CN108534811B - Cavity length demodulation algorithm of short-cavity optical fiber Fabry-Perot sensor - Google Patents
Cavity length demodulation algorithm of short-cavity optical fiber Fabry-Perot sensor Download PDFInfo
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Abstract
The invention discloses a cavity length demodulation algorithm of a short-cavity optical fiber Fabry-Perot sensor, and belongs to the technical field of optical fiber sensing. The method is characterized in that broadband light emitted by a white light source is adopted to irradiate the short-cavity fiber Fabry-Perot sensor, the reflection spectrum of the short-cavity fiber Fabry-Perot sensor is collected, an original reflection spectrum signal is moved for a certain distance along the abscissa direction of a power spectrum density graph to obtain a newly added reflection spectrum signal, the moving distance of the newly added reflection spectrum signal is smaller than the period length of the reflection spectrum signal, the phase difference between the original spectrum signal and the newly added spectrum signal is obtained by an ellipse fitting method, and an actual absolute cavity length value is obtained according to a Fabry-Perot cavity length calculation formula. The invention solves the problem of cavity length demodulation when the spectrum acquired by the demodulation system of the short-cavity optical fiber Fabry-Perot sensor is incomplete, and reduces the requirement of the system on the spectrum range of a light source.
Description
Technical Field
The invention belongs to the technical field of optical fiber sensing, and particularly relates to a cavity length demodulation algorithm of a short-cavity optical fiber Fabry-Perot sensor.
Background
The optical fiber Fabry-Perot sensor is an important type in a phase type optical fiber sensor, has small and exquisite appearance and is easy to manufacture, and compared with the similar electronic sensors, the optical fiber Fabry-Perot sensor has the advantages of small volume, light weight, high sensitivity, no electromagnetic interference influence, remote sensing and the like. Due to the multiple selectivity of Fabry-Perot cavity materials, the optical fiber sensor can be suitable for severe industrial and military environments such as high temperature, high pressure, strong chemical corrosion, strong electromagnetic interference and the like, such as the measurement of pressure and temperature under a deep oil well, the health monitoring of bridges and dams, the sound wave detection of nuclear explosion experimental sites, the health monitoring of large-scale electric power and energy equipment and the like, and can also be applied to the measurement of internal pressure in the biomedical field and the like.
The optical fiber Fabry-Perot sensing system is divided into a sensor and a demodulation system. The cavity length demodulation is the construction of the whole demodulation system, and directly influences the demodulation precision, the stability of the system and other performances. Currently, the mainly used demodulation methods are: phase demodulation and intensity demodulation. The earlier used intensity demodulation method has the advantages of high response speed, simple structure, low cost and the like, but the demodulation precision is low due to the influence of the fluctuation of the optical power of a light source and the larger loss of light in an optical fiber.
At present, fourier transform methods in phase demodulation methods are widely used. The method has the advantages of large dynamic range and no influence of phase noise. However, due to the fence effect existing in the fourier transform method, the effective information points are blocked, and the frequency resolution is reduced. The frequency resolution is improved only by increasing the number of sampling points and improving the spectrum measurement range, and the Fabry-Perot cavity length demodulation method is not suitable for the Fabry-Perot sensing system with a narrow light source spectrum. Correlation demodulation in phase demodulation reduces the spectral measurement range requirements compared to fourier transform methods, but at the same time requires the presence of a complete period of signal within the measured spectral range. The Fabry-Perot sensors with the cavity length smaller than 30 mu m belong to the Fabry-Perot sensors with the short cavity length, for example, the Fabry-Perot sensors with the cavity length of 20 mu m are taken as the Fabry-Perot sensors, when the central wavelength of an ASE light source is 1550nm, the distance between two adjacent peaks of a reflected spectrum signal is calculated to be about 62nm, the spectrum width of the ASE light source is generally about 40nm, the spectrum signal with the complete period cannot be obtained, and the spectrum signal cannot be resolved by using a correlation method.
In the related technology, for example, in a cavity length demodulation algorithm of an optical fiber F-P sensor (patent number: CN 1831485A), a quality evaluation method of a mean square error to a cavity length estimator of an F-P sensing head is provided. The light source used in the examples provided by the patent was in the range of 80nm, the spectral sequence length was 2000, and the average cavity length was measured to be 303.9 μm. Through calculation, the captured spectrum has at least 1 complete spectrum period and requires more sampling points. In "an extrinsic fiber Fabry-Perot cavity length demodulation method" (patent No. CN 103697923A), a multi-wavelength intensity demodulation method is proposed, which aims at cavity length demodulation of more than 100 μm and needs a plurality of lasers with different wavelengths as light sources to measure a plurality of return intensity values. From the above-mentioned known documents, there is no need for a method of demodulating an incomplete spectrum using a spectroscopic method in a demodulation system to obtain a cavity length and a scheme in which the demodulation accuracy of the cavity length is low in this case.
