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

Abstract

The invention discloses a laser self-mixing interference displacement measurement method and device based on complex exponential transformation. The method comprises the following steps: S1, obtaining a self-mixing interference signal P; s2, taking an imaginary number unit i * P as an index, and constructing a complex index self-mixing interference signal Xi * P, where X is a base number; s3, time-frequency transformation is carried out on the complex exponential self-mixing interference signal Xi * P, a time-frequency matrix M = [t, f, A] is obtained, and t is time; f is frequency; a is a corresponding matrix amplitude; s4, extracting a frequency ft corresponding to the maximum amplitude At at each moment t, recording the frequency ft as an instantaneous frequency, and constructing a new matrix N = [t, ft]; and S5, carrying out integration on the instantaneous frequency ft to obtain the reconstruction displacement at the t moment. The method gets rid of the dependence of a reconstruction algorithm based on time-frequency spectrum integration on pre-estimation of a target motion direction in advance, and realizes high-precision real-time reconstruction of steady-state or unsteady-state displacement.

Description

Technical Field

[0001] The invention belongs to the technical field of optical measurement, and in particular relates to a laser self-mixing interference displacement measurement method and device based on complex exponential transformation. Background Art

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

[0003] The integral reconstruction algorithm based on the time-frequency spectrum eliminates the reliance on the estimation of the optical feedback coefficient and the linewidth broadening factor, and processes the stationary or non-stationary signal with a relatively simple system device to obtain a high-resolution reconstructed displacement. However, it still needs to calculate the target motion direction in advance based on the time domain signal characteristics. This step significantly increases the computational complexity and poses a challenge to the real-time computing 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. Preprocessing the self-mixing interference signal to obtain the normalized self-mixing interference signal P0(t); 2. Obtaining the flip signal R(t) by analyzing P0(t); 3. Studying the main frequency change 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 speed according to the frequency, and using the generalized regression neural network to calculate the signal segment between the two sampling points to achieve speed recovery; 5. Reconstructing the vibration using the integral operation of the restored speed. The above displacement reconstruction methods rely 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 of the invention

[0005] In order to solve the problems existing in the above-mentioned prior art, the present invention provides a laser self-mixing interference displacement measurement method and device based on complex exponential transformation, which gets rid of the dependence on advance estimation of the target motion direction based on the time-frequency spectrum integration reconstruction algorithm, and realizes high-precision real-time reconstruction of steady-state or non-steady-state displacement.

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

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

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

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

[0010] S3: 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 corresponding matrix amplitude.

[0011] S4: Extract the maximum amplitude A at each time t according to the time-frequency matrix M t The corresponding frequency f t , recorded as 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, the step S1 further comprises: performing DC isolation 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: 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 moment t is extracted. t The corresponding frequency f t Specifically:

[0017] For every moment t i Amplitude included Traverse and identify each moment t i The maximum amplitude included And find the corresponding instantaneous frequency f according to the j value 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 calculation formula of the reconstructed displacement is specifically:

[0019]

[0020] Where D t is the reconstruction displacement at time t; λ is the laser wavelength; ft is the instantaneous frequency.

[0021] On the other hand, the present invention provides a laser self-mixing interference displacement measurement device based on complex exponential transformation, including a light source emission system, a signal acquisition system, and a signal processing and storage system connected in sequence.

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

[0023] The signal acquisition system is used to receive feedback light reflected from the surface of the target object, generate a laser self-mixing interference signal, and convert it into a current signal.

[0024] The signal processing and storage system is used to amplify and filter the current signal, calculate the reconstructed displacement based on the self-mixing interference signal obtained after processing, and store all the data generated during 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 laser, and a gas laser.

[0026] On the other hand, the present invention also provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the laser self-mixing interference displacement measurement method based on complex exponential transformation as described in any embodiment of the present invention is implemented.

[0027] On the other hand, the present invention further provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the laser self-mixing interference displacement measurement method based on complex exponential transformation as described in any embodiment of the present invention is implemented.

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

[0029] The present invention projects the traditional laser self-mixing interference signal into the complex exponential space and applies time-frequency transformation to mine the implicit information of the object's motion direction, thus realizing the synchronous determination of the frequency symbol during the velocity integral reconstruction. Compared with the prior art, the present invention can directly determine the object's motion direction during the time-frequency transformation of the signal, thereby avoiding the extra step of obtaining the object's motion direction information and realizing the synchronization of displacement reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is an overall flow chart of the laser self-mixing interference displacement measurement method based on complex exponential transformation described in the present invention;

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

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

[0033] Figure 4 This is a diagram of experimental results of the laser self-mixing interference displacement measurement method based on complex exponential transformation described in the present invention. DETAILED DESCRIPTION

[0034] In order to make the objectives, technical solutions and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in combination with specific embodiments of the present application and with reference to the accompanying drawings.

[0035] Embodiment 1

[0036] This embodiment provides a laser self-mixing interference displacement measurement method based on complex exponential transformation, see Figure 1 As shown, the following steps are included:

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

[0038] As a preferred implementation of this embodiment, the step S1 further includes: performing DC isolation processing on the acquired self-mixing interference signal P to remove the DC component in the signal.

