Method for calculating phase difference in fiber optic sensing system

Abstract

The application provides a phase difference calculation method in an optical fiber sensing system, and relates to the field of optical fiber sensing monitoring. Laser emitted by an ultra-stable laser is divided into two paths by a beam splitter. One path is used as signal light, and the other path is used as reference light. The signal light and the reference light are frequency beat by a beam combiner, frequency divided by a 1 / N frequency divider, and phase detected on a phase detector with a local oscillation radio frequency signal. The phase detected signal is filtered by a low pass filter. The filtered signal is phase tracked by an adjustable phase shifter, and phase information is extracted after the phase tracking and low pass filtering. The method can process data by hardware, has a small data operation amount, and reduces the requirement for computer operation capacity. The method can obtain relevant data in real time, improves the real-time performance of the system, and can realize real-time monitoring. In addition, the range of the calculated phase difference is positive and negative infinity, the problem of 2pi cycle ambiguity is avoided, and ultra-long range and ultra-high precision monitoring is realized.

Description

Technical Field

[0001] This application relates to the field of fiber optic sensing and monitoring, and in particular to a method for calculating the phase difference in a fiber optic sensing system. Background Technology

[0002] Optical fiber, as a highly efficient optical transmission medium, not only carries optical signals but also serves as a sensitive element for sensing changes in the surrounding environment. Changes in the external environment (such as humidity, strain, and temperature) cause changes in the parameters of the sensing fiber (such as refractive index and radius), which in turn alter the parameters of the detected optical signal (such as intensity, phase, polarization, and wavelength). Therefore, by processing the detected signal, the changes in the external environment can be demodulated. This characteristic of optical fiber can be used to monitor changes in external environmental conditions. Compared to traditional sensing technologies, fiber optic sensing technology offers advantages such as high reliability, resistance to electromagnetic interference, ease of implementation, low cost, and wide monitoring range, and has been widely applied in practical scenarios. Long-distance fiber optic sensing technology is needed in fields such as power transmission line safety monitoring, perimeter security, and seismic signal monitoring to effectively measure parameters such as temperature, strain, and vibration.

[0003] Fiber optic sensing technology can be categorized into polarization modulation (PMC) and phase modulation (PM) technologies. Polarization modulation refers to changing the polarization characteristics of light waves in an optical fiber by means of a measured signal. By detecting the change in the polarization state of the light, changes in the external environment can be measured. Phase modulation refers to changing the phase of light waves propagating in an optical fiber by means of a measured signal according to a certain rule. The amount of change in the optical phase can reflect changes in the external environment.

[0004] In existing fiber optic sensing systems based on phase change, the method for calculating phase difference typically involves processing large amounts of data using relevant software. This is done by directly recording the time-domain data after interference in the system, followed by performing calculations such as Fourier transforms to derive the phase change. Because the calculation involves trigonometric function changes, the results often contain 2π-period ambiguity. Furthermore, this approach suffers from the large amount of data processed, computational speed limited by computer processing power, and difficulty in timely data calculation. When the measurement range is large and involves many periods, it fails to calculate ambiguity beyond the 2π period, making it difficult to determine accurate data. Summary of the Invention

[0005] Based on this, the present invention proposes a simplified method for calculating phase difference. This method requires less data, thus reducing the demands on computer processing power; it can also generate relevant data in real time, improving the system's real-time performance and enabling near-real-time monitoring; furthermore, it can calculate phase difference over a range of positive and negative infinity, avoiding the problem of 2π periodic ambiguity. This method can be used for phase difference calculation in various systems and is not limited to fiber optic sensing systems.

[0006] This invention proposes a method for calculating phase difference in an optical fiber sensing system using a simple device, and describes its feasibility and specific implementation calculation method. This method utilizes a simple device and does not require complex data calculations, thus quickly and accurately calculating phase change information in the link. This method can detect a wider range of optical frequency phase changes (-∞ to +∞) and eliminates ambiguity in the 2π period.

[0007] In one embodiment, the laser emitted by the ultra-stable laser is split into two paths by a beam splitter.

