shape of the wavefront to be measured of the Fourier-transformed light, and based on the signal about the spot shape Provided is a wavefront evaluation method using information entropy characterized in that the flatness of the wavefront to be measured is quantitatively evaluated by calculating and outputting the flatness of the wavefront to be measured as one numerical value To do.
[0012]
The present invention also includes subjecting a measured wavefront of incident light to Fourier transform, photographing a spot shape of the measured wavefront of the Fourier-transformed light as a spatial power spectrum of a photoelectric field, and converting the spatial power spectrum to discrete Fourier An autocorrelation of the wavefront to be measured is obtained by conversion, a probability distribution of information in the autocorrelation of the wavefront to be measured is obtained, and an information entropy obtained from the probability distribution is output as a single numerical value. A wavefront evaluation method using information entropy characterized by quantitatively evaluating the flatness of a wavefront.
[0013]
Further, the present invention Fourier transforms the wavefront to be measured of the incident light, photographs the spot shape of the wavefront to be measured of the Fourier-transformed light, performs calculation processing based on the signal about the spot shape, The flatness of the wavefront to be measured is output as a single numerical value to quantitatively evaluate the flatness of the wavefront to be measured, and the wavefront to be measured is determined by an optimization algorithm using the single numerical value as a cost value. The present invention provides an aberration correction method characterized by optimizing the shape of a deformable mirror used for correcting the aberration and correcting the aberration.
[0014]
The present invention also includes subjecting a measured wavefront of incident light to Fourier transform, photographing a spot shape of the measured wavefront of the Fourier-transformed light as a spatial power spectrum of a photoelectric field, and converting the spatial power spectrum to discrete Fourier An autocorrelation of the wavefront to be measured is obtained by conversion, a probability distribution of information in the autocorrelation of the wavefront to be measured is obtained, and an information entropy obtained from the probability distribution is output as a single numerical value. The flatness of the wavefront is quantitatively evaluated, and the shape of the variable mirror used for correcting the wavefront to be measured is optimized and the aberration is corrected by an optimization algorithm using the one numerical value as a cost value. An aberration correction method is provided.
[0015]
The present invention also includes an optical system including a single lens and a CCD camera, and a digital signal processing device. The measured wavefront of incident light is captured by the CCD camera via the lens, and the digital A wavefront flatness evaluation apparatus characterized by quantitatively evaluating the flatness of the wavefront to be measured by calculating and outputting the flatness of the wavefront to be measured as one numerical value by a signal processing device. provide.
[0016]
The one lens is preferably a Fourier transform lens that Fourier transforms a wavefront to be measured.
[0017]
The present invention also includes an optical system including a single lens and a CCD camera, and a digital signal processing device. The measured wavefront of incident light is captured by the CCD camera via the lens, and the digital A wavefront flatness evaluation device that quantitatively evaluates the flatness of the wavefront to be measured by calculating and outputting the flatness of the wavefront to be measured as one numerical value by a signal processing device, and the wavefront to be measured A variable mirror that is used for the correction of the aberration, the shape of the variable mirror is optimized and the aberration is corrected by an optimization algorithm using the one numerical value as a cost value. A focus microscope apparatus is provided.
[0018]
The one lens is preferably a Fourier transform lens that Fourier transforms a wavefront to be measured of incident light.
[0019]
DETAILED DESCRIPTION OF THE INVENTION
DESCRIPTION OF EMBODIMENTS Embodiments of a wavefront evaluation method using information entropy according to the present invention will be described with reference to the drawings based on examples. Before describing the embodiments of the present invention, first, the principle of the present invention will be briefly described.
[0020]
What needs to be performed in aberration correction in a microscope, which is one of the objects of the present invention, is “to flatten the detected wavefront”. That is, it is not necessary to actually measure the shape of the wavefront, and it is only necessary to obtain some value representing the flatness of the wavefront. Therefore, the present inventors considered using a simple wavefront sensor that outputs the flatness of the wavefront as a single numerical value as one effective solution.
[0021]
Specifically, as the role of this wavefront sensor, the inventors of the present invention are provided with an optical system including only a CCD camera and a Fourier transform lens as one lens, as shown in an embodiment described later. A wavefront evaluation method using information entropy for quantitatively evaluating wavefront flatness using a wavefront flatness evaluation apparatus, that is, a wavefront flatness evaluation method (Wavefront-correlation information entropy method, hereinafter, Invented WIEM).
