JP2017037013A - Mode dispersion coefficient measuring apparatus and mode dispersion coefficient measuring method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To easily measure impulse response characteristics of an optical fiber using not a transmission system using a revolution experiment system, but a short optical fiber.SOLUTION: A mode dispersion coefficient measuring apparatus according to the present invention is configured to measure the mode dispersion coefficient of an optical fiber 91 to be measured in which a plurality of modes are propagated in the fiber, and comprises: an input-side single-mode fiber 92#1; an output-side single-mode fiber 92#2; a wide-band light source 94#1 which emits measurement light having a predetermined wavelength width; an optical spectrum analyzer 95#1 which detects a transmission light spectrum of the measurement light having passed through the optical fiber 91 to be measured; and a signal arithmetic part 96 which generates a time waveform by subjecting the detected transmission light spectrum to Fourier transformation, and calculates a dispersion coefficient of mode dispersion from a standard deviation when the time waveform is found by approximation with a Gaussian distribution.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a mode dispersion coefficient measuring apparatus and a mode dispersion coefficient measuring method using a multi-core optical fiber.

  In an optical fiber communication system, transmission capacity is limited by nonlinear effects and fiber fuses that occur in an optical fiber. In order to alleviate these restrictions, space such as parallel transmission using a multi-core fiber having a plurality of cores in one optical fiber, or mode multiplexing transmission using a multi-mode fiber having a plurality of propagation modes in the core. Multiplexing techniques have been studied (see Non-Patent Documents 1 and 2).

  In transmission using a multi-core fiber, signal quality deteriorates when crosstalk occurs between the cores. Therefore, in order to suppress crosstalk, the cores must be separated by a certain distance or more. In general, in order to ensure sufficient transmission quality in an optical communication system, it is desirable to set the power penalty to 1 dB or less. For that purpose, as described in Non-Patent Documents 1 and 3, the crosstalk must be set to −26 dB or less. I must.

  On the other hand, if MIMO technology is used, it is possible to compensate for crosstalk at the receiving end, reduce the inter-core distance, and reduce the power penalty to less than 1 dB by signal processing even if the crosstalk is -26 dB or more. It is possible to improve the space use efficiency. However, when the MIMO technology is applied, if the group delay difference (DMD: Differential Mode Delay) between a plurality of signal lights generated in the transmission path is large, the impulse response width of the transmission path is increased, and the signal processing is increased. Invite.

  In general, as described in Non-Patent Document 2, DMD between a plurality of modes propagating through the same core can be reduced by controlling the refractive index distribution of the optical fiber. The relationship between the crosstalk amount between the cores and the DMD is clarified by Non-Patent Document 4, and it is known that the DMD increases as the distance between the cores decreases. That is, even if the inter-core crosstalk is allowed, there is a lower limit of the inter-core distance in order not to increase the DMD, and it has been found that there is a limit to improving the space utilization efficiency.

  On the other hand, even in an optical fiber having a large DMD, as described in Non-Patent Document 5, the impulse response width of the optical fiber can be reduced by positively causing coupling between modes in the fiber.

  In general, the impulse response width of the optical fiber is measured by constructing a loop experiment system including the optical fiber and performing long-distance transmission using a signal, or described in Non-Patent Document 6. As described above, the MIMO signal processing is performed, and the impulse response width can be obtained from the calculation result. In addition, the loop experiment is a transmission path including a fiber configured in a loop shape and can propagate a distance that is an integral multiple of the fiber used by circulating the signal, and is used as a simulation test for long-distance transmission. It is what.