Disclosure of Invention
The invention aims to provide a cavity length demodulation algorithm of a short-cavity optical fiber Fabry-Perot sensor, which solves the problems that the cavity length and the cavity length demodulation precision are low because the incomplete spectrum cannot be demodulated by using a spectrum method in the prior art, and simultaneously solves the problem that the light source bandwidth is required to be wider.
The technical scheme adopted by the invention is as follows:
a cavity length demodulation algorithm of a short-cavity optical fiber Fabry-Perot sensor is characterized in that:
the algorithm process is as follows:
collecting the reflection spectrum of the short-cavity optical fiber Fabry-Perot sensor, moving the original reflection spectrum signal for a certain distance along the abscissa direction of a power spectrum density graph to obtain a newly added reflection spectrum signal, wherein the moving distance is smaller than the period length of the reflection spectrum signal, solving the phase difference between the original spectrum signal and the newly added spectrum signal by using an ellipse fitting method, and obtaining an actual absolute cavity length value according to a Fabry-Perot cavity length calculation formula.
The cavity length demodulation algorithm of the short-cavity optical fiber Fabry-Perot sensor is characterized in that:
the method comprises the following steps:
step 1: wavelength-frequency domain transformation: converting the wavelength domain into the frequency domain of spectral data of a reflection spectrum of a short-cavity fiber Fabry-Perot sensor collected by a spectrum analyzer in a demodulation system by using a formula f (c/lambda), namely converting the abscissa of a power spectral density graph from the wavelength lambda of light waves into the frequency f of the light waves to obtain a periodic frequency domain power spectral density graph, wherein c is the vacuum light speed;
step 2: calculating the offset m of the spectral signalxCalculating the maximum of the relative intensity of the spectral signal S (f)maxAnd S (f) of minimum valueminMean value; formula (II)Comprises the following steps:
mx＝(S(f)max-S(f)min)/2
and step 3: coordinate transformation, namely establishing a simplified ellipse fitting equation, and translating a reflection spectrum signal S (f) along the direction of an f axis by a distance tau to obtain two signals s (f) and s (f + tau) with the same amplitude and angular frequency, wherein the tau is less than the period of s (f); the relative intensity values of the two signals are respectively used as the horizontal and vertical coordinate axes of the Lissajous figure, the drawn Lissajous figure is an ellipse, the included angle between the long axis or the short axis of the ellipse and the X axis of the XY coordinate system is always 45 degrees, the coordinate system is rotated by 45 degrees anticlockwise to obtain a new coordinate system of X 'Y', and the ellipse is translated to the direction of the origin of the X 'Y' coordinate system
The focus F of the ellipse at this time1And F2On the X' axis and symmetrical with respect to the origin, let the coordinates of n points on the ellipse be (X)i',yi') the elliptic equation is:
and 4, step 4: solving an overdetermined equation set by using a least square method to obtain a correlation coefficient; establishing a linear equation set AX as 1 according to the elliptic equation obtained in the step 3; i.e. the matrix form is as follows:
solving correlation coefficients a and b according to an algorithm solved by an overdetermined equation set;
and 5: judging whether the offset is proper: according to the step 4, the correlation coefficients a and b are substituted to obtain an ellipse fitting equation, the residual standard deviation of the equation is S, and whether S meets the threshold Sm (0)<Sm<1) (ii) a If the m does not meet the requirement, m is obtained by calculation in the step 2xBased on the step length of 0.1, a new m is obtainedxExecuting the steps 3 and 4 until the threshold value Sm is met, and then executing the steps 6 and 7;
step 6: and (3) calculating the phase difference and the signal period of the signal according to the ratio of the correlation coefficients: the correlation coefficients a and b are a major semi-axis a and a minor semi-axis b of the ellipse; thus the phase difference
Can be expressed as:
obtaining a signal period according to the relation between the phase difference and the period:
and 7: according to the calculation formula of the cavity length
And obtaining the Fabry-Perot cavity length value.
The invention has the following advantages:
1. the invention adopts the Lissajous figure improvement algorithm, and the cavity length value of the Fabry-Perot cavity can be calculated without a spectrum signal of a complete period. The invention solves the fence effect in Fourier transform, reduces the frequency resolution and shortens the spectral measurement range. The spectrum demodulation method is suitable for spectrum signal demodulation with short cavity length, large spectrum period and incomplete period in a shorter spectrum range, and reduces the requirement on the bandwidth of a light source.
