Spectral interferogram phase extraction method, system, equipment and medium

Abstract

The invention belongs to the technical field of spectral resolution interference, and discloses a spectral interferogram phase extraction method, system and device and a medium, and the method comprises the steps: enabling the inter-frame phase shift to present a linear trend along a spectral component axis through employing an interpolation function in an interferogram reconstruction process, and the feasibility of extracting the phase from the spectral resolution interferogram by the tilt phase shift algorithm is revealed. Then iteration is carried out according to the sequence of the spectrum phase, the phase shift along the spectrum component axis and the phase shift along the space direction based on the principle of least squares in the method, and finally multiple iteration processes are completed under the constraint condition to obtain the high-precision spectrum phase. The technical scheme of the invention has excellent performance of high precision and high noise resistance, and is suitable for measurement of various morphology heights.

Description

Technical Field

[0001] The present invention belongs to the technical field of spectral resolved interferometry, and particularly relates to a method, system, device and medium for extracting the phase of a spectral interference pattern. Background Art

[0002] Spectrally Resolved Interferometry (SRI) is an advanced measurement technique based on the principle of low-coherence light interference, which solves the absolute distance in the spectral domain. After obtaining the spectrally resolved interference pattern with spectral dispersion of the interference beam, algorithms such as Fourier transform, wavelet transform and multi-step phase shift can be used to extract the phase, and then high-precision one-dimensional profile information can be obtained. Since the height information at a point is determined by the linear relationship between the phase information of the spectral component axis and the wavenumber, SRI can avoid the phase ambiguity problem and has excellent anti-noise performance.

[0003] Although methods such as Fourier transform, window Fourier transform and wavelet transform are widely used in phase extraction, they require high-frequency fringes on the spectral component axis of the interference pattern, which limits the performance of SRI in measuring physical quantities with short optical path differences. In addition, although the time phase shift algorithm has the ability to extract the phase with high precision and is not limited by the fringe frequency, only the multi-step phase shift algorithm, especially the five-step phase shift algorithm, can be applied to the phase extraction in SRI due to its immunity to phase shift misalignment. This algorithm not only requires obtaining five frames of interference patterns, but also requires uniform phase shift, increasing the experimental complexity and cost.

[0004] It should be noted that high-performance algorithms such as random phase shift algorithm and advanced iterative algorithm are difficult to be popularized in SRI. This is because the phase shifts of different wavelengths along the spectral component axis are different, which conflicts with the assumption of frame-to-frame phase shift consistency relied on by these high-performance algorithms. This limitation further highlights the deficiencies and challenges of the existing technology in SRI phase extraction. Therefore, developing new phase extraction algorithms to overcome these defects and improve the measurement accuracy and applicability of SRI is an important direction of current research. Summary of the Invention

[0005] The purpose of the present invention is to provide a method, system, device and medium for extracting the phase of a spectral interference pattern to solve the problems existing in the above-mentioned prior art.

[0006] To achieve the above object, the present invention provides a method for extracting the phase of a spectral interference pattern, including:

[0007] Step 1: Obtain a spectral interference pattern;

[0008] Step 2: Interpolate and reconstruct the intensity information of the spectral interference pattern to obtain the reconstructed spectral interference pattern;

[0009] Step 3: Calculate the phase of the reconstructed spectral interferogram;

[0010] Step 4: Calculate the phase shift along the wavenumber axis and the phase shift along the spatial axis of the reconstructed spectral interferogram based on the phase;

[0011] Step 5: Repeat Steps 3 to 4 for iteration until a preset convergence condition is met, and output the phase diagram of the spectral interferogram.

[0012] Optionally, the process of obtaining the spectral interferogram specifically includes: obtaining a spectral interferogram in a spectral resolution interference system, where each frame of the spectral interferogram contains spatial axis information and wavenumber axis information.