H. Takara et al. , “1.01-Pb / s (12 SDM / 222 WDM / 456 Gb / s) Cross-managed Transmission with 91.4-b / s / Hz Aggregate Spectral Efficiency”, in EcoC2012, paper Th. 3. C. 1 (2012). T.A. Sakamoto et al. , “Differential Mode Delay Managed Transmission Line for WDM-MIMO System Using Multi-Step Index Fiber,” J. Lightwave Technol. vol. 30, pp. 2783-2787 (2012). T.A. Ohara et al. "Over-1000-Channel Ultradense WDM Transmission with Supercontinuum Multicarrier Source", IEEE J. Lighttw. Technol. , Vol. 24, pp. 2311-2317 (2006). T.A. Sakamoto et al. , “Coupled Multicore Fiber Design With Low Interdifferential Mode Delay for High-Density Space Division Multiplexing”, J. Lighttw. Technol. , Vol. 33, no. 6, pp. 1175-11811, (2015). C. Antonelli et al. , “The delay spread in fibers for SDM transmission: dependency on fiber parameters and perturbations”, Opt. Express, Vol. 23, p. 2196 (2015). R. Ryf et al. , “1705-km transmission over coupled-core fiber supporting 6 spatial models”, ECOC2014, paper PD. 3.2 (2014). R. Ryf et al. “Mode-division multiplexing over 96 km of two-mode fiber using coherent 6 × 6 MIMO processing”, J. et al. Lighttw. Technol. , Vol. 30, pp. 521-531 (2012). ITU-T Recommendation G. 650.2, Clause 5.1.4 (2007).

  The impulse response width of the optical fiber is a guideline for the MIMO signal processing load at the receiving end, and is a parameter that greatly affects the transmission system. Therefore, it is important to grasp the impulse response characteristics of the optical fiber to be used. However, at present, as described above, in order to measure the impulse response characteristics, a transmission system using a loop experiment system is constructed and evaluated, and a short optical fiber (for example, several tens of km or less) is simply evaluated. A method for measuring the impulse response width has not yet been studied.

  An object of the present invention is to make it possible to easily measure the impulse response characteristics of an optical fiber using a short optical fiber without using a transmission system using a loop experiment system.

  The present invention relates to an apparatus and a method for measuring a modal dispersion coefficient, in which an optical fiber having a plurality of propagation modes and in which coupling occurs between the plurality of propagation modes is to be measured. Multiple propagation modes are excited using a single-mode fiber on the incident side, and multiple propagation modes are received using a single-mode fiber on the output side. The mode dispersion coefficient is calculated from the standard deviation when the waveform is approximated by a Gaussian distribution.

Specifically, the mode dispersion coefficient measuring apparatus according to the present invention is:
A mode dispersion coefficient measuring apparatus for measuring a mode dispersion coefficient of an optical fiber to be measured in which a plurality of modes propagate in a fiber,
An input-side single mode fiber connected to the input end of the optical fiber to be measured;
An output-side single mode fiber connected to the output end of the optical fiber to be measured;
Measuring light having a predetermined wavelength width, a transmitter that enters the input-side single mode fiber; and
A receiving unit connected to the output-side single mode fiber and detecting a transmitted light spectrum of the measurement light after passing through the input-side single mode fiber, the optical fiber to be measured, and the output side single mode fiber;
A signal calculation unit that calculates a dispersion coefficient due to mode dispersion from a standard deviation when the transmitted light spectrum detected by the reception unit is Fourier-transformed to generate a time waveform and the time waveform is approximated by a Gaussian distribution; ,
Is provided.

In the mode dispersion coefficient measuring apparatus according to the present invention,
The optical fiber to be measured is a multi-core fiber in which a plurality of core regions are arranged in a cladding region having a refractive index smaller than that of the core region,
The measured optical fiber and the input-side single mode fiber are connected so that light is incident on the plurality of core regions,
The measured optical fiber and the output-side single mode fiber may be connected so that light guided through the plurality of core regions is coupled to a propagation mode of the output-side single mode fiber.

  In the mode dispersion coefficient measuring apparatus according to the present invention, an impulse response spread of the measured optical fiber may be smaller than a group delay difference between modes of the measured optical fiber.

Specifically, the mode dispersion coefficient measurement method according to the present invention is:
A mode dispersion coefficient measurement method for measuring a mode dispersion coefficient of an optical fiber to be measured in which a plurality of modes propagate in a fiber,
In the state where the input end of the optical fiber to be measured is connected to the input side single mode fiber, and the output end of the optical fiber to be measured is connected to the output side single mode fiber,
The transmitter connected to the input-side single mode fiber enters measurement light having a predetermined wavelength width into the input-side single mode fiber,
The receiver connected to the output side single mode fiber detects the transmitted light spectrum of the measurement light after passing through the input side single mode fiber, the measured optical fiber and the output side single mode fiber,
The signal calculation unit generates a time waveform by Fourier transforming the transmitted light spectrum detected by the receiving unit, and calculates the dispersion coefficient due to mode dispersion from the standard deviation obtained by approximating the time waveform with a Gaussian distribution. To do.

