Method, apparatus, medium, and computer program product for demodulating white light interferometry signals

Abstract

The application relates to the technical field of optical detection, and specifically provides a white light interference signal demodulation method, equipment, medium and computer program product. The method comprises the following steps: interference light intensity signal data which is non-uniformly distributed in a wave number domain is processed by using a non-uniform fast Fourier transform to obtain spectrum information of the interference light intensity signal data and determine a first optical path difference; the measurement resolution of the non-uniform fast Fourier transform is analyzed, if the measurement resolution is lower than a preset threshold, a to-be-measured optical path difference sequence is constructed in a preset fine measurement range with the first optical path difference as the center; the spectrum amplitude of each to-be-measured optical path difference in the to-be-measured optical path difference sequence is calculated by using a non-uniform discrete Fourier transform to obtain an amplitude spectrum of the to-be-measured optical path difference sequence; and a second optical path difference is determined according to the spectrum peak of the amplitude spectrum. The application effectively balances the demodulation accuracy and efficiency through NUFFT coarse positioning and NUDFT local fine adjustment.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical detection technology, in particular to a white light interference signal demodulation method, device, medium and computer program product. BACKGROUND

[0002] White light spectral interferometry (FD-OCT) has the characteristics of non-contact, high precision and fast speed, and is often used to measure optical and geometric parameters such as refractive index, thickness, distance and displacement, or indirectly measure physical quantities such as temperature and pressure. From the application scene, this technology is mainly used to detect biological tissues, thin films or parts.

[0003] In the FD-OCT system, white light source is used for interference, and grating and other spectral elements are used to separate the interference light of different wavelengths. However, the spectral characteristics of such elements result in uneven interference light intensity signals in the wave number domain, so that the Fourier transform (FFT) method cannot be used to process such signals. In order to solve the problem, researchers have proposed many data processing methods, such as peak-to-peak signal processing algorithm, wave number interpolation resampling signal processing algorithm or maximum likelihood estimation signal processing algorithm. However, the above methods all have the problem of contradiction between measurement accuracy and efficiency. The peak-to-peak method has poor adaptability to environmental noise, poor stability, is greatly affected by environmental noise, and has low measurement accuracy. The wave number resampling algorithm is related to the spectral range, and needs to resample in the wave number domain. The maximum likelihood estimation method has high measurement accuracy, but has large calculation amount and low demodulation efficiency. SUMMARY

[0004] The purpose of the present application is to overcome the shortcomings of the prior art, and to provide a white light interference signal demodulation method, device, medium and computer program product, which improves the signal demodulation accuracy and efficiency.

[0005] To achieve the above purpose, the present application adopts the following technical scheme:

[0006] In a first aspect, the present application provides a white light interference signal demodulation method, comprising:

[0007] The non-uniform fast Fourier transform is used to process the non-uniformly distributed interference light intensity signal data in the wave number domain, to obtain the spectral information of the interference light intensity signal data and determine the first optical path difference;

[0008] The measurement resolution of the non-uniform fast Fourier transform is analyzed, and if the measurement resolution is lower than a preset threshold, a to-be-measured optical path difference sequence is constructed in a preset fine measurement range with the first optical path difference as the center.

[0009] The frequency spectrum amplitude of each optical path difference to be measured in the sequence of optical path differences to be measured is calculated by non-uniform discrete Fourier transform, and an amplitude spectrum of the sequence of optical path differences to be measured is obtained.

[0010] A second optical path difference is determined according to a spectrum peak of the amplitude spectrum.

[0011] Further, the interference light intensity signal data non-uniformly distributed in the wave number domain is processed by using the non-uniform fast Fourier transform to obtain the frequency spectrum information of the interference light intensity signal data, including:

[0012] The interference light intensity signal data is convoluted and interpolated with a window function at uniformly oversampled points to obtain a uniformly sampled data sequence.

[0013] Fast Fourier transform is performed on the data sequence to obtain a convolution function spectrum.

[0014] The convolution function spectrum is deconvoluted to obtain the frequency spectrum information of the interference light intensity signal data.

