Method for correcting symmetrical demodulation error of zero difference by fitting an ellipse in space

Abstract

The application discloses a method for correcting error of homodyne symmetrical demodulation by fitting an ellipse in space, which comprises the following steps: taking three-way output data of a fiber 3X3 coupler as a whole of three-dimensional ellipse, fitting a general equation of the plane where the ellipse is located by using a least square method, establishing a new three-dimensional coordinate space by using the plane and its normal line, converting the original three-dimensional coordinate space ellipse into the new three-dimensional coordinate space, obtaining a two-dimensional plane ellipse, fitting a general equation of the two-dimensional plane ellipse by using the least square method, obtaining fitting coordinates of the original three-dimensional space ellipse by using the relationship between the new and old three-dimensional coordinate spaces, and obtaining direct current component, alternating current component coefficient and phase error of the three-way output data by using the maximum and minimum values of three components of the fitting coordinates of the original three-dimensional space ellipse, so as to correct error of homodyne symmetrical demodulation calculation. The application is different from the traditional method of processing two-way output data, and can more objectively obtain system error of a fiber sensing system and is less affected by system random noise.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology for fiber optic sensing systems, and specifically to a method for correcting zero-difference symmetric demodulation errors by spatial elliptic fitting. Background Technology

[0002] Fiber optic interferometry, due to its high sensitivity and ability to detect weak signals, is widely used in fields such as seismic acoustic wave detection, sonar early warning, and pipeline gas leak monitoring. The null-difference symmetric demodulation algorithm (NPS algorithm) based on a fiber optic 33 coupler is a commonly used algorithm for extracting phase signals from fiber optic interferometry sensing systems. However, factors such as the splitting ratio and phase error of the 33 coupler in the fiber optic interferometry sensing system, the sensitivity error of the photodetector, and other system noise affect the accuracy of the NPS algorithm in extracting the system's phase signal [Zhao ZQ, Demokan MS, MacAlpine M. Improved demodulation scheme for fiber optic interferometers using an asymmetric 33 coupler[J]. Journal of Lightwave Technology, 1997, 15(11): 2059-2068.].

[0003] The calculation of zero-difference symmetric demodulation in fiber optic interferometric sensing systems has been a focus of attention. Among the commonly used methods, the piezoelectric ceramic (PZT) modulation method is the most common. This method adds a PZT periodic vibration signal to the fiber optic interferometric sensing system and then extracts the maximum and minimum values ​​of the three interference signals to calculate the DC and AC component coefficients [Li Rizhong. Research on Key Technologies of DFB Fiber Laser Hydrophones [D]. Wuhan: Huazhong University of Science and Technology, 2014: 67-93.]. This method increases the hardware cost of the system and cannot correct the phase error of the three interference signals. Two-dimensional ellipse fitting parameter estimation is also a commonly used method. This method arbitrarily selects two of the three interference signals to form a Lissajous two-dimensional ellipse, and then fits and corrects the relevant parameters of zero-difference symmetric demodulation [Liu Juncheng, Zhang Zichao, Yu Bo, et al. Polarization analysis and processing in the demodulation process of 33 coupler [J]. Acta Photonica Sinica, 2019, 48(1):15-24.]. This method does not consider the relationship between the three interference signals as a whole. In fact, due to the influence of noise, the error correction parameters obtained by fitting different two signals will have deviations. Considering the three interference signals as a whole and using three-dimensional ellipse parameter estimation is a more objective method. Among them, the method of converting the three-dimensional ellipse into a two-dimensional ellipse by matrix singular value decomposition solves the problem of three-dimensional ellipse fitting very well, but the computational load is large [Zhang Huayong, Wang Liwei, Shi Qingping, et al. A new algorithm for demodulation of signals by 33 coupler in time division multiplexing system of fiber optic hydrophone [J]. Chinese Journal of Lasers, 2011, 38(5):0505011.]. Summary of the Invention

[0004] This invention provides a method for correcting zero-difference symmetric demodulation errors by fitting spatial ellipses, in order to solve the problems of low accuracy, large computational load, and high hardware cost in existing technologies for correcting demodulation errors.

[0005] This invention provides a method for correcting zero-difference symmetric demodulation errors through spatial ellipse fitting, comprising:

[0006] Step 1: Obtain the three-channel output data of the 3×3 fiber coupler. Construct a three-dimensional ellipse in the three-dimensional coordinate system using the three-channel output data as three-dimensional coordinate components. Record the current three-dimensional coordinate system as the original three-dimensional coordinate system.

