JP4002163B2 - Method and apparatus for measuring phase difference between pulses - Google Patents

Description

ここで、（１）式の添字ｐは、個々のパルスに付された番号であり、ｐについての和は、観測時間内に到来した全てのパルスについて取るものとする。
このパルス列全体のスペクトルは、個々のパルスのスペクトルｖ（ω）と、櫛状のスペクトル関数ｋ（ω）＝Σ_ｐｅｘｐ［ｉｐ（ωＴ＋δΦ）］との積で表される。
【０００６】
関数ｋ（ω）は、周期（２π／Ｔ）をもって繰り返す線スペクトル構造を呈する。この各線スペクトルの幅は、観測時間内に入るｐの個数に反比例して決まり、一方、各線スペクトルの中心の角周波数は、下記（２）式で与えられる。
【数２】
ω_Ｎ＝（２π／Ｔ）Ｎ−（δΦ）／Ｔ ・・・・・・・・・・・・ （２）即ち、キャリア・エンベロープ位相の変動に起因するパルス間位相差δΦは、パルス列の櫛状スペクトルに対し、２π／Ｔの整数倍位置から、−δΦ／Ｔだけの一様な変位をひき起こす。
かかる変位がランダムに生じると、パルス列のスペクトルを光周波数コムとして利用する際、絶対光周波数の変動となり、使用に耐えない。それ故、近年、パルス間位相差δΦの測定、更にはその制御が注目される所となっている。
【０００７】
この櫛状スペクトルの変位に直接基づいて、パルス間位相差δΦを測定する、所謂、ヘテロダイン法が、例えば、非特許文献１（Science 誌288巻（2000年） 635-639頁）に、広刊されている。
即ち、パルスのスペクトルｖ（ω）が、１オクターブを起える広がりを持つ場合に、その長波長部分を取り出し、それにつき第２高調波を発生する。この第２高調波発生過程において、周波数変位も、−２δΦ／Ｔと、２倍されることとなる。この第２高調波光を、元のパルスの短波長部分と合波して、光検出器で受光する。
このとき後者の周波数変位（−δΦ／Ｔ）と、前者のそれ（−２δΦ／Ｔ）の差の信号（δΦ／Ｔ）が、光検出器出力に現れる。これは、光検出器が光電界に対し二乗特性を有し、差周波発生器（混合器）として作用するからである。
以上では、δΦの符号が不定になるが、上記合波の以前に、何れかの周波数に既知の変位を与えておけば、少なくとも０周りでの符号の不定性は解消可能である。実際、上記刊行物では、元のパルス側に音響光学素子を作用させることで、これを行っている。
【０００８】
このヘテロダイン法では、上述したように、パルスに、１オクターブ以上のスペクトル広がりが要求される。かかる広いスペクトルを、直接発生できるパルスレーザー光源は、存在し難く、いきおい光源外部での白色光発生によるスペクトル拡張が必要となる。
不幸にして、非線形光学過程である白色光発生によって、超オクターブのスペクトル拡張が得られるのは、入射パルスが十分高いピークパワーを有する場合に限られる。
一般に、光源のパルス幅が長いほど、また、繰り返し周波数が高い程、必要なピークパワーを得るための平均出力は比例して増加し、それ故に、ここでの困難さが増す。
例えば、通信波長帯のパルス光源について、かかる白色光発生は、スーパーコンティニウム光発生と呼ばれ、その実施も現在までに１０年近くの長きに及ぶが、１０ＧＨｚ以上の繰り返しの光源からの超オクターブ光は、未だ得るに至っておらず、当然ながら、ヘテロダイン法の適用も見ていないのである。
【０００９】
現状はおくとして、より普遍的に、周波数標準・超多波長光源、何れの光周波数コムの応用においても、周波数間隔は、広い方が望ましい。
前者においては、未知光の周波数を定める際に、（２）式中の、最寄りの標準線のＮの決定が、また後者では、コム中の各線の光濾波器による分離が必要である。周波数間隔が狭いと、これらが非常に困難となるからである。
しかるに、コムの周波数変位の測定が、高い繰り返し、即ち、広い周波数間隔の場合程、行ない難いのは、この上ない不都合である。
それ故、ヘテロダイン法以外の、高いピークパワーを要さない測定法が、明らかに必要とされる。
【００１０】
かかる測定法として、相関法が、例えば、非特許文献２（Optics Letter 誌21巻（1996年） 2008-2010頁）に、広刊されている。
図６は、これに拠った従来例のパルス間位相差測定方法を示す図である。
図６（ａ）に示す構成において、被測定光パルス列は、入射窓６０２より入射し、半透鏡６０３に達し２光束に分岐される。
そのうち一方は、固定反射器６０４に向かい、折り返されて再び半透鏡６０３に戻る光路を辿る。他方は、掃引反射器６０５にて折り返されて、半透鏡６０３に戻る。
ここで、掃引反射器６０５は、固定反射器６０４側の光路と等遅延となる平衡位置６０７から、丁度被測定パルス間隔だけ余分に遅延を与える点まで、後退させてある。
さらに、掃引反射器６０５は、変位器６０６に装着され、該反射器側の光路の固定反射器６０４側の光路に対する遅延を、被測定パルス間隔Ｔの周りで掃引できる。
各々半透鏡６０３に戻った２光束は、該所において再び合波された後、出射窓６０９に達する。入射窓６０２より出射窓６０９に至る光路は、真空容器６０１中にあり、光は真空中を伝搬する。
【００１１】
出射窓６０９を経た合波光は、レンズ６２１により非線形結晶６２２中に結焦され、該結晶６２２で発生した第２高調波光が、レンズ６２３により集光されて光検出器６２４に導かれる。
本従来例で、掃引反射器６０５を掃引しつつ、光検出器６２４の出力を記録すると、例えば、図６（ｂ）に細実線で示した振動する干渉相関波形が得られる。
この干渉相関波形の上側包絡線を、フィッティングにより決定して、図６（ｂ）中の破線を得る。
次に、この包絡線の頂点からの、振動の山の時間ズレを読み取る。さらに、振動の周期を読み取り、その角周波数を得る。
最後に、上の時間ズレにこの角周波数を乗じて、パルス間位相差δΦが得られ、かくして、本従来例により、パルス間位相差測定が実現されているのである。
【００１２】
【非特許文献１】
Science 誌288巻（2000年） 635-639頁
【非特許文献２】
Optics Letter 誌21巻（1996年） 2008-2010頁
【非特許文献３】
Journal of Optical Society of America 誌72巻（1982年）156-160頁
【特許文献】
特許第２７４７１７６号明細書 「トリガ発生回路」
【００１３】
【発明が解決しようとする課題】
しかし、上述した従来のパルス間位相差測定方法には、以下のような問題がある。
その第１の問題は、上述した包絡線のフィッティングによる決定に係る問題である。前述した固定反射器側の光路を経たパルスと、前述した掃引反射器側の光路を経たパルスの波形が、厳密に相似となる理想的な場合、包絡線は、左右対称な関数になることが保証されている。
しかしこれ以上の何らの性質も、先験的（アプリオリ）には与えられない。即ち、包絡線の幅、さらに関数形自体もが、一般に未知なのである。
かかる条件下で、敢えて尤もらしい関数形を仮定してフィッティングを行なわざるを得ない。厄介なことに、良く波形に仮定される関数形である1/coshに対してすら、包絡線は複雑な関数形となる。
仮に、この関数形が妥当であったとしても、その幅と頂点（中心）位置を未知量とするフィッティング計算自体、非線形なフィッティングに属し、数値計算上の陥穽に満ちている。
これらの結果、総じて、フィッティングで求まる包絡線の頂点位置に、高い精度は期待し難い。いきおい、従来例の測定法では、測定されるパルス間位相差の精度が高くない。
【００１４】
第２の問題は、結果の確度に関する問題である。
機器に偏差があれば、如何に繰り返し精度が高くても、真値とは限らないので、偏差を知って除去する校正手順を備えることが一般に望まれるが、とりわけ今の場合においては、これが肝要である。
そもそも従来例において、通常の干渉計では空気中に構成される、半透鏡、固定反射器および掃引反射器からなる系を、真空容器中に構築してあるのは、固定反射器側の光路と、掃引反射器側の光路の間の、位相の不平衡による装置偏差を慮ってのことである。
そこで、ここでの位相と測定偏差について、以下により詳しく説明しよう。
【００１５】
一般に、光路の伝搬位相の周波数依存性をφ（ω）と書き、これを中心角周波数ω_０の周りでTalor展開するとき、２次以上の項は、パルス波形の変形を引き起こし、上記包絡線の中心対称性すら失わせる。それ故、従来例においては、２次以上の高次項は、全くあってはならない。
そこで、より低次の項を、下記（３）式のように表現する。
【数３】
φ（ω）＝τ_ｐω_０＋τ_ｇ（ω−ω_０） ・・・・・・・・・・・ （３）
ここで、τ_ｐはω_０における伝搬遅延、τ_ｇは群遅延である。
かかる伝搬位相を有する光路に、解析信号ｖ（ｔ）を入射すると、出射パルスの解析信号は、ｖ（ｔ−τ_ｇ）ｅｘｐ（ｉφ_０）となり、余分な位相変化、φ_０＝−（τ_ｇ−τ_ｐ）ω_０を伴う。
この位相変化は、正に式の示す通り、伝搬遅延と群遅延が等しくないことに起因して、生じるものである。
【００１６】
ところで、従来例の相関法において意図されているところは、パルスｖ（ｔ）に（群）遅延τ_ｇ＝Ｔを与えて作るｖ（ｔ−Ｔ）の、隣のパルスｖ（ｔ−Ｔ）ｅｘｐ（ｉδΦ）との比較である。
この際、遅延を与えることで、余分の位相変化φ_０が生じてしまうと、これと測定すべきパルス間位相差δΦとを区別することは、全く不可能であり、装置偏差となる。
パルス周期分の遅延に伴う余分の位相変化は、具体的に下記（４）式で表される。
【数４】
φ_０＝−ｍ_ｏω_０Ｔ ・・・・・・・・・・・・・・・・・・・・ （４）
ここで、係数ｍ_ｏは、１波長分の伝搬に伴なって生ずる、エンベロープ位相のキャリア位相からの遅れを表す量であり、光路の屈折率ｎと群屈折率ｎ_ｇを用いて、ｍ_ｏ＝（ｎ_ｇ−ｎ）／ｎ_ｇと書け、これを空気について勘定すると、１．５μｍ波長帯において、１．１×１０^−６程度の値を得る。
このｍ_ｏによるφ_０は、２０ＧＨｚのパルス繰り返し（Ｔ＝５０ｐｓ）に対してすら、４．０ｄｅｇと、全く無視できない値となり、より短波長または低繰り返しの場合、更に大きくなる。この故に、遅延光路を空気内に構築することは許されず、真空容器中に封じているのである。
【００１７】
ところで、係数ｍ_ｏは、ガラスの如き固体では、上の空気に比して格段に大きな値となる。例えば、良く用いられる石英ガラスでは、同じく１．５μｍ波長帯において、１．２％程度の値を示す。
これにより、固定反射器側の光路と、掃引反射器側の光路の間で、通過するガラスの量に差異があると、余分の位相変化が生じて装置偏差が惹起される。
今、ガラスの量の不均等１μｍについて、φ_０を勘定すると、４．３ｄｅｇと、やはり無視できない値となる。
従来例において、このようなガラス通過の不均等が生ずる虞のある箇所は、半透鏡６０３である。
それ故、図６（ａ）に見るように、光を２分するミラー膜と、合波するミラー膜を、各々平行基板の表と裏に配した特殊な半透鏡を用いることで、これに対処している。ここでの基板には、平行度の著しく高いものが要求される。
例えば、２分時の入射点と合波時の入射点が、１ｃｍ離れている時、平行度３０秒の基板であっても、厚みの不均等が１．５μｍに及ぶ故、全然使用に耐えない。かくの如き微妙な平行度に、装置偏差が全面的に依存するのでは、装置の確度の保証が非常な難事となる。
このような場合、半透鏡といった一部の部品の品質に負うよりも、寧ろ、装置偏差を校正・除去する手順を備える方が、コスト的に有利かつ長期的な確度保証も容易である。しかしながら、従来例は、かかる校正手段を欠いている。
【００１８】
さらに、上述した如く、従来例方法においては、光路の伝搬位相φ（ω）の２次以上の項は、全く許容されない。
ところが、一般に誘電体蒸着膜ミラーは、特に、特性域端の波長で、大きな高次位相を持つことが知られている。とりわけ被測定光が、広いスペクトルを有する場合に、この高次位相の影響が避けがたくなる。
従来例方法は、この高次位相に全く対処不能なため、広いスペクトルを有する光コムを、直接測定することはできなかった。
事実、前述の非特許文献２でも、光コムでなく、白色光発生により光コムを生成する前のレーザーパルスが、測定対象とされているのである。
第３の問題は、従来例方法は、上記ヘテロダイン法に比しては、格段に低いピークパワーしか要さないものの、依然、非線形効果を用いているために、感度に制限がある問題である。
