A method for rapid mode decomposition of anti-noise fiber laser

Abstract

The present invention discloses a method for fast mode decomposition of anti-noise fiber laser, including: obtaining a spot to be decomposed with noise, rearranging the eigenmodes into vectors in sequence, and then multiplying the N eigenmode vectors pairwise to obtain a coefficient matrix A; obtaining a mode information vector X based on the coefficient matrix A; determining the errors of the elements in the mode information vector X based on the L2 norm of the pseudo-inverse matrix A<supgt;‑1< / supgt>, and deleting the elements with larger errors until at least 2N‑1 elements remain in the mode information vector X; establishing a nonlinear equation system based on the remaining elements in the mode information vector X, obtaining the mode coefficients and mode phases of each eigenmode restored, and generating a first reconstructed spot therefrom to obtain the mode decomposition result. The present invention is applied to the field of fiber laser mode decomposition. Based on the matrix analysis method, redundant feature information is screened and removed, so as to improve the measurement accuracy of mode coefficients and mode phases in a noise environment.

Description

Technical Field

[0001] The present invention relates to the technical field of fiber laser mode decomposition, and specifically to an anti-noise fiber laser mode decomposition method based on screening redundant feature information by matrix analysis. Background Art

[0002] Mode decomposition refers to characterizing the proportion of different modes and the inter-mode phase in fiber lasers, which is closely related to beam quality and is of great significance to research fields such as multi-mode fiber laser communication, multi-mode nonlinearity, and high-power fiber lasers. However, among the existing several mode decomposition techniques:

[0003] The spatial filtering imaging method (J.W. Nicholson, et al., Opt. Express 16, 7233 - 7243 (2008).) obtains the mode proportion and phase of the beam by performing Fourier analysis on the light intensity distributions at different distances. This method requires a relatively wide spectral width of the light source and cannot be applied to narrow linewidth or single-frequency lasers.

[0004] The correlation filtering method using a computer-generated hologram (T. Kaiser, et al., Opt. Express 17, 9347 - 9356 (2009).) can quickly and real-time measure the proportion of eigenmodes, but an additional reference light is required to determine the mode phase. In addition, the preparation of the computer-generated hologram is difficult, and each computer-generated hologram can only measure a specific system, with very poor practicality.

[0005] The method of using computer numerical analysis for mode decomposition only needs to measure the near-field or far-field light intensity distribution of the fiber output beam. Its principle is to find the mode coefficients and mode phases that can make the reconstructed light spot match the measured light spot to the greatest extent under the condition of known fiber eigenmode distribution. It has low requirements for experimental instruments and is the most concerned solution in recent years. In the prior art, someone has realized mode decomposition using the Gerchberg-Saxton algorithm (O. Shapira, et al., Phys. Rev. Lett. 94, 143902 (2005)), but this method has a slow convergence speed and low accuracy. Similarly, there is also the line search algorithm that directly enumerates different combinations of mode coefficients (R. Brüning, et al., Appl. Opt. 52, 7769 - 7777 (2013).), which also has problems such as too long calculation time and low accuracy and cannot be widely applied.

[0006] The pattern decomposition method based on the stochastic parallel gradient descent algorithm (L. Huang, et al., Opt. Express 23, 4620 - 4629 (2015).) is a relatively mature method at present. However, this method is prone to falling into local minima, resulting in the inability to obtain the global optimal solution. In particular, the decomposition speed of the stochastic parallel gradient descent algorithm is only on the order of 10 Hz, and as the number of patterns increases, the decomposition speed will further decrease, and the decomposition accuracy will further decrease, far from meeting the application requirements.

[0007] The above several methods are all iterative algorithms and require a long calculation time. The non-iterative pattern decomposition algorithm can effectively improve the decomposition speed. The pattern decomposition method based on machine learning is a representative of non-iterative algorithms (Y. An, et.al., Opt. Express 27(7), 10127 - 10137(2019).), but it requires a high-performance computing platform and a long network training time. Nevertheless, at present, only a decomposition speed of 30 Hz has been achieved.

