A random phase shift measurement method based on dynamic mode decomposition

Abstract

The application provides a random phase shift measurement method based on dynamic mode decomposition, comprising: obtaining three frames of random phase shift interferograms of an object to be measured, performing difference and normalization processing to obtain a first interferogram sequence without background; performing difference and algebraic operation on the first interferogram sequence to generate an equal-step second interferogram sequence; expanding the second interferogram sequence into a column vector form and constructing a data matrix X and a data matrix in time sequence; performing singular value decomposition on the data matrix to calculate an approximate matrix; performing characteristic analysis on the approximate matrix to extract eigenvalues and eigenvectors, and mapping the eigenvectors back to the space of the second interferogram sequence to reconstruct the dynamic mode of the second interferogram sequence; and recovering the phase distribution of the object to be measured according to the amplitude angle information of the main mode in the dynamic mode. The application breaks through the limitation of the existing algorithm that at least four frames of interferograms are required, and can realize stable phase demodulation under any unknown phase shift condition.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical interferometry, more particularly to a random phase shift measurement method based on dynamic mode decomposition. BACKGROUND

[0002] Phase shift interferometry is a high-precision interferometry technique, which is applied to key links such as surface profile detection and micro-nano structure characterization in the semiconductor field. By introducing a controllable phase shift, a series of interference fringe patterns are obtained, and the phase information of the measured object is extracted through phase demodulation. Traditional phase extraction algorithms usually rely on known phase shift values, however, in actual measurement, due to the influence of instrument errors and external disturbances, it is often challenging to accurately obtain the phase shift value.

[0003] To solve the above problems in the prior art, a phase shift interference demodulation algorithm based on dynamic mode decomposition is proposed, which has high precision and robustness. The main process is to extract the main dynamic behavior in the interference pattern sequence as a low-order mode. However, since the interference pattern data in phase shift interferometry usually contains three main modes, the dynamic mode decomposition technique requires at least four equidistant interference images when used for phase demodulation, which limits its application in high-speed dynamic scenes or conditions where the number of image frames is limited, and puts higher requirements on data acquisition and processing.

[0004] Therefore, how to improve the application efficiency of phase shift interference in high-speed dynamic scenes or conditions where the number of image frames is limited is a problem that needs to be solved by those skilled in the art. SUMMARY

[0005] Therefore, the present application provides a random phase shift measurement method based on dynamic mode decomposition, which differentiates and normalizes three frames of random phase shift interference patterns to remove the background mode, then constructs a set of equidistant phase shift interference pattern sequences through algebraic operation, and finally applies dynamic mode decomposition to the constructed sequence to complete phase demodulation. Breakthrough the limitation of at least four equidistant interference patterns required by existing algorithms, and realize stable phase demodulation under any unknown phase shift conditions.

[0006] To achieve the above purpose, the present application provides the following technical scheme:

[0007] A random phase shift measurement method based on dynamic mode decomposition, comprising:

[0008] Step S1, obtaining three frames of random phase shift interference patterns of the object to be measured, and differentiating and normalizing the three frames of random phase shift interference patterns to obtain a first interference pattern sequence without background;

[0009] Step S2, performing difference and algebraic operation on the first interference pattern sequence to generate a second equidistant interference pattern sequence;

[0010] Step S3, the second interferogram sequence is unfolded into a column vector form, and data matrix X and data matrix Y are constructed in time sequence;

[0011] Step S4, singular value decomposition is performed on data matrix X to calculate approximation matrix ;

[0012] Step S5, eigenvalue analysis is performed on approximation matrix , eigenvalues and eigenvectors are extracted, and the eigenvectors are mapped back to the space of the second interferogram sequence to obtain dynamic mode of the second interferogram sequence;

[0013] Step S6, the mode corresponding to the positive frequency component in is selected, denoted as ; wherein the first two columns of the dynamic mode are taken as the main mode; and the phase distribution of the object to be measured is recovered according to the amplitude angle information of the main mode.

