High-precision sweep-frequency interferometric distance measurement method for eliminating residual nonlinearity

Abstract

The application discloses a high-precision sweep-frequency interference distance measurement method for eliminating residual nonlinearity. The method comprises the following steps: obtaining a measurement interference signal and an auxiliary interference signal of a sweep-frequency laser light source through a sweep-frequency interference absolute distance measurement system; constructing a differential equation of an optical frequency and an auxiliary interferometer phase, and obtaining an optical frequency signal by solving the differential equation; constructing a high-order orthogonal basis according to the optical frequency signal, and performing orthogonal decomposition on the measurement interference signal in the optical frequency domain by using the high-order orthogonal basis to obtain a distance value to be measured. The application obtains an optical frequency variation based on the idea of solving the differential equation, and then performs high-order Fourier transform on the optical frequency domain of the measurement interferometer, so that the residual nonlinearity introduced due to the large difference between the arm lengths of the auxiliary and measurement interferometers can be eliminated, and a super-high-precision distance measurement result is further obtained. In addition, the method is not limited by the nonlinearity of laser, and high distance measurement precision can still be obtained for a medium-long distance target to be measured.

Description

Technical Field

[0001] This invention relates to the field of laser ranging technology, and in particular to a high-precision swept-frequency interferometric ranging method for eliminating residual nonlinearity. Background Technology

[0002] Frequency Modulated Continuous Wave (FMCW) laser ranging is a cutting-edge technology for achieving high-precision, large-size, non-cooperative three-dimensional measurement of targets, and it has significant application value in high-end manufacturing fields such as aerospace. The core of FMCW laser ranging is to achieve high-precision absolute distance measurement through frequency-modulated laser beat interferometry. This method has advantages such as a large measurement range, no ranging blind zone, and no dependence on cooperative targets.

[0003] FMCW laser ranging systems utilize a relatively linear frequency-modulated laser as the light source. The emitted and echo signals are interfered to form a stable beat frequency signal to calculate the target distance. Therefore, FMCW ranging systems have extremely stringent requirements for the linearity of laser frequency modulation. However, in practical applications, laser frequency modulation is affected by factors such as temperature control and the external environment, resulting in non-linearity. This further causes frequency ambiguity in the target beat frequency signal, leading to false sidelobes and "ghosting" phenomena, which significantly limit the accuracy and range resolution of the ranging system.

[0004] To overcome the effects of frequency sweep nonlinearity, researchers both domestically and internationally have proposed different solutions from both hardware and software perspectives. Hardware technologies primarily include the photoelectric phase-locked loop (PLL) feedback control method, which compares the beat frequency signal of the auxiliary interferometer with a fixed-frequency external reference signal using a lock-in amplifier. The error signal is then fed back to the laser's drive control module, achieving linear frequency modulation control of the laser. However, this method has a relatively complex structure and parameter tuning process, is highly sensitive to environmental conditions, and is prone to lockout. Furthermore, this method is challenging for lasers with high sweep speeds and large sweep ranges. Software methods mainly include: ① Equal-frequency interval resampling method: This method uses the beat frequency signal of the auxiliary interferometer path as a clock signal and extracts its peak-valley points or zero points as feature points to resample the beat frequency signal of the measurement interferometer path, ensuring accurate frequency information and measurement results. However, this method requires an auxiliary interferometer longer than twice the arm length difference of the measuring interferometer, which places stringent requirements on the system sampling rate and the calibration accuracy of the auxiliary interferometer. Furthermore, due to the significant difference between the auxiliary and measuring interferometers, the ranging results are affected by residual nonlinearity. ② Phase ratio method: This method only requires knowing the optical path difference of the auxiliary interferometer and can obtain the distance to the target by solving for and comparing the phases of the measuring and auxiliary interferometers. This method requires high-precision phase extraction and is generally not suitable for measuring non-cooperative targets. ③ Non-uniform Fourier transform method: This method uses Fourier transform on the signal in the optical frequency domain to convert the non-uniformly sampled signal from the time domain to the frequency domain for frequency domain analysis, ultimately enabling the extraction of the target distance.