[0013] Optionally, Step 2 specifically includes:

[0014] Extract the data points of the row pixels of each frame of the spectral interferogram to obtain a number of sub-intervals, and define a cubic spline interpolation function on each sub-interval; where the interpolation function satisfies the continuity of numerical values, first-order, and second-order derivatives;

[0015] Reconstruct the light intensity values on the row pixels in an equally spaced interpolation manner based on the spline interpolation function, and generate a reconstructed spectral interferogram according to the reconstructed light intensity values; where the reconstructed spectral interferogram is uniformly distributed along the wavenumber axis.

[0016] Optionally, the iteration of repeating Steps 3 to 4 specifically includes:

[0017] Assume that the phase shift of the frame is known, and use the least squares principle to solve the phase of the spectral resolution interferogram;

[0018] Assume that the phase shift of the spectral interferogram along the spatial axis is known, and combine the phase to calculate the phase shift of the spectral interferogram along the wavenumber axis;

[0019] Based on the phase of the spectral interferogram and the phase shift along the wavenumber axis, calculate the phase shift along the spatial axis;

[0020] Repeat the above steps for iteration until a preset convergence condition or a preset number of iterations is met, and output the phase diagram of the spectral interferogram.

[0021] Optionally, the preset convergence condition is specifically:

[0022]

[0023] In the formula, m represents the number of iterations, n is the serial number of the spectral resolution interferogram, x is the spatial position axis of the line profile to be measured, k is the wavenumber axis representing the spectral component, δ1, δ n are the phase shifts of the first and nth spectral resolution interferograms; u1, u nis the tilt coefficient of the first and nth spectral resolution interferograms; ε1 and ε2 are set precision thresholds. When the phase distribution that meets the precision threshold is obtained or after a certain number of iterations, an accurate spectral resolution phase diagram can be obtained.

[0024] A spectral interferogram phase extraction system, comprising:

[0025] A data acquisition module for acquiring spectral interferograms;

[0026] An interferogram reconstruction module for interpolating and reconstructing the intensity information of the spectral interferogram to obtain a reconstructed spectral interferogram;

[0027] A phase distribution calculation module for calculating the phase of the reconstructed spectral interferogram; calculating the phase shift of the reconstructed spectral interferogram along the wavenumber axis and the phase shift along the spatial axis based on the phase; repeating the above steps for iteration until a preset convergence condition is met, and outputting the phase diagram of the spectral interferogram.

[0028] An electronic device, comprising a memory and a processor, the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to execute a spectral interferogram phase extraction method as described above.

[0029] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements a spectral interferogram phase extraction method as described above.

[0030] The technical effects of the present invention are:

[0031] The present invention reconstructs the information of the spectral resolution interferogram and realizes the accurate extraction of the phase from the spectral resolution interferogram with random phase shift. In the process of interferogram reconstruction, this embodiment uses an interpolation function to make the inter-frame phase shift show a linear trend along the spectral component axis, revealing the feasibility of the tilt phase shift algorithm to extract the phase from the spectral resolution interferogram. Subsequently, in the proposed method, based on the least squares principle, iteration is performed in the order of spectral phase, phase shift along the spectral component axis, and phase shift along the spatial direction. Finally, multiple iteration processes are completed under the constraint conditions to obtain a high-precision spectral phase. The numerical simulation of the step microstructure profile shows that this method has excellent performance of high precision and high noise tolerance, and is applicable to the measurement of various topography heights. Description of the Drawings

[0032] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0033] The accompanying drawings, which form a part of this application, are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation to this application. In the drawings:

[0034] Figure 1 It is the specific method execution flow in this embodiment.

[0035] Figure 2 It is the spectral resolution interferogram reconstruction process in this embodiment.

[0036] Figure 3 It is a schematic diagram of the optical path system used in this embodiment.

[0037] Figure 4 It is a comparison example of the step height measurement errors under different algorithms in this embodiment. Among them, Figure 4 in (a) is the comparison under different signal-to-noise ratio conditions, Figure 4 in (b) is the comparison under different step height conditions.

