Distance demodulation method for extremely multi-wavelength interferometry based on two-dimensional Fourier transform

Abstract

The present invention discloses a distance demodulation method for extremely multi-wavelength interference ranging based on two-dimensional Fourier transform, including absolute distance measurement and small relative displacement measurement. The method of the present invention only needs to perform a two-dimensional Fourier transform on the two-dimensional spectrum after the nonlinear dispersion effect is corrected, so as to obtain characteristic parameters related to the distance information, and then inversely solve the distance information or relative displacement information. The steps are simple, the amount of error introduced is small, the measurement is faster, and the accuracy is higher; when measuring the absolute distance, the present invention only requires the optical comb repetition frequency F r Lock, F is only needed when measuring small relative distances r 、F 0 At the same time, they are locked, so when measuring absolute distance, common commercial optical combs fully meet the requirements; in the present invention, the envelope fringe spatial frequency related to the distance to be measured is highly sensitive to the overall fringe frequency, and has good noise resistance to the jitter of the original power spectrum of the optical comb and the background.

Description

Technical Field

[0001] The invention belongs to the technical field of spectral data processing methods, and in particular relates to an extremely multi-wavelength interference ranging distance demodulation method based on two-dimensional Fourier transform. Background Art

[0002] Since 2000, when Minoshima et al. of the National Institute of Advanced Industrial Science and Technology (AIST) of Japan first proposed the new concept of absolute length measurement using femtosecond laser pulses, researchers from various countries have successively proposed and implemented distance measurement methods based on various principles, such as distance measurement methods combining incoherent and coherent principles, and non-interference distance measurement methods based on the time-of-flight principle. In particular, based on the spectral interferometry method first proposed by KNJoo and SWKim in 2006, the new optical comb distance measurement technology proposed by Dutch scientist SA Berg et al. in 2012 used a VIPA (Virtually Imaged Phased-Array) spectrometer with extremely high resolution to independently present the interference information of each comb tooth of the optical frequency comb on a two-dimensional detector, so as to combine the multi-wavelength interferometry method to achieve a wide range and high-precision absolute distance measurement.

[0003] In the technology proposed by SABerg et al., the accurate acquisition of distance information mainly depends on the processing of two-dimensional spectral information. First, it is necessary to extract the two-dimensional spectral information, that is, to perform high-precision frequency calibration on each comb tooth detected, and accurately obtain the interference intensity of each comb tooth, so as to accurately obtain the "comb tooth intensity-frequency" relationship curve, that is, one-dimensional spectral interference data. Subsequently, the extracted one-dimensional spectral interference data is Fourier transformed to obtain the "pseudo-time domain spectrum", and the components containing distance information in the "pseudo-time domain spectrum" are filtered out separately for inverse Fourier transformation, so as to obtain a "standardized power spectrum" that is only sensitive to distance information and has the same relative strength between each comb tooth. Finally, the phase corresponding to each comb tooth power is solved and phase unwrapped to obtain the "comb tooth frequency-phase" change curve at the distance to be measured. By accurately fitting the slope of the "comb tooth frequency-phase" change curve, the distance information to be measured can be accurately obtained.

[0004] However, the technology proposed by SABerg et al. involves a complex two-dimensional spectral data processing process. The processing algorithms corresponding to each step will not only directly introduce certain measurement errors, but also constrain the overall measurement rate and limit the real-time measurement of distance. In addition, the power spectrum of the optical frequency comb itself has a certain degree of jitter, which will cause a certain degree of error in the accuracy of the comb tooth frequency calibration and intensity calibration in the two-dimensional spectrum, making the extracted one-dimensional spectrum inaccurate. Therefore, the jitter of the power spectrum of the optical frequency comb itself will also indirectly introduce a certain degree of error to the subsequent processing steps, thereby affecting the final distance measurement accuracy. Summary of the invention

[0005] The invention provides a two-dimensional Fourier transform-based extremely multi-wavelength interference ranging distance demodulation method.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] The distance demodulation method of extremely multi-wavelength interferometric ranging based on two-dimensional Fourier transform includes absolute distance measurement and small relative displacement measurement;

[0008] The absolute distance measurement includes the following steps:

[0009] Step 1, nonlinear dispersion correction: Based on the dispersion model of VIPA and grating, nonlinear correction is performed on the obtained two-dimensional spectral data to obtain two-dimensional spectral data in which the comb teeth are linearly related to the spatial position;

[0010] Step 2: Close the distance to 0 ( The two-dimensional spectrum after nonlinear correction of the reference spectrum is taken as the reference spectrum, and the reference spectrum is subjected to two-dimensional Fourier transform to obtain its amplitude spectrum, i.e., the comb-tooth background structure; the spatial frequency components of the comb-tooth background structure are accurately obtained from it. With direction ;

[0011] Step 3: Set the distance to be measured to The two-dimensional spectrum after nonlinear correction is used as the spectrum to be demodulated, and a two-dimensional Fourier transform is performed to obtain the amplitude spectrum;

[0012] Step 4: Spectral energy modulation relationship introduced based on distance information:

[0013]

[0014] in, is the 0-frequency component of the comb-tooth background structure amplitude spectrum, For distance The 0-frequency component of the two-dimensional spectrum amplitude spectrum, is the modulation coefficient; the comb background structure is eliminated from the amplitude spectrum obtained in step 3 to more accurately obtain the envelope fringe spatial frequency of the spectrum to be demodulated after linear correction With direction ;

[0015] Step 5: According to the spatial period of the envelope fringes The intensity variation cycle of the comb teeth Relationship: ,in is the angle between the comb teeth and the periodic direction of the envelope fringe, Is with distance information Related functions; use the direction of the comb background structure obtained in step 2 And the one obtained in step 4 , , solve for the distance information ;

[0016] The small relative displacement measurement includes the following steps:

[0017] Step 1, nonlinear dispersion correction: Based on the dispersion model of VIPA and grating, nonlinear correction is performed on the obtained two-dimensional spectral data to obtain two-dimensional spectral data in which the comb teeth are linearly related to the spatial position;

[0018] Step 2: Close the distance to 0 ( The two-dimensional spectrum after nonlinear correction of the reference spectrum is taken as the reference spectrum, and the reference spectrum is subjected to two-dimensional Fourier transform to obtain its amplitude spectrum, i.e., the comb-tooth background structure; the spatial frequency components of the comb-tooth background structure are accurately obtained from it. With direction ;

[0019] Step 3: Set the distances to be measured as The two-dimensional spectrum after nonlinear correction is used as the spectrum to be demodulated, and a two-dimensional Fourier transform is performed to obtain the amplitude spectrum and the phase spectrum, where is a small relative displacement;

[0020] Step 4: When the distance changes at a nanometer or even smaller scale, the corresponding envelope fringe spatial frequency The change of cannot be identified in the amplitude spectrum; according to the spatial frequency position coordinates of the envelope fringes in the amplitude spectrum obtained in step 3, at the same position coordinates of the phase spectrum, take the nearby The average value of the phase within the pixel range is taken as the phase corresponding to the spatial frequency of the envelope fringe in this formula. ; Using the same method, the distance is The phase corresponding to the spatial frequency of the linearly corrected two-dimensional spectral envelope fringe ;

[0021] Step 5: Use the phase information obtained in step 4 to calculate the phase difference of the envelope fringes before and after the relative displacement. , combined with the relationship between phase change and envelope fringe spatial frequency change: , measuring tiny relative displacements .

[0022] Furthermore, in step one, the comb teeth with different spatial intervals are moved spatially, so that envelope fringes with uniform period and single frequency are finally presented.

[0023] Furthermore, in step 2, all directions are expressed as angles relative to the vertical direction, with the clockwise direction being positive and the counterclockwise direction being negative.

[0024] Furthermore, by performing a two-dimensional Fourier transform on the corrected two-dimensional spectrum only once, characteristic parameters related to the distance information can be obtained, and then the absolute distance information or relative displacement information can be inversely solved.

[0025] Furthermore, when measuring absolute distance, only the repetition rate of the optical comb needs to be adjusted. Locking is only required when measuring small relative displacements Lock at the same time.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] 1. The present invention only needs to perform a two-dimensional Fourier transform on the corrected two-dimensional spectrum to obtain characteristic parameters related to distance information (spatial period, direction, and phase of the envelope fringes), and then inversely resolve the distance information or relative displacement information. The steps are simple, the amount of error introduced is small, the measurement is faster, and the accuracy is higher.