[0022]
Furthermore, in order to demonstrate the effectiveness of the wavefront flatness evaluation apparatus and flatness evaluation method of the present invention, as shown in the examples described later, this flatness evaluation apparatus is embedded, and additional wavefront sensors and the like are separately added. An adaptive optical confocal microscope apparatus (a confocal microscope apparatus according to the present invention) that dynamically corrects aberrations without using an optical system (apparatus, system) was created.
[0023]
The wavefront flatness evaluation apparatus and flatness evaluation method invented (suggested) here are not limited to application to confocal microscope apparatuses, but all kinds of wavefront evaluations, particularly wavefronts in adaptive optical systems. It can be used as a monitor. Moreover, the aberration of optical systems, such as a confocal microscope, can be correct | amended using these flatness evaluation apparatuses and flatness evaluation methods.
[0024]
(Example)
FIG. 1 shows a wavefront flatness evaluation method proposed by the present inventors, that is, a wavefront flatness evaluation apparatus 1 which is an optical system (apparatus) for carrying out WIEM. In short, FIG. 1 is a minimum system configuration diagram for WIEM. The wavefront flatness evaluation device (optical system) 1 includes a Fourier transform lens (FT lens) 2, a CCD camera 3, and a digital signal processing device 4 which are a single lens. As described above, the wavefront flatness evaluation device (optical system) 1 has an extremely simple configuration of an optical system including the Fourier transform lens 2 and the CCD camera 3 and a digital signal processing device 4, and therefore, this embodiment to be described later. Can be easily embedded in the confocal microscope apparatus (see FIG. 3).
[0025]
The Fourier transform lens 2 performs Fourier transform on the measured wavefront Φ (x, y) of the incident light h. The CCD camera 3 captures the spot shape of the wavefront to be measured Φ (x, y) of the light h subjected to Fourier transform. Note that the focal point thus formed on a surface such as the image receiving surface of the CCD camera 3 is referred to as a confocal spot, and the shape of the confocal spot is referred to as a spot shape.
[0026]
The digital signal processing device 4 performs a calculation process for quantitatively evaluating the flatness of the wavefront to be measured based on the signal about the spot shape photographed by the CCD camera 3. That is, the digital signal processing device 4 performs calculation processing based on the signal regarding the spot shape and outputs the flatness of the wavefront to be measured as one numerical value. This calculation process will be specifically described below as a wavefront flatness evaluation method.
[0027]
The operation of the wavefront flatness evaluation apparatus 1 according to this embodiment and the wavefront flatness evaluation method (WIEM) of the present invention using the wavefront flatness evaluation apparatus 1 will be described with reference to FIG. In the wavefront flatness evaluation apparatus (optical system) 1, the measured wavefront (wavefront) Φ (x, y) of the incident light (coherent light) h is Fourier-transformed by the Fourier transform lens 2, and the spot shape is CCD camera. 3 is taken. Since the CCD camera 3 responds to the light intensity, the photo is taken as shown by the following formula (1): photoelectric field W (x, y) = exp [iΦ (x, y) ] Is a spatial power spectrum C ^ ([mu], [nu]). That is, the CCD camera 3 captures a spatial power spectrum C ^ (μ, ν). Here, the spatial power spectrum is a signal obtained by decomposing and displaying a spatial structure into the frequency of the structure, that is, a signal of the square of the absolute value of the spatial spectrum. (In FIG. 1, the description of “squared” in the CCD camera 3 indicates that a spatial power spectrum is captured by the CCD camera 3 as meant by this definition.)
[0028]
C ^ (μ, ν) = | Fourier [W (μ, ν)] | ² (1)
[0029]
Here, Fourier [W (μ, ν)] represents the Fourier transform of the photoelectric field W (x, y). Here, since the spatial power spectrum C ^ (μ, ν) is sampled by the CCD camera 3, it is a discrete function regarding μ and ν.