  The above inventions can be combined as much as possible.

  With the optical fiber of the present invention, it is possible to evaluate the impulse response characteristics of an optical fiber using a short optical fiber without propagating a signal in a transmission system using a loop test system, so that the evaluation of the characteristics can be performed easily and inexpensively. It can be performed.

The 1st example of a structure of the mode dispersion coefficient measuring apparatus which concerns on embodiment of this invention is shown. The 2nd example of a structure of the mode dispersion coefficient measuring apparatus which concerns on embodiment of this invention is shown. An example of a cross-sectional view of a two-core fiber is shown. An example of the impulse response width of a two-core fiber is shown. An example of the propagation distance dependence of the impulse response width of a two-core fiber is shown. An example of the acquired wavelength versus transmitted light characteristic is shown. An example of the waveform after Fourier-transform of acquisition data is shown. An example of the wavelength dependence of a dispersion coefficient is shown. An example of the calculation result of the mode dispersion coefficient with respect to the connection condition with the single mode fiber at the input / output end is shown.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In addition, this invention is not limited to embodiment shown below. These embodiments are merely examples, and the present invention can be implemented in various modifications and improvements based on the knowledge of those skilled in the art. In the present specification and drawings, the same reference numerals denote the same components.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
1 and 2 show an example of the configuration of the mode dispersion coefficient measuring apparatus of the present embodiment. The mode dispersion coefficient measuring apparatus of the present embodiment includes a transmission unit, a reception unit, and a signal calculation unit 96.

  The transmission unit emits measurement light having a predetermined wavelength width, and is, for example, a broadband light source 94 # 1 or a wavelength variable light source 94 # 2. The receiving unit detects a transmitted light spectrum of the measurement light, and is, for example, an optical spectrum analyzer 95 # 1 or a power meter 95 # 2. The optical fiber to be measured 91 is connected to the transmitting unit and the receiving unit via single mode fibers 92 # 1 and 92 # 2. The single mode fiber 92 # 1 functions as an input side single mode fiber, and the single mode fiber 92 # 2 functions as an output side single mode fiber.

  In FIG. 1, the mode dispersion coefficient measuring apparatus of this embodiment emits an optical frequency comb as the measurement light from the broadband light source 94 # 1, and the optical spectrum analyzer 95 # 1 measures the power for each wavelength. A transmitted light spectrum, which is data of transmitted light, is acquired. In FIG. 2, in the mode dispersion coefficient measuring apparatus of the present embodiment, the wavelength variable light source 94 # 2 of the transmission unit changes the wavelength of the measurement light with a predetermined wavelength width, and the power meter 95 # 2 By measuring the received light power, a transmitted light spectrum that is data of wavelength versus transmitted light is acquired.

The obtained wavelength versus transmitted light data is sent to the signal calculation unit 96. The signal calculation unit 96 converts the obtained data into data of frequency versus transmitted light, and performs Fourier transform to obtain a time waveform of time versus transmitted light. And the signal calculating part 96 calculates the dispersion coefficient by mode dispersion | distribution from the standard deviation at the time of calculating | requiring and obtaining a time waveform by Gaussian distribution.
Hereinafter, a method for calculating the mode dispersion coefficient will be described based on specific measurement data.

  FIG. 3 shows an example of a cross-sectional structure of the optical fiber 91 to be measured used for measurement. A measured optical fiber 91 shown in FIG. 3 is a two-core fiber including cores 11 # 1 and 11 # 2. In the measurement, the relative refractive index difference Δ of the cores 11 # 1 and 11 # 2 with respect to the clad 12 is 0.35%, and the core radius is 4.5 μm. There are three core distances D of 20, 25, and 40 μm.

  FIG. 4 shows the measurement result of the impulse response width using the impulse which is a technique related to the present invention. Impulse was incident on all cores of the optical fiber, and the impulse response width was measured on the exit side. L41B and L42B indicated by broken lines indicate pulses in a configuration (back-to-back) that does not include a two-core fiber. L41T, L42T, L43T1, and L43T2 indicated by solid lines indicate pulses in a configuration including a two-core fiber. Each fiber is evaluated with a fiber length of 10 km or more. However, it is understood that the impulse response spread is small in the optical fiber with D = 20, 25 μm, and the impulse response characteristic cannot be accurately grasped. On the other hand, in the fiber of D = 40 μm, since coupling between modes does not occur in the fiber, DMD between cores due to structural errors due to manufacturing errors between cores is observed.

