Patent Application
20250123138
The present disclosure relates to a signal processing device and a signal processing method for processing a signal obtained by performing DAS-P, and a vibration detection system including the signal processing device.
As a means for measuring physical vibration, applied to an optical fiber, in a distributed manner in a longitudinal direction of the optical fiber, there is a known method called distributed acoustic sensing (DAS) by which pulsed test light is injected into a measurement target optical fiber and backscattered light resulting from Rayleigh scattering is detected (Non Patent Literature 1).
In DAS, vibration sensing is performed by capturing changes, in the optical path length of an optical fiber, resulting from physical vibration applied to the optical fiber. By detecting vibration, it is possible to detect movement or the like of an object around the measurement target optical fiber.
As a method for detecting backscattered light in DAS, there is a technique for measuring the intensity of light scattered from each point on the measurement target optical fiber, and observing temporal changes in the intensity of the scattered light. This technique is called DAS-intensity (DAS-I). Although DAS-I characteristically simplifies the device configuration, it is impossible to quantitatively calculate a change in the optical path length of a fiber, resulting from vibration, on the basis of the scattered light intensity, and therefore, DAS-I is a qualitative measurement method (Non Patent Literature 2).
On the other hand, DAS-phase (DAS-P), which is a technique for measuring the phase of light scattered from each point on the measurement target optical fiber and observing temporal changes in the phase, has also been researched and developed. Although the device configuration and the signal processing in DAS-P are more complicated than those in DAS-I, a phase changes linearly with respect to changes, in the optical path length of a fiber, resulting from vibration, and the rate of change is also uniform in the longitudinal direction of the optical fiber. Thus, vibration can be quantitatively measured, and the vibration applied to the measurement target optical fiber can be faithfully reproduced (Non Patent Literature 2, for example).
In measurement by DAS-P, pulsed light is injected into the measurement target optical fiber, and the phase of scattered light at a time t for injecting the pulsed light is measured, in a distributed manner, in the longitudinal direction of the optical fiber. That is, the phase θ(1, t) of the scattered light is measured, with the distance from the incidence end of the optical fiber set to a distance 1.
The pulsed light is repeatedly injected into the measurement target optical fiber at time intervals T, so that the temporal change θ(1, nT) in the phase of the scattered light at time t=nT (n being an integer) is measured at each point in the longitudinal direction of the measurement target optical fiber. In practice, however, the time for measuring at the point of the distance 1 is later than the time for injecting the pulse by the time during which the pulsed light propagates from the incidence end to the distance 1. Further, it should be noted that the time at which a measuring instrument measures is delayed by the time required for the scattered light to return to the incidence end. It is known that the magnitude of physical vibration applied to the section from the distance 1 to a distance 1+δ1 at each time nT is proportional to the difference δθ(1, nT) between the phase θ(1+δ1, nT) at the distance 1+δ1 and the phase θ(1, nT) at the distance 1. That is, the expression shown below is satisfied when time zero is the reference time.
As device configurations for detecting the phase of scattered light, there are a direct detection configuration that directly detects backscattered light from the measurement target optical fiber with a photodiode or the like, and a configuration that uses coherent detection to detect backscattered light multiplexed with separately prepared reference light (Non Patent Literature 1, for example).
Mechanisms for performing coherent detection and calculating a phase are specifically classified into two kinds, which are a mechanism for software-based processing using Hilbert transform, and a mechanism for hardware-based processing using a 90-degree optical hybrid. In both kinds of methods, an in-phase component I(1, nT) and a quadrature component Q(1, nT) of scattered light are acquired, and the phase is calculated according to the expression shown below.
However, an output value by the four-quadrant arctangent operator Arctan is within the range of (−π, π] in radians, and 2 mπ+θ(1, nT) all have the same vector direction in an x-y plane (m being an integer), and accordingly, the uncertainty of 2 mπ exists in θcal(1, nT) calculated as above. Therefore, as a more accurate evaluation method for θ(1, nT), signal processing such as phase unwrapping is further performed. Given that the phase after unwrapping is represented by θcalunwrap in general phase unwrapping, in processing in ascending order of time, for example, θcalunwrap is set to the same as θcal at the start point of the phase unwrapping, and θcalunwrap (1, pT) to θcalunwrap (1, (p+1) T) are then sequentially calculated as shown below, with p representing an integer.
On condition that
The superscript “unwrap” indicates a phase after unwrapping. Note that, as the calculation procedures in actual distributed vibration measurement, a phase unwrapping process is often performed on a difference, calculated in advance, in phase value between points as in Expression (1).