[0015] Further, the interference light intensity signal data is convoluted and interpolated with a window function at uniformly oversampled points to obtain a uniformly sampled data sequence, including:

[0016] Let be the uniformly oversampled interpolation points, ; wherein, , represents the minimum value of the wave number in the non-uniformly sampled points of the interference light intensity signal, represents the maximum value of the wave number in the non-uniformly sampled points of the interference light intensity signal; represents the serial number of the oversampled interpolation points; is the number of oversampled points, ; R is the oversampling rate, and N is the number of non-uniformly sampled points;

[0017] The window function is a Gaussian bell function, and the Gaussian bell function is expressed as wherein, is a positive real number parameter;

[0018] The calculation formula of the convolution interpolation is as follows:

[0019] ;

[0020] wherein, represents the uniformly sampled data sequence obtained by convolution interpolation; represents the non-uniformly sampled points; represents the interference light intensity signal data of the non-uniformly sampled points.

[0021] Further, the convolution function spectrum information is deconvoluted to obtain the spectrum information of the interference light intensity signal, comprising:

[0022] The spectrum of the Gaussian bell function is , ω represents the angular frequency;

[0023] The convolution function spectrum is the product of the spectrum of the Gaussian bell function and the spectrum of the interference light intensity signal data, and the calculation formula of the spectrum information of the interference light intensity signal data is as follows:

[0024] ;

[0025] Among them, S (ω) represents the spectrum of the interference light intensity signal data; S (ω) represents the convolution function spectrum.

[0026] Further, the measurement resolution of the non-uniform fast Fourier transform is analyzed, comprising:

[0027] The measurement resolution of the non-uniform fast Fourier transform is the same as that of the discrete Fourier transform, and the expression of the discrete Fourier transform is as follows:

[0028] 1;

[0029] Among them, is the spectrum line number; is the data sequence after interpolation and uniformization; is the sequence number;

[0030] The expression of the sampling frequency is as follows:

[0031] ;

[0032] The expression of the angular frequency is as follows:

[0033] ;

[0034] The measurement resolution of the discrete Fourier transform is ;

[0035] The measurement resolution of the non-uniform fast Fourier transform is .

[0036] Further, a to-be-measured optical path difference sequence is constructed in a preset fine measurement range with the first optical path difference as the center, comprising:

[0037] With the first optical path difference as the center, is the distance, and the fine measurement range is set ;

[0038] In the fine measurement range, a sequence of optical path differences to be measured is constructed with a step size of , , ; wherein, is the length of the sequence of optical path differences to be measured, .

[0039] Further, before processing the non-uniformly distributed interference light intensity signal data in the wave number domain using the non-uniform fast Fourier transform to obtain the spectral information of the interference light intensity signal data, the method further comprises: calibrating the wave number value corresponding to each non-uniform sampling point in the interference light intensity signal by Hilbert transform.

[0040] Further, calibrating the wave number value corresponding to each non-uniform sampling point in the interference light intensity signal by Hilbert transform comprises:

[0041] performing high-pass filtering on the interference light intensity signal to filter out the direct current component;

[0042] performing Hilbert transform on the filtered signal to obtain a quadrature signal thereof;

[0043] calculating the ratio of the filtered signal to the quadrature signal and performing arctangent operation to solve the wrapped phase;

[0044] performing unwrapping operation on the wrapped phase to obtain continuous phase information;

[0045] calibrating the wave number value corresponding to each non-uniform sampling point according to the relationship between the continuous phase information and the optical path difference.

[0046] In a second aspect, the present application further provides an electronic device, comprising: a processor, and a memory storing a program, the program comprising instructions which, when executed by the processor, cause the processor to perform the demodulation method of white light interference signal described above.

[0047] In a third aspect, the present application further provides a non-transitory machine readable medium storing computer instructions, the computer instructions being used to cause the computer to perform the demodulation method of white light interference signal described above.

[0048] In a fourth aspect, the present application further provides a computer program product, comprising computer program / instructions, characterized in that the computer program / instructions are executed by a processor to implement the demodulation method of white light interference signal described above.