[0008] Currently, the most promising one to be popularized is the pattern decomposition scheme based on matrix analysis proposed by Manuylovich et al. (E.S. Manuylovich, et al., Nat. Commun. 11(1), 5507(2020).). It divides the complex non-linear pattern decomposition problem into two simple steps: solving a linear equation system and a simple non-linear equation system, which greatly improves the calculation efficiency. In the ideal case without noise, the decomposition speed of the spot image containing 3 - 8 patterns is even as high as 100,000 frames per second, and it can accurately decompose images containing up to 49 patterns at most (E.S. Manuylovich, et al., Opt. Express 29(22), 36769(2021).). However, in practical applications, due to the influence of the thermal noise of the camera and the ambient background light, etc., the collected spot images often have strong noise interference, which is also one of the main limiting factors of all pattern decomposition methods based on spot measurement. For example Figure 1 is the typical result of the original matrix analysis pattern decomposition method in the case of containing noise and not containing noise. As shown in the appendix Figure 1 As shown, the original matrix analysis pattern decomposition method can accurately perform pattern decomposition only in the case of no noise. However, when containing noise, the gap between the reconstructed spot and the spot to be measured will become larger, indicating that the measurement accuracy of the pattern coefficients and pattern phases of this method becomes worse in a noisy environment. Summary of the Invention

[0009] In view of the problem of poor anti-noise ability of the above-mentioned existing mode decomposition technology, the present invention provides an anti-noise fiber laser mode decomposition method, which is based on the matrix analysis method, and screens and eliminates redundant feature information to improve the measurement accuracy of mode coefficients and mode phases in a noisy environment.

[0010] To achieve the above object, the present invention provides a fast anti-noise fiber laser mode decomposition method, including the following steps 1-step 5.

[0011] Step 1, through the given parameters of the optical system to be measured, obtain the eigenmode distribution supported by the optical system to be measured, obtain the noisy spot to be decomposed with m×m pixels containing N eigenmodes output by the optical system to be measured, and arrange the gray-scale data of the spot pattern of the spot to be decomposed from a two-dimensional matrix distribution into a vector data form, and denote it as vector I.

[0012] Step 2, rearrange the N eigenmodes in sequence into m 2 ×1-dimensional vectors, and then multiply these N eigenmode vectors pairwise to form -dimensional matrix, and denote it as coefficient matrix A. The expression of coefficient matrix A is:

[0013]

[0014] Step 3, obtain the mode information vector X based on the coefficient matrix A.

[0015] In another embodiment, solve the linear equation X = A -1 I based on the coefficient matrix A and the vector I to obtain the mode information vector X, where A -1 is the pseudo-inverse matrix of the coefficient matrix A, and A -1 =(A T A) -1 A T , where the superscript T represents matrix transpose.

[0016] The mode information vector X contains the mode coefficients and mode phase information of N eigenmodes, and its expression is:

[0017]

[0018] γ2γ3cos(θ2 - θ3),…,γ2γ N cos(θ2 - θ N ),…,γ N-1 γ N cos(θ N-1 -θ N )) T

[0019] In the formula, γ iand θ i respectively represent the mode coefficient and mode phase of the i-th eigenmode, where the mode phase refers to the relative phase, that is, the first phase θ1 is 0.

[0020] In the current technology, the solution of the mode decomposition method based on the original matrix analysis is to solve the values of the mode coefficient and mode phase only through the first 2N - 1 elements in the mode information vector X. However, the mode information vector X contains a total of N(N + 1) / 2 elements. When N ≥ 3, the number of elements in X exceeds the number of unknowns (2N - 1) to be solved. For this, the present invention provides a way of information screening, which can screen out elements with stronger anti-noise ability rather than only the first 2N - 1 elements to solve the mode coefficient and phase, that is, the following steps 4 - 5.

[0021] Step 4: Obtain the error ΔX(ζ) of the ζ-th element in the mode information vector X, and delete the elements with larger error ΔX(ζ) in the mode information vector X until there are at least 2N - 1 elements remaining in the mode information vector X.

