Demodulation device and demodulation method for long-distance optical fiber sensor

Abstract

The invention discloses a long-distance optical fiber sensor demodulation device and method, and the device comprises a sweep frequency laser which is configured to scan a preset wavelength range in a stepping manner, and generates a trigger pulse when stepping one wavelength. And the signal generator receives the trigger pulse and outputs a driving pulse. And the semiconductor optical amplifier is used for converting the driving pulse into a high-power optical pulse. The first port of the circulator is connected with the light output end of the semiconductor light amplifier, the second port of the circulator is connected with the grating array to be detected, and the third port of the circulator outputs a reflected light signal. The photoelectric detector receives reflected light signals and converts the reflected light signals into electric signals, the data acquisition card synchronously acquires trigger pulses and the electric signals, and the computer is used for processing data based on a wavelength demodulation formula and a position demodulation formula so as to realize synchronous demodulation of the wavelength and the position of the grating array. According to the invention, synchronous demodulation of the wavelength and the position of the grating array is realized, and accurate multi-point monitoring in the long-distance optical fiber sensor based on the grating array is also realized.

Description

Technical Field

[0001] The present invention relates to the technical field of optical fiber sensing, and in particular to a demodulation device and a demodulation method for a long-distance optical fiber sensor. Background Art

[0002] With the development of fiber optic sensing technology, distributed fiber optic sensors have gradually become a core tool in the field of long-distance monitoring due to their ability to achieve continuous multi-point monitoring along the entire optical fiber. In particular, long-distance fiber optic sensors have broad application prospects in the field of structural health monitoring of oil and gas pipelines, tunnels, and bridges. However, existing technologies still have the following problems: 1. Limitations of traditional fiber Bragg grating (FBG): The monitoring capability of a single point or a limited area cannot meet the needs of long-distance and large-scale distributed sensing.

[0003] 2. Conflict between wavelength and position demodulation: Existing demodulation technologies (such as time division multiplexing and wavelength division multiplexing) generally focus on demodulation in a single dimension, making it difficult to achieve synchronous, high-precision demodulation of wavelength (representing changes in physical quantities) and position (representing spatial distribution).

[0004] 3. Long-distance signal attenuation and interference: During long-distance transmission, optical signals are easily affected by factors such as scattering and noise, resulting in a decrease in demodulation accuracy.

[0005] For example, Patent No. 201610296552.0 proposes a fiber Bragg grating wavelength demodulation method based on a DFB laser, which aims to overcome the limitations of existing demodulation technologies. This method achieves wavelength demodulation by emitting two short-pulse lasers with different driving currents, utilizing the linear relationship between the current and wavelength of the DFB laser, and calculating the slope based on the power difference of the reflected light from the fiber Bragg grating. Although this method simplifies the wavelength demodulation process, it does not solve the positioning problem of the multi-grating array; Patent No. 202211692875.3 discloses a system and method for downhole temperature and vibration monitoring of oil and gas wells. It uses FBG-FP interferometry technology to achieve simultaneous monitoring of multiple physical quantities, but there is a risk of signal confusion in long-distance scenarios. Summary of the Invention

[0006] In order to solve the technical problems mentioned in the background technology, the present invention provides a long-distance optical fiber sensor demodulation device and demodulation method.

[0007] The present invention adopts the following technical solution, a long-distance optical fiber sensor demodulation device, comprising: The frequency-sweeping laser is configured to scan a preset wavelength range in a step-by-step manner, generating a trigger pulse for each wavelength step, and the step interval t1 satisfies: t1≥2nL / c, where L is the total length of the fiber, n is the refractive index of the fiber, and c is the speed of light 3×10 8 m / s; A signal generator receives the trigger pulse and outputs a drive pulse, wherein the pulse width t2 of the drive pulse satisfies: t2<nL1 / c, where L1 is the spacing between adjacent gratings, n is the refractive index of the fiber, and c is the speed of light 3×10 8 m / s; a semiconductor optical amplifier (SOA), whose electrical input end is connected to the signal generator and whose optical input end is connected to the optical output end of the swept laser, and is used to convert the driving pulse into a high-power optical pulse; a circulator, wherein a first port of the circulator is connected to the optical output end of the semiconductor optical amplifier, a second port of the circulator is connected to the grating array to be measured, and a third port of the circulator outputs a reflected light signal; a photoelectric detector, receiving the reflected light signal and converting it into an electrical signal; a data acquisition card for synchronously acquiring the trigger pulse and the electrical signal, with a sampling rate satisfying the Nyquist sampling theorem; The computer is used for processing data based on the wavelength demodulation formula and the position demodulation formula to realize the wavelength and position synchronous demodulation of the grating array.

