Double-scan high-precision ranging method based on range spectrum signal reconstruction

Abstract

A dual-scan high-precision ranging method based on distance spectrum signal reconstruction belongs to the field of laser interferometry ranging. The present invention addresses the problem of reduced signal-to-noise ratio caused by multiplying interference signals in order to offset Doppler frequency shift in the dual-scan frequency-interference ranging method. It includes: based on the dual-scan FMCW structure, first obtaining the auxiliary and measurement interference signals corresponding to the up-scan and down-scan lasers, then performing phase resolution on the auxiliary interference signals, and obtaining the distance spectrum containing Doppler information through NUDFT respectively; then indexing the range of the distance spectrum containing only Doppler information, and using the indexed distance spectrum information to construct interference measurement signals based on the DSR algorithm that have eliminated the noise introduced by nonlinear broadening, and finally multiplying the reconstructed measurement signal and performing NUDFT with the auxiliary signal after multiplication to obtain high-precision distance information. The present invention is used for high-precision ranging.

Description

Technical Field

[0001] The invention relates to a double-sweep high-precision distance measurement method based on distance spectrum signal reconstruction, and belongs to the field of laser interferometry distance measurement. Background Art

[0002] With the growing development of high-end manufacturing and large-scale scientific equipment, large-scale three-dimensional precision measurement is becoming increasingly widespread and urgent in the manufacturing and construction of aerospace, ships, high-speed rail, automobiles, wind power and hydropower, radar, and large-scale scientific research facilities. With the development of coherent detection technology, FMCW laser ranging technology, based on light source frequency modulation and heterodyne interferometry, plays an important role in surface inspection, metrology, and three-dimensional topography measurement of industrial products due to its advantages of no ranging ambiguity, strong anti-interference ability, high ranging accuracy, and applicability to non-cooperative targets.

[0003] Traditional FMCW ranging methods require the target to remain stationary during measurement. However, in real-world measurements, target vibrations caused by the external environment not only cause time delays but also shift the frequency of the laser beam returning from the moving target due to the Doppler effect, leading to significant ranging errors when extracting target distance information. Three main approaches are currently used to mitigate the Doppler effect: 1. The earliest approach employed triangular wave frequency modulation, which uses the frequency difference between forward and reverse frequency modulation to offset the Doppler shift introduced by target vibration, thereby accurately extracting the target's absolute distance. However, because triangular wave modulation cannot simultaneously capture Doppler information during both forward and reverse frequency sweeps, this method cannot compensate for high-frequency vibrations in real time. 2. The vibration signal is decoupled by combining an FMCW system with a Doppler vibrometer system. This solution acquires the vibration signal from the Doppler vibrometer system and then processes it with the FMCW system to obtain the absolute distance value after the vibration signal has been eliminated. However, this approach, which uses two systems, inevitably introduces noise and complicates the optical path. In 2001, Schneider et al. used two lasers simultaneously sweeping in both forward and reverse directions. Because the Doppler effect affects the interference signals from the two frequency-modulated lasers equally, they could multiply the forward and reverse signals to obtain a sum-frequency term to cancel the Doppler term, thereby obtaining the absolute distance to the target. This dual-sweep method, which can compensate for vibration signals in real time, has been widely used in FMCW ranging in vibrating environments.

[0004] Current demodulation methods based on dual-scan systems typically require multiplying the up-scan and down-scan signals to eliminate the effects of target vibration. However, this multiplication process introduces multiple additive noises, and the level of these noises is primarily related to the laser's frequency-scanning nonlinearity and the system's return light power. Existing solutions use methods based on nonuniform Fourier transforms to correct frequency-scanning nonlinearities, but fail to consider the impact of the noise introduced during the multiplication process on the final measurement accuracy. Existing research on absolute distance measurement technology based on dual-semiconductor laser frequency-scanning interferometry uses a phase-locked loop to reduce system nonlinearity, but similarly fails to analyze the noise during the multiplication process and requires a relatively complex setup. Summary of the Invention

[0005] Aiming at the problem that the signal-to-noise ratio is reduced due to multiplication of interference signals in the ranging method to offset the Doppler frequency shift, the present invention provides a dual-scan high-precision ranging method based on range spectrum signal reconstruction.

[0006] The present invention provides a double-scan high-precision distance measurement method based on range spectrum signal reconstruction, comprising:

[0007] Two tunable lasers are used to perform up-sweep and down-sweep frequency modulation at selected working wavelengths;

[0008] The laser emitted by the tunable laser DFB1 is measured by the interferometer to obtain the measurement interference signal I m1 , the auxiliary interference signal I is obtained through the auxiliary interferometer a1 The laser emitted by the tunable laser DFB2 is measured by the interferometer to obtain the measured interference signal I m2 , the auxiliary interference signal I is obtained through the auxiliary interferometer a2 ;

