JP3686588B2 - Optical fiber strain measurement method and apparatus - Google Patents

Description

【００１８】
ここで、ｚは光ファイバに沿ったパルス光入射端からの距離、νはブリルアン後方散乱光の光周波数、ｃは真空中での光速、ｎ_０は光ファイバの屈折率、Ｐは入射パルス光の全パワー、α_Ｚは光ファイバの減衰係数である。ｇ(ν, ν_Ｂ) はブリルアン利得スペクトルであり、式（２）で表わされるローレンツ関数で与えられる。また、その形状はｚに依存しなと仮定している。ν_Ｂはｇ(ν,ν_Ｂ) がピークパワーｈとなるときの光周波数であり、ｗはｇ(ν, ν_Ｂ) の半値全幅である。ｐ_１２、λ、ρ、ｖ_Ａはそれぞれ光ファイバの光弾性係数、入射光の波長、光ファイバの密度、光ファイバ中での音速である。ｔはパルス光を入射してからその散乱光が検出されるまでの時間である。
【００１９】
光周波数がｆ_０のパルス光を入射し、それによってピークパワー周波数がν_Ｂのブリルアン散乱光が生じたとする。この差ｓ_Ｂ（＝ｆ_０−ν_Ｂ）はブリルアン周波数シフトと呼ばれ、次式で与えられる。
【００２０】
【数２】
ｓ_Ｂ＝2n₀v_A/λ （５）
【００２１】
ただしｖ_Ａは
【００２２】
【数３】

【００２３】
で与えられる。ここで、Ｅはヤング率、κはポアソン比である。光ファイバにひずみが発生すると、式（６）の関係にしたがって、ｖ_Ａが変化し、その結果式（５）のｓ_Ｂも変化する。したがって、ｆ_０を一定に保つと、ひずみの変化に応じてν_Ｂが変化することになる。このν_Ｂの変化は、光ファイバに作用している応力によって生じるひずみの大きさと比例関係があることが見出されている（T. Horiguchi, T. Kurashima, and M. Tateda.“Tensile strain dependence of Brillouin frequency shift in silica optical fibets,”IEEE Photonics Technol. Lett., vol. 1, no. 5, pp. 107-108, 1989.）。
【００２４】
そこで、予め、ひずみεの変化Δεと、ブリルアン散乱光パワースペクトルのピークパワー周波数ν_Ｂの変化Δν_Ｂとの関係を求めておくことにより、得られたν_Ｂの値からひずみεを求めることができる。ひずみの計測点、すなわちセンシング用光ファイバ１０の入射端からの距離ｚは、パルス光を光ファイバに入射してからブリルアン散乱光を検出するまでの時間ｔから式（４）より求められる。また空間分解能Δｚは、光ファイバに入射するパルス光の幅をτとすると、Δｚ＝ｃτ／（２ｎ_０）で与えられる。このようにブリルアン散乱光を利用したひずみ計測技術では、ひずみは散乱光のパワースペクトルのピークパワー周波数ν_Ｂから間接的に求められるので、ひずみ計測精度を向上させるためには、ピークパワー周波数ν_Ｂを高精度に決定しなければならない。
【００２５】
次に、図２を参照しながら、具体的にこれまでに提案されたν_Ｂの算出方法について説明する。
第１工程は、センシング用光ファイバに沿った各計測点について、光周波数を変数として解析を行うための準備をする工程であり、各計測点について光周波数を変数として、計測されたブリルアン散乱光のパワーをソートする工程である。
【００２６】
前述したように従来の装置では、光周波数を固定してパルス光を入射し、そのブリルアン散乱光のパワーを計測する。そして次に光周波数をある所定量だけ変化させて再び光周波数を固定し、散乱光パワーを計測することを繰り返す。この処理によって各光周波数について計測点を変数としたパワーが得られるので、これをもとに各計測点毎に、光周波数を変数としたパワーのデータを得る。以下ではこの工程をソートとよぶ。より具体的には、ｉ番目の計測点までの距離をｚ_ｉ（ｉ＝１〜Ｉ、Ｉは全計測点数）、ｊ番目の光周波数をν_ｉ（ｊ＝１〜Ｊ、Ｊは全計測周波数点数）、その時のパワーの計測値を
【００２７】
【外１】

【００２８】
とすると、まずν_ｊを所定の光周波数値にセットし、ｚ_ｉを変化させて
【００２９】
【外２】

【００３０】
を計測し、ｚ_Ｉまでの計測が終わったところでν_ｊを次の光周波数へと変化させν_Ｊまで計測を行っていく。
【００３１】
本工程では、あるｚ_ｉを選択して固定し、ν_ｊについて
【００３２】
【外３】

【００３３】
をソートする工程である。その結果得られた
【００３４】
【外４】

【００３５】
は、同一のｚ_ｉを有しν_ｊを変数としてソートされたものであること、また各ｚ_ｉについて独立に処理がなされることから、表記を簡単化するために以下ではこれを
【００３６】
【外５】

【００３７】
と書くこととする。
【００３８】
第２工程は、第１工程において得られたパワー
【００３９】
【外６】

【００４０】
から、前述のブリルアン散乱光のピークパワーを与えるピークパワー周波数ν_Ｂを算出する工程である。式（２）はνについての非線形関数であるため、解析解は得られない。そこで、以下のように線形化して解く方法が提案されている（C. N. Pannell, J. Dhliwayo, D. J. Webb, “How to estimate the accuracy of a Brillouin distributed temperature sensor, ”in Proceedings of OFS'97, pp. 524-527, 1997.）。この方法では、式（２）の逆数をとることによってνについての２次関数と考え、評価関数Ｅ_ｒとして
【００４１】
【数４】

【００４２】
を考える。ここで、係数ａ_１，ａ_２，ａ_３はそれぞれ、
【００４３】
【数５】

【００４４】
であり、Ｗ_ｊは逆数をとったことによる変化を避けるための重み、σ_ｊはパワーの計測値に含まれるノイズの標準偏差である。また計測値の全体に対してあてはめ計算を行うのではなく、通常はあるしきい値を設定しそれ以上の値を有するピークパワー周波数近傍に対してあてはめ計算を行うので、その計算に用いる部分をあらためてｊ（＝１〜Ｊ）で表わす。簡単のためにσ_ｊが一定であるとすると、（９），（１０）よりν_Ｂは、
【００４５】
【数６】

【００４６】
と求められる。式（７）を最小化する条件から、最小２乗法を用いてａ_２，ａ_３を求め、この結果を式（１１）に代入することによりν_Ｂを算出する。
【００４７】
第３工程は光ファイバに沿った求めるべき全ての計測点について第２工程を繰り返す工程である。すなわち、ｚ_ｉ変化させながら
【００４８】
【外７】