[0022] In another embodiment, the vector L2 norm ||·|| is used to characterize the error ΔX(ζ) of the ζ-th element in the solution X of the system of equations, and this error ΔX(ζ) is proportional to the matrix A -1 the ζ-th row vector (A -1 ) ζ of the L2 norm, that is:

[0023] ΔX(ζ) ∝ ||(A -1 ) ζ ||

[0024] Therefore, the L2 norm ||(A -1 the ζ-th row vector (A -1 ) ζ in the pseudo-inverse matrix A -1 ) ζ || is used to characterize the error ΔX(ζ) of the ζ-th element in the mode information vector X, and at least 2N - 1 elements with the same label ζ and smaller values in ||(A -1 ) ζ || are screened out, and then they are used as the new system of nonlinear equations in step 5 to solve the mode coefficient and mode phase.

[0025] Step 5: Based on the remaining elements in the mode information vector X, establish a system of nonlinear equations, obtain the mode coefficients and mode phases of each eigenmode restored, and generate the first reconstructed light spot therefrom to obtain the mode decomposition result.

[0026] In another embodiment, the process of solving the mode coefficients and mode phases of each eigenmode restored is as follows:

[0027] Perform the first solution of the non - linear equation system to obtain N mode coefficients and N mode phases, and determine whether all N mode coefficients are positive:

[0028] If so, output the N mode coefficients and N mode phases obtained from the first solution;

[0029] Otherwise, substitute the absolute values of the N mode coefficients into the non - linear equation system for the second solution to obtain N mode phases, and then output the absolute values of the N mode coefficients obtained from the first solution and the N mode phases obtained from the second solution.

[0030] In another embodiment, the generation process of the first reconstructed light spot is as follows: Reconstruct the light field of the optical system to be measured by using the obtained mode coefficients and mode phases, and obtain the reconstructed light intensity distribution after taking the square of the modulus, that is, the first reconstructed light spot.

[0031] Preferably, the present invention also provides a mode decomposition method that can avoid local optimum, which is used to reduce the problem of the decline in mode decomposition accuracy caused by the numerical solution of the non - linear equation system falling into a local optimum solution. The specific process is as follows:

[0032] When decomposing the pattern of each frame of image, not only use the redundant feature information screening mode decomposition method in the above steps 1 - 5 to obtain the first reconstructed light spot, but also perform mode decomposition on the light spot to be decomposed with noise based on the original matrix analysis mode decomposition method to obtain N mode coefficients and N mode phases, and obtain the second reconstructed light spot therefrom. Then calculate the correlation coefficients of the first reconstructed light spot, the second reconstructed light spot and the light spot to be measured respectively, use the correlation coefficient as the coincidence accuracy, and take the result that is more coincident with the light spot to be measured in the two methods as the mode decomposition result of the light spot of this frame of image.

[0033] Compared with the prior art, the beneficial technical effects of the present invention are as follows:

[0034] Based on the original matrix analysis mode decomposition method, in the process of mode decomposition, the present invention is not limited to directly using the first 2N - 1 elements in the mode information vector X to solve the values of the mode coefficients and mode phases. Instead, it first removes some elements in the mode information vector X that are greatly affected by noise, and solves the mode coefficients and mode phases based on the remaining elements in the mode information vector X, thereby greatly improving the measurement accuracy of the mode coefficients and mode phases in a noisy environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] 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 for the description of the embodiments or the prior art. 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 the structures shown in these drawings.

