Spectroscopic interferometric displacement measurement system and method with adjustable working distance based on a fiber double-michelson configuration

Abstract

The present application belongs to the field of optical spectrum interference displacement measurement, and discloses a spectrum interference displacement measurement system and method with adjustable working distance based on a fiber double Fizeau structure. The system comprises a light source, a first fiber circulator, a second fiber circulator, a first light path, a second light path, a spectrometer and a computer. The first light path is provided with a first fiber collimator, a first flat beam splitter and a mirror, and the mirror is installed on a manual linear displacement stage. The second light path is provided with a second fiber collimator, a second flat beam splitter and a measured sample. The interference light generated by the two Fizeau structures converges at the second fiber circulator, and the change of the optical path caused by the change of the working distance of the second light path is compensated by adjusting the position of the mirror, so that the working distance is flexibly adjusted. The present application has the advantages of arbitrary adjustment of the working distance, strong anti-interference ability of the common light path, small volume and low cost of the all-fiber structure.

Description

Technical Field

[0001] This invention belongs to the field of optical spectral interferometric displacement measurement, specifically relating to a spectral interferometric displacement measurement system and method with adjustable working distance based on a fiber optic double Friesian structure. Background Technology

[0002] Fiber optic spectral interferometry displacement measurement technology is an important research direction in the field of precision measurement. A spectral interferometer utilizes a low-coherence light source, splitting the emitted light into a measurement end and a reference end using a beam splitter. Interference is generated by the optical path difference between the two beams, and the optical path difference is calculated by acquiring the spectral interference signal through a spectrometer, thus achieving displacement measurement. Compared with traditional laser interferometry, fiber optic white-light interferometry can perform absolute measurements of static physical parameters and has advantages such as high sensitivity, intrinsic safety, and resistance to electromagnetic interference. The spectral interferometer only requires a single signal acquisition to calculate the displacement, resulting in high measurement efficiency and a measurement frequency exceeding 10 kHz. Furthermore, the fiber optic device has a simple structure, allowing the measurement end to be miniaturized and installed as a sensor on various devices, making it widely applicable.

[0003] Commonly used fiber optic interferometer structures include Michelson interferometers, Mach-Zehnder interferometers, and Fizeau interferometers. Among these, the Fizeau interferometer employs a common-path interference structure, with the measurement and reference ends propagating in the same direction. It boasts advantages such as simple construction, excellent anti-interference capabilities, and measurement accuracy down to the nanometer level. For example, a measurement system based on the Fizeau common-path structure has been proposed in related technologies. This system uses reflection from the fiber optic probe end face to form the reference light and reflection from the surface of the object under test to form the probe light, allowing both beams to propagate in the same fiber. This effectively cancels phase jitter caused by factors such as temperature drift and vibration (see Chinese Patent CN210533292U). Furthermore, some solutions achieve simplified sample displacement measurement by having the reference arm and sample arm share a common optical interference path, allowing the split optical signals to return to the reference and interference beams respectively in the same optical path (see Chinese Patent CN205014951U).

[0004] However, an inherent drawback of the Fizeau interferometer is that its working distance is directly related to the spectrometer resolution. Because the reference and measurement beams in the Fizeau interferometer propagate along the same path, the measurable optical path difference is limited by the spectrometer resolution, typically reaching only about 2 mm. In the aforementioned common-path scheme, the distance between the optical interference path and the sample is limited to within 1 mm. This makes the fiber optic probe highly susceptible to collisions with the sample, potentially damaging both the precision sample and the probe, and severely restricting the application scenarios of the Fizeau interferometric displacement measurement system.

[0005] In addition, Chinese patent CN108050941A discloses a frequency-modulated continuous wave laser interferometric fiber displacement sensor, which calculates displacement by the initial phase offset of the beat frequency signal and has a measurement accuracy of up to 10 nm. However, it uses a single-frequency tunable laser as the light source, which is different from the low-coherence optical spectrum interference principle, and the optical path structure is a single-stage Fizeau type, so the working distance is still limited.