[0008] Furthermore, the starting wavelength and ending wavelength of the frequency sweeping laser cover the Bragg wavelength range of all gratings in the grating array, and the frequency sweeping speed is dynamically adjusted according to the total length of the optical fiber to ensure that the scanning cycle time does not exceed the single maximum acquisition time of the data acquisition card.

[0009] Furthermore, the working mode of the signal generator is a burst mode, the triggering mode is an external trigger, and the pulse amplitude is set to be higher than the trigger voltage threshold of the semiconductor optical amplifier.

[0010] Furthermore, the wavelength demodulation algorithm is based on the formula: λ i =λ0+Δλ×i; Wherein, λ0 is the starting wavelength, Δλ is the step wavelength, i is the number of steps, and the number of steps is calculated by associating the timestamp with the step interval time.

[0011] Furthermore, the grating position demodulation is based on optical time domain reflectometry technology, and the calculation formula is: D = (c × t) / 2n; Where D represents the grating position, c is the speed of light 3×10 8 m / s, n is the refractive index of the optical fiber, and t represents the time from the emission of the light pulse to the reception of the reflected light signal.

[0012] Furthermore, the grating array comprises a plurality of gratings with the same or different Bragg wavelengths, and the grating array is connected in series via a delay fiber, and the length of the delay fiber is verified by the position demodulation formula.

[0013] Furthermore, it also includes an optical attenuator connected between the third port of the circulator and the photodetector, for adjusting the intensity of the reflected light signal.

[0014] The present invention also provides a long-distance optical fiber sensor demodulation method, which uses the above-mentioned long-distance optical fiber sensor demodulation device, comprising the following steps: Set the sweep parameters of the swept laser, including the starting wavelength, ending wavelength, step interval, and sweep speed, to ensure that the Bragg wavelength range of the grating array is covered; Generate trigger pulses through the frequency sweep laser to synchronize the trigger signal generator and the data acquisition card; The signal generator generates a driving pulse according to the trigger pulse, drives the semiconductor optical amplifier to generate a light pulse and injects it into the grating array; Collect the reflected light signal from the grating array and record the emission and reception timestamps of the light pulses; The time domain signal is divided into multiple time windows according to the step interval time, and the wavelength and time information of the reflection peak are extracted in each window; The central wavelength of each grating is calculated based on the wavelength demodulation formula, and its spatial position is demodulated using the position demodulation formula, and the wavelength and position information are associated to generate sensing data.

[0015] Furthermore, the extraction of the reflection peak comprises the following steps: Filter and suppress noise on the signal in each time window; The peak detection algorithm is used to locate the wavelength value and time delay corresponding to the reflection peak; The accuracy of wavelength and position demodulation is optimized through interpolation algorithms.

[0016] Furthermore, a dynamic calibration step is included: After the initial sweep, the step interval of the swept laser or the pulse parameters of the signal generator are adjusted based on the demodulation results to optimize signal integrity over long-distance transmission.

[0017] Compared with the existing technology, the long-distance fiber optic sensor demodulation device and demodulation method designed in this invention realizes the synchronous demodulation of the wavelength and position of the grating array by combining an optimized wavelength demodulation algorithm with optical time domain reflectometry (OTDR) technology. At the same time, it also realizes precise multi-point monitoring in long-distance fiber optic sensors based on grating arrays. Through optimized pulse width and time domain segmentation technology, signal crosstalk is reduced, and the accuracy and reliability of distributed sensing are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Schematic diagram of the overall structure of the long-distance optical fiber sensor demodulation device of the present invention; Figure 2 This is a schematic diagram of wavelength and position demodulation principle in the present invention; Figure 3 Schematic diagram of the experimental results of wavelength demodulation using a group of grating arrays in the present invention; Figure 4 The results of the wavelength demodulation experiment using two sets of grating arrays in the embodiment of the present invention are shown in FIG. Figure 1 ; Figure 5 The results of the wavelength demodulation experiment using two sets of grating arrays in the embodiment of the present invention are shown in FIG. Figure 2 ; Figure 6 Schematic diagram of demodulation results using multiple grating arrays in an embodiment of the present invention. DETAILED DESCRIPTION

[0019] In order to facilitate those skilled in the art to understand the technical solution of the present invention, the following is further described with reference to the accompanying drawings. It should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present invention.

