Laser self-mixing interference displacement measurement method and device based on complex exponential transformation

Abstract

The application discloses a laser self-mixing interference displacement measurement method and device based on complex exponential transformation, and the method comprises the following steps: S1, obtaining a self-mixing interference signal P; S2, constructing a complex exponential self-mixing interference signal X by taking i*P as an index i*P , wherein X is a base number; S3, performing time-frequency transformation on the complex exponential self-mixing interference signal X i*P , to obtain a time-frequency matrix M=[t, f, A], wherein t is time, f is frequency, and A is a corresponding matrix amplitude; S4, extracting a maximum amplitude A t corresponding to each time t t , denoted as an instantaneous frequency, and constructing a new matrix N=[t, f t ]; S5, performing integration on the instantaneous frequency f t , to obtain a reconstructed displacement at the time t. The application is free from the dependence of a target motion direction on an advance estimation based on a time-frequency spectrum integral reconstruction algorithm, and high-precision real-time reconstruction of a steady-state or non-steady-state displacement is realized.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of optical measurement, and particularly relates to a laser self-mixing interference displacement measurement method and device based on complex exponential transformation. BACKGROUND

[0002] In the field of self-mixing interference, displacement reconstruction is a very important application. The displacement reconstruction methods proposed by predecessors: fringe counting method, phase unwrapping method, orthogonal phase expansion method, neural network algorithm, and spectrum processing method, have one or more limitations, including but not limited to: the need for prior estimation of the motion direction, high dependence on accurate estimation of the optical feedback coefficient and the line width broadening factor, poor effect when processing non-stationary signals, and high overall system complexity.

[0003] The integral reconstruction algorithm based on time-frequency spectrum eliminates the dependence on the estimation of the optical feedback coefficient and the line width broadening factor, and processes stationary signals or non-stationary signals with a relatively simple system device to obtain a reconstructed displacement with high resolution. However, it still needs to calculate the target motion direction in advance according to the time domain signal characteristics, which significantly increases the calculation complexity and poses a challenge to the real-time operation capability of the system.

[0004] The document with DOI number 10.1109 / JLT.2022.3201098 designs a displacement reconstruction method based on time-frequency processing, which includes: 1. pre-processing the self-mixing interference signal to obtain a normalized self-mixing interference signal P0(t); 2. obtaining a flip signal R(t) by analyzing P0(t); 3. studying the main frequency variation of the self-mixing interference signal according to the short-time Fourier transform coefficient, and using the flip signal R(t) to determine the frequency sign; 4. obtaining the velocity according to the frequency, and calculating the signal segment between two sampling points using a generalized regression neural network to realize the recovery of the velocity; 5. reconstructing the vibration using the integral operation of the recovered velocity. The above displacement reconstruction method depends on the accurate judgment of the flip signal R(t), which is not conducive to the simplicity and real-time performance of displacement reconstruction. SUMMARY

[0005] To solve the problems existing in the prior art, the present application provides a laser self-mixing interference displacement measurement method and device based on complex exponential transformation, which eliminates the dependence on prior estimation of the target motion direction based on the integral reconstruction algorithm of time-frequency spectrum, and realizes high-precision real-time reconstruction of steady-state or non-steady-state displacement.

[0006] The technical solution of the present application is as follows:

[0007] On the one hand, the present application provides a laser self-mixing interference displacement measurement method based on complex exponential transformation, which includes the following steps:

[0008] S1: Obtain the self-mixing interference signal P.

[0009] S2: Construct a complex exponential self-mixing interference signal X using the imaginary unit i*P as the exponent. i*P , where X is the base.

[0010] S3: For the complex exponential self-mixing interference signal X i*P Perform time-frequency transformation to obtain the time-frequency matrix M = [t, f, A], where t is time, f is frequency, and A is the magnitude of the corresponding matrix.

[0011] S4: Extract the maximum amplitude A at each time t based on the time-frequency matrix M. t The corresponding frequency f t Let f be the instantaneous frequency, and construct a new matrix N = [t, f]. t ].