【００４９】
から
【００５０】
【外８】

【００５１】
を得て、ｚ_Ｉまで第２工程を繰り返す工程である。
【００５２】
以上説明した方法では、入射光のパルス幅が十分に長く、散乱光のパワースペクトルが式（２）で表されるローレンツ関数で与えられる場合が想定されている。しかし、空間分解能を上げるために入射パルス幅を短くしていくと、散乱光のパワースペクトルはローレンツ関数とは異なり、パワーが広範囲に分布するようになることが実験的に確認されている（A. Fellay, L. Thevenaz, M. Facchini, M.Nikles, and P. A. Robert,“Distributed sensing using stimulated Brillouin scattering : towards ultimate resolution,”in Proceedings of OFS'97, pp. 324-327, 1997.）。
【００５３】
また、このパワースペクトルの広がりは理論的にも示されており、その結果としてパルス幅が１０ｎｓ程度以下になると、ピークパワー周波数ν_Ｂの決定精度すなわちひずみ計測精度がパルス幅に逆比例して急激に劣化することも明らかにされている（H. Naruse, and M. Tateda, “Trade-off between the spatial and frequency resolution in measuring the power spectrum of the Brillouin backscattered light in an optical fiber,”Appl. Opt., vol. 38, no. 31, pp. 6516-6521, 1999.)。
【００５４】
本発明は、このような問題に鑑みてなされたもので、その目的とするところは、ひずみの計測に最適な入射パルス光の強度形状を提供するとともに、その入射パルス光を用いて計測されたブリルアン散乱光のパワースペクトルに対して、そのピークパワー周波数を精度良く決定する光ファイバひずみ計測方法及びその装置を提供することにある。
【００５５】
【課題を解決するための手段】
このような目的を達成するために、請求項１に記載の発明は、光ファイバに発生している長さ方向のひずみを求める光ファイバひずみ計測方法において、一定の光周波数の連続光を信号光と参照光とに分岐する第１の工程と、該分岐された信号光を、任意の１つの光周波数をもち、パルスの半値全幅とパルスの立ち上がり時間とパルスの立下り時間のそれぞれが等しい三角形入射パルス光に変換する第２の工程と、前記三角形入射パルス光を前記光ファイバに入射させる第３の工程と、前記光ファイバにおいて発生したブリルアン後方散乱光と前記分岐された参照光とを合波し、該合波光を検出して電気信号に変換して、前記任意の１つの光周波数におけるブリルアン後方散乱のパワーの計測値を、前記光ファイバに沿った各計測点を変数として計測する第４の工程と、前記任意の１つの光周波数は所定の間隔の複数の光周波数の１つであり、前記第２の工程は、前記信号光を、前記所定の間隔の複数の光周波数の１つをもち、パルスの半値全幅とパルスの立ち上がり時間とパルスの立下り時間のそれぞれが等しい三角形入射パルス光に変換し、前記所定の間隔の複数の光周波数の全ての光周波数について、第２〜第４の工程を行うことにより、前記所定の間隔の複数の光周波数毎に前記各計測点におけるブルリアン後方散乱のパワーの計測値を得る第５の工程と、該得られた前記所定の間隔の複数の光周波数毎の前記各計測点におけるブルリアン後方散乱のパワーの計測値から、前記各計測点毎に、前記所定の間隔の複数の光周波数の各々を変数として前記ブルリアン後方散乱のパワーの計測値を並べる第６の工程と、前記各計測点の１つの計測点について、前記所定の間隔の複数の光周波数の各々を変数として並べられたブルリアン後方散乱のパワーの計測値を多項式で近似し、該多項式の近似によって得られた関数により、ピークパワー周波数を算出する第７の工程と、前記光ファイバに沿って求めるべき全ての計測点のデータについて前記第７工程を繰り返す第８の工程とを有することを特徴とするものである。
【００５６】
また、請求項２に記載の発明は、請求項１に記載の発明において、前記第７の工程では、前記各計測点の１つの計測点における、前記多項式の近似によって得られた関数と前記所定の間隔の複数の光周波数の１つの光周波数についてのブリルアン後方散乱のパワーの計測値により表された関係式の係数を最小２乗法により求め、該求められた係数により前記ピークパワー周波数を算出することを特徴とするものである。
【００５７】
また、請求項３に記載の発明は、光ファイバに発生している長さ方向のひずみを求める光ファイバひずみ計測装置において、一定の光周波数の連続光を発生させる発光手段と、該発光手段により発生された連続光を信号光と参照光とに分岐する分岐手段と、該分岐手段により分岐された信号光を、任意の１つの光周波数をもち、パルスの半値全幅とパルスの立ち上がり時間とパルスの立下り時間のそれぞれが等しい三角形入射パルス光に変換する光変換手段と、該光変換手段により変換された三角形入射パルス光を前記光ファイバに入射するとともに、該光ファイバで発生したブリルアン後方散乱光を出射する光結合手段と、該光結合手段により出射されたブリルアン後方散乱光と前記分岐手段によって分岐された参照光とを合波する合波手段と、該合波手段による合波光を検出して電気信号に変換し、前記任意の１つの光周波数におけるブリルアン後方散乱のパワーの計測値を、前記光ファイバに沿った各計測点を変数として計測する計測手段と、前記任意の１つの光周波数は所定の間隔の複数の光周波数の１つであり、前記光変換手段により、前記信号光を、前記所定の間隔の複数の光周波数の１つをもち、パルスの半値全幅とパルスの立ち上がり時間とパルスの立下り時間のそれぞれが等しい三角形入射パルス光に変換して、前記計測を前記所定の間隔の複数の光周波数の全ての光周波数について行い、前記所定の間隔の複数の光周波数毎に前記各計測点におけるブルリアン後方散乱のパワーの計測値を得る手段と、該得られた前記所定の間隔の複数の光周波数毎の前記各計測点におけるブルリアン後方散乱のパワーの計測値から、前記各計測点毎に、前記所定の間隔の複数の光周波数の各々を変数として前記ブルリアン後方散乱のパワーの計測値を並べる手段と、前記各計測点の１つの計測点について、前記所定の間隔の複数の光周波数の各々を変数として並べられたブルリアン後方散乱のパワーの計測値を多項式で近似し、該多項式の近似によって得られた関数により、ピークパワー周波数を算出する手段とを備えることを特徴とするものである。
また、請求項４に記載の発明は、請求項３に記載の発明において、前記算出手段は、前記各計測点の１つの計測点における、前記多項式の近似によって得られた関数と前記所定の間隔の複数の光周波数の１つの光周波数についてのブルリアン後方散乱のパワーの計測値により表された関係式の係数を最小２乗法により求め、該求められた係数により前記ビークパワー周波数を算出することを特徴とするものである。
【００５８】
【発明の実施の形態】
以下、図面を参照して本発明の実施例について説明する。
まず、ひずみ計測に最適な入射光強度のパルス光形状を数値解析によって求め、次に計測されたブリルアン後方散乱光パワーからそのピークパワー周波数を求める方法について説明する。
【００５９】
今、時間領域において、図３に示すように強度Ｐ_Ｉ(t) が変化する入射パルス光を考える。この場合、Ｐ_Ｉ(t) は以下のようにモデル化される。
１）；Ｐ_Ｉ(t) はｔ＝０に関して対称である。すなわち、Ｐ_Ｉ(t) ＝Ｐ_Ｉ(-t)である。
２）；パルス光の強度をその最大値で正規化して表す。すなわち、Ｐ_Ｉ(0) ＝１、Ｐ_Ｉ(-∞）＝Ｐ_Ｉ(∞）＝０とする。
３）；パルス幅を半値全幅τで定義する。すなわち、Ｐ_Ｉ(-τ/2) ＝Ｐ_Ｉ( τ/2）＝1/2 である。
４）；Ｐ_Ｉ(t) が０から１に立上がったり、１から０に下がるのに要する時間、すなわち立上がり／下がり時間をΔτとする。Δτ＝０は、強度がステップ的に立上がる／下がる矩形パルス光を与える。また、０≦Δτ≦τである。
５）；立上がりの場合には、０≦Ｐ_Ｉ(t) ≦1/2 を開始区間、1/2 ≦Ｐ_Ｉ(t) ≦１を終了区間と呼び、逆に立下がりの場合には、１≧Ｐ_Ｉ(t) ≧1/2 を開始区間、1/2 ≧Ｐ_Ｉ(t) ≧０を終了区間と呼ぶ。両区間で強度は、(-τ/2，1/2 ）または（τ/2，1/2 ）に関して点対称とする。
６）；開始と終了区間の急峻さをｍ次べき乗関数（曲率パラメータｍ）で与える。
７）；Ｐ_Ｉ(t) は立上がり開始／下がり終了区間では上に凸でなく、立上がり終了／下がり開始区間では下に凸でない、すなわちｍ≧１とする。ｍ＝１はパワーが直線的に立上がる／下がる台形パルス光、ｍ＝∞は矩形パルス光を与える。
８）；入射光は、図３に示すような振幅変調のみを受けている。
９）；パルスの持続時間中、パルスは一定の光周波数ｆ_０である。
１０）；パルス光の位相は滑らかに変化し、その強度は非負である。
【００６０】
この場合、Ｐ_Ｉ(t) は、
【００６１】
【数７】

【００６２】
で与えられる。ここで、Ｔ_１，Ｔ_２はそれぞれ立下がり開始、終了時刻であり、
【００６３】
【数８】
Ｔ_１＝（τ−Δτ）/２ (13）
Ｔ_２＝（τ＋Δτ）/２ (14）
【００６４】
である。この強度Ｐ_Ｉ(t) をもつパルス光の電界Ｅ(t) は
【００６５】
【数９】

【００６６】
で与えられるので、そのパワースペクトルＰ_Ｐ(f) は、
【００６７】
【数１０】

【００６８】
で求められる。ここで、ｆは入射光についての光周波数を表わす変数、ｉは虚数単位である。一例として、τが１、１０、１００ｎｓの場合について、曲率パラメータｍを１、２、３、∞としてパワースペクトルＰ_Ｐ（β）を算出した結果を図４に示す。
【００６９】
図４（ａ）はｒ＝0.５、（ｂ）はｒ＝１の場合を示している。これらのパラメータβとｒは、それぞれ以下の式（１７）、（１８）で定義される正規化入射光周波数と正規化立上がり／下がり時間である。
【００７０】
【数１１】
β＝（ｆ−ｆ_０）/(w/2) (17)
ｒ＝Δτ／τ (18)
【００７１】
ここで、０≦ｒ≦１であり、ｒ＝０は矩形パルス光を表す。また本発明では、式（２）のローレンツ関数の半値全幅ｗの値として、これまでに報告されている平均的な値である３０ＭＨｚを用いることとする（例えば T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada,“Development of a distributed sensing technique using Brillouin scattering,”J. Lightwave Technol., vol. 13, NO. 7, pp. 1296-1303, 1995.)。
【００７２】
図４の縦軸は、算出されたそれぞれのパワースペクトルＰ_Ｐ（β）を、それと同じパルス幅をもつ矩形パルス光のピークパワー
【００７３】
【数１２】
Ｐ_Ｐ(0)_ｍ＝∞
【００７４】
で正規化した値である。図４は、ｍの値が大きくなるにつれて、入射パルス光のピークパワーは減少すること、また、メインローブのすそは広がり、より大きなサイドローブがメインローブからより離れた周波数に形成されていることを示している。前者の効果はｒ＝１の場合、後者の効果はｒ＝0.５の場合により大きい。
【００７５】
図５は、入射パルス幅τとピークパワーＰ_Ｐ(0) との関係を示した図である。図５では、各ピークパワーＰ_Ｐ(0) を相対量として示した値である。図５より、ピークパワーはいずれのｍとｒの組み合わせに対してもパルス幅の２乗に比例していると考えることができる、入射光のパルス幅τとそのパワースペクトルの半値全幅Ｗ_ｉｎとの関係を図６に示す。
【００７６】
図６の縦軸は、Ｗ_ｉｎをブリルアン利得スペクトルの半値全幅ｗ（＝３０ＭＨｚ）で正規化した値である。図６より、Ｗ_ｉｎはτに逆比例することがわかる。したがって、図４、５、６より、入射パルス光パワースペクトルＰ_Ｐ（β）はパルス幅τが大きい場合には入射光周波数ｆ_０（β＝０）のまわりの狭いプロファイルとなり、逆にτが小さくなると広い周波数に分布することがわかる。パルス幅τが同じであっても、ｍが大きくなるほどすなわち立上がり／下がりが急峻になるほどＰ_Ｐ（β）は広がり、矩形パルス光に対するパワースペクトルが最も広がっている。
【００７７】
ここで以下の２つのことを仮定して、ブリルアン後方散乱光のパワースペクトルを求める。
１）；ポンプ光の消耗がない、すなわち入射パルス光からブリルアン後方散乱光へのエネルギーの伝達量が無視できる。
２）；光ファイバ中の多くの散乱点で発生したブリルアン後方散乱光の電界には互いに位相相関がなく、後方散乱光のパワーに関して重ね合わせの原理が成り立つ。別な言い方をすると、他の場所で生じた後方散乱光によるブリルアン利得への影響は無視でき、このブリルアン利得によってスペクトルが狭くなる効果が無視できる。
【００７８】
上述の仮定により、ブリルアン後方散乱光の周波数に依存する因子Ｈ（ν）は、
【００７９】
【数１３】