[0049] The application provides a white light interference signal demodulation method. The application can effectively balance the demodulation precision and efficiency, and can complete high-precision calculation of the white light interference signal under the time complexity of BRIEF DESCRIPTION OF DRAWINGS

[0050] In order to more clearly illustrate the embodiments of the application or the technical solutions in the prior art, the drawings needed in the embodiments or the prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the application, and other embodiments can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0051] Figure 1 is a flowchart of a white light interference signal demodulation method provided by the embodiment of the application;

[0052] Figure 2 is a comparison diagram of the effect of the non-uniform fast Fourier transform and the fast Fourier transform;

[0053] Figure 3 is a comparison diagram of the effect of the non-uniform fast Fourier transform and the demodulation method of the embodiment of the application;

[0054] Figure 4 is a structural diagram of an electronic device provided by the embodiment of the application. DETAILED DESCRIPTION

[0055] The embodiments of the application will be described in detail below with reference to the drawings. Although some embodiments of the application are shown in the drawings, it should be understood that the application can be implemented in various forms, and should not be interpreted as being limited to the embodiments described herein, on the contrary, these embodiments are provided to make the application more thorough and complete. It should be understood that the drawings and embodiments of the application are only for exemplary purposes, and are not used to limit the protection scope of the application.

[0056] As shown in Figure 1 , the embodiment of the application provides a white light interference signal demodulation method. Figure 1 is a flowchart of the white light interference signal demodulation method, and the flowchart only shows the logical order of the method of the embodiment, and under the premise of not conflicting with each other, the steps shown or described can be completed in an order different from that shown in the embodiment of the application. Figure 1

[0057] Referring to Figure 1 ​The method of the embodiment of the present application specifically comprises the following steps:

[0058] Step S101: processing the interference light intensity signal data non-uniformly distributed on the wave number domain by using a non-uniform fast Fourier transform (NUFFT) to obtain the spectrum information of the interference light intensity signal data and determine a first optical path difference.

[0059] Step S101 specifically comprises:

[0060] Step S1011: performing convolution interpolation on the interference light intensity signal data and a window function at uniformly oversampled points to obtain a uniformly sampled data sequence.

[0061] In the embodiment of the present application, the window function adopts a Gaussian bell function, and the Gaussian bell function is expressed as wherein, is a positive real number parameter, which determines the width of the bell curve.

[0062] Let be the uniformly oversampled interpolation point, ; wherein, , represents the minimum value of the wave number in the non-uniformly sampled points of the interference light intensity signal, represents the maximum value of the wave number in the non-uniformly sampled points of the interference light intensity signal; represents the serial number of the oversampled interpolation point; is the number of oversampled points, ; R is the oversampling rate, and N is the number of non-uniformly sampled points;

[0063] The calculation formula of the convolution interpolation is as follows:

[0064] ;

[0065] wherein, represents the uniformly sampled data sequence obtained by the convolution interpolation; represents the non-uniformly sampled point; represents the interference light intensity signal data of the non-uniformly sampled point.

[0066] Step S1012: performing a fast Fourier transform (FFT) on the data sequence to obtain the convolution function spectrum , .

[0067] Step S1013: performing a deconvolution operation on the convolution function spectrum to obtain the spectrum information of the interference light intensity signal data.

[0068] The spectrum of the Gaussian bell function is expressed as , represents the angular frequency;

[0069] According to the convolution property of Fourier transform, the convolution function spectrum is the product of the spectrum of the Gaussian bell function and the spectrum of the interference light intensity signal data, and the calculation formula of the spectrum information of the interference light intensity signal data is as follows:

[0070] .

[0071] wherein, represents the spectrum of the interference light intensity signal data.

[0072] Step S102: analyzing the measurement resolution of the non-uniform fast Fourier transform, and if the measurement resolution is lower than a preset threshold, constructing a to-be-measured optical path difference sequence in a preset fine measurement range with the first optical path difference as the center.