2. The invention introduces two concepts of coordinate conversion and residual standard deviation, and fits a Lissajous figure with an ellipse figure on two signals with the same frequency and amplitude, wherein the included angle between the major axis or the minor axis and the abscissa is always 45 degrees. And rotating by 45 degrees through coordinate conversion, judging and searching only proper signal offset by using a residual standard deviation concept, further converting the ellipse into a positive ellipse with the center of the ellipse at the origin of coordinates, converting a general 6-parameter elliptic equation into a two-parameter elliptic equation, simplifying the establishment of the elliptic equation and obtaining accurate correlation coefficients a and b.
3. The cavity length value of the Fabry-Perot cavity is obtained through phase calculation, the phase resolution ratio in demodulation changes faster than the frequency resolution ratio, and the absolute cavity length value at the moment can be reflected more accurately.
Drawings
Fig. 1 is a schematic structural diagram of an embodiment of the present invention.
FIG. 2 is a flowchart illustrating an operation according to an embodiment of the present invention.
Fig. 3 is a diagram of a signal transformed to a frequency domain with an offset.
FIG. 4 is a Lissajous diagram of the signal S (f) and the signal S (f + τ).
Fig. 5 is a lissajous figure after coordinate transformation and translation.
Detailed Description
The present invention will be described in detail with reference to specific embodiments.
In order to make the objects, technical solutions and advantages of the present invention clearer, the present invention will be described in further detail with reference to the accompanying drawings, and it is apparent that the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The utility model provides a chamber length demodulation algorithm of short chamber optic fibre Fabry-Perot sensor, adopts ellipse fitting method to carry out the absolute chamber length value demodulation of high accuracy to the short chamber optic fibre Fabry-Perot sensor reflectance spectrum that the spectrometer gathered, its characterized in that: collecting the reflection spectrum of the short-cavity optical fiber Fabry-Perot sensor, translating the reflection spectrum signal S (f) along the f-axis direction for a distance tau to obtain a translated spectrum signal S (f + tau), solving the phase difference between the spectrum signal S (f) and the spectrum signal S (f + tau) by using an ellipse fitting method, and obtaining an actual absolute cavity length value according to a Fabry-Perot cavity length calculation formula. High-resolution cavity length demodulation with a narrow spectral range is realized, and thus measured physical quantity information with high resolution is obtained.
An embodiment of the invention is described below:
FIG. 1 shows a measurement system suitable for measuring the cavity length of a Fabry-Perot cavity, wherein broadband light emitted by an ASE white light source in the system irradiates a short-cavity optical fiber Fabry-Perot sensor through an optical circulator, reflected light is emitted from a port 3 of the optical circulator and is converted into an electric signal through a spectrometer, a demodulation circuit collects the signal and carries out cavity length calculation by using a program written by the algorithm, and an upper computer displays the calculation result. Selecting an ASE white light broadband light source as a system light source, wherein the spectral range of the light source is 1524nm-1570nm, the central wavelength is as follows: 1550 nm. Taking a short cavity fiber Fabry-Perot sensor with a cavity length of 20 μm as an example, the distance between two adjacent peaks of a reflected spectrum signal is about 62nm, and one cycle cannot be completely acquired by measurement of the system.
Referring to fig. 2, a cavity length demodulation algorithm of a short cavity fiber fabry-perot sensor, which adopts an ellipse fitting method to demodulate the reflected spectrum of the short cavity fiber fabry-perot sensor acquired by a spectrometer, and carries out high-precision absolute cavity length value demodulation, and is characterized in that: the method comprises the steps of collecting a reflection spectrum of a short-cavity optical fiber Fabry-Perot sensor, moving an original reflection spectrum signal for a certain distance along the abscissa direction of a power spectrum density graph to obtain a newly added reflection spectrum signal, wherein the moving distance is smaller than the period length of the reflection spectrum signal, solving a phase difference between the original spectrum signal and the newly added spectrum signal by using an ellipse fitting method, and obtaining an actual absolute cavity length value according to a Fabry-Perot cavity length calculation formula. High-resolution cavity length demodulation with a narrow spectral range is realized, and thus measured physical quantity information with high resolution is obtained.
The method comprises the following specific steps:
step 1: the method comprises the steps of wavelength-frequency domain conversion, wherein spectrum data of a reflection spectrum of a short-cavity fiber Fabry-Perot sensor collected by a spectrum analyzer in a demodulation system, namely the distribution relation of the power spectrum density in a power spectrum density graph about light wave wavelength, conversion from a wavelength domain to a frequency domain is carried out through a formula f which is c/lambda, namely the abscissa of the power spectrum density graph is converted from the light wave wavelength lambda into the light wave frequency f, and a periodic frequency domain power spectrum density graph is obtained, wherein c is the vacuum light speed.
