JP2015105909A - Ofdr optical fiber measuring method using group delay calculation and device implementing the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a technique for performing high-efficiency signal processing on an interference signal observed by an OFDR-based measuring device, capable of ensuring far higher processing speed than a conventional STFT-based signal processing speed, and ensuring slight burden on a CPU.SOLUTION: A signal processing method based on OFDR optical fiber measurement according to the present invention calculates a group delay from an initial signal of Bragg wavelengths and a shifted signal by means of a phase differential scheme, a Z-transform scheme, or the like, and obtains a Bragg wavelength shift distribution.

Description

  The present invention relates to signal processing in an optical fiber sensing technique using optical frequency domain reflectometry.

  When a regular fringe (diffraction grating) is formed by irradiating the core of an optical fiber with ultraviolet rays, it matches the period (refractive index) of the fringe among various wavelengths of light transmitted through the optical fiber. Only the wavelength is bounced (reflected). Since the period of the stripes expands and contracts due to strain and temperature, such an optical fiber becomes a sensor (Fiber Bragg Grating: FBG). The optical frequency domain reflectometry (OFDR) system, in which multiple FBGs are placed on a single optical fiber, is known to be excellent for measuring static strain, displacement, pressure, and temperature using the entire fiber. It has been.

  The FBG usually measures strain (or temperature) by observing the shift of the reflection spectrum. The most representative device for observing the FBG reflection spectrum is a spectrum analyzer. As a typical example, an Anritsu spectrum analyzer has a sweep speed of several Hz. In this case, the sweep speed is the measurement speed (frequency). The company's FBG sensor monitor is specially used for FBG measurement, which has a measurement speed of 1.2 kHz or higher.

There is an example in which the distortion / vibration of the object to be measured is measured by tracking the intensity modulation of the reflected signal, instead of directly observing the FBG reflection spectrum itself. As shown in FIG. 12, the reflected signal from the FBG is observed with a light receiver. The light receiver has a wavelength-dependent photovoltaic characteristic as shown in FIG. As a result, a Bragg wavelength shift caused by a strain change of the object to be measured is observed as a change in electromotive force. This technique has demonstrated measurements at up to 250Hz.
As described above, examples of high-speed measurement using the FBG can be seen, but these use the FBG only for single point measurement. In the case of an FBG sensor monitor, quasi-distribution type measurement is possible by multiplexing and measuring FBGs.

In the example shown in Patent Document 1, an outline of an OFDR multi-point strain measurement apparatus is shown. FIG. 13 is a diagram showing the basic configuration, and the main components are as follows.
D1, D2, D3, D4: Light intensity detector C1: 5% -95% broadband coupler C2-C5: 50% -50% broadband coupler R1-R4: Termination where total reflection occurs FC / PC1-3: Optical fiber FC / PC connector for coupling BNC1-3: BNC connector for light intensity voltage conversion output FBG1-2: Optical fiber with five FBGs placed in the detector The laser beam is supplied from a wavelength tunable light source and the detector is swept while the wavelength is swept Measure the intensity of reflected light. Since data processing uses a fast Fourier transform or a digital filter, it is necessary to perform measurement at every light wave number at regular intervals. The light intensity measured by the detector D1 periodically changes at a light wave number interval Δk (= π / nL) expressed by the following equation. Using the light intensity at the detector D1, which periodically changes with respect to the light wave number, as a trigger, the intensity of the reflected light from each FBG as the sensor unit is measured by the detectors D2, D3.

The OFDR type distribution measurement system developed by the present inventors uses a light source whose wavelength sweep speed is 100 nm / sec at the maximum, and the measurement speed of our laboratory system is 10 Hz. The signal processing efficiency of the observed interference signal also greatly affects the measurement speed. The current OFDR measurement uses a wavelength sweep width of 8 nm and a reference arm of L length (the difference in path length between the two total reflection ends for the detector D1 signal) of 20 m. A binary file is 0.76 MB in one measurement. It becomes size. This size affects the data storage speed and the measurement speed. Also, if this is measured at 10Hz for 5 minutes, it will be more than 2GB, and if you are measuring for a long time, you will have to prepare a large storage. After obtaining measurement data in the laboratory, analysis work is performed to calculate strain information. The analysis for outputting the Bragg wavelength distribution takes a little less than 1 second for one measurement data.
Currently, it is difficult to monitor strain in the laboratory in real time. This is because the storage and analysis of measurement data and the signal processing of strain information cannot be performed in parallel at high speed. To do these in parallel, experientially, it takes more than a second to make a single measurement. As described above, when the measurement speed is 10 Hz, it means that only the measurement data is stored, and the strain fluctuation is finally grasped after analysis after the experiment.