[0005] In summary, although the software algorithms mentioned above have a good correction effect on nonlinearity, they usually use a first-order approximation for the theoretical model of the beat frequency signal, which introduces inherent biases. Therefore, in medium- to long-range target distance measurement and when the nonlinearity of the laser sweep frequency deteriorates, the nonlinearity correction performance of these methods will decrease, thus severely limiting the ranging accuracy. Summary of the Invention

[0006] To address the problems in existing technologies, this invention provides a high-precision swept-frequency interferometric ranging method that eliminates residual nonlinearity. This method obtains the optical frequency variation by solving differential equations, and then performs a high-order Fourier transform on the optical frequency domain of the measuring interferometer. This eliminates the residual nonlinearity introduced by the large difference in arm length between the auxiliary and measuring interferometers, thereby obtaining ultra-high precision ranging results. Furthermore, this method is not limited by laser nonlinearity and can still achieve high ranging accuracy for targets at medium to long distances.

[0007] This invention provides a high-precision swept-frequency interferometric ranging method for eliminating residual nonlinearity, comprising:

[0008] S1. Obtain the measurement interference signal I from the swept-frequency laser source using a swept-frequency interferometric absolute distance measurement system. m (t) and auxiliary interference signal I a (t);

[0009] S2. Construct the differential equations for the optical frequency and the phase of the auxiliary interferometer, and obtain the optical frequency signal ω(k) by solving the differential equations. n );

[0010] S3, based on the optical frequency signal ω(k n A higher-order orthogonal basis is constructed, and the measured interference signal is orthogonally decomposed in the optical frequency domain using the higher-order orthogonal basis to obtain the distance value to be measured.

[0011] Optionally, the measurement interference signal I in S1 m (t) and auxiliary interference signal I a The formulas for (t) are expressed as follows:

[0012]

[0013]

[0014] Where A1 and A2 represent the amplitudes of the auxiliary interference signal and the measured interference signal, respectively; τ a and τ m These represent the group delay of the output optical signal from the swept-frequency laser source after passing through the auxiliary interferometer and the short and long arms of the measuring interferometer, respectively; The phase of the output optical signal from the swept-frequency laser source after being delayed by the auxiliary interferometer group is... The phase of the output optical signal from the swept-frequency laser source after the delay of the measurement interferometer group.

[0015] Optionally, S2 specifically includes:

[0016] S21, Regarding the formula for auxiliary interference signals Perform a Taylor expansion to obtain the formula:

[0017]

[0018] S22. Convert the time t in the auxiliary interferometric signal formula into a sampling point k, and unwrap the converted formula to obtain the phase of the auxiliary interferometer. The phase calculation formula for the auxiliary interferometer is as follows:

[0019] φ a (k n =unwrap[angle(I a (k n ))]

[0020] Where unwrap() represents the unwrap function, angle() is the phase function, and k n This is the nth sampling point;

[0021] S23. Construct differential equations for the optical frequency and the phase of the auxiliary interferometer based on the formulas in S21 and S22;

[0022] S24. Solve the differential equation using the Runge-Kutta method to obtain the optical frequency signal ω(k n ).

[0023] Optionally, the formula for the differential equation is:

[0024]

[0025] Where, ω(k) n ) represents the laser light frequency corresponding to each sampling point, and N is the total number of sampling points.

[0026] Optionally, the solution formula in S24 specifically includes:

[0027]

[0028] Where h is the time interval.

[0029] Optionally, based on the optical frequency information ω(k) obtained from the solution... n Formula (5) and equation (6) form a higher-order orthogonal basis, specifically:

[0030]

[0031] Among them, R m For a series of optical path differences, a selection can be made near the optical path difference to be measured, where R m，1 R is the minimum value of a series of optical path differences. m,L Let be the maximum value of a series of optical path differences, c be the speed of light, and m and L be variables.