[0006] In summary, existing Fizeau interferometric displacement measurement techniques have significant shortcomings when extending the working distance: on the one hand, the traditional single-stage Fizeau common-path structure has a short working distance and is prone to collision with the measured object; on the other hand, existing two-stage interferometry schemes, whether based on high-resolution spectrometers (without physical optical path compensation) or using light sources different from those used in low-coherence spectral interferometry, fail to achieve flexible and adjustable working distance with a simple all-fiber dual Fizeau tandem structure. Therefore, there is an urgent need to develop a low-cost all-fiber spectral interferometric displacement measurement system that can achieve flexible and adjustable working distance while maintaining the simplicity of the common-path structure and its anti-interference advantages. Summary of the Invention

[0007] To address the shortcomings of the existing technologies, this invention provides a spectral interferometric displacement measurement system and method based on an adjustable working distance of a fiber optic dual Fizeau structure. This aims to solve the problems of short working distance and easy collision with the sample in existing Fizeau interferometers, while avoiding the drawbacks of large system size and high cost caused by using polarization devices or discrete optical components. The result is a fully fiber optic spectral interferometric displacement measurement system with flexible and adjustable working distance, simple structure, and strong anti-interference capability.

[0008] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0009] A first aspect of the present invention is to provide a spectral interferometric displacement measurement system with adjustable working distance based on a fiber optic dual Friesian structure, comprising a light source for providing low-coherence light, and further comprising:

[0010] First fiber optic circulator and second fiber optic circulator;

[0011] The light source is connected to the first fiber optic circulator, and the first fiber optic circulator is connected to the second fiber optic circulator;

[0012] The first optical path is connected to the first fiber optic circulator, and a first fiber optic collimator, a first flat beam splitter and a reflector are arranged sequentially along the optical transmission direction. The reflector is mounted on a manual linear displacement stage.

[0013] The second optical path is connected to the second fiber optic circulator, and a second fiber optic collimator, a second flat beam splitter, and the sample to be tested are arranged sequentially along the optical transmission direction.

[0014] A spectrometer is connected to the second fiber optic circulator;

[0015] A computer, connected to the spectrometer signal, is used to calculate the displacement.

[0016] The optical path of the light reflected by the first flat beam splitter and transmitted through the second flat beam splitter is matched with the light transmitted through the first flat beam splitter and reflected by the second flat beam splitter, generating a spectral interference signal. When the distance between the second flat beam splitter and the sample under test changes, the position of the reflector is changed by adjusting the manual linear displacement stage to adjust the working distance.

[0017] Furthermore, the beam splitting ratio of the first flat beam splitter is 50:50.

[0018] Furthermore, the surface of the first flat beam splitter coated with a beam-splitting film faces the first fiber collimator, and the surface coated with an anti-reflection film faces the reflector.

[0019] Furthermore, the beam splitting ratio of the second flat beam splitter is determined based on the reflectivity of the sample being tested.

[0020] Furthermore, the surface of the second flat beam splitter coated with a beam-splitting film faces the second fiber collimator, and the surface coated with an anti-reflection film faces the sample under test.

[0021] A second aspect of the present invention is to provide a measurement method according to said system, comprising the following steps:

[0022] The attitudes of the first flat beam splitter and the reflector in the first Fiso structure are adjusted to be perpendicular to the optical axis of the first fiber collimator, and the attitudes of the second flat beam splitter and the second fiber collimator in the second Fiso structure are adjusted to be perpendicular to the surface of the sample being tested.

[0023] The position of the reflector is adjusted so that the optical path of the light reflected by the first flat beam splitter and transmitted through the second flat beam splitter is matched with the optical path of the light transmitted through the first flat beam splitter and reflected by the second flat beam splitter, thereby obtaining a spectral interference signal.

[0024] Extract the system background light and subtract it from the spectral interference signal;

[0025] The displacement is calculated based on the spectral interference signal after removing the background light.

[0026] Furthermore, the attitude adjustment is based on the judgment that the light intensity received by the spectrometer reaches its maximum value.

[0027] Furthermore, the algorithm for calculating the displacement of the spectral interferometric signal includes:

[0028] The signal shaping step involves extracting the envelope caused by the spectral shape of the light source through the maximum point, removing the signal envelope and re-superimposing a Gaussian envelope, and multiplying the signal with the superimposed Gaussian envelope by a Hanning window to suppress spectral leakage.

[0029] The non-uniform fast Fourier transform and inverse transform steps involve performing a non-uniform fast Fourier transform on the shaped signal to convert the non-equally spaced wavelength amplitude signals into equally spaced wavenumber amplitude signals, selecting the required frequency signal after the transformation, setting other values ​​to zero, and restoring the spectral interference signal with other irrelevant signals filtered out through the inverse fast Fourier transform.