The signal processing of the OFDR type distribution measurement system of the present inventors employs a technique based on a short time Fourier transform (STFT). The short-time Fourier transform is a technique for performing analysis of measurement data and signal processing of strain information at high speed, and is presented in Patent Document 1. However, in patent document 1, it describes by the term spectrogram analysis. FIG. 10 shows a conceptual diagram of the STFT. A constant wave number section of the interference signal is extracted by applying a window function with a certain wavelength as the center wavelength to the interference signal. A frequency spectrum is calculated by performing a fast Fourier transformation (FFT) analysis on the interference signal section in the extracted window function. Since the frequency corresponds to the fiber position, the spatial distribution of the reflected light intensity at a certain wavelength is obtained by FFT. That is, it is one of the longitudinal sections in the spectrogram. Then, the reflection intensity spatial distribution can be calculated over all wave numbers (wavelengths) by shifting the window functions one after another while overlapping the window functions and similarly performing the FFT operation. That is, the spectrogram can be drawn so as to sweep in the wavelength direction. In this method, a Hamming window is adopted as the window function.
Table 1 shows examples of STFT calculation conditions that have been used in this study. In this case, the FFT must be performed 1400 times for the interval of 7455 data points. STFT is a CPU-intensive operation that calculates many FFTs.

Japanese Patent Laid-Open No. 2005-147900 “OFDR Strain Continuous Distribution Measuring Device” published on June 9, 2005

  The problem to be solved by the present invention is to propose a new highly efficient signal processing technique in an OFDR measurement device that can perform processing much faster than conventional STFT signal processing and has a light burden on the CPU. It is in.

The signal processing method of OFDR optical fiber measurement according to the present invention is a group of an initial signal of an observed Bragg wavelength and a shifted signal in an OFDR optical fiber measurement device in which a plurality of FBGs are arranged in one optical fiber. It is characterized by calculating a Bragg wavelength shift distribution by calculating a delay.
In the first form of the group delay calculation, the group delay calculation detects the phases of the initial signal and the shifted signal, performs phase unwrapping, calculates the respective phase inductions, and calculates the difference between them. 2. The signal processing method for OFDR optical fiber measurement according to claim 1, wherein a phase differential method for performing time group delay calculation is used.
The second form of the group delay calculation is to detect the phase of the initial signal and the shifted signal, perform a Fourier transform on each of them, obtain a frequency response, calculate an impulse response by an inverse Fourier transform, and calculate the impulse response. The Z conversion method for calculating the group delay using the above is used.
In the third form of the group delay calculation, the phase of the initial signal and the shifted signal is detected, Fourier transform is performed on each of the signals, a frequency response is obtained, an impulse response is calculated by convolution integration, and the impulse response is calculated. It was assumed that a Z conversion method was used to calculate the group delay.
In the above embodiment, the impulse response h (k) and kh (k) are subjected to a window function for noise processing to extract the next function in a specific section, and the FFT is calculated repeatedly by changing the extraction position. The group delay was calculated as the sum.

  The OFDR optical fiber measurement apparatus of the present invention is shifted from the initial signal of the Bragg wavelength in the OFDR measurement apparatus using a plurality of FBGs arranged on one optical fiber and utilizing the periodic change of the interference intensity of light. And a signal processing means for calculating a Bragg wavelength shift distribution by calculating a group delay from the obtained signal.

The signal processing method of the OFDR optical fiber measurement of the present invention can perform processing at a much higher speed than the signal processing by the conventional STFT, and the burden on the CPU is light. realizable.
The Z conversion technique shows a tendency not to depend on the wavelength sweep width, and shows a higher spatial resolution than the conventional STFT technique. In addition, regarding the measurement time, the method using the Z transformation is several times faster than the group delay method using phase differentiation.
Further, in the Z conversion method in which the impulse response is calculated by convolution integration and the group delay is calculated using the impulse response, the calculation efficiency is several tens of times that of the conventional STFT method.

  The OFDR optical fiber measuring device of the present invention includes a signal processing means for calculating a group delay from an initial signal of a Bragg wavelength and a shifted signal and obtaining a distribution of the Bragg wavelength shift. The measurement apparatus can provide an OFDR measurement apparatus that can perform processing at a significantly higher speed than signal processing, can reduce the burden on the CPU, and can realize highly efficient signal processing.