[0012] S5: For the instantaneous frequency f t Integrate to obtain the reconstructed displacement at time t.

[0013] Preferably, step S1 further includes: performing DC blocking processing on the acquired self-mixing interference signal P to remove the DC component in the signal.

[0014] Preferably, the base X in step S2 includes, but is not limited to, the natural base e and 10.

[0015] Preferably, the time-frequency transformation method in step S3 includes, but is not limited to: short-time Fourier transform and wavelet transform.

[0016] Preferably, in step S4, the maximum amplitude A at each time t is extracted. t The corresponding frequency f t Specifically:

[0017] For each time t i Included amplitude Perform a traversal and identify each time step t. i Maximum amplitude included And find the corresponding instantaneous frequency f based on the value of j. t Where i is a non-negative integer less than or equal to the total number of time series, j is a non-negative integer less than or equal to the total number of frequency series, and j is related to the instantaneous frequency f. t One-to-one correspondence.

[0018] Preferably, the formula for calculating the reconstructed displacement is as follows:

[0019]

[0020] In the formula, D t f is the reconstructed displacement at time t; λ is the laser wavelength; ft is the instantaneous frequency.

[0021] In another aspect, the present application provides a laser self-mixing interference displacement measurement device based on complex exponential transformation, comprising a light source emitting system, a signal acquisition system, a signal processing and storage system connected in sequence.

[0022] The light source emitting system is used for emitting laser to the surface of the target object.

[0023] The signal acquisition system is used for receiving the feedback light reflected by the surface of the target object, generating a laser self-mixing interference signal, and converting the laser self-mixing interference signal into a current signal.

[0024] The signal processing and storage system is used for amplifying and filtering the current signal, and calculating a reconstructed displacement according to the self-mixing interference signal obtained after processing, and storing all data generated in the displacement measurement process.

[0025] Preferably, the laser used for emitting the light source in the light source emitting system includes but is not limited to a semiconductor laser, a fiber laser, a solid-state laser, and a gas laser.

[0026] In still another aspect, the present application further provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the laser self-mixing interference displacement measurement method based on complex exponential transformation according to any one of the embodiments of the present application when executing the computer program.

[0027] In still another aspect, the present application further provides a computer readable storage medium having a computer program stored thereon, wherein the computer program is executable on a processor to implement the laser self-mixing interference displacement measurement method based on complex exponential transformation according to any one of the embodiments of the present application.

[0028] Compared with the prior art, the present application has the following technical effects:

[0029] The present application projects the traditional laser self-mixing interference signal into a complex exponential space, and performs time-frequency transformation to mine the hidden object motion direction information, and realizes synchronous determination of the speed integral reconstructed time-frequency sign. Compared with the prior art, the present application can directly determine the motion direction of the object in the process of performing time-frequency transformation of the signal, thereby avoiding an additional step of obtaining the object motion direction information, and realizing synchronization of displacement reconstruction. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 is the overall flowchart of the laser self-mixing interference displacement measurement method based on complex exponential transformation according to the present application;

[0031] Figure 2is a simulation result figure of the vibration displacement reconstruction of simple harmonic motion according to the present application;

[0032] Figure 3 is a simulation result figure of the non-stationary displacement reconstruction according to the present application;

[0033] Figure 4 is a simulation result figure of the laser self-mixing interference displacement measurement method based on complex exponential transformation according to the present application. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical scheme and advantages of the present application clearer, the technical scheme of the present application will be described clearly and completely below by combining the specific embodiments of the present application and referring to the drawings.

[0035] Embodiment One

[0036] The present embodiment provides a laser self-mixing interference displacement measurement method based on complex exponential transformation, as shown in the accompanying drawings, comprising the following steps: Figure 1

[0037] S1: Obtain the self-mixing interference signal P.

[0038] As a preferred embodiment of the present embodiment, the step S1 further comprises: performing direct current removal processing on the obtained self-mixing interference signal P to remove the direct current component in the signal.

[0039] S2: Take the imaginary unit i*P as the index to construct the complex exponential self-mixing interference signal X i*P , wherein X is the base number.