[0030]
Next, the spatial power spectrum C ^ ([mu], [nu]) is subjected to discrete Fourier transform on a computer built in the digital signal processing device 4, thereby obtaining the formula (2) according to Wiener-Khinchin's theorem. As shown in the above, autocorrelation (also referred to as autocorrelation function) C (x, y) of the original wavefront (original wavefront to be measured) is obtained. Here, the autocorrelation is obtained by integrating f (x) × f * (x + χ) with respect to x from minus infinity (−∞) to plus infinity (+ ∞) with respect to the function f (x). It is a function that can be obtained. Here, f * (x) is a complex conjugate function of the function f (x). The Wiener Hinchin theorem is a theorem that the autocorrelation function of a spatial signal and the spatial power spectrum of the signal have a Fourier transform relationship.
[0031]
C (x, y) = W (x, y) & W (x, y) (2)
[0032]
However, the symbol & on the right side of Equation (2) represents the autocorrelation of the photoelectric field W (x, y). Further, the autocorrelation C (x, y) of the original wavefront in Expression (2) and the spatial power spectrum C ^ ([mu], [nu]) in Expression (1) are in a Fourier transform pair relationship. At this point, the wavefront Φ (x, y) that was originally invisible as a phase is indirectly visualized.
[0033]
Next, the absolute value of the autocorrelation C (x, y) of the original wavefront obtained here is taken, and the information in the autocorrelation C (x, y) of the original wavefront is obtained by normalizing it with the total energy. The probability distribution P (x, y) is obtained by the equation (3). (This corresponds to the description “convert to probability distribution” in the digital signal processing device 4 in FIG. 1.)
[0034]
[Expression 1]

[0035]
Finally, by substituting this probability distribution P (x, y) into the following equation (4), one value (numerical value) ε called information entropy is obtained (output). (This corresponds to the description “calculate information entropy” in the digital signal processing device 4 in FIG. 1.)
[0036]
[Expression 2]

[0037]
However, here, when P (x, y) = 0, it is defined as −P (x, y) log P (x, y) = 0, and the base of the logarithm does not matter.
[0038]
Here, the information entropy refers to a value obtained by a formula (4) from a certain probability distribution P (x, y). The information entropy ε obtained as described above has the following characteristics similar to physical entropy. That is, the higher the flatness of the probability distribution P (x, y), the larger the value of the information entropy ε. Now, the relationship represented by the following formula (5) is established.
[0039]
P (x, y) to C (x, y) = W (x, y) & W (x, y) (5)
[0040]
However, the symbol ~ on the left side of Expression (5) indicates that the value of P (x, y) is proportional to the value of C (x, y). Further, the symbol & on the right side of the equation (5) represents the autocorrelation of the photoelectric field W (x, y). Therefore, the information entropy ε takes a larger value as the flatness of the wavefront W (x, y) to be detected is higher. At this time, it is assumed that the intensity component of the wavefront to be detected is sufficiently flat compared with the phase structure of the wavefront and has a sufficient spatial extent. In order to show this feature, several examples of one-dimensional wavefronts and information entropy ε (information obtained from the wavefront Φ (x, y) by the procedure as described above), which is one numerical value obtained from the WIEM. FIG. 2 shows the entropy ε (also referred to as WIEM value). It can be seen from FIG. 2 that the information entropy (WIEM value) ε increases as the wavefront becomes flatter.
[0041]
The greatest advantage of WIEM is that the wavefront flatness evaluation apparatus (optical system, WIEM system) of the present invention used in WIEM has a simple configuration as shown in the embodiment of FIG. Therefore, this wavefront flatness evaluation device can be easily “embedded” (applied) in an optical system (device, system) that requires wavefront evaluation. As an example of such an optical system, the present inventors created a confocal microscope apparatus 11 in which the above-described WIEM system and a wavefront correcting variable mirror (thin film variable mirror) 21 are embedded (FIG. 3 described later). reference).
[0042]
The present inventors use this confocal microscope apparatus 11 to optimize the shape of the variable mirror 21 by an optimization algorithm using information entropy (WIEM value) ε, which is a single numerical value, as a cost value. The spherical aberration generated by (caused by) the refractive index mismatching layer (fused silica layer, glass layer) 25 placed before the measurement sample) 24 (see FIG. 3 described later) was corrected. In this embodiment, a genetic algorithm is used as an example of the optimization algorithm. Here, the genetic algorithm is to calculate cost values in multiple states, of which multiple states with more optimal values are adopted, a new state is created as an alternative to the state that has not been adopted, and trials are performed. It is an algorithm that optimizes the state by performing similar trials.