その感度は、通常のレーザーパルスの測定には十分と考えられるものの、光コム、あるいはその一部の波長帯域を抽出した光に対しては、不十分なままに留まっていたのである。
【００１９】
以上述べたように、従来のパルス間位相差測定方法には、（１）正当な試行関数が一般に存在しない包絡線へのフィッティングが介在するために、測定精度が低く、（２）光路間の位相の不平衡に関しては、低次の不平衡にも校正手段を欠く結果、測定確度の保証が困難で、さらに高次の不平衡には全く対処不能、また、（３）非線形効果を用いるため、測定感度が一般の光コムに適用するには不十分、という解決すべき問題があった。
本発明は、前記従来技術の問題点を解決するためになされたものであり、本発明の目的は、一般の光コムに対しても感度が十分で、精度が高く、かつ校正手段を備え、確度が保証されたパルス間位相差測定方法および装置を提供することにある。
本発明の前記ならびにその他の目的と新規な特徴は、本明細書の記述及び添付図面によって明らかにする。
【００２０】
【課題を解決するための手段】
本願において開示される発明のうち、代表的なものの概要を簡単に説明すれば、下記の通りである。
本発明のパルス間位相差測定方法は、被測定光パルス列を２光束に分岐し、この２光束の一方を第１の光路に伝搬させ、またその他方を第２の光路に伝搬させ、前記第１の光路と前記第２の光路との相対的遅延時間差を、該被測定光パルス列の繰り返し周期の近傍の線形干渉相関信号の包絡線が検知される範囲に設定し、前記第１の光路を伝搬した光と前記第２の光路を伝搬した光とを合波して干渉させ、上記第２の光路の光路長を可変とし、上記合波して得られた干渉光の強度を前記第２の光路の光路長を変化させつつ時系列的に記録し、前記記録された強度データ列をフーリエ変換し、得られる周波数領域での位相を外挿し、求まる零周波数での位相の値から、前記被測定光パルス列内のパルス間位相差を測定することを特徴とする。
【００２１】
本発明のパルス間位相差測定装置は、被測定光パルス列を、第１の光路を伝搬する第１の光束と第２の光路を伝搬する第２の光束の２つの光束に分岐し、かつ、前記第１の光路を伝搬した第１の光束と前記第２の光路を伝搬した第２の光束とを合波して干渉させる半透鏡と、前記第１の光路内に配置され、前記半透鏡で分岐された第１の光束を折り返して前記半透鏡に返す固定反射器と、前記第２の光路内に移動可能に配置され、前記半透鏡で分岐された第２の光束を折り返して前記半透鏡に返す反射器と、前記反射器の位置を、前記第１の光路と前記第２の光路との相対的遅延時間差が前記被測定光パルス列の繰り返し周期の近傍の線形干渉相関信号の包絡線が検知される範囲となる第１の位置に設定するとともに、前記第１の位置の周りで前記反射器を移動させて前記第２の光路の光路長を可変させる移動手段と、前記第１の位置の周りで前記反射器を移動させて、前記第２の光路の光路長を可変させたときに、前記半透鏡から出射される前記合波して得られた干渉光の強度を検出する光検出器と、前記光検出器から得られる干渉光の強度を時系列的に記録する記録手段と、前記記録手段に記録された強度データ列に基づき、前記被測定光パルス列内のパルス間位相差を算出する算出手段とを備え、前記算出手段は、前記記録された強度データ列をフーリエ変換し、得られる周波数領域での位相を外挿し、求まる零周波数での位相の値から、パルス間位相差を算出し、前記半透鏡、前記固定反射器、並びに、前記反射器は、真空容器内に配置されることを特徴とする。
【００２２】
装置偏差を校正・除去するために、上記第１の光路と前記第２の光路との相対的遅延時間差を、零近傍の線形干渉相関信号の包絡線が検知される範囲に設定し、上記第２の光路の光路長を変化させつつ上記合波して得られた干渉光の強度を記録し、これをフーリエ変換して得られる周波数領域での位相を記録・保存し、上記外挿の前に、該記録・保存しておいた位相を減算することにより、上記２光路間の位相の不均等による誤差を完全に除去することができる。
【００２３】
本発明のパルス間位相差測定方法は、データ採取時間の短縮のために、被測定光パルス列を２光束に分岐し、この２光束の一方を第１の光路に伝搬させ、またその他方を第２の光路に伝搬させ、前記第１の光路と前記第２の光路との相対的遅延時間差を、該被測定光パルス列の繰り返し周期に所定の遅延量を加えた値に設定し、前記第１の光路を伝搬した光と前記第２の光路を伝搬した光とを合波して干渉させ、前記所定の遅延量は線形干渉相関信号の包絡線が検知されなくなる程度の値とし、上記合波して得られた干渉光を波長成分に分光し、該分光された各波長成分の強度を並列的に記録し、前記記録された強度データ列に基づき、前記被測定光パルス列内のパルス間位相差を測定することを特徴とする。
【００２４】
本発明のパルス間位相差測定装置は、被測定光パルス列を、第１の光路を伝搬する第１の光束と第２の光路を伝搬する第２の光束の２つの光束に分岐し、かつ、前記第１の光路を伝搬した第１の光束と前記第２の光路を伝搬した第２の光束とを合波して干渉させる半透鏡と、前記第１の光路内に配置され、前記半透鏡で分岐された第１の光束を折り返して前記半透鏡に返す固定反射器と、前記第２の光路内に移動可能に配置され、前記半透鏡で分岐された第２の光束を折り返して前記半透鏡に返す反射器と、前記反射器の位置を、前記第１の光路と前記第２の光路との相対的遅延時間差が前記被測定光パルス列の繰り返し周期に所定の遅延量を加えた値となる第１の位置に設定する移動手段と、前記半透鏡から出射される前記合波して得られた干渉光を波長成分に分光するスペクトログラフと、前記スペクトログラフで分光された各波長成分の光の強度を検出する線形光検出器列と、前記線形光検出器列で検出された強度に基づき、前記被測定光パルス列内のパルス間位相差を算出する算出手段とを備え、前記所定の遅延量は線形干渉相関信号の包絡線が検知されなくなる程度の値であり、前記半透鏡、前記固定反射器、並びに、前記反射器は、真空容器内に配置されることを特徴とする。
【００２５】
上記並列的に記録された干渉光の波長毎の強度データから、パルス間位相差を求めるためには、算出手段において、記録された強度データ列から波長毎の干渉位相を算出し、得られる周波数領域での位相を外挿し、求まる零周波数での位相の値を、パルス間位相差の測定値とすればよい。
また、装置偏差を校正・除去するために、上記第１の光路と前記第２の光路との相対的遅延時間差を、零に所定の遅延量を加えた値に設定し、前記所定の遅延量は線形干渉相関信号の包絡線が検知されなくなる程度の値であり、上記合波して得られた干渉光を波長成分に分光し、該分光された各波長成分の強度を並列的に記録し、これから算出される波長毎の干渉位相を記録・保存し、上記外挿の前に、該記録・保存しておいた位相を減算することにより、上記２光路間の位相の不均等による誤差を完全に除去することができる。
【００２６】
［作用］
従来のパルス間位相差測定方法に関る問題の３、すなわち、感度の制限の所以は、従来法が非線形結晶を用いて得られる（非線形）干渉相関信号を採取している点にある。
これに対して、合波光を直接、二乗特性を有する光検出器で受光して得られる（線形）干渉相関信号から、パルス間位相差を求め得れば、非線形光学効果を全く介在させずに測定が行なえ、感度の問題が解決されるのは明らかである。
本発明者は、この点について考究を進め、線形干渉信号の利用が、同時に、従来法に係る残余の問題にも十分な解決を与えることを見出すに至った。
これは、干渉相関信号をフーリエ変換した空間では、光路間の位相不平衡を全次数にわたって除去でき、さらに、残りの位相は必ず直線的となることが証明されるからである。パルス間位相差は、この直線的位相を零周波数に外挿した値として求められる。
従来の非線形相関信号では、位相不平衡の信号への影響が複雑であるが故、かかるフーリエ空間での装置偏差の一般的ディコンボリューションは許容されなかった。
さらに、二乗光検出器で採取した線形干渉相関信号に、畢竟、フーリエ変換を作用させるならば、その順序を転じて、光学的なフーリエ変換すなわち分光器を作用させた後に、二乗検出器で受光しても、結果は数学的に等価となる。
この性質に立ち、分光されたスペクトル成分を二乗光検出器列によって並列的に受光すれば、極めて短時間のうちにデータ採取を行なう構成も実現できる。
【００２７】
【発明の実施の形態】
以下、図面を参照して本発明の実施の形態を詳細に説明する。
なお、実施の形態を説明するための全図において、同一機能を有するものは同一符号を付け、その繰り返しの説明は省略する。
［本発明の基本構成］
図１は、本発明のパルス間位相差測定方法の基本構成を示す図である。
図中、被測定光パルス列は、入射窓１０２より入射し、半透鏡１０３に達し２光束に分岐される。うち一方は、固定反射器１０４に向かい、折り返されて再び半透鏡１０３に戻る光路を辿る。他方は、掃引反射器１０５にて折り返されて、半透鏡１０３に戻る。
ここで、掃引反射器１０５は、変位器１０６に装着され、該変位器１０６は、長行程変位器１０８に積載されている。
しかして、長行程変位器１０８によって、掃引反射器１０５の位置を、固定反射器１０４側の光路と等遅延となる平衡位置（第２の位置）１０７、および、該位置から丁度被測定パルス間隔Ｔだけ余分に遅延を与える点まで後退した位置（第１の位置）の間で、切り替えることができる。
【００２８】
さらに、変位器１０６によって、掃引反射器１０５を、上記切り替えのできる位置それぞれの周りで掃引できる。
各々半透鏡１０３に戻った２光束は、該所において再び合波された後、出射窓１０９に達する。入射窓１０２より出射窓１０９に至る光路は、真空容器１０１中にあり、光は真空中を伝搬する。
出射窓１０９を経た合波光（所謂、干渉光）は、光検出器１１０に入射する。光検出器１１０は、二乗特性を有し、出射窓１０９を経た合波光の強度を検出する。光検出器１１０の出力は、波形記憶装置１１８に記録され、計算機１２０によって表示・解析される。
【００２９】
本発明の測定方法において、長行程変位器１０８によって、掃引反射器側の光路の遅延をＴだけ余分に設定し、掃引反射器１０５を掃引しつつ、光検出器１１０の出力を記録すると、例えば、図２（ａ）に細実線で示した振動する干渉相関波形が得られる。
ここで得る（線形）干渉相関信号に対しても、従来例の（非線形）干渉相関信号について行なわれたのと同様の手順により、パルス間位相差δΦを読み取ることができる。
即ち、干渉相関波形の上側包絡線を、フィッティングにより決定して、図１（ａ）中の破線を得る。次に、この包絡線の頂点からの、振動の山の時間ズレを読み取り、別途、振動の周期から求めた角周波数を乗じれば良い。
しかしこの手順には、依然、フィッティングが含まれる。但し、ここでの包絡線は、従来例のそれとは異なり、未知関数と言う訳ではなく、通常の分光手段によって得られる被測定光パルス列のスペクトルから計算でき、従って、ここでのフィッティングは、関数の平行移動という単一パラメータのそれに帰される。
【００３０】
これは、従来例に比して幾許か進歩が認められるものの、依然繁雑さを免れない。特に、現実に採取されるデータは、図２（ａ）の如き滑らかな振動波形ではなく、図２（ｂ）に例示するような、離散的な時系列データを連ねたものであることに留意されたい。
このような疎なデータからは、各々の振動の山の位置と高さは、直接には得られず、先ず、個々の振動に対して局所的に放物線等にフィッティングを行なって、それらを求める必要がある。
しかして初めて、それら振動の山の位置と高さを入力として、包絡線へのフィッティングを実行できるのである。また、この手順には、装置偏差を除去する過程が含まれておらず、その点でも不徹底なものに留まっている。
【００３１】
そこで、本発明者は、離散的な時系列データとして採取された干渉相関信号をフーリエ変換し、周波数空間においてパルス間位相差δΦを読み取る手順に想到した。
以下、かかる手順の原理につき説明する。
掃引反射器１０５側の光路と、固定反射器１０４側の光路の遅延時間の差を、（τ＋ＮＴ）と書こう。ここで、τは、変位器１０６による掃引に係る遅延であり、Ｎは、長行程変位器１０８によるパルス間隔Ｔ分の遅延の切り替えを表している。
このとき、式（１）のパルス列に対して観測される干渉相関信号Ｓ_１（τ）は、下記（５）式のように表される。
【００３２】
【数５】