[0014] Further, step S1 comprises:

[0015] The light intensity expression of the three-frame random phase shift interferogram is:

[0016] ；

[0017] ， ， ；

[0018] wherein, is the intensity of light at the k index position in the nth frame of interferogram; n is the frame number of the interferogram; k is the position index of the pixel point in the interferogram; K is the total number of pixels of the interferogram; is a background light intensity term; is a modulation amplitude term; is a to-be-measured phase term; is the phase shift step of the nth frame of interferogram;

[0019] The difference operation is performed on the three-frame random phase shift interferogram, and the expression is:

[0020] ;

[0021] In the formula, is a difference value diagram;

[0022] The L2 norm of the three-frame random phase shift interferogram is calculated, and the expression is:

[0023] ;

[0024] wherein, is the L2 norm;

[0025] According to the L2 norm, normalization operation is performed on three frames of random phase shift interferograms, and the expression is:

[0026] ;

[0027] wherein, is the normalized graph; is a phase shift step, wherein , , ;

[0028] A global constant is introduced, and a new modulation amplitude term is redefined;

[0029] The first sequence of interferograms is obtained, and the expression is:

[0030] ;

[0031] wherein, , is the value of the nth frame of interferogram after removing the background at the kth pixel point; .

[0032] Further, step S2 comprises:

[0033] Randomly select two frames in the first sequence of interferograms, and set them as and , , , difference and algebraic operation is performed, and the expression is:

[0034] ;

[0035] wherein, is the difference signal; is the sum signal;

[0036] Normalization processing is performed to construct a second sequence of interferograms , and the expression is:

[0037] ;

[0038] The second sequence of interferograms is arranged, and the expression is:

[0039] ;

[0040] wherein, .

[0041] Further, the step S3 comprises:

[0042] The expression of the sequence of interferograms is:

[0043] ;

[0044] wherein, is the intensity of the light at the kth index position in the nth frame of interferogram; n is the frame number of the interferogram; k is the position index of the pixel point in the interferogram; is the background light intensity term, which has been removed in the second sequence of interferograms; is the modulation amplitude term; is the phase to be measured term; is the phase shift step of the nth frame of interferogram;

[0045] The Fourier transform is performed on the second sequence of interferograms, and the frequency domain expression obtained is:

[0046] ;

[0047] wherein, is the frequency domain signal after the Fourier transform; is the unit impulse; and are spatial modes with different oscillation frequencies, respectively and ;

[0048] The size of each frame of interferogram in the second sequence of interferograms is set as , and each frame of matrix-form interferogram is rearranged as a column vector in column priority;

[0049] The second sequence of interferograms is divided into a data matrix and a data matrix , and the expression is:

[0050] ;

[0051] wherein, is the column vector of each frame of interferogram; N is the number of frames of the second sequence of interferograms; is the interferogram data matrix of the first N-1 frames; Y is the interferogram data matrix of the last N-1 frames.

[0052] Further, the step S4 comprises:

[0053] The data matrix X is selected to perform singular value decomposition, and the expression is:

[0054] ;

[0055] wherein U is a left singular vector matrix; Σ is a singular value matrix; is a right singular vector matrix is a conjugate transpose of the left singular vector matrix U;

[0056] constructing a linear dynamic model , constructing an approximation matrix using singular value decomposition result of the data matrix X:

[0057] ;

[0058] wherein is a conjugate transpose of the left singular vector matrix U; is a right singular vector matrix; is a transpose matrix of the singular value matrix Σ.

[0059] Further, the step S5 comprises:

[0060] performing eigenvalue decomposition on the approximation matrix to obtain eigenvalues and eigenvectors, expressed as:

[0061] ;

[0062] wherein is an eigenvalue; is an eigenvector;

[0063] projecting the eigenvectors back to the space of the second interferogram sequence to obtain a dynamic mode of the second interferogram sequence, expressed as:

[0064] ;

[0065] wherein is a left singular vector matrix of the second interferogram sequence.

[0066] Further, the step S6 comprises: according to amplitude angle information of a main mode in the dynamic mode , restoring a phase distribution of the object to be measured

[0067] selecting a mode corresponding to a positive frequency component in , denoted as ; wherein the first two columns of the dynamic mode are taken as the main mode;

[0068] calculating The amplitude information and the argument information of the wrapped phase are obtained, and the phase distribution of the object to be measured is recovered, and the expression is:

[0069]

[0070] In the formula, is the recovered wrapped phase map; is a four-quadrant arctangent function; is a dynamic mode of a positive frequency dynamic mode; is a real part of ; and is an imaginary part of .