[0043]
In this embodiment, a genetic algorithm is used as an example of an optimization algorithm. However, the present invention is not limited to this, and other optimization algorithms such as a simulated annealing method (annealing optimization algorithm), a trial-and-error, and the like. (Repeat the act of performing a random trial, comparing the error with the error of the previous trial, adopting the one with the smaller error, and comparing the value with the next random trial. It is also possible to use an optimization algorithm).
[0044]
FIG. 3 is a schematic configuration diagram of the confocal microscope apparatus 11 of the present embodiment. That is, FIG. 3 shows a configuration diagram of the confocal microscope apparatus 11 incorporating the variable mirror 21 and the WIEM system as described above. The confocal microscope apparatus 11 includes a light source 12, a polarizer 14, a pinhole 16 for condensing and expanding light from the light source 12, lenses 15, 17, and 26 (the lens 26 is a Fourier transform lens), a light beam A polarizing beam splitter 19 and a beam splitter 18 for separating the bundle, a half-wave plate 20 used for increasing the light utilization efficiency, a variable mirror 21, an objective lens 22, a scanning stage 23, and a detector. It comprises a CCD camera 27, a control unit (control device) 28, and a digital signal processing device 29.
[0045]
As a feature of the present invention, an optical system composed of a lens 26 and a CCD camera 27 and a digital signal processing device 29 are provided (embedded) in the confocal microscope apparatus 11 of the present embodiment. The flatness evaluation apparatus 1a, that is, the WIEM system is configured. As described above, the lens 26 is a Fourier transform lens and has a focal length of 200 mm. The lens 26, the CCD camera 27, and the digital signal processing device 29 that constitute the wavefront flatness evaluation apparatus 1a are the Fourier transform lens 2 and the CCD camera 3 that constitute the wavefront flatness evaluation apparatus 1 shown in FIG. , And the digital signal processing device 4 respectively.
[0046]
As the light source 12 of the confocal microscope apparatus 11, for example, a He—Ne laser having a wavelength λ of 632.8 nm, which is a monochromatic light source, is used. The control unit 28 is connected to the scanning stage 23, the variable mirror 21, and the CCD camera 27, and controls each of them. The scanning stage 23 is controlled by the control unit 28 and can be moved in the Z-axis direction (up and down direction on the paper surface) as indicated by an arrow a by, for example, a piezoelectric element.
[0047]
In the confocal microscope apparatus 11 according to the present invention, scanning in the optical axis direction is possible without performing mechanical scanning by giving the variable mirror 21 arbitrary defocusing (movement of the image receiving surface).
[0048]
That is, according to the principle of the confocal microscope apparatus 11 of the present invention, the defocusing of the objective lens 22 is changed by the control unit 28 by changing the shape of the variable mirror 21 installed in the confocal microscope apparatus 11 of the present invention. Alternatively, the height of the sample (measurement object) 24 is measured from the value of the confocal intensity acquired with the shape of the variable mirror (compensation mirror) 21 higher than that.
[0049]
Next, the operation of the confocal microscope apparatus 11 of the present invention will be described with reference to FIG. The laser light ha from the light source 12 passes through the polarizer 14, is magnified by the lens 15 and the pinhole 16, collimated, and then the lens 17, the beam splitter 18, the polarization beam splitter 19, and the half-wave plate (half-wave) The light passes through a wave plate 20 and is reflected by a variable mirror (thin film variable mirror) 21 located on the left in FIG. Then, the light is condensed on the surface of the sample 24 placed on the scanning stage 23 by the objective lens 22 through the polarizing beam splitter 19. At this time, a fused silica layer 25 which is a refractive index mismatching layer having a thickness of 3.4 mm, for example, is present between the objective lens 22 and the sample 24, thereby causing spherical aberration.