[0009] For the sampling point sequence k i Auxiliary interference signal collected at all times - I a1 (k i ) and auxiliary interference signal I a2 (k i ) respectively solve the phase to obtain the auxiliary interference signal phase and auxiliary interference signal phase two And further calculate the orthogonal basis corresponding to the measured interference signal The orthogonal basis corresponding to the measured interference signal Using signal orthogonal basis Sum signal orthogonal basis 2 The interference signal I m1 (k i ) and measure the interference signal I m2 (k i) is subjected to non-uniform Fourier transform to obtain the range spectrum X(R) containing Doppler information corresponding to the tunable laser DFB1 upward sweep. m1 ) and the range spectrum X(R) containing Doppler information corresponding to the tunable laser DFB2 downscan m2 );where R m1 is the range of the up-scan distance spectrum, R m2 is the range of the down-scan distance spectrum; from the distance spectrum X(R m1 ) and distance spectrum X(R m2 ) in which the index only contains the distance spectrum of Doppler information, and the indexed distance spectrum X′(R m1 ) and the indexed distance spectrum X′(R m2 ), by the indexed distance spectrum X′(R m1 ) and the indexed distance spectrum X′(R m2 ) to reconstruct the signal and obtain the reconstructed measurement interference signal I′ m1 (k i ) and reconstruct the measured interference signal I′ m2 (k i ); where k i is the i-th value in the sampling point sequence, i = 1, 2, 3, ..., K; K is the number of sampling points in the sampling point sequence;

[0010] Reconstruct the measured interference signal I' m1 (k i ) and reconstruct the measured interference signal I′ m2 (k i ) are multiplied to obtain the reconstructed sum-frequency signal I mix_m (k i );

[0011] Based on the auxiliary interference signal a1 (k i ) and auxiliary interference signal I a2 (k i ) Construct the sum frequency orthogonal basis of auxiliary interference signal R mix is the distance spectrum range corresponding to the sum frequency orthogonal basis;

[0012] For reconstructed sum frequency signal I mix_m (k i ) and the sum frequency orthogonal basis Perform non-uniform Fourier transform to obtain the final range spectrum X that eliminates the Doppler term mix (R mix ), for the final distance spectrum X mix (R mix ) to find the peak and obtain the distance of the target to be measured.

[0013] According to the double-scan high-precision ranging method based on range spectrum signal reconstruction of the present invention,

[0014] Measuring interference signal I m1 (k i ) and measure the interference signal I m2 (k i ) is expressed as:

[0015]

[0016]

[0017] Where A m1 To measure the interference signal I m1 (k i ) amplitude, Δω1(k i ) is the laser angular frequency variation of the tunable laser DFB1, n air is the refractive index of air, R d is the distance to the target to be measured, c is the speed of light in vacuum, ω 01 is the starting angular frequency of the tunable laser DFB1, τ m To measure the group delay introduced by the distance to the target in the interferometer, Δτ m (k i ) is the measurement interferometer group delay introduced by the target vibration, ω 01 Δτ m (k i ) is the Doppler term corresponding to the tunable laser DFB1, n m1 (k i ) is the measured interference signal I m1 (k i ) in the noise signal;

[0018] A m2 To measure the interference signal I m2 (k i ) amplitude, Δω2(k i ) is the laser angular frequency variation of the tunable laser DFB2, ω 02 is the starting angular frequency of the tunable laser DFB2, ω 02 Δτ m (k i ) is the Doppler term corresponding to the tunable laser DFB2, n m2 (k i ) is the measured interference signal I m2 (k i ) in the noise signal.

[0019] According to the double-scan high-precision ranging method based on range spectrum signal reconstruction of the present invention,

[0020] Auxiliary interference signal I a1 (k i ) and auxiliary interference signal I a2 (k i ) is expressed as:

[0021]

[0022]

[0023] Where A a1 is the auxiliary interference signal I a1 The amplitude, R a Optical path difference between the long and short arms of the auxiliary interferometer, τ a is the group delay of the auxiliary interferometer; A a2 is the auxiliary interference signal I a2 The amplitude of

[0024] Auxiliary interference signal phase 1 and auxiliary interference signal phase two Expressed as:

[0025]

[0026]

[0027] According to the double-scan high-precision ranging method based on range spectrum signal reconstruction of the present invention,

[0028] The orthogonal basis corresponding to the measured interference signal The orthogonal basis corresponding to the measured interference signal for:

[0029]

[0030]

[0031] Where R m1,1 R is the range of the up-scan distance spectrum m1 The lower limit of R is the range of the up-scan distance spectrum m1 Upper limit of

[0032] R m2,1 is the down-scan range spectrum range R m2 The lower limit of is the down-scan range spectrum range R m2 upper limit.

[0033] According to the double-scan high-precision ranging method based on range spectrum signal reconstruction of the present invention,

[0034] Distance spectrum X(Rm1 ) and distance spectrum X(R m2 ) are:

[0035]

[0036]

[0037] according to

[0038]

[0039] Rewrite formula (9) and formula (10) into matrix form:

[0040]

[0041]

[0042] Where I m1 =[I m1 (k1),…,I m1 (k K )],I m2 =[I m2 (k1),…,I m2 (k K )].

[0043] According to the double-scan high-precision ranging method based on range spectrum signal reconstruction of the present invention,

[0044] Indexed distance spectrum X′(R m1 ) and the indexed distance spectrum X′(R m2 )for:

[0045]

[0046]

[0047] is the distance spectrum X′(R m1 ), is the distance spectrum X′(R m1 )'s index range upper limit; is the distance spectrum X′(R m2 ), is the distance spectrum X′(R m2 ) is the upper limit of the index range.

[0048] According to the double-scan high-precision ranging method based on range spectrum signal reconstruction of the present invention,

[0049] Reconstruct the measured interference signal I′m1 and reconstruct the measured interference signal I′ m2 for:

[0050]

[0051]

[0052] Where I′ m1 =[I′ m1 (k1),…,I′ m1 (k K )],I′ m2 =[I′ m2 (k1),…,I′ m2 (k K )].