[0071] Compared with the prior art, the beneficial effects of the present application are:

[0072] The method of the present application performs difference and normalization processing on three frames of random phase shift interferograms to remove background modes, and then constructs a set of equal-step phase shift interferogram sequences through algebraic operation, and finally applies dynamic mode decomposition to the constructed sequences to complete phase demodulation. The present application breaks through the limitation of the prior art that at least four frames of equal-step interferograms are required, and can realize stable phase demodulation under any unknown phase shift condition. BRIEF DESCRIPTION OF DRAWINGS

[0073] In order to more clearly illustrate the technical solutions in the embodiments of the present application or 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 embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of the provided drawings.

[0074] Figure 1 is a flowchart of the method of the present application;

[0075] Figure 2 is the reference phase distribution corresponding to different types of stripes obtained by simulation in the present application, and a-c correspond to open stripes, closed stripes and complex stripes, respectively;

[0076] Figure 3 is the phase distribution result corresponding to the three types of stripes of open stripes, closed stripes and complex stripes extracted under the simulation condition in the present application: the first line in the figure corresponds to the demodulated phase, wherein the color bar is the phase value at the corresponding pixel point, and the unit is rad; the second line corresponds to the error map of the extracted phase, wherein the x-axis and the y-axis are the pixel coordinates of the image, the unit is pixel, the z-axis and the color bar are the error values at the corresponding pixel points, and the unit is rad;

[0077] Figure 4 ​A schematic diagram of an optical path system structure used in the present application;

[0078] In the figure, 1, laser; 2, first lens; 3, pinhole; 4, second lens; 5, polarizer; 6, beam splitter; 7, liquid crystal spatial light modulator; 8, sample of the measured object; 9, first plano-convex lens; 10, second plano-convex lens; 11, camera;

[0079] Figure 5 The phase distribution results extracted in the method embodiment of the present application: the first row corresponds to the demodulated phase, wherein the color bar is the phase value at the corresponding pixel point, and the unit is rad; the second row corresponds to the error map of the extracted phase, wherein the x-axis and the y-axis are the pixel coordinates of the image, the unit is pixel, the z-axis and the color bar are the error values at the corresponding pixel points, and the unit is rad. DETAILED DESCRIPTION

[0080] In order to further understand the content, characteristics and effects of the present application, the following examples are given, and the details are described with reference to the accompanying drawings. It should be noted that the present examples are descriptive, not limiting, and the protection scope of the present application cannot be limited by this.

[0081] The technical solutions in the embodiments of the present application will be described clearly and completely in combination with the accompanying drawings of the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application.

[0082] Glossary:

[0083] MATLAB: Signal Processing Toolbox is a powerful professional tool set that provides comprehensive support for signal generation, analysis, filtering, transformation and visualization.

[0084] awgn function: a core function in MATLAB Signal Processing Toolbox, the main function of which is to add Gaussian white noise to the input signal to simulate the inevitable random noise interference in real communication or measurement systems.

[0085] Peaks: is a built-in example function in MATLAB Signal Processing Toolbox, which generates a mathematical function with multiple local maxima and minima, which is often used to demonstrate 3D plotting, surface fitting, interpolation, optimization and other graphics and numerical functions.

[0086] As shown in Figure 1 A random phase shift measurement method based on dynamic mode decomposition, comprising:

[0087] Step S1, three frames of random phase shift interferograms of the object to be measured are acquired, and difference and normalization processing is performed on the three frames of random phase shift interferograms to obtain a first interference graph sequence without background, including the following steps:

[0088] Step S1-1, the light intensity expression of the three frames of random phase shift interferograms is:

[0089] ；

[0090] ， ， ；

[0091] wherein, is the light intensity of the k index position in the nth frame of interferogram; n is the frame number of the interferogram; k is the position index of the pixel point in the interferogram; K is the total number of pixels in the interferogram; is the background light intensity term; is the modulation amplitude term; is the phase to be measured term; is the phase shift step of the nth frame of interferogram.

[0092] Step S1-2, difference operation is performed on the three frames of random phase shift interferograms, and the expression is:

[0093] ;

[0094] wherein, is the difference value graph.

[0095] Step S1-3, normalization operation is performed on the three frames of random phase shift interferograms, including the following steps:

[0096] The L2 norm of the three frames of random phase shift interferograms is calculated, and the expression is:

[0097] ;

[0098] wherein, is the L2 norm;

[0099] According to the L2 norm of the three frames of random phase shift interferograms, normalization operation is performed, and the expression is:

[0100] ;

[0101] wherein, is the normalized graph; is the phase shift step, wherein , , .

