JP4074033B2 - Wavefront error detection apparatus and wavefront error detection method - Google Patents

Description

【００３８】
ここで、Φは動径多項式であり、次式（２）〜（７）で表される。
【００３９】
【数２】

【００４０】
【数３】

【００４１】
【数４】

【００４２】
【数５】

【００４３】
【数６】

【００４４】
【数７】

【００４５】
ツェルニケ（Zernike）多項式は直交関数系であるので、各項の係数値Ａpq，Ｂpqは独立に決定でき、各項は光学収差に対応している。さらに、rに対して低次の項はザイデル収差に対応し、第二項はティルト、第三項は焦点外れ、第四項は非点収差、第五項はコマ収差を表す。以降で各項をツェルニケ（Zernike）モードあるいは単にモードと総称する。今、波面誤差の中でも特に支配的な項となる第四項まで（２次まで）で近似できるものと仮定する。従って、本発明においては、可変形状鏡４において、ツェルニケ（Zernike）多項式で展開可能な任意の波面収差を任意の周波数と任意の振幅とで重畳可能である。
【００４６】
図３は、上式（１）の第二項のティルトに関する係数値Ａ11を横軸に検出光強度（検出光強度の直流成分振幅（Normalized Optical Power））を縦軸にとって検出光強度のツェルニケ（Zernike）係数依存性を表したものである。検出光強度は各検出器の位置（マルチモードファイバ１７〜２２に対応）により異なり、２３は、マルチモードファイバ１７（位置ａ）の検出器出力を、２４は、マルチモードファイバ１８（位置b）及び２２（位置f）の検出器出力、２５は、マルチモードファイバ１９（位置c）及び２１（位置e）の検出器出力、そして、２６は、マルチモードファイバ２０（位置d）の検出器出力を示す。各出力とも原点に関して非対称な特性を持ち、また原点付近では傾きが一定な直線となることが特徴である。原点付近の傾きに関してファイバの幾何学的な配置によりファイバ１９及び２１（位置cとe）、及び、ファイバ１８及び２２（位置bとf）とは各々同じ特性を持ち、またファイバ１７と２０（位置aとd）、ならびに、ファイバ１８，２２（位置ｂ, ｆ）とファイバ１９，２１（位置ｃ, ｅ）とは大きさが等しく反対符号の関係となる。従って、これらの傾きは、2種類の定数α，βを使って表すことができ、ファイバ１７〜２２（位置ａ, ｂ, ｃ, ｄ, ｅ, ｆ）のそれぞれの出力の原点付近での傾きは、(α, β, −β, −α, −β, β)とベクトル的に表現できる。
【００４７】
図４は、上式（１）の第二項のＡ11と直交方向のティルトに関する係数値Ｂ11を横軸に検出光強度（検出光強度の直流成分振幅（Normalized Optical Power））を縦軸にとって表したものである。２７、２８、２９はそれぞれ、ファイバ１７及び２０（位置ａとｄ）、ファイバ１８及び１９（位置ｂとｃ）、そして、ファイバ２１及び２２（位置ｅとｆ）の検出器出力を表し、Ａ11と同様に原点に関して非対称な特性を持つことが特徴である。位置ａ〜ｆの原点付近での検出器出力の傾きベクトルは１種類の定数γを用いて(０, γ, γ, ０, −γ, −γ)と表すことができる。Ａ11 、Ｂ11の場合において原点での各傾きベクトルに関して内積演算を実行すると０となる。このことは、Ａ11、Ｂ11の場合において各検出器出力が直交関係にあることを意味している。
【００４８】
図５は、上式（１）の第三項の焦点外れに関する係数値Ａ20を横軸に検出光強度（検出光強度の直流成分振幅（Normalized Optical Power））を縦軸に表したもので、全てのファイバの検出器出力３０が位置によらず等しい特性を持つことを示している。各位置ａ〜ｆの検出器出力とも原点に関して対称な特性を持ち、さらに、原点付近では傾きベクトルが(0, 0, 0, 0, 0, 0)となることが特徴である。
【００４９】
図６は、上式（１）の第四項の非点収差に関する係数値Ａ22を横軸に検出光強度（検出光強度の直流成分振幅（Normalized Optical Power））を縦軸に表したもので、検出器出力３１は位置ａ及びｄのファイバ（検出器）１７及び２０、検出器出力３２は、位置ｂ, ｃ, ｅ, ｆのファイバ（検出器）による特性を示す。３１及び３２はファイバ（検出器）の位置により異なる特性を示すものの、全てが原点に関して対称な特性を持ち、図５の場合と同様に原点付近では傾きが0となることが特徴である。
【００５０】
図７は、上式（１）の第四項のＡ22と直交する方向の非点収差に関する係数値Ｂ22を横軸に検出光強度（検出光強度の直流成分振幅（Normalized Optical Power））を縦軸に表したものである。特性３３は位置ａ及びｄの検出器出力、特性３４は位置ｂ, ｃ, ｅ, ｆにおける検出器出力を示す。図６と同様に、２種類の特性３３及び３４はいずれも原点に関して対称な特性を持ち、原点付近では傾きが0となることが特徴である。
【００５１】
従って、原点付近の傾きベクトルに着目すると、ティルトの波面誤差を分離することができる。すなわち、波面誤差が十分に小さい領域では上記傾きベクトルを各ファイバ（検出器）からの光強度信号を成分に持つベクトルとの内積演算することでティルト成分を分離することが可能となる。
【００５２】
しかしながら、このままでは各係数変化に対して、対称に強度変化する焦点外れ成分、及び、非点収差成分を分離することはできない。この課題解決のため外部から周期的で且つ微小振幅の正弦波信号（ディザー信号）を特定の既知波面収差に割り当てて重畳する。この既知波面収差として焦点外れ成分を割り当てる場合、波面誤差の焦点外れ項成分、非点収差項の直交二成分を分離できる。以下にその原理を説明する。
【００５３】
まず、焦点外れ成分に関するディザー信号を可変形状鏡（図１の４）を介して重畳する。これにより光強度信号は重畳信号に応じて変化する。次にこの光強度信号の振幅を同期検波法により取り出す。取り出した信号、すなわち、振幅は、焦点外れ量を微小に変化させた時の光強度変化の実効値を表す。この操作を波面誤差の係数値を連続的に変化させながら実行し、波面誤差係数値−光強度変化の実効値特性を得る。このとき、各ファイバ（検出器）毎の光強度変動分の原点付近の傾きを要素に持つベクトルを考える。連続的に変化させる波面誤差係数の種類毎に得られる各ベクトルはティルト以外の波面誤差成分に関して互いに直交関係となる。すなわち、波面誤差が十分に小さい領域では上記変動分の傾きベクトルを各検出器からの光強度変動の実効値信号に乗算することで、焦点外れ、非点収差の成分を分離することが可能となる。
【００５４】
図８は既知波面収差として焦点外れに関するディザー信号を重畳した状態で焦点外れに関する係数値Ａ20を連続的に変化させた場合の検出光強度変動の実効値（検出光強度の交流成分振幅 (Amplitude of Power Oscillations)）を縦軸に係数値Ａ20を横軸にとって表したものである。検出器の位置ａ〜ｆによらず光強度変動は全て等しい特性３５となる。原点に関して反対称の特性を持ち原点付近での傾きは近似的に定数値となり、この値をηとする。光強度変動分の原点付近での傾きは、検出器ａ〜ｆの順序を持つ要素をもつ強度変動の傾きベクトル (η, η, η, η, η, η)として表すことが可能である。
【００５５】
図９は焦点外れのディザー信号を入力した状態で非点収差に関する係数値Ａ22を横軸に、検出光強度変動の実効値（検出光強度の交流成分振幅(Amplitude of Power Oscillations)）を縦軸にとって表したもので、ファイバ（検出器）１７及び２０（位置ａ及びｄ）の出力変動３６は常に０であり、原点付近の傾きは０となる。その他のファイバ（検出器）の出力変動特性３７及び３８は全て直線的に変化し、傾きの絶対値が等しく符号の異なる２種類の特性であらわされる。すなわち、ファイバ（検出器）１８及び２１（位置ｂとｅ）の傾きをεとするとファイバ（検出器）１９及び２２（位置ｃとｆ）の傾きは−εとなる。強度変動の傾きベクトルは (ε,−ε/２,−ε/２, ε,−ε/２,−ε/２)として表される。このベクトルと焦点外れに関する係数値Ａ20を連続的に変化させた場合の強度変動の傾きベクトル (η, η, η, η, η, η)との内積演算を行うと０になる。このことはこれらのベクトルが直交していることを意味する。
【００５６】
同様に、図１０は、非点収差に関する係数値Ｂ22を横軸に、検出光強度変動の実効値（検出光強度の交流成分振幅(Amplitude of Power Oscillations)）を縦軸にとって表したもので、傾きの絶対値が等しく符号の異なる２種類の特性３９及び４０で表される。強度変動の傾きベクトルは(０, ζ, −ζ, ０, ζ, −ζ)となり、図８、図９の傾きベクトルと直交することが分かる。一方、波面誤差内にティルト成分のみが存在する場合、光強度変動の実効値は係数値の変化に対して常に０となる。
【００５７】
従って、波面誤差が十分に小さい領域では上記変動分の傾きベクトルを各検出器からの光強度変動の実効値信号に乗算することで、焦点外れの波面誤差成分と非点収差の波面誤差成分とを分離することが可能となる。
【００５８】
以上では２種類の傾きベクトル要素の特徴の違いを用いることでZernike波面誤差成分を分離できることを示した。このベクトルを合成して12×5行列とし、その逆行列(5×12行列)を求めれば、この逆行列を用いてZernike波面誤差係数を推定することができる。以下にZernike誤差係数推定法を説明する。
【００５９】
まず、６個の光強度の傾き要素と６個の光強度変動の傾き要素をあわせて１２要素のベクトルとし、さらにこの１２要素のベクトルを行ベクトルとして、ティルト、焦点外れ、非点収差の５種類のZernike波面誤差モード毎に列方向に並べて[12×5]行列を構成する。この12×5行列を以下ではObservation Matrix（オブザベーション行列）[O(12,5)]と総称し、次式(8)のように定義する。
【００６０】
【数８】

【００６１】
実際に観測される信号は次のように定義する。すなわち焦点外れに関するディサー信号を重畳した状態で６個の各検出器により得られた光強度信号から、６個の直流成分(p_a, p_b, p_c, p_d, p_e, p_f)と６個の変動実効値成分(o_a, o_b, o_c, o_d, o_e, o_f)を取り出し次式(9)のような12元ベクトルで表す。以降ではこのベクトルをMeasurement Vector （観測信号ベクトル）[M(12,1)]と総称する。
【００６２】
【数９】