[0053] According to the double-scan high-precision ranging method based on range spectrum signal reconstruction of the present invention,

[0054] Reconstructed sum frequency signal I mix_m for:

[0055] I mix_m =I′ m1 ⊙I′ m2 , (17)

[0056] I mix_m =[I mix_m (k1),…,I mix_m (k K )]; auxiliary interference signal sum frequency orthogonal basis for:

[0057]

[0058] In the formula is the sum frequency phase of the auxiliary interference signal;

[0059]

[0060] Final distance spectrum X mix (R mix )for:

[0061]

[0062] In the formula R mix,1 is the distance spectrum range R corresponding to the sum frequency orthogonal basis mix The lower limit, R mix,L is the distance spectrum range R corresponding to the sum frequency orthogonal basis mix upper limit.

[0063] According to the double-scan high-precision ranging method based on range spectrum signal reconstruction of the present invention,

[0064] The measurement interference signal I is obtained by the tunable laser DFB1 and the tunable laser DFB2. m1 , auxiliary interference signal I a1 , measure interference signal II m2 and auxiliary interference signal I a2 The process is:

[0065] The laser beams emitted by tunable lasers DFB1 and DFB2 at the selected operating wavelengths are isolated by isolators, combined by a 50:50 coupler, and then split by a 99:1 coupler. 99% of the split beam serves as the incident signal for the measurement interferometer, and 1% of the beam serves as the incident signal for the auxiliary interferometer.

[0066] The measuring interferometer uses a 99:1 coupler to split the incident signal of the measuring interferometer. 99% of the light is focused to the target surface by the focusing system, and 1% of the light is used as the reference light of the measuring interferometer. The light reflected by the target and the reference light are combined and interfered by a 50:50 coupler to output the output beam of the measuring interferometer. The output beam of the measuring interferometer is wavelength-split by two wavelength division multiplexers and then photoelectrically converted by a balanced photodetector to obtain the measuring interference signal I m1 and measure the interference signal I m2 ;

[0067] The auxiliary interferometer uses a 50:50 coupler to split the incident signal of the auxiliary interferometer to obtain the measurement path and reference path of the auxiliary interferometer. The two signals are then combined and interfered by a 50:50 coupler to output the output beam of the auxiliary interferometer. The output beam of the auxiliary interferometer is wavelength-split by two wavelength division multiplexers and then photoelectrically converted by a balanced photodetector to obtain the auxiliary interference signal I a1 and auxiliary interference signal I a2 .

[0068] According to the double-scan high-precision ranging method based on range spectrum signal reconstruction of the present invention,

[0069] The operating wavelength of the tunable laser DFB1 is 1550nm, and its sweep range for upsweep is 1nm;

[0070] The operating wavelength of the tunable laser DFB2 is 1560 nm, and the down-sweep frequency range thereof is 1 nm.

[0071] Beneficial effects of the present invention: The method of the present invention reduces the noise level introduced by the multiplication process without increasing the system cost, and further improves the measurement capability of the dual-scan system.

[0072] Compared to the existing method of directly multiplying the measurement signals and performing NUDFT, the DSR reconstruction method of the present invention achieves a significantly lower noise level in the range spectrum than the NUDFT method, under the condition that the signal-to-noise ratio of the measurement signal is equal to -25dB. The measurement accuracy of the existing direct NUDFT method and the DSR method (range spectrum reconstruction method) of the present invention has been verified to be 216.1346μmμm and 63.7414μm, respectively; and the absolute errors are 20.9μm and 1.4μm, respectively. These results demonstrate that the DSR construction method of the present invention greatly improves measurement accuracy and has high application value and potential in long-distance, non-cooperative measurement conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is a flow chart of the double-scan high-precision ranging method based on range spectrum signal reconstruction according to the present invention;

[0074] Figure 2 This is a schematic diagram of a swept frequency interferometry absolute distance measurement system. In the figure, TLS represents a tunable laser; OC represents an optical coupler; PD represents a photodetector; and DAQ represents data acquisition.

[0075] Figure 3 Schematic diagram of a measurement system for implementing the method of the present invention;

[0076] Figure 4 It is a schematic diagram of the multiplication noise model; m1 is the measured interference signal corresponding to DFB1, I m2 is the measured interference signal 2 corresponding to DFB2, n1 is the noise signal in the measured interference signal 1, n2 is the noise signal in the measured interference signal 2, A is the amplitude of the signal spectrum after Fourier transformation, and f is the frequency value in the spectrum;

[0077] Figure 5 Schematic diagram of distance spectrum corresponding to up-scan and down-scan in the method of the present invention;

[0078] Figure 6 is a spectrum diagram of the measured signal before and after signal reconstruction in the method of the present invention;

[0079] Figure 7 This is a comparison diagram of the distance spectrum obtained by the method of the present invention (DSR reconstruction method) and the existing direct NUDFT method;

[0080] Figure 8 This is a comparison diagram of measured distance values ​​obtained by performing multiple measurements using the method of the present invention (DSR reconstruction method) and the existing direct NUDFT method. DETAILED DESCRIPTION

[0081] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0082] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0083] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention. Specific implementation method 1.

[0085] First, let's introduce the basic principles of FMCW: Figure 2 As shown, the DFB is used as a swept laser source, and its output optical signal can be expressed as:

[0086]

[0087] Where E0 represents the amplitude of the output optical signal, The real-time phase of the optical signal output by the swept laser source.