[0020] In the following detailed description, for ease of explanation, numerous specific details are set forth to provide a comprehensive understanding of the embodiments of the present invention. However, it is apparent that one or more embodiments may be practiced without these specific details. In addition, in the following description, descriptions of known structures and techniques are omitted to avoid unnecessarily obscuring the concepts of the present invention. like Figure 1 FIG. 1 is a schematic diagram of the overall structure of the long-distance optical fiber sensor demodulation device of the invention, comprising: The frequency-sweeping laser is configured to scan a preset wavelength range in a step-by-step manner, generating a trigger pulse for each wavelength step, and the step interval t1 satisfies: t1≥2nL / c, where L is the total length of the fiber, n is the refractive index of the fiber, and c is the speed of light 3×10 8 m / s; In a specific implementation, the starting wavelength and the ending wavelength of the sweep laser cover the Bragg wavelength range of all gratings in the grating array, and the sweep speed is dynamically adjusted according to the total length of the optical fiber to ensure that the scanning cycle time does not exceed the single maximum acquisition time of the data acquisition card.

[0021] It includes a signal generator, which receives the trigger pulse and outputs a driving pulse, and the pulse width t2 of the driving pulse satisfies: t2<nL1 / c, where L1 is the spacing between adjacent gratings, n is the refractive index of the fiber, and c is the speed of light 3×10 8m / s; in a specific implementation, the working mode of the signal generator is a burst mode, the triggering mode is an external trigger, and the pulse amplitude is set to be higher than the trigger voltage threshold of the semiconductor optical amplifier.

[0022] a semiconductor optical amplifier (SOA), whose electrical input end is connected to the signal generator and whose optical input end is connected to the optical output end of the swept laser, and is used to convert the driving pulse into a high-power optical pulse; a circulator, wherein a first port of the circulator is connected to the optical output end of the semiconductor optical amplifier, a second port of the circulator is connected to the grating array to be measured, and a third port of the circulator outputs a reflected light signal; a photoelectric detector, receiving the reflected light signal and converting it into an electrical signal; a data acquisition card for synchronously acquiring the trigger pulse and the electrical signal, with a sampling rate satisfying the Nyquist sampling theorem; The computer is used to process data based on the wavelength demodulation formula and the position demodulation formula to achieve synchronous demodulation of the wavelength and position of the grating array. In specific implementation, the wavelength demodulation algorithm is based on the formula: λ i =λ0+Δλ×i; Wherein, λ0 is the starting wavelength, Δλ is the step wavelength, i is the number of steps, and the number of steps is calculated by associating the timestamp with the step interval time.

[0023] The grating position demodulation is based on optical time domain reflectometry technology, and the calculation formula is: D = (c × t) / 2n; Where D represents the grating position, c is the speed of light 3×10 8 m / s, n is the refractive index of the optical fiber, and t represents the time from the emission of the light pulse to the reception of the reflected light signal.

[0024] In addition, in some embodiments, an optical attenuator is further included, which is connected between the third port of the circulator and the photodetector and is used to adjust the intensity of the reflected light signal.

[0025] The present invention sets a frequency sweeping laser to scan the wavelength in a step-by-step manner, outputting a trigger pulse for each wavelength value step to a signal generator and a data acquisition card. The signal generator immediately outputs a pulse wave based on the received trigger signal and sends it to the electrical input end of a semiconductor optical amplifier (SOA). The optical input end of the SOA is connected to the frequency sweeping laser. The SOA generates pulsed light based on the received pulse wave and enters port 1 of a circulator. Port 2 of the circulator outputs the pulsed light to a grating array to generate a sensor light signal, which is reflected back to the circulator. Port 3 of the circulator enters the optical input port of a photodetector. The output end of the photodetector is connected to the input end of a data acquisition card. The output port of the data acquisition card is connected to a computer, and data processing of the sensor signal is finally completed on the computer. In the present invention, each wavelength value of the frequency sweeping laser has a corresponding trigger signal in the time domain diagram of the data acquisition card. By analyzing the reflected light signal from the grating array between the trigger signals, wavelength and position measurement of the fiber Bragg grating array can be achieved.