【００６３】
一方、波面に含まれる波面誤差をZernike Error Vector（ツェルニケエラーベクトル（波面誤差成分））［Ｚ（1,5）］として定義し、次式（１０）のように表す。
【００６４】
【数１０】

【００６５】
すると、次のような関係が成り立つ。
【００６６】
【数１１】

【００６７】
[O]は計算によって予め算出できるので、波面誤差[Z]の推定を行うためには実測値[M]に[O]の逆行列を左側から乗算すればよいことが分かる。しかしながら、[O]は12×5の要素を持ち正方行列ではないためそのままでは逆行列が存在しない。このため次のような手順を考える。
【００６８】
まず、［Ｏ］の転置行列［Ｏ^t］を式（８）の両辺に左から乗算する。
【００６９】
【数１２】

【００７０】
式（１２）右辺の｛［Ｏ^t］［Ｏ］｝部分は次式（１３）で表される５×５の正方行列になる。
【００７１】
【数１３】

【００７２】
この正方行列の行列式は次式（１４）のように計算できる。
【００７３】
【数１４】

【００７４】
この行列式がゼロで無い値をとるとき、式（１３）の逆行列は次のように計算できる。
【００７５】
【数１５】

【００７６】
次にこの逆行列を式（１２）の両辺に左から乗算すると
【００７７】
【数１６】

【００７８】
となり、波面収差量を算出できることが分かる。
【００７９】
今、式（１６）左辺の｛［Ｏ^t］［Ｏ］｝^-1［Ｏ］^tをEstimation Matrix （エスティメーション行列）E（５，１２）として次のように定義する。
【００８０】
【数１７】

【００８１】
ここで、各要素は次のように書き表せる。
【００８２】
【数１８】

【００８３】
【数１９】

【００８４】
【数２０】

【００８５】
【数２１】

【００８６】
【数２２】

【００８７】
【数２３】

【００８８】
このEstimation Matrixを用いれば、式（２４）で示すように１回の行列演算で波面収差を５つのツェルニケモード別に推定できることがわかる。
【００８９】
【数２４】