In measurement by DAS, there is noise of the measuring instrument, such as thermal noise of a photodiode (PD) for detecting light, noise at the subsequent electrical stage, or shot noise caused by light. Therefore, the intensity and the phase of the scattered light to be measured are also affected by the noise of the measuring instrument.
In particular, when the phase of scattered light is measured, the large influence of noise of the measuring instrument increases not only the uncertainty of the phase, but also the probability of a measurement value being significantly different from the ideal phase value to be obtained in the absence of noise.
For example, as for the vector of measured scattered light in a system where the in-phase component is represented by the abscissa axis and the quadrature component is represented by the ordinate axis in coherent detection, the direction of the vector of no noise corresponds to the phase to be measured. However, when the influence of noise is large, the vector is directed in the opposite direction, which increases the probability that a difference between the phase value to be actually measured and the ideal phase value of no noise is about the n radian. Such an aspect leads to erroneous recognition that a large physical force has been applied to the optical fiber, when the magnitude of vibration is calculated according to Expression (1). Also, when the influence of noise becomes large, the number of points at which the integer q is erroneously selected increases in the unwrapping process shown in Expression (3), and a phase value difference of 2n or larger, which is not actually present, appears between the front and rear of the point of the erroneous selection. Such a phase value difference also leads to erroneous recognition that a large physical force has been applied to the optical fiber, when the magnitude of vibration is calculated according to Expression (1).
To accurately measure the phase, it is necessary to reduce the influence of noise of the measuring instrument. The influence of noise of the measuring instrument is increased by decreasing the intensity of scattered light, as long as the noise of the measuring instrument can be regarded as the same level at each point and each time. Accordingly, increasing the intensity of scattered light at each point and each time can reduce the influence of noise of the measuring instrument.
The reason why the intensity of scattered light drops is not only the loss caused by the absorption and the scattering accompanying the propagation of pulsed light as a probe in the measurement target optical fiber. Since pulsed light having a finite duration is injected into the measurement target optical fiber to detect scattering of the pulsed light, the scattered light is interfered with by a large number of scattered substances very finely distributed in the measurement target optical fiber. As a result of the interference, a point at which the intensity of the scattered light drops appears, depending on the distribution of the scattered substances in the longitudinal direction of the measurement target optical fiber at each time. This phenomenon is called fading (Non Patent Literature 3).
Therefore, when the phase of scattered light in DAS-P is measured, there is a problem of appearing a point at which the intensity of scattered light drops at each time due to fading, as a result of reduction of the influence of noise of the measuring instrument.
As a means for solving the problem, there is a method for increasing the peak intensity of the light pulse to be simply injected. However, when the peak intensity is increased, a nonlinear effect occurs, and the characteristics of the pulsed light change in response to the propagation in the measurement target optical fiber. Because of this, the peak intensity of the light pulse allowed to be injected is limited, and the above problem is not sufficiently solved in some cases.
To solve the above problem, there are a suggested phase measurement method and a suggested signal processing device capable of reducing the influence of noise of a measuring instrument without any increase in the peak intensity of the incident light pulse in measuring the phase of scattered light in DAS-P (Patent Literature 1).
According to Patent Literature 1, to solve the above problem, pulsed light, obtained by arraying and wavelength-multiplexing pulses with different optical frequency components at time intervals at which changes in the fiber state resulting from vibration are negligible, is injected into the measurement target optical fiber, scattered light vectors are created by plotting scattered light with the respective wavelengths from the measurement target optical fiber in a two-dimensional plane in which the in-phase components are represented by the abscissa axis and the quadrature components are represented by the ordinate axis, directions of the created scattered light vectors are matched by rotating the created scattered light vectors for each wavelength at each point on the measurement target optical fiber, a new vector is generated by averaging the vectors having the directions matched, and a phase is calculated from the values of the in-phase component and the quadrature component of the generated new vector.
In the measurement by DAS-P, there is also a problem of trade-off between the measurement distance and the measurable upper limit of the vibrational frequencies. When a light pulse of a single frequency is used, the long measurement distance delays the time at which scattered light returns from the far end, with respect to the pulse incident time. Therefore, there is the upper limit of the repetition frequency at which light pulses are injected so that the scattered light from the far end and the scattered light from the vicinity of the incidence end obtained by injecting the next light pulse are not multiplexed and do not interfere with each other. In view of this, from the sampling theorem, vibration of vibrational frequencies higher than the Nyquist frequency, which is 1/2 of the repetition frequency, cannot be correctly measured due to aliasing.