[0050]
The light hb reflected by the sample (sample) 24 passes through the polarizing beam splitter 19 and the half-wave plate 20 again and is reflected again by the variable mirror (deformation mirror, compensation mirror) 21, and then the polarizing beam splitter 19, It passes through the lens 26 via the beam splitter 18. The lens 26 is a Fourier transform lens, and Fourier transforms the measured wavefront Φ (x, y) of the incident light. Then, a confocal spot is formed on the image receiving surface of the CCD camera 27.
[0051]
At this time, if the aberration is canceled by the variable mirror (correction mirror) 21, the wavefront of the light after passing through the variable mirror (correction mirror) twice should be flat. Therefore, in the confocal microscope apparatus (system) 11, the information entropy (WIEM value) ε of the wavefront in the plane S from the confocal image obtained by the CCD camera 27 is converted by the digital signal processing apparatus 29 connected to the CCD camera 27. Calculate. That is, based on the above-described wavefront flatness evaluation method, information entropy (WIEM value) ε, which is one numerical value, is calculated (output). Further, in this digital signal processing device 29, as shown in FIG. 3, a variable mirror ((3) is calculated by using a genetic algorithm using the value, that is, information entropy (WIEM value) ε as a cost value. The shape of the deformable mirror 21 is optimized.
[0052]
In a conventional optical system such as a confocal microscope apparatus, a pinhole and a point detector are used as measurement apparatuses, whereas in the confocal microscope apparatus 11 of the present embodiment, a CCD camera 27 is used and an image sensor of the CCD camera 27 is used. The confocal measurement is performed by measuring the light intensity on a certain range of pixels. That is, in the confocal microscope apparatus 11 of the present embodiment, the wavefront according to the present invention can be easily obtained by replacing the pinhole and point detector used in the conventional confocal microscope apparatus with the CCD camera 27. The flatness evaluation apparatus 1a, that is, the WIEM optical system (WIEM system) can be embedded.
[0053]
(Experimental example)
Here, in practice, the digital signal processing device 29 optimizes the shape of the variable mirror (compensation mirror) 21 via the control unit 28 by calculating the WIEM value ε as a cost value using a genetic algorithm. An attempt was made to eliminate aberrations. In the genetic algorithm, 30 individuals having a voltage value applied to each drive electrode (not shown) of the variable mirror (compensation mirror) 21 as genes are used, and generations are changed up to 70 generations. In the generational alternation, 21 individuals are randomly mated with the next generation parents in descending order of the WIEM value ε among the generations, and mutations are given as appropriate. In addition, a measurement object (in the embodiment shown in FIG. 3, the sample 24 is placed under the refractive index mismatching layer (in the embodiment shown in FIG. 3, the fused silica layer 25 is placed as the refractive index mismatching layer). For reference, a normal plane mirror is used instead of the sample 24 for reference.
[0054]
FIG. 4 shows the confocal axis response after being optimized in this way. That is, FIG. 4 is a graph showing the axial response of the confocal microscope. Each axis response in FIG. 4 is measured using a variable mirror 21 optimized with a genetic algorithm using different cost values. In this measurement, one axis of the CCD camera 27 (one pixel is 11 μm × 11 μm) is regarded as a confocal pinhole, and these axis responses are measured. The line indicated by A in the figure indicates the confocal axial response before optimization, and the line indicated by D indicates the axial response after optimization by WIEM. From this, it can be seen that the combination of WIEM and the genetic algorithm corrects the spherical aberration and enhances the strength of the axial response.
[0055]
Note that the line indicated by C in the figure is a case where optimization is performed so as to maximize the pinhole output value without using WIEM. That is, the line indicated by C optimizes the shape of the deformable mirror 21 using the output from the 11 μm × 11 μm square pinhole. It can be seen that this method also corrects the aberration and increases the signal intensity. This method is very sensitive to pinhole position determination. The result when the position of the pinhole in the actual optimization is shifted by one pixel in each horizontal direction is indicated by a line indicated by B. That is, the line indicated by B optimizes the shape of the deformable mirror 21 using the output from the square pinhole shifted by one pixel vertically and horizontally. However, although the signal intensity is increased to some extent here, it is considered that the asymmetry at the position indicated by the arrow g on the right side of the signal has not been eliminated, and the aberration has not been compensated.