【００９０】
式（１８）〜式（２３）をみると各要素は傾きベクトルα〜ζの逆数に比例することが分かる。従って、式（２４）の演算を要素毎に見れば、各ファイバからの検出光強度の直流成分、ならびに、変動成分のそれぞれに対して、先に求めた傾きベクトルα〜ζの逆数に比例した量を乗算することで波面誤差を５種類のツェルニケモード毎に分離して推定できることを意味する。以降では、Estimation Matrix をツェルニケ（Zernike）モード分離用の行列（図１１）として用いる。なお、Estimation Matrixの行ベクトル間で内積をとると全ての組み合わせでゼロとなり、各々のフィルタは完全に直交していることが分かる。
【００９１】
図１２に、上記の波面誤差成分の分離方法を実現するために必要な演算部分の構成を示す。図において、１４１は局部発振器、４２は可変形状鏡（図１の４）の電極に対する電位分配係数（Actuator Matrix (13×5)）、４３はＤＡ変換器、４４はＡＤ変換器、４５は光強度信号の直流成分、４６は光強度変動の変動成分、４７は観測信号ベクトル（Measurement DATA (12×1)）、４８は積算器、１４９は局部発振正弦波信号、１５０は遅延器、１５１は積算器、５６はツェルニケ（Zernike）モード分離用の行列（Estimation Matrix (5×12)）、５７は波面誤差算出値（Zernike Error Vector (5×1)）、５８は増幅器（State Estimator）、５９は補償信号である。
【００９２】
動作について説明する。焦点外れに関するディザー信号を重畳するために、局部発振器４１により単一の周波数の正弦波４９を発生させる。この正弦波４９は制御対象となる可変形状鏡（図１の４）の電極に対する分配係数４２を乗算した後、ＤＡ変換器４３によりアナログ信号に変換して可変形状鏡（図１の４）へと送られる。分配係数４２は可変形状鏡の構造や材質により決定され、ツェルニケ（Zernike）モードの焦点外れ成分のみを変化させるような複数電極への電圧分配比に設定しておく。次に光強度検出器（図１の８）により得られた複数の光強度信号をＡＤ変換器４４によりディジタル信号に変換してさらに、直流成分４５と変動成分４６とを分離抽出した後、観測ベクトル４７を生成する。なお、直流成分４５はＡＤ変換後の信号を積算器４８を用いて積算平均することで得ることができる。また、変動成分４６は直交復調方式により抽出する。すなわち、局部発振器１４１により周波数が可変形状鏡駆動用周波数と等しい正弦波１４９を発生させ、遅延器１５０で位相調整した局部発振信号をＡＤ変換後の観測信号に乗算し、積算器１５１を用いて積算平均する。これにより変動成分の実効値を抽出することができる。ここで、遅延器１５０は局部発振信号と観測信号との間の位相ずれを補正するために設けられる。このように演算し、光強度検出器（図１の８）により得られた複数の光強度信号から、直流成分と交流成分とを分離して、かつ、各々の振幅（実効値）を算出する。
【００９３】
こうして生成された観測ベクトル４７にツェルニケ（Zernike）モード分離用の行列５６を乗算することによりツェルニケ（Zernike）モード毎に分離された波面誤差成分５７が取り出される。算出されたツェルニケ（Zernike）モード毎の波面誤差成分５７は増幅器５８により利得が調整されて補償信号５９となる。補償信号５９は、可変形状鏡（図１の４）の電極の電位分布への変換行列である分配係数行列４２が乗算された後、ＤＡ変換器４３によりアナログ信号に変換されて可変形状鏡(図１の４)へと送られる。この分配係数行列４２は実測値により予め準備可能であり、ツェルニケ（Zernike）モード分離用の行列５６と予め乗算したものを用意し、１回の乗算で可変形状鏡に送信する補償信号を算出することも可能である。以上の操作を連続的に繰り返すことで波面誤差の検出と補償を行うことができる。
【００９４】
本発明は、以上のように構成されているので、図１３及び図１４に示した従来のファイバカプラで発生していたような電極とファイバ間の放電やファイバ表面への粉塵の付着もなく、一種類のディザー周波数のみで波面誤差の分離検出が可能となるため、コスト低減が図れるとともに、可変形状鏡の応答周波数に対する要求を緩和でき、また、可変形状鏡面上の連成振動も発生しない。従って、図１６の従来のマルチディザー方式補償光学系の課題を解決する有力な方法となる。この結果、衛星と地上間の空間光通信において光アンテナにより受信したレーザ光を集光する際のスポットの広がりを最小化でき、効率良くシングルモードファイバに結合させることが可能となる。
【００９５】
【発明の効果】
この発明は、波面収差を受けた光を導入するためのアンテナ手段と、上記アンテナ手段により導入した上記光に任意の波面収差を任意の周波数で重畳するための可変形状鏡と、上記可変形状鏡により波面収差が重畳された光を集光するための集光手段と、上記集光手段の後側焦点面近傍に集光した光の強度を光軸上とその周囲の複数点において独立に検出するための複数の検出器を有する光強度検出手段と、上記光強度検出手段で検出された各々の光強度信号からその直流成分と交流成分を分離するとともに、各々の振幅を算出する算出手段と、上記算出手段により得られた複数個の振幅を成分とするベクトルに対して任意の要素をもつ行列を乗算する行列乗算手段と、上記行列乗算手段により算出された結果を可変形状鏡に加えるためのインターフェイス手段と、を備え、上記行列乗算手段における上記行列の行数が波面収差を多項式で展開した場合の展開次数に対応するとともに、上記行列の列数が上記光強度検出手段の上記検出器の個数の２倍に対応し、かつ、上記行列の行ベクトル同士が互いに直交関係をなす波面誤差検出装置であるので、電極とファイバ間の放電やファイバ表面への粉塵の付着もなく、一種類のディザー周波数のみで波面誤差の分離検出が可能となるため、コスト低減が図れるとともに、可変形状鏡の応答周波数に対する要求を緩和でき、また、可変形状鏡面上の連成振動も発生しないという効果が得られる。
【００９６】
また、可変形状鏡においてツェルニケ（Zernike） 多項式で展開可能な任意の波面収差を任意の周波数と任意の振幅とで重畳可能であるため、単一周波数で波面誤差検出を行うことができる。
【００９７】
また、集光手段の焦点面上から離間して光強度検出手段が設けられ、集光手段と光強度検出手段との間に、集光手段により集光された集光光を光強度検出手段に導入するための光伝送手段が設けられているので、集光スポットの広がりとして現れる波面誤差の影響を容易に検知することができる。
【００９８】
また、光伝送手段が、光軸上に設けられたシングルモードファイバと、光軸の周辺部に設けられた複数のマルチモードファイバとから構成されているので、波面検出のためにマルチモードファイバを通常用いて、シングルモードファイバは光強度変動による推定誤差軽減の目的とした観測強度規格化の際に用いることができ、効率よく、波面誤差検出を行うことができる。
【００９９】
また、光伝送手段の各マルチモードファイバの中心を光軸を中心とした正６角形の頂点に一致させ、かつ、マルチモードファイバを最密に配置しているので、幾何学的な配置に各ファイバが設けられているので、ファイバに対応して設けられた検出器のそれぞれの出力の原点付近での傾きをを２種類以下の定数を用いて示すことができ、演算を容易にすることができる。
【０１００】
また、算出手段において、光強度検出手段で検出された各々の光強度信号から、直交復調方式により、直流成分と交流成分を分離して、かつ、各々の振幅を算出するようにしたので、簡易な演算部により構成することができ、演算時間を短縮することができるとともに、演算部の製造コストも安価に抑えることができる。
【０１０１】
また、ツェルニケ（Zernike）多項式の展開係数の値を横軸に、検出光強度の直流成分の振幅を縦軸にとった場合の横軸原点付近の傾きを要素の一部とする行列を上記行列乗算手段が用いるようにしたので、容易にティルトの波面誤差を分離することができる。
【０１０２】
また、ツェルニケ（Zernike）多項式の展開係数の値を横軸に、検出光強度の交流成分の振幅を縦軸にとった場合の横軸原点付近の傾きを要素の一部とする行列を行列乗算手段が用いるようにしたので、容易に焦点外れ成分及び非点収差成分を分離することができる。
【０１０３】
また、ツェルニケ（Zernike）多項式の展開係数の値を横軸に、検出光強度の直流成分の振幅を縦軸にとった場合の横軸原点付近の傾きの逆数に比例した量を要素の一部とする行列を上記行列乗算手段が用いるようにしたので、容易にティルトの波面誤差を分離することができる。
【０１０４】
また、ツェルニケ（Zernike）多項式の展開係数の値を横軸に、検出光強度の交流成分の振幅を縦軸にとった場合の横軸原点付近の傾きの逆数に比例した量を要素の一部とする行列を行列乗算手段が用いるようにしたので、容易に焦点外れ成分及び非点収差成分を分離することができる。
【０１０５】
また、この発明は、波面収差を受けた光を導入するための光導入工程と、光導入工程で導入した光に焦点外れに関する波面収差を任意の周波数で重畳するための重畳工程と、重畳工程で波面収差が重畳された光を集光するための集光工程と、集光工程で集光した光の強度を光軸上とその周囲の複数点において複数の検出器により独立に検出する光強度検出工程と、光強度検出工程で検出された各々の光強度信号からその直流成分と交流成分を分離するとともに、各々の振幅を算出する算出工程と、算出工程により得られた複数個の振幅を成分とするベクトルに対して任意の要素をもつ行列を乗算する行列乗算工程と、算出工程により算出された結果に基づき焦点外れに関する波面収差を重畳するように制御する制御工程と、を備え、行列乗算工程における行列の行数が波面収差を多項式で展開した場合の展開次数に対応するとともに、行列の列数が光強度検出工程の検出器の個数の２倍に対応し、かつ、行列の行ベクトル同士が互いに直交関係をなす波面誤差検出方法であるので、電極とファイバ間の放電やファイバ表面への粉塵の付着もなく、一種類のディザー周波数のみで波面誤差の分離検出が可能となるため、コスト低減が図れるとともに、可変形状鏡の応答周波数に対する要求を緩和でき、また、可変形状鏡面上の連成振動も発生しないという効果が得られる。
【０１０６】
また、重畳工程においてツェルニケ（Zernike） 多項式で展開可能な任意の波面収差を任意の周波数と任意の振幅とで重畳可能であるので、単一周波数で波面誤差検出を行うことができる。
【０１０７】
また、集光工程と光強度検出工程との間に、集光工程により集光された集光光を光強度検出工程に導入するための光伝送工程をさらに備えているので、集光スポットの広がりとして現れる波面誤差の影響を容易に検知することができる。
【０１０８】
また、光伝送工程が、光軸上に設けられたシングルモードファイバと、光軸の周辺部に設けられた複数のマルチモードファイバとを用いて光伝送を行うようにしたので、波面検出のためにマルチモードファイバを通常用いて、シングルモードファイバは光強度変動による推定誤差軽減の目的とした観測強度規格化の際に用いることができ、効率よく、波面誤差検出を行うことができる。
【０１０９】
また、各マルチモードファイバの中心を光軸を中心とした正６角形の頂点に一致させて配置し、かつ、マルチモードファイバを最密に配置して、光伝送を行うようにしたので、幾何学的な配置に各ファイバが設けられているので、ファイバに対応して設けられた検出器のそれぞれの出力の原点付近での傾きをを２種類以下の定数を用いて示すことができ、演算を容易にすることができる。
【０１１０】
また、算出工程において、光強度検出工程で検出された各々の光強度信号から、直交復調方式により、直流成分と交流成分を分離して、かつ、各々の振幅を算出するようにしたので、簡易な演算部により構成することができ、演算時間を短縮することができるとともに、演算部の製造コストも安価に抑えることができる。
【０１１１】
また、ツェルニケ（Zernike）多項式の展開係数の値を横軸に、検出光強度の直流成分の振幅を縦軸にとった場合の横軸原点付近の傾きを要素の一部とする行列を上記行列乗算工程において用いるようにしたので、容易にティルトの波面誤差を分離することができる。
【０１１２】
また、ツェルニケ（Zernike）多項式の展開係数の値を横軸に、検出光強度の交流成分の振幅を縦軸にとった場合の横軸原点付近の傾きを要素の一部とする行列を上記行列乗算工程において用いるようにしたので、容易に焦点外れ成分及び非点収差成分を分離することができる。
【０１１３】
また、ツェルニケ（Zernike）多項式の展開係数の値を横軸に、検出光強度の直流成分の振幅を縦軸にとった場合の横軸原点付近の傾きの逆数に比例した量を要素の一部とする行列を上記行列乗算工程において用いるようにしたので、容易にティルトの波面誤差を分離することができる。
【０１１４】
また、ツェルニケ（Zernike）多項式の展開係数の値を横軸に、検出光強度の交流成分の振幅を縦軸にとった場合の横軸原点付近の傾きの逆数に比例した量を要素の一部とする行列を上記行列乗算工程において用いるようにしたので、容易に焦点外れ成分及び非点収差成分を分離することができる。
【図面の簡単な説明】
【図１】 本発明の波面誤差検出装置の構成を示す構成図である。
【図２】 本発明の波面誤差検出装置に設けられた光ファイバアレイの構成を示した側面図である。
【図３】 本発明における検出光強度のティルトに関するツェルニケ（Zernike）係数（A11）に対する依存性を示したグラフである。
【図４】 本発明における検出光強度のティルトに関するツェルニケ（Zernike）係数（B11）に対する依存性を示したグラフである。
【図５】 本発明における検出光強度の焦点外れに関するツェルニケ（Zernike）係数（A20）に対する依存性を示したグラフである。
【図６】 本発明における検出光強度の非点収差に関するツェルニケ（Zernike）係数（A22）に対する依存性を示したグラフである。
【図７】 本発明における検出光強度の非点収差に関するツェルニケ（Zernike）係数（B22）に対する依存性を示したグラフである。
【図８】 本発明における焦点外れに関するディザー信号を重畳した状態における検出光強度変動のツェルニケ（Zernike）係数（A20）に対する依存性を示したグラフである。
【図９】 本発明における焦点外れに関するディザー信号を重畳した状態における検出光強度変動のツェルニケ（Zernike）係数（A22）に対する依存性を示したグラフである。
【図１０】 本発明における焦点外れに関するディザー信号を重畳した状態における検出光強度変動のツェルニケ（Zernike）係数（B22）に対する依存性を示したグラフである。
【図１１】 本発明におけるツェルニケ（Zernike）モード分離用の[12×5]行列を示した説明図である。
【図１２】 波面誤差成分のツェルニケ（Zernike）モード毎の分離法を行う演算部の構成を示したブロック図である。
【図１３】 光ファイバ端面の高速回転に基づく従来のファイバカプラの正面図である。
【図１４】 光ファイバ端面の高速回転に基づく従来のファイバカプラの側面図である。
【図１５】 従来のファイバカプラにおける光ファイバ位置と検出光強度の関係を示したグラフである。
【図１６】 従来のマルチディザー方式補償光学系の構成を示した説明図である。
【符号の説明】
１ 大気擾乱、２ 光アンテナ、３ 揺らぎを受けた波面、４ 可変形状鏡、５ダイクロイックビームスプリッタ、６ 集光レンズ、７ 光ファイバアレイ、８ 光強度検出器、９ 波面誤差演算部、１０ 可変形状鏡制御部、１１ 揺らぎ補償された波面、１２ 光受信機、１３ 光送信機、１４ 送信用レーザ光源、１５ コリメートレンズ、１６ 光軸上に設置されるシングルモードファイバ、１７ 光軸周辺（位置a）に設置されるマルチモードファイバ、１８ 光軸周辺（位置b）に設置されるマルチモードファイバ、１９ 光軸周辺（位置c）に設置されるマルチモードファイバ、２０ 光軸周辺（位置d）に設置されるマルチモードファイバ、２１ 光軸周辺（位置e）に設置されるマルチモードファイバ、２２ 光軸周辺（位置f）に設置されるマルチモードファイバ、２３ 位置aの検出器の出力、２４ 位置b及び位置fの検出器の出力、２５ 位置c及び位置eの検出器の出力、２６ 位置dの検出器の出力、２７ 位置a及び位置dの検出器の出力、２８ 位置b及び位置cの検出器の出力、２９ 位置e及び位置fの検出器の出力、３０ 位置a〜fの検出器の出力、３１ 位置a及び位置dの検出器の出力、３２ 位置b, c, e, fの検出器の出力、３３ 位置a及び位置dの検出器の出力、３４ 位置b, c, e, fの検出器の出力、３５ 位置a〜fの検出器の出力変動の実効値、３６ 位置a及び位置dの検出器の出力変動の実効値、３７ 位置b及び位置eの検出器の出力変動の実効値、３８ 位置c及び位置fの検出器の出力変動の実効値、３９ 位置a及び位置dの検出器の出力変動の実効値、４０ 位置b, c, e, fの検出器の出力変動の実効値、４２ 可変形状鏡の電極に対する電位分配係数、４３ DA変換器、４４ AD変換器、４５ 光強度信号の直流成分、４６ 光強度変動の変動成分、４７ 観測信号ベクトル、４８ 積算器、５６ ツェルニケ（Zernike）モード分離用の行列、５７ 波面誤差算出値、５８ 増幅器、５９ 補償信号、６０ 側面を金蒸着したシングルモードファイバ、６１ 走査用電極、６２ 走査用電極、６３ ファイバ回転中心と光軸が一致した場合の光強度変化、６４ ファイバ回転中心と光軸が一致しない場合の光強度変化、６５ レーザ光、６６ 可変形状鏡、６７ 集光レンズ、６８ 対象物、６９ 光強度点検出器、７０ 波面制御部、１４１ 局部発振器、１４９ 局部発振正弦波信号、１５０ 遅延器、１５１ 積算器。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a wavefront error detection device and a wavefront error detection method, and in particular, in optical communication using laser light between a satellite and the ground, wavefront error detection for detecting a wavefront error of a laser beam disturbed by atmospheric fluctuations. The present invention relates to an apparatus and a wavefront error detection method.
[0002]
[Prior art]
Radio waves are currently used for communication transmission (feeder link) between the satellite and the ground, but in the future, it is required to perform optical communication using laser light. However, the transmission capability between the satellite and the ground using laser light is greatly affected by fluctuations in the atmosphere existing on the propagation path. In other words, the wavefront of the laser beam received by the optical antenna is disturbed by fluctuations in the atmosphere, and even if this is imaged, the focused spot spreads and the reception efficiency is significantly reduced. Therefore, a mechanism (fiber coupler) for efficiently coupling the laser beam condensed by the optical antenna to the single mode fiber is required.
[0003]
FIGS. 13 and 14 are front views showing a conventional fiber coupler shown in, for example, “A novel optical fiber based conical scan tracking device”: SPIE Vol.1522 (1991) pp.243-251 by UA Johann et al. It is a figure and a side view. The tracking method in the conventional fiber coupler shown in FIG. 13 and FIG. 14 extracts an error signal from the fluctuation of the amplitude of the received light incident on the fiber by vibrating the end face of the fixed optical fiber at a high speed leaving a movable range. Realize spatial tracking. In these drawings, reference numeral 60 denotes a single mode fiber (optical fiber) whose side surface is vapor-deposited with gold, and is fixed in a cantilever manner. Therefore, the end surface on the non-fixed side is indicated by a two-dot chain line A in FIG. It is movable within range. 61 and 62 are electrodes installed in the vicinity of the end face of the single mode fiber 60, and the electrodes 61 and 62 are installed at positions orthogonal to each other.
[0004]