Non Patent Literature 4 has been suggested as a method for solving the above problem. According to Non Patent Literature 4, to solve the above problem, pulsed light obtained by arraying pulses with different optical frequency components at equal intervals and performing wavelength-multiplexing thereon is injected into the measurement target optical fiber, and scattered light with the respective wavelengths from the measurement target optical fiber is plotted in a two-dimensional plane in which the in-phase components are represented by the abscissa axis and the quadrature components are represented by the ordinate axis, to create scattered light vectors. The phase is calculated from the obtained scattered light vectors. Given that the sampling rate upper limit determined from the measurement distance on condition of a single optical frequency is represented by fs, the sampling rate upper limit can be N×fs by N-wave multiplexing. Note that the wavelength multiplexing number “N” is a natural number.
Here, in implementing the frequency multiplexing method disclosed in Non Patent Literature 4, when a phase change is calculated by simply combining the angles of the scattered light vectors obtained at the respective optical frequencies without correcting the angular difference between the respective optical frequencies, the calculated phase change is distorted compared with the actual phase change, and an accurate vibrational waveform cannot be measured. To counter this problem, Non Patent Literature 4 suggests a method for correctly estimating the frequency of a signal having a vibrational frequency exceeding the Nyquist frequency fv on condition of the single frequency, by first calculating the temporal phase difference of the respective optical frequencies and then combining the calculated phase differences of the respective optical frequencies. That is, it is possible to estimate frequencies up to the frequency N×fv without aliasing. By this suggested technique, however, the angular differences between the respective optical frequencies are not obtained, and therefore, any vibrational waveform cannot be measured.
As a countermeasure for this problem, Non Patent Literature 5 suggests a measurement method capable of measuring a vibrational waveform under the condition that the sampling rate upper limit is increased to N×fs, by correcting the angular differences between the respective optical frequencies using a correction frequency. By the suggested method, a compensation optical frequency is used in addition to the main optical frequencies to improve the sampling rate, and a probe pulse train is used such that a component regarding a main optical frequency and a component regarding the compensation optical frequency regularly are injected into the measurement target fiber at timings allowed to be regarded as the same. Thus, the angular difference between the component regarding the main optical frequency and the component regarding the compensation optical frequency is corrected, and the angular differences between the respective main optical frequencies are corrected.
Further, in the trade-off between the measurement distance and the upper limit of the measurable vibrational frequencies, a more severe requirement is added, because phase unwrapping needs to be performed correctly. When the absolute value of the magnitude of the phase change, with adjacent light pulses subjected to sampling, changes by more than π, phase unwrapping cannot be uniquely performed, which leads to failed phase unwrapping (Non Patent Literature 6).
Therefore, there is a constraint that the upper limit of the absolute value of the magnitude of a phase change at adjacent sampling points is π. Even within the range of the Nyquist frequency or lower, as the vibrational frequency becomes higher, the phase change at adjacent sampling points becomes larger. Therefore, when the vibration amplitude becomes larger, a further requirement is added to the upper limit of the measurable vibrational frequencies. By the suggested method disclosed in Non Patent Literature 5, a vibrational waveform can be measured, and accordingly, this method is also effective in alleviating such constraints.
Non Patent Literature 5 also suggests an optical frequency pulse forming method and a reception signal processing method for simultaneously implementing a frequency multiplexing method by which pulses with different optical frequencies are injected at different times so as to improve the sampling rate, and the frequency multiplexing method disclosed in Patent Literature 1 as a countermeasure against fading.
Note that the relationship between the magnitude of a phase change and the amount of distortion applied to a fiber by vibration is explained in Non Patent Literature 7, for example. According to Non Patent Literature 7, when a fiber having an entire length 1 is elongated by Δ1 due to a distortion amount c, the increase amount Δϕ of the phase change resulting from the elongation by Δ1 in light passing is shown in the expression below.
Here, k=2πn/Δ represents the propagation constant, n represents the effective refractive index of the fiber, pp represents the Poisson's ratio, and p11, and p12 represent the strain-optic tensor components. For example, given λ=1555 nm near a normal communication wavelength band, n=1.47, μp=0.17, p11=0.121, and p12=0.271. Therefore, it is known that the following expression is satisfied (Non Patent Literature 8).
Here, K=4.6×106 m−1. Using this relational expression, it is possible to replace the requirement for the magnitude of a phase change with the requirement for a distortion amount.