[0008] One path passes through an optical fiber circulator and becomes the signal light. After being frequency-shifted by an acousto-optic modulator, the signal light reaches the reflector. The radio frequency signal source drives the frequency of the acousto-optic modulator.

[0009] The local oscillator radio frequency signal emitted by the radio frequency signal source is divided by a 2 / N frequency divider;

[0010] The other path serves as a reference light, which beats the signal light returned from the fiber optic circulator through a beam combiner, undergoes photoelectric conversion through a photodetector, is divided by a 1 / N divider, and is then phase-detected with the local oscillator radio frequency signal on a phase detector, and filtered by a low-pass filter.

[0011] The filtered signal is phase-tracked by an adjustable phase shifter, and the phase information is extracted after the phase detection and low-pass filtering of the signal is maintained in real time.

[0012] Furthermore, let the frequency of the light emitted by the ultrastable laser be v0, and the phase be... The normalized electric field expression is:

[0013] The electric field of the optical signal driven by the acousto-optic modulator is expressed as: If the driving frequency is f / 2, then the frequency of the signal light after modulation by the acousto-optic modulator is v0+f / 2.

[0014] Furthermore, the signal light is transmitted via the fiber optic link and reflected back to the local location by a mirror at the far end. During transmission, the phase change introduced by temperature and environmental changes is represented as follows: The electric field of the signal light can then be expressed as: The radio frequency signal converted by the detector after beating the reference light is represented as: The phase difference is then calculated. This refers to the change information of the optical fiber.

[0015] Furthermore, the radio frequency signal after beat frequency division is represented as follows after being divided by a 1 / N divider: Meanwhile, the drive signal of AOM is divided by a 2 / N divider and expressed as sin[(2πf) / N]. After passing through an adjustable phase shifter, the phase shift is... The signal after the two frequency divisions are phase-detected and low-pass filtered is represented as follows: Mediation is needed at this time. Size makes Approaching zero, at this time According to real-time recording Calculated Size.

[0016] Another embodiment is a method for calculating the phase difference in an optical fiber sensing system, comprising the following steps:

[0017] The first ultra-stable laser is split by the first beam splitter. One beam remains locally as the first local oscillator beam, and the other beam is transmitted as a signal beam through the first circulator and the first acousto-optic modulator via a long-distance optical fiber link to the other side. After passing through the second acousto-optic modulator and the second optical fiber circulator, it forms the second signal beam, which undergoes heterodyne interference with the local oscillator beam of the second ultra-stable laser.

[0018] The first radio frequency signal source drives the first acousto-optic modulator to a certain frequency, and divides the local oscillator radio frequency signal emitted by the first radio frequency signal source by a first 2 / N frequency divider.

[0019] The first local oscillator light and the first signal light returned by the first fiber optic circulator are beat by the first beam combiner, then photoelectric conversion is performed by the first photodetector, and after being divided by the first 1 / N frequency divider, they are phase-detected by the first local oscillator radio frequency signal on the first phase detector and filtered by the first low-pass filter. The filtered signal is phase-tracked by the first adjustable phase shifter, and the phase information is extracted after the phase detection and low-pass filtering signal is maintained in real time.

[0020] Meanwhile, the second ultra-stable laser is split by the second beam splitter. One beam remains locally as the second local oscillator, and the other beam is transmitted as a signal beam through the second circulator and the second acousto-optic modulator via a long-distance optical fiber link to the other side. After passing through the first acousto-optic modulator and the first optical fiber circulator, the signal beam is formed and undergoes heterodyne interference with the first local oscillator beam of the first ultra-stable laser.

[0021] The second radio frequency signal source drives the second acousto-optic modulator at a frequency, and divides the local oscillator radio frequency signal emitted by the second radio frequency signal source by a second 2 / N frequency divider;

[0022] The second local oscillator light and the second signal light returned from the second fiber optic circulator are beat by the second combiner, then photoelectric conversion is performed by the second photodetector, and after being divided by the second 1 / N divider, they are phase-detected by the second local oscillator radio frequency signal on the second phase detector, and then filtered by the second low-pass filter. The filtered signal is phase-tracked by the second adjustable phase shifter, and the phase information is extracted after the phase detection and low-pass filtering signal is maintained in real time.