[0028] 2. When measuring absolute distance, the present invention only requires the optical comb repetition rate Lock. Only required for small relative distance measurements So when measuring absolute distance, common commercial optical combs can fully meet the requirements.

[0029] 3. In the present invention, the envelope fringe spatial frequency related to the distance to be measured is highly sensitive to the overall fringe frequency and has good noise resistance to the jitter of the original power spectrum of the optical comb and the background. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 2D spectrum data when the measured distance is 0 and 11 mm in the embodiment;

[0031] Figure 2 VIPA dispersion capability curve schematic diagram in the embodiment;

[0032] Figure 3 Schematic diagram of the nonlinear dispersion distribution and correction principle of VIPA in the embodiment;

[0033] Figure 4 is a target schematic diagram of nonlinear dispersion distribution and linear dispersion distribution of the grating in the embodiment;

[0034] Figure 5 2. It is a comparative schematic diagram of the two-dimensional spectrum before and after linear correction in the embodiment;

[0035] Figure 6Schematic diagram of the relationship between the envelope fringe characteristic parameters and the comb teeth background structure in the embodiment. DETAILED DESCRIPTION

[0036] To implement the above method, the present invention provides the following technical solutions:

[0037] The extremely multi-wavelength interferometric distance demodulation method based on two-dimensional Fourier transform includes absolute distance measurement and small relative displacement measurement.

[0038] The absolute distance information demodulation includes the following steps:

[0039] Step 1: Nonlinear dispersion correction. Since the VIPA spectrometer has a serious nonlinear dispersion effect, it is first necessary to perform nonlinear correction on the obtained two-dimensional spectral data based on the dispersion model of VIPA and grating to obtain two-dimensional spectral data with a linear relationship between the comb teeth and the spatial position.

[0040] Step 2: Use the nonlinearly corrected two-dimensional spectrum with a distance close to 0 as the reference spectrum, perform a two-dimensional Fourier transform on the reference spectrum, and obtain its amplitude spectrum (hereinafter referred to as the "comb tooth background structure"). Accurately obtain the spatial frequency components of the comb tooth structure With direction .

[0041] Step 3: Set the distance to be measured to The two-dimensional spectrum after nonlinear correction is used as the spectrum to be demodulated, and the amplitude spectrum is obtained by two-dimensional Fourier transform.

[0042] Step 4: Spectral energy modulation relationship introduced based on distance information:

[0043]

[0044] in, is the 0-frequency component of the comb-tooth background structure amplitude spectrum, For distance The 0-frequency component of the two-dimensional spectrum amplitude spectrum, is the modulation coefficient. The comb tooth background structure is eliminated from the amplitude spectrum obtained in step 3, so as to more accurately obtain the envelope fringe spatial frequency of the spectrum to be demodulated after linear correction. With direction .

[0045] Step 5: According to the spatial period of the envelope fringes The intensity variation cycle of the comb teeth The relationship between: ,in is the angle between the comb teeth and the periodic direction of the envelope fringe, Is with distance information Use the direction of the comb background structure obtained in step 2 , and the value obtained in step 4 , , the distance information can be solved simply, quickly and stably .

[0046] The measurement of small relative displacement information includes the following steps:

[0047] Step 1: Nonlinear dispersion correction. Since the VIPA spectrometer has a serious nonlinear dispersion effect, it is first necessary to perform nonlinear correction on the obtained two-dimensional spectral data based on the dispersion model of VIPA and grating to obtain two-dimensional spectral data with a linear relationship between the comb teeth and the spatial position.

[0048] Step 2: Use the two-dimensional spectrum after nonlinear correction close to 0 as the reference spectrum, perform a two-dimensional Fourier transform on the reference spectrum, and obtain its amplitude spectrum. From this, the spatial frequency components of the comb structure can be accurately obtained. With direction .

[0049] Step 3: Set the distances to be measured as The two-dimensional spectrum after nonlinear correction is used as the spectrum to be demodulated, and a two-dimensional Fourier transform is performed to obtain the amplitude spectrum and the phase spectrum, where A small relative displacement.