[0036] Figure 1 Schematic diagram of the change of the decomposition accuracy of the original matrix analysis mode decomposition method with the noise level in the embodiments of the present invention, where: (a) is a schematic diagram of the spot to be measured without noise, (b) is a schematic diagram of the reconstructed spot without noise, (c) is a schematic diagram of the difference between the reconstructed spot and the spot to be measured without noise, (d) is a schematic diagram of the spot to be measured with noise, (e) is a schematic diagram of the reconstructed spot with noise, (f) is a schematic diagram of the difference between the reconstructed spot and the spot to be measured with noise;

[0037] Figure 2 Flowchart of the mode decomposition method in the embodiments of the present invention;

[0038] Figure 3 Results of calculating 30 times for 15 elements in the solution X of the equation in the embodiments of the present invention under the conditions of using ideal spots and spots with noise, Figure 3 (a) - (l) respectively correspond to the 15 elements of X. The solid line represents the case of using an ideal noise-free spot, and the dashed line represents the case of using a spot with noise;

[0039] Figure 4 Matrix A in the embodiments of the present invention -1 Schematic diagram of the values of the L2 norms of the row vectors;

[0040] Figure 5 Schematic diagram of a typical decomposition result in a noise environment in the embodiments of the present invention, where: (a) is a schematic diagram of the spot to be measured with noise under the original matrix analysis method, (b) is a schematic diagram of the reconstructed spot under the original matrix analysis method, (c) is a schematic diagram of the difference between the reconstructed spot and the spot to be measured under the original matrix analysis method, (d) is a schematic diagram of the spot to be measured with noise under the method of the present invention, (e) is a schematic diagram of the reconstructed spot under the method of the present invention, (f) is a schematic diagram of the difference between the reconstructed spot and the spot to be measured under the method of the present invention;

[0041] Figure 6 Schematic diagram of the comparison of the decomposition accuracy and the accuracy of the original matrix analysis method in a noise environment in the embodiments of the present invention.

[0042] The realization, functional characteristics, and advantages of the objectives of the present invention will be further described with reference to the embodiments and the accompanying drawings. Detailed implementation manners

[0043] Next, in combination with the accompanying drawings in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0044] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the ability of those of ordinary skill in the art to implement. When the combination of technical solutions results in contradictions or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0045] As Figure 2 shown, a method for rapid mode decomposition of anti-noise fiber lasers disclosed in this embodiment mainly includes the following steps:

[0046] Step 1: Arrange the grayscale data of the spot pattern of the spot to be decomposed with noise from a two-dimensional matrix distribution into a vector data form to obtain vector I. Among them, the spot to be decomposed with noise contains m×m pixels of N eigenmodes.

[0047] Step 2: Rearrange the N eigenmodes in sequence into m 2 ×1-dimensional vectors, and then multiply the N eigenmode vectors pairwise to obtain -dimensional coefficient matrix A;

[0048] Step 3: Solve the linear equation X = A -1 I based on the coefficient matrix A and vector I to obtain the mode information vector X. Among them, A -1 is the pseudo-inverse matrix of the coefficient matrix A. Among them, A -1 is the pseudo-inverse matrix of the coefficient matrix A. The mode information vector X contains the mode coefficients and mode phase information of N eigenmodes;

[0049] Step 4: Use the ζ-th row vector (A -1 ) -1 in the pseudo-inverse matrix A ζ The L2 norm ||(A -1 ) ζ || represents the error ΔX(ζ) of the ζ-th element in the mode information vector X, and delete the elements with larger error ΔX(ζ) in the mode information vector X until there are at least 2N - 1 elements left in the mode information vector X;

[0050] Step 5: Based on the remaining elements in the mode information vector X, establish a system of non-linear equations to obtain the mode coefficients and mode phases for each eigenmode recovery, and generate a first reconstructed light spot therewith. Perform mode decomposition on the light spot to be decomposed with noise based on the original matrix analysis mode decomposition method to obtain N mode coefficients and N mode phases, and obtain a second reconstructed light spot therewith. Calculate the correlation coefficients of the first reconstructed light spot, the second reconstructed light spot and the light spot to be measured respectively, and output the N mode coefficients and N mode phases with higher correlation coefficients as the mode decomposition result.

[0051] In this embodiment, the proposed eigenmode is a linearly polarized eigen transverse mode.

[0052] In this embodiment, the light spot image with noise is generated by simulation according to the actual optical system parameters, including the fiber type, fiber core diameter, fiber numerical aperture, and laser wavelength. The parameters are selected as:

[0053] The fiber is a step-index fiber, the core diameter is 25 μm, the numerical aperture is 0.08, and the laser wavelength is 1.064 μm.