[0030] The phase extraction and unwrapping steps extract the phase of the spectral interference signal after filtering out other irrelevant signals, and use a point-by-point phase unwrapping algorithm to unfold the folded phase;

[0031] The least squares fitting step involves performing a least squares fit between the expanded phase and the wavenumber and amplitude, and then dividing the slope obtained from the fit by... The displacement is obtained.

[0032] Working principle of the invention:

[0033] This invention employs a dual-Frieso structure cascaded optical path configuration. Low-coherence light emitted from the light source enters the first optical path via a first fiber optic circulator, is collimated by a first fiber optic collimator, and then incident on a first flat beam splitter. A portion of the light is reflected by the first flat beam splitter, transmitted through a second flat beam splitter, and reflected by the sample to reach the spectrometer. The other portion of the light is transmitted through the first flat beam splitter, reflected by the second flat beam splitter, and also reaches the spectrometer. The two beams interfere at the spectrometer. When the working distance of the second optical path (i.e., the distance between the second flat beam splitter and the sample under test) changes, the position of the reflecting mirror is adjusted by a manual linear displacement stage, altering the propagation path length of the reflected light in the first optical path. This compensates for the optical path difference caused by the change in working distance, ensuring that the two interfering beams always maintain optical path matching and that the spectrometer can stably receive the interference signal. Because this compensation mechanism is not dependent on the resolution limitations of the spectrometer, the working distance can be arbitrarily adjusted.

[0034] Compared with the prior art, the present invention has the following advantages:

[0035] (1) This invention uses a dual Fizeau structure in series and a movable mirror in the first optical path to compensate for the change in optical path caused by the change in working distance of the second optical path. This breaks through the bottleneck of small working distance of traditional Fizeau interferometers, realizes flexible and adjustable working distance, and effectively avoids the risk of collision between the fiber optic probe and the sample under test.

[0036] (2) In this invention, the two interference beams are transmitted in a common optical path manner in their respective Fizeau structures. The propagation direction of the measurement end and the reference end is consistent, which can effectively offset the influence of external factors such as environmental vibration and temperature drift on the optical path, and the system has excellent stability.

[0037] (3) The system of the present invention uses optical fiber devices and optical fiber circulators to realize the connection between the components. It does not require polarization devices or discrete optical elements, has a compact structure, is easy to integrate and miniaturize, and can be installed on large equipment with limited space, making it widely applicable.

[0038] (4) The present invention can replace the second flat beam splitter with different splitting ratios according to the surface reflectivity of the sample being measured, thereby achieving high-precision measurement of different types of samples and improving the applicability of the system.

[0039] (5) The measurement method proposed in this invention is applicable to most spectrometers, and the accuracy of the solution method can reach 10 nm, which improves the applicability and accuracy of the system. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the spectral interferometric displacement measurement system with adjustable working distance based on the fiber optic double Friesian structure of the present invention;

[0041] Figure 2 This invention represents the optimal beam splitting ratio of the second flat beam splitter for samples with different reflectivities.

[0042] Figure 3 This is a schematic diagram illustrating the principle of adjustable optical path matching and working distance of the present invention;

[0043] Figure 4 This is a comparison of the signals of the present invention and the Michelson structure-spectral interferometry system under the same environment over one hour.

[0044] Figure 5 The comparison is between the spectral signal under the second flat beam splitter with the optimal splitting ratio and background light removal and the spectral signal under the second flat beam splitter with a non-optimal splitting ratio and without background light removal, and the noise of the solution results.

[0045] Figure 6 This is a flowchart of the algorithm for calculating displacement from spectral interferometric signals.

[0046] Wherein, 1 is the light source; 2 is the first fiber optic circulator; 3 is the first fiber optic collimator; 4 is the first flat beam splitter; 5 is the reflector; 6 is the manual linear displacement stage; 7 is the second fiber optic circulator; 8 is the second fiber optic collimator; 9 is the second flat beam splitter; 10 is the sample under test; and 11 is the spectrometer. Detailed Implementation

[0047] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings. The following examples are for illustrative purposes only and should not be considered as limiting the scope of the invention.