[0050] Step 4: When the distance changes at a scale of nm or even smaller, the corresponding envelope fringe spatial frequency The change of cannot be identified in the amplitude spectrum. According to the spatial frequency position coordinates of the envelope fringes in the amplitude spectrum obtained in step 3, at the same position coordinates of the phase spectrum, take the nearby The average value of the phase within the pixel range is taken as the phase corresponding to the spatial frequency of the envelope fringe in this formula. Using the same method, we can obtain the distance The phase corresponding to the spatial frequency of the linearly corrected two-dimensional spectral envelope fringe .

[0051] Step 5: Use the phase information obtained in step 4 to calculate the phase difference of the envelope fringes before and after the relative displacement. . Combining the relationship between phase change and envelope fringe spatial frequency change: , can simply, quickly and stably measure tiny relative displacements .

[0052] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0053] Figure 1The two-dimensional spectrum data when the measured distance is 0 and 11 mm is formed by the femtosecond laser frequency comb carrying the distance information passing through the VIPA spectrometer and imaging on the array detector. The left side is 0 mm and the right side is 11 mm. The vertical direction is the VIPA dispersion direction and the horizontal direction is the grating dispersion direction. Since both VIPA and grating elements have a certain degree of nonlinear dispersion characteristics, Figure 1 The spatial period of the two-dimensional envelope fringes shown on the right side of the image is not uniform, and there is a certain degree of curvature. That is, at different positions on the two-dimensional detector, the spatial length (number of pixels) spanned at the same frequency interval varies non-uniformly, causing the spatial period of the two-dimensional envelope fringes to become uneven and the frequency to become non-single. In addition, because the optical frequency comb with a fixed frequency interval appears as a series of independently distinguishable comb tooth circular spots in the extremely high-resolution orthogonal dispersion spectrometer, and each comb tooth is separated by a certain spatial distance, this advantage makes it possible to move the comb teeth with different spatial intervals in space, so that the final envelope fringes have a uniform period and a single frequency.

[0054] 1.1 Correction of nonlinear dispersion of VIPA.

[0055] According to the VIPA back focal plane intensity distribution formula:

[0056] (Formula 1)

[0057] in: , is the refractive index of the VIPA material, For different wavelengths of light, is the change coordinate of the VIPA dispersion direction, , are the incident angle and the refraction angle inside the VIPA, is the beam waist radius before entering the VIPA, is the focal length of the VIPA rear imaging system, is the focal length of the VIPA front cylindrical lens, are the reflectivity of the front and rear surfaces of VIPA respectively. According to formula 1, the interference maximum matching condition is obtained: , it can be transformed to obtain different light wave frequencies with the intensity at the maximum interference when the light waves of different frequencies are in the same interference order (m=1) About Location Function: (Formula 2), which is subsequently referred to as the "interference maximum frequency-position" variation curve. The linear dispersion capability relationship in the VIPA direction can be further obtained through Formula 2. Indicates the spatial length (number of pixels) spanned by a certain frequency interval.

[0058] (Formula 3)

[0059] In this case, a light comb with a wavelength of 760nm, a bandwidth of 10nm, and a repetition rate of 811MHz was used as the light source. , , , , , , pixel size is 5.5um, detector size is After substituting each parameter into Formula 3, the linear dispersion capability curve in this case is obtained, as shown in Figure 2 As shown. The goodness of fit of the first-order linear model reaches 0.9999999433, so it is reasonable to use the dispersion capacity of VIPA ( ) is approximately regarded as a linear change, so the corresponding original function "interference maximum frequency-position" change curve Therefore, the nonlinear dispersion correction in the VIPA direction is to change the distribution of the "interference maximum frequency-position" nonlinear dispersion curve that is close to the quadratic function to the target distribution of the linear dispersion straight line, such as Figure 3 In order to make full use of the detector pixels, that is, to fill the detector target surface as much as possible with the linearly corrected spectrum, it is stipulated that the median slope of the "nonlinear dispersion curve" of VIPA is used as the slope of the "linear distribution line".