【００８０】
で与えられる（H. Naruse, and M. Tateda, “Trade-off between the spatial and frequency resolution in measuring the power spectrum of the Brillouin backscattered light in an optical fiber,”Appl. Opt., vol. 38, no. 31, pp. 6516-6521, 1999.)。ただし、ｓ_Ｂはブリルアン周波数シフトであり、ｆ_０とν_Ｂの差である。正規化立上がり／下がり時間ｒが0.５と１の場合について、パワー幅τを１、１０、１００ｎｓとして、急峻さｍを変化させながら式（１９）より算出したブリルアン後方散乱光のパワースペクトルを図７に示す。図７の横軸αは次式（２０）で定義される正規化周波数である。
【００８１】
【数１４】
α＝（ν−ν_Ｂ）/(w/2) (20)
【００８２】
図７の縦軸は、正規化ブリルアン後方散乱光パワー
【００８３】
【数１５】
Ｈ(α）／Ｈ(0)_ｍ＝∞
【００８４】
である。
ここで
【００８５】
【数１６】
Ｈ(0)_ｍ＝∞
【００８６】
は、矩形パルス光の最大パワーである。いずれのτとｒの組み合わせに対しても、ｍ＝１の場合にパワースペクトルは最も狭く、ピークパワーが最も大きくなることがわかる。
【００８７】
図８は、いろいろな入射パルス形状について計算したブリルアン後方散乱光パワースペクトルのピークパワーＨ（０）を示す図である。図８より、パルス幅が同じ場合には、三角形パルス光（ｍ＝１かつｒ＝１）が最大のピークパワーを与え、ｍが大きくなるかｒが０に近づくにつれてピークパワーが減少し、矩形パルス光（ｍ＝∞またはｒ＝０）で最小になることがわかる。また、入射パルス光パワースペクトルのピークパワーＰ_Ｐ（０）は図５に示したように常にパルス幅τの２乗に比例するのに対し、図８ではτ＝１、１００ｎｓ付近の曲線の傾きはそれぞれほぼ２、１であるため、ブリルアン後方散乱光パワースペクトルのピークパワーＨ（０）は、パルス幅が短い場合にはτ^２に比例し、長い場合にはτに比例することがわかる。
【００８８】
図９は、ブリルアン後方散乱光パワースペクトルの広がりを示している図である。図９の縦軸は、正規化半値全幅Ｗ_Ｂ/wである。Ｗ_Ｂはブリルアン後方散乱光パワースペクトルから数値的に算出した半値全幅の値である。Ｗ_Ｂ/wの値は、パワー幅τが数１００ｎｓ以上ではほぼ１に収束しており、数１０ｎｓまでは緩やかに変化し、数ｎｓ以下ではτに逆比例して大きくなっていく。また、パルス幅が同じ場合、ｍが１に近づくにつれてブリルアン後方散乱光パワースペクトルの半値全幅は小さくなる。また、正規化立上り／下がり時間ｒ＝１は0.５より狭いスペクトルをつくる。
【００８９】
上述したブリルアン後方散乱光パワースペクトルが得られる理由は、次のように考えることができる。ブリルアン利得スペクトルｇ(ν,ν_Ｂ) は、そのピークパワー周波数ν_Ｂの両側に分布し、そのパワーはν_Ｂからの周波数差が大きくなるにつれて急峻に減少していく。したがって、入射パルス光パワースペクトルのピークパワー周波数ｆ₀近傍にパワーが、主にブリルアン後方散乱光パワースペクトルのピークパワー周波数ν_Ｂにおけるピークパワー形成に寄与することになる。
【００９０】
その結果、入射パルス光パワースペクトルが狭い、すなわち入射パルス幅が長い場合には、ブリルアン後方散乱光パワースペクトルの広がりはこの散乱現象に伴う広がりが支配的要因であるため、ブリルアン利得スペクトルの半値全幅ｗの値を保つ。また、入射パルス幅に比例する入射光パワーは、スペクトルの広がりがほぼ一定のブリルアン後方散乱光を生じさせるので、ブリルアン後方散乱光のピークパワーはパルス幅に比例することになる。それに対して入射パルス光パワースペクトルが広がるすなわち入射パルス幅が短くなると、この入射パルス光パワースペクトルの広がりがブリルアン後方散乱光パワースペクトルの広がりの支配的要因となる。
【００９１】
そのため、ブリルアン後方散乱光パワースペクトルは、入射パルス光パワースペクトルが入射パルス幅に逆比例して広がっていくのを反映して、同様に広がっていく。この場合、入射パルス光のパワーはそのピークパワー周波数ν_Ｂを中心にブリルアン利得スペクトルの半値全幅ｗの数１０倍の広い周波数に分布するので、ブリルアン後方散乱光のピークパワーは、入射パルス光ピークパワーが入射パルス幅の２乗に比例することを反映して、パルス幅の２乗に比例して変化する。パルス幅が同じ場合にはｍとｒが１に近づくにつれて、入射パルス光パワースペクトルはより大きなピークパワーとより急峻なプロファイルを持つために、ブリルアン後方散乱光パワースペクトルのピークパワーは大きくなっていく。
【００９２】
上述した解析に基づいて、観測されたブリルアン後方散乱光に重畳しているノイズによって生じるピークパワー周波数計測誤差について見積る。光電変換によって得られる電気信号パワーは、受信光信号パワーの２乗に比例した値であるので、受信光信号パワースペクトルの最大値Ｈ（０）を信号Ｈ_Ｓ、電気信号パワーに含まれるノイズの２乗平均値をＨ_Ｎとすると、信号対雑音比ＳＮＲは（Ｈ_Ｓ／Ｈ_Ｎ）^２で与えられる。
【００９３】
ピークパワー周波数近傍において、ブリルアン後方散乱光パワースペクトルＨ（α）が２次関数で近似でき、Ｈ（α）＋Ｈ_Ｎの最大値がα＝Δα（≠０）で観測されたとする。この場合、ピークパワー周波数計測誤差Δαは、
【００９４】
【数１７】
Δα＝1/｛Ｋ（ＳＮＲ)^１／４｝ (21)
【００９５】
で与えられる（H. Naruse, and M. Tateda, “Trade-off between the spatial and frequency resolution in measuring the power spectrum of the Brillouin backscattered light in an optical fiber,”Appl. Opt., vol. 38, no. 31, pp. 6516-6521, 1999.)。ここでＫは、パルス幅τ、立上がり／下がり時間Δτ、急峻さｍによって決まる定数である。
【００９６】
いろいろなパルス形状について数値的にΔαを求めることによって、ブリルアン後方散乱光パワースペクトルのピークパワー周波数計測誤差へ与えるｍとｒの影響について調べる。この計算において、式（２１）は、Δαに与えるＳＮＲとパルス形状の影響とが独立であることを示しているので、以下ではＳＮＲ＝１に固定して考える。
【００９７】
ここで、もう一つの仮定、すなわち、ノイズは計測装置に固有で、信号パワーに無関係の小さい一定値である仮定を加える。さらにブリルアン後方散乱光パワースペクトルのピークパワーは入射光強度のパルス形状に依存するので、いろいろなｍとｒの組み合わせについて、ピークパワーからある一定の小さい値だけパワーが減少する周波数からΔαを計算した。Δαの計算結果は、図９に示したブリルアン後方散乱光パワースペクトルの広がりとほぼ同様な特性を示していた。すなわち、パワー幅が十分長い場合には、ｒやｍの値によらず、
【００９８】
【数１８】