[0054] In this embodiment, the light spot image to be measured is obtained through simulation of the actual optical system, rather than actually acquired by building an experimental system. On the one hand, it is used to show statistically that the acquisition of hundreds of thousands of total light spot images demonstrating the anti-noise ability of this embodiment will be rather cumbersome and require a large amount of preprocessing time. On the other hand, the light spots generated by computer simulation are easier to quantitatively control the image signal-to-noise ratio, which provides convenience for quantitatively and intuitively showing the advantages of the present invention. In addition, in this embodiment, the correlation coefficient C between the sample light spot and the reconstructed light spot will be used to evaluate the accuracy of mode decomposition, and its specific expression is:

[0055]

[0056] In the formula, (x, y) represents the spatial coordinates, I m represents the light intensity distribution of the light spot sample to be measured, I r represents the light intensity distribution of the reconstructed light spot, is the average light intensity of the light spot sample to be measured, is the average light intensity of the reconstructed light spot.

[0057] The optical field output by the optical fiber can be obtained by the linear superposition of the eigenmodes, and the intensity distribution is the square of the modulus of the optical field. After taking the square of the modulus of the optical field, image noise is added to obtain the noisy spot image, that is, the sample of the noisy spot to be measured. Specifically, the eigenmodes supported by the optical system to be measured are calculated by simulation, and the number of eigenmodes included in the sample is set (not exceeding the maximum number of modes supported by the optical fiber under this parameter. In this embodiment, the optical fiber of the selected optical system supports at most 10 linearly polarized eigenmodes, and the first 5 eigenmodes are taken as the number of modes in this embodiment). Then, the mode coefficients and mode phases of each eigenmode are randomly generated, and thus noise-free samples of different spot images are generated.

[0058] In this embodiment, the spot intensity distribution is discretized into 100×100 data points. In the actual spot acquisition system, the noise type of the acquired image is usually "additive white Gaussian noise". In the simulation, two-dimensional discrete Gaussian distribution data with the same number of pixels as the ideal spot is generated. According to the given signal-to-noise ratio and the power of the ideal spot, the variance of the Gaussian noise is set, and the noise data is directly added to the ideal intensity data to obtain the noisy spot image with the given signal-to-noise ratio. In addition, since the intensity measured in the actual system is non-negative, after adding "additive white Gaussian noise" with a specific power level in the simulation, all "negative intensity" distributions are reset to 0.

[0059] In the specific implementation process, the noisy spot image represented by the 100×100 matrix is rearranged into a 10000×1 column vector data, which is the vector I.

[0060] According to the eigenmode distribution calculated by simulation and the set number of eigenmodes, the coefficient matrix A of the linear equation is generated. In one embodiment, the coefficient matrix A can be expressed as:

[0061]

[0062] Then, based on the vector I and the pseudo-inverse matrix A -1 =(A T A) -1 A T , the matrix equation X = A - 1 I is directly solved to obtain the mode information vector X. In the specific implementation process, the mode coefficients and mode phases corresponding to each element of the mode information vector X are:

[0063]

[0064] Among them, γ1-γ5 are the mode coefficients, and θ1-θ5 are the mode phases.

[0065] Figure 3Results of calculating 30 times for 15 elements in the pattern information vector X under the conditions of using ideal light spots and noisy light spots. Figure 3 (a) - 3(l) correspond to the 15 elements in equation (2). The solid line represents the case of using an ideal noise - free light spot, and the dashed line represents the case of using a noisy light spot. As shown in the appendix Figure 3 It can be seen that the calculation accuracy of the 2nd, 3rd, 8th, 9th, and 10th elements in the pattern information vector X is significantly more affected by noise than the remaining elements. Deleting these elements that are more affected by noise and solving the pattern coefficients and pattern phases from the remaining elements will greatly improve the accuracy of pattern decomposition.