In the frequency multiplexing system disclosed in Non Patent Literature 5, the total number of usable optical frequencies obtained by combining the multiplexing number allocated to improvement of the sampling rate and the multiplexing number allocated to reduction of fading noise can be evaluated as the number obtained by dividing the total usable frequency bandwidth determined from the sampling rate of an analog/digital (A/D) converter (hereinafter also referred to as an AD board circumstantially) that converts an analog signal into a digital signal by the occupied bandwidth per component determined from the pulse width of each optical frequency component, and is finite. Therefore, the multiplexing number allocated to reduction of fading noise decreases in a situation where the multiplexing number allocated to improvement of the sampling rate increases due to detecting high-frequency vibration or the like, where the total usable frequency bandwidth is limited by need to use an AD board with a small sampling rate, or where measurement with high spatial resolution needs to be performed, and the occupied bandwidth per component increases to reduce the pulse width of each optical frequency component.
When the multiplexing number allocated to reduction of fading noise becomes smaller, the correction of the angular difference between the respective main optical frequencies described in Background Art cannot be completely performed, the angular difference between the respective main optical frequencies remains, and a point where the calculated phase change remains distorted with respect to the actual phase change appears. When the remaining angular difference between the main optical frequencies is large, phase connection errors also increase. Furthermore, when a compensation optical frequency is injected, crosstalk into the main optical frequencies occurs due to the compensation optical frequency, and distortion associated with the crosstalk also occurs. The phase connection errors associated with the distortion also becomes a problem.
The present disclosure aims to remove the influence of an uncorrected angular difference, even in a state where the multiplexing number allocated to reduction of fading noise is small and the angular difference between the respective main optical frequencies is completely uncorrectable.
The present disclosure suggests a method for removing, in a state where correction of the angular difference between the respective main optical frequencies cannot be completely performed, and where the angular difference between the respective main optical frequencies remains, the influence of the remaining angular difference by means of signal processing, to decrease phase connection errors and the like, and thus, make the calculated phase change closer to the actual phase change.
Specifically, according to the present disclosure, in a frequency-multiplexed phase OTDR, a component D(1, mTN) regarding a period NTN, which is extracted with δθ0unwrap(1, mTN), obtained by performing a phase connection process on a phase change δθ0(1, mTN) caused in the section of a distance 1 to a distance 1+δ1 from the incidence end, filtered through a multi-bandpass filter, is subtracted from δθ0(1, mTN).
Specifically, by a signal processing device and a signal processing method of the present disclosure,
Specifically, a vibration detection system of the present disclosure includes:
A program of the present disclosure is a program for getting a computer to function as the individual functional units included in the signal processing device according to the present disclosure, and is a program for getting the computer to carry out the individual steps included in the signal processing method implemented in the signal processing device according to the present disclosure.
According to the present disclosure, the influence of an uncorrected angular difference can be removed, even in a state where the multiplexing time allocated to reduction of fading noise is small and the angular difference between the respective main optical frequencies is completely uncorrectable.
The following is a detailed description of an embodiment of the present disclosure, with reference to the drawings. Note that the present disclosure is not limited to the embodiment described below. These embodiment are merely an example, and the present disclosure can be carried out in forms with various modifications and improvements based on the knowledge of those skilled in the art. Note that components denoted by the same reference numeral in this specification and the drawings are the same as each other.
Note that the present disclosure is effective as a process of removing an angular difference, not only in a state where a process of removing distortion is performed with the use of a compensation optical frequency as disclosed in Non Patent Literature 5 before the signal processing, to be performed, suggested by the present disclosure, but also in a state where the angular difference between the respective main optical frequencies completely remains with no compensation optical frequency used. The present disclosure also suggests a method for reducing distortion caused by crosstalk resulting from a compensation optical frequency in a state where the compensation optical frequency disclosed in Non Patent Literature 5 is used.
A CW light source 1, a coupler 2, and an optical modulator 3 correspond to the light source. A 90-degree optical hybrid 7 and balance detectors (13 and 14) correspond to the light receiver. The light receiver performs coherent detection, using the 90-degree optical hybrid 7. A signal processing device 17 corresponds to the signal processing unit. However, it is not always necessary to use a 90-degree optical hybrid for the reception system, and some other device or signal processing may be used, as long as an in-phase component and a quadrature component of scattered light can be measured. The signal processing device of the present disclosure can also be implemented in a computer and a program, and the program can be recorded on a recording medium or be provided through a network.