[0040] As a preferred embodiment of the present embodiment, the base number X in the step S2 includes but is not limited to: natural base e, 10, and the natural base e is preferentially selected as the base number.

[0041] S3: Perform time-frequency transformation on the complex exponential self-mixing interference signal X i*P to obtain a time-frequency matrix M=[t,f,A], wherein t is the time; f is the frequency; and A is the corresponding matrix amplitude.

[0042] As a preferred embodiment of the present embodiment, the time-frequency transformation mode in the step S3 includes but is not limited to: short-time Fourier transform, wavelet transform, and the short-time Fourier transform is preferentially selected as the time-frequency transformation mode.

[0043] Further, the maximum amplitude A t at each time t corresponds to the frequency f t ​The essence is the instantaneous frequency with the direction of motion. In the conventional time-frequency transform, the obtained instantaneous frequency does not have the direction information of the object motion, so it cannot distinguish the direction of the object motion, that is, it cannot obtain the displacement information of the object by velocity integration. The embodiment re-explores the hidden object motion direction information by projecting the traditional laser self-mixing interference signal into the complex exponential space and applying the time-frequency transform.

[0044] The following detailed principle is explained in base e, and the rest is the same.

[0045] The laser self-mixing interference signal P can be represented as P = cosφ f , wherein φ f is the phase information of the target object.

[0046] The complex exponential self-mixing interference signal e i*P is constructed by taking the imaginary unit i*P as the index.

[0047] The obtained complex exponential self-mixing interference signal is expanded by the Taylor formula to obtain:

[0048]

[0049] Further, according to the Euler formula, cosφ f is expanded to obtain:

[0050]

[0051] According to the above expansion, it is easy to obtain:

[0052]

[0053] The binomial expansion of the above formula is obtained:

[0054]

[0055] wherein, is the binomial coefficient, which is specifically represented as:

[0056]

[0057] In summary, the time-domain expression of the complex exponential self-mixing interference signal can be represented as:

[0058]

[0059] The Fourier transform of the time-domain expression is performed to obtain the frequency-domain expression F(ω), which is represented as:

[0060]

[0061] In the formula, δ(ω) represents the impulse function.

[0062] Analysis of the frequency domain expression reveals that positive and negative frequencies are represented in the value n-2k, where n is a positive integer and k is a positive integer between 0 and n. When n-2k = ω, δ(n-2k-ω) corresponds to the component with frequency ω. Since the n and k corresponding to ±ω are different, the amplitudes corresponding to the positive and negative frequency components in the spectrum are also different. Furthermore, a positive frequency in the spectrum indicates that the target object is moving towards the signal acquisition instrument; a negative frequency in the spectrum indicates that the target object is moving away from the signal acquisition instrument.

[0063] S4: Extract the maximum amplitude A at each time t based on the time-frequency matrix M. t The corresponding frequency f t Let f be the instantaneous frequency, and construct a new matrix N = [t, f]. t ].

[0064] In a preferred embodiment of this example, step S4 extracts the maximum amplitude A at each time t. t The corresponding frequency f t Specifically:

[0065] For each time t i Included amplitude Perform a traversal and identify each time step t. i Maximum amplitude included And find the corresponding instantaneous frequency f based on the value of j. t Where i is a non-negative integer less than or equal to the total number of time series, j is a non-negative integer less than or equal to the total number of frequency series, and j is related to the instantaneous frequency f. t One-to-one correspondence.

[0066] S5: For the instantaneous frequency f t Integrate to obtain the reconstructed displacement at time t.

[0067] In a preferred embodiment of this invention, the formula for calculating the reconstructed displacement in step S5 is as follows:

[0068]

[0069] In the formula, D t f is the reconstructed displacement at time t; λ is the laser wavelength; f t This refers to the instantaneous frequency.

[0070] To verify the effectiveness and superiority of the method provided in this embodiment, some specific examples are provided below:

[0071] Application Example 1:

[0072] See Figure 2As shown in Table 1, a vibration displacement reconstruction simulation test of the method described in this embodiment was performed, and the simulation parameters were set as shown in Table 1.