[0023] Furthermore, let the light frequencies emitted by the first and second ultrastable lasers be ν and ν, respectively. 10 and v 20 The phases are all The normalized electric field expressions are as follows: and

[0024] The electric fields of the optical signals after being driven by the first and second acousto-optic modulators are respectively expressed as: and The driving frequencies of the first and second acousto-optic modulators are both f / 2. Therefore, the frequencies of the signal light after modulation by the first and second acousto-optic modulators are respectively v. 10 +f / 2 and v 20 +f / 2.

[0025] Furthermore, the phase change information of the fiber optic link can be recovered by heterodyne interferometry of the first ultrastable laser. The phase change information of the fiber optic link was recovered by heterodyne interferometry using a second ultrastable laser. The electric fields of the signal light after the two phase changes can be expressed as follows: and

[0026] The beat frequencies of each detector and the radio frequency signals converted by the first and second detectors are respectively represented as follows: and

[0027] By cross-correlation of the phase changes on both sides of the cross-correlation function, the time difference T between the arrival points of the two signal lights at the vibration occurrence location is calculated. The cross-correlation function is:

[0028]

[0029] The distance difference l between the location of the disturbance and the two lasers is: l = C * T; where C is the speed of light in the optical fiber;

[0030] The location of the disturbance can be determined based on the total link length L of the optical fiber.

[0031] Compared with the prior art, the present invention has the following beneficial technical effects:

[0032] Existing methods for calculating phase difference rely on software to process large amounts of data. This approach suffers from drawbacks such as large data volumes, computational speed limitations imposed by computer processing power, inability to obtain relevant data promptly, and inability to calculate ambiguity beyond a 2π period when the detection range is wide and the period is long. This invention proposes a simplified method for calculating phase difference. This method uses hardware for data processing, reducing the amount of computation and lowering the requirements for computer processing power. Furthermore, it can obtain relevant data in real time, improving the system's real-time performance and enabling near-real-time monitoring. Additionally, it can calculate phase difference over a range of positive and negative infinity, avoiding the 2π period ambiguity problem and achieving ultra-long-range, ultra-high-precision monitoring. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the device for calculating phase difference in the fiber optic sensing system of the present invention;

[0034] Figure 2 This is a schematic diagram of a two-sided device, representing another embodiment of phase difference calculation in the fiber optic sensing system of the present invention. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0036] In the accompanying drawings of specific embodiments of the present invention, in order to better and more clearly describe the working principle of each component in the system and show the connection relationship of each part in the device, only the relative positional relationship between each component is clearly distinguished. It does not constitute a limitation on the signal transmission direction, connection sequence, or size, dimension, and shape of each part within the component or structure.

[0037] Devices for calculating phase difference in fiber optic sensing systems, such as Figure 1 As shown, the specific process of calculating the phase difference in a fiber optic sensing system using this device is as follows:

[0038] The laser emitted by the ultra-stable laser Laser is split into two paths by beam splitter BS1. One path serves as the signal light, which passes through an optical fiber circulator C, then undergoes frequency shifting by an acousto-optic modulator AOM before reaching the reflector M. The radio frequency (RF) signal source drives the frequency of the RF modulator AOM. The other path split by beam splitter BS1 serves as the reference light. The reference light and the signal light returning from the optical fiber circulator C are beat-frequency-matched by beam combiner BS2, then undergo photoelectric conversion by photodetector PD, followed by frequency division by 1 / N divider, and finally phase-detected by the local oscillator RF signal split from the AOM driving signal source on a phase detector. The signal is then filtered by a low-pass filter LPF, and the local oscillator RF signal emitted by the RF signal source is further divided by frequency divider 2 / N and phase-tracked by an adjustable phase shifter and controller (not shown in the figure). The phase-detected and low-pass-filtered signal is maintained in real time, and then the phase information is extracted.