[0048] like Figure 1 As shown, the spectral interferometric displacement measurement system based on a fiber optic dual-Frieso structure with adjustable working distance provided by the present invention includes a light source 1 for providing low-coherence light. The light source 1 is connected to a first optical path section via a first fiber optic circulator 2. The first fiber optic circulator 2 is connected to a second fiber optic circulator 7. The second fiber optic circulator 7 connects the second optical path section to a spectrometer 11. The first optical path sequentially includes a first fiber optic collimator 3, a first flat beam splitter 4, and a reflector 5, with the reflector 5 mounted on a manual linear displacement stage 6. The second optical path sequentially includes a second fiber optic collimator 8, a second flat beam splitter 9, and the sample 10 to be measured. The signal from the spectrometer 11 is transmitted to a computer, and the computer performs displacement calculations.

[0049] The first flat beam splitter 4 needs to be a beam splitter with a splitting ratio of 50:50 to maximize the contrast of the spectral interference signal. The surface of the first flat beam splitter 4 coated with the beam splitting film must face the first fiber collimator 3, and the surface coated with the anti-reflection film must face the reflecting mirror 5.

[0050] The splitting ratio of the second flat beam splitter 9 needs to be adjusted according to the reflectivity of the sample under test to maximize the contrast of the spectral interference signal. The surface of the second flat beam splitter 9 coated with the beam splitting film must face the second fiber collimator 8, and the surface coated with the antireflection film must face the sample under test 10.

[0051] The optical path lengths of the light reflected by the first flat beam splitter 4 and transmitted through the second flat beam splitter 9, and the light transmitted through the first flat beam splitter 4 and reflected by the second flat beam splitter 9, must be matched to generate a spectral interference signal. When the distance between the second flat beam splitter 9 and the sample 10 under test changes, the working distance can be adjusted by adjusting the position of the reflecting mirror 5.

[0052] A spectral interferometric displacement measurement method based on an optical fiber dual Friesian structure with adjustable working distance includes the following steps:

[0053] Step 1: Adjust the orientation of the first flat beam splitter 4 and the reflector 5 so that they are both perpendicular to the first fiber collimator 3;

[0054] Step 2: Adjust the orientation of the second flat beam splitter 9 so that it is perpendicular to the second fiber collimator 8. Taking the second flat beam splitter 9 and the second fiber collimator 8 as a whole, adjust their orientation so that they are perpendicular to the sample 10 under test;

[0055] Step 3: Adjust the manual linear displacement stage 6 to match the optical path so that the spectrometer 11 receives the spectral interference signal;

[0056] Step 4: Extract and subtract the system background light, and calculate the displacement based on the obtained spectral interference signal.

[0057] Step 1 involves adjusting the orientation of the first flat beam splitter 4 and the reflector 5 so that they are both perpendicular to the first fiber collimator 3. Specifically, this involves:

[0058] Step 1-1: Turn on the light source 1 and the spectrometer 11, and transmit the signal from the spectrometer 11 to the computer. Connect the light source 1, the first fiber collimator 3, and the spectrometer 11 to the first fiber optic circulator 2 in sequence according to the optical path transmission order;

[0059] Steps 1-2: Cover the reflector 5. Based on the intensity of light received by the spectrometer 11, adjust the orientation of the first flat beam splitter 4 so that it is perpendicular to the optical axis of the first fiber collimator 3. When the intensity of light received by the spectrometer 11 is at its maximum, it can be considered that the first flat beam splitter 4 is completely perpendicular to the optical axis 3 of the first collimator.

[0060] Steps 1-3: Remove the obstruction of reflector 5. Based on the intensity of light received by spectrometer 11, adjust the orientation of reflector 5 so that it is perpendicular to the optical axis of the first fiber collimator 3. When the intensity of light received by spectrometer 11 is at its maximum, it can be considered that reflector 5 is completely perpendicular to the optical axis of the first fiber collimator 3.

[0061] Step 2 involves adjusting the orientation of the second planar beam splitter 9 so that it is perpendicular to the second fiber collimator 8. Taking the second planar beam splitter 9 and the second fiber collimator 8 as a whole, the orientation is adjusted so that they are perpendicular to the sample 10 under test, specifically as follows:

[0062] Step 2-1: Disconnect the light source 1 and the spectrometer 11 from the first fiber optic circulator 2. Connect the light source 1, the second fiber optic collimator 8, and the spectrometer 11 to the second fiber optic circulator 7 in sequence according to the optical path transmission order;

[0063] Step 2-2: Cover the sample 10 to be tested. Using the intensity of light received by the spectrometer 11 as a criterion, adjust the orientation of the second flat beam splitter 9 so that it is perpendicular to the optical axis of the second fiber collimator 8. When the intensity of light received by the spectrometer 11 is at its maximum, it can be considered that the second flat beam splitter 9 is completely perpendicular to the optical axis of the second fiber collimator 8. The splitting ratio of the second flat beam splitter needs to be adjusted according to the reflectivity of the sample to maximize the contrast of the spectral interference signal. Figure 2 As shown. The surface of the second flat beam splitter coated with the beam-splitting film must face the second collimator, and the surface coated with the anti-reflection film must face the sample being tested.