It is a figure explaining the group delay of a Bragg spectrum by envelope shift. It is a figure explaining the difference of the output by STFT and group delay calculation. It is a figure which shows the phase distribution of a frequency response. It is a figure explaining phase unwrapping. It is a flowchart of the group delay calculation using phase differentiation. It is a flowchart of the group delay calculation using Z transformation which computes an impulse response by inverse Fourier transform. It is a flowchart of the group delay calculation using Z conversion which calculates | requires an impulse response by convolution integration. It is a flowchart of the group delay calculation using Z transformation which calculates | requires an impulse response by the convolution integral which added the noise process. It is a figure explaining the area extraction using the window function performed in the process of noise processing. It is a conceptual diagram of STFT. It is a figure explaining the relationship between the photovoltaic power of a Bragg spectrum, and a wavelength shift. It is a figure explaining the strain measurement system by FBG. It is a figure which shows the outline | summary of the multipoint distortion measuring apparatus of OFDR system.

The principle and characteristics of group delay calculation, which is a new OFDR signal processing proposed by the present invention, will be described. The interference signal generated by OFDR is a superposition of the Bragg spectrum with a carrier wave having a frequency according to each position. When a Bragg spectrum at a certain position (a certain frequency) is taken out, it is as shown in FIG. The frequency of the carrier wave is constant as long as the same position is seen, and the Bragg wavelength shift is expressed by an envelope (amplitude modulation) shift of the signal. This envelope shift corresponds to “group delay”.
The interference signal of the FBG reflected light acquired by the OFDR is a superposition of reflection spectra in each minute section when the FBG length is divided into minute sections. Each reflection spectrum is obtained by multiplying a Bragg spectrum by a carrier having a frequency linearly correlated with a section position. That is, the envelope of the reflection spectrum corresponds to the Bragg spectrum. By calculating the envelope shift before and after experiencing the strain variation, the strain variation can be measured, but the envelope shift corresponds to the group delay. Therefore, if the group delay is calculated in the frequency domain, the strain variation in each section in the FBG can be acquired in a distributed manner.

と表現される。フーリエ変換によるｆ_１(ｋ)，ｆ_２(ｋ)の周波数スペクトルをＦ_１(ω)，Ｆ_２(ω)とすれば、それらの関係は周波数応答Ｈ(ｋ)を用いて

と表される。ここで周波数応答Ｈ(ｋ)の位相をφ(ω)とすれば、群遅延Ｔ_ｇ(ω)は

となる。群遅延は周波数の関数として算出される。周波数が位置に対応していることを考えれば、上述のように群遅延を求めることでブラッグ波長シフトの分布を求めることができる。 Assuming that the interference signal before the strain change is f ₁ (k) and the interference signal after the strain change is f ₂ (k), these two use the impulse response h (k).

It is expressed. If the frequency spectra of f ₁ (k) and f ₂ (k) by the Fourier transform are F ₁ (ω) and F ₂ (ω), the relationship between them uses the frequency response H (k).

It is expressed. If the phase of the frequency response H (k) is φ (ω), the group delay T _g (ω) is

It becomes. Group delay is calculated as a function of frequency. Considering that the frequency corresponds to the position, the Bragg wavelength shift distribution can be obtained by obtaining the group delay as described above.

  If the difference between STFT and group delay calculation is explained in terms of calculation, the STFT calculates the spatial distribution of reflected light intensity over the entire wavelength component. To make it easier to understand, if you look at the axis from different directions, it is an operation that calculates the spatial distribution of the Bragg “spectrum”. On the other hand, in the group delay calculation, the spatial distribution of Bragg “wavelength shift” is calculated. As shown in FIG. 2, the output from the STFT has a larger amount of information because the spectrum shape can be observed, but the calculation cost is higher. Of course, in order to output the Bragg wavelength shift, the STFT operation must be performed on the two signals before and after the shift. On the other hand, since only the Bragg wavelength shift is calculated in the group delay calculation, only information such as distortion change can be extracted, but the calculation cost is reduced accordingly.