[0026] like Figure 2 The figure shows the principle diagram of wavelength and position demodulation in the present invention. Each wavelength step of a swept laser generates a short pulse, which is amplified by the SOA and then fed into the grating array. Since the swept laser steps at fixed intervals, the collected time-domain signal is divided equally according to the time interval. The optical signal received within each interval represents the reflected light at the current wavelength. Assuming the starting wavelength of the grating scan is λ0nm, the swept laser increases the wavelength by Δλ with each step. The wavelength demodulation formula is as follows: λi = λ0 + Δλ × i, where i is the number of steps, which can be determined from the time and the step interval. Temperature can be demodulated by demodulating the grating's center wavelength. Weak grating positioning utilizes optical time-domain reflectometry, recording the time from the start of light pulse transmission to its return to the transmitter. Based on the speed of light in the transmission medium, the test position of the optical cable can be calculated. The test position formula is: D = (c × t) / 2n, where D represents the test distance, c is the speed of light (3 × 108 m / s), and t represents the time from the emission of the light pulse to the receipt of the reflected light signal.

[0027] The present invention also provides a demodulation method based on the above-mentioned long-distance optical fiber sensor demodulation device, comprising the following steps: Set the sweep parameters of the swept laser, including the starting wavelength, ending wavelength, step interval, and sweep speed, to ensure that the Bragg wavelength range of the grating array is covered; The swept laser generates trigger pulses, synchronizing the trigger signal generator and data acquisition card. In practice, the start and end wavelength settings for the swept laser scan must encompass all Bragg wavelengths of the entire grating array. The scanning wavelength interval and scanning speed depend on the total length of the grating array. Each wavelength step generates a trigger signal. The time between two trigger signals must ensure that the previous trigger signal has been reflected from the fiber tail and returned to the photodetector. Specifically, the interval is t1 = 2nL / c.

[0028] The signal generator generates a drive pulse based on the trigger pulse, driving the semiconductor optical amplifier (SOA) to generate a light pulse that is then injected into the grating array. In practice, the signal generator uses an external trigger. Upon receiving the trigger signal, a pulse is generated immediately. The pulse width depends on the distance between two adjacent gratings in the grating array. A pulse can only encompass one grating; specifically, the pulse width is t2 = nL1 / c.

[0029] Collect the reflected light signal from the grating array and record the emission and reception timestamps of the light pulses; The time domain signal is divided into multiple time windows at step intervals, and the wavelength and time information of the reflection peak are extracted in each window. In specific implementation, the extraction of the reflection peak includes the following steps: Filter and suppress noise on the signal in each time window; A peak detection algorithm is used to locate the time delay corresponding to the reflection peak; The accuracy of wavelength and position demodulation is optimized through fitting algorithms.

[0030] The center wavelength of each grating is calculated based on the wavelength demodulation formula, and its spatial position is demodulated using the position demodulation formula. The wavelength and position information are then correlated to generate sensor data. Specifically, the wavelength measurement method uses a sampling rate of S and a sampling time of T. The sampling time is less than the sweep time of two cycles. Therefore, the number of sampling points, M, = ST. For a laser sweep rate of v and a step wavelength of Δλ, the laser sweeps from the center wavelength λ to λ + Δλ over a time period of Δt = Δλ / v. During this phase, the data acquisition card captures n = SΔt. The rising edge of the laser trigger pulse determines the start time of the laser sweep. For M sampling points, the sweep start point, Ps, is located. At this point, the grating wavelength is recorded as the sweep start wavelength, λ0, set by the sweep laser. Thereafter, the grating wavelength is incremented by Δλ every n points. The formula is as follows: λi = λ0 + Δλ × i. In practice, the position measurement method improves upon optical time-domain reflectometry. A swept laser emits a pulse signal at each wavelength to a signal generator, which, upon triggering, generates a pulse signal for the SOA. The SOA injects a high-power light pulse into the optical fiber and receives the reflected and scattered light generated by the light pulse as it travels through the optical cable. The time it takes for the light pulse to travel back to the transmitter is recorded. Based on the speed of light in the fiber, the distance between each grating in the fiber can be calculated. The position measurement formula is: D = (c × t) / 2n, where D represents position, c is the speed of light (3 × 108 m / s), n is the fiber's refractive index, and t represents the time from the emission of the light pulse to the receipt of the reflected light signal.