[0060] The corresponding actual processing algorithm is as follows: First, create an empty two-dimensional matrix of the same size as the original spectrum to store the new spectrum after linear correction. The entire row of pixels ( )Move all to frequency The corresponding pixel row in the target straight line distribution ( ) and store it into an empty two-dimensional matrix, such as Figure 3 Because equally spaced pixels are equivalent to discrete sampling of continuous space, if the original distribution Line and After linearization correction, the corresponding new If the difference is less than one pixel, the original distribution The data of each row are superimposed and stored in the same row of the empty two-dimensional matrix.

[0061] 1.2 Correction of nonlinear dispersion of grating.

[0062] According to the light intensity distribution formula of the back focal plane of the grating:

[0063] (Formula 4)

[0064] in, , , , 、 are the diffraction angle and change coordinates of the grating dispersion direction, is the number of effective grating lines, is the grating slit width, is the grating constant. According to formula 4, the interference maximum matching condition is obtained: , it can be transformed to obtain different light wave frequencies with the intensity at the maximum interference when the light waves of different frequencies are in the same interference order (m=1) About Location Function: (Formula 5), ​​which is subsequently referred to as the "interference maximum frequency-position" variation curve of the grating. Through (Formula 5), ​​the linear dispersion ability relationship of the grating direction can be further obtained:

[0065] (Formula 6)

[0066] In this case, in order to make the grating have sufficient resolution to meet the requirements of the spectrometer system, a 1800-line grating was used and the detector was placed The spatial position is (-0.67m, -0.65m). Similar to VIPA, the nonlinear dispersion correction in the grating direction is to change the nonlinear curve distribution of the grating's "interference maximum frequency-position" to a linear target straight line distribution, and use the median slope of the grating's "nonlinear dispersion curve" as the slope of the "linear dispersion line", such as Figure 4 shown.

[0067] The corresponding actual processing algorithm is similar to the VIPA linear correction, that is, the entire column of pixels where the intensity of different light wave frequencies with the maximum interference is located ( )Move all to frequency The corresponding pixel column in the target linear dispersion line ( ) and store it in an empty two-dimensional matrix. After completing the linear correction of the above nonlinear dispersion, the two-dimensional spectrum data with relatively uniform envelope fringe period can be obtained, such as Figure 5 shown.

[0068] Extract characteristic parameters of the comb-tooth background structure from the two-dimensional spectrum with a measured distance of 0, mainly including: the frequency of the comb-tooth background structure and the direction of the comb teeth (A comb tooth column refers to a column of comb teeth of the same order in the VIPA dispersion direction). The specific processing flow is: first, extend the linearly corrected two-dimensional spectrum to a certain extent to increase the FFT resolution and make the frequency reading more accurate. Then perform a two-dimensional Fourier transform and obtain the amplitude spectrum. From the amplitude spectrum, identify the approximate area where the spatial frequency components corresponding to the comb tooth column are located, and then use the two-dimensional Gaussian fitting method to fit the center of the area. Calculate the spatial frequency and direction corresponding to the center in the amplitude spectrum, that is, the spatial frequency of the comb tooth column and direction .

[0069] Extract the characteristic parameters of the envelope fringes from the two-dimensional spectrum at a measured distance of 11 mm, mainly including: the spatial period of the envelope fringes , the direction of the envelope fringe period . The specific processing flow is: extend the linearly corrected spectrum 0 and perform a two-dimensional Fourier transform to obtain its amplitude spectrum and phase spectrum. According to the law of the spatial frequency convolution of the envelope fringes near the comb-tooth background structure frequency, it is easy to identify the approximate area of ​​the amplitude spectrum where the spatial frequency of the envelope fringes is located, and then use two-dimensional Gaussian fitting to obtain the center of the area, and then obtain the exact position of the spatial frequency of the envelope fringes in the amplitude spectrum. Combined with the accurate position of the comb-tooth background structure frequency, the period of the envelope fringes in the two-dimensional detector can be accurately obtained. and direction .

[0070] Extract the phase difference of the spatial frequencies of two envelope fringes from the two-dimensional spectrum at the measured distances of 11mm and 11mm+10nm The specific processing flow is as follows: First, based on the envelope fringe frequency position in the 11mm amplitude spectrum, take the envelope fringe near the same position in its phase spectrum. The average value of the phase within the pixel range is taken as the phase corresponding to the current envelope fringe frequency. Secondly, the phase corresponding to the envelope fringe of 11mm+10nm is obtained in the same way. Finally, the phase difference associated with the small relative displacement is calculated. .