A measuring instrument 31 measures scattered light from a measurement target optical fiber 6 as follows. Continuous light with a single wavelength that is an optical frequency f0 is emitted from the CW light source 1, and is split into reference light and probe light by the coupler 2. The probe light is shaped into a wavelength-multiplexed light pulse 4 by the optical modulator 3. As the light pulse 4, a multiple pulse using a compensation optical frequency as disclosed in Non Patent Literature 5 can be used. The light pulse 4 may be of any kind as long as a compensation method as disclosed in Non Patent Literature 5 can be achieved. An example configuration thereof is illustrated in
N×M optical frequency components f1 to fNM are to be used for the main pulse, and N+1 groups of them arranged in order are prepared (201). The whole sequence is divided by M (M being a natural number) as illustrated by 202, and N(N+1) pulse pairs are generated. A compensation optical frequency fNM+i is added to each of the N+1 pulse pairs in 202, to generate pulse pairs 203. The light pulse pairs to be actually injected on the basis of the pulse pairs 203 are designed as illustrated by 204. As a result, a pulse pattern in which N(N+1) pulse pairs are arranged at constant time intervals is generated.
Here, the compensation optical frequency fNM+i is added to the pulse pairs having the pulse pair number 1+k(N+1) (k=0, 1, . . . , (N−1)). Accordingly, given N=3, and M=1, for example, the pulse pairs having optical frequencies f1, f2, and f3 are repeatedly injected into the measurement target optical fiber 6. In this example, when k=0, a compensation optical frequency f4 is added to the pulse pairs including the optical frequency f1. When k=1, the optical frequency f4 is added to the pulse pairs including the optical frequency f2. When k=2, the optical frequency f4 is added to the pulse pairs including the optical frequency f3.
Given that the interval between pulse pairs is TN, the period of the pulse pattern is N(N+1)TN. The limitation on the minimum value, as small as possible, of TN depending on the length of the measurement target optical fiber 6 is lowered to 1/N times of a limitation where a single frequency pulse is used. Also, in the configuration in
In
The light pulse 4 is injected into the measurement target optical fiber 6 via a circulator 5. Light scattered at each point in the longitudinal direction of the measurement target optical fiber 6 returns to the circulator 5 as backscattered light, and is injected into one input portion of the 90-degree optical hybrid 7. The reference light split by the coupler 2 is injected into the other input portion of the 90-degree optical hybrid 7.
The internal configuration of the 90-degree optical hybrid 7 may be any configuration that has the functions of a 90-degree optical hybrid. An example configuration is illustrated in
The two outputs of the coupler 11 are detected by the balance detector 13, and an electrical signal 15 that is an analog in-phase component Ianalog is output. The two outputs of the coupler 12 are detected by the balance detector 14, and an electrical signal 16 that is an analog quadrature component Qanalog is output.
The electrical signal 15 and the electrical signal 16 are sent to the signal processing device 17 that includes an AD conversion element 17a and an AD conversion element 17b capable of sampling the optical frequency bands of signals without aliasing. In the signal processing device 17, the digitized signals of the in-phase component Idigital and the quadrature component Qdigital output from the AD conversion element 17a and the AD conversion element 17b are separated by a signal processing unit 17c into signals with the respective bands of optical frequencies f0+f1(i=1, 2, . . . , NM+1) constituting the light pulse 4. As a specific signal processing method, any method may be used, as long as Iimeasure (i=1, 2, . . . , NM+1) and Qimeasure (i=1, 2, . . . , NM+1), which are signals with the respective bands, can be accurately separated from Idigital and Qdigital. For example, a calculation method for compensating for a phase delay by filtering Idigital and Qdigital through a bandpass filter whose center frequency is f0+f1 can be used. Given that the pulse width of each optical frequency component is represented by W, the passband can be set to 2/W.
Alternatively, after the in-phase component and the quadrature component in an analog electrical signal state are separated into optical frequency components by an analog electrical filter, AD conversion may be performed by the AD conversion element 17a and the AD conversion element 17b.
A signal processing unit 17d performs phase calculation, on the basis of Iimeasure and the Qimeasure acquired by the signal processing unit 17c. First, a complex vector ri is created on an x-y plane in which the in-phase component is represented by the x-axis (real number axis) and the quadrature component is represented by the y-axis (imaginary number axis).
The time at which the top of the pulse pair k is injected is expressed as k×TN+n×N×TN (n being an integer) Taking the optical frequency at the top of each pulse pair as a reference wavelength, the vectors, calculated in Expression (1-1) in the bands of M different optical frequencies excluding the compensation optical frequencies constituting the pulse pairs, are averaged by the method disclosed in Patent Literature 1, and thus, the phase at the position at a distance z from the incidence end is calculated. The state of the measurement target optical fiber 6 at the position at the distance z from the incidence end in the longitudinal direction of the measurement target optical fiber 6 is measured at time k×TN+n×N×TN+z/ν (n being an integer), with the propagation time of the light pulse being taken into consideration.