ここで、ｕは個々のパルスのエネルギーである。（５）式中のｐによる和は、単なる乗算定数に帰されるので、以下、τとＮを含む部分、ｓ_１（τ）＝１＋Ｒｅ［ｇ_１（τ）ｅｘｐ（ｉＮδΦ）］を用いて議論を進めよう。
また、ｇ_１（τ）は電場相関関数と呼ばれ、光路間に位相不平衡がない場合の表式は、下記（６）式で与えられる。
【００３３】
【数６】

なお、この電場相関関数は、この場合に、ｇ_１（０）＝１となるように規格化されている。通常、パルス間の裾は無視できるので、前述の（６）式の積分の上下限で、Ｔ→∞とおいても良い。
【００３４】
さて、前述の（６）式のτについてのフーリエ変換は、ｖ（ｔ）のフーリエ変換ｖ（ω）を用いて、｜ｖ（ω）｜^２と表される。
これはパルスのスペクトルに他ならない。もし、光路間に位相不平衡φ（ω）が存在すると、これに、ｅｘｐ［−ｉφ（ω）］が乗ぜられる。
ここで、遅延時間の正確な原点は、予め知り得ないことに留意せねばならない。まさにそれ故に、包絡線をフィッティングにより決定することで、相関信号上の遅延時間原点（包絡線の中心）を定めることが必要だったのである。即ち、実際に得られる干渉相関信号の横軸には、一般に未知の零偏差τ_０が含まれている。
以上を考慮して、測定データｓ_１（τ＋τ_０）のフーリエ変換を作ると、下記（７）式が得られる。
【００３５】
【数７】

さらに、この（９）式の、ＤＣ成分δ（０）以外の位相を抽出すると、下記（８）式が得られる。
【００３６】
【数８】

これが、本発明の、周波数空間におけるパルス間位相差δΦの読み取り手順を表す基本式となる。
【００３７】
先ず、パルス間位相差の測定に先立ち、長行程変位器１０８を操作して、掃引反射器１０５側の光路を、固定反射器１０４側の光路と等遅延（Ｎ＝０）に設定し、光路間の位相不平衡φ（ω）データを準備する。
即ち、この状態において、掃引反射器１０５を掃引しつつ、光検出器１１０の出力を波形記憶装置１１８に記録し、計算機１０において、得た干渉相関波形をフーリエ変換し、その位相、−ωτ_０−φ（ω）を装置偏差データとして記録・保存する。この装置偏差データの採取は、原理的には、測定装置組立て後、一回だけ実施すれば事足りる。
また、必ずしも、被測定光パルス列を入射して行なう必要もなく、スペクトル域を同じうする任意の光源を用いて行なえる。何となれば、Ｎ＝０の場合、（７）式において、光源の性質は｜ｖ（ω）｜^２に集約され、かつ該所からの位相への寄与は無いからである。
さらに、本方法は感度が高い故、適当な白色光源、例えば、ハロゲンランプ等を光源として、容易にこれを行なえる。
さすれば、光検出器１１０の全感度帯域にわたって、装置偏差データ、−ωτ_０−φ（ω）が得られるので、これを計算機１２０に記憶・保存しておけば良い。
【００３８】
爾後のパルス間位相差測定時には、長行程変位器１０８によって、掃引反射器側の光路の遅延をＴだけ余分（Ｎ＝１）に設定する。ここで、掃引反射器１０５を掃引しつつ、光検出器１１０の出力を記録し、得た干渉相関波形をフーリエ変換する。このフーリエ変換の位相から、記憶・保存して置いた装置偏差データを差し引く。
この結果、位相、δΦ−ωτ_０が得られる。かくして光路間の位相不平衡φ（ω）は、全次数にわたって除去された。
他方、零偏差τ_０は、依然として残っていると考えなければならない。付故なら、装置偏差データ採取時の零偏差が、今の測定の零偏差に一致する保証は何もないからである。
図２（ｃ）に、このような装置偏差データ除去後の位相を、（７）式の大きさと供に示した。
【００３９】
被測定光パルス列のスペクトル｜ｖ（ω）｜^２が検知できる範囲では、位相が１本の直線に乗っていることが見て取れる。この直線を零周波数に向かって外挿し、縦軸に対する切片を求める。その位相値が、求めるパルス間位相差δΦを与える。これは、位相の表式、δΦ−ωτ_０からの当然の帰結である。
このような切片（と傾き）を求めるための数値解析操作は、直線回帰として良く知られている。今の場合、被測定光スペクトルが存在しない周波数点での無意味な位相データの影響を排除するには、この直線回帰計算を重み関数つきで行なう。重み関数としては、例えば、スペクトル｜ｖ（ω）｜^２を用いるのが、余分な計算を要さず、自動化にも都合がよい。
以上ここまでで、本発明の基本構成とその動作を詳らかにしたので、以下では、本発明の各種実施の形態の構成について説明する。
【００４０】
［実施の形態１］
干渉相関信号をフーリエ変換して、所期の結果を得るには、遅延時間τを、高精度の一定刻みで変えつつ、光検出器の出力を採取・記録する必要がある。しかも、所謂、折り返し現象を防ぐためには、この遅延刻みが、被測定光の含む最短波長の光振動周期の１／２未満でなければならないことは、サンプリング定理の教えるところである。
現在の、良く校正された高分解能変位器をもってすれば、図１に示した基本構成でもこれを行なえる。但し、これは、測定装置が外界からの振動の影響を受けず、半透鏡あるいは固定反射器が、全く揺動しないとしてのことである。このためには、通常、それら部品を非常に慣性の大きな床板に固着する必要があり、いきおい、測定器が重厚長大となり、その可搬性が犠牲とならざるを得ない。
より軽便で可搬性に富む測定器を実現するには、振動の影響を含めた遅延時間差を不断に監視し、信号採取タイミングを決める機構を付加すれば良い。これを行なった構成を、図３（ａ）に示す。
【００４１】
図３（ａ）に示す、本発明の実施の形態１のパルス間位相差測定方法において、遅延時間差監視用の単色光源３１１から出射した監視光は、反射器３１２を経て、被測定光パルス列に平行に入射窓３０２に入射する。
爾後、監視光は、被測定光パルス列と同様、半透鏡３０３に達し２光束に分岐され、うち一方は、固定反射器３０４に向かい、折り返されて再び半透鏡３０３に戻り、他方は、掃引反射器３０５にて折り返されて、半透鏡３０３に戻る。
各々半透鏡３０３に戻った監視光の２光束は、該所において再び合波された後、出射窓３０９に達する。出射窓３０９を出た合波光は、反射器３１３を経て、光検出器３１４に入射する。
トリガ発生器３１５は、この光検出器３１４の出力を参照して、信号採取タイミングを決定し、波形記憶装置３１８にトリガ信号を供給してそれを通知する。
より具体的に、トリガ発生器３１５は、光検出器３１４の出力に対する位相ロックループ（ＰＬＬ）を内蔵し、必要に応じて逓倍された繰り返しで、トリガ信号を発生することができる。残余は、図１の基本構成に準ずる。
【００４２】
ここでの単色光源３１１は、被測定光パルス列の繰り返し周期Ｔを超える可干渉時間を有する必要があるが、パルス間位相差δΦを求める目的には、絶対的光周波数（波長）精度は要さない。従って、かかる監視用に通常用いられる気体レーザーの他、半導体ＤＦＢレーザー等を適用することもできる。
但し、装置偏差データの採取時と被測定パルス測定時で、単色光源の波長がくい違うのは、厳密には望ましくないので、後者を用いる場合、測定の直前に装置偏差データの採取を行なうことが推奨される。
元より、レーザー光源を用いる遅延時間監視法は、ここで示したものに留まらない。例えば、２周波Ｈｅ−Ｎｅ安定化レーザー、若しくは、光周波数シフターによりこれと等価に構築した光源によるヘテロダイン測距法は良く知られていて、半透鏡３０３上の監視光入射位置に、偏光分離膜を付加すれば、これも本発明に適用できる。
また、直線偏光のレーザーによる場合でも、固定反射器側または掃引反射器側、何れか一方の監視光光路に、１／４波長板を挿入して円偏光となし、生じた干渉光を偏光を分離して測定すれば、所謂、双方向計数法を行なうこともできる。
かかる場合のトリガ発生器３１５の詳細は、例えば、特許文献（特許第２７４７１７６号明細書「トリガ発生回路」）に開示されている。このように、広知の遅延時間監視（測距）手法を随意組み込んで、本発明を実施できることは言うまでもない。
【００４３】
本実施の形態では、変位器３０６に、梃による行程増倍機構を装備した圧電素子（ＰＺＴ）を用い、この掃引が終了し干渉相関信号を得ると即時に、それを解析してパルス間位相差を表示するプログラムを、計算機３２０上に装備した。
干渉相関信号のデータ点数２５６に対し、解析プログラムは０．１秒程度で実行でき、これは変位器３０６の復帰動作時間内に納まる。従って、データ採取・解析サイクルをループ動作させ、毎秒５回程度の頻度で、間断なくパルス間位相差を刻々更新・表示する測定が実現した。
図３（ｂ）に、この計算機プログラムの流れ図を示す。自動化されたプログラムのロバスト（無謬）性を高めるために、フーリエ位相へのアンラップ演算（ステップ３５４）と、振幅へのＤＣ成分除去操作（ステップ３５７）が加えられている。
前者は、atan2関数により得られる位相が、値域（−π，π）に折り畳まれているのを、滑らかに開く操作である。これを怠ると、時としてスペクトルの途中で位相の折り畳みが起きた時、直線回帰に失敗する。
また、後者は、直線回帰に、ＤＣ成分の位相（常に０に決まっていて何ら情報にならない）が加味されるのを防ぐ目的がある。
残余のステップは、［本発明の基本構成］において既述の解析法の忠実なコーディングであり、重ねての説明は割愛できよう。
【００４４】
［実施の形態２］
前述した如く、本発明では、線形相関における二乗検出器とフーリエ変換の可換性に立って、分光されたスペクトル成分を二乗光検出器列によって並列的に受光することで、極めて短時間にデータ採取を行なう構成が採り得る。これを、図４（ａ）に示す。
図４（ａ）に示す、本発明の実施の形態２のパルス間位相差測定方法において、図中、被測定光パルス列は、入射窓４０２より入射し、半透鏡４０３に達し２光束に分岐される。うち一方は、第１の固定反射器４０４に向かい、折り返されて再び半透鏡４０３に戻る光路を辿る。他方は、第２の固定反射器４０５にて折り返されて、半透鏡４０３に戻る。
ここで、第２の固定反射器４０５は、長行程変位器４０８に積載されている。しかして、長行程変位器４０８によって、第２の固定反射器４０５の位置を、第１の固定反射器４０４側の光路と等遅延となる平衡位置４０７から適当な遅延τ_０分だけ後退した位置（第２の位置）、および、該位置からさらに丁度被測定パルス間隔Ｔだけ余分に遅延を与える点まで後退した位置（第１の位置）の間で、切り替えることができる。
【００４５】
各々半透鏡４０３に戻った２光束は、該所において再び合波された後、出射窓４０９に達する。入射窓４０２より出射窓４０９に至る光路は、真空容器４０１中にあり、光は真空中を伝搬する。
出射窓４０９を経た合波光は、スペクトログラフ４１６に入射し分光され、各波長成分が線形光検出器列４１７にて受光される。
線光検出器列４１７からのスペクトル強度出力は、読出し装置４１９を介して、計算機４２０によって表示・解析される。
この実施例において記録される各波長成分毎の強度データは、下記（９）の表式に比例する。
【数９】