[0102] where, when the interference fringes in the three-frame random phase-shift interferograms are greater than 1, there are the following approximations:

[0103] ;

[0104] Step S1-4, obtaining the background-removed phase-shift interference sequence, including the following steps:

[0105] Introducing a global constant , and redefining the new modulation amplitude term ;

[0106] Obtaining the first interference sequence, the expression is:

[0107]

[0108] In the formula, , is the value of the n-th frame of interference image after removing the background at the k-th pixel point; .

[0109] Step S2, performing difference and algebraic operation on the first interference sequence to construct the equal-step interference sequence, including the following steps:

[0110] Step S2-1, randomly selecting two frames in the first interference sequence, denoted as and , , , performing difference and algebraic operation, the expression is:

[0111] ;

[0112] In the formula, is the difference signal; is the sum signal.

[0113] Step S2-2, performing normalization processing to construct the second interference sequence , the expression is:

[0114] ;

[0115] Arranging the second interference sequence, the expression is:

[0116] ;

[0117] In the formula, .

[0118] ​Step S3, unfolding the second interferogram sequence into column vector form and constructing data matrix X and data matrix Y of the second interferogram sequence in time sequence, including the following steps:

[0119] The expression of the second interferogram sequence is:

[0120] ;

[0121] In the formula, is the intensity of light at the k index position in the nth frame of interferogram; n is the frame number of the interferogram; k is the position index of the pixel point in the interferogram; is the background light intensity term; is the modulation amplitude term; is the phase to be measured term; is the phase shift step of the nth frame of interferogram.

[0122] The Fourier transform of the second interferogram sequence is performed, and the frequency domain expression obtained is:

[0123] ;

[0124] In the formula, is the frequency domain signal after Fourier transform; is a unit impulse; and are spatial modes with different oscillation frequencies, and the oscillation frequencies are and ;

[0125] The size of each frame of interferogram in the second interferogram sequence is set to , and each frame of matrix form interferogram is rearranged as column vector in column priority.

[0126] The second interferogram sequence is divided into data matrix and data matrix , as shown in the expression:

[0127] ;

[0128] In the formula, is the column vector of each frame of interferogram; N is the frame number of the interferogram in the interferogram sequence; is the interferogram data matrix of the first N-1 frames; Y is the interferogram data matrix of the last N-1 frames.

[0129] Step S4, singular value decomposition is performed on the data matrix X to calculate the approximate matrix ;

[0130] The data matrix X is selected to perform singular value decomposition, and the expression is:

[0131] ;

[0132] wherein U is a left singular vector matrix; Σ is a singular value matrix; is a right singular vector matrix is a conjugate transpose of the left singular vector matrix U.

[0133] constructing a linear dynamic model , constructing an approximate matrix using singular value decomposition results of the data matrix X:

[0134] ;

[0135] wherein is a conjugate transpose of the left singular vector matrix U; is a right singular vector matrix; is a transpose matrix of the singular value matrix Σ.

[0136] Step S5, performing characteristic analysis on the approximate matrix , extracting eigenvalues and eigenvectors, and mapping the eigenvectors back to the space of the second interferogram sequence to obtain a dynamic mode of the second interferogram sequence.

[0137] performing eigenvalue decomposition on the approximate matrix to obtain eigenvalues and eigenvectors, and the expression is:

[0138] ;

[0139] wherein is an eigenvalue; is an eigenvector.

[0140] projecting the eigenvector back to the space of the second interferogram sequence to obtain a dynamic mode of the second interferogram sequence, and the expression is:

[0141] ;

[0142] Step S6, selecting a mode corresponding to a positive frequency component in , denoted as ; wherein are the first two columns of the dynamic mode as principal modes; and according to the amplitude angle information of the principal modes, restoring the phase distribution of the object to be measured.

[0143] The object to be measured refers to a target or sample that is being measured for a phase distribution.

[0144] The background component of the second interferogram sequence has been removed by the difference operation, the dynamic mode The first two columns correspond to its main modes. Select the mode corresponding to the positive frequency component in the middle, denoted as Then, the phase distribution of the object under test is recovered by calculating the amplitude angle information of , and the expression is:

[0145] ;

[0146] In the formula, is the recovered wrapped phase map; is the four-quadrant inverse tangent function; is the positive frequency dynamic mode of the dynamic mode ; is the real part of ; is the imaginary part of .