[0007] Step 2: Use the least squares method to fit the general equation of the plane containing the ellipse in three-dimensional space, construct a new three-dimensional space coordinate system with the plane containing the ellipse in three-dimensional space and the normal of the plane, and construct the coordinate transformation relationship between the new three-dimensional space coordinate system and the original three-dimensional space coordinate system.

[0008] Step 3: The coordinate transformation relationship between the new three-dimensional spatial coordinate system and the original three-dimensional spatial coordinate system is used to transform the ellipse in three-dimensional space to the new three-dimensional spatial coordinate system, and obtain the ellipse in two-dimensional plane. Two coordinate components form the ellipse in two-dimensional plane, and the third coordinate component fluctuates slightly around the average value due to noise.

[0009] Step 4: Use the least squares method to fit the general equation of the ellipse in the two-dimensional plane, and obtain the fitting values ​​of the two coordinate components of the ellipse in the two-dimensional plane based on the general equation of the ellipse in the two-dimensional plane.

[0010] Step 5: Obtain the fitting values ​​of the three coordinate components of the ellipse in the original three-dimensional space based on the fitting values ​​of the two coordinate components of the ellipse in the two-dimensional plane in the new three-dimensional space, the average value of the third coordinate component, and the coordinate transformation relationship between the new three-dimensional space coordinate system and the original three-dimensional space coordinate system.

[0011] Step 6: Based on the maximum and minimum values ​​of the three components in the fitting quantity of the ellipse in the original three-dimensional space, obtain the DC component, AC component, and phase error of the three output data of the 3×3 fiber coupler, and complete the correction of the zero-difference symmetrical demodulation calculation error.

[0012] Furthermore, the general equation of the plane containing the ellipse in three-dimensional space, fitted using the least squares method, is as follows:

[0013] Ax + By + Cz + 1 = 0

[0014] Where A, B, and C are the undetermined coefficients of the plane equation, and x, y, and z are the coordinates of the original three-dimensional ellipse.

[0015] Furthermore, the coordinate transformation relationship between the new three-dimensional spatial coordinate system and the original three-dimensional spatial coordinate system is constructed as follows:

[0016]

[0017]

[0018]

[0019]

[0020] Where I1, I2, and I3 are the coordinates of the original three-dimensional spatial coordinate system corresponding to the three output data of the fiber coupler, I′1, I′2, and I′3 are the coordinates of the new three-dimensional spatial coordinate system corresponding to the coordinates of the original three-dimensional spatial coordinate system after transformation, and A, B, and C are the undetermined coefficients of the plane equation.

[0021] Furthermore, the general equation for fitting an ellipse in a two-dimensional plane using the least squares method is:

[0022] b1x2 +b2y 2 +b3xy+b4x+b5y+1=0

[0023] Where b1 to b5 are the undetermined coefficients of the general equation of the ellipse.

[0024] Furthermore, the specific method of step 6 is as follows:

[0025] The current component, AC component coefficients, and phase error of the three signals are obtained using the following formulas:

[0026] D = (I f_max +I f_min ) / 2

[0027] a=(I f_max -I f_min ) / 2

[0028] θ 2,1 =arccos[(I f2 -D2) / a2]+2π / 3

[0029] θ 3,1 =arccos[(I f3 -D3) / a3]+4π / 3

[0030] Where D is the current component; a is the AC component coefficient; θ 2,1 θ represents the phase error between the second signal and the first signal. 3,1 The phase error between the third signal and the first signal; I f_max The maximum value of the fitted quantity; I f_min The minimum value of the fitted quantity; I f2 To calculate the second signal fitting value corresponding to the maximum value of the first signal fitting value; I f3 This is the value of the third signal that corresponds to the maximum value of the first signal fitting value.