[0088] The frequency ω(t) of the optical signal is:

[0089]

[0090] The interference signal of the DFB swept laser source passing through the Mach-Zehnder interferometer can be expressed as:

[0091]

[0092] where σ r and σ m represents the photoelectric conversion coefficient of the photodetector under different light intensity conditions, τ is the group delay of the light signal passing through the short arm and long arm of the Mach-Zehnder interferometer; A and B represent the amplitude and DC bias of the signal, respectively, and t is time;

[0093] right The n-order Taylor expansion is expressed as:

[0094]

[0095] Generally speaking, the higher-order terms introduced by the laser source's frequency-sweep nonlinearity can be ignored in the above equation, so the phase of the interference signal is linearly related to the laser frequency. If the laser frequency is linearly modulated in time, the interference signal is a standard cosine signal that varies with time, and the group delay can be directly determined using the Fourier transform. However, since it is difficult to ensure that the frequency modulation characteristics of the laser source are completely linear in practice, nonlinear correction methods are required. Generally, an auxiliary interferometer should be used to correct the frequency modulation nonlinearity in the measurement interferometer signal.

[0096] In addition, in complex industrial measurement environments, the target will vibrate, and the impact of the introduced Doppler effect on the measured interference signal can be expressed as:

[0097]

[0098] Among them A m is the measured signal amplitude, Δω(t) is the time-varying laser angular frequency change during the sweep, and τ m0 is the group delay introduced by the distance to the target in the measurement interferometer, Δτ m (t) is the group delay variation caused by target vibration during the sweep, and ω0 is the start sweep angular frequency of the laser.

[0099] The first term in the formula contains information about the target distance, and the second term is related to the Doppler effect, where the angular frequency ω0 of the laser is approximately 2π×200THz, which is much larger than the change in angular frequency Δω(t). Therefore, the second term is the group delay Δτ m The change in (t) is small but cannot be ignored, indicating that the Doppler effect deteriorates the measurement accuracy.

[0100] use Figure 3 Perform ranging and express the auxiliary and measurement interference signals corresponding to the upscan and downscan obtained as:

[0101] I a1 (t) = A a1 exp[-jΔω1(t)τ a ],

[0102] I a2 (t) = A a2 exp[-jΔω2(t)τ a ],

[0103] I m1 (t) = A m1 exp[-j[Δω1(t)τ m0 +ω 01 Δτ m (t)+ω 01 τ m0 +Δω1(t)Δτm (t)],

[0104] I m2 (t) = A m2 exp[-j[Δω2(t)τ m0 +ω 02 Δτ m (t)+ω 02 τ m0 +Δω2(t)Δτ m (t)],

[0105] Among them I a1 and I a2 is the auxiliary interference signal corresponding to the two lasers, with amplitudes of A and a1 and A a2 , and the angular frequency changes of the two lasers are expressed as Δω1(t) and Δω2(t), respectively, where Δω2(t) is negative. τ a is the group delay of the auxiliary interferometer. m1 and I m2 are the measurement interferometer signals corresponding to the two lasers, with amplitudes A and m1 and A m2 .

[0106] By multiplying the measurement interference signals corresponding to the two DFB lasers, the Doppler effect can be eliminated to obtain the final target distance information. The formula is expressed as:

[0107]

[0108] Due to Δτ m Much smaller than τ m0 , that is, the second term in the above formula can be ignored. Since Δω1 and Δω2 are unknown and have nonlinear characteristics, an auxiliary interferometer signal is required to correct the frequency modulation nonlinearity.

[0109] As can be seen from the above, eliminating the Doppler term requires multiplying the measurement interference signals of the two DFB lasers. Due to the nonlinear effect of the laser frequency modulation, the beat frequency signal obtained by the measurement interferometer will have a spectrum broadening. Therefore, before multiplying, the measurement signal needs to be filtered out by a bandpass filter BPF to remove the useful signal. The specific process is as follows: Figure 4 shown.

[0110] Assume that the amplitudes of the corresponding signals after filtering of the two DFB lasers are A and m1 and A m2 The power spectral density of the noise is ρ1 and ρ2 respectively; the spectrum broadening is B1 and B2 respectively. As the spectrum broadening of the beat signal increases, the amount of noise introduced also increases. The signal-to-noise ratio of the up-sweep and down-sweep signals before multiplication is expressed as:

[0111]

[0112] The signal after multiplication can be expressed as:

[0113]

[0114] Furthermore, the total energy of the signal term and the noise term after multiplication is expressed as:

[0115]

[0116]

[0117] The signal-to-noise ratio of the signal after multiplication can be expressed as:

[0118]

[0119] Furthermore, it is deduced that the change in the signal-to-noise ratio compared to the up-scan signal after multiplication can be expressed as:

[0120]

[0121] Assume that the sweep characteristics of DFB1 and DFB2 are similar, that is, B1=B2=B,ρ1=ρ2=ρ;then the above formula can be expressed as:

[0122]

[0123] The above equation shows that multiplying the two measurement signals will cause the signal-to-noise ratio to drop by at least 3dB, and this drop in signal-to-noise ratio is primarily related to the beat frequency signal spectrum broadening bandwidth and the return light power. For a given return light power, the drop in signal-to-noise ratio increases with increasing nonlinear broadening bandwidth; for a given nonlinear broadening amount, the drop in signal-to-noise ratio increases with decreasing return light power. Furthermore, in FMCW, ranging accuracy and signal-to-noise ratio are inversely proportional, as shown below:

[0124]

[0125] Therefore, the measurement accuracy will deteriorate as the signal-to-noise ratio decreases. In order to eliminate the nonlinear broadening and the noise introduced therein during the multiplication process, this embodiment proposes a demodulation method based on range spectrum signal reconstruction.