[0039] S2: Using the imaginary unit i*P as the exponent, construct a complex exponential self-mixing interference signal X i*P , where X is the base.

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

[0041] S3: 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 corresponding matrix amplitude.

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

[0043] Furthermore, the maximum amplitude A at each moment t t The corresponding frequency f t, which is essentially an instantaneous frequency with a moving direction. In conventional time-frequency transformation, the instantaneous frequency obtained does not carry the moving direction information of the object, so it is impossible to distinguish the moving direction of the object, that is, it is impossible to obtain the displacement information of the object through velocity integration. However, this embodiment projects the traditional laser self-mixing interference signal into the complex exponential space and applies time-frequency transformation to re-explore the implicit moving direction information of the object.

[0044] The following is a detailed explanation of the principle using e as the base, and the same applies to other bases.

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

[0046] Using the imaginary unit i*P as the exponent, construct the complex exponential self-mixing interference signal e i*P .

[0047] The obtained complex exponential self-mixing interference signal is expanded using Taylor's formula to obtain:

[0048]

[0049] Furthermore, according to Euler's formula, cosφ f Expand it to get:

[0050]

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

[0052]

[0053] Perform binomial expansion on the above formula to obtain:

[0054]

[0055] in, is the binomial coefficient, which is specifically expressed as:

[0056]

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

[0058]

[0059] The time domain expression is subjected to Fourier transform to obtain the frequency domain expression F(ω), which is expressed as:

[0060]

[0061] Where δ(ω) represents the impulse function.

[0062] Analysis of the frequency domain expression shows that positive and negative frequencies are expressed 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 a frequency of ω. Since n and k corresponding to ±ω are different, the amplitudes corresponding to the positive and negative frequency components in the spectrum are also different. At the same time, when the frequency of the spectrum is positive, it means that the target object is moving in the direction close to the signal acquisition instrument; when the frequency of the spectrum is negative, it means that the target object is moving in the direction away from the signal acquisition instrument.

[0063] S4: Extract the maximum amplitude A at each time t according to the time-frequency matrix M t The corresponding frequency f t , recorded as instantaneous frequency, and construct a new matrix N = [t,f t ].

[0064] As a preferred implementation of this embodiment, the maximum amplitude A at each time t is extracted in step S4. t The corresponding frequency f t Specifically:

[0065] For every moment t i Amplitude included Traverse and identify each moment t i The maximum amplitude included And find the corresponding instantaneous frequency f according to the j value 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] As a preferred implementation of this embodiment, the calculation formula for reconstructing the displacement in step S5 is specifically:

[0068]

[0069] Where D t is the reconstruction displacement at time t; λ is the laser wavelength; f t is the instantaneous frequency.

[0070] In order to verify the effectiveness and superiority of the method provided in this embodiment, some specific cases are provided below:

[0071] Application example 1:

[0072] See also Figure 2As shown, the method described in this embodiment is subjected to a vibration displacement reconstruction simulation test of simple harmonic motion, and the simulation parameter settings are shown in Table 1.

[0073] Table 1 Parameter setting table

[0074] symbol meaning value C Optical feedback coefficient 0.5 α Linewidth broadening factor 3 N Number of sampling points 24k <![CDATA[f s ]]> Sampling frequency 800kHz F The frequency of the object's vibration 100Hz A Amplitude of object vibration 1.625um λ wavelength 650nm

[0075] The simulated self-mixing interference signal P corresponds to Figure 2 (a) The blue stripe part.

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

[0077] The complex exponential self-mixing interference signal e i*P Perform time-frequency transformation to obtain a time-frequency matrix M, which can be displayed as follows by visualization means: Figure 2 (b) except the red curve. Figure 2 As shown in the color bar shown in (b), the energy corresponding to the color from blue to yellow is from low to high. It is easy to see from the figure that the positive and negative frequency harmonic energies are clearly distinguished by the method described in this embodiment.

[0078] Extract the maximum amplitude A at each moment t t The corresponding frequency f t , recorded as the instantaneous frequency, and construct a new matrix N. The new matrix N can be displayed as follows by visualization: Figure 2 The red curve part in (b) actually expresses 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 the blue curve part of (d), the reference displacement is expressed as Figure 2 In the red curve part of (d), the error between the two is expressed in Figure 2 (e), it is easy to obtain that the root mean square error under this condition is 16nm. The results show that the laser self-mixing interference displacement measurement method based on complex exponential transformation described in this embodiment realizes the synchronous determination of frequency symbols during velocity integral reconstruction, eliminating the difficulties of parameter estimation and direction calculation in the laser self-mixing interference integral reconstruction method.

[0080] Application Example 2:

[0081] In order to verify the effect of the laser self-mixing interference displacement measurement method based on complex exponential transformation proposed in this embodiment under different line width broadening factors α and optical feedback coefficients C, simulations are performed for different parameter conditions of α and C. The reconstructed root mean square error is shown in Table 2.