ここで、ｖ（λ）とφ（λ）は、それぞれ、前出の被測定光パルスのスペクトル振幅ｖ（ω）と光路間位相不平衡φ（ω）を、波長λの関数に変換したものである。
【００４６】
余弦関数の引数を見ると、（８）式の右辺に等価であることに気付く。即ち、この干渉位相を抽出できれば、前と同様に、位相不平衡（装置偏差）φ（λ）の校正が行なえ、さらにパルス間位相差δΦが算出可能である。
幸いにして、かかるスペクトル干渉信号に、非特許文献３（Journal of Optical Society of America誌72巻（1982年）156-160頁）において広知の手順を応用することで、その干渉位相を一般的に抽出することができる。
即ち、（９）式の信号を複素数に変換した後、形式的に逆フーリエ変換し、‘みなし時間’上の時系列を作ると、３つの‘信号’が、τ_０の間隔をおいて現れる。この信号は、実は、図２（ａ）の干渉相関信号について示した包絡線に一致する。上で、線形干渉相関信号の包絡線は、被測定光パルス列のスペクトルから原理的に計算できると述べたのは、今の事情を意図していたのである。
うち、時間軸上最も左側の信号（先頭信号）だけを抜き出し、形式的なフーリエ変換により波長軸上に戻し、その位相を求めれば干渉位相が得られる。
【００４７】
ここで、３つの信号から１つを抜き出すためには、そもそも、それらの間に重なりがあってはならず、そのために、意図的な遅延τ_０を与えて、信号間に間隔を作るのである。
この遅延量としては、線形干渉相関信号の包絡線が検知されなくなる程度が、最低必要である。即ち、今の被測定光パルス列の場合、図２（ｂ）の横軸の範囲、１３０ｆｓを超える遅延を与えておけば良い。勿論、測定前に、予め包絡線の広がりは知り得ないので、かかる下限遅延量に厳密にτ_０を合わせ込むのは、実践的指針とはなし難い。
寧ろ、スペクトログラフ４１６の分解能を光周波数で表し、その逆数をとって得られる時間の１／３を目安に、τ_０を設定する方が実際的である。これは、分光手段の分解能で決まるτ_０の上限への設定に、相当している。
【００４８】
図４（ｂ）に、本実施例の計算機４２０上に装備した解析プログラムのフローチャートを示す。
プログラム中、装置偏差除去に至る迄の操作（ステップ４５１〜ステップ４５４）について、ここまでに詳らかに述べた。続く装置偏差除去（ステップ４５５）に用いる位相不平衡φ（λ）は、以下によって準備される。
パルス間位相差の測定に先立ち、長行程変位器４０８を操作して、第２の固定反射器４０５を、第１の固定反射器４０４側の光路と等遅延となる平衡位置４０７から上記遅延τ_０の分だけ後退した位置（Ｎ＝０）に置く。
この状態において採取したスペクトル干渉信号について、複素化からフーリエ変換に至る操作（ステップ４５１〜ステップ４５４）を行ない、得られる位相、−（２πｃ／λ）τ_０−φ（λ）を装置偏差データとして記録・保存する。
ここで、この位相に次段のアンラップを施したものを、装置偏差データとして記録・保存してもよいが、必ずしも必要ではなく好みに任される。万一、ここの位相に折り畳みが生じていて、これが装置偏差データとして本番の測定の際に減算されたとしても、そこでのアンラップ（ステップ４５７）により対処されるからである。なお、この事情は、前述した図３の実施の形態１においても同断である。
本実施例においても、装置偏差データの準備に、被測定光パルス列自体の入射は要さず、スペクトル域を同じうする任意の光源、あるいは白色光源を用いてこれを行なえる。
【００４９】
爾後のパルス間位相差測定時には、長行程変位器４０８によって、第２の固定反射器４０５側の光路の遅延をＴだけ余分（Ｎ＝１）に設定する。ここで得たスペクトル干渉信号を、解析プログラムに入力する。記憶・保存して置いた装置偏差データ考差し引いた結果、位相、δΦ−（２πｃ／λ）τ_０が得られる。かくして光路間の位相不平衡φ（λ）が、全次数にわたって除去された。
他方、前と同様、依然として残っていると考えられる零偏差τ_０から分離して、パルス間位相差δΦを求めるために、直線回帰演算を行なう（ステップ４５８）。
しかして、ここでの位相は、λではなくλ^−１について線形である故、波長点を横座標とした直線回帰はできない。そこで、測定波長範囲とデータ点数とから、各波長点に対する（角）周波数座標２πｃ／λを算出し（ステップ４６０）、この横座標を用いて直線回帰演算を行なう。この結果求まる切片（定数項）が、パルス間位相差δΦを与える。
【００５０】
［実施の形態３］
以上で本発明の主要な実施例については、述べ終えた。ところで、図１に示した本発明の基本構成において、真空容器１０１の内部を見るに、長行程変位器１０８を除いては、図６（ａ）の真空容器６０１と変わる所がない。さらに、この長行程変位器は、装置偏差データの準備にのみ、使用されることは、前述した通りであって、測定装置組上げ時に該偏差データを採取し記録・保存してあれば、通常使用時にはこれを要さない。
以上から、本発明方法は、従来例装置に付加する形での実施も可能である。これを図５（ａ）に示す。
図５（ａ）に示す、本発明の実施の形態３のパルス間位相差測定方法において、図中、被測定光パルス列は、入射窓５０２より、真空容器５０１中の光学系に入射する。爾後、該光学系の動作は、上記基本構成に準ずる。
【００５１】
出射窓５０９を経た合波光は、レンズ５２１により非線形結晶５２２中に結焦され、従来例方法に必要な第２高調波光を発生する。レンズ５２３により集光された、第２高調波光と、非線形結晶５２２によって該第２高調波光に変換されずに残った基本波光の内、後者が、分配鏡５２５にて分離され、光検出器５１０に導かれる。
光検出器５１０の出力は、波形記憶装置５１８に記録され、計算機５２０によって表示・解析される。残余の、第２高調波光は、従来例の光検出器５２４に入射する。
一般に、非線形結晶５２２に入射した基本波光の全てが、第２高調波光に変換される訳ではないので、かかる構成が可能である。また、基本波光と第２高調波光の間には、１オクターブもの光周波数の差が存するため、前者を反射し後者を透過するような分配鏡５２５も、容易に入手できる。
本実施の形態における本発明の動作は、既述の基本構成の動作に徴して明らか故，その説明を割愛する。
【００５２】
さて、本発明において開示せられた干渉相関信号のフーリエ空間における解析手法は、これを従来例方法に適用して、該方法の改良に資することもできる。
以下では、これにつき述べ、その効果と限界を明らかにすることにより、かかる適用をして、本発明と異なる独立の創案と主張されることを無からしめよう。
図５（ａ）において、波形記憶装置５１８を従来例の光検出器５２４の出力につなぎ替え、従来例の干渉相関信号を記録し、これを計算機５２０によって表示・解析することを考える。
かくして図５（ｂ）に例示したように、離散的な時系列データとして、非線形干渉相関信号が得られる。この非線形干渉相関信号を、図３（ｂ）の流れ図に従って、フーリエ変換して解析しよう。
図５（ｃ）に、この場合の‘装置データ’を用いて、装置偏差除去を行なった後の位相を、フーリエ変換の大きさと伴に示した。
【００５３】
つごう３箇所にスペクトルの山が現れ、それぞれのスペクトルの範囲では、位相が１本の直線に乗っていることが見て取れる。このうち中央のスペクトルに対する直線を零周波数に向かって外挿し、縦軸に対する切片を求める。その位相値が、求めるパルス間位相差δΦを与える。これは、中央のスペクトル部分の位相が、前と同様の表式、δΦ−ωτ_０を持つからである。
なお、この中央のスペクトルは、本発明の線形干渉相関信号をフーリエ変換して得るスペクトルと、等しい周波数点に現れる（図５（ｃ）を図２（ｃ）と対照されたい）。
さらに、右端のスペクトル（中央のそれの２倍の周波数点に現れる）に対する位相を、零周波数に外挿すると、２δΦで縦軸を切る。即ち、２δΦを得るが、これは独立のパルス間位相差測定法とはならない。
前述の位相アンラップについての議論に照らして、実験的に得られる位相は全て２πの剰余系に折り畳まれている。かかる状態で求まる２δΦを１／２すると、その値域はπとなり、δΦの本来の値域２πを覆えない。換言すると、二意的な値しか得られないからである。
【００５４】
ここまで見た所から、従来例方法でも、本発明のデータ解析法を援用すれば、光路間位相不平衡の影響を除いて、確度の高い測定が可能となる。
ところが、装置偏差除去過程で、差し引かれるべき‘装置データ’の性質が、本発明の線形干渉相関信号と、従来例の非線形なそれとでは、全然異なるのである。今の場合も、掃引反射器５０５を平衡位置５０７に置いて採取した（非線形）干渉信号について、フーリエ変換を行ない、得られる位相として、装置偏差除去に用いるデータを準備できる。
ところが、この‘装置データ’には光源の性質が複雑な形で含まれ、厳密な意味の装置データではないのである。いきおい、この校正データの採取は、必ず被測定光パルス列を光源として行なう必要がある。
従って、従来例方法に本発明の解析法を適用する場合、校正データの採取を、測定の度に行なう必要があり、装置組立て後、一回だけ実施すれば事足りた本発明の場合と、この点で大きく異なる。
【００５５】
これからすると、皮肉にも、長行程変位器は、従来例装置にこそ必要不可欠な機構なのである。また、必ず、被測定光パルス列を入射して行なうことが必要で、スペクトル域を同じうする別光源、謂わんや、白色光源を代用することは許されない。もっとも、従来例方法では、感度的に、白色光源、例えば、ハロゲンランプ等に対して信号を得ること自体が、そもそもの不可能事であった。
以上で、本発明の解析法は、従来方法と共に用いても十分効果があるが、本発明本来の構成と共に用いる時、更に格別の効果を挙げることが、首肯されたと信ずる。
以上、本発明者によってなされた発明を、前記実施の形態に基づき具体的に説明したが、本発明は、前記実施の形態に限定されるものではなく、その要旨を逸脱しない範囲において種々変更可能であることは勿論である。
【００５６】
【発明の効果】
本願において開示される発明のうち代表的なものによって得られる効果を簡単に説明すれば、下記の通りである。
（１）本発明によれば、パルス間位相差測定方法が線形の干渉現象に基づくので、一般の光コムに対して常に十分な感度を有し、パルス間位相差を精度高く読み取る自動化できる解析手段を装備し、かつ光路間の位相不平衡の影響を完全かつ一般的に除去する校正手段を備え確度の高い測定が行うことが可能となる。
（２）本発明によれば、パルス間位相差測定方法には、干渉相関信号を採取する時間領域の構成と、スペクトル干渉を観測する周波数領域の構成が存し、前者は小型化に有利な一方、後者では極く短時間にデータ採取が行なえ、実施上の広い自由度を有する。
（３）本発明によれば、従来例装置に付加する形で極く低コストかつ資源を有効活用して実施することもできるので、工業的に大きな効果を得ることが可能となる。
【図面の簡単な説明】
【図１】本発明のパルス間位相差測定方法の基本構成を示す図である。
【図２】本発明によるパルス間位相差導出の原理を説明する図である。
【図３】本発明の実施の形態１のパルス間位相差測定方法を示す図である。
【図４】本発明の実施の形態２のパルス間位相差測定方法を示す図である。
【図５】本発明の実施の形態３のパルス間位相差測定方法を示す図である。
【図６】従来例のパルス間位相差測定方法を示す図である。
【符号の説明】
１０１，３０１，４０１，５０１，６０１…真空容器、１０２，３０２，４０２，５０２，６０２…入射窓、１０３，３０３，４０３，５０３，６０３…半透鏡、１０４，３０４，４０４，４０５，５０４，６０４…固定反射器、１０５，３０５，５０５，６０５…掃引反射器、１０６，３０６，５０６，６０６…変位器、１０７，３０７，４０７，５０７，６０７…平衡位置、１０８，３０８，４０８…長行程変位器、１０９，３０９，４０９，５０９，６０９…出射窓、１１０，３１０，３１４，５１０，５２４，６２４…光検出器、１１８，３１８，５１８…波形記憶装置、１２０，３２０，４２０，５２０…計算機、３１１…単色光源、３１２，３１３…反射鏡、３１５…トリガ発生器、４１６…スペクトログラフ、４１７…線形光検出器列、４１９…読出し装置、５２１，５２３，６２１，６２３…レンズ、５２２，６２２…非線形結晶、５２５…分配鏡。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an inter-pulse phase difference measurement method and apparatus for accurately measuring a phase difference between adjacent pulses in an optical pulse train that repeats with a constant period, and particularly to a repetitive pulse train that does not necessarily have high intensity in an optical comb application. The present invention relates to a highly accurate inter-pulse phase difference measuring method and apparatus for evaluating carrier envelope phase fluctuations.
[0002]
[Prior art]
The phase difference between adjacent pulses in an optical pulse train that repeats with a constant period is an amount related to the relationship between the pulse envelope (envelope) and the optical oscillation (carrier) inside it, so-called carrier envelope phase fluctuation. That is, when there is no fluctuation of the carrier envelope phase, the inter-pulse phase difference is also zero.
In recent years, it has been pointed out that the phenomenon changes depending on the carrier-envelope phase of an optical pulse having a remarkably high intensity that causes a significant optical nonlinear effect.
In such a case, unless a light pulse whose carrier envelope phase is controlled to be constant is used, the phenomenon cannot be expected to occur in a predictable manner. Therefore, as part of the sex evaluation of the repetitive pulse light source used, Measurement of the phase difference between pulses is indispensable.
Even without such ultra-high-intensity light, there is generally an aspect in which fluctuation of the carrier-envelope phase becomes a problem in a repetitive pulse train.
[0003]
This is the case when trying to use a comb-like spectrum associated with a repetitive pulse train, a so-called frequency comb.
In a pulse train having a constant carrier envelope phase, each optical frequency of the comb-like spectrum is an exact integer multiple of the pulse repetition frequency. Here, since the pulse repetition frequency can be controlled with high accuracy by means such as an atomic clock, it is possible to fix each optical frequency of the comb-like spectrum with extremely high accuracy.
Such a frequency comb can realize high optical frequency accuracy with a large number of spectrums, which has been difficult with conventional optical frequency stabilization methods, and can be applied to optical frequency standards or high-density wavelength division multiplexing communications. Is expected.
[0004]
Considering an optical pulse train that repeats at a constant period T, the time waveform of any one pulse is represented as e (t). Further, for convenience of expressing the phase, an analysis signal v (t) corresponding to a pulse electric field e (t) that is a real number will be introduced by e (t) = Rev (t).
At this time, the analysis signal of the next pulse is generally expressed in the form of v (t) exp (iδΦ). The phase δΦ that has appeared here corresponds to the carrier, envelope, and relative displacement between the two phases that occurred after the period T.
Considering such a phase, the expression of the analysis signal V (t) of the entire pulse train is constructed as the following expression (1).
[0005]
[Expression 1]