The operation will be described. When a potential is applied between the single mode fiber 60 whose side surface is vapor-deposited with gold and the electrode 61 installed in the vicinity of the end face, the fiber is displaced in the direction perpendicular to the optical axis by Coulomb force. Two-dimensional displacement control is possible by installing the electrode 62 at a position orthogonal to the electrode 61. By applying a sine wave signal to the electrode 61 and a cosine wave signal to the electrode 62 with the same amplitude, the fiber can be scanned in a circular shape (two-dot chain line A). FIG. 15 shows the relationship between the fiber position and the detected light intensity. When the scanning signal is not applied to the electrode and the fiber center coincides with the peak position of the optical signal, the detected light intensity 63 is a constant value even when the scanning signal is applied to the electrode. On the other hand, when the fiber center does not coincide with the peak position, the detection signal 64 changes according to the scanning period. This technique is to extract this light intensity signal change 64 as an error signal by the synchronous detection method, and to control the position of the rotation center of the fiber so as to minimize the error signal. The aim is to achieve the optimum coupling efficiency.
[0005]
On the other hand, although not for optical communication, there is a very high possibility that multi-dither system compensation optical technology for correcting beam distortion of high-power laser light can be used as means for tracking received light. As a conventional example, “Analysis and simulation results of wavefront controllability in a multi-dither compensation optical system” by Ichinose et al .: Optics, Vol. 21, No. 10 (1992) pp. 714-719 will be described with reference to FIG. In the figure, 65 is a laser beam, 66 is a deformable mirror whose shape can be varied independently for each region, 67 is a condensing lens for condensing the laser beam 65 reflected by the deformable mirror 66, and 68 is a condensing lens 67. , 69 is a point detector that detects the intensity of reflected light from the object 68, and 70 is a wavefront controller that receives the signal from the point detector 69 and performs wavefront control.
[0006]
The operation will be described. The conventional multi-dither type compensation optical system shown in FIG. 16 performs phase modulation at individual frequencies for each minute region of the laser light, separates and detects each frequency component from the light intensity signal at the beam condensing point, and indirectly. This is a method for detecting a wavefront. First, the laser beam 65 is incident on a deformable mirror 66 whose shape can be varied independently for each region. A sine wave signal (dither signal) having a small amplitude and a constant value is input to the deformable mirror 66 by assigning different frequencies for each region on the surface of the deformable mirror 66. The direct current component of the dither signal is a control parameter for wavefront compensation. Next, the reflected light intensity from the object 68 placed on the focal plane of the condenser lens 67 is detected by the point detector 69. The detected light intensity signal is sent to the wavefront control unit 70 and separated and detected for each frequency component by the synchronous detection method. The detection signal includes a difference component between the original wavefront deviation and the DC component of the sine wave input to the deformable mirror 66, and this value represents the deviation from the original wavefront. Therefore, the condition for aligning the wavefront is when the value of each frequency component of the light intensity is zero. That is, the wavefront controller 70 compensates the wavefront error by controlling the DC component of the dither signal so as to minimize the value of each frequency component of the light intensity, and the spot of the spot on the object 68 of the laser beam 65 is compensated. The spread can be minimized. The feature is that a single-element point detector is sufficient as a detector for wavefront detection, and that it does not require special computations for wavefront detection and compensation, and is high-speed.
[0007]
[Problems to be solved by the invention]
Conventional fiber coupler technology for optical communication is configured as shown in FIGS. 13 and 14, and has the following problems. First, since the optical fiber 60 is mechanically rotated, the time responsiveness is impaired and resonance vibration is generated. This reduces the accuracy of wavefront error detection. In addition, since the Coulomb force is used to rotate the fiber, there are problems such as discharge between the electrode and the fiber and adhesion of dust to the fiber surface. Further, depending on the type of wavefront error included, there may be no rotation center position where the error signal is zero. For example, when coma is included, the light intensity spot shape to be formed is asymmetric on the focal plane. Therefore, a method for detecting a wavefront error without rotating the optical fiber 60 and tracking the received optical signal to the optical fiber core is required.
[0008]
On the other hand, the tracking method using the conventional multi-dither compensation optical system of FIG. 16 can be a method for solving the above-mentioned problems such as discharge between the electrode and the fiber and adhesion of dust to the fiber surface. Still exists. That is, since the wavefront region that can be detected and compensated is determined by the number of divisions of the deformable mirror 66, it is necessary to increase the number of divisions in order to compensate for higher-order wavefront errors, which increases the manufacturing cost of the deformable mirror 66. Inevitable. In addition, since the types of dither frequencies assigned to each area increase with an increase in the number of divisions, it is necessary to install a processing system including a synchronous detection unit for the dither frequency, and an increase in cost is inevitable. On the other hand, since the deformable mirror 66 has a finite frequency response characteristic, the frequency that can be used as a dither signal is limited to this range. Furthermore, since the adjacent regions in the deformable mirror 66 are vibrated at different frequencies, the generation of coupled vibration is unavoidable, and the problem of overcoming the decrease in the stability limit value of the system associated therewith is a problem.
[0009]
Therefore, when tracking the received optical signal using a compensation optical system based on the dither method, the dither input means reduces the number of divisions of the deformable mirror and the type of the dither frequency and is less affected by the coupled vibration. There is a strong demand to establish a wavefront detection and compensation method with
[0010]
The present invention has been made to solve such a problem, and can separate and detect a wavefront error with only one type of dither frequency without discharge between the electrode and the fiber and adhesion of dust to the fiber surface. An object of the present invention is to obtain a wavefront error detection device and a wavefront error detection method that can reduce costs and that do not generate coupled vibration on a deformable mirror.
[0011]
[Means for Solving the Problems]
The present invention comprises an antenna means for introducing light subjected to wavefront aberration, the above Introduced by antenna means the above A deformable mirror for superimposing an arbitrary wavefront aberration on light at an arbitrary frequency; the above Condensing means for condensing the light on which the wavefront aberration is superimposed by the deformable mirror; the above A light intensity detecting means having a plurality of detectors for independently detecting the intensity of the light collected near the rear focal plane of the light collecting means at a plurality of points on and around the optical axis; the above A calculation means for separating the direct current component and the alternating current component from each light intensity signal detected by the light intensity detection means, and calculating each amplitude; the above Matrix multiplication means for multiplying a vector having a plurality of amplitude components obtained by the calculation means by a matrix having an arbitrary element; Matrix multiplication means Interface means for adding the result calculated by the step to the deformable mirror, the above In matrix multiplication means the above The number of rows in the matrix corresponds to the expansion order when the wavefront aberration is expanded with a polynomial, the above The number of columns in the matrix the above Of light intensity detection means the above Corresponds to twice the number of detectors, and the above This is a wavefront error detection device in which matrix row vectors are orthogonal to each other.
[0012]
In addition, an arbitrary wavefront aberration that can be developed by a Zernike polynomial in a deformable mirror can be superimposed at an arbitrary frequency and an arbitrary amplitude.
[0013]
Further, a light intensity detecting means is provided apart from the focal plane of the light collecting means, and the light intensity collected by the light collecting means is collected between the light collecting means and the light intensity detecting means. An optical transmission means is provided for introduction into the network.
[0014]
The optical transmission means is composed of a single mode fiber provided on the optical axis and a plurality of multimode fibers provided on the periphery of the optical axis.
[0015]
Further, the center of each multimode fiber of the optical transmission means is made to coincide with the apex of a regular hexagon with the optical axis as the center, and the multimode fibers are arranged in a close-packed manner.
[0016]
Further, the calculation means separates the direct current component and the alternating current component from each light intensity signal detected by the light intensity detection means by an orthogonal demodulation method, and calculates each amplitude.
[0017]
Further, the above matrix is a matrix in which the slope of the origin near the horizontal axis when the expansion coefficient value of the Zernike polynomial is on the horizontal axis and the amplitude of the DC component of the detected light intensity is on the vertical axis is part of the above elements Used by multiplication means.
[0018]