Here, v represents the speed of light in the measurement target optical fiber 6. Further, with the time required for scattered light to propagate back to the incidence end being taken into consideration, the measurement time at the measuring instrument is expressed as k×TN+n×N×TN+2z/ν (n being an integer). The phase calculated at the point of the distance z is expressed as follows.
Here, the measurement time at the measuring instrument is explicitly expressed.
In this embodiment, the phase θ (z, mTN+2z/ν) at the measurement time mTN+2z/ν (m being an integer) is calculated as shown below, using k and n, which satisfy mTN+2z/ν=kTN+nNTN+2z/ν.
The phase change, caused by vibration applied to the section from a distance z1 to a distance z2 on the measurement target optical fiber 6, is then calculated as the difference between Expression (1-3a) and Expression (1-3b), or as Expression (1-3c).
Since the time at the moment of measurement of the state of the measurement target optical fiber 6 does not include the time required for scattered light to return to the incidence end as described above, the time at the point of the distance zi is mTN+z1/ν, the time at the point of the distance z2 is time mTN+z2/ν, and there is a time difference (z1-z2)/ν between these times. However, since the difference between the distances z1 and z2 is about the same as the spatial resolution and is usually set to several meters to several tens of meters, the time difference (z1-z2)/ν is several tens to several hundreds of ns, which is very short with respect to the scale of temporal changes of the normal vibration to be measured. Accordingly, the difference in time at which the state of the measurement target optical fiber 6 is measured is negligible. Thus, the vibration applied to the corresponding section can be correctly measured.
However, θ(z, mTN+2z/ν) includes a distortion term derived from an angular difference between the optical frequencies regarding the top of each pulse pair. Non Patent Literature 5 suggests a method for correcting the distortion term derived from the angular difference, using a compensation optical frequency. To completely correct the distortion term derived from the angular difference between different optical frequencies, it is necessary to correct the angular difference between the optical frequencies at the tops of two appropriate pulse pairs.
When positive integers i and j satisfying i<j are selected as appropriate, the optical frequency at the top of the pulse pair j is represented by fjpf, and the optical frequency of the pulse pair i is represented by fipf, the angular difference ϕ(z, fjpf, fipf) can be developed with fNM+i as shown below.
Here, i and j are positive integers, and satisfy i<j.
In the pulse pair 203 optical frequency combination that is used as an example, the optical frequency fNM+i is added to the pulse pairs with the pulse pair numbers 1+k(N+1) (k=0, 1, . . . , (N−1)). Accordingly, a pulse pair where the optical frequency fNM+i exists and a pulse pair different optical frequency or frequencies exist always become the same once within the period N(N+1)TN. For example, given N=3 and M=1, the number of pulse pairs constituting the pulse pattern is 12. In this example, the first pulse pair includes the optical frequency f1 and the optical frequency f4, the fifth pulse pair includes the optical frequency f2 and the optical frequency f4, and the ninth pulse pair includes the optical frequency f3 and the optical frequency f4. Accordingly, in the pulse pattern, a pulse pair where the optical frequency f4 exists and a pulse pair where one of the other frequencies f1, f2, and f3 exists always become the same once. Thus, each term on the right-hand side of Expression (1-4) can be calculated by the same principle as the method disclosed in Patent Literature 1. With the use of the obtained value of $(z, fjpf, fipf), the phase is calculated from 0(z, mTN+2z/ν).
For example, when the change in phase from the time m′TN+2z/ν to mTN+2z/ν is calculated, Expression (1-5) should be used.
However, the integer i(m′) is selected so that m′-i(m′) is an integral multiple of N, and the integer i(m) is selected so that m-i(m) is an integral multiple of N. As for the actual calculation procedures, a phase difference between two points is calculated, so that a phase change caused in the section between the two points is calculated. In view of this, a phase change caused in the section between a distance 1 and a distance 1+δ1 from the incidence end can be calculated according to Expression (1-6), with the reference being time zero as in Expression (1-3c), for example. On the left-hand side of Expression (1-6), 50 represents the difference between two points, and therefore, the symbol of delta δ is added, and the subscript 0 indicates that time zero is used as the reference. Also, on the left-hand side, a delay associated with propagation of light in the measurement target optical fiber 6 is simplified in a format that is not explicitly expressed.