Here, the subscript p in the equation (1) is a number assigned to each pulse, and the sum of p is taken for all pulses that arrive within the observation time.
The spectrum of the entire pulse train is composed of the spectrum v (ω) of each pulse and the comb-like spectrum function k (ω) = Σ. _p It is expressed as a product of exp [ip (ωT + δΦ)].
[0006]
The function k (ω) exhibits a line spectral structure that repeats with a period (2π / T). The width of each line spectrum is determined in inverse proportion to the number of ps within the observation time, while the angular frequency at the center of each line spectrum is given by the following equation (2).
[Expression 2]
ω _N = (2π / T) N− (δΦ) / T (2) That is, the inter-pulse phase difference δΦ due to the fluctuation of the carrier envelope phase is a comb-like shape of the pulse train. The spectrum causes a uniform displacement of −δΦ / T from an integer multiple of 2π / T.
If such a displacement occurs randomly, when the spectrum of the pulse train is used as an optical frequency comb, the absolute optical frequency fluctuates and cannot be used. Therefore, in recent years, the measurement of the phase difference δΦ between pulses and the control thereof have attracted attention.
[0007]
A so-called heterodyne method for directly measuring the inter-pulse phase difference δΦ based directly on the displacement of the comb-like spectrum is disclosed in, for example, Non-Patent Document 1 (Science Journal, Volume 288 (2000) pp. 635-639). Has been.
That is, when the spectrum of the pulse v (ω) has a spread that causes one octave, the long wavelength portion is extracted, and the second harmonic is generated for each portion. In this second harmonic generation process, the frequency displacement is also doubled to -2δΦ / T. This second harmonic light is combined with the short wavelength portion of the original pulse and received by a photodetector.
At this time, a signal (δΦ / T) of a difference between the latter frequency displacement (−δΦ / T) and the former frequency (−2δΦ / T) appears in the photodetector output. This is because the photodetector has a square characteristic with respect to the optical electric field and acts as a difference frequency generator (mixer).
In the above, the sign of δΦ is indefinite, but if a known displacement is given to any frequency before the above multiplexing, the indefiniteness of the sign around at least 0 can be eliminated. In fact, in the above publication, this is done by acting an acousto-optic element on the original pulse side.
[0008]
In this heterodyne method, as described above, the pulse is required to have a spectral spread of one octave or more. There is no pulse laser light source that can directly generate such a wide spectrum, and it is necessary to expand the spectrum by generating white light outside the light source.
Unfortunately, the generation of white light, which is a non-linear optical process, provides a super-octave spectral extension only when the incident pulse has a sufficiently high peak power.
In general, the longer the pulse width of the light source and the higher the repetition frequency, the proportionately increases the average power to obtain the required peak power, and therefore increases the difficulty here.
For example, for a pulsed light source in the communication wavelength band, such white light generation is called supercontinuum light generation, and its implementation has been nearly 10 years so far, but it is a super octave from a repetitive light source of 10 GHz or more. Light has not yet been obtained and, of course, has not seen the application of the heterodyne method.
[0009]
As far as the present situation is concerned, it is more universally desirable that the frequency interval is wide in the application of the frequency standard / super multi-wavelength light source, any optical frequency comb.
In the former, when determining the frequency of the unknown light, it is necessary to determine N of the nearest standard line in the equation (2), and in the latter, it is necessary to separate each line in the comb by an optical filter. This is because these are very difficult if the frequency interval is narrow.
However, it is extremely inconvenient that the measurement of the frequency displacement of the comb is difficult to perform as the repetition is high, that is, in the case of a wide frequency interval.
Therefore, a measurement method that does not require high peak power other than the heterodyne method is clearly needed.
[0010]
As such a measuring method, a correlation method is widely published in, for example, Non-Patent Document 2 (Optics Letter, Vol. 21 (1996), pages 2008-2010).
FIG. 6 is a diagram showing a conventional pulse phase difference measuring method based on this.
In the configuration shown in FIG. 6A, the measured optical pulse train is incident from the incident window 602, reaches the semi-transparent mirror 603, and is branched into two light beams.
One of them goes to the fixed reflector 604 and follows an optical path that is folded back and returns to the semi-transparent mirror 603 again. The other is folded back by the sweep reflector 605 and returned to the semi-transparent mirror 603.
Here, the sweep reflector 605 is retracted from the balanced position 607 where the delay is equal to the optical path on the fixed reflector 604 side to a point where an extra delay is given just by the measured pulse interval.
Further, the sweep reflector 605 is mounted on the displacement device 606 and can sweep the delay of the optical path on the reflector side with respect to the optical path on the fixed reflector 604 around the measured pulse interval T.
The two light fluxes returning to the respective semi-transparent mirrors 603 are combined again at that place, and then reach the exit window 609. The optical path from the entrance window 602 to the exit window 609 is in the vacuum vessel 601 and light propagates in the vacuum.
[0011]
The combined light that has passed through the emission window 609 is focused into the nonlinear crystal 622 by the lens 621, and the second harmonic light generated by the crystal 622 is condensed by the lens 623 and guided to the photodetector 624.
In this conventional example, when the output of the photodetector 624 is recorded while sweeping the sweep reflector 605, for example, an oscillating interference correlation waveform indicated by a thin solid line in FIG. 6B is obtained.
The upper envelope of the interference correlation waveform is determined by fitting to obtain a broken line in FIG.
Next, the time deviation of the peak of the vibration from the vertex of the envelope is read. Furthermore, the period of vibration is read and the angular frequency is obtained.
Finally, by multiplying the above time deviation by this angular frequency, the inter-pulse phase difference δΦ is obtained, and thus the inter-pulse phase difference measurement is realized by this conventional example.
[0012]
[Non-Patent Document 1]
Science Journal Volume 288 (2000) 635-639
[Non-Patent Document 2]
Optics Letter Vol.21 (1996) 2008-2010
[Non-Patent Document 3]
Journal of Optical Society of America, Vol. 72 (1982) 156-160
[Patent Literature]
Japanese Patent No. 2747176 “Trigger Generation Circuit”
[0013]
[Problems to be solved by the invention]
However, the conventional pulse phase difference measuring method described above has the following problems.
The first problem is related to the determination by the envelope fitting described above. In the ideal case where the waveform of the pulse that has passed through the optical path on the fixed reflector side described above and the waveform of the pulse that has passed through the optical path on the sweep reflector side described above are strictly similar, the envelope may be a symmetrical function. Guaranteed.
However, no further properties are given a priori. That is, the width of the envelope and the function form itself are generally unknown.
Under such conditions, fitting must be performed assuming a plausible function form. To complicate matters, even for 1 / cosh, the function form often assumed for waveforms, the envelope becomes a complex function form.
Even if this function form is appropriate, the fitting calculation itself, which uses the width and the vertex (center) position as an unknown quantity, belongs to a non-linear fitting, and is full of numerical calculation pitfalls.
As a result, generally, it is difficult to expect high accuracy in the vertex position of the envelope obtained by fitting. Obviously, in the conventional measurement method, the accuracy of the phase difference between pulses is not high.
[0014]
The second problem is related to the accuracy of the results.
If there is a deviation in the instrument, no matter how high the repeatability is, it is not necessarily a true value, so it is generally desirable to have a calibration procedure that knows and removes the deviation, but this is especially important in the present case. It is.
In the first place, in the conventional example, a system composed of a semi-transparent mirror, a fixed reflector, and a sweep reflector, which is configured in the air in a normal interferometer, is constructed in a vacuum vessel with an optical path on the fixed reflector side. Considering device deviations due to phase imbalance between the optical paths on the sweep reflector side.
The phase and measurement deviation here will be explained in more detail below.
[0015]
In general, the frequency dependence of the propagation phase of the optical path is written as φ (ω), which is the central angular frequency ω ₀ When the Talor expansion around is performed, the terms of the second and higher order cause deformation of the pulse waveform, and even the central symmetry of the envelope is lost. Therefore, in the conventional example, there should be no higher-order terms of the second order or higher.
Therefore, the lower-order term is expressed as the following equation (3).
[Equation 3]
φ (ω) = τ _p ω ₀ + Τ _g (Ω-ω ₀ (3)
Where τ _p Is ω ₀ Propagation delay at τ _g Is the group delay.
When the analysis signal v (t) is incident on the optical path having such a propagation phase, the analysis signal of the outgoing pulse is v (t−τ _g ) Exp (iφ ₀ ), Extra phase change, φ ₀ =-(Τ _g −τ _p ) Ω ₀ Accompanied by.
This phase change is caused by the fact that the propagation delay and the group delay are not equal as shown in the equation.
[0016]
By the way, what is intended in the correlation method in the conventional example is that the (group) delay τ is added to the pulse v (t). _g = T is a comparison of v (t−T) produced by giving T with the adjacent pulse v (t−T) exp (iδΦ).
At this time, by giving a delay, an extra phase change φ ₀ If this occurs, it is completely impossible to distinguish this from the inter-pulse phase difference δΦ to be measured, resulting in a device deviation.
The extra phase change accompanying the delay of the pulse period is specifically expressed by the following equation (4).
[Expression 4]
φ ₀ = -M _o ω ₀ T (4)
Where the coefficient m _o Is a quantity representing the delay of the envelope phase from the carrier phase, which occurs with propagation of one wavelength, and the refractive index n of the optical path and the group refractive index n _g And m _o = (N _g -N) / n _g When this is counted for air, it is 1.1 × 10 5 in the 1.5 μm wavelength band. ^-6 Get a degree value.
This m _o By φ ₀ Is even 4.0 deg even for a pulse repetition of 20 GHz (T = 50 ps), and becomes a value that cannot be ignored at all. For this reason, it is not allowed to build a delay optical path in the air, and it is sealed in a vacuum vessel.
[0017]
By the way, the coefficient m _o In a solid such as glass, the value is much larger than that of the air above. For example, a commonly used quartz glass shows a value of about 1.2% in the same 1.5 μm wavelength band.
Thus, if there is a difference in the amount of glass passing between the optical path on the fixed reflector side and the optical path on the sweep reflector side, an extra phase change occurs and an apparatus deviation is caused.
Now, about 1μm of glass quantity unevenness, ₀ Is 4.3 deg, a value that cannot be ignored.
In the conventional example, the half-transparent mirror 603 is a place where such non-uniformity of glass passage may occur.
Therefore, as shown in FIG. 6 (a), a special semi-transparent mirror in which the mirror film for dividing the light into two and the mirror film for multiplexing are arranged on the front and back of the parallel substrate, respectively, is used. It is addressed. The substrate here is required to have a remarkably high degree of parallelism.
For example, when the incident point at the time of 2 minutes and the incident point at the time of multiplexing are 1 cm apart, even if the substrate has a parallelism of 30 seconds, the thickness unevenness reaches 1.5 μm, so it can withstand use at all. Absent. If the apparatus deviation depends entirely on such a fine parallelism, it is very difficult to guarantee the accuracy of the apparatus.
In such a case, rather than relying on the quality of some parts such as a semi-transparent mirror, it is rather advantageous in terms of cost and easier long-term accuracy assurance to have a procedure for calibrating / removing the apparatus deviation. However, the prior art lacks such calibration means.
[0018]
Furthermore, as described above, in the conventional method, a second-order or higher term of the propagation phase φ (ω) of the optical path is not allowed at all.
However, it is generally known that a dielectric deposited film mirror has a large high-order phase particularly at a wavelength at the end of the characteristic region. In particular, when the light to be measured has a wide spectrum, the influence of this higher-order phase is unavoidable.
Since the conventional method cannot cope with this higher-order phase at all, an optical comb having a wide spectrum cannot be directly measured.
In fact, even in the above-mentioned Non-Patent Document 2, the laser pulse before the generation of the optical comb by the generation of white light, not the optical comb, is the measurement object.
The third problem is that although the conventional method requires much lower peak power than the above heterodyne method, it still uses the nonlinear effect and has a limited sensitivity. .
Although its sensitivity is considered sufficient for normal laser pulse measurement, it remained insufficient for light extracted from an optical comb or a part of its wavelength band.
[0019]
As described above, in the conventional inter-pulse phase difference measurement method, (1) the fitting to an envelope in which there is generally no valid trial function is involved, the measurement accuracy is low, and (2) between the optical paths. As for the phase imbalance, it is difficult to guarantee the measurement accuracy as a result of the lack of calibration means even for the lower-order imbalance, and it is impossible to deal with the higher-order imbalance at all. (3) Because the nonlinear effect is used. However, there is a problem to be solved that the measurement sensitivity is insufficient to be applied to a general optical comb.
The present invention was made to solve the problems of the prior art, and the object of the present invention is sufficient for general optical combs, high in accuracy, and provided with calibration means. An object is to provide a method and an apparatus for measuring a phase difference between pulses with guaranteed accuracy.
The above and other objects and novel features of the present invention will become apparent from the description of this specification and the accompanying drawings.
[0020]
[Means for Solving the Problems]
Of the inventions disclosed in this application, the outline of typical ones will be briefly described as follows.
In the inter-pulse phase difference measuring method of the present invention, the optical pulse train to be measured is split into two light beams, one of the two light beams is propagated to the first optical path, and the other is propagated to the second optical path. The relative delay time difference between the first optical path and the second optical path is calculated in the vicinity of the repetition period of the measured optical pulse train. Range in which the envelope of the linear interference correlation signal is detected And the light propagating through the first optical path and the light propagating through the second optical path are combined to interfere with each other, the optical path length of the second optical path is made variable, and the optical signal is combined. The intensity of the interference light recorded is recorded in time series while changing the optical path length of the second optical path, and the recorded intensity data string Fourier transform, extrapolate the obtained phase in the frequency domain, and from the obtained phase value at the zero frequency, A phase difference between pulses in the optical pulse train to be measured is measured.
[0021]
The inter-pulse phase difference measuring apparatus of the present invention branches a measured optical pulse train into two light fluxes, a first light flux propagating in a first optical path and a second light flux propagating in a second optical path, and A semi-transparent mirror that multiplexes and interferes with the first light beam that has propagated through the first optical path and the second light beam that has propagated through the second optical path; and the semi-transparent mirror that is disposed in the first optical path. A fixed reflector that folds back the first light beam branched in step S2 and returns it to the semi-transparent mirror, and a movable reflector that is movably disposed in the second optical path, and folds back the second light beam branched by the semi-transparent mirror to return the half beam. The reflector returned to the reflector and the position of the reflector are such that the relative delay time difference between the first optical path and the second optical path is near the repetition period of the optical pulse train to be measured. Range in which the envelope of the linear interference correlation signal is detected And a moving means for moving the reflector around the first position to vary the optical path length of the second optical path, and the first position around the first position. A photodetector that detects the intensity of the interference light obtained by combining the light emitted from the semi-transparent mirror when the reflector is moved to vary the optical path length of the second optical path; Recording means for recording the intensity of the interference light obtained from the photodetector in time series, and calculation means for calculating the inter-pulse phase difference in the measured optical pulse train based on the intensity data train recorded on the recording means And The calculation means Fourier-transforms the recorded intensity data sequence, extrapolates the phase in the obtained frequency domain, calculates the inter-pulse phase difference from the phase value at the obtained zero frequency, The semi-transparent mirror, the fixed reflector, and the reflector are arranged in a vacuum container.
[0022]
Dress In order to calibrate / remove the position deviation, the relative delay time difference between the first optical path and the second optical path is set to near zero. Range in which the envelope of the linear interference correlation signal is detected Is set, and the intensity of the interference light obtained by the above multiplexing is recorded while changing the optical path length of the second optical path, and the phase in the frequency domain obtained by Fourier transform is recorded and stored. By subtracting the recorded / stored phase before the extrapolation, the error due to the phase non-uniformity between the two optical paths can be completely removed.
[0023]
In the inter-pulse phase difference measuring method of the present invention, in order to shorten the data collection time, the optical pulse train to be measured is split into two light beams, one of the two light beams is propagated to the first optical path, and the other one is the first. 2, the relative delay time difference between the first optical path and the second optical path is determined as the repetition period of the measured optical pulse train. Value obtained by adding a predetermined delay amount to And the light propagating through the first optical path and the light propagating through the second optical path are combined and interfered, The predetermined delay amount is a value such that the envelope of the linear interference correlation signal is not detected, The interference light obtained by the above multiplexing is divided into wavelength components, the intensities of the divided wavelength components are recorded in parallel, and based on the recorded intensity data sequence, It is characterized by measuring a phase difference between pulses.
[0024]
The inter-pulse phase difference measuring apparatus of the present invention branches a measured optical pulse train into two light fluxes, a first light flux propagating in a first optical path and a second light flux propagating in a second optical path, and A semi-transparent mirror that multiplexes and interferes with the first light beam that has propagated through the first optical path and the second light beam that has propagated through the second optical path; and the semi-transparent mirror that is disposed in the first optical path. A fixed reflector that folds back the first light beam branched in step S2 and returns it to the semi-transparent mirror, and a movable reflector that is movably disposed in the second optical path, and folds back the second light beam branched by the semi-transparent mirror to return the half beam. The reflector to be returned to the mirror, the position of the reflector, the relative delay time difference between the first optical path and the second optical path is the repetition period of the measured optical pulse train Value obtained by adding a predetermined delay amount to A moving means for setting the first position to be, a spectrograph for splitting the interference light obtained by the combination emitted from the semi-transparent mirror into wavelength components, and each wavelength component dispersed by the spectrograph A linear photodetector array for detecting the intensity of the light, and a calculation means for calculating the inter-pulse phase difference in the measured optical pulse train based on the intensity detected by the linear photodetector array, The predetermined delay amount is a value such that the envelope of the linear interference correlation signal is not detected, The semi-transparent mirror, the fixed reflector, and the reflector are arranged in a vacuum container.
[0025]
In order to determine the inter-pulse phase difference from the intensity data for each wavelength of the interference light recorded in parallel, the calculation means calculates the interference phase for each wavelength from the recorded intensity data string, and the obtained frequency The phase value at the zero frequency obtained by extrapolating the phase in the region may be used as the measured value of the phase difference between pulses.
In order to calibrate / remove the apparatus deviation, the relative delay time difference between the first optical path and the second optical path is set to zero. Value obtained by adding a predetermined delay amount to Set to The predetermined delay amount is a value such that the envelope of the linear interference correlation signal is not detected, The interference light obtained by the above multiplexing is divided into wavelength components, the intensities of the separated wavelength components are recorded in parallel, and the interference phase for each wavelength calculated therefrom is recorded and stored, By subtracting the recorded / stored phase before insertion, the error due to the phase unevenness between the two optical paths can be completely removed.
[0026]
[Action]
The third problem related to the conventional method for measuring the phase difference between pulses, that is, the limitation of sensitivity is that the conventional method collects (nonlinear) interference correlation signals obtained using a nonlinear crystal.
On the other hand, if the phase difference between pulses can be obtained from the (linear) interference correlation signal obtained by directly receiving the combined light with a photodetector having a square characteristic, the nonlinear optical effect is not involved at all. Obviously, the measurement can be done and the sensitivity problem is solved.
The present inventor has studied this point, and has found that the use of a linear interference signal at the same time provides a sufficient solution to the remaining problem related to the conventional method.
This is because it is proved that in the space where the interference correlation signal is Fourier transformed, the phase imbalance between the optical paths can be removed over all orders, and the remaining phases are always linear. The inter-pulse phase difference is obtained as a value obtained by extrapolating this linear phase to zero frequency.
In the conventional nonlinear correlation signal, since the influence on the signal of the phase imbalance is complicated, the general deconvolution of the apparatus deviation in the Fourier space is not allowed.
Furthermore, if a Fourier transform is applied to the linear interference correlation signal collected by the square light detector, the order is changed, and after the optical Fourier transform, that is, the spectroscope is applied, the light is received by the square detector. Even so, the results are mathematically equivalent.
In view of this property, a configuration in which data is collected in an extremely short time can be realized if the spectral components obtained by the spectrum are received in parallel by the square light detector array.
[0027]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
Note that components having the same function are denoted by the same reference symbols throughout the drawings for describing the embodiment, and the repetitive description thereof will be omitted.
[Basic configuration of the present invention]
FIG. 1 is a diagram showing the basic configuration of the inter-pulse phase difference measuring method of the present invention.
In the figure, a measured optical pulse train is incident from an incident window 102, reaches a semi-transparent mirror 103, and is branched into two light beams. One of them goes to the fixed reflector 104 and follows the optical path that is folded back and returns to the semi-transparent mirror 103 again. The other is folded back by the sweep reflector 105 and returned to the semi-transparent mirror 103.
Here, the sweep reflector 105 is mounted on a displacement device 106, and the displacement device 106 is mounted on a long stroke displacement device 108.
Thus, the long-path displacement device 108 changes the position of the sweep reflector 105 to the equilibrium position (second position) 107 that is equally delayed with the optical path on the fixed reflector 104 side, and the measured pulse interval from the position. It is possible to switch between positions retracted to a point that gives an extra delay by T (first position).
[0028]
Furthermore, the displacer 106 allows the sweep reflector 105 to be swept around each of the switchable positions.
The two light fluxes returning to the semi-transparent mirror 103 are combined again at that place and then reach the exit window 109. The optical path from the entrance window 102 to the exit window 109 is in the vacuum vessel 101, and light propagates in the vacuum.
The combined light (so-called interference light) that has passed through the exit window 109 enters the photodetector 110. The photodetector 110 has a square characteristic and detects the intensity of the combined light that has passed through the emission window 109. The output of the photodetector 110 is recorded in the waveform storage device 118 and displayed and analyzed by the computer 120.
[0029]
In the measurement method of the present invention, when the optical path delay on the sweep reflector side is set to an extra T by the long stroke displacer 108 and the output of the photodetector 110 is recorded while sweeping the sweep reflector 105, for example, The oscillating interference correlation waveform indicated by the thin solid line in FIG.
For the (linear) interference correlation signal obtained here, the inter-pulse phase difference δΦ can be read by the same procedure as that performed for the (nonlinear) interference correlation signal of the conventional example.
That is, the upper envelope of the interference correlation waveform is determined by fitting to obtain a broken line in FIG. Next, it is only necessary to read the time lag of the peak of the vibration from the vertex of the envelope and separately multiply the angular frequency obtained from the vibration period.
However, this procedure still involves fitting. However, unlike the conventional example, the envelope here is not an unknown function, and can be calculated from the spectrum of the optical pulse train to be measured obtained by ordinary spectroscopic means. Therefore, the fitting here is a function Is attributed to that of a single parameter of translation.
[0030]
Although some progress is recognized as compared with the conventional example, it still remains complicated. In particular, the data actually collected is not a smooth vibration waveform as shown in FIG. 2A, but is a series of discrete time series data as exemplified in FIG. 2B. I want to be.
From such sparse data, the position and height of each vibration peak cannot be obtained directly. First, a local parabola is fitted to each vibration to obtain them. There is a need.
For the first time, fitting to the envelope can be executed using the position and height of the peaks of these vibrations as inputs. In addition, this procedure does not include a process of removing the apparatus deviation, and the process remains incomplete.
[0031]
Therefore, the present inventor has come up with a procedure for performing Fourier transform on the interference correlation signal collected as discrete time series data and reading the inter-pulse phase difference δΦ in the frequency space.
Hereinafter, the principle of this procedure will be described.
Let us write (τ + NT) as the difference in delay time between the optical path on the sweep reflector 105 side and the optical path on the fixed reflector 104 side. Here, τ is a delay associated with sweeping by the displacer 106, and N represents switching of the delay by the pulse interval T by the long stroke displacer 108.
At this time, the interference correlation signal S observed for the pulse train of Equation (1) ₁ (Τ) is expressed as the following equation (5).
[0032]
[Equation 5]