[0064] Steps 2-3: Remove the obstruction from the sample 10 under test, and use fixtures to fix the second fiber collimator 8 and the second flat beam splitter 9 as a whole. Based on the intensity of the light received by the spectrometer 11, adjust the orientation of this whole assembly so that the second fiber collimator 8 and the second flat beam splitter 9 are perpendicular to the sample 10 under test. When the light intensity received by the spectrometer 11 is at its maximum, it can be considered that the second fiber collimator 8 and the second flat beam splitter 9 are perpendicular to the sample 10 under test.

[0065] Before adjusting the manual linear displacement stage 6 as described in step 3, the light source 1 and the spectrometer 11 need to be disconnected from the second fiber optic circulator 7. The light source 1, the first fiber optic collimator 3, and the incident end of the second fiber optic circulator 7 are connected to the first fiber optic circulator 2 in sequence according to the optical path transmission order. The output end of the first fiber optic circulator 2, the second fiber optic collimator 8, and the spectrometer 11 are connected to the second fiber optic circulator 7 in sequence according to the optical path transmission order.

[0066] Step 3 involves matching the optical path lengths of the light reflected by the first flat beam splitter and transmitted through the second flat beam splitter, and the light transmitted through the first flat beam splitter and reflected by the second flat beam splitter. When the optical path difference between the two beams is less than the measurement range of the spectrometer, the spectrometer will receive a spectral interference signal. When the distance between the second collimator, the second flat beam splitter, and the sample changes, the optical path length of the light transmitted through the first flat beam splitter and reflected by the second flat beam splitter changes. Adjusting the position of the reflecting mirror adjusts the optical path length of the light reflected by the first flat beam splitter and transmitted through the second flat beam splitter. Therefore, arbitrary adjustment of the working distance is possible.

[0067] Step 4 involves extracting the system background light by simultaneously blocking the reflector 5 and the sample 10 under test, reading the signal from the spectrometer 11 10 times, and averaging the results to obtain the system background light signal that is independent of the spectral interference signal.

[0068] Step 4, subtracting the system background light, involves removing the obstruction between the reflector 5 and the sample 10 after extracting the system background light, reading the signal from the spectrometer 11, and subtracting the extracted system background light signal.

[0069] Step 4 describes an algorithm for calculating the displacement of spectral interferometric signals, which includes signal shaping, non-uniform fast Fourier transform and inverse transform, phase extraction and unwrapping, and least squares fitting steps, such as... Figure 6 As shown.

[0070] The signal shaping step includes extracting the envelope caused by the spectral shape of the light source through the maximum point, removing the signal envelope and re-superimposing a Gaussian envelope, and multiplying the signal with the superimposed Gaussian envelope by a Hanning window to suppress spectral leakage.

[0071] The non-uniform fast Fourier transform and inverse transform steps include performing a non-uniform fast Fourier transform on the shaped signal to convert the non-equally spaced wavelength amplitude signals into equally spaced wavenumber amplitude signals. Then, the desired frequency signal after the transform is selected, other values ​​are set to zero, and the signal is restored to a spectral interference signal with other irrelevant signals filtered out using an inverse fast Fourier transform.

[0072] The phase extraction and unwrapping steps include extracting the phase of the spectral interference signal after filtering out other irrelevant signals, and using a point-by-point phase unwrapping algorithm to unfold the folded phase.

[0073] The least squares fitting step includes performing a least squares fit between the expanded phase and the wavenumber and amplitude, and dividing the slope obtained from the fit by... The displacement is obtained.

[0074] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several modifications and improvements can be made without departing from the inventive concept, and these all fall within the protection scope of the present invention.