[0039] The specific method for solving the phase is as follows: Let the frequency of the light emitted by the ultra-stable laser be v0, and the phase be... The normalized electric field expression for an optical signal is: The electric field of the optical signal driven by the acousto-optic modulator (AOM) is expressed as follows: If the driving frequency is f / 2, then the frequency of the signal light after modulation by the acousto-optic modulator (AOM) is v0 + f / 2. Therefore, the normalized electric field expression of the reference light is: The signal light is transmitted via an optical fiber link and reflected back to the local location by a mirror at the far end. During transmission, temperature and environmental changes alter the phase of the transmitted laser light. This phase change is represented as: The electric field of the signal light can then be expressed as:

[0040] After the signal light is transmitted through the optical fiber, changes in temperature and environment will alter the phase of the transmitted laser. The radio frequency signal, which beats the reference light and is converted by the detector, is represented as: The signal light returns to the local location via a long-link optical fiber, and its relative phase change with respect to the reference light is: Therefore, the phase difference is calculated. This allows us to know information about changes in the optical fiber, such as vibration.

[0041] In the device of this embodiment, the signal is preprocessed in hardware. First, the radio frequency signal after beat frequency is divided by 1 / N by a 1 / N divider and then represented as follows: Meanwhile, the drive signal for AOM is divided by 2 / N by a 2 / N divider, expressed as sin[(2πf) / N], and then passes through an adjustable phase shifter, with a phase shift of... The adjustment range can be positive or negative infinity. Then, the signal after the two frequency-divided signals are phase-detected by a phase detector and filtered by a low-pass filter (LPF) is expressed as: Mediation is needed at this time. Size makes Approaching zero, according to the principle of function limits, at this point...

[0042] This method, based on real-time recording Able to directly obtain The magnitude of the value is used to obtain information about the changes in the optical fiber in the link caused by vibration, etc. Because... If the adjustable range is positive or negative infinity, then... Its detection range is positive and negative infinity, which can effectively avoid... The detection range has an ambiguity of 2π cycles. Therefore, phase change information can be obtained without complex data processing using this method, and the detection range is -∞ to +∞, eliminating the 2π cycle ambiguity.

[0043] like Figure 2 As shown, in another preferred embodiment, an ultra-stable laser can be placed on each side to simultaneously monitor the phase change information of the fiber optic link using a bidirectional beat-and-shoot method. Since the ultra-stable lasers on both sides only pass through the fiber optic link on one side, the signal light on each side is emitted by the other laser and passes through the fiber optic link only once, without having to pass through the fiber optic link twice. This can make the signal-to-noise ratio of the beat frequency detection on both sides higher. Furthermore, by combining the link phase change information monitored on both sides, the location of vibrations and other disturbances on the fiber optic link can be located based on the time difference of the signal arrival on both sides.

[0044] In the experimental scheme using two ultrastable lasers engaging in a counter-attack, the echo signal of circulator C in the previous embodiment is transformed into an optical signal emitted by the laser at the opposite end. The first ultrastable laser Laser1 is split by the first beam splitter BS1, with one beam remaining locally as the first local oscillator, and the other beam being transmitted as a signal beam through the first circulator C1 and the first acousto-optic modulator AOM1 via a long-distance optical fiber link to the opposite end. After passing through the second acousto-optic modulator AOM2 and the second optical fiber circulator C2, the signal beam forms the second signal beam, which undergoes heterodyne interference with the local oscillator beam of the second ultrastable laser Laser2.

[0045] The first radio frequency signal source drives the first acousto-optic modulator AOM1 to a certain frequency, and divides the local oscillator radio frequency signal emitted by the first radio frequency signal source by the first 2 / N frequency divider.

[0046] The first local oscillator light and the first signal light returned by the first fiber optic circulator C1 are beat by the first combiner BS3, then photoelectric conversion is performed by the first photodetector PD1, and after being divided by the first 1 / N frequency divider, they are phase-detected by the first local oscillator radio frequency signal on the first phase detector, and then filtered by the first low-pass filter LPF1. The filtered signal is phase-tracked by the first adjustable phase shifter, and the phase information is extracted after the phase detection and low-pass filtering signal is maintained in real time.