[0038] Label description: 1. Light source; 2. Beam expanding and collimating module; 3. Beam splitter; 4. PZT; 5. Interference objective lens; 6. Sample; 7. First plano-convex lens 1; 8. Slit; 9. Second plano-convex lens; 10. Blazed grating; 11. Filter turntable; 12. Third plano-convex lens; 13. Camera. Detailed implementation manners

[0039] Now, various exemplary implementation manners of the present invention will be described in detail. This detailed description should not be considered as a limitation to the present invention, but rather as a more detailed description of certain aspects, characteristics, and implementation schemes of the present invention.

[0040] It should be understood that the terms described in the present invention are only for describing specific implementation manners and are not used to limit the present invention. Additionally, for the numerical ranges in the present invention, it should be understood that each intermediate value between the upper and lower limits of the range is also specifically disclosed. Each intermediate value within any stated value or stated range, as well as each smaller range between any other stated value or intermediate value within the stated range, is also included in the present invention. The upper and lower limits of these smaller ranges can be independently included or excluded from the range.

[0041] Without departing from the scope or spirit of the present invention, various improvements and changes can be made to the specific implementation manners of the specification of the present invention, which are obvious to those skilled in the art. Other implementation manners obtained from the specification of the present invention are obvious to those skilled in the art. The specification and embodiments of this application are only exemplary.

[0042] As used herein, terms such as "comprising", "including", "having", "containing", etc. are all open-ended terms, meaning including but not limited to.

[0043] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. The present application will be described in detail below with reference to the drawings and in conjunction with the embodiments.

[0044] As Figure 1 - Figure 4 As shown, in this embodiment, a method for extracting the phase of a spectral interference pattern is provided, including:

[0045] Step 1: Obtain a spectral interference pattern;

[0046] Step 2: Interpolate and reconstruct the intensity information of the spectral interference pattern to obtain a reconstructed spectral interference pattern;

[0047] Step 3: Calculate the phase of the reconstructed spectral interference pattern;

[0048] Step 4: Calculate the phase shift along the wavenumber axis and the phase shift along the spatial axis of the reconstructed spectral interference pattern based on the phase;

[0049] Step 5: Repeat Steps 3 to 4 for iteration until a preset convergence condition is met, and output the phase diagram of the spectral interference pattern.

[0050] As the size of semiconductor devices continues to shrink, the influence of the contour accuracy of microstructures on device performance becomes more and more significant. Spectral resolution interference can achieve surface topography measurement accurate to the nanometer level, ensuring that the size and shape of micro-device structures meet the design requirements, thereby improving the quality and performance of the final product. Traditional surface measurement methods such as contact probes or scanning electron microscopes often have contact interference or destructiveness, especially in the surface measurement of flexible materials or thin-film devices, which may lead to measurement errors. At the same time, spectral resolution interference is a non-contact measurement technology that can avoid damage to the material surface and ensure the integrity and accuracy of the measurement. By achieving high-precision contour measurement through spectral resolution interference, defects or unqualified microstructures can be detected early in the manufacturing process, reducing the defective product rate and improving production efficiency. This is particularly important for large-scale production of semiconductor devices, which can effectively reduce production costs and improve the controllability of the production process.

[0051] Based on this, this embodiment mainly embodies an iterative method of tilt phase shift based on a spectral interferogram reconstruction strategy, aiming to improve the accuracy of phase extraction in spectral interference technology, the ability to resist environmental noise, and the ability to have a wider scene adaptability. Specifically, in this embodiment, a cubic interpolation function is selected as the specific expression of the reconstruction function, the phase of the spectral interferogram, the phase shift along the wave number axis, and the phase shift along the spatial axis are iterated in sequence, a blazed grating is selected as the dispersion component, the contour of the step structure is used as the measurement object in a specific implementation case, and the step height error is used as the measurement standard.