Also, matrix multiplication is performed with a matrix whose slope is near the origin on the horizontal axis when the Zernike polynomial expansion coefficient value is on the horizontal axis and the AC component amplitude of the detected light intensity is on the vertical axis. Means.
[0019]
Also, an amount proportional to the reciprocal of the slope near the origin of the horizontal axis when the expansion coefficient value of the Zernike polynomial is plotted on the horizontal axis and the DC component amplitude of the detected light intensity is plotted on the vertical axis The matrix multiplication means uses a matrix as a part.
[0020]
Also, an amount proportional to the reciprocal of the slope near the origin of the horizontal axis when the expansion coefficient value of the Zernike polynomial is plotted on the horizontal axis and the amplitude of the AC component of the detected light intensity is plotted on the vertical axis The matrix multiplication means uses a matrix as a part.
[0021]
The present invention also includes a light introducing step for introducing light subjected to wavefront aberration, a superimposing step for superimposing wavefront aberration relating to defocusing on the light introduced in the light introducing step at an arbitrary frequency, and a superimposing step. A light collecting step for collecting the light with wavefront aberration superimposed on it, and light for detecting the intensity of the light collected in the light collecting step independently by a plurality of detectors at a plurality of points on and around the optical axis. An intensity detection step, a calculation step for separating the DC component and the AC component from each light intensity signal detected in the light intensity detection step, and calculating each amplitude, and a plurality of amplitudes obtained by the calculation step A matrix multiplying step of multiplying a vector having a component as a component by a matrix having an arbitrary element, and a control step of controlling to superimpose wavefront aberration related to defocus based on the result calculated by the calculating step, Matrix multiplication The number of rows in the matrix corresponds to the expansion order when the wavefront aberration is expanded by a polynomial, the number of columns in the matrix corresponds to twice the number of detectors in the light intensity detection step, and the matrix row vector This is a wavefront error detection method in which they are orthogonal to each other.
[0022]
In addition, any wavefront aberration that can be developed with a Zernike polynomial in the superimposing step can be superimposed with any frequency and any amplitude.
[0023]
Moreover, the optical transmission process for introduce | transducing the condensing light condensed by the condensing process to a light intensity detection process is further provided between the condensing process and the light intensity detection process.
[0024]
In the optical transmission step, optical transmission is performed using a single mode fiber provided on the optical axis and a plurality of multimode fibers provided on the periphery of the optical axis.
[0025]
In addition, the center of each multimode fiber is arranged so as to coincide with the apex of a regular hexagon centered on the optical axis, and the multimode fibers are arranged closest to each other to perform optical transmission.
[0026]
In the calculation step, the direct current component and the alternating current component are separated from each light intensity signal detected in the light intensity detection step by the orthogonal demodulation method, and each amplitude is calculated.
[0027]
In addition, the above matrix is a matrix in which the horizontal axis represents the Zernike polynomial expansion coefficient value and the vertical axis represents the amplitude of the DC component of the detected light intensity. Used in the multiplication step.
[0028]
In addition, the above matrix is a matrix in which the horizontal axis is the Zernike polynomial expansion coefficient value and the amplitude of the AC component of the detected light intensity is the vertical axis, and the slope near the origin is part of the element. Used in the multiplication step.
[0029]
Also, an amount proportional to the reciprocal of the slope near the origin of the horizontal axis when the expansion coefficient value of the Zernike polynomial is plotted on the horizontal axis and the DC component amplitude of the detected light intensity is plotted on the vertical axis The matrix used as a part is used in the matrix multiplication step.
[0030]
Also, an amount proportional to the reciprocal of the slope near the origin of the horizontal axis when the expansion coefficient value of the Zernike polynomial is plotted on the horizontal axis and the amplitude of the AC component of the detected light intensity is plotted on the vertical axis The matrix used as a part is used in the matrix multiplication step.
[0031]
DETAILED DESCRIPTION OF THE INVENTION
Embodiment 1 FIG.
FIG. 1 shows an embodiment of a wavefront error detection device and a wavefront error detection method according to the present invention. The configuration of the apparatus and the wavefront detection / compensation method are similar to those of the conventional multi-dither compensation optical system shown in FIG. 16, except for the following three points. That is, the light intensity detected at one point is detected at a plurality of points on and around the optical axis, the dither signal given at a plurality of frequencies is given at a single frequency, and each of the deformable mirrors The dither signal frequency assigned in the region is assigned to a specific wavefront aberration type (defocus described later). Specific embodiments will be described below.
[0032]
In FIG. 1, 1 is a laser light wavefront (atmospheric turbulence) subjected to turbulent wavefront aberration due to atmospheric fluctuations, 2 is an optical antenna for introducing laser light 1, and 3 is subjected to fluctuations introduced by the optical antenna 2. A wavefront 4 is a deformable mirror that superimposes a wavefront aberration related to defocusing on the light 3 introduced by the optical antenna 2 at an arbitrary frequency, and 5 is a light reflected by the deformable mirror 4 that is introduced into a condenser lens 6 described later. A dichroic beam splitter 6 for condensing the light on which wavefront aberration is superimposed by the deformable mirror 4, and 7 for focusing the light collected on the rear focal plane of the condensing lens 6 on the optical axis. And an optical fiber array for transmitting independently at a plurality of points around it, 8 is a light intensity detector comprising a plurality of detectors for independently detecting the intensity of each light transmitted by the optical fiber array 7, and 9 is a light A DC component and an AC component are separated from each light intensity signal detected by the degree detector 8 and each amplitude (effective value) is calculated, and a vector having the plurality of amplitudes as components is calculated. A wavefront error calculating unit that multiplies a matrix having an arbitrary element once or a plurality of times, and 10 is a deformable mirror control unit having interface means for adding the result calculated by the wavefront error calculating unit 9 to the deformable mirror 4 It is. Reference numeral 11 denotes a wavefront in which fluctuation is compensated.
[0033]
As shown in FIG. 1, the wavefront error detection apparatus of the present invention includes an optical system including an optical antenna 2, a deformable mirror 4, a condensing lens 6, an optical fiber array 7, and a light intensity detector 8, and a wavefront error calculation unit. 9 and the deformable mirror control unit 10. Since FIG. 1 shows an apparatus configuration for performing spatial optical communication, an optical receiver 12, a dichroic beam splitter 5, an optical transmitter 13, and a transmission laser light source 14 for performing optical communication are also described. is doing.
[0034]
Next, the operation will be described. In FIG. 1, a laser wavefront 1 disturbed by atmospheric fluctuations is received by an optical antenna 2 and a known wavefront error is superimposed by a deformable mirror 4. Next, the light is condensed by the condenser lens 6 via the dichroic beam splitter 5. The effect of the wavefront error appears as the spread of the focused spot. In order to detect the spread of the spot, an optical fiber array 7 having a plurality of multimode fibers is installed near the rear focal position optical axis of the condenser lens 6 and a corresponding light intensity detector 8 is provided. Connecting. FIG. 2 shows a layout of the optical fiber array 7. The influence of wavefront aberration included in the received signal appears as a change in the ratio of the light intensity detected by each detector.
[0035]
As shown in FIG. 2, the optical fiber array 7 is arranged on a single mode fiber 16 on the optical axis, and a plurality of multimode fibers 17 to 22 are arranged on the periphery thereof. The multimode fibers 17 to 22 are arranged such that the regular hexagonal apex centered on the optical axis coincides with the centers of the multimode fibers 17 to 22, and the fibers 16 to 22 are arranged in close proximity to each other. Has been. Moreover, each fiber 16-22 is accommodated in the tubular exterior 7a. The optical fiber array 7 is configured as described above, and constitutes an optical transmission means for introducing the condensed light into the light intensity detector 8 arranged at a position away from the focal plane of the condenser lens 6. Yes. Note that it is desirable to use only the fiber around the optical axis and the detector corresponding to it for wavefront error detection, and the observation intensity standardization for the purpose of reducing the estimation error due to the fluctuation of the optical intensity is on the optical axis (center part). Used when.
[0036]
Next, a change in signal intensity at each detector (multimode fibers 17 to 22) when a wavefront having a known wavefront error is incident will be described. The wavefront error is expressed in the form of series expansion with a Zernike polynomial as shown in the following equation (1).
[0037]
[Expression 1]