[0073] Table 1 Parameter Setting Table

[0074] Symbol Meaning Value C Optical feedback coefficient 0.5 α Linewidth enhancement factor 3 N Number of sampling points 24k f s ]]> Sampling frequency 800 kHz F Object vibration frequency 100 Hz A Object vibration amplitude 1.625 um λ Wavelength 650 nm

[0075] The self-mixing interference signal P obtained from the simulation corresponds to Figure 2 (a) The blue stripe section.

[0076] Using the imaginary unit i*P as the exponent, a complex exponential self-mixing interference signal e is constructed. i*P .

[0077] For the complex exponential self-mixing interference signal e i*P Perform time-frequency transformation to obtain the time-frequency matrix M, which can be displayed through visualization. Figure 2 (b) The portion excluding the red curve. According to Figure 2 As shown in the color bars in (b), the energy ranges from low to high according to the color from blue to yellow. It is clear from the figure that the method described in this embodiment clearly distinguishes between positive and negative frequency harmonic energies.

[0078] Extract the maximum amplitude A at each time t t The corresponding frequency f t Let be the instantaneous frequency, and construct a new matrix N. The new matrix N can be displayed visually as follows: Figure 2 The red curve in (b) essentially represents the instantaneous frequency of the object's displacement.

[0079] For the instantaneous frequency f t Integrate to obtain the reconstructed displacement at time t. The reconstructed displacement is expressed as... Figure 2 In (d), the blue curve represents the reference displacement as... Figure 2 The error between the two is represented by the red curve in (d). Figure 2 In (e), it is easy to obtain that the root mean square error under this condition is 16 nm. The results show that the laser self-mixed interferometric displacement measurement method based on complex exponential transform described in this embodiment realizes the synchronous determination of the frequency sign during velocity integral reconstruction, and eliminates the difficulties in parameter estimation and direction calculation in the laser self-mixed interferometric integral reconstruction method.

[0080] Application Example 2:

[0081] To verify the effectiveness of the laser self-mixing interferometry displacement measurement method based on complex exponential transform proposed in this embodiment under different linewidth broadening factors α and optical feedback coefficients C, simulations were performed under different parameter conditions of α and C. The reconstructed root mean square error is shown in Table 2.

[0082] Table 2 Comparison table of root mean square error under different line width expansion factor a and optical feedback coefficient c

[0083] C / α 3 4 5 6 0.1 16.4 nm 16.7 nm 15.7 nm 15.1 nm 0.5 14.8 nm 16.0 nm 15.2 nm 13.5 nm 1.0 14.4 nm 13.6 nm 12.1 nm 10.9 nm 1.4 16.0 nm 15.2 nm 13.6 nm 13.4 nm 1.8 21.6 nm 23.2 nm 23.6 nm 23.5 nm

[0084] The results show that the laser self-mixing interference displacement measurement method based on complex exponential transformation proposed in the embodiment has smaller root mean square error under different line width expansion factor a and optical feedback coefficient c, and the method is robust to line width expansion factor a and optical feedback coefficient c.

[0085] Application Example Three:

[0086] To verify the effect of the laser self-mixing interference displacement measurement method based on complex exponential transformation proposed in the embodiment on non-stationary displacement reconstruction, the non-stationary vibration displacement is simulated and reconstructed. The processing result is shown in FIG. 3. Figure 3 As can be seen from the figure, the time-frequency spectrum obtained by the displacement measurement method described in the embodiment still has the characteristics of asymmetric positive and negative frequency energy under the condition, and a smaller reconstruction error of 20.3 nm is obtained, which shows that the method has robustness for non-stationary displacement reconstruction.

[0087] Application Example Four:

[0088] To verify the effect of the laser self-mixing interference displacement measurement method based on complex exponential transformation proposed in the embodiment on displacement reconstruction of noisy signals, the self-mixing signals with different noises are simulated and reconstructed. The processing result is shown in Table 3.