【００９９】
が成り立ち、Δαは一定値をとる。それに対してパルス幅が短くなるにつれて、曲線は傾きが−１の直線に近づき，数ｎｓ程度以下のパルス幅に対しては、
【０１００】
【数１９】
logΔα∝−logτ (23)
【０１０１】
なる関係がほぼ成り立ち、Δαはパルス幅に逆比例する。図１０に正規化ピークパワー周波数計測誤差
【０１０２】
【数２０】
Δα／Δα_ｍ＝∞
【０１０３】
を示す
【０１０４】
【数２１】
Δα_ｍ＝∞
【０１０５】
は、矩形パルス光のピークパワー周波数計測誤差である。図１０より、ｍが１に近づくにつれてΔαが減少していくことがわかる。また、数１００ｎｓ以上のτに対して、すべてのΔαは１に収束するが、入射パルス幅が短くなるとそれぞれのパルス形状に対応した値に収束していくこともわかる。この減少の程度は、ｒが0.５より１の場合の方が大きい。
【０１０６】
ここで、ピークパワー周波数計測誤差に与える立上がり／下がり時間の影響を詳しく調べるために、ｍに関して最も高い計測精度を与えるｍ＝１の場合について、ｒとΔαとの関係を求める。τ＝１、１０、１００ｎｓとして、ｒを０から１まで0.１刻みで変化させてΔαの値を算出した。図１１は、Δαを矩形パルス光（ｒ＝０）のピークパワー周波数計測誤差Δα_{ｒ＝ 0}で正規化した結果を示している。正規化ピークパワー周波数計測誤差Δα／Δα_{ｒ＝ 0}は、ｒに関して単調に減少しており、ｒ＝１がΔαを最小にすることを示している。三角形パルス光（ｍ＝１かつｒ＝１）の場合、τ＝１、１０、１００ｎｓにおけるΔα／Δα_{ｒ＝ 0}の値はそれぞれ0.４６、0.５３、0.９１である。したがって、例えば三角パルス光の場合、パルス幅が１０ｎｓ程度以下になるとピークパワー周波数計測誤差は、矩形パルス光の場合の約１／２である。
【０１０７】
以上の解析は、入射パルス光の急峻さｍと正規化立上がり／下がり時間ｒが１に近づくにつれて、そのパワースペクトルは入射光周波数ｆ_０（β＝０）により多くのパワーが集中するために、ブリルアン後方散乱光パワースペクトルはピークパワー周波数ν_Ｂにおいてより大きなパワーをもち、その半値全幅も小さくなることを示している。その結果、ｍ＝１かつｒ＝１の場合にΔαは最小になる。したがって、入射光強度のパルス形状が三角形（ｍ＝１かつｒ＝１）の場合に、パルス幅によらずにピークパワー周波数計測精度は最も高くなる。
【０１０８】
次に、三角形入射パルス光を用いて計測されたブリルアン後方散乱光パワーから、そのピークパワー周波数の求め方について説明する。図７より、ブリルアン後方散乱光のパワーはピークパワー周波数に関して対称に分布し、滑らかに変化することがわかるから、光周波数とその光周波数において観測されたブリルアン後方散乱光パワーとの関係を次の多項式（２４）で近似し、その係数からピークパワー周波数を算出する。
【０１０９】
【数２２】

【０１１０】
例えばブリルアン後方散乱光パワーを２次関数で近似すれば、
【０１１１】
【数２３】

【０１１２】
となることから、ピークパワー周波数 ν_Ｂは-a_１／２a_２より求められる。
【０１１３】
今、ｊ番目の計測周波数をν_ｊにおいて計測されたパワーを
【０１１４】
【外９】

【０１１５】
に対して、評価関数Ｅ_ｒとして
【０１１６】
【数２４】

【０１１７】
を考え、最小２乗法を用いて係数を決定する。係数ａ_０、ａ_１、ａ_２は、Ｅ_rを最小化する条件
【０１１８】
【数２５】

【０１１９】
より導入かれる。
【０１２０】
【数２６】

【０１２１】
を連立して解くことによって、つぎのように求められる。
【０１２２】
【数２７】

【０１２３】
ただし、係数Ａ_１からＢ_３は以下の式で与えられる。
【０１２４】
【数２８】

【０１２５】
【数２９】

【０１２６】
以下、図１２に示されたフローチャートに基づいて本発明の実施例を具体的に説明する。装置構成については、従来技術のパルス化装置４において、連続した信号光を三角形パルス光を発生するものに変えること以外は従来のものと同様である。
【０１２７】
ν_Ｂを求めるための第１工程は、従来の技術で説明した第１工程と同じで、センシング用光ファイバに沿った各計測点について、光周波数を変数として計測されたブリルアン散乱光のパワー
【０１２８】
【外１０】

【０１２９】
をソートする工程である。本工程は、各計測点において、光周波数についてソートしたパワー
【０１３０】
【外１１】

【０１３１】
を得る工程である。
【０１３２】
第２工程は、光周波数とその光周波数において観測されたブリルアン後方散乱光のパワー
【０１３３】
【外１２】

【０１３４】
との関係を多項式で近似し、その係数を最小２乗法を用いて求め、それよりピークパワー周波数ν_Ｂを算出する工程である。なお、
【０１３５】
【外１３】

【０１３６】
は従来の技術で説明したように、ｊのうちしきい値以上のパワーを有する部分である。
第３工程は、求めるべき全ての計測点のデータについて第２工程を繰り返す工程である。
【０１３７】
【発明の効果】
以上説明したように本発明によれば、入射光強度のパワー形状とそれによって生じるブリルアン後方散乱光パワースペクトルとの間の関係を解析し、最適な入射パルス形状を提供するとともに、計測されたブリルアン後方散乱光パワーからピークパワー周波数を算出するあてはめ方法を提供している。これにより、高空間分解能計測の際に、矩形パルス光を入射する場合に比べ、ひずみ計測誤差を約５０％に低減できる利点がある。
【図面の簡単な説明】
【図１】従来の光ファイバひずみ計測装置の一例を説明するための図である。
【図２】計測されたブリルアン散乱光のピークパワー周波数を算出するための従来方法を説明するためのフローチャートである。
【図３】入射光強度のパルス形状モデルを説明するための図である。
【図４】いろいろな強度形状をもつ入射パルス光のパワースペクトルを説明するための図である。
【図５】入射光のパルス幅とピークパワーとの関係を説明するための図である。
【図６】入射光のパルス幅と半値全幅との関係を説明するための図である。
【図７】いろいろな入射光強度のパルス形状に対するブリルアン後方散乱光のパワースペクトルを説明するための図である。
【図８】入射光のパルス幅とブリルアン後方散乱光パワースペクトルのピークパワーとの関係を説明するための図である。
【図９】入射パルス幅とブリルアン後方散乱光パワースペクトルの半値全幅との関係を説明するための図である。
【図１０】入射パルス幅とピークパワー周波数計測誤差との関係を説明するための図である。
【図１１】入射光のパルス立ち上がり／下がり時間とピークパワー周波数計測誤差との関係を説明するための図である。
【図１２】本発明の実施例を具体的に説明するためのフローチャートである。
【符号の説明】
１ 光源
２ 光分岐器
３ 光周波数シフタ
４ パルス化装置
５ 光方向性結合器
６ 光合波器
７ 光検出器
８ 信号処理部
１０〜１７ 光ファイバ
１８ 信号線[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an optical fiber strain measurement method and apparatus, and more particularly, to an optical fiber strain measurement method and apparatus for continuously measuring strain in the length direction using an optical fiber as a sensor. More specifically, a sensing optical fiber is fixed to a measurement target such as concrete, steel structure, ground, etc., and the strain generated in the measurement target is measured with the sensing optical fiber fixed thereto. Applied.
[0002]
[Prior art]
Currently, strain cages are commonly used for strain measurement. The strain gauge has the advantage that the spatial resolution is as high as the gauge length of several millimeters to several centimeters, and local strain can be easily measured with high accuracy. However, there are the following drawbacks. 1) Measurements are discrete points with gauges attached, and many gauges need to be densely attached for continuous measurement. 2) It is necessary to supply power to the gauge via a power line that also serves as a signal line, and handling of the power line is complicated in multipoint measurement. 3) There are drawbacks such as being affected by electromagnetic noise such as lightning. On the other hand, the optical fiber strain measurement method has an advantage that long-distance measurement over several kilometers to several tens of kilometers can be continuously performed along the optical fiber and is not affected by the electromagnetic noise described above.
[0003]
In this way, strain gages are suitable for cases where the position of remarkable strain generation is known or predictable and the measurement range is narrow. It is suitable when measurement of
[0004]
Due to these characteristics, the optical fiber strain measurement technology is expected to be applied to large structures such as tunnels and civil engineering structures such as dikes. Strain measurement for structures (H. Naruse, “Distributed fiber optic sensors using Brillouin scattering and their application,” in Proceedings of OFMC99, pp. 100-105, 1999.), river bank collapse detection (H. Naruse, Y. (Uchiyama, T. Kurashima, and S. Unno, “River levee change detection using distributed fiber optic strain sensor,” IEICE Trans. Electron., Vol. E83-C, no. 3, pp. 462-467, 2000.) Has been demonstrated through experiments.
[0005]
Recently, it has also been applied to hull damage detection of America's Cup boats (H. Murayama, K. Kageyama, I. Kimpara, A. Shimada, and H. Naruse, “Structural health monitoring of IACC yachts using fiber optic distributed strain sensors: a technical challenge for America's cup 2000, "SPIE's 7th Annual International Symposium on Smart Structures and Materials, vol. 3896, pp. 312-323, 2000.).
[0006]
As an example of a conventional optical fiber strain measuring device, an optical fiber strain measuring device (Japanese Patent Application No. 8-243760, optical fiber strain measuring device) will be described.
FIG. 1 is a block diagram showing this optical fiber strain measuring apparatus, in which reference numeral 1 is a light source, 2 is an optical splitter, 3 is an optical frequency shifter, 4 is a pulsing device, 5 is an optical directional coupler, 6 Is an optical multiplexer, 7 is a photodetector, 8 is a signal processing unit, 10 to 17 are optical fibers, and 18 is a signal line.
[0007]
The light source 1 generates continuous light having a constant optical frequency, and is a light source that emits continuous light having a single wavelength. The optical branching device 2 branches the generated continuous light into signal light and reference light. The incident end is connected by the light source 1 and the optical fiber 11, and the continuous light emitted from the light source 1 is used as two outgoing ends. The light is emitted. One branched light emitted from the optical branching device 2 is called signal light, and the other branched light is called reference light.
[0008]
The optical frequency shifter 3 is inserted for performing coherent detection by a photodetector 7 described later in order to detect the power of the weak Brillouin scattered light generated in the optical fiber with high sensitivity. The end is connected to one outgoing end of the optical branching device 2 by an optical fiber 12. The optical frequency shifter 3 shifts the optical frequency of the incident signal light by a Brillouin frequency shift described later.
[0009]
The pulsing device 4 converts continuous signal light into pulsed light, and an incident end thereof and an output end of the optical frequency shifter 3 are connected by an optical fiber 13. The pulsing device 4 performs amplitude modulation so that the electric field envelope becomes a rectangular wave in the time domain, and converts the incident light into pulsed light having a time width of about 10 ns to 1 μs.
[0010]
The optical directional coupler 5 enters pulsed light into the sensing optical fiber 10 and emits Brillouin scattered light generated in the optical fiber 10, and has an incident end, an incident / exit end, and an exit end. Light incident from the incident end is emitted from the incident / exit end, and light incident from the incident / exit end is emitted from the exit end. The incident end of the optical directional coupler 5 is connected to the pulsing device 4 by the optical fiber 14 and the pulsed light is incident thereon. The pulsed light emitted from the optical directional coupler 5 enters the sensing optical fiber 10. Backscattered light generated in the sensing optical fiber 10 by the emitted pulsed light is incident on the incident / exit end.
[0011]
The optical multiplexer 6 combines the emitted Brillouin scattered light and the reference light, and has two incident ends and one outgoing end. One input end of the optical multiplexer 6 and the output end of the optical branching device 2 described above are connected by an optical fiber 15, and the other input end and the output end of the optical directional coupler 5 are connected by an optical fiber 16. It is connected. As a result, the backscattered light emitted from the sensing optical fiber 10 and the reference light emitted from the optical branching device 2 are incident on the optical multiplexer 6 and are combined here.
[0012]
The photodetector 7 detects the combined light, converts it into an electrical signal, measures the power of the Brillouin scattered light and obtains its spectrum, detects the incident light, and converts the incident light power into electric power. Convert and output. The incident end of the photodetector 7 is connected to the emission end of the optical multiplexer 6 by an optical fiber 17.
[0013]
The signal processing unit 8 is for performing arithmetic processing on the obtained scattered light power spectrum, performs arithmetic processing on the detected scattered light power, and obtains distortion generated in the sensing optical fiber 10.
[0014]
In such a configuration, the continuous light emitted from the light source 1 enters the optical branching device 2 and is branched into signal light and reference light. This signal light is incident on the optical frequency shifter 3 and the optical frequency is shifted. The light emitted from the optical frequency shifter 3 enters the pulsing device 4 and is converted into pulsed light having a time width of about 10 ns to 1 μs. The pulsed light emitted from the pulsing device 4 passes through the optical directional coupler 5 and enters the sensing optical fiber 10.
[0015]
When the pulsed light is incident on the sensing optical fiber 10, it undergoes Rayleigh scattering or Brillouin scattering in the sensing optical fiber 10 to generate backscattered light. The backscattered light is incident on one incident end of the optical multiplexer 6 through the optical directional coupler 5 and the optical fiber 16. The reference light emitted from the optical branching device 2 described above enters the optical multiplexer 6 through the optical fiber 15 and is combined with the backscattered light described above. The combined light emitted from the optical multiplexer 6 enters the photodetector 7 and is detected, and a detection signal corresponding to the received power is output from the photodetector 7 to the signal processing unit 8.
[0016]
Brillouin scattered light is light that is scattered while returning to the incident end while causing a periodic change in the refractive index of the material when the light incident on the material propagates through the material. Light power P_B(z, ν) is given as follows.
[0017]
[Expression 1]