[0038]
Here, Φ is a radial polynomial and is expressed by the following equations (2) to (7).
[0039]
[Expression 2]

[0040]
[Equation 3]

[0041]
[Expression 4]

[0042]
[Equation 5]

[0043]
[Formula 6]

[0044]
[Expression 7]

[0045]
Since the Zernike polynomial is an orthogonal function system, the coefficient values Apq and Bpq of each term can be determined independently, and each term corresponds to an optical aberration. Further, a low-order term with respect to r corresponds to Seidel aberration, the second term is tilt, the third term is out of focus, the fourth term is astigmatism, and the fifth term is coma. In the following, each term will be collectively referred to as Zernike mode or simply mode. Now, it is assumed that the wavefront error can be approximated up to the fourth term (up to the second order), which is a particularly dominant term. Therefore, in the present invention, in the deformable mirror 4, any wavefront aberration that can be developed by the Zernike polynomial can be superimposed at any frequency and any amplitude.
[0046]
FIG. 3 shows a Zernike (Zernike) of the detected light intensity with the coefficient value A11 relating to the tilt of the second term of the above equation (1) as the horizontal axis and the detected light intensity (DC component amplitude of the detected light intensity (Normalized Optical Power)) as the vertical axis. Zernike) represents the coefficient dependency. The detected light intensity varies depending on the position of each detector (corresponding to the multimode fibers 17 to 22), 23 is the detector output of the multimode fiber 17 (position a), and 24 is the multimode fiber 18 (position b). And 22 (position f) detector output, 25 is the detector output of multimode fiber 19 (position c) and 21 (position e), and 26 is the detector output of multimode fiber 20 (position d). Indicates. Each output has an asymmetric characteristic with respect to the origin, and is characterized by a straight line having a constant slope near the origin. Fibers 19 and 21 (positions c and e) and fibers 18 and 22 (positions b and f) have the same characteristics, respectively, and fibers 17 and 20 ( The positions a and d), and the fibers 18 and 22 (positions b and f) and the fibers 19 and 21 (positions c and e) are equal in size and have opposite signs. Therefore, these inclinations can be expressed by using two types of constants α and β, and the inclinations of the respective outputs of the fibers 17 to 22 (positions a, b, c, d, e, and f) near the origin. Can be expressed in vector form as (α, β, −β, −α, −β, β).
[0047]
FIG. 4 is a graph in which the horizontal axis represents the coefficient value B11 relating to the tilt in the direction orthogonal to the second term A11 of the above equation (1), and the detected light intensity (normalized optical power) is plotted on the vertical axis. It is a thing. 27, 28 and 29 represent the detector outputs of fibers 17 and 20 (positions a and d), fibers 18 and 19 (positions b and c), and fibers 21 and 22 (positions e and f), respectively. It is characterized by having an asymmetric characteristic with respect to the origin as in the case of. The inclination vector of the detector output near the origin of the positions a to f can be expressed as (0, γ, γ, 0, −γ, −γ) using one kind of constant γ. In the case of A11 and B11, when the inner product calculation is executed for each inclination vector at the origin, it becomes 0. This means that in the case of A11 and B11, the detector outputs are in an orthogonal relationship.
[0048]
FIG. 5 is a graph in which the horizontal axis represents the coefficient value A20 related to defocusing in the third term of the above equation (1), and the detected light intensity (DC component amplitude of the detected light intensity (Normalized Optical Power)) is represented on the vertical axis. It shows that the detector output 30 of all fibers has the same characteristics regardless of position. The detector outputs at the respective positions a to f have characteristics symmetrical with respect to the origin, and further, the inclination vector is (0, 0, 0, 0, 0, 0) near the origin.
[0049]
FIG. 6 shows the coefficient value A22 related to astigmatism in the fourth term of the above equation (1) on the horizontal axis and the detected light intensity (DC component amplitude of the detected light intensity (Normalized Optical Power)) on the vertical axis. The detector output 31 shows the characteristics of the fibers (detectors) 17 and 20 at the positions a and d, and the detector output 32 shows the characteristics of the fibers (detectors) at the positions b, c, e, and f. Although 31 and 32 show different characteristics depending on the position of the fiber (detector), all have symmetrical characteristics with respect to the origin, and the feature is that the inclination is zero near the origin as in the case of FIG.
[0050]
FIG. 7 shows the detected light intensity (DC component amplitude of the detected light intensity (Normalized Optical Power)) with the coefficient value B22 relating to astigmatism in the direction orthogonal to A22 in the fourth term of the above equation (1) as the horizontal axis. It is represented on the axis. Characteristic 33 indicates the detector output at positions a and d, and characteristic 34 indicates the detector output at positions b, c, e, and f. Similar to FIG. 6, the two types of characteristics 33 and 34 are both symmetric with respect to the origin, and the inclination is zero near the origin.
[0051]
Therefore, focusing on the tilt vector near the origin, the tilt wavefront error can be separated. That is, in a region where the wavefront error is sufficiently small, the tilt component can be separated by calculating the inner product of the tilt vector with a vector having the light intensity signal from each fiber (detector) as a component.
[0052]
However, it is impossible to separate an out-of-focus component and an astigmatism component whose intensity changes symmetrically with respect to each coefficient change. In order to solve this problem, a sine wave signal (dither signal) having a periodic and minute amplitude from the outside is assigned to a specific known wavefront aberration and superimposed. When an out-of-focus component is assigned as this known wavefront aberration, the defocus term component of the wavefront error and the two orthogonal components of the astigmatism term can be separated. The principle will be described below.
[0053]
First, the dither signal related to the out-of-focus component is superimposed via the deformable mirror (4 in FIG. 1). As a result, the light intensity signal changes according to the superimposed signal. Next, the amplitude of the light intensity signal is extracted by the synchronous detection method. The extracted signal, that is, the amplitude represents the effective value of the change in light intensity when the amount of defocus is minutely changed. This operation is executed while continuously changing the coefficient value of the wavefront error to obtain the effective value characteristic of the wavefront error coefficient value-light intensity change. At this time, a vector having an inclination near the origin corresponding to the light intensity fluctuation for each fiber (detector) as an element is considered. The vectors obtained for each type of wavefront error coefficient to be continuously changed are orthogonal to each other with respect to wavefront error components other than tilt. In other words, in a region where the wavefront error is sufficiently small, it is possible to separate out-of-focus and astigmatism components by multiplying the effective value signal of the light intensity fluctuation from each detector by the inclination vector for the fluctuation. Become.
[0054]
FIG. 8 shows the effective value of the fluctuation in the detected light intensity (Amplitude of the detected light intensity (Amplitude of amplitude) when the coefficient value A20 relating to the defocus is continuously changed with the dither signal relating to the defocus as the known wavefront aberration superimposed. Power Oscillations)) is plotted on the vertical axis and the coefficient value A20 on the horizontal axis. Regardless of the detector positions a to f, the light intensity fluctuations all have the same characteristic 35. It has antisymmetric characteristics with respect to the origin, and the slope near the origin is approximately a constant value, and this value is η. The inclination of the light intensity fluctuation near the origin can be expressed as an intensity fluctuation inclination vector (η, η, η, η, η, η) having elements having the order of detectors a to f.
[0055]
FIG. 9 shows the coefficient value A22 relating to astigmatism in the state where an out-of-focus dither signal is input, and the effective value of detected light intensity fluctuation (Amplitude of Power Oscillations) on the vertical axis. The output fluctuation 36 of the fibers (detectors) 17 and 20 (positions a and d) is always 0, and the inclination near the origin is 0. The output fluctuation characteristics 37 and 38 of other fibers (detectors) all change linearly, and are expressed by two kinds of characteristics having the same absolute value of inclination and different signs. That is, if the inclination of the fibers (detectors) 18 and 21 (positions b and e) is ε, the inclination of the fibers (detectors) 19 and 22 (positions c and f) is −ε. The gradient vector of the intensity fluctuation is expressed as (ε, −ε / 2, −ε / 2, ε, −ε / 2, −ε / 2). When the inner product operation of this vector and the gradient vector (η, η, η, η, η, η) of the intensity fluctuation when the coefficient value A20 relating to defocusing is continuously changed, 0 is obtained. This means that these vectors are orthogonal.
[0056]
Similarly, FIG. 10 shows the coefficient value B22 related to astigmatism on the horizontal axis and the effective value of detected light intensity fluctuation (Amplitude of Power Oscillations) on the vertical axis. It is represented by two types of characteristics 39 and 40 having the same absolute value of inclination and different signs. The gradient vector of the intensity fluctuation is (0, ζ, −ζ, 0, ζ, −ζ), which is found to be orthogonal to the gradient vectors of FIGS. On the other hand, when only the tilt component exists in the wavefront error, the effective value of the light intensity fluctuation is always 0 with respect to the change of the coefficient value.
[0057]
Therefore, in an area where the wavefront error is sufficiently small, the effective value signal of the fluctuation of the light intensity from each detector is multiplied by the fluctuation gradient vector, thereby defocusing the wavefront error component and astigmatism wavefront error component. Can be separated.
[0058]
The above shows that the Zernike wavefront error component can be separated by using the difference in the characteristics of the two types of gradient vector elements. If this vector is combined into a 12 × 5 matrix and its inverse matrix (5 × 12 matrix) is obtained, the Zernike wavefront error coefficient can be estimated using this inverse matrix. The Zernike error coefficient estimation method will be described below.
[0059]
First, the six light intensity gradient elements and the six light intensity fluctuation gradient elements are combined into a 12-element vector. Further, the 12-element vector is used as a row vector, and tilt, defocus, and astigmatism 5 are obtained. A [12 × 5] matrix is formed by arranging in the column direction for each type of Zernike wavefront error mode. Hereinafter, this 12 × 5 matrix is collectively referred to as an Observation Matrix [O (12,5)] and is defined as the following equation (8).
[0060]
[Equation 8]

[0061]
The actually observed signal is defined as follows. That is, from the light intensity signals obtained by each of the six detectors with the dither signal related to defocusing superimposed, six DC components (p _a , p _b , p _c , p _d , p _e , p _f ) And six variable RMS components (o _a , o _b , o _c , o _d , o _e , o _f ) And is represented by a 12-element vector as in the following equation (9). Hereinafter, this vector is collectively referred to as Measurement Vector (observation signal vector) [M (12,1)].
[0062]
[Equation 9]

[0063]
On the other hand, the wavefront error included in the wavefront is defined as Zernike Error Vector (Zernike error vector (wavefront error component)) [Z (1,5)] and is expressed as the following equation (10).
[0064]
[Expression 10]

[0065]
Then, the following relationship is established.
[0066]
## EQU11 ##

[0067]
Since [O] can be calculated in advance by calculation, it can be seen that in order to estimate the wavefront error [Z], the actually measured value [M] is multiplied by the inverse matrix of [O] from the left side. However, since [O] has 12 × 5 elements and is not a square matrix, there is no inverse matrix as it is. Therefore, consider the following procedure.
[0068]
First, the transposed matrix [O] of [O] ^t ] From both sides of the equation (8).
[0069]
[Expression 12]

[0070]
{[O on the right side of Formula (12) ^t ] [O]} is a 5 × 5 square matrix expressed by the following equation (13).
[0071]
[Formula 13]

[0072]
The determinant of this square matrix can be calculated as the following equation (14).
[0073]
[Expression 14]

[0074]
When this determinant takes a non-zero value, the inverse matrix of equation (13) can be calculated as follows.
[0075]
[Expression 15]

[0076]
Next, multiply this inverse matrix from both sides of equation (12) from the left.
[0077]
[Expression 16]

[0078]
Thus, it can be seen that the amount of wavefront aberration can be calculated.
[0079]
Now, the {[O ^t ] [O]} ^-1 [O] ^t Is defined as the following: Estimation Matrix E (5, 12).
[0080]
[Expression 17]

[0081]
Here, each element can be expressed as follows.
[0082]
[Formula 18]

[0083]
[Equation 19]

[0084]
[Expression 20]

[0085]
[Expression 21]

[0086]
[Expression 22]

[0087]
[Expression 23]

[0088]
Using this Estimation Matrix, it can be seen that the wavefront aberration can be estimated for each of the five Zernike modes by a single matrix calculation as shown in Equation (24).
[0089]
[Expression 24]