[0066] Equivalently, in this embodiment, the L2 norm of each row vector of the pseudo - inverse matrix A -1 can be calculated, that is, ||(A -1 ) ζ ||, to determine which elements in X are more affected by noise. Figure 4 Let be the L2 norm of each row vector of the pseudo - inverse matrix A -1 matrix. As shown in the appendix Figure 4 it can be seen that the values of the 2nd, 3rd, 8th, 9th, and 10th in ||(A -1 ) ζ || are much larger than other values. Therefore, the corresponding redundant elements in the pattern information vector X can be screened out, that is, X(2), X(3), X(8), X(9), and X(10). The remaining elements in the pattern information vector X form a non - linear equation system, that is:

[0067]

[0068] By numerically solving equation (3), the pattern coefficients γ1 - γ5 and the pattern phases θ2 - θ5 can be obtained. Among them, the pattern phase is the relative phase, that is, θ1 is 0.

[0069] It should be noted that the above - mentioned method for screening redundant elements in the pattern information vector X is only one embodiment of the present invention. For those of ordinary skill in the art, without creative work, a method for screening elements with stronger anti - noise ability based on matrix - analysis pattern decomposition in any case can also be obtained according to the method of this embodiment.

[0070] During the process of numerically solving equation (3), if all the obtained pattern coefficients γ1 - γ5 are positive, the solution result is the result of "information - redundant pattern decomposition" in this embodiment; if there are negative numbers among the obtained pattern coefficients γ1 - γ5, then after taking the absolute values of all pattern coefficients, substitute them into equation (3) for the second numerical solution to obtain the new pattern phases θ2 - θ5. Finally, take the absolute values of the pattern coefficients obtained from the first numerical solution and the pattern phases obtained from the second numerical solution as the result of "information - redundant pattern decomposition" in this embodiment.

[0071] After obtaining the result of "information redundancy mode decomposition" in this embodiment, the optical field of the fiber laser is reconstructed. After taking the square of the mode, the first reconstructed light spot is obtained, and then the correlation coefficient with the ideal light spot to be measured is calculated. Figure 5 Compare it with the correlation coefficient of the mode decomposition based on the original matrix analysis. Figure 5 It is a typical decomposition result of adopting the present invention in a noise environment in an embodiment. As shown in the appendix Figure 5 As shown, under the same noise, the decomposition accuracy of the redundant feature information screening mode decomposition in this embodiment reaches 0.9869, while the decomposition accuracy of the mode decomposition based on the original matrix analysis is only 0.5956.

[0072] Further preferably, to avoid falling into a local optimum when numerically solving equation (3), this embodiment provides a mode decomposition method that can avoid local optima. The process is as follows:

[0073] If the correlation coefficient of the redundant feature information screening mode decomposition with the ideal light spot to be measured is higher, then take the result of the redundant feature information screening mode decomposition as the result of this mode decomposition. If the correlation coefficient of the mode decomposition based on the original matrix analysis is higher, then take the result of the original matrix analysis mode decomposition as the result of this mode decomposition.

[0074] Figure 6 For the comparison of the decomposition accuracy of the method of the present invention and the accuracy of the original matrix analysis method in a noise environment, specifically: at intervals of 1 dB between the signal-to-noise ratio SNR of 5 - 60 dB, the method of the present invention and the method based on the original matrix analysis are respectively used for 2000 times of mode decomposition, and the results of the 2000 times are averaged as the calculation accuracy of the two methods under this signal-to-noise ratio condition. As shown in the appendix Figure 6 As shown, the mode decomposition accuracy based on the present invention is greater than 0.95, while the decomposition accuracy of the mode decomposition method based on the original matrix analysis is less than 0.9 when the signal-to-noise ratio is below 30 dB. It can be seen that the method of the present invention can greatly improve the measurement accuracy of the mode coefficient and mode phase in a noise environment.

[0075] The above are only the preferred embodiments of the present invention, and do not limit the patent scope of the present invention accordingly. Any equivalent structural transformation made under the inventive concept of the present invention, or direct / indirect application in other related technical fields, is included in the patent protection scope of the present invention.