[0018]
Here, z is the distance from the incident end of the pulsed light along the optical fiber, ν is the optical frequency of the Brillouin backscattered light, c is the speed of light in vacuum, n₀Is the refractive index of the optical fiber, P is the total power of the incident pulsed light, α_ZIs the attenuation coefficient of the optical fiber. g (ν, ν_B) Is a Brillouin gain spectrum, which is given by the Lorentz function expressed by the equation (2). It is assumed that the shape does not depend on z. ν_BIs g (ν, ν_B) Is the optical frequency at the peak power h, and w is g (ν, ν_B) Full width at half maximum. p₁₂, Λ, ρ, v_AAre the photoelastic coefficient of the optical fiber, the wavelength of the incident light, the density of the optical fiber, and the speed of sound in the optical fiber. t is the time from when the pulsed light is incident until the scattered light is detected.
[0019]
Optical frequency is f₀, And the peak power frequency is ν_BSuppose that Brillouin scattered light is generated. This difference_B(= F₀−ν_B) Is called Brillouin frequency shift and is given by the following equation.
[0020]
[Expression 2]
s_B= 2n₀v_A/ λ (5)
[0021]
However, v_AIs
[0022]
[Equation 3]

[0023]
Given in. Here, E is Young's modulus and κ is Poisson's ratio. When strain occurs in the optical fiber, v_AChanges, and as a result, s in equation (5)_BAlso changes. Therefore, f₀Is kept constant according to the change in strain._BWill change. This ν_BIs found to be proportional to the magnitude of strain caused by the stress acting on the optical fiber (T. Horiguchi, T. Kurashima, and M. Tateda. “Tensile strain dependence of Brillouin frequency. shift in silica optical fibets, "IEEE Photonics Technol. Lett., vol. 1, no. 5, pp. 107-108, 1989.).
[0024]
Therefore, the change Δε of the strain ε and the peak power frequency ν of the Brillouin scattered light power spectrum in advance._BChange in Δν_BObtained by obtaining the relationship with_BThe strain ε can be obtained from the value of. The strain measurement point, that is, the distance z from the incident end of the sensing optical fiber 10 is obtained from equation (4) from the time t from when the pulsed light is incident on the optical fiber until the Brillouin scattered light is detected. The spatial resolution Δz is expressed as Δz = cτ / (2n, where τ is the width of the pulsed light incident on the optical fiber.₀). Thus, in strain measurement technology using Brillouin scattered light, the strain is the peak power frequency ν of the power spectrum of the scattered light._BIn order to improve the strain measurement accuracy, the peak power frequency ν_BMust be determined with high accuracy.
[0025]
Next, with reference to FIG._BThe calculation method of will be described.
The first step is a step of preparing for analysis using the optical frequency as a variable for each measurement point along the sensing optical fiber. The measured Brillouin scattered light using the optical frequency as a variable for each measurement point This is the process of sorting the powers of
[0026]
As described above, in the conventional apparatus, pulsed light is incident with the optical frequency fixed, and the power of the Brillouin scattered light is measured. Then, the optical frequency is changed by a predetermined amount, the optical frequency is fixed again, and the scattered light power is measured repeatedly. By this processing, power with the measurement point as a variable is obtained for each optical frequency. Based on this, power data with the optical frequency as a variable is obtained for each measurement point. Below, this process is called sorting. More specifically, the distance to the i-th measurement point is z_i(I = 1 to I, I is the total number of measurement points), jth optical frequency is represented by ν_i(J = 1 to J, where J is the total number of measurement frequencies)
[0027]
[Outside 1]

[0028]
First, ν_jIs set to a predetermined optical frequency value and z_iChange
[0029]
[Outside 2]

[0030]
Measure z_IWhen the measurement up to_jTo the next optical frequency and v_JI will continue to measure.
[0031]
In this process, there is a certain z_iSelect and fix ν_jabout
[0032]
[Outside 3]

[0033]
It is the process of sorting. As a result
[0034]
[Outside 4]

[0035]
Is the same z_iHas ν_jAre sorted as variables, and each z_iIn order to simplify the notation, this is described below.
[0036]
[Outside 5]

[0037]
I will write.
[0038]
The second step is the power obtained in the first step
[0039]
[Outside 6]

[0040]
From the peak power frequency ν giving the peak power of the aforementioned Brillouin scattered light_BIs a step of calculating. Since equation (2) is a nonlinear function with respect to ν, an analytical solution cannot be obtained. Therefore, the following linearization method has been proposed (CN Pannell, J. Dhliwayo, DJ Webb, “How to estimate the accuracy of a Brillouin distributed temperature sensor,” in Proceedings of OFS'97, pp. 524-527, 1997.). In this method, the inverse function of equation (2) is taken to consider it as a quadratic function for ν, and the evaluation function E_rAs
[0041]
[Expression 4]

[0042]
think of. Where coefficient a₁, A₂, A₃Respectively
[0043]
[Equation 5]

[0044]
And W_jIs the weight to avoid changes due to the reciprocal, σ_jIs the standard deviation of the noise contained in the power measurement. In addition, instead of performing the fitting calculation for the entire measured value, the fitting calculation is usually performed for the peak power frequency vicinity that has a certain threshold value and a higher value. Represented by j (= 1 to J). Σ for simplicity_jIs constant, from (9) and (10), ν_BIs
[0045]
[Formula 6]

[0046]
Is required. From the condition for minimizing Equation (7), a₂, A₃And substituting this result into equation (11)_BIs calculated.
[0047]
The third step is a step in which the second step is repeated for all measurement points to be obtained along the optical fiber. That is, z_iWhile changing
[0048]
[Outside 7]

[0049]
From
[0050]
[Outside 8]