Here, u is the energy of each pulse. (5) Since the sum by p in the equation is simply attributed to a multiplication constant, hereinafter, a part including τ and N, s ₁ (Τ) = 1 + Re [g ₁ Let us proceed with the discussion using (τ) exp (iNδΦ)].
G ₁ (Τ) is called an electric field correlation function, and the expression when there is no phase imbalance between optical paths is given by the following expression (6).
[0033]
[Formula 6]

In this case, the electric field correlation function is expressed as g ₁ It is standardized so that (0) = 1. Usually, since the tail between pulses can be ignored, the upper and lower limits of the integration in the above-described equation (6) may be set as T → ∞.
[0034]
Now, the Fourier transform for τ in the above-mentioned equation (6) uses the Fourier transform v (ω) of v (t), and | v (ω) | ² It is expressed.
This is nothing but the spectrum of the pulse. If there is a phase imbalance φ (ω) between the optical paths, it is multiplied by exp [−iφ (ω)].
Here, it should be noted that the exact origin of the delay time cannot be known in advance. Exactly, therefore, it was necessary to determine the origin of the delay time (the center of the envelope) on the correlation signal by determining the envelope by fitting. That is, the horizontal axis of the actually obtained interference correlation signal generally has an unknown zero deviation τ ₀ It is included.
Considering the above, measured data s ₁ (Τ + τ ₀ The following formula (7) is obtained.
[0035]
[Expression 7]

Further, when a phase other than the DC component δ (0) of the equation (9) is extracted, the following equation (8) is obtained.
[0036]
[Equation 8]