The present invention proposes a new approach based on group delay calculation as a signal processing technique that replaces the conventional signal processing by STFT operation. In the present invention, two types of approaches are proposed as signal processing techniques based on group delay calculation. One is a “method using phase differentiation”, which is a method for directly calculating the group delay. The other is a “method using Z transformation”. This is a technique for bringing a differential operation into the Z region.
First, a method using phase differentiation is used. In this method, the group delay is calculated by performing phase differentiation of the frequency response as shown in the equation. Here, it is necessary to consider the labor and uncertainty of phase unwrapping. The phase of the frequency response periodically varies in the range of −π to π as illustrated in FIG. In order to perform phase differentiation, phase “unwrapping” must be performed. That is, when the phase crosses the boundary of −π or π, it is necessary to make the phase ± 2π as shown in FIG. A further problem here is unwrapping “uncertainty”. There is uncertainty in determining whether the phase variation crosses the boundary of -π or π. For example, when the phase that was 0 becomes 2π / 3 at the next point, it becomes 2π / 3 due to an increase in phase by 2π / 3, or 2π / 3 by a decrease in phase by -4π / 3. I don't know if it was. In the case of a phase decrease of −4π / 3 minutes, the boundary is crossed, so unwrapping is necessary. It is necessary to determine whether or not to unwrap, for example, by setting an acceptance criterion for the phase change width between points.
FIG. 5 shows the calculation flow of this method. In this method, the phase is obtained for each of the two signals f ₁ and f ₂ and unwrapping is performed. After differentiating the phase, the group delay is obtained by calculating the difference between the two values. However, although the above method is much improved in calculation speed compared to the conventional STFT method, it is sufficiently troublesome in real-time signal processing and operation stability with problems of unwrapping and uncertainty. It was not satisfactory.

となるため、位相は

と表される。このとき群遅延は

となるが、実関数であるために

となる。この計算をＺ領域で行うために、サンプル波数間隔をＴとして

を用いると群遅延は

と表される。Ｚ＝ｅｊ・Ｔより

となる。ここでＺ変換をＺ[ ]で表すと

となるので、Ｚ領域での群遅延は

で表され、これを周波数領域にすると、フーリエ変換をfft[ ]で表して

となる。
式(13)より、微分およびアンラッピングを行わずに群遅延を計算できる。しかしフーリエ変換や、周波数応答Ｈからインパルス応答ｈを算出するときに逆フーリエ変換を用いるため、演算過程でノイズ除去を行う必要が出てくる。 Therefore, the method recommended by the present inventors is the “method using Z transformation”. This is a technique for bringing a differential operation into the Z region.
A method using this Z conversion will be described below. The method using the Z transformation does not have to worry about the unwrapping effort and uncertainty described in the method using phase differentiation. It is also a feature of this method that it is generally not necessary to perform a differential operation with a high calculation cost. This technique skillfully avoids differential operations by bringing them into the Z region. The mathematical derivation is shown below.
When frequency response H is expressed by amplitude A and phase π

Therefore, the phase is

It is expressed. At this time, the group delay is

But because it is a real function

It becomes. To perform this calculation in the Z region, the sample wavenumber interval is T

Using, the group delay is

It is expressed. From Z = ej · T

It becomes. Here, Z conversion is expressed as Z [].

Therefore, the group delay in the Z region is

In the frequency domain, the Fourier transform is represented by fft [].

It becomes.
From Equation (13), the group delay can be calculated without performing differentiation and unwrapping. However, since the inverse Fourier transform is used when calculating the impulse response h from the Fourier transform or the frequency response H, it is necessary to remove noise in the calculation process.

FIG. 6 shows a calculation flow of the above method. Basically, each of the two signals f ₁ and f ₂ is subjected to Fourier transform, a frequency response is obtained, and an impulse response is calculated by inverse Fourier transform. The group delay is calculated using the impulse response.
There are two timings for calculating the window function (Han window) for noise removal and one timing for zero padding. In order to remove noise due to the inverse Fourier transform, an operation performed on the impulse response h at the timing of the window 2 shown in FIG. 6 is essential. In the case of window 1 in which a window function is applied before Fourier transform of each of the two interference signals f ₁ and f ₂ , the characteristics of the group delay calculation result change depending on the presence or absence of this calculation. The Han window is used because the amplitude becomes zero at both ends of the window. In this method, a Hann window was adopted.
Zero padding is a process of adding 0 columns of the same length after the f ₁ signal and before the f ₂ signal. This may make it difficult to generate noise when calculating the frequency response. However, since the amount of data is doubled, the calculation cost increases accordingly.