[0051]
Get z_IThis is a step of repeating the second step.
[0052]
In the method described above, it is assumed that the pulse width of the incident light is sufficiently long and the power spectrum of the scattered light is given by the Lorentz function expressed by the equation (2). However, it has been experimentally confirmed that when the incident pulse width is shortened to increase the spatial resolution, the power spectrum of the scattered light differs from the Lorentz function and the power is distributed over a wide range (A Fellay, L. Thevenaz, M. Facchini, M. Nikles, and PA Robert, “Distributed sensing using stimulated Brillouin scattering: towards ultimate resolution,” in Proceedings of OFS'97, pp. 324-327, 1997.).
[0053]
The spread of the power spectrum is theoretically shown. As a result, when the pulse width is about 10 ns or less, the peak power frequency ν_BIt has also been clarified that the accuracy of determination of strain, that is, strain measurement accuracy, deteriorates rapidly in inverse proportion to the pulse width (H. Naruse, and M. Tateda, “Trade-off between the spatial and frequency resolution in measuring the power spectrum of the Brillouin backscattered light in an optical fiber, "Appl. Opt., vol. 38, no. 31, pp. 6516-6521, 1999.).
[0054]
The present invention has been made in view of such problems, and the object of the present invention is to provide an intensity shape of incident pulsed light that is optimal for strain measurement and to measure the intensity of the incident pulsed light. An object of the present invention is to provide an optical fiber strain measurement method and apparatus for accurately determining the peak power frequency of the power spectrum of Brillouin scattered light.
[0055]
[Means for Solving the Problems]
  In order to achieve such an object, the invention according to claim 1 is an optical fiber strain measurement method for obtaining a strain in a length direction generated in an optical fiber, wherein continuous light having a constant optical frequency is transmitted as signal light. And a first step of branching into the reference light, and the branched signal light,anyA second step of converting into a triangular incident pulsed light having one optical frequency and equal to each of the full width at half maximum of the pulse, the rising time of the pulse, and the falling time of the pulse, and the triangular incident pulsed light is incident on the optical fiber A third step of combining the Brillouin backscattered light generated in the optical fiber and the branched reference light, detecting the combined light and converting it to an electrical signal,anyA fourth step of measuring a measurement value of Brillouin backscattering power at one optical frequency using each measurement point along the optical fiber as a variable;The arbitrary one optical frequency is one of a plurality of optical frequencies at a predetermined interval, and the second step is to pulse the signal light with one of the plurality of optical frequencies at the predetermined interval. Converted to triangular incident pulsed light with the same full width at half maximum, pulse rise time and pulse fall time., All of the plurality of optical frequencies at the predetermined intervalOptical frequencyAbout the 5th process of obtaining the measured value of the power of the Brillouin backscattering in each said measurement point for every several optical frequency of the said predetermined | prescribed space | interval by performing the 2nd-4th process, and this obtained From the measured value of the power of the Brillouin backscattering at each measurement point for each of the plurality of optical frequencies at the predetermined interval, the plurality of optical frequencies at the predetermined interval are used as variables for each of the measurement points. A sixth step of arranging the scattered power measurement values, and a measurement value of the power of Brillouin backscattering arranged with each of the plurality of optical frequencies at the predetermined interval as a variable for one measurement point of each measurement point And a seventh step of calculating a peak power frequency by a function obtained by approximation of the polynomial, and data of all measurement points to be obtained along the optical fiber. It is characterized in that it has an eighth step of repeating said seventh step to have.
[0056]
  Further, in the invention according to claim 2, in the invention according to claim 1, in the seventh step, the function obtained by approximation of the polynomial at the one measurement point of the measurement points and the predetermined A coefficient of a relational expression represented by a measured value of Brillouin backscattering power for one optical frequency of a plurality of optical frequencies with an interval of is obtained by a least square method, and the peak power frequency is calculated by the obtained coefficient. It is characterized by this.
[0057]
  According to a third aspect of the present invention, there is provided an optical fiber strain measuring device for obtaining a strain in a length direction generated in an optical fiber, a light emitting means for generating continuous light having a constant optical frequency, and the light emitting means. Branching means for branching the generated continuous light into signal light and reference light, and the signal light branched by the branching means,anyLight converting means having one optical frequency and converting the pulse full width at half maximum, the pulse rising time and the pulse falling time into equal triangular incident pulse light, and the triangular incident pulse light converted by the light converting means Is incident on the optical fiber and emits Brillouin backscattered light generated in the optical fiber, Brillouin backscattered light emitted by the optical coupling means, and reference light branched by the branching means Combining means for combining, and detecting the combined light by the combining means and converting it to an electrical signal,anyMeasured power of Brillouin backscattering at one optical frequency using each measurement point along the optical fiber as a variableMeasuring means to,The arbitrary one optical frequency is one of a plurality of optical frequencies at a predetermined interval, and the signal conversion means has the signal light as one of the plurality of optical frequencies at the predetermined interval by the optical conversion means. The full width at half maximum, the rise time of the pulse, and the fall time of the pulse are each converted into a triangular incident pulse light., Measuring all of the plurality of optical frequencies at the predetermined intervalOptical frequencyMeans for obtaining a measurement value of the power of Brillouin backscattering at each measurement point for each of the plurality of optical frequencies at the predetermined interval, and each of the measurements for the plurality of optical frequencies at the obtained predetermined interval. A means for arranging the measured values of the power of the Brillouin backscattering with each of the plurality of optical frequencies at the predetermined interval as a variable from the measured value of the power of the Brillouin backscattering at a point; For one measurement point, the measured value of the power of Brillouin backscattering arranged with each of the plurality of optical frequencies at the predetermined interval as a variable is approximated by a polynomial, and by a function obtained by approximation of the polynomial, Means for calculating a peak power frequency.
  According to a fourth aspect of the present invention, in the invention according to the third aspect, the calculation means includes the function obtained by approximation of the polynomial and the predetermined interval at one measurement point of each measurement point. Calculating a coefficient of a relational expression expressed by a measured value of the power of Brillouin backscattering for one optical frequency of the plurality of optical frequencies by the least square method, and calculating the beak power frequency by the calculated coefficient. It is a feature.
[0058]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments of the present invention will be described below with reference to the drawings.
First, a description will be given of a method for obtaining a pulse light shape having an optimum incident light intensity for strain measurement by numerical analysis, and then obtaining a peak power frequency from the measured Brillouin backscattered light power.
[0059]
Now, in the time domain, as shown in FIG._IConsider an incident pulsed light with varying (t). In this case, P_I(t) is modeled as follows.
1); P_I(t) is symmetric with respect to t = 0. That is, P_I(t) = P_I(-t).
2): The intensity of the pulsed light is normalized and expressed by the maximum value. That is, P_I(0) = 1, P_I(-∞) = P_I(∞) = 0.
3); The pulse width is defined by the full width at half maximum τ. That is, P_I(-τ / 2) = P_I(τ / 2) = 1/2.
4); P_IThe time required for (t) to rise from 0 to 1 or to fall from 1 to 0, that is, the rise / fall time is defined as Δτ. Δτ = 0 gives a rectangular pulse light whose intensity rises / falls stepwise. Further, 0 ≦ Δτ ≦ τ.
5); In case of rising, 0 ≦ P_I(t) ≤1 / 2 starts, 1/2 ≤P_I(t) ≦ 1 is called the end section. Conversely, when falling, 1 ≧ P_I(t) ≧ 1/2 starts, 1/2 ≧ P_I(t) ≧ 0 is called the end section. Intensities in both sections are point-symmetric with respect to (−τ / 2,1 / 2) or (τ / 2,1 / 2).
6); The steepness of the start and end sections is given by an m-th power function (curvature parameter m).
7); P_I(t) is not convex upward in the rising start / falling end section, and is not convex in the rising end / falling start section, that is, m ≧ 1. m = 1 gives trapezoidal pulsed light whose power rises / falls linearly, and m = ∞ gives rectangular pulsed light.
8) The incident light is only subjected to amplitude modulation as shown in FIG.
9); For the duration of the pulse, the pulse has a constant optical frequency f₀It is.
10); The phase of the pulsed light changes smoothly and its intensity is non-negative.
[0060]
In this case, P_I(t) is
[0061]
[Expression 7]

[0062]
Given in. Where T₁, T₂Are the fall start and end times respectively.
[0063]
[Equation 8]
T₁= (Τ-Δτ) / 2 (13)
T₂= (Τ + Δτ) / 2 (14)
[0064]
It is. This strength P_IThe electric field E (t) of the pulsed light with (t) is
[0065]
[Equation 9]

[0066]
The power spectrum P is given by_P(f) is
[0067]
[Expression 10]

[0068]
Is required. Here, f is a variable representing the optical frequency of incident light, and i is an imaginary unit. As an example, when τ is 1, 10, 100 ns, the power spectrum P is set with the curvature parameter m being 1, 2, 3, ∞._PThe result of calculating (β) is shown in FIG.
[0069]
4A shows a case where r = 0.5, and FIG. 4B shows a case where r = 1. These parameters β and r are the normalized incident light frequency and the normalized rise / fall time defined by the following equations (17) and (18), respectively.
[0070]
## EQU11 ##
β = (f−f₀) / (W / 2) (17)
r = Δτ / τ (18)
[0071]
Here, 0 ≦ r ≦ 1, and r = 0 represents rectangular pulse light. Further, in the present invention, the average value 30 MHz reported so far is used as the value of the full width at half maximum w of the Lorentz function of Equation (2) (for example, T. Horiguchi, K. Shimizu, T Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol., Vol. 13, NO. 7, pp. 1296-1303, 1995.).
[0072]
The vertical axis in FIG. 4 indicates the calculated power spectrum P._P(Β) is the peak power of rectangular pulse light with the same pulse width.
[0073]
[Expression 12]
P_P(0)_{m = ∞}
[0074]
The value normalized by. FIG. 4 shows that as the value of m increases, the peak power of the incident pulse light decreases, and the skirt of the main lobe widens, and a larger side lobe is formed at a frequency farther from the main lobe. Is shown. The former effect is greater when r = 1 and the latter effect is greater when r = 0.5.
[0075]
FIG. 5 shows the incident pulse width τ and the peak power P_PIt is the figure which showed the relationship with (0). In FIG. 5, each peak power P_PThis is a value indicating (0) as a relative quantity. From FIG. 5, it can be considered that the peak power is proportional to the square of the pulse width for any combination of m and r, and the pulse width τ of the incident light and the full width at half maximum W of the power spectrum._inFIG. 6 shows the relationship.
[0076]
The vertical axis in FIG._inIs normalized by the full width at half maximum w (= 30 MHz) of the Brillouin gain spectrum. From FIG._inIt can be seen that is inversely proportional to τ. Therefore, from FIGS. 4, 5 and 6, the incident pulse light power spectrum P_P(Β) indicates the incident light frequency f when the pulse width τ is large.₀It turns out that it becomes a narrow profile around (β = 0), and conversely, when τ becomes small, it is distributed over a wide frequency. Even if the pulse width τ is the same, as m increases, that is, as the rise / fall becomes steep, P_P(Β) spreads, and the power spectrum for rectangular pulse light is most spread.
[0077]
Here, the power spectrum of the Brillouin backscattered light is obtained assuming the following two things.
1); pump light is not consumed, that is, the amount of energy transferred from incident pulsed light to Brillouin backscattered light is negligible.
2); The electric field of Brillouin backscattered light generated at many scattering points in the optical fiber has no phase correlation with each other, and the principle of superposition is established with respect to the power of backscattered light. In other words, the influence on the Brillouin gain due to the backscattered light generated in other places can be ignored, and the effect of narrowing the spectrum by this Brillouin gain can be ignored.
[0078]
Based on the above assumption, the factor H (ν) depending on the frequency of the Brillouin backscattered light is
[0079]
[Formula 13]