[0073] wherein, the analyzing the measurement resolution of the non-uniform fast Fourier transform comprises:

[0074] The measurement resolution of the non-uniform fast Fourier transform is the same as the measurement resolution of the discrete Fourier transform, and the expression of the discrete Fourier transform is as follows:

[0075] 1;

[0076] wherein, is the spectral line number; is the data sequence after interpolation and uniformization; is the sequence number.

[0077] The expression of the sampling frequency is as follows:

[0078] ;

[0079] The expression of the angular frequency is as follows:

[0080] ;

[0081] The measurement resolution of the discrete Fourier transform is ;

[0082] The measurement resolution of the non-uniform fast Fourier transform is .

[0083] Since the resolution of the non-uniform fast Fourier transform is related to the width of the wave number domain , the measurement resolution is generally low. For example, for a laser light source with a center wavelength of 840 nm and a width of 40 nm, the width of the wave number domain can be calculated as = 356.39 mm -1The resolution is =17.63μm, which cannot meet the requirement of high-precision measurement, and therefore the algorithm accuracy needs to be improved.

[0084] A sequence of to-be-measured optical path differences is constructed in a preset fine measurement range centered on the first optical path difference, including:

[0085] The first optical path difference is taken as the center, is the distance, and the fine measurement range is set.

[0086] In the fine measurement range, a sequence of to-be-measured optical path differences is constructed with as the step size, . ; wherein, is the length of the sequence of to-be-measured optical path differences, .

[0087] Step S103: The frequency spectrum amplitude of each to-be-measured optical path difference in the sequence of to-be-measured optical path differences is calculated through non-uniform discrete Fourier transform (NUDFT), and the amplitude spectrum of the sequence of to-be-measured optical path differences is obtained.

[0088] Step S103 specifically includes:

[0089] Non-uniform discrete Fourier transform is performed on the to-be-measured optical path differences in the sequence of to-be-measured optical path differences, and the frequency spectrum information of the to-be-measured optical path differences is obtained;

[0090] The corresponding frequency spectrum amplitude is calculated according to the frequency spectrum information of the to-be-measured optical path differences;

[0091] The amplitude spectrum of the sequence of to-be-measured optical path differences is constructed based on the frequency spectrum amplitude of each to-be-measured optical path difference in the sequence of to-be-measured optical path differences.

[0092] Step S104: The second optical path difference is determined according to the spectrum peak of the amplitude spectrum.

[0093] The to-be-measured optical path difference corresponding to the spectrum peak position of the amplitude spectrum of the sequence of to-be-measured optical path differences is the second optical path difference.

[0094] In addition, according to the convolution interpolation formula , it can be known that when the non-uniform fast Fourier transform is used to process the interference light intensity signal, the non-uniform wave number value of the interference light received by the CCD pixel needs to be used, and therefore the sequence of wave numbers needs to be calibrated. Because the sequence to be calibrated is in the phase of the cosine term in the light intensity function, the Hilbert transform method can be used to process it after the direct current term is filtered out by high-pass filtering.

[0095] Therefore, before step S101, the application further calibrates the wave number value corresponding to each non-uniform sampling point in the interference light intensity signal through Hilbert transform, and the specific steps are as follows:

[0096] The interference light intensity signal is high-pass filtered to filter out the direct current component;

[0097] The filtered signal is subjected to Hilbert transform to obtain its quadrature signal;

[0098] The wrapped phase is calculated by calculating the ratio of the filtered signal to the quadrature signal and performing arctangent operation;

[0099] The wrapped phase is unwrapped to obtain continuous phase information;

[0100] According to the relationship between the continuous phase information and the optical path difference, the wave number value corresponding to each non-uniform sampling point is calibrated.

[0101] In order to intuitively compare the NUFFT algorithm with the FFT algorithm, and verify that the effect of the NUFFT algorithm is better than that of the FFT algorithm in the case of non-uniform sampling, the application embodiment simulates the two algorithms, and sets the optical path difference to 10 mm, i.e. 10 7 nm, the form of the simulated original light intensity signal can be set as , wherein the wavelength is in nm, and the range is set to 825 nm-835 nm, in order to simulate the case of non-uniform sampling, 2048 sampling points are randomly generated in the wavelength range, and the result is shown in Figure 2 .