[0032] Optionally, the measured interference signal can be decomposed in the optical frequency domain using the higher-order orthogonal basis to obtain the distance spectrum information, specifically:

[0033]

[0034] Where N represents the total number of sampling points of the signal, n air R represents the refractive index of air. d Represents the distance to be measured, when R m =2n air R d When, X(R) mTo obtain the maximum value, by analyzing the distance spectrum X(R) m Peak finding is used to obtain the distance R to be measured. d .

[0035] Optionally, S1 specifically includes:

[0036] The output laser signal E(t) of the swept-frequency laser source is first split by an isolator and a 99:1 coupler ①; 99% of the laser signal enters the measurement interferometer, and is then split again by a 99:1 coupler ②. 99% of the light is focused onto the target surface by the focusing system, and 1% serves as the reference light for the measurement interferometer. The light reflected from the target and the reference light are combined and interfered with by a 50:50 coupler ③; finally, the signal is converted into photoelectric signal I by the first balanced photodetector BPD1 and the acquisition card for data acquisition, thus obtaining the measurement interferometer signal. m (t); Similarly, after being split by the 99:1 coupler ①, another 1% laser signal enters the auxiliary interferometer, passes through the 50:50 optical coupler ④ and optical coupler ⑤ for interferometric beat frequency, and finally undergoes photoelectric conversion and data signal acquisition by the second balanced photodetector BPD2 and the acquisition card to obtain the auxiliary interferometric signal I. a (t).

[0037] This invention acquires the measurement interference signal and auxiliary interference signal of a swept-frequency laser source using a swept-frequency interferometric absolute distance measurement system. It constructs differential equations for the optical frequency and the phase of the auxiliary interferometer, and obtains the optical frequency variation based on solving these differential equations. Then, a high-order Fourier transform is performed on the optical frequency domain of the measurement interferometer to eliminate residual nonlinearity introduced by the large difference in arm length between the auxiliary and measurement interferometers, thereby obtaining ultra-high precision ranging results. Furthermore, this method is not limited by laser nonlinearity and can still achieve high ranging accuracy for targets at medium to long distances. Attached Figure Description

[0038] Figure 1 A flowchart of a high-precision swept-frequency interferometric ranging method for eliminating residual nonlinearity is provided in an embodiment of the present invention;

[0039] Figure 2 This is a structural diagram of the sweep interferometer absolute distance measurement system provided in an embodiment of the present invention;

[0040] Figure 3 A flowchart of the high-order NUDFT algorithm provided in an embodiment of the present invention;

[0041] Figure 4 A comparison diagram of the distance spectrum solved by the first-order NUDFT method and the higher-order NUDFT method provided in the embodiments of the present invention;

[0042] Figure 5A comparison chart of multiple measurement results of the first-order NUDFT method and the higher-order NUDFT method provided in the embodiments of the present invention. Detailed Implementation

[0043] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0044] Example

[0045] Figure 1 A flowchart of a high-precision swept-frequency interferometric ranging method for eliminating residual nonlinearity is provided in this embodiment of the invention. The method specifically includes the following steps:

[0046] S1. Obtain the measurement interference signal I from the swept-frequency laser source using a swept-frequency interferometric absolute distance measurement system. m (t) and auxiliary interference signal I a (t);

[0047] S2. Construct the differential equations for the optical frequency and the phase of the auxiliary interferometer, and obtain the optical frequency signal ω(k) by solving the differential equations. n );

[0048] S3, based on the optical frequency signal ω(k n A higher-order orthogonal basis is constructed, and the measured interference signal is orthogonally decomposed in the optical frequency domain using the higher-order orthogonal basis to obtain the distance value to be measured.