  As a result of measuring the DMD of an optical fiber with D = 20, 25 μm using the interference method described in Non-Patent Document 7 using an optical fiber with a length of 30 m or less, the optical fiber with D = 20 μm has a wavelength of about 180 ps / km. A DMD of about 50 ps / km was observed in an optical fiber having a DMD of D = 25 μm. Thus, the impulse response width of the optical fiber in which mode coupling occurs during propagation is smaller than the DMD of the optical fiber. Here, the impulse response width is defined by the width of the time when the power drops from the peak value of the pulse by a predetermined ratio (for example, 50%, 10%, 1%, etc.).

  On the other hand, in an optical fiber in which mode coupling does not occur during propagation, the impulse response characteristics are obtained from waveforms obtained when pulses are simultaneously applied to two cores, and the two waveforms when the respective cores in the figure are excited are shown. It will be the sum of them. In this case, since two pulses separated by DMD are observed as in the case of an optical fiber with D = 40 μm, the impulse response width is approximately the same as the interval between two pulses, that is, the DMD value. .

  The expression DMD usually refers to a group delay difference between modes in a number mode fiber capable of propagating a plurality of propagation modes in the same core in a single core, but in the present specification, it has a broad meaning. For example, in a two-core fiber, if the structure of each core is a single-mode structure, two-mode propagation occurs when viewed as the entire optical fiber. Thus, regardless of whether the cores in which the propagating modes are localized are the same or different, the group delay difference between these modes is used as the DMD of the optical fiber.

  FIG. 5 shows a result of measuring an impulse response width by constructing a loop experiment system, which is a technique related to the present invention, and propagating a signal over a long distance. The impulse response width here is a time width that takes 10% of the peak value of the pulse. By propagating over a long distance, the characteristics of an optical fiber with D = 20, 25 μm can be observed, but it is not economical to construct a loop experiment.

  FIG. 6 shows an example of the measurement result of wavelength versus transmitted light characteristics. In the measurement of FIG. 6, using the mode dispersion coefficient measuring apparatus shown in FIG. 2, a two-core fiber with D = 20 μm was transmitted as the optical fiber to be measured 91, and the wavelength versus transmitted light characteristic was measured in the signal calculation unit 96. The transmitted light characteristic is a value obtained by dividing the incident light power to the single mobile fiber 92 # 1 from the intensity of light emitted from the single mode fiber 92 # 2.

  When mode coupling does not occur during propagation of an optical fiber, periodic power fluctuations are observed as described in Non-Patent Document 7. However, in the case of a two-core fiber of D = 20 μm in which modes are coupled during propagation, such periodic fluctuations were not clearly observed as shown in FIG.

  FIG. 7 shows a result of converting the wavelength of the data obtained in the measurement of the wavelength vs. transmitted light characteristic into a frequency and performing a Fourier transform. By Fourier transform, the unit of the horizontal axis becomes time. When a 2-core fiber with D = 40 μm is used as the optical fiber 91 to be measured, the power fluctuates with a period of 725 ps. However, when a 2-core fiber with D = 20, 25 μm is used as the optical fiber 91 to be measured, There is no significant power fluctuation. Further, when a 2-core fiber with D = 20, 25 μm is used as the optical fiber 91 to be measured, it can be seen that a Gaussian distribution waveform is obtained, as indicated by L71M and L72M. In polarization mode dispersion, according to Non-Patent Document 8, it is known that when the frequency vs. transmitted light characteristic of an optical fiber is Fourier-transformed, a Gaussian distribution is similarly obtained. For this reason, it is expected that the same tendency can be obtained in the coupling between the fundamental mode and the higher order mode as well as the coupling between the polarization modes.

  Therefore, the signal calculation unit 96 obtains L71F and L72F by fitting the waveforms of L71M and L72M shown in FIG. 7 with a Gaussian distribution. Accordingly, the signal calculation unit 96 can obtain the dispersion coefficient of the optical fiber 91 to be measured from the standard deviation <Δτ> of the Gaussian distribution, similarly to the calculation of the polarization mode dispersion coefficient.