[0102] According to Figure 2 , it can be seen that when the sampling is random, the signal peak appears very serious broadening phenomenon, and the NUFFT algorithm can still obtain the signal corresponding peak. According to the wavelength range of 825 nm-835 nm, the wave number domain width =91.2094 mm -1 , therefore the resolution is 0.0689 mm, according to , the calculation result (optical path difference coarse measurement value) is 0.0689x(146-1)=9.9905 mm, compared with the true value 10 mm, the error is 0.0095 mm<0.0689 mm, therefore it can be considered that the error is caused by the resolution factor. According to the simulation result, when the sampling is non-uniform, the accuracy of the NUFFT algorithm is higher than that of the FFT algorithm.

[0103] Using the same conditions, a simulation comparison was performed between the NUFFT algorithm and the results of the further refinement calculation using Non-Uniform Discrete Fourier Transform (NUDFT) in this invention. The refinement step size of NUDFT was also compared. The value is 0.01 mm. The simulation results are as follows: Figure 3 As shown, the red curve represents NUFFT with a resolution of 0.0689 mm, and the blue curve represents the result of the refinement calculation with a resolution of 0.01 mm. According to... Figure 3 It can be seen that the refined calculation has a higher resolution, a smoother spectrum, and the measurement results are closer to the actual values ​​with smaller errors.

[0104] An embodiment of the present invention also provides a non-transitory machine-readable medium storing a computer program, wherein the computer program, when executed by a computer's processor, is used to cause the computer to perform a demodulation method for white light interference signals according to an embodiment of the present invention.

[0105] An embodiment of the present invention also provides a computer program product, including a computer program, wherein the computer program, when executed by a computer processor, is used to cause the computer to perform the demodulation method for white light interference signals according to an embodiment of the present invention.

[0106] An embodiment of the present invention also provides an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor. The memory stores a computer program executable by the at least one processor, which, when executed by the at least one processor, causes the electronic device to perform the demodulation method for white light interference signals according to an embodiment of the present invention.

[0107] refer to Figure 4 The present invention will now describe a structural block diagram of an electronic device that can serve as an embodiment of the present invention, serving as an example of a hardware device applicable to various aspects of the present invention. The electronic device is intended to represent various forms of digital electronic computer devices, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the present invention described and / or claimed herein.

[0108] like Figure 4As shown, the electronic device includes a computing unit 101 that can perform various appropriate actions and processes in accordance with a computer program stored in a read only memory (ROM) 102 or a computer program loaded into a random access memory (RAM) 103 from a storage unit 108. In the RAM 103, various programs and data required for operation of the electronic device can also be stored. The computing unit 101, the ROM 102, and the RAM 103 are connected to each other through a bus 104. An input / output (I / O) interface 105 is also connected to the bus 104.

[0109] A plurality of components in the electronic device are connected to the I / O interface 105, including an input unit 106, an output unit 107, a storage unit 108, and a communication unit 109. The input unit 106 can be any type of device that can input information to the electronic device, and can receive inputted numerical or character information, as well as generate key signal inputs related to user settings and / or function controls of the electronic device. The output unit 107 can be any type of device that can present information, and can include, but is not limited to, a display, a speaker, a video / audio output terminal, a vibrator, and / or a printer. The storage unit 108 can include, but is not limited to, a magnetic disk, an optical disk. The communication unit 109 allows the electronic device to exchange information / data with other devices through a computer network such as the Internet and / or various telecommunication networks, and can include, but is not limited to, a modem, a network card, an infrared communication device, and / or a wireless communication transceiver, such as a Bluetooth device, a WiFi device, a WiMax device, a cellular communication device, and / or the like.