[0126] The specific scheme of the method of the present invention is as follows:

[0127] In order to eliminate the influence of nonlinear broadening on the measurement results, this embodiment adopts non-uniform Fourier transform. The purpose of non-uniform Fourier transform is to convert the non-uniformly sampled signal from the time domain to the frequency domain for frequency domain analysis.

[0128] Combine Figures 1 to 4 As shown, the present invention provides a dual-scan high-precision ranging method based on range spectrum signal reconstruction, comprising:

[0129] Two tunable lasers are used to perform up-sweep and down-sweep frequency modulation at selected working wavelengths;

[0130] The laser emitted by the tunable laser DFB1 is measured by the interferometer to obtain the measurement interference signal I m1 , the auxiliary interference signal I is obtained through the auxiliary interferometer a1 The laser emitted by the tunable laser DFB2 is measured by the interferometer to obtain the measured interference signal I m2 , the auxiliary interference signal I is obtained through the auxiliary interferometer a2 ;

[0131] For the sampling point sequence k i Auxiliary interference signal collected at all times - I a1 (k i ) and auxiliary interference signal I a2 (k i ) respectively solve the phase to obtain the auxiliary interference signal phase and auxiliary interference signal phase two And further calculate the orthogonal basis corresponding to the measured interference signal The orthogonal basis corresponding to the measured interference signal Using signal orthogonal basis Sum signal orthogonal basis 2 The interference signal I m1 (k i ) and measure the interference signal I m2 (k i ) is subjected to non-uniform Fourier transform to obtain the range spectrum X(R) containing Doppler information corresponding to the tunable laser DFB1 upward sweep. m1 ) and the range spectrum X(R) containing Doppler information corresponding to the tunable laser DFB2 downscan m2 );where R m1 is the range of the up-scan distance spectrum, R m2 is the range of the down-scan distance spectrum; from the distance spectrum X(R m1 ) and distance spectrum X(R m2 ) in which the index only contains the distance spectrum of Doppler information, and the indexed distance spectrum X′(R m1 ) and the indexed distance spectrum X′(R m2 ), by the indexed distance spectrum X′(R m1 ) and the indexed distance spectrum X′(R m2 ) to reconstruct the signal and obtain the reconstructed measurement interference signal I′m1 (k i ) and reconstruct the measured interference signal I′ m2 (k i ); where k i is the i-th value in the sampling point sequence, i = 1, 2, 3, ..., K; K is the number of sampling points in the sampling point sequence;

[0132] Reconstruct the measured interference signal I' m1 (k i ) and reconstruct the measured interference signal I′ m2 (k i ) and multiply to obtain the reconstructed sum-frequency signal I mix_m (k i );

[0133] Based on the auxiliary interference signal a1 (k i ) and auxiliary interference signal I a2 (k i ) Construct the sum frequency orthogonal basis of auxiliary interference signal R mix is the range of the distance spectrum corresponding to the sum frequency orthogonal basis;

[0134] For reconstructed sum frequency signal I mix_m (k i ) and the sum frequency orthogonal basis Perform non-uniform Fourier transform (NUDFT) to obtain the final range spectrum X that eliminates the Doppler term mix (R mix ), for the final distance spectrum X mix (R mix ) to find the peak and obtain the distance of the target to be measured.

[0135] The signal's non-uniform Fourier transform (NUDFT) results are similar to conventional Fourier transform results, both producing spectral results with equal frequency resolution. This makes the non-uniform Fourier transform a suitable method for processing frequency-modulated interferometric ranging signals. Unlike traditional nonlinear correction algorithms, the non-uniform Fourier transform method does not require interpolation of the auxiliary interferometer signal and is therefore less affected by the sampling rate. Furthermore, the algorithm does not require calculating the phase of the measured signal, making it less affected by signal noise and capable of achieving high accuracy even for non-cooperative targets. Furthermore, this method does not require the addition of complex hardware costs. The range spectrum after the non-uniform Fourier transform is a standard sinc curve, and further subdivision can yield high-precision measurement results.

[0136] For the up-down dual-scan FMCW system, in order to solve the problem that the signal multiplication leads to a decrease in the signal-to-noise ratio and further affects the measurement accuracy, the signal processing flow based on the range spectrum signal reconstruction in this embodiment is as follows: Figure 1The basic principle is as follows: first, the auxiliary and measurement interference signals corresponding to the upscan and downscan are obtained. The auxiliary interference signals are then phase-deconstructed and the range spectra containing Doppler information are obtained using NUDFT. Then, the range spectrum range containing only Doppler information is indexed, and the indexed range spectrum information is used to construct a measurement signal based on the DSR algorithm that eliminates the noise introduced by nonlinear broadening. Finally, the reconstructed measurement signal is multiplied and NUDFT is performed with the auxiliary signal after the multiplication to obtain high-precision range information.