[0056]
In order to explain this reason, information entropy (WIEM value) ε of a wavefront having spherical aberration and defocus, a pinhole output at an ideal position (see pinhole (a) in FIG. 5), and a pin Consider the output characteristics of a pinhole (see pinhole (b) in FIG. 5) when the holes are shifted by 11 μm in the vertical and horizontal directions in the light receiving surface of the CCD camera. As in the case of the confocal microscope apparatus 11 of FIG. 3, the state of those values when it is assumed that a confocal spot is obtained using a lens having a focal length of 200 mm is shown in FIGS. Shown in (c). Here, in (a) ′ (b) ′ (c), the horizontal (horizontal) axis is the spherical aberration coefficient of the wavefront to be detected, and the vertical (vertical) axis is the defocus (defocus) coefficient.
[0057]
From this, it can be seen that both the WIEM value ε and the pinhole output at the ideal position have only one peak Pa at a point where the spherical aberration and the defocus are both 0 (FIGS. 5 (a) ′ (c )reference). In other words, the wavefront can be optimized using either of these values as the cost value. However, when the position of the pinhole is shifted (see FIG. 5B), the aspect is greatly different. The pinhole output accompanied by the position shift has four peaks P1, P2, P3, and P4 on the spherical aberration-defocus plane, and none of them shows the optimum solution (see FIG. 5B ′). For example, in the case of FIG. 4 described above, it seems that the optimization algorithm has found a solution in which the spherical aberration is not canceled, which exists on the defocused line.
[0058]
This problem is not a mathematical search problem but a problem that occurs when converting a physical state into a numerical value. Therefore, it cannot be solved by improving the optimization algorithm itself. On the other hand, in order to calculate the information entropy (WIEM value) ε, as can be seen from the equation (4), the position information is not used, and only the intensity histogram in the confocal shape is used. For this reason, in WIEM, it is possible to eliminate arbitraryness such as determination of the optical axis.
[0059]
The WIEM value reflects all the lateral (lateral) confocal spot shapes, whereas the pinhole output reflects only the local light intensity. If the cost function for calculating the cost value is global, the globality of the search required for the optimization algorithm is reduced, and it is simpler and simpler, such as the simulated annealing method already described. Optimization with an algorithm with a small amount of calculation and search becomes possible. In such an application, since a single trial involves physical measurement, the time required for optimization can be dramatically reduced by reducing the search amount.
[0060]
Further, if the cost value itself reflects global information, the risk of convergence to a local solution during optimization is reduced. This also suggests that the information entropy (WIEM value) ε is more suitable as a cost value than the pinhole output.
[0061]
Next, FIG. 6 shows a confocal axis response when not only spherical aberration but also defocus is simultaneously corrected via the control unit 28 shown in FIG. That is, FIG. 6 is a diagram illustrating the confocal axis response optimized using two different cost values. (A) is a case where WIEM is used, and (b) is a case where a pinhole output of 11 μm × 11 μm is used. Each line indicated by E to H shows the different generations of the confocal axis response in the optimization process. In FIG. 6, the manner in which the axial response is improved according to the generational change in the genetic algorithm is indicated by lines E to H. The line indicated by F indicates the 14th generation of the genetic algorithm, the line indicated by G indicates the 28th generation, and the line indicated by H indicates the 70th generation. The line indicated by E represents the confocal axis response before optimization. Here, as shown in FIG. 6 (a), when WIEM is used, defocus is correctly corrected in each generation, whereas as shown in FIG. 6 (b), when a pinhole is used. It can be seen that there is fluctuation in the defocus position correction. This is thought to be because the pinhole (selection of the pixel position of the CCD camera) was not perfect, so that the optimization algorithm was focused on a non-zero solution as shown in FIG. 5 (b) '. It is done.
[0062]
In summary, the present inventors have developed a wavefront evaluation method using information entropy, that is, a wavefront flatness evaluation method (Wavefront Correlation Information Entropy Method, WIEM) and a wavefront flatness evaluation apparatus using this method. Invented. Since the wavefront flatness evaluation apparatus using the method of the present invention is realized by a combination of an extremely simple optical system and a digital signal processing apparatus, it can be easily embedded in various optical systems (apparatuses). Is possible. The aberration of the optical system in which the wavefront flatness evaluation device is embedded can be easily corrected.