[0080]
(H. Naruse, and M. Tateda, “Trade-off between the spatial and frequency resolution in measuring the power spectrum of the Brillouin backscattered light in an optical fiber,” Appl. Opt., Vol. 38, no. 31, pp. 6516-6521, 1999.). However, s_BIs the Brillouin frequency shift and f₀And ν_BIs the difference. When the normalized rise / fall time r is 0.5 and 1, the power spectrum of the Brillouin backscattered light calculated from the equation (19) while changing the steepness m with the power width τ of 1, 10, 100 ns As shown in FIG. The horizontal axis α in FIG. 7 is a normalized frequency defined by the following equation (20).
[0081]
[Expression 14]
α = (ν−ν_B) / (W / 2) (20)
[0082]
The vertical axis in FIG. 7 represents the normalized Brillouin backscattered light power.
[0083]
[Expression 15]
H (α) / H (0)_{m = ∞}
[0084]
It is.
here
[0085]
[Expression 16]
H (0)_{m = ∞}
[0086]
Is the maximum power of the rectangular pulse light. It can be seen that for any combination of τ and r, the power spectrum is the narrowest and the peak power is the largest when m = 1.
[0087]
FIG. 8 is a diagram showing the peak power H (0) of the Brillouin backscattered light power spectrum calculated for various incident pulse shapes. From FIG. 8, when the pulse width is the same, the triangular pulse light (m = 1 and r = 1) gives the maximum peak power, and the peak power decreases as m increases or r approaches 0. It can be seen that the pulse light (m = ∞ or r = 0) is minimized. Also, the peak power P of the incident pulsed light power spectrum_P(0) is always proportional to the square of the pulse width τ as shown in FIG. 5, whereas in FIG. 8, the slopes of the curves near τ = 1 and 100 ns are almost 2 and 1, respectively. The peak power H (0) of the scattered light power spectrum is τ when the pulse width is short.²It can be seen that it is proportional to τ, and is proportional to τ if it is long.
[0088]
FIG. 9 is a diagram showing the spread of the Brillouin backscattered light power spectrum. The vertical axis in FIG. 9 represents the normalized full width at half maximum W_B/ w. W_BIs the full width at half maximum calculated numerically from the Brillouin backscattered light power spectrum. W_BThe value of / w converges to almost 1 when the power width τ is several hundred ns or more, changes gently until several tens of ns, and increases in inverse proportion to τ when the power width τ is several ns or less. When the pulse width is the same, the full width at half maximum of the Brillouin backscattered light power spectrum decreases as m approaches 1. Also, the normalized rise / fall time r = 1 produces a spectrum narrower than 0.5.
[0089]
The reason why the above-described Brillouin backscattered light power spectrum can be obtained can be considered as follows. Brillouin gain spectrum g (ν, ν_B) Is its peak power frequency ν_BThe power is distributed on both sides of_BAs the frequency difference from becomes larger, it decreases sharply. Therefore, the peak power frequency f of the incident pulsed light power spectrum₀Power in the vicinity, mainly peak power frequency ν of Brillouin backscattered light power spectrum_BThis contributes to the peak power formation at.
[0090]
As a result, when the incident pulse light power spectrum is narrow, that is, when the incident pulse width is long, the broadening of the Brillouin backscattered light power spectrum is dominated by the scattering associated with this scattering phenomenon, so the full width at half maximum of the Brillouin gain spectrum is Keep the value of w. In addition, since the incident light power proportional to the incident pulse width generates Brillouin backscattered light with a substantially constant spectrum, the peak power of the Brillouin backscattered light is proportional to the pulse width. On the other hand, when the incident pulse light power spectrum is broadened, that is, when the incident pulse width is shortened, the spread of the incident pulse light power spectrum becomes the dominant factor of the spread of the Brillouin backscattered light power spectrum.
[0091]
For this reason, the Brillouin backscattered light power spectrum spreads similarly, reflecting that the incident pulsed light power spectrum spreads in inverse proportion to the incident pulse width. In this case, the power of the incident pulsed light is its peak power frequency ν_BThe peak power of Brillouin backscattered light reflects that the peak power of the incident pulse light is proportional to the square of the incident pulse width, since it is distributed over a wide frequency that is several tens of times the full width at half maximum w of the Brillouin gain spectrum. Thus, it changes in proportion to the square of the pulse width. When the pulse width is the same, as m and r approach 1, the peak power of the Brillouin backscattered light power spectrum increases because the incident pulsed light power spectrum has a larger peak power and a steeper profile. .
[0092]
Based on the analysis described above, the peak power frequency measurement error caused by the noise superimposed on the observed Brillouin backscattered light is estimated. Since the electric signal power obtained by photoelectric conversion is a value proportional to the square of the received optical signal power, the maximum value H (0) of the received optical signal power spectrum is set to the signal H._S, The mean square value of the noise included in the electric signal power is H_NThen, the signal-to-noise ratio SNR is (H_S/ H_N)²Given in.
[0093]
Near the peak power frequency, the Brillouin backscattered light power spectrum H (α) can be approximated by a quadratic function, and H (α) + H_NIs observed at α = Δα (≠ 0). In this case, the peak power frequency measurement error Δα is
[0094]
[Expression 17]
Δα = 1 / {K (SNR)^1/4} (twenty one)
[0095]
(H. Naruse, and M. Tateda, “Trade-off between the spatial and frequency resolution in measuring the power spectrum of the Brillouin backscattered light in an optical fiber,” Appl. Opt., Vol. 38, no. 31, pp. 6516-6521, 1999.). Here, K is a constant determined by the pulse width τ, the rise / fall time Δτ, and the steepness m.
[0096]
The effect of m and r on the peak power frequency measurement error of the Brillouin backscattered light power spectrum is examined by calculating Δα numerically for various pulse shapes. In this calculation, equation (21) shows that the SNR given to Δα and the influence of the pulse shape are independent, so the following is considered with SNR = 1 fixed.
[0097]
Here, another assumption is added, namely the assumption that the noise is a small constant value that is specific to the measuring device and is independent of the signal power. Furthermore, since the peak power of the Brillouin backscattered light power spectrum depends on the pulse shape of the incident light intensity, Δα is calculated from the frequency at which the power decreases by a certain small value from the peak power for various combinations of m and r. . The calculation result of Δα showed almost the same characteristics as the spread of the Brillouin backscattered light power spectrum shown in FIG. That is, when the power width is sufficiently long, regardless of the values of r and m,
[0098]
[Expression 18]

[0099]
Thus, Δα takes a constant value. On the other hand, as the pulse width becomes shorter, the curve approaches a straight line having a slope of −1. For a pulse width of about several ns or less,
[0100]
[Equation 19]
logΔα∝−logτ (23)
[0101]
Is substantially established, and Δα is inversely proportional to the pulse width. Figure 10 shows the normalized peak power frequency measurement error.
[0102]
[Expression 20]
Δα / Δα_{m = ∞}
[0103]
Indicate
[0104]
[Expression 21]
Δα_{m = ∞}
[0105]
Is a peak power frequency measurement error of the rectangular pulse light. FIG. 10 shows that Δα decreases as m approaches 1. It can also be seen that for Δτ of several hundred ns or more, all Δα converge to 1, but when the incident pulse width becomes shorter, it converges to a value corresponding to each pulse shape. The degree of this decrease is larger when r is 1 than 0.5.
[0106]
Here, in order to investigate in detail the influence of the rise / fall time on the peak power frequency measurement error, the relationship between r and Δα is obtained for m = 1 which gives the highest measurement accuracy with respect to m. Δτ was calculated by changing r from 0 to 1 in increments of 0.1, with τ = 1, 10, 100 ns. In FIG. 11, Δα is a peak power frequency measurement error Δα of rectangular pulse light (r = 0)._{r = 0}Shows the normalized result. Normalized peak power frequency measurement error Δα / Δα_{r = 0}Is monotonically decreasing with respect to r, indicating that r = 1 minimizes Δα. In the case of triangular pulse light (m = 1 and r = 1), Δα / Δα at τ = 1, 10, 100 ns_{r = 0}Are 0.46, 0.53, and 0.91, respectively. Therefore, for example, in the case of triangular pulse light, when the pulse width is about 10 ns or less, the peak power frequency measurement error is about ½ that of rectangular pulse light.
[0107]
The above analysis shows that as the steepness m of the incident pulse light and the normalized rise / fall time r approach 1, the power spectrum becomes the incident light frequency f.₀Since more power is concentrated in (β = 0), the Brillouin backscattered light power spectrum has a peak power frequency ν_BIt has a larger power and the full width at half maximum is smaller. As a result, Δα is minimized when m = 1 and r = 1. Therefore, when the pulse shape of the incident light intensity is a triangle (m = 1 and r = 1), the peak power frequency measurement accuracy is the highest regardless of the pulse width.
[0108]
Next, how to obtain the peak power frequency from the Brillouin backscattered light power measured using the triangular incident pulse light will be described. From FIG. 7, it can be seen that the power of the Brillouin backscattered light is distributed symmetrically with respect to the peak power frequency and changes smoothly, so the relationship between the optical frequency and the Brillouin backscattered light power observed at the optical frequency is as follows. Approximation is performed using a polynomial (24), and the peak power frequency is calculated from the coefficient.
[0109]
[Expression 22]