[0049] Specifically, the embodiment of the present invention employs a semiconductor laser swept interferometer absolute distance measurement system structure, as shown in the system structure diagram below. Figure 2 As shown in the figure, the laser operates at a wavelength of 1550 nm, with a frequency sweep range of approximately 1.5 nm. The output laser signal E(t) is first split by an isolator and a 99:1 coupler ①; one beam (99%) enters the measurement interferometer, and is split again by a 99:1 coupler ②. 99% of the light is focused onto the target surface by the focusing system, and 1% serves as the reference light for the measurement interferometer. The light reflected from the target and the reference light are finally combined and interfered with by a 50:50 coupler ③; finally, the first balanced photodetector BPD1 and the data acquisition card DQA perform photoelectric conversion and data signal acquisition to obtain the measurement interferometer signal I. m (t); Similarly, after being split by the 99:1 coupler ①, another beam (1%) enters the auxiliary interferometer, and then passes through the 50:50 optical couplers ④ and ⑤ for interferometric beat frequency. Finally, it undergoes photoelectric conversion and data signal acquisition through the first balanced photodetector BPD2 and the data acquisition card DQA to obtain the auxiliary interference signal I. a(t).

[0050] In this embodiment, the distributed feedback laser (DFB) is used as a frequency-sweeping laser source, and its output optical signal can be expressed as:

[0051]

[0052] Where E0 represents the amplitude of the output optical signal, To represent the real-time phase of the output optical signal from the frequency-sweeping laser source, the frequency of the optical signal can be further expressed as:

[0053]

[0054] The interference signals of the DFB swept-frequency laser source, through an auxiliary interferometer and a measuring interferometer, are expressed as follows:

[0055]

[0056] Where A1 and A2 represent the amplitudes of the auxiliary interference signal and the measured interference signal, respectively, τ a and τ m These represent the group delay of the output optical signal from the swept-frequency laser source after passing through the auxiliary interferometer and the short and long arms of the measuring interferometer, respectively; The phase of the output optical signal from the swept-frequency laser source after being delayed by the auxiliary interferometer group is... The phase of the output optical signal of the swept-frequency laser source after the group delay of the measuring interferometer; for formulas (3) and (4) and The Taylor expansion can be expressed as:

[0057]

[0058] If the laser frequency is linearly modulated in time, the interference signal is a time-varying standard cosine signal, and the group delay can be directly determined using Fourier transform. However, since it is difficult to ensure that the frequency modulation characteristics of the laser source are completely linear in practice, a nonlinear correction method is required. In the above equation, the higher-order terms introduced by the laser source sweep frequency nonlinearity are very small and negligible. Therefore, for traditional demodulation methods, usually only the first-order term of the Taylor expansion is retained. Thus, the phase of the interference signal can be considered to be linearly related to the laser frequency. Therefore, the group delay τ of the auxiliary interferometer is first calibrated. a Then, by obtaining the multiple relationship between the phase or frequency information of the auxiliary interferometer and the measuring interferometer, the measured distance is further calculated. However, when the arm length difference of the auxiliary interferometer is fixed, the time delay τ of the measuring interferometer arm length increases. mAs the distance increases (i.e., the measured distance increases), the influence of higher-order terms, i.e., residual nonlinearity, gradually increases, further deteriorating the ranging results. Therefore, retaining the second order of the Taylor expansion is necessary; however, due to the group delay τ in the third-order terms... m The magnitude of the cube is extremely small and can be completely ignored for measurements over a medium to long range.

[0059] Based on this, this invention proposes a high-precision ranging method to eliminate the influence of residual nonlinearity. First, optical frequency variation information is obtained by solving differential equations. Then, a high-order Fourier transform (high-order NUDFT) is performed on the optical frequency domain of the measuring interferometer to obtain ultra-high-precision ranging results. See section 3 for details. Figure 3 This is a flowchart of the algorithm for the higher-order NUDFT method.

[0060] First, convert the above time t into sampling point k (k1) <k n <k N (This is represented by the symbol ) . The phase of the auxiliary interferometer is obtained through the unpacking operation:

[0061] φ a (k n =unwrap[angle(I a (k n (7)

[0062] Where unwrap() represents the unwrap function, and angle() is the phase function;

[0063] Then, based on equations (5) and (7), differential equations for the optical frequency and the phase of the auxiliary interferometer are constructed:

[0064]

[0065] Furthermore, the Runge-Kutta method is used to solve the differential equation to obtain the optical frequency signal ω(k n The specific calculation formula is as follows:

[0066]