[0047] Meanwhile, the second ultra-stable laser Laser2 is split by the second beam splitter BS2. One beam remains locally as the second local oscillator, and the other beam is transmitted as a signal beam through the second circulator C2 and the second acousto-optic modulator AOM2 via a long-distance optical fiber link to the other side. After passing through the first acousto-optic modulator AOM1 and the first optical fiber circulator C1, the signal beam is formed and undergoes heterodyne interference with the first local oscillator beam of the first ultra-stable laser Laser1.

[0048] The second radio frequency signal source drives the second acousto-optic modulator AOM2 at a frequency, and divides the local oscillator radio frequency signal emitted by the second radio frequency signal source by the second 2 / N frequency divider;

[0049] The second local oscillator light and the second signal light returned by the second fiber optic circulator C2 are beat-frequency through the second combiner BS4, photoelectric conversion is performed by the second photodetector PD2, and after being divided by the second 1 / N frequency divider, they are phase-detected with the second local oscillator radio frequency signal on the second phase detector. The signal is then filtered by the second low-pass filter LPF2. The filtered signal is phase-tracked by the second adjustable phase shifter, and the phase information is extracted after the phase detection and low-pass filtering of the signal is maintained in real time.

[0050] The phase change information of the fiber optic link was recovered by heterodyne interferometry at the Laser1 end of the first ultra-stable laser. The phase change information of the fiber optic link was recovered by heterodyne interferometry at the Laser2 end of the second ultra-stable laser. and The solution method is the same as that using a single laser.

[0051] Let the frequencies of the light emitted by the first and second ultrastable lasers be v0 and v2, respectively. 10 and v 20 The phases are all The normalized electric field expressions are as follows: and

[0052] The electric fields of the optical signals after being driven by the first and second acousto-optic modulators AOM1 and AOM2 are respectively expressed as: and The driving frequencies of the first and second acousto-optic modulators are both f / 2. Therefore, the frequencies of the signal light after modulation by the first and second acousto-optic modulators are respectively v. 10 +f / 2 and v 20 +f / 2.

[0053] The phase change information of the fiber optic link was recovered after heterodyne interferometry using the first ultrastable laser. The phase change information of the fiber optic link was recovered by heterodyne interferometry using a second ultrastable laser. The electric fields of the signal light after the two phase changes can be expressed as follows: and

[0054] The beat frequency and the radio frequency signals of PD1 and PD2 converted by the first and second detectors are respectively represented as follows: and

[0055] Since the vibrations occur at different locations on the link, the signals detected on both sides arrive at the vibration locations at different times. Therefore, a cross-correlation function is used to cross-correlate the signals detected on both sides.

[0056] The cross-correlation function R(T) is: The time difference T between the arrival of the two signals at the location of the vibration can be obtained. Combined with the speed of light C in the optical fiber, the distance difference between the location of the vibration disturbance and the two lasers can be calculated as: l = CT. Based on the total link length L of the optical fiber, the location of the vibration disturbance can be pinpointed.

[0057] This invention is not limited to fiber optic sensing systems; it is applicable to sensing systems for space light, atmospheric turbulence monitoring, and other applications.

[0058] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0059] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method of calculating phase difference in an optical fiber sensing system, characterized by, The method comprises the following steps: The laser emitted by the super-stable laser is split into two paths by a beam splitter; One path is used as signal light after passing through a fiber-optic circulator and a sound-light modulator, and reaches a mirror, and a radio frequency signal source drives the sound-light modulator; The local oscillator radio frequency signal emitted by the radio frequency signal source is divided by a 2 / N frequency divider; The other path is used as reference light, and the signal light returned by the fiber-optic circulator is beat by a beam combiner, and then is photoelectrically converted by a photoelectric detector, and is divided by a 1 / N frequency divider, and then is phase-detected with the local oscillator radio frequency signal in a phase detector, and is filtered by a low-pass filter; The filtered signal is phase-tracked by an adjustable phase shifter, and the phase information of the signal after phase detection and low-pass filtering is extracted in real time.

2. The method of claim 1, wherein, Let the frequency of the light emitted by the super-stable laser be , the phase be , and the normalized electric field be represented as: , The electric field of the light signal driven by the acousto-optic modulator is represented as: ) , the driving frequency is , and the frequency of the signal light after modulation by the acousto-optic modulator is .