[0090]
It can be seen from the equations (18) to (23) that each element is proportional to the reciprocal of the inclination vectors α to ζ. Therefore, when the calculation of Expression (24) is seen for each element, it is proportional to the reciprocal of the inclination vectors α to ζ obtained previously for each of the direct current component and the fluctuation component of the detected light intensity from each fiber. This means that the wavefront error can be estimated separately for each of the five types of Zernike modes by multiplying the quantity. In the following, the Estimation Matrix is used as a matrix for Zernike mode separation (FIG. 11). Note that if the inner product is calculated between the row vectors of the estimation matrix, it becomes zero in all combinations, and it can be seen that the filters are completely orthogonal.
[0091]
FIG. 12 shows a configuration of a calculation portion necessary for realizing the above-described wavefront error component separation method. In the figure, 141 is a local oscillator, 42 is a potential distribution coefficient (Actuator Matrix (13 × 5)) for electrodes of the deformable mirror (4 in FIG. 1), 43 is a DA converter, 44 is an AD converter, and 45 is a light. The direct current component of the intensity signal, 46 is the fluctuation component of the light intensity fluctuation, 47 is the observation signal vector (Measurement Data (12 × 1)), 48 is the integrator, 149 is the local oscillation sine wave signal, 150 is the delay device, 151 is An integrator 56 is a matrix for separating Zernike mode (Estimation Matrix (5 × 12)), 57 is a wavefront error calculation value (Zernike Error Vector (5 × 1)), 58 is an amplifier (State Estimator), 59 Is a compensation signal.
[0092]
The operation will be described. In order to superimpose a dither signal related to defocusing, a local oscillator 41 generates a single frequency sine wave 49. The sine wave 49 is multiplied by a distribution coefficient 42 for the electrodes of the deformable mirror (4 in FIG. 1) to be controlled, and then converted into an analog signal by the DA converter 43 to the deformable mirror (4 in FIG. 1). Sent. The distribution coefficient 42 is determined by the structure and material of the deformable mirror, and is set to a voltage distribution ratio to a plurality of electrodes that changes only the defocus component in the Zernike mode. Next, a plurality of light intensity signals obtained by the light intensity detector (8 in FIG. 1) are converted into digital signals by the AD converter 44, and the DC component 45 and the fluctuation component 46 are separated and extracted, and then observed. A vector 47 is generated. The DC component 45 can be obtained by integrating and averaging the signal after AD conversion using the integrator 48. The fluctuation component 46 is extracted by an orthogonal demodulation method. That is, a local oscillator 141 generates a sine wave 149 having a frequency equal to the frequency for driving a deformable mirror, a local oscillation signal whose phase is adjusted by a delay unit 150 is multiplied by an observation signal after AD conversion, and an integrator 151 is used. Accumulated average. Thereby, the effective value of the fluctuation component can be extracted. Here, the delay device 150 is provided to correct a phase shift between the local oscillation signal and the observation signal. Thus, the direct current component and the alternating current component are separated from a plurality of light intensity signals obtained by the light intensity detector (8 in FIG. 1), and the amplitude (effective value) of each is calculated. .
[0093]
A wavefront error component 57 separated for each Zernike mode is extracted by multiplying the Zernike mode separation matrix 56 by the observation vector 47 thus generated. The gain of the wavefront error component 57 for each calculated Zernike mode is adjusted by an amplifier 58 to become a compensation signal 59. The compensation signal 59 is multiplied by a distribution coefficient matrix 42, which is a conversion matrix into the potential distribution of the electrodes of the deformable mirror (4 in FIG. 1), and then converted into an analog signal by the DA converter 43, thereby transforming the deformable mirror ( It is sent to 4) in FIG. This distribution coefficient matrix 42 can be prepared in advance based on actually measured values. A matrix 56 for separating the Zernike mode is preliminarily multiplied, and a compensation signal to be transmitted to the deformable mirror is calculated by one multiplication. It is also possible. The wavefront error can be detected and compensated by repeating the above operation continuously.
[0094]
Since the present invention is configured as described above, there is no discharge between the electrode and the fiber and adhesion of dust to the fiber surface as occurred in the conventional fiber coupler shown in FIGS. Since the wavefront error can be separated and detected with only one kind of dither frequency, the cost can be reduced, the requirement for the response frequency of the deformable mirror can be relaxed, and the coupled vibration on the deformable mirror does not occur. Therefore, this is an effective method for solving the problems of the conventional multi-dither type compensation optical system of FIG. As a result, it is possible to minimize the spread of the spot when condensing the laser beam received by the optical antenna in the spatial optical communication between the satellite and the ground, and it is possible to efficiently couple to the single mode fiber.
[0095]
【The invention's effect】
The present invention comprises an antenna means for introducing light subjected to wavefront aberration, the above Introduced by antenna means the above A deformable mirror for superimposing an arbitrary wavefront aberration on light at an arbitrary frequency; the above Condensing means for condensing the light on which the wavefront aberration is superimposed by the deformable mirror; the above A light intensity detecting means having a plurality of detectors for independently detecting the intensity of the light collected near the rear focal plane of the light collecting means at a plurality of points on and around the optical axis; the above A calculation means for separating the direct current component and the alternating current component from each light intensity signal detected by the light intensity detection means, and calculating each amplitude; the above Matrix multiplication means for multiplying a vector having a plurality of amplitude components obtained by the calculation means by a matrix having an arbitrary element; Matrix multiplication means Interface means for adding the result calculated by the step to the deformable mirror, the above In matrix multiplication means the above The number of rows in the matrix corresponds to the expansion order when the wavefront aberration is expanded with a polynomial, the above The number of columns in the matrix the above Of light intensity detection means the above Corresponds to twice the number of detectors, and the above Since the wavefront error detector is a matrix whose row vectors are orthogonal to each other, there is no discharge between the electrode and the fiber, and no dust adheres to the fiber surface, making it possible to detect and detect wavefront errors using only one type of dither frequency. As a result, the cost can be reduced, the demand for the response frequency of the deformable mirror can be relaxed, and the coupled vibration on the deformable mirror surface can be prevented.
[0096]
In addition, since any wavefront aberration that can be developed by a Zernike polynomial in the deformable mirror can be superimposed at any frequency and any amplitude, wavefront error detection can be performed at a single frequency.
[0097]
Further, a light intensity detecting means is provided apart from the focal plane of the light collecting means, and the light intensity collected by the light collecting means is collected between the light collecting means and the light intensity detecting means. Since the optical transmission means for introduction into the light source is provided, it is possible to easily detect the influence of the wavefront error that appears as the spread of the focused spot.
[0098]
Further, since the optical transmission means is composed of a single mode fiber provided on the optical axis and a plurality of multimode fibers provided on the periphery of the optical axis, the multimode fiber is used for wavefront detection. Normally used, the single mode fiber can be used for normalizing the observation intensity for the purpose of reducing the estimation error due to the fluctuation of the light intensity, and the wavefront error can be detected efficiently.
[0099]
In addition, since the center of each multimode fiber of the optical transmission means coincides with the apex of a regular hexagon centered on the optical axis, and the multimode fibers are arranged in the closest packing, Since the fiber is provided, the inclination of the output of each detector provided corresponding to the fiber near the origin can be indicated using two or less constants, which facilitates the calculation. it can.
[0100]
Further, in the calculation means, the direct current component and the alternating current component are separated from each light intensity signal detected by the light intensity detection means by the orthogonal demodulation method, and each amplitude is calculated. The calculation unit can be configured to shorten the calculation time, and the manufacturing cost of the calculation unit can be reduced.
[0101]
Further, the above matrix is a matrix in which the slope of the origin near the horizontal axis when the expansion coefficient value of the Zernike polynomial is on the horizontal axis and the amplitude of the DC component of the detected light intensity is on the vertical axis is part of the above elements Since the multiplication means is used, the tilt wavefront error can be easily separated.
[0102]
Also, matrix multiplication is performed with a matrix whose element is the slope near the origin of the horizontal axis when the expansion coefficient value of the Zernike polynomial is on the horizontal axis and the AC component amplitude of the detected light intensity is on the vertical axis. Since the means is used, the defocus component and astigmatism component can be easily separated.
[0103]
In addition, when the expansion coefficient value of the Zernike polynomial is on the horizontal axis and the amplitude of the DC component of the detected light intensity is on the vertical axis, an amount proportional to the reciprocal of the slope near the horizontal axis origin is part of the element Since the matrix multiplication means uses the matrix, the tilt wavefront error can be easily separated.
[0104]
In addition, when the expansion coefficient value of the Zernike polynomial is plotted on the horizontal axis, and the amplitude of the AC component of the detected light intensity is plotted on the vertical axis, an amount proportional to the reciprocal of the inclination near the horizontal axis origin is part of the element. Since the matrix multiplication means uses the matrix, the defocus component and astigmatism component can be easily separated.
[0105]
The present invention also includes a light introducing step for introducing light subjected to wavefront aberration, a superimposing step for superimposing wavefront aberration relating to defocusing on the light introduced in the light introducing step at an arbitrary frequency, and a superimposing step. A light collecting step for collecting the light with wavefront aberration superimposed on it, and light for detecting the intensity of the light collected in the light collecting step independently by a plurality of detectors at a plurality of points on and around the optical axis. An intensity detection step, a calculation step for separating the DC component and the AC component from each light intensity signal detected in the light intensity detection step, and calculating each amplitude, and a plurality of amplitudes obtained by the calculation step A matrix multiplying step of multiplying a vector having a component as a component by a matrix having an arbitrary element, and a control step of controlling to superimpose wavefront aberration related to defocus based on the result calculated by the calculating step, Matrix multiplication The number of rows in the matrix corresponds to the expansion order when the wavefront aberration is expanded by a polynomial, the number of columns in the matrix corresponds to twice the number of detectors in the light intensity detection step, and the matrix row vector Because it is a wavefront error detection method in which they are orthogonal to each other, there is no discharge between the electrode and the fiber and adhesion of dust to the fiber surface, so it is possible to detect and detect the wavefront error with only one type of dither frequency, The cost can be reduced, the requirement for the response frequency of the deformable mirror can be relaxed, and the coupled vibration on the deformable mirror surface is not generated.
[0106]
Further, since any wavefront aberration that can be developed by a Zernike polynomial can be superimposed at any frequency and any amplitude in the superimposing step, wavefront error detection can be performed at a single frequency.
[0107]
Moreover, since the light transmission process for introduce | transducing the condensing light condensed by the condensing process to a light intensity detection process is further provided between a condensing process and a light intensity detection process, The influence of the wavefront error that appears as a spread can be easily detected.
[0108]
In addition, since the optical transmission process uses a single mode fiber provided on the optical axis and a plurality of multimode fibers provided on the periphery of the optical axis, the optical transmission process is performed for wavefront detection. In general, a multimode fiber is normally used, and a single mode fiber can be used for normalization of observation intensity for the purpose of reducing an estimation error due to fluctuations in light intensity, and wavefront error can be detected efficiently.
[0109]
In addition, the center of each multimode fiber is arranged so as to coincide with the apex of a regular hexagon centered on the optical axis, and the multimode fibers are arranged closest to each other so as to perform optical transmission. Since each fiber is provided in a geometrical arrangement, the slope of the output of each detector provided corresponding to the fiber can be indicated using the constants of two or less types. Can be made easier.
[0110]
In the calculation process, the direct current component and the alternating current component are separated from each light intensity signal detected in the light intensity detection process by the orthogonal demodulation method, and each amplitude is calculated. The calculation unit can be configured to shorten the calculation time, and the manufacturing cost of the calculation unit can be reduced.
[0111]
Further, the above matrix is a matrix in which the slope of the origin near the horizontal axis when the expansion coefficient value of the Zernike polynomial is on the horizontal axis and the amplitude of the DC component of the detected light intensity is on the vertical axis is part of the above elements Since it is used in the multiplication step, the tilt wavefront error can be easily separated.
[0112]
In addition, the above matrix is a matrix in which the horizontal axis is the Zernike polynomial expansion coefficient value and the amplitude of the AC component of the detected light intensity is the vertical axis, and the slope near the origin is part of the element. Since it is used in the multiplication step, the defocus component and astigmatism component can be easily separated.
[0113]
In addition, when the expansion coefficient value of the Zernike polynomial is on the horizontal axis and the amplitude of the DC component of the detected light intensity is on the vertical axis, an amount proportional to the reciprocal of the slope near the horizontal axis origin is part of the element Is used in the matrix multiplication step, the tilt wavefront error can be easily separated.
[0114]
In addition, when the expansion coefficient value of the Zernike polynomial is plotted on the horizontal axis, and the amplitude of the AC component of the detected light intensity is plotted on the vertical axis, an amount proportional to the reciprocal of the inclination near the horizontal axis origin is part of the element. Is used in the matrix multiplication step, the defocus component and astigmatism component can be easily separated.
[Brief description of the drawings]
FIG. 1 is a configuration diagram showing a configuration of a wavefront error detection device of the present invention.
FIG. 2 is a side view showing a configuration of an optical fiber array provided in the wavefront error detection device of the present invention.
FIG. 3 is a graph showing the dependency of the detected light intensity on the Zernike coefficient (A11) with respect to the tilt of the detected light in the present invention.
FIG. 4 is a graph showing the dependence of the detected light intensity on the Zernike coefficient (B11) regarding the tilt of the detected light in the present invention.
FIG. 5 is a graph showing the dependence of the detected light intensity on the Zernike coefficient (A20) regarding the defocusing of the detected light intensity in the present invention.
FIG. 6 is a graph showing the dependence of the detected light intensity on the Zernike coefficient (A22) regarding astigmatism in the present invention.
FIG. 7 is a graph showing the dependence of the detected light intensity on the Zernike coefficient (B22) regarding astigmatism in the present invention.
FIG. 8 is a graph showing the dependence of detected light intensity fluctuation on the Zernike coefficient (A20) in a state where a dither signal related to defocusing is superimposed in the present invention.
FIG. 9 is a graph showing the dependency of detected light intensity fluctuation on the Zernike coefficient (A22) in a state where a dither signal related to defocusing is superimposed in the present invention.
FIG. 10 is a graph showing the dependency of detected light intensity fluctuation on the Zernike coefficient (B22) in a state where a dither signal related to defocusing is superimposed in the present invention.
FIG. 11 is an explanatory diagram showing a [12 × 5] matrix for Zernike mode separation in the present invention.
FIG. 12 is a block diagram illustrating a configuration of a calculation unit that performs a separation method for each Zernike mode of wavefront error components.
FIG. 13 is a front view of a conventional fiber coupler based on high-speed rotation of an optical fiber end face.
FIG. 14 is a side view of a conventional fiber coupler based on high-speed rotation of an optical fiber end face.
FIG. 15 is a graph showing a relationship between an optical fiber position and a detected light intensity in a conventional fiber coupler.
FIG. 16 is an explanatory diagram showing a configuration of a conventional multi-dither type compensation optical system.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Atmospheric turbulence, 2 Optical antenna, 3 Wave surface which received fluctuation, 4 Variable shape mirror, 5 Dichroic beam splitter, 6 Condensing lens, 7 Optical fiber array, 8 Light intensity detector, 9 Wavefront error calculating part, 10 Variable shape Mirror control unit, 11 fluctuation-compensated wavefront, 12 optical receiver, 13 optical transmitter, 14 transmitting laser light source, 15 collimating lens, 16 single mode fiber installed on the optical axis, 17 optical axis periphery (position a ), Multimode fiber installed around 18 optical axis (position b), 19 multimode fiber installed around optical axis (position c), 20 around optical axis (position d) Multimode fiber installed, 21 Multimode fiber installed around the optical axis (position e), 22 Multimode fiber installed around the optical axis (position f) 23, output of detector at position a, 24 output of detector at position b and f, 25 output of detector at position c and e, 26 output of detector at position d, 27 position a and position d 28, output of detectors at positions b and c, 29 output of detectors at positions e and f, 30 output of detectors at positions a to f, 31 detector at positions a and d 32, outputs of detectors at positions b, c, e, f, 33 outputs of detectors at positions a and d, 34 outputs of detectors at positions b, c, e, f, 35 positions a to f The effective value of the output fluctuation of the detector at 36, the effective value of the output fluctuation of the detector at the position a and the position d, 37 The effective value of the output fluctuation of the detector at the position b and the position e, and the detection of the 38 position c and the position f Effective value of output fluctuation of detector, 39 Effective value of output fluctuation of detector at position a and position d, 40 Effective value of output fluctuation of detector at positions b, c, e, f, 42 Variable shape mirror Potential distribution coefficient for the electrodes, 43 DA converter, 44 AD converter, 45 DC component of light intensity signal, 46 Fluctuation component of light intensity fluctuation, 47 Observation signal vector, 48 integrator, 56 For Zernike mode separation Matrix, 57 wavefront error calculation value, 58 amplifier, 59 compensation signal, 60 single-mode fiber with gold-deposited side, 61 scanning electrode, 62 scanning electrode, 63 Light intensity when fiber rotation center and optical axis coincide Change, 64 Light intensity change when fiber rotation center and optical axis do not match, 65 Laser light, 66 Deformable mirror, 67 Condensing lens, 68 Object, 69 Light intensity point detector, 70 Wavefront controller, 141 Local Oscillator, 149 Local oscillation sine wave signal, 150 delay device, 151 integrator.