[0110]
For example, if the Brillouin backscattered light power is approximated by a quadratic function,
[0111]
[Expression 23]

[0112]
Therefore, the peak power frequency ν_BIs -a₁/ 2a₂More demanded.
[0113]
Now the jth measurement frequency is v_jMeasured power at
[0114]
[Outside 9]

[0115]
, The evaluation function E_rAs
[0116]
[Expression 24]

[0117]
Then, the coefficient is determined using the least square method. Coefficient a₀, A₁, A₂Is E_rCondition to minimize
[0118]
[Expression 25]

[0119]
More introduced.
[0120]
[Equation 26]

[0121]
Can be obtained as follows.
[0122]
[Expression 27]

[0123]
Where coefficient A₁To B₃Is given by:
[0124]
[Expression 28]

[0125]
[Expression 29]

[0126]
Hereinafter, an embodiment of the present invention will be specifically described based on the flowchart shown in FIG. The apparatus configuration is the same as that of the prior art except that in the pulse generator 4 of the prior art, continuous signal light is changed to one that generates triangular pulse light.
[0127]
ν_BIs the same as the first step described in the prior art, and the power of the Brillouin scattered light measured using the optical frequency as a variable at each measurement point along the sensing optical fiber.
[0128]
[Outside 10]

[0129]
It is the process of sorting. This process is the power sorted by optical frequency at each measurement point.
[0130]
[Outside 11]

[0131]
It is the process of obtaining.
[0132]
The second step is the optical frequency and the power of the Brillouin backscattered light observed at that optical frequency.
[0133]
[Outside 12]

[0134]
Is approximated by a polynomial, and the coefficient is obtained by using the least square method, from which the peak power frequency ν_BIs a step of calculating. In addition,
[0135]
[Outside 13]

[0136]
Is a portion of j that has a power equal to or greater than a threshold, as described in the prior art.
A 3rd process is a process of repeating a 2nd process about the data of all the measurement points which should be calculated | required.
[0137]
【The invention's effect】
As described above, according to the present invention, the relationship between the power shape of the incident light intensity and the resulting Brillouin backscattered light power spectrum is analyzed to provide an optimum incident pulse shape and to measure the measured Brillouin. A fitting method for calculating the peak power frequency from the backscattered light power is provided. Thereby, there is an advantage that the strain measurement error can be reduced to about 50% in comparison with the case where the rectangular pulse light is incident at the time of high spatial resolution measurement.
[Brief description of the drawings]
FIG. 1 is a diagram for explaining an example of a conventional optical fiber strain measuring apparatus.
FIG. 2 is a flowchart for explaining a conventional method for calculating a peak power frequency of measured Brillouin scattered light.
FIG. 3 is a diagram for explaining a pulse shape model of incident light intensity;
FIG. 4 is a diagram for explaining power spectra of incident pulsed light having various intensity shapes;
FIG. 5 is a diagram for explaining a relationship between a pulse width of incident light and a peak power.
FIG. 6 is a diagram for explaining a relationship between a pulse width of incident light and a full width at half maximum.
FIG. 7 is a diagram for explaining power spectra of Brillouin backscattered light with respect to pulse shapes having various incident light intensities.
FIG. 8 is a diagram for explaining the relationship between the pulse width of incident light and the peak power of the Brillouin backscattered light power spectrum.
FIG. 9 is a diagram for explaining the relationship between the incident pulse width and the full width at half maximum of the Brillouin backscattered light power spectrum.
FIG. 10 is a diagram for explaining a relationship between an incident pulse width and a peak power frequency measurement error.
FIG. 11 is a diagram for explaining a relationship between a pulse rise / fall time of incident light and a peak power frequency measurement error.
FIG. 12 is a flowchart for specifically explaining an embodiment of the present invention.
[Explanation of symbols]
1 Light source
2 Optical splitter
3 Optical frequency shifter
4 Pulse generator
5 Optical directional coupler
6 Optical multiplexer
7 Photodetector
8 Signal processor
10-17 optical fiber
18 signal lines

Claims (4)

In the optical fiber strain measurement method to obtain the strain in the length direction generated in the optical fiber,
A first step of branching continuous light of a constant optical frequency into signal light and reference light;
A second step of converting the branched signal light into triangular incident pulse light having any one optical frequency and having the same full width at half maximum of the pulse, rise time of the pulse, and fall time of the pulse;
A third step of causing the triangular incident pulsed light to enter the optical fiber;
Brillouin backscattered light generated in the optical fiber and the branched reference light are combined, the combined light is detected and converted into an electrical signal, and the power of Brillouin backscattering at the arbitrary one optical frequency A fourth step of measuring the measured value of each measurement point along the optical fiber as a variable;
The arbitrary one optical frequency is one of a plurality of optical frequencies at a predetermined interval, and the second step is to pulse the signal light with one of the plurality of optical frequencies at the predetermined interval. The full width at half maximum, the rising time of the pulse, and the falling time of the pulse are converted into triangular incident pulsed light, and the second to fourth steps are performed for all the optical frequencies of the plurality of optical frequencies at the predetermined interval. A fifth step of obtaining a measurement value of the power of Brillouin backscattering at each of the measurement points for each of a plurality of optical frequencies at the predetermined interval,
Based on the obtained measurement value of the power of Brillouin backscattering at each measurement point at each of the plurality of optical frequencies at the predetermined interval, the variable of each of the plurality of optical frequencies at the predetermined interval is made variable for each measurement point. A sixth step of arranging the measurement values of the power of the Brillouin backscattering as
For one measurement point of each of the measurement points, a measurement value of the power of Brillouin backscattering arranged with each of the plurality of optical frequencies of the predetermined interval as a variable was approximated by a polynomial, and obtained by approximation of the polynomial A seventh step of calculating a peak power frequency by a function;
And an eighth step of repeating the seventh step for all measurement point data to be obtained along the optical fiber.   In the seventh step, at one measurement point of each measurement point, the function obtained by approximation of the polynomial and the power of Brillouin backscattering for one optical frequency of the plurality of optical frequencies at the predetermined interval 2. The optical fiber strain measurement method according to claim 1, wherein a coefficient of a relational expression represented by the measurement value is obtained by a least square method, and the beak power frequency is calculated by the obtained coefficient. In an optical fiber strain measuring device that calculates strain in the length direction generated in an optical fiber,
A light emitting means for generating continuous light of a constant optical frequency;
Branching means for branching continuous light generated by the light emitting means into signal light and reference light;
Light converting means for converting the signal light branched by the branching means into triangular incident pulse light having any one optical frequency and having the same full width at half maximum of the pulse, rising time of the pulse, and falling time of the pulse; ,
A light coupling means for making the triangular incident pulse light converted by the light converting means enter the optical fiber and emitting Brillouin backscattered light generated by the optical fiber;
Multiplexing means for multiplexing the Brillouin backscattered light emitted by the optical coupling means and the reference light branched by the branching means;
Measurement by detecting combined light by the combining means and converting it into an electrical signal, and measuring a measured value of Brillouin backscattering power at any one optical frequency using each measurement point along the optical fiber as a variable Means ,
The arbitrary one optical frequency is one of a plurality of optical frequencies at a predetermined interval, and the signal conversion means has the signal light as one of the plurality of optical frequencies at the predetermined interval by the optical conversion means. The full width at half maximum, the rise time of the pulse, and the fall time of the pulse are converted into triangular incident pulse light, and the measurement is performed for all the optical frequencies of the plurality of optical frequencies of the predetermined interval, and the predetermined interval Means for obtaining a measurement value of the power of Brillouin backscattering at each measurement point for each of a plurality of optical frequencies;
Based on the obtained measurement value of the power of Brillouin backscattering at each measurement point at each of the plurality of optical frequencies at the predetermined interval, the variable of each of the plurality of optical frequencies at the predetermined interval is made variable for each measurement point. Means for arranging the measurement values of the power of the Brillouin backscattering as
For one measurement point of each of the measurement points, a measurement value of the power of Brillouin backscattering arranged with each of the plurality of optical frequencies of the predetermined interval as a variable was approximated by a polynomial, and obtained by approximation of the polynomial An optical fiber strain measuring device comprising: means for calculating a peak power frequency according to a function.   The calculation means is a measured value of the power of Brillouin backscattering for one optical frequency of the function obtained by approximation of the polynomial and a plurality of optical frequencies at the predetermined interval at one measurement point of each measurement point. 4. The optical fiber strain measuring apparatus according to claim 3, wherein the coefficient of the relational expression expressed by the above equation is obtained by a least square method, and the beak power frequency is calculated from the obtained coefficient.

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