[0031] The grating array under test in this invention contains one or more groups of gratings with different or identical Bragg wavelengths. The corresponding reflection peak waveforms can be detected using the method described in this invention. The system's ability to measure spatial position can be verified by connecting delay fibers of varying lengths. During the experiment, the waveforms received by the data acquisition card are recorded, and the position and wavelength of the gratings in the long-distance fiber optic sensor are calculated based on the reflection peak position and delay information in the waveforms.

[0032] like Figure 3 This figure illustrates the results of a wavelength demodulation experiment using a grating array in the present invention. The long-distance fiber optic sensor includes a grating array containing four gratings with different center wavelengths. To ensure that all wavelengths can be detected, the swept laser is preset to a wavelength range of 1545nm to 1555nm. The laser begins sweeping, triggering the data acquisition card to collect the sensor light signal. The data acquisition card uses wavelength demodulation to calculate the center wavelength of each grating from the time-domain signal.

[0033] like Figure 4-5 FIG. 1 is a schematic diagram of the experimental results of wavelength demodulation using two groups of grating arrays in an embodiment of the present invention. Figure 4Using a 0.76m delay fiber patch cable, the laser began frequency sweeping and data recording. In this case, according to the position measurement formula, the spacing between the two grating arrays increased by 0.753m, enabling position demodulation of the long-distance fiber optic sensor. Figure 5 The long-distance fiber optic sensor to be tested is a 2.5km delay fiber optic patch cord connected between two sets of grating arrays. The results are as follows: Figure 5 According to the position measurement formula, the corresponding distance is approximately 2.47 km, which is close to the nominal length of 2.5 km, further proving that the invention can achieve position demodulation of long-distance optical fiber sensors.

[0034] like Figure 6 Figure 2 shows a schematic diagram of the demodulation results using multiple grating arrays in an embodiment of the present invention. In practice, the acquired array is first divided equally according to the wavelength step time interval t1, resulting in a matrix of wavelength number i × time length. Based on the wavelength and position demodulation formulas described in the present invention, the wavelength number i in the matrix is ​​replaced with the demodulation wavelength λi, and the time length is replaced with the demodulation position D.

[0035] Finally, the position and wavelength peaks of each grating are searched, and the coordinates are extracted to realize wavelength and spatial position demodulation.

[0036] In a specific implementation case, the long-distance optical fiber sensor to be measured is two serially connected grating arrays, each array contains four gratings with different wavelengths and positions, and the sensing light signal is demodulated according to step 3 to obtain Figure 5 , demodulate the wavelength and position of the 8 gratings.

[0037] In summary, the long-distance fiber optic sensor demodulation device and demodulation method designed in the present invention realizes the synchronous demodulation of the wavelength and position of the grating array by combining an optimized wavelength demodulation algorithm with optical time domain reflectometry (OTDR) technology. At the same time, it also realizes precise multi-point monitoring in long-distance fiber optic sensors based on grating arrays. Through optimized pulse width and time domain segmentation technology, signal crosstalk is reduced, and the accuracy and reliability of distributed sensing are improved.