  Note that the polarization mode dispersion coefficient obtained by the same procedure is an important parameter (unit: ps / √km) that serves as an indication of the load of MIMO signal processing necessary for polarization separation on the receiving side used in polarization multiplexing transmission. The coefficient obtained this time is not between polarization modes, but between basic and higher order modes, that is, spatial mode dispersion coefficient (SMD coefficient: Spatial mode dispersion coefficient), and is a measure of the MIMO signal processing load in mode multiplex transmission And the unit is similarly ps / √km.

  The measurement shown in FIG. 7 uses the same fiber length as the measurement shown in FIG. 4, and a characteristic difference of D = 20, 25 μm optical fiber, which was not observed in the impulse response evaluation related to the present invention, was observed. Therefore, highly accurate measurement is possible. In this measurement, the wavelength variable light source 94 # 2 shown in FIG. 2 has a wavelength variable width of 10 pm, a wavelength sweep width of 1450 to 1630 nm, and continuously sweeps the wavelength.

  In the case of the mode dispersion coefficient measuring apparatus shown in FIG. 2, the time resolution of the waveform after Fourier transform in the signal calculation unit 96 can be obtained by the reciprocal of the wavelength sweep width in the wavelength variable light source 94 # 2. For example, a time resolution of 0.01 ps or less can be realized under the condition of a wavelength sweep width of 180 nm. In the impulse response method used in the measurement shown in FIG. 4, since the performance of the oscilloscope on the receiving side was 40 GS / s, the time resolution was about 40 ps, which is a significant improvement in time resolution compared to the prior art. Can be realized. As described above, the invention according to this embodiment can improve the time resolution, so that it is possible to improve the measurement accuracy or to test a short optical fiber. In addition, the reciprocal of the frequency resolution in the light receiving unit is the maximum delay time amount that can be acquired, and is 1 pm in this measurement. Therefore, the maximum delay amount is 8 ns when converted at a wavelength of 1550 nm. That is, the frequency resolution may be controlled according to the spatial mode dispersion amount of the optical fiber to be measured.

  As a result, mode dispersion coefficients of 46 ps / √km and 38 ps / √km were obtained for optical fibers with D = 20 and 25 μm, respectively. On the other hand, in the optical fiber of D = 40 μm, the periodic frequency versus transmitted light characteristic observed when mode conversion does not occur in the optical fiber, that is, the Fourier transform waveform is obtained at a specific time. As described in Non-Patent Document 7, the DMD of the optical fiber can be calculated from the time when the spike occurs.

  FIG. 8 shows the calculated wavelength dependence of the mode dispersion coefficient in an optical fiber with D = 20, 25 μm. When the impulse response characteristic of an optical fiber is evaluated by a technique related to the present invention, it is necessary to change the wavelength of incident light as appropriate. On the other hand, in the method according to the present embodiment, the wavelength range of the broadband light source 94 # 1 is widened or the wavelength sweep width of the wavelength tunable light source 94 # 2 is widened. By processing the data by dividing the wavelength for Fourier transform for each desired band, the wavelength dependence of the mode dispersion coefficient can be easily obtained.

  The measurement results so far show that the cores of the single mode fibers 92 # 1 and 92 # 2 are connected to the center of the cross section of the optical fiber 91 to be measured when the optical fiber 91 to be measured is a two-core fiber. It is fused at the output end. FIG. 9 shows the result of measuring the mode dispersion coefficient (ps / √km) by changing the connection conditions at the input / output terminals. “No axial misalignment” is when the single mode fibers 92 # 1 and 92 # 2 are fused by aligning the cores of the single mode fibers 92 # 1 and 92 # 2 with the center of the cross section of the two core fibers. “Core # 1” or “core # 2” refers to a case where the cores of the single-mode fibers 92 # 1 and 92 # 2 and the core 11 # 1 or the core 11 # 2 of the two-core fiber are aligned and fused. From FIG. 9, the measurement result is large in any combination including the case where the core of the single-mode fiber 92 # 1 on the incident side and the cores 11 # 1 and 11 # 2 of the two-core fibers are aligned and connected. It can be confirmed that there is no difference. For this reason, it was confirmed that the connection conditions between the two-core fiber and the single mode fibers 92 # 1 and 92 # 2 do not greatly depend on the input / output conditions.