[0137] In this embodiment, the interference signal I is measured m1 (k i ) and measure the interference signal I m2 (k i ) is expressed as:

[0138]

[0139]

[0140] Where A m1 To measure the interference signal I m1 (k i ) amplitude, Δω1(k i ) is the laser angular frequency variation of the tunable laser DFB1, relative to k i Nonlinear changes, which are caused by the nonlinearity of laser frequency modulation; n air is the refractive index of air, R d is the distance to the target to be measured, c is the speed of light in vacuum, ω 01 is the starting angular frequency of the tunable laser DFB1, τ m To measure the group delay introduced by the distance to the target in the interferometer, Δτ m (k i ) is the measurement interferometer group delay introduced by the target vibration, ω 01 Δτ m (k i ) is the Doppler term corresponding to the tunable laser DFB1, n m1 (k i ) is the measured interference signal I m1 (k i ) in the noise signal;

[0141] A m2 To measure the interference signal I m2 (k i ) amplitude, Δω2(k i ) is the laser angular frequency variation of the tunable laser DFB2, ω 02 is the starting angular frequency of the tunable laser DFB2, ω02 Δτ m (k i ) is the Doppler term corresponding to the tunable laser DFB2, n m2 (k i ) is the measured interference signal I m2 (k i ) in the noise signal.

[0142] Auxiliary interference signal I a1 (k i ) and auxiliary interference signal I a2 (k i ) is expressed as:

[0143]

[0144]

[0145] Where A a1 is the auxiliary interference signal I a1 The amplitude, R a Optical path difference between the long and short arms of the auxiliary interferometer, τ a is the group delay of the auxiliary interferometer; A a2 is the auxiliary interference signal I a2 The amplitude of

[0146] Auxiliary interference signal phase 1 and auxiliary interference signal phase two Expressed as:

[0147]

[0148]

[0149] Furthermore, since the phase signal contains the frequency modulation information of the laser Δω1(k i ) and Δω2(k i ), using the signal to form an orthogonal basis;

[0150] The orthogonal basis corresponding to the measured interference signal The orthogonal basis corresponding to the measured interference signal for:

[0151]

[0152]

[0153] Where R m1,1 R is the range of the up-scan distance spectrum m1 The lower limit of R is the range of the up-scan distance spectrum m1 Upper limit of

[0154] R m2,1 is the down-scan range spectrum range R m2 The lower limit of is the down-scan range spectrum range R m2 upper limit.

[0155] R m1 and R m2 is a series of optical path differences, which can be selected near the optical path difference to be measured. The final distance spectrum information can be obtained by decomposing the measurement interferometer signal using the above orthogonal basis

[0156] Distance spectrum X(R m1 ) and distance spectrum X(R m2 ) are:

[0157]

[0158]

[0159] X(R m1 ) and X(R m2 ) is a standard sinc function. m1 ) as an example, when R m1 =2n air R d When X(R m1 ) takes the maximum value. m1 ) Find the peak and get the distance R to be measured d , eliminating the impact of FM nonlinearity.

[0160] At this time, the distance spectrum X(R m1 ) and distance spectrum X(R m2 ) contains Doppler information, which is the range spectrum containing Doppler information corresponding to the upsweep and downsweep, such as Figure 5 shown.

[0161] according to

[0162]

[0163] Rewrite formula (9) and formula (10) into matrix form:

[0164]

[0165]

[0166] Where I m1 =[I m1 (k1),…,I m1 (k K)],I m2 =[I m2 (k1),…,I m2 (k K )].

[0167] After the non-uniform Fourier transform, the nonlinear broadening is eliminated, but due to the existence of the Doppler effect, the up-scan and down-scan range spectrum information will be broadened. Then only the distance range containing the Doppler information is indexed, such as Figure 5 shown.

[0168] Indexed distance spectrum X′(R m1 ) and the indexed distance spectrum X′(R m2 )for:

[0169]

[0170]

[0171] is the distance spectrum X′(R m1 ), is the distance spectrum X′(R m1 )'s index range upper limit; is the distance spectrum X′(R m2 ), is the distance spectrum X′(R m2 ) is the upper limit of the index range.

[0172] The measurement signal is then reconstructed using the following formula. Specifically, the conjugate term of the orthogonal basis function corresponding to the indexed distance range is calculated and multiplied with the distance information. Figure 5 The shadow part of the image is reconstructed only for the distance range containing Doppler information, so most of the noise caused by nonlinear broadening of the spectrum bandwidth can be eliminated. The spectrum before and after reconstruction is as follows: Figure 6 As shown in the figure, it can be shown that the reconstructed signal eliminates most of the noise signals and improves the signal-to-noise ratio of the measurement signal.

[0173] Reconstruct the measured interference signal I′ m1 and reconstruct the measured interference signal I′ m2 for:

[0174]

[0175]

[0176] Where I′ m1 =[I′ m1 (k1),…,I′ m1 (kK )],I′ m2 =[I′ m2 (k1),…,I′ m2 (k K )].

[0177] Furthermore, the reconstructed upscan and downscan measurement signals are multiplied together to form a new sum-frequency signal. Since the reconstructed measurement interference signal eliminates a large amount of noise, the noise introduced during the multiplication process is greatly reduced. The orthogonal basis is then constructed using the auxiliary signal after multiplication to decompose the measurement signal. Finally, high-precision distance information that eliminates the Doppler effect can be obtained, as follows:

[0178] Reconstructed sum frequency signal I mix_m for:

[0179] I mix_m =I′ m1 ⊙I′ m2 , (17)

[0180] I mix_m =[I mix_m (k1),…,I mix_m (k K )]; auxiliary interference signal sum frequency orthogonal basis for:

[0181]

[0182] In the formula is the sum frequency phase of the auxiliary interference signal;

[0183]

[0184] Final distance spectrum X mix (R mix )for:

[0185]

[0186] In the formula R mix,1 is the distance spectrum range R corresponding to the sum frequency orthogonal basis mix The lower limit, R mix,L is the distance spectrum range R corresponding to the sum frequency orthogonal basis mix The upper limit of the final distance spectrum X mix (R mix ) is the final distance spectrum information solved based on the DSR method.