[0038] The above embodiments are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A long-distance optical fiber sensor demodulation device, characterized in that: include: The frequency sweeping laser is configured to scan a preset wavelength range in a step-by-step manner, generating a trigger pulse for each wavelength step, and the step interval time t1 satisfies: t1≥2nL / c, where L is the total length of the optical fiber, n is the refractive index of the optical fiber, and c is the speed of light 3×10 8 m / s; A signal generator receives the trigger pulse and outputs a drive pulse, wherein the pulse width t2 of the drive pulse satisfies: t2<nL1 / c, where L1 is the spacing between adjacent gratings, n is the fiber refractive index, and c is the speed of light 3×10 8 m / s; A semiconductor optical amplifier (SOA), whose electrical input end is connected to the signal generator and whose optical input end is connected to the optical output end of the frequency-sweeping laser, is used to convert the driving pulse into a high-power optical pulse; A circulator, wherein a first port of the circulator is connected to the optical output end of the semiconductor optical amplifier, a second port of the circulator is connected to the grating array to be measured, and a third port of the circulator outputs a reflected optical signal; A photoelectric detector receives the reflected light signal and converts it into an electrical signal; A data acquisition card, which synchronously acquires the trigger pulse and the electrical signal, and the sampling rate satisfies the Nyquist sampling theorem; The computer is used for processing data based on the wavelength demodulation formula and the position demodulation formula to realize the wavelength and position synchronous demodulation of the grating array.

2. The long-distance optical fiber sensor demodulation device according to claim 1, characterized in that: The starting wavelength and the ending wavelength of the frequency sweeping laser cover the Bragg wavelength range of all gratings in the grating array, and the frequency sweeping speed is dynamically adjusted according to the total length of the optical fiber to ensure that the scanning cycle time does not exceed the single maximum acquisition time of the data acquisition card.

3. The long-distance optical fiber sensor demodulation device according to claim 2, characterized in that: The working mode of the signal generator is a burst mode, the triggering mode is an external trigger, and the pulse amplitude is set to be higher than the trigger voltage threshold of the semiconductor optical amplifier.

4. The long-distance optical fiber sensor demodulation device according to claim 3, characterized in that: The wavelength demodulation algorithm is based on the formula: l i =λ0+Δλ×i; Wherein, λ0 is the starting wavelength, Δλ is the step wavelength, i is the number of steps, and the number of steps is calculated by associating the timestamp with the step interval time.

5. The long-distance optical fiber sensor demodulation device according to claim 4, characterized in that: The grating position demodulation is based on optical time domain reflectometry technology, and the calculation formula is: D = (c × t) / 2n; Where D represents the grating position, c is the light speed 3×10 8 m / s, n is the refractive index of the optical fiber, and t represents the time from the emission of the light pulse to the reception of the reflected light signal.

6. The long-distance optical fiber sensor demodulation device according to claim 5, characterized in that: The grating array comprises a plurality of gratings with the same or different Bragg wavelengths, and the grating array is connected in series via a delay fiber, and the length of the delay fiber is verified by the position demodulation formula.

7. The long-distance optical fiber sensor demodulation device according to claim 1, characterized in that: It also includes an optical attenuator connected between the third port of the circulator and the photoelectric detector, and is used to adjust the intensity of the reflected light signal.

8. A long-distance optical fiber sensor demodulation method, using the long-distance optical fiber sensor demodulation device according to any one of claims 1 to 7, characterized in that: The following steps are involved: Set the scanning parameters of the swept laser, including the starting wavelength, ending wavelength, step interval time and sweep speed, to ensure that the Bragg wavelength range of the grating array is covered; Generate a trigger pulse through the frequency sweep laser to synchronize the trigger signal generator and the data acquisition card; The signal generator generates a driving pulse according to the trigger pulse, drives the semiconductor optical amplifier (SOA) to generate an optical pulse and injects it into the grating array; Collect the reflected light signal of the grating array and record the emission and reception timestamps of the light pulses; The time domain signal is divided into multiple time windows according to the step interval time, and the wavelength and time information of the reflection peak are extracted in each window; The central wavelength of each grating is calculated based on the wavelength demodulation formula, and its spatial position is demodulated through the position demodulation formula, and the wavelength and position information are associated to generate sensing data.

9. The long-distance optical fiber sensor demodulation method according to claim 8, characterized in that: The extraction of the reflection peak comprises the following steps: Filter and suppress noise on the signal in each time window; A peak detection algorithm is used to locate the time delay corresponding to the reflection peak; The accuracy of wavelength and position demodulation is optimized through fitting algorithms.

10. The long-distance optical fiber sensor demodulation method according to claim 9, characterized in that: A dynamic calibration step is also included: After the initial scan, the step interval of the swept laser or the pulse parameters of the signal generator are adjusted based on the demodulation results to optimize signal integrity over long distances.

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