[0052] To achieve the above object, this embodiment provides a method for extracting the phase of a spectral interferogram by an iterative method after reconstructing the intensity information of the spectral interferogram. The specific process includes the following steps:

[0053] In the spectral domain, the coordinate axes of the intensity interferogram collected at the imaging end are the spatial position and the wave number axis, and the mathematical expression is written as:

[0054]

[0055] Among them, the subscript n is the spectral resolution interferogram number, x is the spatial position axis of the line profile to be measured, k is the wave number axis representing the spectral component, I r (k), I s (k) are the intensities of the reference arm and the test arm, and their distributions are related to the source spectrum function. The phase φ(x, k) satisfies the relationship φ(x, k) = 4πkh at the spatial position x and the wave number k, where h is the height at the spatial position x, and δ n (x, k) is the phase shift.

[0056] Based on this, in spectral resolution interference, the phase shift sensitivities of different wave numbers are different, and there is a non-linear mapping between the position of the spectral component in the interferogram and the pixel coordinates. Therefore, the phase shift distribution between frames is uneven and unknown. In this embodiment, data points {[k1, I n (x, k1)], [k2, I n (x, k2)], …, [k P , I n (x, k P )]} are extracted from each row of pixels of each interferogram in turn (the total number of pixels in one row is P), and a cubic spline interpolation function Γ(k) is defined on each sub-interval [k p , k p+1 .

[0057] Furthermore, it is determined by the numerical continuity, first-order and second-order derivative continuity of the interpolation function to ensure the smooth transition of the curve. After determining Γ(k), the light intensity values on the row pixels are reconstructed by equidistant interpolation, and a linear relationship is presented between the reconstructed pixel coordinates and the wavenumber. In addition, the phase shifts of different wavenumbers are linearly related to the wavenumber itself, and thus the image reconstruction essentially realizes the regular mapping between the pixel coordinates and the inter-frame phase shifts.

[0058] Based on this, the reconstructed interferogram becomes uniform along the wavenumber axis, and the inter-frame is a linearly inclined phase shift along the wavenumber direction. For the sake of easy expression, let the phase shift δ n (x, k) be decomposed into the uniform phase shift δ n (x) along the x-axis and the inclined phase shift δ n (k) + u n sum of k, where u n is the inclination coefficient. The reconstructed spectral resolution interferogram Ir n (x, k) is expressed as:

[0059] Ir n (x, k) = A(k) + B(k)cos[φ(x, k) + δ n (x) + δ n (k) + u n k]

[0060] Based on this, the proposed inclined phase shift iterative method can extract the phase from at least 3 frames of spectral resolution interferograms with random phase shifts. Assuming that the phase shifts δ n (x, k) of N frames are known, the phase φ(x, k) of the spectral resolution interferogram is to be found. The theoretical interferogram is expressed as:

[0061] Ir n (x, k) = a(k) + b(x, k)cosδ n (x, k) + c(x, k)sinδ n (x, k)

[0062] where the unknowns a(k) = A(k), b(x, k) = B(k)cos[φ(x, k)], c(x, k) = -B(k)sin[φ(x, k)]. Let Is n (x, k) represent the experimental interferogram, and then the least squares error is:

[0063]

[0064] For the known δ n (x, k), the least squares criterion should be satisfied: It is represented by a matrix as:

[0065] X = U -1 V

[0066] where

[0067] X = [a(x,k), b(x,k), c(x,k)] T

[0068]

[0069] To ensure the non - singularity of matrix U, at least three interferograms with different phase shifts are required for calculation. The phase is calculated by the following formula:

[0070] φ(x,k) = tan -1 [-c(x,k) / b(x,k)]

[0071] Furthermore, assuming that the phase shift δ n (x) along the x - axis is known, and combining the obtained φ(x,k), find the phase shift δ n (k)+u n k. The theoretical interference light intensity is expressed as:

[0072] Ir n (x,k) = a'(k)+b'(k)cos[φ'(x,k)]+c'(k)sin[φ'(x,k)]

[0073] where the unknowns are a'(k) = A(k), b'(k) = B(k)cos[δ n (k)+unk], c'(k) = - B(k)sin[δ n (k)+unk], the known quantity is φ'(x,k) = φ(x,k)+δ n (x), and then the least - square error of the wave number k column in the nth frame is:

[0074]

[0075] In the formula, Q is the number of pixels in a column. Usually, the number of pixels in an interference pattern column or row is much larger than 3. Therefore, there is no need to worry about the non - singularity problem of the matrix. Applying the least - square method gives the matrix equation:

[0076] X' = U' -1 V'

[0077] where

[0078] X' = [a'(k), b'(k), c'(k)] T

[0079]

[0080] Furthermore, the phase shift D of the k-th column of wavenumbers in the n-th frame n (k) is calculated as follows:

[0081] D n (k) = tan -1 [-c'(k) / b'(k)]

[0082] To address the uncertainty of the wrapped arctangent function in the tilt amount of the reconstructed spectral-resolved interferogram along the k-axis, after phase-unwrapping D n (k), a linear regression is performed to obtain the tilt phase shift δ n (k) + u n k along the k-axis.

[0083] Furthermore, by combining the known phase φ(x,k) in the first step and the known phase shift δ n (k) + u n k along the k-direction in the second step, the phase shift δ n (x) along the x-axis is obtained. Assuming that A(k) and B(k) are invariant in each row of pixels, the theoretical interferogram is expressed as:

[0084] Ir n (x,k) = a'(x) + b'(x)cos[φ”(x,k)] + c'(x)sin[φ”(x,k)]

[0085] where the unknowns are a”(x) = A(k), b”(x) = B(k)cosδ n (x), c”(x) = -B(k)sinδ n (x), and the known φ”(x,k) = φ(x,k) + δ n (k) + u n k. Furthermore, the least-squares error for the x-th row of spatial positions in the n-th frame is:

[0086]

[0087] Applying the least-squares criterion gives the matrix equation:

[0088] X” = U” -1 V”

[0089] where

[0090] X” = [a”(x), b”(x), c”(x)] T

[0091]

[0092] Furthermore, the phase shift D of the x-th row of spatial positions in the n-th frame n (x) is calculated as follows:

[0093] Dn f(x) = tan -1 [-c”(x) / b”(x)]

[0094] For D n linear regression of f(x) gives a uniform phase shift δ along the x-axis n f(x).

[0095] Based on this, the iterative process completes the closed loop and sets the convergence condition as:

[0096]

[0097] where m represents the number of iterations, and ε1, ε2 are set precision thresholds (e.g., 1e-5). When a phase distribution that meets the precision threshold is obtained or after a certain number of iterations, an accurate spectral resolution phase map can be obtained.

[0098] This embodiment proposes a high-performance random phase shift algorithm applicable to the phase extraction of spectral interferograms, which mainly solves the applicability problem of the random phase shift algorithm in SRI. The main feature of this embodiment is that by reconstructing the relationship between the pixel position and the wave number in the spectral interferogram, the pixel position and the phase shift present a linear mapping, and further, the iterative calculation method in this embodiment can be directly used to extract the phase from at least three frames of randomly phase-shifted spectral interferograms. This embodiment is significantly superior to the commonly used Fourier transform method and the three-step phase shift algorithm in the industry in terms of accuracy, universality, and robustness. In short, the proposed random phase shift method not only eliminates the limitations of the phase shift in SRI but also breaks the traditional view that the phase shift method is not suitable for solving spectral interferograms. This embodiment provides a reference for the random phase shift method adopted in SRI, which will promote the practical and high-quality application of SRI in the profile measurement scenario in the semiconductor field.