Claims

1. A method for rapid mode decomposition of anti-noise fiber laser, characterized in that, It includes the following steps: Step 1: Arrange the grayscale data of the spot image of the spot to be decomposed with noise from a two-dimensional matrix distribution into a vector data form to obtain vector I, where the spot to be decomposed with noise contains m×m pixels of N eigenmodes; Step 2, rearrange the N eigenmodes into an m 2 ×1-dimensional vector in sequence, and then multiply the N eigenmode vectors pairwise to obtain the coefficient matrix A; Step 3: Based on the coefficient matrix A, obtain the mode information vector X, where the mode information vector X contains the mode coefficients and mode phase information of N eigenmodes; Step 4: Obtain the error ΔX(ζ) of the ζ-th element in the mode information vector X, and delete the elements with larger error ΔX(ζ) in the mode information vector X until at least 2N - 1 elements remain in the mode information vector X; Step 5: Based on the remaining elements in the mode information vector X, establish a non-linear equation set, obtain the mode coefficients and mode phases restored for each eigenmode, and generate the first reconstructed spot therefrom to obtain the mode decomposition result.

2. The anti-noise optical fiber laser fast mode decomposition method according to claim 1, characterized in that In Step 3, the obtaining of the mode information vector X based on the coefficient matrix A is specifically as follows: Solve the linear equation X = A -1 based on the coefficient matrix A and the vector I to obtain the pattern information vector X, where A -1 is the pseudo-inverse matrix of the coefficient matrix A, which is: A -1 = (A T A) -1 A T In the formula, the superscript T represents matrix transpose.

3. The anti-noise optical fiber laser fast mode decomposition method according to claim 1, characterized in that In Step 4, the obtaining of the error ΔX(ζ) of the ζ-th element in the mode information vector X is specifically as follows: Using the pseudo-inverse matrix A -1 in the ζ-th row vector of (A -1 ) ζ The L2 norm ||(A -1 ) ζ || represents the error ΔX(ζ) of the ζ-th element in the pattern information vector X.

4. The anti-noise optical fiber laser fast mode decomposition method according to claim 1, wherein, In Step 5, the establishing of a non-linear equation set based on the remaining elements in the mode information vector X and obtaining the mode coefficients and mode phases restored for each eigenmode specifically include: Perform the first solution of the non-linear equation set to obtain N mode coefficients and N mode phases, and judge whether all N mode coefficients are positive: If so, output the N mode coefficients and N mode phases obtained from the first solution; Otherwise, substitute the absolute values of the N mode coefficients into the non-linear equation set for the second solution to obtain N mode phases, and then output the absolute values of the N mode coefficients obtained from the first solution and the N mode phases obtained from the second solution.

5. The anti-noise optical fiber laser fast mode decomposition method according to any one of claims 1 to 4, characterized in that, In Step 5, the obtaining of the mode decomposition result is specifically as follows: Based on the original matrix analysis mode decomposition method, perform mode decomposition on the spot to be decomposed with noise to obtain N mode coefficients and N mode phases, and obtain the second reconstructed spot therefrom; Calculate the correlation coefficients of the first reconstructed spot, the second reconstructed spot and the spot to be measured respectively, and output the N mode coefficients and N mode phases with higher correlation coefficients as the mode decomposition result.

6. The anti-noise optical fiber laser fast mode decomposition method according to claim 5, wherein, The correlation coefficient is specifically as follows: Wherein, (x, y) represents spatial coordinates, and I m represents the light intensity distribution of the spot of the sample to be measured, and I r represents the light intensity distribution of the reconstructed spot, is the average light intensity of the spot of the sample to be measured, is the average light intensity of the reconstructed spot.

7. The anti-noise optical fiber laser fast mode decomposition method according to any one of claims 1 to 4, characterized in that, The spot to be decomposed with noise is obtained by simulating the actual optical system to be measured.

8. The anti-noise optical fiber laser fast mode decomposition method according to any one of claims 1 to 4, characterized in that The eigenmode is a linearly polarized eigen transverse mode.

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