[0147] Example 1:

[0148] The simulation generates an interference fringe pattern, and the expressions of the fringe pattern background and the modulation degree are:

[0149] ;

[0150] In the formula, -1≤x≤1, -1≤y≤1, the phase shift of the three frames of interferograms is randomly generated, and white Gaussian noise with a signal-to-noise ratio of 45dB generated by the awgn function in MATLAB is added to the interferograms.

[0151] As shown in a, b, and c in Figure 2 , the phase sets the following three different conditions of the fringe pattern, which correspond to open fringes, closed fringes, and complex fringes, respectively, and the expressions are as follows:

[0152] ;

[0153] In the formula, Peaks is the peak function in MATLAB.

[0154] In order to verify the feasibility and accuracy of the method of the present application, the root mean square error (RMS) of the difference between the estimated phase distribution and the reference phase distribution is selected as a quantitative evaluation index.

[0155] As shown in Figure 3 , the phase distribution obtained by demodulating the method of the present application and the difference between the phase distribution and the reference phase distribution, Figure 3 a, b, and c in correspond to open fringes, closed fringes, and complex fringes, respectively.

[0156] The phase distribution results obtained by the method of this invention are consistent with the reference phase. Figure 3 The error plots for the bottom row of a, b, and c show that their error parameters remain within a very small amplitude range. Table 1 lists the root mean square error (RMS) and processing time corresponding to these three phase distributions.

[0157] Table 1. Demodulation phase root mean square error and computation time under simulation conditions.

[0158]

[0159] As shown in Table 1, the method of the present invention can achieve good demodulation effects on open stripes, closed stripes and complex stripes, which demonstrates the accuracy and efficiency of the method of the present invention.

[0160] Example 2:

[0161] like Figure 4 As shown, an interferometric measurement system was constructed to verify the feasibility and accuracy of the proposed method in experiments. This system was used to acquire real interference fringe patterns to comprehensively evaluate the actual performance of the proposed method. The specific structure and working principle of the system are as follows: a laser 1 as a coherent light source; a collimating and beam expanding unit (composed of a first lens 2, a pinhole 3, and a second lens 4) for beam shaping; a polarizer 5 for polarization control; a beam splitter 6 for beam splitting and combining; a liquid crystal spatial light modulator 7 as a phase modulation element; a sample of the object under test 8; an imaging magnification unit (composed of a first plano-convex lens 9 and a second plano-convex lens 10) for imaging; and a camera 11 for image acquisition. The test arm uses a silicon wafer surface as the target, and the reference arm uses a liquid crystal spatial light modulator to modulate the wavefront to generate the required phase shift.

[0162] In the experiment, the phase distribution of the surface morphology reconstructed by the method of the present invention, such as Figure 5 As shown in Figure a, the error plot is as follows: Figure 5 As shown in Figure b, Table 2 shows the corresponding root mean square error of the phase and the corresponding processing time. The root mean square error of the phase is 0.1460 rad, and the corresponding processing time is 0.0099 s. Similar to the simulation results, while maintaining high accuracy, the calculation time for a single phase demodulation is in the tens of milliseconds, which corresponds to the simulation results. The method of this invention has the technical effect of high accuracy and high efficiency.

[0163] Table 2. Root mean square error of demodulation phase and calculation time under experimental conditions.

[0164]

[0165] It should be noted that the above description of the embodiments is only used to help understand the method of the present application and its core idea. Those skilled in the art can make several improvements and modifications to the present application without departing from the principles of the present application, and these improvements and modifications are also within the protection scope of the claims of the present application.

Claims

1. A method for measuring random phase shift based on dynamic mode decomposition, characterized in that, include: Step S1: Obtain three frames of random phase-shifted interferograms of the object under test, and perform differential and normalization processing on the three frames of random phase-shifted interferograms to obtain the first interferogram sequence after removing the background; Step S2: Perform difference and algebraic operations on the first interferogram sequence to generate a second interferogram sequence with equal step size; Step S3: Expand the second interferogram sequence into column vector form, and construct data matrix X and data matrix Y in chronological order; Step S4: Perform singular value decomposition on the data matrix X to calculate an approximate matrix. ; Step S5, for the approximate matrix Feature analysis is performed to extract eigenvalues ​​and eigenvectors, and the eigenvectors are mapped back to the space of the second interferogram sequence to obtain the dynamic pattern of the second interferogram sequence. ; Step S6, select The mode corresponding to the positive frequency component is denoted as . ;in For the dynamic mode The first two columns are taken as the main modes; the phase distribution of the object under test is recovered based on the argument information of the main modes.