[0067] To eliminate the influence of sweep frequency nonlinearity and residual nonlinearity on the measurement results, a high-order Fourier transform is performed on the measurement interferometric signal in the optical frequency domain. This process can be understood as converting the non-uniformly sampled signal from the time domain to the frequency domain for frequency domain analysis. The measurement interferometric signal and the auxiliary interferometric signal, along with the sampling point k, can be expressed as:

[0068]

[0069] Where ω(k) n ω(k) represents the laser frequency corresponding to each sampling point. n(relative to k) n It changes non-linearly, which is caused by the non-linearity of laser frequency modulation, n air R represents the refractive index of air. d τ represents the distance to be measured. m This represents the group delay difference of the measuring interferometer. The optical frequency information ω(k) is obtained by solving the differential equation. n Combined with formula (5), this signal can form a set of higher-order orthogonal bases, namely:

[0070]

[0071] Where R m For a series of optical path differences, a selection can be made near the optical path difference to be measured. Where R... m，1 R is the minimum value of a series of optical path differences. m,L Let c be the maximum value of a series of optical path differences, and m and L be variables. Therefore, the above orthogonal basis can be used to decompose the measured interference signal in the optical frequency domain to obtain the final high-precision distance spectrum information.

[0072]

[0073] Where N represents the total number of signal points, the above formula ultimately yields X(R) m The distance spectrum of R is a standard sinc function. m =2n air R d When, X(R) m Therefore, the distance spectrum X(R) takes the maximum value. m By finding the peak, the distance R to be measured can be obtained. d This eliminates the effects of frequency modulation nonlinearity and residual nonlinearity.

[0074] Unlike traditional nonlinear correction algorithms, the high-order NUDFT method in this embodiment establishes high-order models of the beat frequency signal and the optical frequency signal, obtains the real-time optical frequency signal by solving differential equations, constructs a high-order orthogonal basis to orthogonally decompose the measured interference signal, which greatly reduces the influence of residual nonlinearity, and finally obtains ultra-high precision ranging results.

[0075] Furthermore, this method does not require interpolation of the auxiliary interferometric signal, thus it is less affected by the sampling rate; simultaneously, the algorithm does not require calculating the phase of the measured signal, therefore it is less affected by signal noise, and can achieve high accuracy even for non-cooperative target measurements; moreover, this method does not require additional complex hardware costs. The distance spectrum after high-order non-uniform Fourier transform is a standard sinc curve, and further subdivision can yield high-precision measurement results.

[0076] Experimental verification

[0077] This embodiment compares the higher-order NUDFT of this invention with the first-order NUDFT in the prior art. Specifically,

[0078] The auxiliary interferometer arm length difference was set to 1m, and the measuring interferometer arm length difference was set to 50m (corresponding to a measurement distance of 25m). The results show that the first-order NUDFT ranging result is 25.001360m, with a deviation of 1360µm from the true value, while the higher-order NUDFT ranging result is 24.999979m, with a deviation of 21µm from the true value. The relative accuracy of the higher-order NUDFT is 64 times higher than that of the first-order NUDFT. See [link / reference] Figure 5 To verify the repeatability of the present invention, 50 measurements were performed. The mean and standard deviation of the first-order NUDFT measurements were 25.001360 m and 2.56 μm, respectively; the mean and standard deviation of the higher-order NUDFT measurements were 24.999970 m and 0.78 μm, respectively. In summary, the higher-order NUDFT based on solving differential equations in this invention can obtain more accurate and precise measurement results compared to the first-order NUDFT.

[0079] Note that the above description is merely a preferred embodiment of the present invention and the technical principles employed. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and various obvious changes, readjustments, and substitutions can be made without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments, and may include many other equivalent embodiments without departing from the concept of the present invention, the scope of which is determined by the scope of the appended claims.