シミュレーションによる検討では、群遅延計算に基づく信号処理手法を採用することで、従来のＳＴＦＴによる手法よりも空間分解能、計測速度が大きく向上され、測定精度に関してもほぼ同様の性能を示すことがわかった。位相微分を用いる手法ではその性能は波長掃引幅に依存するような関係があることがわかった。Ｚ変換を用いた手法では特に空間分解がウィンドウのかけ方に影響されることがわかった。測定速度は位相微分を用いる手法よりも数倍速かった。 Table 2 shows the performance comparison of the signal processing methods based on the group delay calculation using the above-described phase differentiation and Z conversion as demonstration data. Z conversion performs the operations of windows 1 and 2. Since signal processing performance did not depend on the L length in any of the methods and depended on the wavelength sweep width (sweep width), three cases of wavelength sweep widths of 7 nm, 14 nm, and 21 nm were taken up. The measurement time is set to 1 for the STFT calculation that yields an equivalent measurement result.

In the study by simulation, it was found that by adopting a signal processing method based on group delay calculation, the spatial resolution and measurement speed were greatly improved compared to the conventional STFT method, and the measurement accuracy was almost the same. . In the method using phase differentiation, it was found that the performance depends on the wavelength sweep width. In the method using Z transform, it was found that spatial decomposition is particularly affected by the way the window is applied. The measurement speed was several times faster than the method using phase differentiation.

と表せる。上式において、fft( )はフーリエ変換、Ｔは係数、Re( )は複素数関数の実部を示す。
図７を参照しながら信号処理の流れを説明する。
この手法ではインパルス応答ｈ(ｋ)は畳み込み積分により求める。
ｈ(ｋ)＝(ｆ_２*ｆ_１)(ｋ) （15）
フーリエ変換後の関数を高速フーリエ変換fft ( )を用いて
Ｈ(ω)＝fft (ｈ(ｋ)) （16）
Ｈ_ｋ(ω)＝fft (ｋ ｈ(ｋ)) （17）
とすれば、求める群遅延は

となる。群遅延シフトをブラッグ波長シフトあるいはひずみ変動に変換するよう係数Ｔを設定し、角周波数をＦＢＧ位置に対応させることでひずみ分布を得る。
Ｈ_ｋやＨはｈ_ｋやｈのフーリエ変換なので、

とも書くことができる。

となる。これは、ノイズ処理のない場合ではインパルス応答ｈを用いて行ったものである。 The present inventors have developed a signal processing method using a further improved Z transform in addition to the above signal processing method.
This technique will be described below.
As described above, when the phase of the frequency response H (ω) is φ (ω), the group delay T _g (ω) is expressed by Expression (3). If the impulse response h is used,

It can be expressed. In the above equation, fft () is the Fourier transform, T is the coefficient, and Re () is the real part of the complex function.
The flow of signal processing will be described with reference to FIG.
In this method, the impulse response h (k) is obtained by convolution integration.
h (k) = (f ₂ * f ₁ ) (k) (15)
Using the fast Fourier transform fft ()
H (ω) ＝ fft (h (k)) (16)
H _k (ω) = fft (kh (k)) (17)
If so, the desired group delay is

It becomes. A coefficient T is set so as to convert the group delay shift into the Bragg wavelength shift or distortion fluctuation, and the distortion distribution is obtained by making the angular frequency correspond to the FBG position.
H _k and H are Fourier transforms of h _k and h, so

Can also be written.

It becomes. This is performed using the impulse response h in the case of no noise processing.

上につくハットマークは、一部分であることを意味する。
その一部分について群遅延を求めると

となる。ちなみに、抜きだす作業は窓関数をかけることで行うが、これは窓を通るもの以外は０にする作業である。
図９に示すように、この抜き出す位置を変えて（窓関数をずらして）

を何度も計算し、それらの総和で群遅延を求めると

が得られる。何度も計算した分母と分子それぞれの総和を割ることは、“重みづけして平均化する”ことに相当するので、この過程でノイズは抑えられることとなる。
この処理はＦＦＴ長の縮小により算出されるひずみ点数が減少する、すなわち空間分解能が低下する反面、ノイズを大きく低減する効果がある。空間分解能、ノイズ低減効果、信号処理時間は窓関数とそのスライドの長さにより調整される。この作業はＳＴＦＴ演算中の計算過程に似ているが、窓関数の長さ、窓関数をスライドする長さともにＳＴＦＴの場合よりはるかに大きく設定しても十分な効果が得られることが大きなメリットである。 In the case of performing noise processing, as shown in FIG. 8, the noise processing method is obtained by additionally modifying the above signal processing method.
A window function is applied to the impulse responses h (k) and kh (k) to extract the next function in a specific interval.