[0187] Combine Figure 3 As shown, in this embodiment, the tunable laser DFB1 and the tunable laser DFB2 obtain a measurement interference signal Im1 , auxiliary interference signal I a1 , measure interference signal II m2 and auxiliary interference signal I a2 The process is:

[0188] Figure 3 This is the absolute distance measurement system structure using a dual-semiconductor laser swept frequency interferometer: both lasers are frequency-tunable semiconductor lasers:

[0189] The laser beams emitted by tunable lasers DFB1 and DFB2 at the selected operating wavelengths are isolated by isolators, combined by a 50:50 coupler, and then split by a 99:1 coupler. 99% of the split beam serves as the incident signal for the measurement interferometer, and 1% of the beam serves as the incident signal for the auxiliary interferometer.

[0190] The measuring interferometer uses a 99:1 coupler to split the incident signal of the measuring interferometer. 99% of the light is focused to the target surface by the focusing system, and 1% of the light is used as the reference light of the measuring interferometer. The light reflected by the target and the reference light are combined and interfered by a 50:50 coupler to output the output beam of the measuring interferometer. The output beam of the measuring interferometer is wavelength-split by two wavelength division multiplexers WDM1 and WDM2, and then photoelectrically converted by balanced photodetectors BPD1 and BPD2 to obtain the measuring interference signal I m1 and measure the interference signal I m2 ;

[0191] The auxiliary interferometer uses a 50:50 coupler to split the incident signal of the auxiliary interferometer to obtain the measurement path and reference path of the auxiliary interferometer. The two signals are then combined and interfered by a 50:50 coupler to output the output beam of the auxiliary interferometer. The output beam of the auxiliary interferometer is wavelength-split by two wavelength division multiplexers WDM3 and WDM4, and then photoelectrically converted by balanced photodetectors BPD3 and BPD4 to obtain the auxiliary interference signal I a1 and auxiliary interference signal I a2 .

[0192] Two tunable laser DFBs have frequency modulation in opposite directions. The outputs of DFB1 and DFB2 are combined using a 50:50 coupler and then split into the measurement interferometer and auxiliary interferometer respectively. Ultimately, the auxiliary and measurement interference signals corresponding to the upscan and downscan can be obtained.

[0193] In this embodiment, the operating wavelength of the tunable laser DFB1 is 1550 nm, and the sweep range of the upsweep is 1 nm;

[0194] The operating wavelength of the tunable laser DFB2 is 1560 nm, and the down-sweep frequency range thereof is 1 nm.

[0195] Figure 7 As shown, compared with the existing method of directly multiplying the measurement signals to perform NUDFT, under the condition that the signal-to-noise ratio of the measurement signal is equal to -25dB, the distance spectrum noise level obtained by the DSR reconstruction method of the present invention is significantly lower than that of the NUDFT method. Figure 8 The multiple measurement results shown show that the existing direct NUDFT method and the DSR method of the present invention have measurement accuracies of 216.1346 μm and 63.7414 μm, respectively, with absolute errors of 20.9 μm and 1.4 μm, respectively. These results demonstrate that the DSR construction method of the present invention significantly improves measurement accuracy and has high application value and potential in long-distance, non-cooperative measurement conditions.

[0196] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in conjunction with other described embodiments.

Claims

1. A dual-scan high-precision ranging method based on range spectrum signal reconstruction, characterized in that include, Two tunable lasers are used to perform up-sweep and down-sweep frequency modulation at selected working wavelengths; The laser emitted by the tunable laser DFB1 is measured by the interferometer to obtain the measurement interference signal , the auxiliary interference signal is obtained through the auxiliary interferometer The laser emitted by the tunable laser DFB2 is measured by the interferometer to obtain the measurement interference signal 2 , the auxiliary interference signal 2 is obtained through the auxiliary interferometer ; For the sampling point sequence Auxiliary interference signal collected at all times and auxiliary interference signal 2 The phase of the auxiliary interference signal is obtained by solving the phase and auxiliary interference signal phase two , and further calculate the orthogonal basis corresponding to the measured interference signal The orthogonal basis corresponding to the measured interference signal ; Using the signal orthogonal basis Sum signal orthogonal basis 2 The interference signal is measured and measure interference signal II Perform non-uniform Fourier transform to obtain the distance spectrum containing Doppler information corresponding to the tunable laser DFB1 upward scan The distance spectrum containing Doppler information corresponding to the downsweep of the tunable laser DFB2 Where is the up-scan distance spectrum range, is the range of the down-scan distance spectrum; and distance spectrum The index contains only the distance spectrum of Doppler information, and the indexed distance spectrum is obtained and indexed distance spectrum , by the indexed distance spectrum and indexed distance spectrum Perform signal reconstruction to obtain the reconstructed measurement interference signal and reconstruct the measured interference signal II ;in is the i-th value in the sampling point sequence, i=1, 2, 3, ..., K; K is the number of sampling points in the sampling point sequence; The reconstructed measured interference signal and reconstruct the measured interference signal II Multiply to obtain the reconstructed sum frequency signal ; Based on the auxiliary interference signal and auxiliary interference signal 2 Constructing the sum frequency orthogonal basis of auxiliary interference signal ; is the distance spectrum range corresponding to the sum frequency orthogonal basis; Reconstructing the sum frequency signal With the sum frequency orthogonal basis Perform non-uniform Fourier transform to obtain the final range spectrum with Doppler term eliminated , for the final distance spectrum Find the peak and get the distance to the target to be measured.