[0082] Table 2 Comparison of RMS error under different line width broadening factors α and optical feedback coefficients C

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

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

[0085] Application example three:

[0086] In order to verify the effect of the laser self-mixing interference displacement measurement method based on complex exponential transformation proposed in this embodiment on the reconstruction of non-stationary displacement, the non-stationary vibration displacement is simulated and reconstructed. The processing results are shown in Figure 2. Figure 3 As shown in the figure, it can be seen that the asymmetric characteristic of the positive and negative frequency energy of the time-frequency spectrum obtained by the displacement measurement method described in this embodiment under this condition still exists, and a small reconstruction error with a root mean square error of 20.3nm is obtained, indicating that the method is robust to non-stationary displacement reconstruction.

[0087] Application example 4:

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

[0089] Table 3 Comparison of reconstruction errors 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 close to 10 nm. It can be seen that the method is also robust to noise signals.

[0092] Embodiment 2

[0093] Correspondingly, this embodiment provides a laser self-mixing interference displacement measurement device based on complex exponential transformation, which is used to implement the laser self-mixing interference displacement measurement method based on complex exponential transformation described in Example 1, including 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 feedback light reflected from the surface of the target object, generate a laser self-mixing interference signal, and convert it into a current signal.

[0096] The signal processing and storage system is used to amplify and filter the current signal, calculate the reconstructed displacement based on the self-mixing interference signal obtained after processing, and store all the data generated during the displacement measurement process.

[0097] Furthermore, the laser used for emitting the light source in the light source emitting system includes but is not limited to: semiconductor laser, fiber laser, solid laser, gas laser, preferably semiconductor laser.

[0098] In order to verify the effectiveness and superiority of the device provided in this embodiment, some specific cases are provided below:

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

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

[0101] The light source emission system uses a multi-longitudinal mode laser diode as the light source, with an output wavelength of 650nm and a power of 7mW. The diode is driven by a constant current power supply with an operating 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, wherein the photodiode is integrated into the LD package to detect changes in interference intensity, which are then converted into current signals and acquired by the data acquisition card DAC.

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

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

[0105] Embodiment 3

[0106] This embodiment provides an electronic device, which includes: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the laser self-mixing interference displacement measurement method based on complex exponential transformation as described in any embodiment of the present invention is implemented.

[0107] Embodiment 4

[0108] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the laser self-mixing interference displacement measurement method based on complex exponential transformation as described in any embodiment of the present invention is implemented.

[0109] In the embodiments of the present application, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can represent the existence of A alone, the existence of A and B at the same time, and the existence of B alone. Among them, A and B can be singular or plural. The character " / " generally indicates that the previous and next associated objects are in an "or" relationship. "At least one of the following" and similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b and c can be represented by: a, b, c, a and b, a and c, b and c, or a and b and c, where a, b, c can be single or multiple.

[0110] Those of ordinary skill in the art will appreciate that the various units and algorithm steps described in the embodiments disclosed herein can be implemented in a combination of electronic hardware, computer software, and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0111] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0112] In several embodiments provided in the present application, if any function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory; hereinafter referred to as: ROM), random access memory (Random Access Memory; hereinafter referred to as: RAM), disk or optical disk, and other media that can store program codes.

[0113] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A laser self-mixing interference displacement measurement method based on complex exponential transformation, characterized in that: The following steps are involved: S1: Obtain self-mixing interference signal P; S2: Using the imaginary unit i*P as the exponent, construct a complex exponential self-mixing interference signal X i*P , where X is the base; S3: the complex exponential self-mixing interference signal X i*P Perform time-frequency transformation to obtain a time-frequency matrix M = [t, f, A], where t is time; f is the frequency; A is the corresponding matrix amplitude; S4: Extract the maximum amplitude A at each time t according to the time-frequency matrix M t The corresponding frequency f t , recorded as 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 interference displacement measurement method based on complex exponential transformation according to claim 1 is characterized in that: The step S1 also includes: performing DC isolation processing on the acquired self-mixing interference signal P to remove the DC component in the signal.

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

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

5. The laser self-mixing interference displacement measurement method based on complex exponential transformation 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 every moment t i Amplitude included Traverse and identify each moment t i The maximum amplitude included And find the corresponding instantaneous frequency f according to the j value 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 interference displacement measurement method based on complex exponential transformation according to claim 1 is characterized in that: The calculation formula of the reconstructed displacement is specifically: Where D t is the reconstruction displacement at time t; λ is the laser wavelength; f t is the instantaneous frequency.

7. A laser self-mixing interference displacement measurement device based on complex exponential transformation, characterized in that: The device is used to implement the laser self-mixing interference displacement measurement method based on complex exponential transformation as described in any one of claims 1 to 6, comprising a light source emission system, a signal acquisition system, and a signal processing and storage system connected in sequence; A light source emission system, used for emitting laser light to the surface of a target object; A signal acquisition system, used to receive 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 self-mixing interference signal obtained after processing, and store all the data generated during the displacement measurement process.

8. The laser self-mixing interference displacement measurement device based on complex exponential transformation according to claim 7, characterized in that: The laser used for emitting the light source in the light source emitting system includes but is not limited to: semiconductor laser, fiber laser, solid laser, gas laser.

9. 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 as described in any one of claims 1 to 6 when executing the computer program.

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

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