Step 2: calculating the offset m of the spectral signalxI.e. calculating the spectral informationMaximum of number relative intensity S (f)maxAnd S (f) of minimum valueminMean value; the formula is as follows:
mx＝(S(f)max-S(f)min)/2
and step 3: and (3) coordinate transformation, establishing a simplified ellipse fitting equation, and translating the reflection spectrum signal S (f) along the f-axis direction by a distance tau to obtain two signals s (f) and s (f + tau) with the same amplitude and angular frequency, wherein the tau is less than the period of s (f). The relative intensity values of the two signals are respectively used as the horizontal and vertical coordinate axes of the Lissajous figure, the drawn Lissajous figure is an ellipse, the included angle between the long axis of the Lissajous figure and the X axis of the XY coordinate system is 45 degrees, the coordinate system is rotated anticlockwise by 45 degrees to obtain a new coordinate system of an X 'Y' coordinate system, and the coordinate conversion relation in the XY coordinate system and the X 'Y' coordinate system is as follows:
simultaneously translating the ellipse to the direction of the origin of coordinates of X' Y
The focus F of the ellipse at this time1And F2On the X' axis and symmetrical with respect to the origin, let the coordinates of n points on the ellipse be (X)i',yi') the elliptic equation is:
and 4, step 4: and solving the overdetermined equation set by using a least square method to obtain a correlation coefficient. Establishing a linear equation set AX as 1 according to the elliptic equation obtained in the step 3; i.e. the matrix form is as follows:
and solving the correlation coefficients a and b according to an algorithm for solving the overdetermined equation set.
And 5: judging whether the offset is proper: and (4) obtaining an ellipse fitting equation by substituting the correlation coefficients a and b according to the step 4, wherein the residual standard deviation of the equation is S, and the residual standard deviation S can be expressed as:
it is judged whether S satisfies the threshold Sm (0)<Sm<1) (ii) a If the m does not meet the requirement, m is obtained by calculation in the step 2xBased on the step length of 0.1, a new m is obtainedxExecuting the steps 3 and 4 until the threshold value Sm is met, and then executing the steps 6 and 7;
step 6: and (3) calculating the phase difference and the signal period of the signal according to the ratio of the correlation coefficients: the correlation coefficients a, b are the major half axis a and the minor half axis b of the ellipse, so that the phase difference
Can be expressed as:
the signal period obtained from the relationship between the phase difference and the period can be expressed as:
and 7: according to the calculation formula of the cavity length
And obtaining the Fabry-Perot cavity length value.
Referring to FIG. 3, the original signal with offset is shown, and the offset m is obtained by estimationxIs 105. The original signal is S (f), and the translated signal is S (f + τ), where τ is 600 GHz. Drawing letterThe Lissajous figure (figure 4) of the signal S (f) and the signal S (f + tau) is converted into the X 'Y' coordinate system from the XY coordinate system by coordinate conversion and translated to the direction of the origin of coordinates
A positive ellipse is obtained (fig. 5). The coordinate transformation of the Lissajous figure from figure 4 to figure 5 realizes the simplification of establishing an elliptic equation, and establishes an elliptic equation containing 2 unknowns:
and establishing a positive over definite equation set to obtain a and b. And substituting an ellipse equation to obtain the requirement that the residual standard deviation S is 0.172 and is greater than the threshold Sm is 0.05. The offset value is increased by step size 0.1, and when m is calculated to be 110, the remaining standard deviation S is 0.0300, which is smaller than the requirement of threshold value 0.05. At this time, m is 110, which is the offset value of this signal. Further, the phase difference is obtained
The period T is 7503 and the cavity length L is 19.992 μm.
The invention is not limited to the examples, and any equivalent changes to the technical solution of the invention by a person skilled in the art after reading the description of the invention are covered by the claims of the invention.