Claims (20)

Antenna means for introducing light subjected to wavefront aberration;
A deformable mirror for superimposing an arbitrary wavefront aberration at an arbitrary frequency on the light introduced by the antenna means;
Condensing means for condensing the light on which the wavefront aberration is superimposed by the deformable mirror;
A light intensity detecting means having a plurality of detectors for independently detecting the intensity of the light collected near the rear focal plane of the light collecting means at a plurality of points on and around the optical axis;
A calculation means for separating the direct current component and the alternating current component from each light intensity signal detected by the light intensity detection means, and calculating each amplitude;
Matrix multiplication means for multiplying a vector having a plurality of amplitude components obtained by the calculation means by a matrix having an arbitrary element;
Interface means for adding the result calculated by the matrix multiplication means to the deformable mirror;
With
The number of rows of the matrix in the matrix multiplication means corresponds to the expansion order when the wavefront aberration is expanded by a polynomial, and the number of columns of the matrix corresponds to twice the number of detectors of the light intensity detection means. A wavefront error detection apparatus, wherein the row vectors of the matrix are orthogonal to each other.   2. The wavefront error detecting device according to claim 1, wherein an arbitrary wavefront aberration that can be developed by a Zernike polynomial can be superimposed at an arbitrary frequency and an arbitrary amplitude in the deformable mirror. The light intensity detecting means is provided apart from the focal plane of the light collecting means,
An optical transmission means is provided between the light collecting means and the light intensity detecting means for introducing the condensed light collected by the light collecting means into the light intensity detecting means. The wavefront error detection apparatus according to claim 1 or 2. The optical transmission means is
A single mode fiber provided on the optical axis;
The wavefront error detection device according to claim 3, comprising: a plurality of multimode fibers provided in a peripheral portion of the optical axis.   The center of each said multimode fiber of the said optical transmission means is made to correspond to the vertex of the regular hexagon centering on the said optical axis, and the said multimode fiber is arrange | positioned closest. Wavefront error detection device.   The calculating means is characterized in that the direct current component and the alternating current component are separated from each light intensity signal detected by the light intensity detecting means by an orthogonal demodulation method and each amplitude is calculated. Item 6. The wavefront error detection device according to any one of Items 1 to 5.   The matrix multiplication means described above is a matrix in which the Zernike polynomial expansion coefficient value is on the horizontal axis and the slope of the origin of the detected light intensity on the vertical axis is a part of the element near the horizontal axis origin. The wavefront error detection device according to claim 1, wherein the wavefront error detection device is used.   The matrix multiplication means described above is a matrix in which the Zernike polynomial expansion coefficient value is on the horizontal axis and the AC axis amplitude of the detected light intensity is on the vertical axis, and the slope near the origin of the horizontal axis is part of the element. The wavefront error detection device according to claim 1, wherein the wavefront error detection device is used.   The amount proportional to the reciprocal of the slope near the origin of the horizontal axis when the expansion coefficient value of the Zernike polynomial is plotted on the horizontal axis and the amplitude of the DC component of the detected light intensity is plotted on the vertical axis. 9. The wavefront error detection apparatus according to claim 1, wherein the matrix multiplication means uses a matrix to be used.   The amount proportional to the reciprocal of the slope near the origin of the horizontal axis when the expansion coefficient of the Zernike polynomial is plotted on the horizontal axis and the AC component amplitude of the detected light intensity is plotted on the vertical axis 10. The wavefront error detection apparatus according to claim 1, wherein the matrix multiplication means uses a matrix to be processed. A light introduction process for introducing light subjected to wavefront aberration;
A superimposing step for superimposing wavefront aberration related to defocusing on the light introduced in the light introducing step at an arbitrary frequency;
A condensing step for condensing the light on which the wavefront aberration is superimposed in the superimposing step;
A light intensity detection step of independently detecting the intensity of the light collected in the light collection step by a plurality of detectors at a plurality of points on and around the optical axis;
A calculation step for separating the direct current component and the alternating current component from each light intensity signal detected in the light intensity detection step, and calculating each amplitude;
A matrix multiplication step of multiplying a vector having a plurality of amplitude components obtained by the calculation step by a matrix having an arbitrary element;
A control step of controlling to superimpose the wavefront aberration related to the defocus based on the result calculated by the calculation step;
With
The number of rows of the matrix in the matrix multiplication step corresponds to the expansion order when the wavefront aberration is expanded by a polynomial, and the number of columns of the matrix corresponds to twice the number of detectors in the light intensity detection step. A wavefront error detection method, wherein the row vectors of the matrix are orthogonal to each other.   12. The wavefront error detection method according to claim 11, wherein an arbitrary wavefront aberration that can be developed by a Zernike polynomial can be superimposed at an arbitrary frequency and an arbitrary amplitude in the superimposing step. The method further comprises a light transmission step for introducing the condensed light collected by the light collecting step into the light intensity detecting step between the light collecting step and the light intensity detecting step. The wavefront error detection method according to claim 11 or 12. The optical transmission process is
14. The wavefront error detection method according to claim 13, wherein optical transmission is performed using a single mode fiber provided on the optical axis and a plurality of multimode fibers provided in the periphery of the optical axis.   The optical transmission is performed by arranging the centers of the multimode fibers so as to coincide with the vertices of a regular hexagon centered on the optical axis, and arranging the multimode fibers in the closest arrangement. The wavefront error detection method according to claim 14.   In the calculation step, the direct current component and the alternating current component are separated from each light intensity signal detected in the light intensity detection step by an orthogonal demodulation method, and each amplitude is calculated. Item 16. The wavefront error detection method according to any one of Items 11 to 15.   The matrix multiplication step described above is a matrix in which the Zernike polynomial expansion coefficient value is on the horizontal axis and the slope of the detected light intensity DC component is on the vertical axis, and the slope near the origin of the horizontal axis is part of the element. The wavefront error detection method according to any one of claims 11 to 16, wherein the wavefront error detection method is used.   The matrix multiplication step described above is a matrix in which the Zernike polynomial expansion coefficient value is plotted on the horizontal axis and the AC axis amplitude of the detected light intensity is plotted on the vertical axis, and the slope near the origin of the horizontal axis is part of the element. The wavefront error detection method according to claim 11, wherein the wavefront error detection method is used in the method.   The amount proportional to the reciprocal of the slope near the origin of the horizontal axis when the expansion coefficient value of the Zernike polynomial is plotted on the horizontal axis and the amplitude of the DC component of the detected light intensity is plotted on the vertical axis. The wavefront error detection method according to claim 11, wherein a matrix to be used is used in the matrix multiplication step.   The amount proportional to the reciprocal of the slope near the origin of the horizontal axis when the expansion coefficient of the Zernike polynomial is plotted on the horizontal axis and the AC component amplitude of the detected light intensity is plotted on the vertical axis 20. The wavefront error detection method according to claim 11, wherein a matrix to be used is used in the matrix multiplication step.

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