The processes described so far are the signal processing to be performed by the signal processing unit 17d.
A signal processing unit 17e performs the eventual phase calculation. The procedures to be carried out by the signal processing unit 17e differ between a conventional method and the present disclosure.
By a conventional method, a phase connection process is performed on the above δθ0(1, mTN), to obtain the eventual vibration change. That is, δθ0unwrap(1, mTN) obtained by performing a phase connection process on δθ0(1, mTN) is set as the eventual vibrational waveform. The superscript “unwrap” indicates that the phase connection process has been performed. However, the multiplexing number allocated to improvement of the sampling rate increases in detecting high-frequency vibration or the like. An AD board with a small sampling rate needs to be used, and an available total frequency bandwidth is limited. It is necessary to perform measurement with high spatial resolution, and the occupied bandwidth per component becomes wider so as to reduce the pulse width of each frequency component. When the multiplexing number allocated to the reduction of fading noise becomes smaller in such a situation, sufficient fading noise reduction cannot be performed. As a result, the accuracy of estimation of the angular difference ϕ(z, fjpf, fipf) is degraded, the correction of the angular difference between the respective main optical frequencies described in Background Art cannot be completely performed, the distortion resulting from the angular difference between the respective main optical frequencies remains, and a point where the calculated phase change remains distorted with respect to the actual phase change appears.
In the present disclosure, as a countermeasure for the above problem, calculation for removing the distortion remaining, after the process performed by the signal processing unit 17d, is performed. The procedures are shown in
A phase change δθ0(1, mTN) caused in the section between the distance 1 and the distance 1+δ1 from the incidence end is subjected to a phase connection process, to calculate δθ0unwrap(1, mTN) (S101).
A component regarding the period NTN is extracted with δθ0unwrap(1, mTN) filtered through the bandpass filter, and is set as D(1, mTN) (S102). δθ0(1, mTN)−D(1, mTN), obtained by subtracting D(1, mTN) from δθ0(1, mTN) before phase connection, is set as new updated δθ0(1, mTN) (S103).
A phase connection process is performed on the new 50o(1, mTN) (S101).
When the distortion has not been sufficiently removed (S104), the above procedures are repeated.
The remaining distortion is removed through such procedures.
The reason that the distortion can be removed, using a bandpass filter, with the use of D(1, mTN), which is a component regarding the period NTN, is because the distortion changes in the period NTN. The period NTN is a period in which the same optical frequencies repeat in a plurality of light pulses, and is period in which the top frequency fi(m)pf of a pulse pair i(m) is switched, for example. When the difference between the estimated value of ϕ(z, fjpf, fipf) at the signal processing unit 17d and the actual value is expressed as δϕ(z, fjpf, fipf), the distortion, remaining in δθ0(1, mTN) calculated by the signal processing unit 17d, is expressed according to Expression (1-6) as shown below.
The distortion expressed by Expression (7) depends on the top frequency fi(m)pf of the pulse pair i(m), but the top frequency fi(m)pf of the pulse pair i(m) is switched per period NTN. Therefore, the distortion expressed by Expression (7) is a component that changes per period NTN, the distortion expressed by Expression (7) can be estimated by extracting the component that changes per period NTN from δθ0unwrap(1, mTN).
Note that the distortion term does not necessarily change in a sinusoidal waveform, and therefore, attention should be paid to the fact that all the components to be passed through the bandpass filter are harmonic components whose frequencies correspond to integral multiples of 1/NTN. With aliasing being taken into consideration, components exceeding the Nyquist frequency should be subjected to band-passing at a component position on the frequency axis that is returned within the Nyquist frequency range or lower. However, the harmonic components regarding 1/NTN within the frequency range in which aliasing does not occur overlaps with the position on the frequency axis, and therefore, a multi-bandpass filter that substantially passes all harmonic components regarding 1/NTN in the frequency range in which aliasing does not occur is used.
The reason that a component that changes per period NTN is extracted with δθ0unwrap(1, mTN), after the phase connection instead of δθ0(1, mTN) before the phase connection, filtered through the bandpass filter is because δθ0(1, mTN) before the phase connection has the phase value convolved therein from −π to +π. This is because the distortion expressed by Expression (7) is added to and convolved in the actual vibration change, and therefore, the distortion expressed by Expression (7) cannot be extracted using the bandpass filter.