[0031] The beneficial effects of this invention are:

[0032] The method for correcting zero-difference symmetric demodulation error by spatial ellipse fitting of the present invention considers the three output data as a whole, constructs an elliptical model of the three output data, adopts spatial coordinate transformation to transform the ellipse in the three-dimensional coordinate system, and obtains the fitting value through a fitting method. Finally, the parameters required for error correction are obtained based on the fitting value. The present invention differs from the traditional method of processing two output data, obtains the system error of the fiber optic sensing system more objectively, reduces the influence of system random noise, greatly reduces the amount of computation, and can obtain the system error without PZT modulation, without increasing the hardware cost of the system. Attached Figure Description

[0033] The features and advantages of the invention will be more clearly understood by referring to the accompanying drawings, which are schematic and should not be construed as limiting the invention in any way. In the drawings:

[0034] Figure 1 This is a flowchart of a specific embodiment of the present invention;

[0035] Figure 2 A two-dimensional ellipse as described in a specific embodiment of the present invention;

[0036] Figure 3 The fitting curve of a two-dimensional ellipse in a specific embodiment of the present invention;

[0037] Figure 4 The values ​​are those specified in the specific embodiments of the present invention;

[0038] Figure 5 This is a fitting curve in a specific embodiment of the present invention;

[0039] Figure 6 The ellipse in three-dimensional space is used in a specific embodiment of the present invention;

[0040] Figure 7 This is a fitted curve of an ellipse in three-dimensional space in a specific embodiment of the present invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] The present invention will be further illustrated below with reference to specific embodiments. Those skilled in the art should understand that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Modifications to the present invention in various equivalent forms all fall within the scope defined by the appended claims.

[0043] This invention provides a method for correcting zero-difference symmetric demodulation errors through spatial ellipse fitting, comprising:

[0044] Step 1: Acquire the three output data from the 3×3 fiber optic coupler. The output light intensity signals are as follows:

[0045] I1=D1+a1cos(θ) (1)

[0046] I² = D² + a²cos(θ - 2π / 3 + Δθ) 2,1(2)

[0047] I3=D3+a3cos(θ-4π / 3+Δθ 3,1 (3)

[0048] In an ideal fiber optic interferometric sensing system under noise-free conditions, with the 3×3 fiber coupler having a splitting ratio of 1:1:1, and the three photodetectors connected to the 3×3 fiber coupler having the same sensitivity, the three voltage signals acquired by the data card will have the same DC component (D1 = D2 = D3), the same AC component coefficient (a3 = a3 = a3), and a phase difference of 2π / 3, where the phase error θ 2,1 =θ 3,1 =0.

[0049] In practical fiber optic interferometric sensing systems, due to system errors and noise, the DC and AC components of the three signals are not identical, and the phase difference also deviates from 2π / 3. This leads to errors in zero-difference symmetrical demodulation. Therefore, it is necessary to solve for D1, D2, D3, a1, a2, a3, and θ. 2,1 θ 3,1 I1, I2, and I3 are corrected, and then zero-difference symmetric demodulation calculation is performed to improve the phase calculation accuracy of the fiber optic interferometric sensing system.

[0050] In a three-dimensional spatial coordinate system, an ellipse in three-dimensional space is constructed using the three-way output data as three-dimensional coordinate components, and the current three-dimensional spatial coordinate system is denoted as the original three-dimensional spatial coordinate system.

[0051] The data acquisition card acquired I 1(i) I 2(i) and I 3(i) In the three-dimensional space o-xyz, if we take them as coordinate components respectively, we will form the following: Figure 6 The ellipse L1 in the three-dimensional space shown;

[0052] Step 2: Due to noise, the edges of ellipse L1 are irregular, requiring fitting. The general equation of the plane containing the ellipse in three-dimensional space is obtained by fitting using the least squares method:

[0053] Ax + By + Cz + 1 = 0 (4)

[0054] A new 3D coordinate system o'-x'y'z' is constructed using the plane containing the ellipse in 3D space and the plane's normal. The coordinate transformation relationship between the new 3D coordinate system and the original 3D coordinate system is established, and the transformation formula is as follows:

[0055]

[0056]

[0057]

[0058]

[0059] Step 3: Based on the general equation of the plane containing the ellipse in three-dimensional space and the coordinate transformation relationship between the new three-dimensional space coordinate system and the original three-dimensional space coordinate system, transform the ellipse in three-dimensional space to the new three-dimensional space coordinate system to obtain the ellipse in the two-dimensional plane.

[0060] Equation (5) can transform the three-dimensional ellipse L1 in the o-xyz space into a two-dimensional ellipse L2 in the o'-x'y'z' space. The two-dimensional ellipse L2 is as follows: Figure 2 As shown, the coordinate components of L2 are I′ 1(i) 、I' 2(i) .

[0061] Step 4: Use the least squares method to fit the general equation of the ellipse in the two-dimensional plane, and obtain the fitting values ​​of the three coordinate components of the ellipse in the two-dimensional plane based on the general equation of the ellipse in the two-dimensional plane.