The hat mark on the top means a part.
If we find the group delay for that part

It becomes. By the way, the work to extract is performed by applying a window function, but this is the work to set to zero except for the one that passes through the window.
As shown in Fig. 9, change the extraction position (shift the window function)

Is calculated many times, and the group delay is calculated by the sum of them.

Is obtained. Dividing the sum of the denominator and the numerator calculated many times is equivalent to “weighting and averaging”, so that noise is suppressed in this process.
This processing reduces the number of strain points calculated by reducing the FFT length, that is, the spatial resolution is lowered, but has the effect of greatly reducing noise. Spatial resolution, noise reduction effect, and signal processing time are adjusted by the window function and its slide length. This work is similar to the calculation process during STFT operation, but it is a great merit that a sufficient effect can be obtained even if the length of the window function and the length of sliding the window function are set much larger than in the case of STFT. It is.

生成された信号を従来のＳＴＦＴ、提案する改良型群遅延演算を用いて信号処理した結果を表４に示す。なお、計算ソフトには Matlab を用いた。

二つの信号処理手法を比較すると、出力されるブラッグ波長分布の波長測定精度、空間分解能は同等を維持して計算効率が２８倍であることを示している。
本発明の群遅延演算は信号処理速度において従来のＳＴＦＴの数十倍の性能が得られることが確認できた。 Data obtained by verifying the effect of the OFDR optical fiber measurement device using the group delay calculation by the improved Z conversion according to the present invention by simulation is shown below.
In this test, the OFDR system shown in FIG. 13 was used, the sensing area was 5 m (this corresponds to the reference arm length L = 10 m), and the wavelength variable light source wavelength sweep was 10 nm. The width of the window function for noise processing in the group delay calculation is 1.35 nm, and the slide length of the window function is 0.7 nm. Details of the simulation conditions for generating the FBG observation signal are as shown in Table 3.

Table 4 shows the result of signal processing of the generated signal using a conventional STFT and the proposed improved group delay calculation. Matlab was used as the calculation software.

Comparing the two signal processing methods, it is shown that the wavelength measurement accuracy and spatial resolution of the output Bragg wavelength distribution remain the same and the calculation efficiency is 28 times.
It has been confirmed that the group delay calculation of the present invention can achieve several tens of times the performance of the conventional STFT at the signal processing speed.

D1, D2, D3, D4: Light intensity detector C1: 5% -95% broadband coupler C2-C5: 50% -50% broadband coupler R1-R4: Termination where total reflection occurs

Claims (6)

  In an OFDR optical fiber measuring apparatus in which a plurality of FBGs are arranged in one optical fiber, the group delay is calculated from the observed initial signal of the Bragg wavelength and the shifted signal to obtain the Bragg wavelength shift distribution. A signal processing method of an optical fiber measuring apparatus of the OFDR system characterized.   The group delay calculation uses a phase differentiation method that detects the phase of the initial signal and the shifted signal, performs phase unwrapping, calculates each phase induction, and calculates the time group delay from the difference. The signal processing method of OFDR optical fiber measurement according to claim 1.   The group delay calculation detects the phase of the initial signal and the shifted signal, performs a Fourier transform on each, obtains a frequency response, calculates an impulse response by inverse Fourier transform, and uses the impulse response to group delay The signal processing method for OFDR optical fiber measurement according to claim 1, wherein a Z conversion method is used to calculate the value.   The group delay calculation detects the phase of the initial signal and the shifted signal, performs a Fourier transform on each of them, obtains a frequency response, calculates an impulse response by convolution integration, and uses the impulse response to calculate a group delay. 2. The signal processing method of OFDR optical fiber measurement according to claim 1, wherein a Z conversion method to be calculated is used.   Claims: The impulse responses h (k) and kh (k) are multiplied by a window function to extract the next function in a specific interval, the FFT position is repeatedly calculated by changing the extraction position, and the group delay is calculated by summing them. 5. The signal processing method of OFDR optical fiber measurement according to 4.   In an OFDR type measuring device that uses a plurality of FBGs arranged in one optical fiber and makes use of periodic changes in the interference intensity of light, the group delay is calculated from the initial signal of the Bragg wavelength and the shifted signal, and the Bragg wavelength An OFDR optical fiber measuring apparatus comprising signal processing means for obtaining a shift distribution.

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