Claims

1. A spectral interferometric displacement measurement system with adjustable working distance based on a fiber optic dual Friesian structure, comprising a light source (1) for providing low-coherence light, characterized in that, Also includes: First fiber optic circulator (2) and second fiber optic circulator (7); The light source (1) is connected to the first fiber optic circulator (2), and the first fiber optic circulator (2) is connected to the second fiber optic circulator (7). The first optical path is connected to the first fiber optic circulator (2), and a first fiber optic collimator (3), a first flat beam splitter (4) and a reflector (5) are arranged sequentially along the optical transmission direction. The reflector (5) is mounted on a manual linear displacement stage (6). The second optical path is connected to the second fiber optic circulator (7), and a second fiber optic collimator (8), a second flat beam splitter (9) and the sample to be tested (10) are arranged sequentially along the optical transmission direction. The spectrometer (11) is connected to the second fiber optic circulator (7); A computer, connected to the spectrometer (11), is used to calculate the displacement. The optical path matching between the light reflected by the first flat beam splitter (4) and transmitted through the second flat beam splitter (9) and the light transmitted through the first flat beam splitter (4) and reflected by the second flat beam splitter (9) generates a spectral interference signal; when the distance between the second flat beam splitter (9) and the sample under test (10) changes, the position of the reflector (5) is changed by adjusting the manual linear displacement stage (6) to achieve the adjustment of the working distance.

2. The spectral interferometric displacement measurement system with adjustable working distance based on a fiber optic dual Friesian structure according to claim 1, characterized in that, The first flat beam splitter (4) has a beam splitting ratio of 50:

50.

3. The spectral interferometric displacement measurement system with adjustable working distance based on a fiber optic dual Friesian structure according to claim 1, characterized in that, The surface of the first flat beam splitter (4) coated with a beam splitting film faces the first fiber collimator (3), and the surface coated with an anti-reflection film faces the reflector (5).

4. The spectral interferometric displacement measurement system with adjustable working distance based on a fiber optic dual Friesian structure according to claim 1, characterized in that, The splitting ratio of the second flat beam splitter (9) is determined based on the reflectance of the sample (10) being tested.

5. The spectral interferometric displacement measurement system with adjustable working distance based on a fiber optic dual Friesian structure according to claim 1, characterized in that, The surface of the second flat beam splitter (9) coated with a beam splitting film faces the second fiber collimator (8), and the surface coated with an anti-reflection film faces the sample under test (10).

6. A measurement method for a spectral interferometric displacement measurement system based on an adjustable working distance of a fiber optic dual Friesian structure as described in any one of claims 1-5, comprising the following steps: Adjust the orientation of the first flat beam splitter (4) and the reflector (5) in the first Fiso structure to make them perpendicular to the optical axis of the first fiber collimator (3), and adjust the orientation of the second flat beam splitter (9) and the second fiber collimator (8) in the second Fiso structure to make them perpendicular to the surface of the sample (10) under test. Adjust the position of the reflector (5) so that the optical path between the light reflected by the first flat beam splitter (4) and transmitted through the second flat beam splitter (9) and the light transmitted through the first flat beam splitter (4) and reflected by the second flat beam splitter (9) is matched, and a spectral interference signal is obtained. Extract the system background light and subtract it from the spectral interference signal; The displacement is calculated based on the spectral interference signal after removing the background light.

7. The measurement method according to claim 6, characterized in that, The attitude adjustment is based on the judgment that the light intensity received by the spectrometer (11) reaches the maximum value.

8. The measurement method according to claim 6, characterized in that, The algorithm for calculating the displacement of the spectral interferometric signal includes: The signal shaping step involves extracting the envelope caused by the spectral shape of the light source through the maximum point, removing the signal envelope and re-superimposing a Gaussian envelope, and multiplying the signal with the superimposed Gaussian envelope by a Hanning window to suppress spectral leakage. The non-uniform fast Fourier transform and inverse transform steps involve performing a non-uniform fast Fourier transform on the shaped signal to convert the non-equally spaced wavelength amplitude signals into equally spaced wavenumber amplitude signals, selecting the required frequency signal after the transformation, setting other values ​​to zero, and restoring the spectral interference signal with other irrelevant signals filtered out through the inverse fast Fourier transform. The phase extraction and unwrapping steps extract the phase of the spectral interference signal after filtering out other irrelevant signals, and use a point-by-point phase unwrapping algorithm to unfold the folded phase; The least squares fitting step involves performing a least squares fit between the expanded phase and the wavenumber and amplitude, and then dividing the slope obtained from the fit by... The displacement is obtained.

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