Claims (1)
1. A cavity length demodulation algorithm of a short-cavity optical fiber Fabry-Perot sensor is characterized in that:
the algorithm process is as follows:
collecting the reflection spectrum of a short-cavity optical fiber Fabry-Perot sensor, moving an original reflection spectrum signal for a certain distance along the abscissa direction of a power spectrum density graph to obtain a newly added reflection spectrum signal, wherein the moving distance is smaller than the period length of the reflection spectrum signal, solving the phase difference between the original spectrum signal and the newly added spectrum signal by using an ellipse fitting method, and obtaining an actual absolute cavity length value according to a Fabry-Perot cavity length calculation formula;
the method comprises the following steps:
step 1: wavelength-frequency domain transformation: converting the wavelength domain into the frequency domain of spectral data of a reflection spectrum of a short-cavity fiber Fabry-Perot sensor collected by a spectrum analyzer in a demodulation system by using a formula f (c/lambda), namely converting the abscissa of a power spectral density graph from the wavelength lambda of light waves into the frequency f of the light waves to obtain a periodic frequency domain power spectral density graph, wherein c is the vacuum light speed;
step 2: calculating the offset m of the spectral signalxCalculating the maximum of the relative intensity of the spectral signal S (f)maxAnd S (f) of minimum valueminMean value; the formula is as follows:
mx＝(S(f)max-S(f)min)/2
and step 3: coordinate transformation, namely establishing a simplified ellipse fitting equation, and translating a reflection spectrum signal S (f) along the direction of an f axis by a distance tau to obtain two signals s (f) and s (f + tau) with the same amplitude and angular frequency, wherein the tau is less than the period of s (f); the relative intensity values of the two signals are respectively used as the horizontal and vertical coordinate axes of the Lissajous figure, the drawn Lissajous figure is an ellipse, the included angle between the major axis or the minor axis of the ellipse and the X axis of the XY coordinate system is always 45 degrees, the coordinate system is rotated anticlockwise by 45 degrees to obtain a new coordinate system of X 'Y' coordinate system, the ellipse is translated to the direction of the origin of the X 'Y' coordinate by m,
the focus F of the ellipse at this time1And F2On the X' axis and symmetrical with respect to the origin, let the coordinates of n points on the ellipse be (X)i',yi') the elliptic equation is:
and 4, step 4: solving an overdetermined equation set by using a least square method to obtain a correlation coefficient; establishing a linear equation set AX as 1 according to the elliptic equation obtained in the step 3; i.e. the matrix form is as follows:
solving correlation coefficients a and b according to an algorithm solved by an overdetermined equation set;
and 5: judging whether the offset is proper: obtaining an ellipse fitting equation according to the back substitution correlation coefficients a and b in the step 4, judging whether S meets a threshold value S or not, wherein the residual standard deviation of the equation is Sm，0<Sm<1; if the m does not meet the requirement, m is obtained by calculation in the step 2xBased on the step length of 0.1, a new m is obtainedxExecuting the steps 3 and 4 until the threshold value Sm is met, and then executing the steps 6 and 7;
step 6: and (3) calculating the phase difference and the signal period of the signal according to the ratio of the correlation coefficients: the correlation coefficients a and b are a major semi-axis a and a minor semi-axis b of the ellipse; thus the phase difference
Can be expressed as:
obtaining a signal period according to the relation between the phase difference and the period:
and 7: according to the calculation formula of the cavity length
And obtaining the Fabry-Perot cavity length value.
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| CN109141492B (en) * | 2018-10-22 | 2021-04-06 | 西安光微科技有限公司 | Optical fiber Fabry-Perot sensor cavity length demodulation system and demodulation method |
| CN111323059B (en) * | 2018-12-17 | 2021-08-17 | 中国科学院深圳先进技术研究院 | Sensing device based on fiber Bragg grating Fabry-Perot cavity |
| CN110057386A (en) * | 2019-04-30 | 2019-07-26 | 电子科技大学 | The demodulation method and its demodulating equipment of optical fiber FP sensor based on full spectrum |
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| CN110174068A (en) * | 2019-05-23 | 2019-08-27 | 西安工业大学 | A kind of sensitizing type Fabry-perot optical fiber microcavity strain transducer and preparation method thereof |
| CN110595516B (en) * | 2019-09-18 | 2020-12-18 | 华中科技大学 | FPI cavity length demodulation method and system |
| CN110793557B (en) * | 2019-11-12 | 2021-07-02 | 西安工业大学 | Cavity length demodulation method for short-cavity optical fiber Fabry-Perot sensor |
| CN111006611B (en) * | 2019-12-20 | 2021-10-22 | 哈尔滨工业大学（深圳） | Rapid high-precision phase extraction method based on two-step nonlinear phase shifting |
| CN112050942B (en) * | 2020-07-30 | 2021-06-15 | 东北大学 | Optical fiber interference spectrum cavity length correction method based on phase compensation |
| CN114777833B (en) * | 2022-04-29 | 2023-11-28 | 西安和其光电科技股份有限公司 | System and method for adjusting cavity length consistency of extrinsic Fabry-Perot optical fiber sensing probe |
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