[0089] Table 3 Comparison table of reconstruction error under different noises

[0090]

[0091] The results show that when the signal-to-noise ratio exceeds 10 dB, the reconstruction error tends to be stable and approaches 10 nm. Therefore, the method also has strong robustness to noise signals.

[0092] Embodiment Two

[0093] Correspondingly, the embodiment provides a laser self-mixing interference displacement measurement device based on complex exponential transformation, which is used to realize the laser self-mixing interference displacement measurement method based on complex exponential transformation described in Embodiment One, and includes a light source emission system, a signal acquisition system, and a signal processing and storage system connected in sequence.

[0094] The light source emission system is used to emit laser to the surface of the target object.

[0095] The signal acquisition system is used to receive the feedback light reflected by the surface of the target object, generate a laser self-mixing interference signal, and convert it into an electric current signal.

[0096] Signal processing and storage system, for amplifying and filtering the current signal, and calculating the reconstructed displacement according to the self-mixing interference signal after processing, and storing all data generated in the displacement measurement process.

[0097] Further, the laser for emitting the light source in the light source emitting system includes but is not limited to: semiconductor laser, fiber laser, solid-state laser, gas laser. Preferably, the semiconductor laser.

[0098] To verify the effectiveness and superiority of the device provided in this embodiment, some specific cases are provided as follows:

[0099] Based on the device, the laser self-mixing interference signal obtained in the experiment is processed. The experimental device is set as follows:

[0100] In the experiment, the distance between the laser and the target object is set to 0.3m, and the target object is driven by a signal function generator.

[0101] The light source emitting system uses a multi-longitudinal mode laser diode as a light source, with an output wavelength of 650nm and a power of 7mW. The diode is driven by a constant current source with a working current of 20mA. A variable attenuator is placed in the external cavity to attenuate the output laser and adjust the optical feedback level.

[0102] The signal acquisition system includes a photodiode PD and a data acquisition card DAC. The photodiode is integrated into the LD package to detect the change in interference intensity, which is then converted into a current signal and collected by the data acquisition card DAC.

[0103] The signal processing and storage system receives the data of the data acquisition card DAC, and processes the data according to the laser self-mixing interference displacement measurement method based on complex exponential transformation to obtain the reconstructed displacement.

[0104] The reconstruction result is shown in Figure 4 The root mean square error of the reconstruction is 21.3nm. The results show that the device described in this embodiment can effectively process the experimental signal.

[0105] Embodiment three

[0106] The electronic device includes a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor implements the laser self-mixing interference displacement measurement method based on complex exponential transformation as described in any embodiment of the present application when executing the computer program.

[0107] Embodiment four

[0108] The embodiment provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement a complex exponential transformation based laser self-mixing interference displacement measurement method according to any one of the embodiments of the application.

[0109] In the embodiments of the present application, "at least one" refers to one or more, and "multiple" refers to two or more. The "and / or" describes the association relationship of the associated objects, which means that there can be three kinds of relationships, for example, A and / or B can represent the cases of A alone, A and B together, and B alone. Wherein A and B can be singular or plural. The character " / " generally represents that the front and rear associated objects are in an "or" relationship. "At least one of the following" and the like means any combination of these items, including any combination of single or multiple items. For example, at least one of a, b and c can represent: a, b, c, a and b, a and c, b and c, or a and b and c, wherein a, b, and c can be single or multiple.

[0110] Those skilled in the art can realize that the units and algorithm steps described in the embodiments disclosed in the present application can be realized by electronic hardware, computer software and combination of electronic hardware and computer software. Whether the functions are realized by hardware or software depends on the specific application and design constraints of the technical solution. Professional technicians can use different methods to realize the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0111] Those skilled in the art can clearly understand that, for the convenience and brevity of the description, the specific working process of the system, device and unit described above can refer to the corresponding process in the foregoing method embodiments, which will not be described here.