Also, the distortion is not always sufficiently removed by just one operation of calculating D(1, mTN) and obtaining the difference with respect to δθ0(1, mTN) calculated by the signal processing unit 17d. This is because, at a point where a plurality of phase connection errors occur in δθ0unwrap(1, mTN) due to the large distortion expressed by Expression (7), the steep phase change, which is due to the phase connection errors, also has a component regarding the period NTN. Therefore, even though the component regarding the period NTN is extracted with δθ0unwrap(1, mTN) filtered through the bandpass filter, the distortion expressed by Expression (7) cannot be accurately estimated. This is based on the principle that, by repeating the calculation loop as in the procedures shown in
As for the determination whether the distortion is sufficiently removed in step S104, considering that the number of phase connection errors is countable, a time when the number of phase connection errors does not change in accordance with the procedures can be selected.
Considering that it is not possible to do so, on the basis of the steep phase change caused by phase connection errors increases noise on the low-frequency side of the measurement band, a time when noise reduction on the low-frequency side is not observed through the procedures can be also selected. The number of loops is only required to be about ten as a specific numerical value estimated from verification experiments.
Although the above embodiment illustrates an example in which the present disclosure is applied with a compensation optical frequency used, the present disclosure can also be applied according to a similar principle even with no compensation optical frequency used. When no compensation optical frequency is used, the present disclosure is applied to a phase change that is obtained by calculating the difference between two points with respect to θ(z, mTN+2z/ν) before distortion correction using a signal of a compensation optical frequency.
When measurement using a compensation optical frequency, distortion resulting from crosstalk of the compensation optical frequency into the main optical frequency also occurs, but removal thereof can be considered in the same manner.
A phase change δθ0(1, mTN) caused in the section between the distance 1 and the distance 1+δ1 from the incidence end is subjected to a phase connection process, to calculate δθ0unwrap(1, mTN) (S201).
A component regarding the period NTN is extracted with δθ0unwrap(1, mTN) filtered through the bandpass filter, and is set as D1(1, mTN) (S202). A component regarding the period N(N+1)TN is also extracted from δθ0unwrap(1, mTN)−D1(1, mTN) through the bandpass filter, and is set as D2(1, mTN) (S202).
δθ0(1, mTN)−D1(1, mTN)−D2(1, mTN), obtained by subtracting D1(1, mTN) and D2(1, mTN) from δθ0(1, mTN) before phase connection, is set as new updated δθ0(1, mTN) (S203)
The new δθ0(1, mTN) is subjected to a phase connection process, to calculate δθ0unwrap(1, mTN) (S201).
When the distortion is not been sufficiently removed (S204), the above procedures are repeated.
Through these procedures, the distortion caused by crosstalk of a compensation optical frequency into the main optical frequency can be removed at the same time.
The principle of the process using D1(1, mTN) is the same as the principle of the process using D(1, mTN) for removing the remaining distortion that is caused by the angular difference between the respective main optical frequencies and is unremovable by the process performed by the signal processing unit 17d. Meanwhile, the process using D2(1, mTN) corresponds to the removal of the distortion caused by crosstalk of the compensation optical frequency into the main optical frequency. The distortion resulting from crosstalk of the compensation optical frequency into the main optical frequency occurs in the period of the pulse pattern that has been used. Since the period of the pulse pattern is N(N+1)TN as illustrated in
Note that, since the distortion caused by the crosstalk is not a sinusoidal waveform, it is necessary to use a multi-bandpass filter through which all the harmonic components having frequencies corresponding to integral multiples of 1/{N(N+1)TN}passes in actual bandpass filtering. However, since the harmonic components corresponding to integral multiples of 1/{N(N+1)TN}include a harmonic component regarding 1/(NTN), it is necessary in practice to calculate D2(1, mTN) using a multi-bandpass filter through which all the components except for the harmonic component regarding 1/(NTN) among the harmonic components corresponding to integral multiples of 1/{N(N+1)TN}passes. Therefore, in the procedures described above, the component regarding the period N(N+1)TN is also extracted from δθ0unwrap(1, mTN)−D1(1, mTN) with the bandpass filter, and is and set as D2(1, mTN). Alternatively, since D1(1, mTN) and D2(1, mTN) are not individually used in the procedures illustrated in
The reason that bandpass filtering is performed on δθ0unwrap(1, mTN), and the reason that the calculation loop is repeated are the same as those in the procedures illustrated in
Note that the present disclosure is not limited to the embodiment described above without any change, but can be embodied by modifying the components without departing from the scope of the invention at the implementation stage.
The present disclosure can be applied to information and communication industries.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/JP2021/021990 | 6/9/2021 | WO |