[0071] When the VIPA spectrometer structure is stable and the repetition rate of the optical frequency comb is When locked, the comb teeth background structure of the two-dimensional spectrum remains unchanged. Therefore, when the measured distance changes, the relative position of each comb tooth row remains unchanged, but the intensity follows The double beam interference law of (Formula 7) changes, is the distance to be measured. Because after the spectrum is linearly corrected, the frequency of the light wave detected in the vertical direction of the detector changes approximately uniformly with the coordinates, so the independent variable Can be rewritten as ,in is the frequency interval spanned by one pixel in the vertical direction, is the row number of the pixel. Therefore, the change rule of each comb tooth column can be expressed in the form of pixels as independent variables:

[0072]

[0073] in For the serial number The phase of the comb teeth. Figure 6 As shown, the spatial relative position relationship between any two adjacent comb tooth rows can be determined by the same light wave frequency The interference maxima of different orders of the comb teeth in the VIPA dispersion direction , The adjacent comb teeth in the , The frequency interval is fixed and equal to one FSR of VIPA, so the equivalent spatial interval is pixels. And because the intensity variation period of the comb teeth array is: (Formula 8), so the phase difference between two adjacent comb tooth rows can be expressed as: Formula 7 can be further modified to (Formula 9), It is the serial number of the comb teeth row.

[0074] like Figure 6 Center Line As shown in the figure, the envelope fringes in the two-dimensional spectrum are formed by connecting the peak values ​​of the intensity changes of the comb tooth arrays with the closest spatial distance between the comb tooth arrays, so the line segment The spatial length of the envelope fringe corresponds to the spatial period of the envelope fringe. .exist In the geometric relationship , , , horizontal spacing of comb teeth According to the cosine theorem, we can get the line segment ,as well as . And because , so it is proved that the angle between the comb teeth and the periodic direction of the envelope fringe is It is about distance information In summary, once the distance information to be measured is Given, that is Given. At right angles middle, It is also indirectly given. Conclusion: The distance information to be measured The spatial period and direction of the two-dimensional spectrum envelope fringes are determined. Therefore, by obtaining the spatial period and direction of the envelope fringes, the distance information to be measured can be demodulated.

[0075] The corresponding actual processing algorithm is as follows: All directions in the present invention are expressed as angles with the vertical direction, and the clockwise direction is positive and the counterclockwise direction is negative. First, the characteristic parameters of the acquired two-dimensional spectrum are used Calculate the angle between the comb teeth and the periodic direction of the envelope fringe , and then through the triangular relationship Calculate the period of change in the intensity of the comb teeth Finally, the distance to be measured is obtained by solving formula 8: .

[0076] The larger the size of the two-dimensional image, the higher the FFT resolution and the more accurate the amplitude spectrum sampling. However, the extension size of the two-dimensional image is also limited, so the FFT resolution cannot be increased indefinitely. When all are locked, the distance to be measured varies in the order of nm or even smaller, and the corresponding envelope fringe spatial frequency The change of may not be further accurately identified in the amplitude spectrum, but at this time the spatial period of the envelope fringe still has a slight change, which can be approximately regarded as a slight translation of the envelope fringe as a whole in space, which is reflected in the phase information of the envelope fringe, that is, a change of less than The phase change, At this point, the distance to be measured can be solved by using the phase change corresponding to the spatial frequency of the envelope fringe before and after a slight change in distance.

[0077] The specific processing flow is: Differentiate both sides of formula 8 to get:

[0078] ,

[0079] Therefore, the final small relative displacement is:

[0080] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modification, equivalent replacement and improvement made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A distance demodulation method for extremely multi-wavelength interference ranging based on two-dimensional Fourier transform, characterized in that: Including absolute distance measurement and small relative displacement measurement; The absolute distance measurement includes the following steps: Step 1, nonlinear dispersion correction: Based on the dispersion model of VIPA and grating, nonlinear correction is performed on the obtained two-dimensional spectral data to obtain two-dimensional spectral data in which the comb teeth are linearly related to the spatial position; Step 2: Make the distance close to 0, that is within, The central wavelength is the nonlinearly corrected two-dimensional spectrum of as the reference spectrum, and the reference spectrum is subjected to a two-dimensional Fourier transform to obtain its amplitude spectrum, i.e., the comb-tooth background structure; the spatial frequency components of the comb-tooth background structure are accurately obtained from it. With direction ; Step 3: Set the distance to be measured to The two-dimensional spectrum after nonlinear correction is used as the spectrum to be demodulated, and a two-dimensional Fourier transform is performed to obtain the amplitude spectrum; Step 4: Spectral energy modulation relationship introduced based on distance information: ， in, is the 0-frequency component of the comb-tooth background structure amplitude spectrum, For distance The 0-frequency component of the two-dimensional spectrum amplitude spectrum, is the modulation coefficient; the comb background structure is eliminated from the amplitude spectrum obtained in step 3 to more accurately obtain the envelope fringe spatial frequency of the spectrum to be demodulated after linear correction With direction ; Step 5: According to the spatial period of the envelope fringes The intensity variation cycle of the comb teeth The relationship between: ,in is the angle between the comb teeth and the periodic direction of the envelope fringe, Is the distance information Related functions; use the direction of the comb background structure obtained in step 2 And the one obtained in step 4 , , solve for the distance information ; The small relative displacement measurement includes the following steps: Step 1, nonlinear dispersion correction: Based on the dispersion model of VIPA and grating, nonlinear correction is performed on the obtained two-dimensional spectral data to obtain two-dimensional spectral data in which the comb teeth are linearly related to the spatial position; Step 2: Make the distance close to 0, that is The two-dimensional spectrum after nonlinear correction is used as the reference spectrum, and the reference spectrum is transformed into a two-dimensional Fourier transform to obtain its amplitude spectrum, that is, the comb-tooth background structure; the spatial frequency components of the comb-tooth background structure are accurately obtained from it. With direction ; Step 3: Set the distances to be measured as The two-dimensional spectrum after nonlinear correction is used as the spectrum to be demodulated, and a two-dimensional Fourier transform is performed to obtain the amplitude spectrum and the phase spectrum, where is a small relative displacement; Step 4: When the distance changes at a nanometer or even smaller scale, the corresponding envelope fringe spatial frequency The change of cannot be identified in the amplitude spectrum; according to the spatial frequency position coordinates of the envelope fringes in the amplitude spectrum obtained in step 3, at the same position coordinates of the phase spectrum, take the nearby The average value of the phase within the pixel range is taken as the phase corresponding to the spatial frequency of the envelope fringe in this formula. ; Using the same method, the distance is The phase corresponding to the spatial frequency of the linearly corrected two-dimensional spectral envelope fringe ; Step 5: Use the phase information obtained in step 4 to calculate the phase difference of the envelope fringes before and after the relative displacement. , combined with the relationship between phase change and envelope fringe spatial frequency change: , measuring tiny relative displacements .

2. The distance demodulation method based on two-dimensional Fourier transform and extremely multi-wavelength interference ranging according to claim 1 is characterized in that: In step 1 of absolute distance measurement and small relative displacement, the comb teeth with different pixel intervals are moved in space, so that finally envelope fringes with uniform period and single frequency are presented.

3. The distance demodulation method based on two-dimensional Fourier transform and extremely multi-wavelength interference ranging according to claim 1 is characterized in that: In step 3 of absolute distance measurement and small relative displacement, the spectrum after nonlinear correction is zero-extended.

4. The method for distance demodulation based on two-dimensional Fourier transform and extremely multi-wavelength interference ranging according to claim 1 is characterized in that: In step 4 of the absolute distance measurement, the two-dimensional face center fitting algorithm is used to accurately obtain the envelope fringe spatial frequency .

5. The method for distance demodulation based on two-dimensional Fourier transform and extremely multi-wavelength interference ranging according to claim 1 is characterized in that: Only one two-dimensional Fourier transform is performed on the corrected two-dimensional spectrum to obtain characteristic parameters related to the distance information, and then the distance information or relative displacement information is inversely solved.

6. The distance demodulation method based on two-dimensional Fourier transform and extremely multi-wavelength interference ranging according to claim 1 is characterized in that: For absolute distance measurement, only the repetition rate of the optical comb is required. Locking, repetition frequency is only required when measuring small relative displacement Bias frequency Lock at the same time.

Images