[0099] Comparative Example 1: To verify the accuracy, noise resistance, and robustness of this embodiment in the actual measurement scenario, the applicant conducted relevant numerical simulations and used the calculation of the step height of the step structure in the line profile as a measurement standard. The measurement optical path is as Figure 3 shown. In the simulation, a step structure with a height of 5um was established. The center wavelength of the white light source used to generate 3 frames of spectral resolution interferograms is 532nm, the spectral width is 300nm, and the phase shifts of the 3 frames of interferograms are preset at 1.68rad, 2.41rad, and 4.40rad at the center wavelength, and additive Gaussian noise with a signal-to-noise ratio SNR = 20dB is added to the interferograms.

[0100] To compare with the commonly used phase extraction methods in the technical field, in this embodiment, the popular Fourier Transform (FT) and Three-step algorithms in spectral-resolved interferometry are selected for simulation comparison, and the step height is obtained from the difference between the mean lines of the upper and lower surfaces. After extracting the phase from the spectral-resolved interferogram by the three methods, the corresponding restored step heights are 5.0001um, 4.9987um, and 5.0167um respectively. The proposed embodiment in this example accurately and effectively obtains the step height from three frames of randomly phase-shifted spectral-resolved interferograms, with a difference of only 0.1nm from the standard height, and the error precision is at the sub-nanometer level.

[0101] To demonstrate the performance of this embodiment in spectral-resolved interferometry technology, Comparative Example 2 was conducted: First, in this embodiment, the performance of the proposed embodiment compared with the two comparative algorithms of FT and Three-step was compared in the range of signal-to-noise ratio from 15 to 60dB, and other parameters were kept consistent with Comparative Example 1. As Figure 4 (a) shows, the proposed embodiment in this example is significantly better than the FT and Three-step methods in solving the step height. As the noise level increases, the errors of the step heights solved by the Three-step and the proposed embodiment increase, while the accuracy of the FT method mainly depends on the filtering window and the carrier frequency, so it is less sensitive to the noise level. Secondly, in Figure 4 (b), the solving effects of the three algorithms applied to the spectral-resolved interferograms generated by different step heights are compared. It can be seen that the proposed method is better than the Three-step in overall accuracy and is not affected by the step height, and is applicable to the contour measurement environment with various height differences.

[0102] The above takes a certain measurement object as an example to introduce in detail a tilt phase-shift iterative method based on a spectral interferogram reconstruction strategy in this embodiment. In the content of this embodiment, a blazed grating is used as the dispersion component, a slit is used as the contour filter device, a piezoelectric ceramic actuator is used as the mechanical mechanism for generating micro-displacements, an LED light source is used as the broadband light source for illumination, and the height difference of the step structure is used as the measurement reference. This specific spectral-resolved interferometric measurement system is to help relevant industry insiders better understand the idea and execution process of this embodiment.

[0103] This embodiment also provides a spectral-resolved interferometric system for micro-structure contour measurement, including:

[0104] A broadband beam is emitted by a light source 1. After passing through the beam expander and collimator module 2, it enters a beam splitter 3. The transmitted light enters an interference objective lens 5. The interference objective lens has a Mirau interference structure and is clamped by a PZT 4 to achieve positioning and micro-displacement driving. The measurement beam carries the topography information of the object to be measured under the action of the interference objective lens and then returns to the optical path system. After being reflected by the beam splitter, it enters a first plano-convex lens 7 for convergence, and a single contour to be measured is filtered out by a slit 8. The beam containing the contour to be measured is irradiated on a blazed grating 10 after passing through a second plano-convex lens 9, and then undergoes dispersion. After passing through a filter turntable 11 and a third plano-convex lens 12, the spectral interference pattern is collected by the target surface of a camera 13.

[0105] Meanwhile, for specific application measurement objects and algorithm processing flows, for example, the interpolation reconstruction function of the spectral interference pattern is set to quadratic interpolation, linear interpolation or other interpolation function forms, and the iteration order is the phase of the spectral interference pattern, the phase shift along the spatial axis, the phase shift along the wavelength axis or other iteration orders. Methods or application improvements based on the above similar objectives should be regarded as within the scope covered by this embodiment. These changes should fall within the protection scope of the claims attached to this embodiment.