2. The double-scan high-precision ranging method based on range spectrum signal reconstruction according to claim 1, characterized in that: Measuring interference signal and measure interference signal II Expressed as: （1）， （2）， In the formula To measure the interference signal The amplitude of is the laser angular frequency variation of the tunable laser DFB1, is the refractive index of air, is the distance to the target to be measured, is the speed of light in vacuum, is the starting angular frequency of the tunable laser DFB1, To measure the group delay introduced by the distance of the target to be measured in the interferometer, The measurement interferometer group delay introduced by the target vibration, is the Doppler term corresponding to the tunable laser DFB1, To measure the interference signal Noise signal in ; To measure the interference signal The amplitude of is the laser angular frequency variation of the tunable laser DFB2, is the starting angular frequency of the tunable laser DFB2, is the Doppler term corresponding to the tunable laser DFB2, To measure the interference signal Noise signal in .

3. The double-scan high-precision ranging method based on range spectrum signal reconstruction according to claim 2, characterized in that: Auxiliary interference signal 1 and auxiliary interference signal 2 Expressed as: （3）， （4）， In the formula Auxiliary interference signal The amplitude of The optical path difference between the long and short arms of the auxiliary interferometer, is the group delay of the auxiliary interferometer; Auxiliary interference signal 2 The amplitude of Auxiliary interference signal phase 1 and auxiliary interference signal phase two Expressed as: （5）， （6）。 4. The double-scan high-precision ranging method based on range spectrum signal reconstruction according to claim 3, characterized in that: The orthogonal basis corresponding to the measured interference signal The orthogonal basis corresponding to the measured interference signal for: （7）， （8）， In the formula The range of the up-scan distance spectrum The lower limit of The range of the up-scan distance spectrum Upper limit of The range of the down-scan distance spectrum The lower limit of The range of the down-scan distance spectrum upper limit.

5. The double-scan high-precision ranging method based on range spectrum signal reconstruction according to claim 4, characterized in that: Distance Spectrum and distance spectrum They are: （9）， （10）， according to , ， Rewrite formula (9) and formula (10) into matrix form: （11）， （12）， In the formula , .

6. The double-scan high-precision ranging method based on range spectrum signal reconstruction according to claim 5, characterized in that: Indexed distance spectrum and indexed distance spectrum for: （13）， （14）， is the distance spectrum after indexing The lower limit of the index range, is the distance spectrum after indexing The upper limit of the index range; is the distance spectrum after indexing The lower limit of the index range, is the distance spectrum after indexing The upper limit of the index range.

7. The double-scan high-precision ranging method based on range spectrum signal reconstruction according to claim 6, characterized in that: Reconstruction of the measured interference signal and reconstruct the measured interference signal II for: （15）， （16）， In the formula , .

8. The double-scan high-precision ranging method based on range spectrum signal reconstruction according to claim 7, characterized in that: Reconstructing the sum frequency signal for: （17）， ； Sum frequency orthogonal basis of auxiliary interference signal for: （18）， In the formula is the sum frequency phase of the auxiliary interference signal; （19）； Final distance spectrum for: （20）， In the formula , is the distance spectrum range corresponding to the sum frequency orthogonal basis The lower limit of is the distance spectrum range corresponding to the sum frequency orthogonal basis upper limit.

9. The double-scan high-precision distance measurement method based on range spectrum signal reconstruction according to claim 1, characterized in that: The measurement interference signal is obtained by the tunable laser DFB1 and the tunable laser DFB2. , auxiliary interference signal 1 、Measure interference signal 2 and auxiliary interference signal 2 The process is: The laser beams emitted by tunable lasers DFB1 and DFB2 at the selected operating wavelengths are isolated by isolators, combined by a 50:50 coupler, and then split by a 99:1 coupler. 99% of the split beam serves as the incident signal for the measurement interferometer, and 1% of the beam serves as the incident signal for the auxiliary interferometer. The measuring interferometer uses a 99:1 coupler to split the incident signal of the measuring interferometer. 99% of the light is focused to the target surface by the focusing system, and 1% of the light is used as the reference light of the measuring interferometer. The light reflected by the target and the reference light are combined and interfered by a 50:50 coupler to output the output beam of the measuring interferometer. The output beam of the measuring interferometer is wavelength-split by two wavelength division multiplexers and then photoelectrically converted by a balanced photodetector to obtain the measuring interference signal. and measure interference signal II ; The auxiliary interferometer uses a 50:50 coupler to split the incident signal of the auxiliary interferometer to obtain the measurement path and reference path of the auxiliary interferometer. The two signals are then combined and interfered by a 50:50 coupler to output the output beam of the auxiliary interferometer. The output beam of the auxiliary interferometer is wavelength-split by two wavelength division multiplexers, and then photoelectrically converted by a balanced photodetector to obtain an auxiliary interference signal. and auxiliary interference signal 2 .

10. The double-scan high-precision distance measurement method based on range spectrum signal reconstruction according to claim 1, characterized in that: The operating wavelength of the tunable laser DFB1 is 1550nm, and its sweep range for upsweep is 1nm; The operating wavelength of the tunable laser DFB2 is 1560 nm, and the down-sweep frequency range thereof is 1 nm.

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