[0112] In several embodiments provided in the present application, any function realized in the form of a software function unit and sold or used as an independent product can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the parts that make contributions to the prior art or parts of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium, including a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the embodiments of the present application. The foregoing storage medium includes: a U disk, a mobile hard disk, a read-only memory (Read-Only Memory, ROM for short), a random access memory (Random Access Memory, RAM for short), a magnetic disk or an optical disk, and various media that can store program codes.

[0113] The above merely illustrates the embodiments of the present application, and does not limit the patent scope of the present application, and any equivalent structure or equivalent process transformation, or direct or indirect application in other related technical fields, which are made by using the content of the present application specification and drawings, are also included in the patent protection scope of the present application.

Claims

1. A laser self-mixing interferometry displacement measurement method based on complex exponential transform, characterized in that, Includes the following steps: S1: Obtain the self-mixing interference signal P; S2: Construct a complex exponential self-mixing interference signal X using the imaginary unit i*P as the exponent. i*P where X is the base; S3: For the complex exponential self-mixing interference signal X i*P Perform time-frequency transformation to obtain the time-frequency matrix M = [t, f, A], where t is time; f is the frequency; A is the magnitude of the corresponding matrix; S4: Extract the maximum amplitude A at each time t based on the time-frequency matrix M. t The corresponding frequency f t Let f be the instantaneous frequency, and construct a new matrix N = [t, f]. t ]; S5: For the instantaneous frequency f t Integrate to obtain the reconstructed displacement at time t.

2. The laser self-mixing interferometry displacement measurement method based on complex exponential transform according to claim 1, characterized in that, Step S1 further includes: performing DC blocking processing on the acquired self-mixing interference signal P to remove the DC component in the signal.

3. The laser self-mixing interferometry displacement measurement method based on complex exponential transform according to claim 1, characterized in that, The base X in step S2 includes, but is not limited to: the natural base e and 10.

4. The laser self-mixing interferometry displacement measurement method based on complex exponential transform according to claim 1, characterized in that, The time-frequency transformation methods in step S3 include, but are not limited to: short-time Fourier transform and wavelet transform.

5. The laser self-mixing interferometry displacement measurement method based on complex exponential transform according to claim 1, characterized in that, In step S4, the maximum amplitude A at each time t is extracted. t The corresponding frequency f t Specifically: For each time t i Included amplitude Perform a traversal and identify each time step t. i Maximum amplitude included And find the corresponding instantaneous frequency f based on the value of j. t Where i is a non-negative integer less than or equal to the total number of time series, j is a non-negative integer less than or equal to the total number of frequency series, and j is related to the instantaneous frequency f. t One-to-one correspondence.

6. The laser self-mixing interferometry displacement measurement method based on complex exponential transform according to claim 1, characterized in that, The specific formula for calculating the reconstructed displacement is as follows: In the formula, D t f is the reconstructed displacement at time t; λ is the laser wavelength; f t This refers to the instantaneous frequency.

7. A laser self-mixing interferometric displacement measurement device based on complex exponential transform, characterized in that, The device is used to implement the laser self-mixing interferometric displacement measurement method based on complex exponential transformation as described in any one of claims 1-6, comprising a light source emitting system, a signal acquisition system, and a signal processing and storage system connected in sequence; A light source emitting system used to emit laser light onto the surface of a target object; The signal acquisition system is used to receive the feedback light reflected from the surface of the target object, generate a laser self-mixing interference signal, and convert it into a current signal; The signal processing and storage system is used to amplify and filter the current signal, calculate the reconstructed displacement based on the processed self-mixing interference signal, and store all data generated during the displacement measurement process.

8. The laser self-mixing interferometric displacement measuring device based on complex exponential transform according to claim 7, characterized in that, The lasers used to emit light sources in the light source emission system include, but are not limited to: semiconductor lasers, fiber lasers, solid-state lasers, and gas lasers.

9. An electronic device, the electronic device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, when the processor executes the computer program, it implements the laser self-mixing interferometry displacement measurement method based on complex exponential transformation as described in any one of claims 1 to 6.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the laser self-mixing interferometry displacement measurement method based on complex exponential transformation as described in any one of claims 1 to 6.

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