[0106] As mentioned above, the above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for extracting the phase of a spectral interferogram, characterized in that, Comprising: Step 1: Obtain a spectral interferogram; Step 2: Interpolate and reconstruct the intensity information of the spectral interferogram to obtain the reconstructed spectral interferogram; Step 3: Calculate the phase of the reconstructed spectral interferogram; Step 4: Calculate the phase shift along the wavenumber axis and the phase shift along the spatial axis of the reconstructed spectral interferogram based on the phase; Step 5: Repeat Steps 3 to 4 for iteration until a preset convergence condition is met, and output the phase diagram of the spectral interferogram.

2. The method for extracting the phase of a spectral interference pattern according to claim 1, wherein The process of obtaining the spectral interferogram specifically includes: obtaining a spectral interferogram in a spectral resolution interference system, where each frame of the spectral interferogram contains spatial axis information and wavenumber axis information.

3. A method for extracting the phase of a spectral interference pattern according to claim 1, characterized in that, The specific content of Step 2 includes: Extract the data points of the row pixels of each frame of the spectral interferogram to obtain a number of sub-intervals, and define a cubic spline interpolation function on each sub-interval; wherein, the interpolation function satisfies the continuity of numerical values, first-order and second-order derivatives; Reconstruct the intensity values on the row pixels in an equally spaced interpolation manner based on the spline interpolation function, and generate a reconstructed spectral interferogram according to the reconstructed intensity values; wherein, the reconstructed spectral interferogram is uniformly distributed along the wavenumber axis.

4. A method for extracting the phase of a spectral interference pattern according to claim 1, characterized in that The specific content of repeating Steps 3 to 4 for iteration includes: Assume that the phase shift of the frame is known, and use the least squares principle to solve the phase of the spectral resolution interferogram; Assume that the phase shift along the spatial axis of the spectral interferogram is known, and combine the phase to calculate the phase shift along the wavenumber axis of the spectral interferogram; Based on the phase of the spectral interferogram and the phase shift along the wavenumber axis, calculate the phase shift along the spatial axis; Repeat for iteration until a preset convergence condition or a preset number of iterations is met, and output the phase diagram of the spectral interferogram.

5. A method for extracting the phase of a spectral interference pattern according to claim 1, characterized in that, The specific preset convergence condition is: In the formula, m represents the number of iterations, n is the serial number of the spectral resolution interferogram, x is the spatial position axis of the line profile to be measured, k is the wave number axis representing the spectral components, and δ1, δ n are the phase shifts of the first and the nth spectral resolution interferograms; u1, u n are the tilt coefficients of the first and the nth spectral resolution interferograms; ε1 and ε2 are the set precision thresholds. When the phase distribution that meets the precision threshold is obtained or after a certain number of iterations, an accurate spectral resolution phase map can be obtained.

6. A spectral interferogram phase extraction system, characterized in that, Comprising: A data acquisition module for obtaining a spectral interferogram; An interferogram reconstruction module for interpolating and reconstructing the intensity information of the spectral interferogram to obtain the reconstructed spectral interferogram; A phase distribution calculation module for calculating the phase of the reconstructed spectral interferogram; calculating the phase shift along the wavenumber axis and the phase shift along the spatial axis of the reconstructed spectral interferogram based on the phase; Repeat the above steps for iteration until a preset convergence condition is met, and output the phase diagram of the spectral interferogram.

7. An electronic device, characterized in that, Comprising a memory and a processor, the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to execute a method for extracting the phase of a spectral interferogram according to any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, It stores a computer program, and when the computer program is executed by the processor, it implements a method for extracting the phase of a spectral interferogram according to any one of claims 1-5.

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