This is the basic formula representing the reading procedure of the inter-pulse phase difference δΦ in the frequency space of the present invention.
[0037]
First, prior to the measurement of the phase difference between pulses, the long-path displacement device 108 is operated to set the optical path on the sweep reflector 105 side to be equal to the optical path on the fixed reflector 104 side (N = 0). Prepare phase unbalanced φ (ω) data.
That is, in this state, while sweeping the sweep reflector 105, the output of the photodetector 110 is recorded in the waveform storage device 118, and in the computer 10, the obtained interference correlation waveform is Fourier-transformed and its phase, -ωτ ₀ -Φ (ω) is recorded and stored as device deviation data. In principle, it is sufficient to collect the apparatus deviation data only once after the assembly of the measuring apparatus.
In addition, it is not always necessary to perform the measurement by inputting the optical pulse train to be measured, and any light source having the same spectral range can be used. If N = 0, the property of the light source is | v (ω) | ² This is because there is no contribution to the phase from that point.
Furthermore, since the present method has high sensitivity, it can be easily performed using a suitable white light source such as a halogen lamp as a light source.
Then, the device deviation data, −ωτ, over the entire sensitivity band of the photodetector 110. ₀ Since −φ (ω) is obtained, this may be stored and stored in the computer 120.
[0038]
At the time of measuring the phase difference between pulses after the lapse of time, the long path displacement unit 108 sets the delay of the optical path on the sweep reflector side to an extra T (N = 1). Here, while sweeping the sweep reflector 105, the output of the photodetector 110 is recorded, and the obtained interference correlation waveform is Fourier transformed. The device deviation data stored and stored is subtracted from the phase of the Fourier transform.
As a result, the phase, δΦ−ωτ ₀ Is obtained. Thus, the phase imbalance φ (ω) between the optical paths was eliminated over all orders.
On the other hand, zero deviation τ ₀ Must still be considered to remain. This is because there is no guarantee that the zero deviation at the time of device deviation data collection matches the zero deviation of the current measurement.
FIG. 2C shows the phase after the device deviation data is removed together with the size of the equation (7).
[0039]
Spectrum of measured optical pulse train | v (ω) | ² It can be seen that the phase is on a single straight line in the range where can be detected. This straight line is extrapolated toward zero frequency, and an intercept with respect to the vertical axis is obtained. The phase value gives the desired inter-pulse phase difference δΦ. This is the phase expression, δΦ−ωτ ₀ It is a natural consequence of
Such numerical analysis operation for obtaining the intercept (and slope) is well known as linear regression. In this case, in order to eliminate the influence of meaningless phase data at a frequency point where the measured optical spectrum does not exist, this linear regression calculation is performed with a weight function. As a weight function, for example, spectrum | v (ω) | ² Using is convenient for automation because it does not require extra calculation.
Up to this point, the basic configuration and operation of the present invention have been described in detail, and the configuration of various embodiments of the present invention will be described below.
[0040]
[Embodiment 1]
In order to obtain an expected result by Fourier-transforming the interference correlation signal, it is necessary to sample and record the output of the photodetector while changing the delay time τ at a high accuracy in steps. Moreover, in order to prevent the so-called aliasing phenomenon, the sampling theorem teaches that this delay step must be less than half of the light oscillation period of the shortest wavelength included in the light to be measured.
This can be done with the basic configuration shown in FIG. 1 with a current, well calibrated high resolution displacement device. However, this is because the measuring apparatus is not affected by vibrations from the outside, and the semi-transparent mirror or fixed reflector does not swing at all. For this purpose, it is usually necessary to fix these parts to a floor plate having a very large inertia, and the measuring instrument becomes heavy and heavy, and its portability must be sacrificed.
In order to realize a lighter and more portable measuring device, it is sufficient to add a mechanism for continuously monitoring the delay time difference including the influence of vibration and determining the signal collection timing. A configuration in which this is done is shown in FIG.
[0041]
In the inter-pulse phase difference measuring method according to the first embodiment of the present invention shown in FIG. 3A, the monitoring light emitted from the monochromatic light source 311 for monitoring the delay time difference passes through the reflector 312 and becomes a measured optical pulse train. The light enters the incident window 302 in parallel.
After that, the monitoring light reaches the semi-transparent mirror 303 and is split into two light beams as in the optical pulse train to be measured, one of which is directed to the fixed reflector 304 and is returned to the semi-transparent mirror 303 again, and the other is swept and reflected. Returned to the semi-transparent mirror 303 after being folded by the container 305.
The two light beams of the monitoring light that have returned to the respective semi-transparent mirrors 303 are combined again at that place, and then reach the exit window 309. The combined light exiting the exit window 309 enters the photodetector 314 through the reflector 313.
The trigger generator 315 refers to the output of the photodetector 314, determines the signal acquisition timing, supplies the trigger signal to the waveform storage device 318, and notifies it.
More specifically, the trigger generator 315 has a built-in phase lock loop (PLL) for the output of the photodetector 314, and can generate a trigger signal by repeating multiplication as necessary. The remainder conforms to the basic configuration of FIG.
[0042]
The monochromatic light source 311 here needs to have a coherence time exceeding the repetition period T of the optical pulse train to be measured, but absolute optical frequency (wavelength) accuracy is not necessary for the purpose of obtaining the inter-pulse phase difference δΦ. Absent. Therefore, a semiconductor DFB laser or the like can be applied in addition to the gas laser normally used for such monitoring.
However, it is not strictly desirable that the wavelength of the monochromatic light source differs between the time when device deviation data is collected and the time when the measured pulse is measured. If the latter is used, device deviation data should be collected immediately before measurement. Is recommended.
Originally, the delay time monitoring method using a laser light source is not limited to the one shown here. For example, a heterodyne distance measurement method using a two-frequency He-Ne stabilized laser or a light source equivalently constructed by an optical frequency shifter is well known. This can also be applied to the present invention.
Even in the case of using a linearly polarized laser, a quarter wave plate is inserted into either the fixed reflector side or the swept reflector side to form a circularly polarized light, and the generated interference light is polarized. If measurement is performed separately, a so-called bidirectional counting method can be performed.
Details of the trigger generator 315 in such a case are disclosed in, for example, Patent Document (Japanese Patent No. 2747176, “Trigger Generation Circuit”). In this way, it goes without saying that the present invention can be implemented by arbitrarily incorporating the wide delay time monitoring (ranging) technique.
[0043]
In the present embodiment, a piezoelectric element (PZT) equipped with a stroke multiplication mechanism by a scissors is used as the displacer 306, and when this sweep is completed and an interference correlation signal is obtained, it is analyzed and the inter-pulse position is analyzed. A program for displaying the phase difference was installed on the computer 320.
The analysis program can be executed in about 0.1 second with respect to 256 data points of the interference correlation signal, and this is within the return operation time of the displacer 306. Therefore, the data acquisition / analysis cycle was operated in a loop, and the measurement for updating and displaying the phase difference between pulses without interruption was realized at a frequency of about 5 times per second.
FIG. 3B shows a flowchart of this computer program. In order to increase the robustness of the automated program, an unwrap operation to the Fourier phase (step 354) and a DC component removal operation to the amplitude (step 357) are added.
The former is an operation to smoothly open the phase obtained by the atan2 function folded in the range (−π, π). Failure to do this sometimes results in failure of linear regression when phase folding occurs in the middle of the spectrum.
The latter has the purpose of preventing the DC regression from taking into account the phase of the DC component (which is always set to 0 and does not give any information).
The remaining steps are faithful coding of the analysis method described above in [Basic configuration of the present invention], and repeated description will be omitted.
[0044]
[Embodiment 2]
As described above, in the present invention, the spectral components separated in parallel are received by the square photodetector array in parallel with the square detector and the Fourier transform in the linear correlation. A configuration for performing sampling may be employed. This is shown in FIG.
In the inter-pulse phase difference measurement method according to the second embodiment of the present invention shown in FIG. 4A, the measured optical pulse train enters from the entrance window 402, reaches the semi-transparent mirror 403, and is split into two light beams. The One of them goes to the first fixed reflector 404 and follows the optical path that is folded back and returns to the semi-transparent mirror 403 again. The other is folded back by the second fixed reflector 405 and returned to the semi-transparent mirror 403.
Here, the second fixed reflector 405 is mounted on the long stroke displacer 408. Accordingly, the long stroke displacement device 408 moves the position of the second fixed reflector 405 from the equilibrium position 407 that is equal to the optical path on the first fixed reflector 404 side to an appropriate delay τ. ₀ It is possible to switch between a position retracted by the amount (second position) and a position retracted from the position to a point where an extra delay is given just by the measured pulse interval T (first position).
[0045]
The two light fluxes returning to the respective semi-transparent mirrors 403 are combined again at that place, and then reach the exit window 409. An optical path from the entrance window 402 to the exit window 409 is in the vacuum vessel 401, and light propagates in the vacuum.
The combined light that has passed through the emission window 409 enters the spectrograph 416 and is dispersed, and each wavelength component is received by the linear photodetector array 417.
The spectral intensity output from the line light detector array 417 is displayed and analyzed by the computer 420 via the reading device 419.
The intensity data for each wavelength component recorded in this embodiment is proportional to the following expression (9).
[Equation 9]

Here, v (λ) and φ (λ) are obtained by converting the spectral amplitude v (ω) and inter-path phase imbalance φ (ω) of the above-described optical pulse to be measured into a function of wavelength λ, respectively. It is.
[0046]
If you look at the argument of the cosine function, you will notice that it is equivalent to the right side of equation (8). That is, if this interference phase can be extracted, the phase imbalance (device deviation) φ (λ) can be calibrated and the inter-pulse phase difference δΦ can be calculated as before.
Fortunately, the interference phase is generally applied to such a spectrum interference signal by applying the well-known procedure in Non-Patent Document 3 (Journal of Optical Society of America Vol. 72 (1982) 156-160). Can be extracted.
That is, after converting the signal of equation (9) into a complex number and formally performing inverse Fourier transform to create a time series on 'deemed time', three 'signals' are expressed as τ ₀ Appears at intervals. This signal actually matches the envelope shown for the interference correlation signal in FIG. Above, it was intended for the current situation that the envelope of the linear interference correlation signal can be calculated in principle from the spectrum of the measured optical pulse train.
Of these, only the leftmost signal (first signal) on the time axis is extracted, returned to the wavelength axis by a formal Fourier transform, and the phase is obtained to obtain the interference phase.
[0047]
Here, in order to extract one from the three signals, there must be no overlap between them in the first place, so that the intentional delay τ ₀ To create an interval between signals.
As the delay amount, it is necessary to minimize the extent that the envelope of the linear interference correlation signal is not detected. That is, in the case of the current optical pulse train to be measured, a delay exceeding the range of 130 fs in the horizontal axis in FIG. Of course, since the envelope spread cannot be known in advance before measurement, τ is strictly set to such a lower limit delay amount. ₀ It is difficult to provide a practical guideline.
Rather, the resolution of the spectrograph 416 is expressed in terms of optical frequency, and τ is obtained by taking 1/3 of the time obtained by taking its reciprocal as a guide. ₀ It is more practical to set This is determined by the resolution of the spectroscopic means. ₀ This corresponds to setting the upper limit of.
[0048]
FIG. 4B shows a flowchart of the analysis program installed on the computer 420 of this embodiment.
The operation (steps 451 to 454) up to removal of the apparatus deviation during the program has been described in detail so far. The phase imbalance φ (λ) used for subsequent device deviation removal (step 455) is prepared by:
Prior to the measurement of the phase difference between pulses, the long stroke displacement device 408 is operated to move the second fixed reflector 405 from the equilibrium position 407 that is equal in delay to the optical path on the first fixed reflector 404 side. ₀ Is set at a position (N = 0) which is retracted by the amount of.
The spectral interference signal collected in this state is subjected to operations from complexization to Fourier transform (steps 451 to 454), and the resulting phase, − (2πc / λ) τ ₀ -Φ (λ) is recorded and stored as device deviation data.
Here, what is obtained by applying the next stage of unwrapping to this phase may be recorded / saved as device deviation data, but it is not always necessary and left to preference. This is because even if the phase here is folded and this is subtracted as the apparatus deviation data in the actual measurement, it is dealt with by unwrapping (step 457) there. This situation is the same in the first embodiment shown in FIG.
Also in the present embodiment, the preparation of the apparatus deviation data does not require the incidence of the measured optical pulse train itself, and this can be done by using an arbitrary light source having the same spectral range or a white light source.
[0049]
At the time of measuring the phase difference between pulses after the lapse of time, the long-path displacement unit 408 sets the delay of the optical path on the second fixed reflector 405 side to an extra T (N = 1). The spectrum interference signal obtained here is input to the analysis program. As a result of subtracting the device deviation data stored and stored, phase, δΦ− (2πc / λ) τ ₀ Is obtained. Thus, the phase imbalance φ (λ) between the optical paths was removed over all orders.
On the other hand, as before, the zero deviation τ that is still considered to remain ₀ In order to obtain the inter-pulse phase difference δΦ, a linear regression calculation is performed (step 458).
The phase here is not λ but λ ^-1 Therefore, linear regression with the wavelength point as the abscissa is not possible. Therefore, the (angular) frequency coordinate 2πc / λ for each wavelength point is calculated from the measured wavelength range and the number of data points (step 460), and linear regression calculation is performed using the abscissa. The intercept (constant term) obtained as a result gives the inter-pulse phase difference δΦ.
[0050]
[Embodiment 3]
This completes the description of the main embodiment of the present invention. By the way, in the basic configuration of the present invention shown in FIG. 1, the inside of the vacuum vessel 101 is the same as the vacuum vessel 601 in FIG. Furthermore, as described above, this long stroke displacement device is used only for the preparation of device deviation data. If the deviation data is collected, recorded and stored when the measuring device is assembled, it is normally used. Sometimes this is not necessary.
From the above, the method of the present invention can be implemented in a form added to the conventional apparatus. This is shown in FIG.
In the inter-pulse phase difference measurement method according to the third embodiment of the present invention shown in FIG. 5A, the measured optical pulse train enters the optical system in the vacuum vessel 501 through the incident window 502. After that, the operation of the optical system conforms to the above basic configuration.
[0051]
The combined light that has passed through the exit window 509 is focused into the nonlinear crystal 522 by the lens 521, and second harmonic light necessary for the conventional method is generated. Of the second harmonic light collected by the lens 523 and the fundamental light remaining without being converted to the second harmonic light by the nonlinear crystal 522, the latter is separated by the distribution mirror 525, and the photodetector 510 is separated. Led to.
The output of the photodetector 510 is recorded in the waveform storage device 518 and displayed and analyzed by the computer 520. The remaining second harmonic light is incident on the photodetector 524 of the conventional example.
In general, not all of the fundamental wave light incident on the nonlinear crystal 522 is converted into the second harmonic light, so this configuration is possible. In addition, since there is a difference in optical frequency of one octave between the fundamental wave light and the second harmonic light, a distribution mirror 525 that reflects the former and transmits the latter is easily available.
Since the operation of the present invention in this embodiment is obvious from the operation of the basic configuration described above, the description thereof is omitted.
[0052]
Now, the analysis method in the Fourier space of the interference correlation signal disclosed in the present invention can be applied to the conventional method to contribute to the improvement of the method.
In the following, this will be described, and its effects and limitations will be clarified, so that such an application will not be claimed as an independent idea different from the present invention.
In FIG. 5A, it is assumed that the waveform storage device 518 is connected to the output of the conventional photodetector 524, the interference correlation signal of the conventional example is recorded, and this is displayed and analyzed by the computer 520.
Thus, as illustrated in FIG. 5B, a nonlinear interference correlation signal is obtained as discrete time-series data. This nonlinear interference correlation signal will be analyzed by Fourier transform according to the flowchart of FIG.
FIG. 5C shows the phase after removing the device deviation using the “device data” in this case together with the magnitude of the Fourier transform.
[0053]
Spectral peaks appear at three locations, and it can be seen that the phase is on a straight line in each spectral range. Among these, a straight line with respect to the center spectrum is extrapolated toward the zero frequency, and an intercept with respect to the vertical axis is obtained. The phase value gives the desired inter-pulse phase difference δΦ. This is because the phase of the central spectral part is the same as before, δΦ-ωτ ₀ Because it has.
This center spectrum appears at the same frequency point as the spectrum obtained by Fourier transforming the linear interference correlation signal of the present invention (contrast FIG. 5 (c) with FIG. 2 (c)).
Further, if the phase with respect to the rightmost spectrum (appears at a frequency point twice that in the center) is extrapolated to zero frequency, the vertical axis is cut by 2δΦ. That is, although 2δΦ is obtained, this is not an independent pulse phase difference measurement method.
In light of the discussion of phase unwrapping described above, all experimentally obtained phases are folded into a 2π residue system. When 2δΦ obtained in this state is halved, the value range becomes π, and the original value range 2π of δΦ cannot be covered. In other words, only two values can be obtained.
[0054]
From what has been seen so far, even in the conventional method, if the data analysis method of the present invention is used, measurement with high accuracy is possible except for the influence of phase imbalance between optical paths.
However, the property of the “device data” to be subtracted in the device deviation removal process is completely different between the linear interference correlation signal of the present invention and the non-linear one of the conventional example. Even in this case, Fourier transform is performed on the (non-linear) interference signal obtained by placing the sweep reflector 505 at the equilibrium position 507, and data used for apparatus deviation removal can be prepared as the obtained phase.
However, this 'device data' includes the characteristics of the light source in a complex form and is not strictly device data. It is necessary to collect the calibration data using the measured optical pulse train as a light source.
Therefore, when the analysis method of the present invention is applied to the conventional method, it is necessary to collect calibration data every measurement, and in the case of the present invention, which is sufficient to be performed only once after the assembly of the apparatus. The point is very different.
[0055]
From this point, ironically, the long stroke displacement device is an indispensable mechanism for the conventional apparatus. In addition, it is necessary to make the measurement light pulse train incident, and it is not allowed to substitute another light source having the same spectral range, so-called white light source. However, in the conventional method, it has been impossible to obtain a signal from a white light source such as a halogen lamp in terms of sensitivity.
As described above, the analysis method of the present invention is sufficiently effective even when used together with the conventional method. However, it is believed that when the analysis method of the present invention is used together with the original configuration of the present invention, a further special effect has been confirmed.
Although the invention made by the present inventor has been specifically described based on the above-described embodiment, the present invention is not limited to the above-described embodiment, and various modifications can be made without departing from the scope of the invention. Of course.
[0056]
【The invention's effect】
The effects obtained by the representative ones of the inventions disclosed in the present application will be briefly described as follows.
(1) According to the present invention, since the inter-pulse phase difference measurement method is based on a linear interference phenomenon, the analysis is always sufficiently sensitive to a general optical comb and can be automated to accurately read the inter-pulse phase difference. It is possible to perform measurement with high accuracy by providing calibration means equipped with a means and completely and generally eliminating the influence of phase imbalance between optical paths.
(2) According to the present invention, the inter-pulse phase difference measuring method has a time domain configuration for collecting interference correlation signals and a frequency domain configuration for observing spectral interference, and the former is advantageous for downsizing. On the other hand, in the latter, data can be collected in a very short time, and there is a wide degree of freedom in implementation.
(3) According to the present invention, since it can be carried out at an extremely low cost and by effectively utilizing resources in a form added to the conventional apparatus, a large industrial effect can be obtained.
[Brief description of the drawings]
FIG. 1 is a diagram showing a basic configuration of an inter-pulse phase difference measuring method according to the present invention.
FIG. 2 is a diagram illustrating the principle of deriving a phase difference between pulses according to the present invention.
FIG. 3 is a diagram showing a method for measuring a phase difference between pulses according to the first embodiment of the present invention.
FIG. 4 is a diagram showing a method for measuring a phase difference between pulses according to a second embodiment of the present invention.
FIG. 5 is a diagram showing a method for measuring a phase difference between pulses according to a third embodiment of the present invention.
FIG. 6 is a diagram showing a conventional method for measuring the phase difference between pulses.
[Explanation of symbols]
101, 301, 401, 501, 601 ... vacuum vessel, 102, 302, 402, 502, 602 ... entrance window, 103, 303, 403, 503, 603 ... semi-transparent mirror, 104, 304, 404, 405, 504, 604 ... Fixed reflector, 105, 305, 505, 605 ... Sweep reflector, 106, 306, 506, 606 ... Displacer, 107, 307, 407, 507, 607 ... Equilibrium position, 108, 308, 408 ... Long stroke displacement 109, 309, 409, 509, 609 ... exit window, 110, 310, 314, 510, 524, 624 ... photodetector, 118, 318, 518 ... waveform storage device, 120, 320, 420, 520 ... computer 311 ... Monochromatic light source 312, 313 ... Reflector 315 ... Trigger generator 416 ... Spectrograph 417 ... Linear light Out device column, 419 ... read device, 521,523,621,623 ... lens, 522,622 ... nonlinear crystal, 525 ... distributed mirror.