Claims

1. A high-precision swept-frequency interferometric ranging method for eliminating residual nonlinearity, characterized in that, include: S1. Obtain the measurement interference signal I from the swept-frequency laser source using a swept-frequency interferometric absolute distance measurement system. m (t) and auxiliary interference signal I a (t); S2. Construct the differential equations for the optical frequency and the phase of the auxiliary interferometer, and obtain the optical frequency signal ω(k) by solving the differential equations. n ); S3, based on the optical frequency signal ω(k n A higher-order orthogonal basis is constructed, and the measured interference signal is orthogonally decomposed in the optical frequency domain using the higher-order orthogonal basis to obtain the distance spectrum information. The distance value to be measured is obtained based on the distance spectrum information. S2 specifically includes: S21, Regarding the formula for auxiliary interference signals Perform a Taylor expansion to obtain the formula: ω(t) is the frequency of the optical signal; S22. Convert the time t in the auxiliary interferometric signal formula into a sampling point k, and unwrap the converted formula to obtain the phase of the auxiliary interferometer. The phase calculation formula for the auxiliary interferometer is as follows: Where unwrap() represents the unwrap function, angle() is the phase function, and k n This is the nth sampling point; S23. Construct differential equations for the optical frequency and the phase of the auxiliary interferometer based on the formulas in S21 and S22; S24. Solve the differential equation using the Runge-Kutta method to obtain the optical frequency signal ω(k n ).

2. The method according to claim 1, characterized in that, Measurement interference signal I in S1 m (t) and auxiliary interference signal I a The formulas for (t) are expressed as follows: Where A1 and A2 represent the amplitudes of the auxiliary interference signal and the measured interference signal, respectively; τ a and τ m These represent the group delay of the output optical signal from the swept-frequency laser source after passing through the auxiliary interferometer and the short and long arms of the measuring interferometer, respectively; The phase of the output optical signal from the swept-frequency laser source after being delayed by the auxiliary interferometer group is... The phase of the output optical signal from the swept-frequency laser source after the group delay of the measurement interferometer is determined. This represents the real-time phase of the output optical signal from the swept-frequency laser source.

3. The method according to claim 1, characterized in that, The formula for the differential equation is: Where, ω(k) n ) represents the laser light frequency corresponding to each sampling point, and N is the total number of sampling points.

4. The method according to claim 3, characterized in that, The solution formula in S24 is: Where h is the time interval between adjacent sampling points.

5. The method according to claim 1, characterized in that, Based on the optical frequency information ω(k) obtained from the solution n Formula (5) and equation (6) form a higher-order orthogonal basis, specifically: Among them, R m For a series of optical path differences, a selection can be made near the optical path difference to be measured, where R m，1 R is the minimum value of a series of optical path differences. m,L Let be the maximum value of a series of optical path differences, c be the speed of light, and m and L be variables.

6. The method according to claim 5, characterized in that, The measured interference signal is decomposed in the optical frequency domain using the aforementioned high-order orthogonal basis to obtain the distance spectrum information, which is specifically expressed in matrix form as follows: Where N represents the total number of sampling points of the signal, n air R represents the refractive index of air. d Represents the distance to be measured, when R m =2n air R d When, X(R) m To obtain the maximum value, by analyzing the distance spectrum X(R) m Peak finding is used to obtain the distance R to be measured. d .

7. The method according to claim 1, characterized in that, S1 specifically includes: The output laser signal E(t) of the swept-frequency laser source is first split by an isolator and a 99:1 coupler ①; 99% of the laser signal enters the measurement interferometer, and is then split again by a 99:1 coupler ②. 99% of the light is focused onto the target surface by the focusing system, and 1% serves as the reference light for the measurement interferometer. The light reflected from the target and the reference light are combined and interfered with by a 50:50 coupler ③; finally, the signal is converted into photoelectric signal I by the first balanced photodetector BPD1 and the acquisition card for data acquisition, thus obtaining the measurement interferometer signal. m (t); Similarly, after being split by the 99:1 coupler ①, another 1% laser signal enters the auxiliary interferometer, passes through the 50:50 optical coupler ④ and optical coupler ⑤ for interferometric beat frequency, and finally undergoes photoelectric conversion and data signal acquisition by the second balanced photodetector BPD2 and the acquisition card to obtain the auxiliary interferometric signal I. a (t).

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