[0063]
As an example of an apparatus in which such WIEM (flatness evaluation apparatus using WIEM) is embedded, the present inventors have created a confocal microscope apparatus 11 having an aberration correction capability as shown in FIG. In the confocal microscope apparatus 11, a variable mirror (thin film variable mirror) 21 is provided to correct spherical aberration caused by the fused silica layer 25, which is a refractive index mismatch layer between the sample 24 and the objective lens 22. It has been incorporated.
[0064]
The flatness of the wavefront in the confocal microscope apparatus 11 is evaluated by WIEM using the wavefront flatness evaluation apparatus 1a of the present invention embedded in the confocal microscope apparatus (system) 11, and the value is based on the original value. Thus, the shape of the deformable mirror 21 was optimized by a genetic algorithm. As a result, with this confocal microscope apparatus 11, the inventors succeeded in correcting the spherical aberration generated by the fused silica layer 25 having a thickness of 3.4 mm.
[0065]
As described above, the embodiments of the wavefront evaluation method using the information entropy according to the present invention have been described based on the examples. However, the present invention is not particularly limited to such examples, and is described in the claims. It goes without saying that there are various embodiments within the scope of technical matters.
[0066]
【The invention's effect】
According to the present invention having the above-described configuration, it can be easily applied to various optical systems with a simple system, and the flatness of the wavefront can be quantitatively evaluated to easily and reliably use an optical system such as a confocal microscope. It is possible to correct aberrations in the system.
[Brief description of the drawings]
FIG. 1 is a schematic configuration diagram of a wavefront flatness evaluation apparatus (optical system) for carrying out a wavefront flatness evaluation method (WIEM) according to an embodiment of the present invention.
FIG. 2 is a diagram showing examples of several types of wavefronts, autocorrelation shapes, and WIEM values.
FIG. 3 is a schematic configuration diagram of a confocal microscope apparatus 11 of the present embodiment.
FIG. 4 is a graph showing the confocal axis response of a confocal microscope.
FIG. 5 shows the characteristics of the pinhole output when the WIEM value of the wavefront having spherical aberration and defocus, the pinhole output, and the pinhole are shifted by 11 μm in the vertical and horizontal directions in the light receiving surface of the CCD camera 27, respectively. FIG. However, the strength is standardized.
FIG. 6 shows a confocal axis response optimized using two different cost values. (A) is a case where WIEM is used, and (b) is a case where a pinhole output of 11 μm × 11 μm is used.
[Explanation of symbols]
1 Wavefront flatness evaluation system
2, 26 Fourier transform lens
3, 27 CCD camera
4,29 Digital signal processing device
11 Confocal microscope
12 Light source
14 Polarizer
15, 17, 26 Lens
16 pinhole
18 Beam splitter
19 Polarizing beam splitter
20 1/2 wavelength plate
21 Variable mirror (thin film variable mirror)
22 Objective lens
23 Scanning stage
24 samples
25 Index mismatch layer (fused silica layer)
28 Control unit
30 Confocal spot

Claims (2)

Fourier transform the wavefront to be measured of incident light,
Photographing the spot shape of the wavefront to be measured of the Fourier-transformed light as a spatial power spectrum of a photoelectric field ,
Obtain the autocorrelation of the measured wavefront by performing a discrete Fourier transform on the spatial power spectrum,
Obtain the probability distribution of information in the autocorrelation of the measured wavefront,
A wavefront evaluation method using information entropy, characterized by quantitatively evaluating the flatness of the wavefront to be measured by outputting information entropy obtained from the probability distribution as one numerical value. Fourier transform the wavefront to be measured of incident light,
Photographing the spot shape of the wavefront to be measured of the Fourier-transformed light as a spatial power spectrum of a photoelectric field,
Obtain the autocorrelation of the measured wavefront by performing a discrete Fourier transform on the spatial power spectrum,
Obtain the probability distribution of information in the autocorrelation of the measured wavefront,
By outputting information entropy obtained from the probability distribution as one numerical value, the flatness of the wavefront to be measured is quantitatively evaluated ,
An aberration correction method characterized by optimizing the shape of a variable mirror used for correcting the wavefront to be measured and performing aberration correction by an optimization algorithm using the one numerical value as a cost value.

Images