  However, in the mode dispersion coefficient measurement apparatus according to the present embodiment, as described in Non-Patent Document 7, it is necessary to observe multi-path interference associated with the propagation of a plurality of modes. Also in such a mode dispersion coefficient measuring apparatus, it is necessary to excite a plurality of modes of the optical fiber 91 to be measured and receive the power on the light receiving side. That is, even if the target optical fiber 91 to be measured is not a multi-core fiber such as a two-core fiber but a single-core number mode fiber, by exciting and receiving a plurality of modes on the input / output side, Similarly, the mode dispersion coefficient can be measured. A method for exciting and receiving a plurality of modes can be realized, for example, by connecting to a single mode fiber while shifting the axis in the radial direction.

  Moreover, although this embodiment demonstrated the example whose to-be-measured optical fiber 91 is 2 core fiber, this invention is not limited to this. For example, the measured optical fiber 91 may be a multi-core fiber having three or more cores. In this case, the connection of the single-mode fiber 92 # 1 on the incident side is adjusted so as to couple to a mode that propagates through all cores. Thereby, the mode dispersion coefficient measuring apparatus according to the present embodiment can measure the mode dispersion coefficient without depending on the number of cores.

  The present invention can be used as a transmission medium in an optical transmission system.

11 # 1, 11 # 2: Core 12: Clad 91: Optical fiber to be measured 92 # 1, 92 # 2: Single mode fiber 93 # 1, 93 # 2: Fusion splice point 94 # 1: Broadband light source 94 # 2 : Wavelength variable light source 95 # 1: Optical spectrum analyzer 95 # 2: Power meter 96: Signal calculation unit

Claims (4)

A mode dispersion coefficient measuring apparatus for measuring a mode dispersion coefficient of an optical fiber to be measured in which a plurality of modes propagate in a fiber,
An input-side single mode fiber connected to the input end of the optical fiber to be measured;
An output-side single mode fiber connected to the output end of the optical fiber to be measured;
Measuring light having a predetermined wavelength width, a transmitter that enters the input-side single mode fiber; and
A receiving unit connected to the output-side single mode fiber and detecting a transmitted light spectrum of the measurement light after passing through the input-side single mode fiber, the optical fiber to be measured, and the output side single mode fiber;
A signal calculation unit that calculates a dispersion coefficient due to mode dispersion from a standard deviation when the transmitted light spectrum detected by the reception unit is Fourier-transformed to generate a time waveform and the time waveform is approximated by a Gaussian distribution; ,
A mode dispersion coefficient measuring apparatus comprising: The optical fiber to be measured is a multi-core fiber in which a plurality of core regions are arranged in a cladding region having a refractive index smaller than that of the core region,
The measured optical fiber and the input-side single mode fiber are connected so that light is incident on the plurality of core regions,
The measured optical fiber and the output side single mode fiber are connected so that light guided through the plurality of core regions is coupled to a propagation mode of the output side single mode fiber,
The mode dispersion coefficient measuring apparatus according to claim 1. The impulse response spread of the measured optical fiber is smaller than the group delay difference between modes of the measured optical fiber,
The mode dispersion coefficient measuring apparatus according to claim 1 or 2. A mode dispersion coefficient measurement method for measuring a mode dispersion coefficient of an optical fiber to be measured in which a plurality of modes propagate in a fiber,
In the state where the input end of the optical fiber to be measured is connected to the input side single mode fiber, and the output end of the optical fiber to be measured is connected to the output side single mode fiber,
The transmitter connected to the input-side single mode fiber enters measurement light having a predetermined wavelength width into the input-side single mode fiber,
The receiver connected to the output side single mode fiber detects the transmitted light spectrum of the measurement light after passing through the input side single mode fiber, the measured optical fiber and the output side single mode fiber,
The signal calculation unit generates a time waveform by Fourier transforming the transmitted light spectrum detected by the receiving unit, and calculates the dispersion coefficient due to mode dispersion from the standard deviation obtained by approximating the time waveform with a Gaussian distribution. To
Modal dispersion coefficient measurement method.

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