[0110] The computing unit 101 can be various general and / or special purpose processing components having processing and computing capabilities. Some examples of the computing unit 101 include, but are not limited to, a CPU, a graphics processing unit (GPU), various special purpose artificial intelligence (AI) computing units, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any appropriate processor, controller, microcontroller, etc. The computing unit 101 performs various methods and processes described above. For example, in some embodiments, method embodiments of the present creation can be implemented as a computer program tangibly embodied in a machine readable medium, such as the storage unit 108. In some embodiments, part or all of the computer program can be loaded and / or installed onto the electronic device via the ROM 102 and / or the communication unit 109. In some embodiments, the computing unit 101 can be configured to perform the above-described methods by any other appropriate means, such as by means of firmware.

[0111] Computer programs used to implement embodiments of the present application can be written in any combination of one or more programming languages. These computer programs can be provided to a processor or controller of a general purpose computer, special purpose computer, or other programmable data processing apparatus, such that the computer program

[0112] In the context of embodiments of the present application, a machine-readable medium can be a tangible medium that can contain or store program for use by or in connection with an instruction execution system, apparatus, or device. The machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. A machine-readable signal medium can include, but is not limited to, electronic, magnetic, optical, electromagnetic, or infrared signals, or any suitable combination thereof. More specific examples of a machine-readable storage medium will include one or more lines of electrical connections, portable computer disks, hard disk drives, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or Flash memory), optical fiber, portable compact disc read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0113] It should be noted that the term "comprising" and variations thereof as used in embodiments of the present application are to be interpreted generically and do not exclude other steps. The term "based on" is to be interpreted as "based, at least in part, on". The term "one embodiment" means "at least one embodiment". The term "another embodiment" means "at least one additional embodiment". The term "some embodiments" means "at least some embodiments". The terms "a" or "an", as used herein, mean "one or more" unless explicitly stated otherwise.

[0114] The user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data for analysis, stored data, displayed data, etc.) involved in embodiments of the present application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of related data need to comply with relevant laws, regulations and standards of relevant countries and regions, and provide corresponding operation portal for user to choose authorization or refusal.

[0115] The individual steps of the method embodiments provided by the embodiments of the present application can be performed in different orders and / or in parallel. Furthermore, the method embodiments can comprise additional steps and / or omit the performance of the steps shown. The scope of protection of the present application is not limited in this respect.

[0116] The word "comprise" in the specification means that the specific feature, structure or characteristic described can be included in at least one embodiment of the present application. The use of this word in the specification does not mean that the same embodiment is required in all embodiments, nor does it mean that the other embodiments are mutually exclusive of the embodiment described. Each embodiment of the present application is described in a relevant manner, and the same or similar parts of the embodiments are cross-referenced. In particular, for the device, apparatus, system embodiments, the description is relatively simple, as they are substantially similar to the method embodiments, and the relevant parts are cross-referenced to the parts of the method embodiments.

[0117] The above-described embodiments only express several embodiments of the present application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the scope of protection. It should be noted that for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are within the scope of protection of the present application. Therefore, the scope of protection of the present application should be subject to the appended claims.

Claims

1. A demodulation method for white light interference signals, characterized in that, include: The non-uniform fast Fourier transform is used to process the non-uniformly distributed interference light intensity signal data in the wavenumber domain to obtain the spectral information of the interference light intensity signal data and determine the first optical path difference; The measurement resolution of the non-uniform fast Fourier transform is analyzed. If the measurement resolution is lower than a preset threshold, the optical path difference sequence to be measured is constructed with the first optical path difference as the center within a preset precision measurement range. The amplitude spectrum of the optical path difference sequence is obtained by calculating the spectral amplitude of each optical path difference in the optical path difference sequence under test through non-uniform discrete Fourier transform. The second optical path difference is determined based on the spectral peaks of the amplitude spectrum; The non-uniformly distributed interference light intensity signal data in the wavenumber domain is processed using a non-uniform fast Fourier transform to obtain the spectral information of the interference light intensity signal data, including: The interference light intensity signal data is convolved with a window function at uniform oversampling points to obtain a uniformly sampled data sequence. Perform a Fast Fourier Transform on the data sequence to obtain the spectrum of the convolution function; Perform a deconvolution operation on the spectrum of the convolution function to obtain the spectral information of the interference light intensity signal data; The interference light intensity signal data is convolved and interpolated with a window function at uniformly oversampled points to obtain a uniformly sampled data sequence, including: make For uniform oversampling interpolation points, ;in, , This represents the minimum wavenumber among the non-uniform sampling points of the interference light intensity signal. This represents the maximum wavenumber value among the non-uniform sampling points of the interference light intensity signal; Indicates the sequence number of the oversampled interpolation point; The number of oversampling points. R is the oversampling rate, and N is the number of non-uniform sampling points. The window function is a Gaussian bell function, which is expressed as follows: ,in, The parameter is a positive real number. The formula for calculating the convolution interpolation is as follows: ； in, This represents a uniformly sampled data sequence obtained through convolutional interpolation. Indicates non-uniform sampling points; This represents the interference light intensity signal data at non-uniform sampling points.