3. The method of claim 2, wherein the phase difference is calculated by: The signal light is transmitted through the optical fiber link and reflected by the mirror at the far end back to the local end. The phase change introduced during the transmission is represented as: The electric field of the signal light is represented as: ) The radio frequency signal converted by the detector through the beat with the reference light is represented as: The phase difference is the phase change information of the optical fiber link.

4. The method of calculating a phase difference according to claim 3, wherein, The frequency after the radio frequency signal is divided by 1 / N divider and represented as: At the same time, the driving signal of AOM is divided by 2 / N divider and represented as: After the adjustable phase shifter, the phase shift is Then, the signals after the two frequency-divided signals are phase-detected and low-pass filtered and represented as: At this time, by adjusting the size of to make the signal close to zero, at this time ≈ , according to the real-time recording of , the size of is calculated.

5. A method of calculating phase difference in an optical fiber sensing system, characterized by, The method comprises the following steps: The first super-stable laser is split by a first beam splitter, one path is used as the first local oscillator light, and the other path is used as signal light, and is transmitted to the opposite side through a long-distance fiber-optic link via a first circulator and a first sound-light modulator, and then is beat with the first local oscillator light of the first super-stable laser after passing through a second sound-light modulator and a second fiber-optic circulator to form the second signal light; A first radio frequency signal source drives the first sound-light modulator, and the local oscillator radio frequency signal emitted by the first radio frequency signal source is divided by a first 2 / N frequency divider; The first local oscillator light is beat with the first signal light returned by the first fiber-optic circulator by a first beam combiner, and then is photoelectrically converted by a first photoelectric detector, and is divided by a first 1 / N frequency divider, and then is phase-detected with the first local oscillator radio frequency signal in a first phase detector, and is filtered by a first low-pass filter; the filtered signal is phase-tracked by a first adjustable phase shifter, and the phase information of the signal after phase detection and low-pass filtering is extracted in real time. Meanwhile, the second super-stable laser is split by a second beam splitter, one path is used as the second local oscillator light, and the other path is used as signal light, and is transmitted to the opposite side through a long-distance fiber-optic link via a second circulator and a second sound-light modulator, and then is beat with the first signal light of the first super-stable laser after passing through a first sound-light modulator and a first fiber-optic circulator to form the first signal light; A second radio frequency signal source drives the second sound-light modulator, and the local oscillator radio frequency signal emitted by the second radio frequency signal source is divided by a second 2 / N frequency divider; The second local oscillator light is beat with the second signal light returned by the second fiber-optic circulator by a second beam combiner, and then is photoelectrically converted by a second photoelectric detector, and is divided by a second 1 / N frequency divider, and then is phase-detected with the second local oscillator radio frequency signal in a second phase detector, and is filtered by a second low-pass filter; the filtered signal is phase-tracked by a second adjustable phase shifter, and the phase information of the signal after phase detection and low-pass filtering is extracted in real time.

6. The method of calculating a phase difference according to claim 5, wherein the phase difference is calculated by The light frequency emitted by the first and second super-stable lasers is respectively and , the phase is respectively , and the normalized electric field expression is respectively: and , The electric field of the light signal driven by the first and second acousto-optic modulators is respectively represented as: and ) The driving frequency of the first and second acousto-optic modulators is The frequency of the signal light after being modulated by the first and second acousto-optic modulators is respectively and .

7. The method of calculating a phase difference according to claim 6, wherein, The phase change information of the fiber link is recovered after the first super-stable laser heterodyne interference The phase change information of the fiber link is recovered after the second super-stable laser heterodyne interference The electric fields of the two phase-changed signal lights are respectively represented as: ) And ) , The beat frequencies and the radio frequencies converted by the first and second detectors are denoted as: and , respectively. The phase change information of the two sides is correlated by a cross-correlation function, and the time difference T of the positions where the two signal lights reach the vibration is calculated, the cross-correlation function is: ； The distance difference l of the position of the disturbance from the two lasers is l=C*T; wherein C is the propagation speed of light in the fiber; according to the link length L of the whole fiber, the position of the disturbance can be located.

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