2. The random phase shift measurement method based on dynamic mode decomposition according to claim 1, characterized in that, Step S1 includes: The light intensity expression for the three-frame random phase-shifted interferogram is: ； ， ， ； in, Let K be the light intensity at index k in the nth frame of the interferogram; n is the frame number of the interferogram; k is the position index of the pixel in the interferogram; and K is the total number of pixels in the interferogram. Background light intensity; For modulation amplitude; The phase term to be measured; Let n be the phase shift step size of the nth frame of the interferogram; The differential operation is performed on the three frames of random phase-shifted interferograms, and the expression is: ； In the formula, This is a difference graph; The L2 norm of the three random phase-shifted interferograms is calculated using the following expression: ； In the formula, It is an L2 norm; Based on the L2 norm, a normalization operation is performed on the three frames of random phase-shifted interferograms, and the expression is: ； In the formula, Normalized graph; Let be the phase shift step size, where , , ; Introducing global constants And redefine the new modulation amplitude term ; The first interferogram sequence is obtained, and its expression is: ； In the formula, This represents the value of the k-th pixel in the n-th frame of the interferogram after background removal. .

3. The random phase shift measurement method based on dynamic mode decomposition according to claim 2, characterized in that, Step S2 includes: Two frames are randomly selected from the first interferogram sequence, and set as follows: and , , Perform difference and sum algebraic operations, the expression is: ； In the formula, It is a differential signal; For summation signals; Normalization is performed to construct the second interferogram sequence. The expression is: ； The second interferogram sequence is rearranged and expressed as follows: ； In the formula, .

4. The random phase shift measurement method based on dynamic mode decomposition according to claim 3, characterized in that, Step S3 includes: The expression for the interferogram sequence is: ； In the formula, Let be the light intensity at index k in the nth frame of the interferogram; n is the frame number of the interferogram; and k is the position index of the pixel in the interferogram. The background light intensity term has been removed in the second interferogram sequence; For modulation amplitude; The phase term to be measured; Let n be the phase shift step size of the nth frame of the interferogram; Performing a Fourier transform on the second interferogram sequence yields the following frequency domain expression: ； In the formula, This is the frequency domain signal after Fourier transform; For a unit pulse; and For spatial modes with different oscillation frequencies, the oscillation frequencies are respectively and ; The size of each frame of the interferogram in the second interferogram sequence is set to... The interferograms in matrix form of each frame are rearranged into column vectors in column order. ; The second interferogram sequence is divided into a data matrix. and data matrix The expression is: ； In the formula, The column vector of each frame of the interferogram N is the number of frames in the second interferogram sequence; Y is the interferogram data matrix for the first N-1 frames; Y is the interferogram data matrix for the last N-1 frames.

5. The random phase shift measurement method based on dynamic mode decomposition according to claim 1, characterized in that, Step S4 includes: Select the data matrix X and perform singular value decomposition, the expression of which is: ； In the formula, U is the left singular vector matrix; Σ is the singular value matrix; A right singular vector matrix The conjugate transpose of; Constructing a linear dynamic model An approximate matrix is ​​constructed using the singular value decomposition results of the data matrix X. : ； In the formula, It is the conjugate transpose of the left singular vector matrix U; It is a right singular vector matrix; Let be the transpose of the singular value matrix Σ.

6. The random phase shift measurement method based on dynamic mode decomposition according to claim 1, characterized in that, Step S5 includes: For the approximate matrix Eigenvalue decomposition is performed to obtain eigenvalues ​​and eigenvectors, expressed as: ； In the formula, For eigenvalues; For feature vectors; The feature vector Projecting back into the space of the second interferogram sequence yields the dynamic mode of the second interferogram sequence. The expression is: ； In the formula, Let be the left singular vector matrix of the second interferogram sequence.

7. The random phase shift measurement method based on dynamic mode decomposition according to claim 1, characterized in that, Step S6 includes: choose The mode corresponding to the positive frequency component is denoted as . ;in For the dynamic mode The first two columns are used as the dominant mode; Calculate the The phase distribution of the object under test is recovered from the argument information, expressed as: ； In the formula, To recover the package phase map; It is the arctangent function in the four quadrants; For dynamic mode Positive frequency dynamic mode; for The real part; for The imaginary part.

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