Claims (11)

The optical pulse train to be measured is branched into two light beams, one light beam of the branched two light beams is propagated to the first optical path, and the other light beam is propagated to the second optical path. The relative delay time difference from the first optical path is set to a range in which an envelope of a linear interference correlation signal in the vicinity of the repetition period of the measured optical pulse train is detected , and the light propagated through the first optical path and the second optical path A phase difference measurement method between pulses by measuring the phase difference between pulses in the measured optical pulse train by combining and interfering with the light propagated through the optical path of
The optical path length of the second optical path is variable, and the intensity of the interference light obtained by combining is recorded in time series while changing the optical path length of the second optical path, and the recorded intensity data The phase difference between pulses is measured by performing Fourier transform on the sequence , extrapolating the obtained phase in the frequency domain, and measuring the phase difference between pulses in the measured optical pulse train from the obtained phase value at zero frequency. Measuring method. The relative delay time difference between the first optical path and the second optical path is set in a range where an envelope of a linear interference correlation signal near zero is detected, and the optical path length of the second optical path is changed. The intensity of the interference light obtained by the multiplexing is recorded, and the phase in the frequency domain obtained by Fourier transform is recorded and stored, and the recording and storage is performed before the extrapolation. by subtracting the phase, inter-pulse phase difference measuring method according to claim 1, characterized in that to eliminate errors due to unequal phase between said second optical path. The optical pulse train to be measured is branched into two light beams, one light beam of the branched two light beams is propagated to the first optical path, and the other light beam is propagated to the second optical path. The relative delay time difference from the optical path is set to a value obtained by adding a predetermined delay amount to the repetition period of the optical pulse train to be measured, and the light propagated through the first optical path and the light propagated through the second optical path And a phase difference measurement method between pulses for measuring a phase difference between pulses in the optical pulse train to be measured,
The predetermined delay amount is set to such a value that an envelope of a linear interference correlation signal is not detected, the interference light obtained by the multiplexing is spectrally divided into wavelength components, and the intensities of the spectrally separated wavelength components are parallelized. And a phase difference measurement method between pulses, wherein the phase difference between pulses in the measured optical pulse train is measured based on the recorded intensity data train. An interference phase for each wavelength is calculated from the recorded intensity data string, the phase in the obtained frequency domain is extrapolated, and the phase difference between pulses is measured from the obtained phase value at zero frequency. The method for measuring a phase difference between pulses according to claim 3 . The relative delay time difference between the first optical path and the second optical path is set to a value obtained by adding a predetermined delay amount to zero, and the envelope of the linear interference correlation signal is not detected for the predetermined delay amount. It is a value of about, and the interference light obtained by the multiplexing is spectrally divided into wavelength components, the intensities of the spectrally separated wavelength components are recorded in parallel, and the interference phase calculated for each wavelength is recorded. - Save, before the extrapolation, by subtracting the phase that has been said record and store, according to claim 4, characterized in that the removal of errors due to unequal phase between said second optical path Phase difference measurement method between pulses. The measured optical pulse train is split into two light beams, a first light beam propagating in the first optical path and a second light beam propagating in the second optical path, and the first light beam propagating in the first optical path A semi-transparent mirror that multiplexes and interferes with the light beam and the second light beam propagated through the second optical path;
A fixed reflector that is disposed in the first optical path and returns the first light beam branched by the semi-transparent mirror and returns it to the semi-transparent mirror;
A reflector that is movably disposed in the second optical path and returns the second light beam branched by the semi-transparent mirror and returns it to the semi-transparent mirror;
The relative delay time difference between the first optical path and the second optical path is a range where the envelope of the linear interference correlation signal in the vicinity of the repetition period of the measured optical pulse train is detected. A moving means for setting the first position and moving the reflector around the first position to vary the optical path length of the second optical path;
When the reflector is moved around the first position to vary the optical path length of the second optical path, the intensity of the interference light obtained by the multiplexing emitted from the semi-transparent mirror A first photodetector for detecting
Recording means for recording the intensity of the interference light obtained from the first photodetector in time series;
Calculation means for calculating a phase difference between pulses in the measured optical pulse train based on the intensity data train recorded in the recording means;
The calculation means Fourier-transforms the recorded intensity data sequence, extrapolates the phase in the obtained frequency domain, calculates the inter-pulse phase difference from the phase value at the obtained zero frequency,
The apparatus for measuring phase difference between pulses, wherein the semi-transparent mirror, the fixed reflector, and the reflector are arranged in a vacuum vessel. The moving means sets the position of the reflector within a range in which an envelope of a linear interference correlation signal whose relative delay time difference between the first optical path and the second optical path is near zero is detected . And setting the position, moving the reflector around the second position to vary the optical path length of the second optical path,
The recording means moves the reflector around the second position to vary the optical path length of the second optical path, and the intensity of interference light obtained from the first photodetector. Are recorded in time series,
The calculation means records and stores the phase in the frequency domain obtained by Fourier transforming the recorded intensity data string, and subtracts the recorded and stored phase before the extrapolation. The apparatus according to claim 6 , wherein an error due to an uneven phase between the two optical paths is removed. A light source that emits monitoring light incident on the semi-transparent mirror in parallel with the light pulse to be measured;
A second photodetector that detects the intensity of interference light emitted from the semi-transparent mirror and obtained by combining the monitoring light;
The inter-pulse phase difference measuring device according to claim 6 or 7, further comprising means for determining a signal collection timing related to the time-series recording based on an output of the second photodetector. . The measured optical pulse train is split into two light beams, a first light beam propagating in the first optical path and a second light beam propagating in the second optical path, and the first light beam propagating in the first optical path A semi-transparent mirror that multiplexes and interferes with the light beam and the second light beam propagated through the second optical path;
A fixed reflector that is disposed in the first optical path and returns the first light beam branched by the semi-transparent mirror and returns it to the semi-transparent mirror;
A reflector that is movably disposed in the second optical path and returns the second light beam branched by the semi-transparent mirror and returns it to the semi-transparent mirror;
The position of the reflector is set to a first position where the relative delay time difference between the first optical path and the second optical path is a value obtained by adding a predetermined delay amount to the repetition period of the measured optical pulse train. Moving means to
A spectrograph that separates the interference light obtained by combining the light emitted from the semi-transparent mirror into wavelength components;
A linear photodetector array for detecting the intensity of light of each wavelength component dispersed by the spectrograph;
Calculation means for calculating a phase difference between pulses in the measured optical pulse train based on the intensity detected by the linear photodetector train;
The predetermined delay amount is a value such that the envelope of the linear interference correlation signal is not detected,
The apparatus for measuring phase difference between pulses, wherein the semi-transparent mirror, the fixed reflector, and the reflector are arranged in a vacuum vessel. The calculation means calculates an interference phase for each wavelength from the intensity detected by the linear photodetector array, extrapolates the phase in the obtained frequency domain, and calculates the inter-pulse position from the obtained phase value at zero frequency. The phase difference measurement apparatus according to claim 9 , wherein the phase difference is calculated. The moving means sets the position of the reflector to a second position where a relative delay time difference between the first optical path and the second optical path is a value obtained by adding a predetermined delay amount to zero. The predetermined delay amount is a value such that the envelope of the linear interference correlation signal is not detected,
The calculating means calculates, records and stores an interference phase for each wavelength from the intensity detected by the linear photodetector array when the reflector is at the second position, and stores the extrapolation. 10. The inter-pulse phase difference measuring apparatus according to claim 9 , wherein an error due to non-uniform phase between the two optical paths is removed by subtracting the recorded / stored phase before.

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