[0062] By performing least-squares fitting on the two-dimensional ellipse L2, we can obtain I′. 1(i) 、I' 2(i) Fitting quantity I' f1(i) 、I' f2(i) I' 3(i) Due to noise, it fluctuates slightly around its mean, so we take I′. 3(i) The average value is used as its fitted value I' f3(i) The fitted curve is as follows Figure 3 , 5 As shown.

[0063] Step 5: Obtain the fitting values ​​of the three coordinate components of the ellipse in three-dimensional space based on the fitting values ​​of the three coordinate components of the ellipse in the two-dimensional plane and the coordinate transformation relationship between the new three-dimensional space coordinate system and the original three-dimensional space coordinate system.

[0064] Based on the fitted values ​​of the three coordinate components of the ellipse in the two-dimensional plane, and combined with formula (6), the three components I of the three-dimensional ellipse L1 in the o-xyz space can be obtained. 1(i) I 2(i) and I 3(i) Fitting quantity I f1(i) I f2(i) and I f3(i) ,like Figure 7 As shown.

[0065] Step 6: Based on the maximum and minimum values ​​of the three components in the fitting of the ellipse in the original three-dimensional space, obtain the DC component, AC component, and phase error of the three output data of the 3×3 fiber coupler, and complete the correction of the zero-difference symmetrical demodulation calculation error.

[0066] Search I respectively f1(i) I f2(i) and I f3(i) The maximum and minimum values ​​are denoted as I. f1_max I f2_max I f3_max and I f1_min I f2_min I f3_min Then, from equations (1)-(3), we can obtain:

[0067] D1=(I f1_max +I f1_min ) / 2 (9)

[0068] a1=(I f1_max -I f1_min ) / 2 (10)

[0069] D2=(I f2_max +I f2_min ) / 2 (11)

[0070] a2=(I f2_max -I f2_min ) / 2 (12)

[0071] D3=(I f3_max +I f3_min ) / 2 (13)

[0072] a3=(I f3_max -I f3_min ) / 2 (14)

[0073] Remember I f1_max The other two corresponding coordinate components are I f2 I f3 At this time, the value of θ in equations (1)-(3) is 0, so according to equations (2) and (3), we can first obtain I. f2 D2, a2, I f3 D3, a3, then calculate the phase error θ 2,1 θ 3,1 The specific formula is as follows:

[0074] θ 2,1 =arccos[(I f2 -D2) / a2]+2π / 3

[0075] θ 3,1 =arccos[(I f3 -D3) / a3]+4π / 3

[0076] The method of the present invention will be described below by way of example:

[0077] The simulation values ​​for I1, I2, and I3 are as follows:

[0078] I1=4+2cos(θ)+ε (15)

[0079] I2=5+3cos(θ-2π / 3+0.6)+ε (16)

[0080] I3=6+6cos(θ-4π / 3+0.8)+ε (17)

[0081] Where θ = 1 / 2cos(2πt), t is time, and ε is Gaussian white noise.

[0082] The present invention is used to solve the DC component, AC component coefficient and phase error in equations (15)-(17).

[0083] Establish an o-xyz space. The original three-dimensional elliptical coordinates are: I1, I2, I3. The graph of the three-dimensional ellipse is as follows. Figure 5 As shown, the general equation of the plane containing the three-dimensional ellipse, obtained using the least squares method, is:

[0084] -0.1435x-0.0247y-0.0504z+1=0 (17)

[0085] Then, we can find θ1 = -2.6854 and θ2 = -1.1985 in equations (7) and (8), and substitute them into equation (5) to obtain the two-dimensional plane ellipse in the o-x'y'z' space, as shown below. Figure 2 As shown, the general equation of the ellipse is obtained by fitting it using the least squares method:

[0086] 0.0668x 2 +0.1230y 2 +0.1513xy+0.6481x+0.8721y+1=0 (18)

[0087] The average value of I'3(i) is -6.4859.

[0088] Using equation (18) and I′ 3(i) The average value, and equation (6) can be used to fit the original three-dimensional ellipse L1, such as Figure 6 As shown.

[0089] Therefore, D1, D2, D3, a1, a2, a3, and θ can be calculated using equations (9)-(14). 2,1 θ 3,1 Table 1 below shows a list of correction parameters obtained using spatial ellipse fitting.