2. The demodulation method for white light interference signals according to claim 1, characterized in that, Performing a deconvolution operation on the spectral information of the convolution function to obtain the spectral information of the interference light intensity signal includes: The spectrum of the Gaussian bell function is , Indicates angular frequency; The spectrum of the convolution function is the product of the spectrum of the Gaussian bell-shaped function and the spectrum of the interference light intensity signal data. Therefore, the formula for calculating the spectral information of the interference light intensity signal data is as follows: ； in, This represents the spectrum of the interference light intensity signal data; This represents the spectrum of the convolution function.

3. The demodulation method for white light interference signals according to claim 2, characterized in that, The measurement resolution of the non-uniform fast Fourier transform is analyzed, including: The measurement resolution of the non-uniform fast Fourier transform is the same as that of the discrete Fourier transform. The expression for the discrete Fourier transform is as follows: 1； in, Number the spectral lines; The data sequence after interpolation and homogenization; For sequence number; The expression for the sampling frequency is as follows: ； The expression for angular frequency is as follows: ； The measurement resolution of the Discrete Fourier Transform is... ; The measurement resolution of the non-uniform fast Fourier transform is then: .

4. The demodulation method for white light interference signals according to claim 1, characterized in that, Centered on the first optical path difference, within a preset precision measurement range, a sequence of optical path differences to be measured is constructed, including: With the first optical path difference Centered on, Set the precision measurement range for distance. ; Within the scope of precise measurement, Using the step size, construct the optical path difference sequence to be measured. , ;in, The length of the optical path difference sequence to be measured. .

5. The demodulation method for white light interference signals according to claim 1, characterized in that, Before processing the non-uniformly distributed interference light intensity signal data in the wavenumber domain using non-uniform fast Fourier transform to obtain the spectral information of the interference light intensity signal data, the method further includes: calibrating the wave value corresponding to each non-uniform sampling point in the interference light intensity signal using Hilbert transform.

6. The demodulation method for white light interference signals according to claim 5, characterized in that, The wave value corresponding to each non-uniform sampling point in the interference light intensity signal is calibrated by Hilbert transform, including: The interference light intensity signal is subjected to high-pass filtering to remove the DC component; Perform a Hilbert transform on the filtered signal to obtain its orthogonal signals; The wrap phase is calculated by calculating the ratio of the filtered signal to the orthogonal signal and performing an arctangent operation. The wrapped phase is unwrapped to obtain continuous phase information; Based on the relationship between the continuous phase information and the optical path difference, the wave value corresponding to each non-uniform sampling point is calibrated.

7. An electronic device, comprising: A processor and a memory storing a program, characterized in that the program includes instructions that, when executed by the processor, cause the processor to perform a demodulation method for a white light interference signal according to any one of claims 1 to 6.

8. A non-transitory machine-readable medium storing computer instructions, characterized in that, The computer instructions are used to cause the computer to execute the demodulation method for white light interference signals according to any one of claims 1 to 6.

9. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the demodulation method for the white light interference signal as described in any one of claims 1 to 6.

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