[0090]

[0091] Table 1

[0092] The correction parameters obtained in Table 1 are basically consistent with the parameters preset in equations (15)-(17), which shows that it is feasible to correct the zero-difference symmetric demodulation error by fitting the spatial ellipse.

[0093] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A method of fitting a space ellipse to correct for a homodyne symmetrical demodulation error, characterized by, Comprising the following steps: Step 1: Obtain the three-way output data of the fiber 3x3 fiber coupler, and construct an ellipse of three-dimensional space in a three-dimensional coordinate system with the three-way output data as three-dimensional coordinate components; the current three-dimensional coordinate system is recorded as the original three-dimensional coordinate system; Step 2: Fit the general equation of the plane where the ellipse of the three-dimensional space is located by using the least square method, and construct a new three-dimensional coordinate system with the plane where the ellipse of the three-dimensional space is located and the normal line of the plane; construct the coordinate conversion relationship between the new three-dimensional coordinate system and the original three-dimensional coordinate system; Step 3: According to the coordinate conversion relationship between the new three-dimensional coordinate system and the original three-dimensional coordinate system, convert the ellipse of the three-dimensional space to the new three-dimensional coordinate system to obtain the ellipse of a two-dimensional plane, wherein two coordinate components constitute the ellipse of the two-dimensional plane, and the third coordinate component is affected by noise and fluctuates slightly around the average value; Step 4: Fit the general equation of the ellipse of the two-dimensional plane by using the least square method, and obtain the fitting amount of the two coordinate components of the ellipse of the two-dimensional plane according to the general equation of the ellipse of the two-dimensional plane; Step 5: Obtain the fitting amount of the three coordinate components of the ellipse of the original three-dimensional space according to the fitting amount of the two coordinate components of the ellipse of the two-dimensional plane in the new three-dimensional space, the average value of the third coordinate component, and the coordinate conversion relationship between the new three-dimensional coordinate system and the original three-dimensional coordinate system; Step 6: Obtain the direct current component, alternating current component and phase error of the three-way output data of the 3x3 fiber coupler according to the maximum and minimum values of the three components in the fitting amount of the ellipse of the original three-dimensional space, and complete the correction of the error of the homodyne symmetric demodulation.

2. The method for correcting zero-difference symmetric demodulation error by spatial ellipse fitting as described in claim 1, characterized in that, The general equation of the plane where the ellipse of the three-dimensional space is fitted by using the least square method is: Ax+By+Cz+1=0 Wherein, A, B, C are the undetermined coefficients of the plane equation, and x, y, z are the coordinates of the ellipse of the original three-dimensional space.

3. The method of fitting a space ellipse to correct for symmetrical demodulation errors in a homodyne system as claimed in claim 1 or 2, characterized in that, The coordinate conversion relationship between the new three-dimensional coordinate system and the original three-dimensional coordinate system is as follows: Wherein, I1, I2, I3 are the coordinates of the three-way output data of the fiber coupler corresponding to the original three-dimensional coordinate system, I1', I'2, I3' are the coordinates of the new three-dimensional coordinate system corresponding to the coordinates of the original three-dimensional coordinate system after conversion, A, B, C are the undetermined coefficients of the plane equation.

4. The method for correcting zero-difference symmetric demodulation error by spatial ellipse fitting as described in claim 1, characterized in that, The general equation of the ellipse of the two-dimensional plane fitted by using the least square method is: b1x 2 +b2y 2 +b3xy+b4x+b5y+1=0 Wherein, b1~b5 are the undetermined coefficients of the general equation of the ellipse.

5. The method for correcting zero-difference symmetric demodulation error by spatial ellipse fitting as described in claim 1, characterized in that, The specific method of step 6 is: The current component, alternating current component coefficient and phase error of the three-way signal are obtained by the following formula respectively: D = (I f_max + I f_min ) / 2 a = (I f_max - I f_min ) / 2 θ 2,1 = arccos[(I f2 -D2) / a2]+2π / 3 θ 3,1 = arccos[(I f3 -D3) / a3]+4π / 3 Wherein, D is the current component; a is the AC component coefficient; θ 2,1 is the phase error between the second signal and the first signal; θ 3,1 is the phase error between the third signal and the first signal; I f_max is the maximum value of the fitting quantity; I f_min is the minimum value of the fitting quantity; I f2 is the second signal fitting quantity corresponding to the calculation of the maximum value of the first signal fitting quantity; I f3 is the third signal fitting quantity corresponding to the calculation of the maximum value of the first signal fitting quantity.

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