Dynamic beam shaping method and system based on spatial light modulator

Abstract

The invention relates to a dynamic light beam shaping system and method based on a spatial light modulator. The system comprises a laser light source module, a beam expanding collimation light path, a light beam modulator, a focusing optical assembly, a detection and feedback module and a control and optimization module. According to the method, the uniformity of the output flat-topped beam can be corrected by virtue of a random parallel gradient descent (SPGD) algorithm and combining a Zernike polynomial as a control variable. Meanwhile, a composite performance index comprehensively considering energy distribution and shape features is constructed, the correction process of the flat-topped beam is accelerated by adopting a mode of gradually improving Zernike polynomial orders in multiple stages, the convergence trend of the performance index is used as a judgment basis of stage switching, stage independent variable dimension expansion is implemented, and the correction precision of the flat-topped beam is improved. And the convergence speed is obviously improved. Besides, adaptive selection of disturbance amplitude and learning rate parameters in the SPGD algorithm is realized by using noise estimation and a local linearity index, and the robustness of the system to noise and environmental disturbance is enhanced.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of laser shaping, in particular to a dynamic beam shaping method and system based on a spatial light modulator. BACKGROUND

[0002] Flat-top beam shaping has wide applications in ultrafast laser processing, microscopic illumination and optical tweezers. In order to obtain a flat-top beam, the commonly used schemes include diffractive optical elements, microlens arrays, freeform optical elements and superstructures. However, the traditional flat-top beam shaping devices are designed for specific light sources and cannot be dynamically adjusted. If the light source is replaced or the beam quality deteriorates, the device may not work properly. Compared with the fixed structure of the beam shaping device, the spatial light modulator as a dynamic beam modulation device has the advantage of programmability. It can generate a variety of flat-top spots by loading a phase map and can compensate for the distortion of the incident beam to a certain extent.

[0003] In the prior art, the method of directly measuring the incident light wavefront distortion by a wavefront sensor and loading a compensation phase needs to add a beam splitter and a wavefront sensor in the optical path, which not only reduces the energy utilization of the system, but also increases the complexity and cost of the system, which is not conducive to popularization in industrial laser processing and other scenes. Therefore, the wavefront sensor-free technology that measures the light intensity distribution of the output surface by a camera and updates the phase map by means of the stochastic parallel gradient descent (SPGD) algorithm is more widely used.

[0004] Although the wavefront sensor-free beam shaping scheme based on the SPGD algorithm has a simple structure, it still has the following shortcomings: first, as a parallel optimization algorithm, the high-dimensional optimization independent variable of the SPGD algorithm will significantly slow down its convergence speed, and in beam shaping, the control variable of the phase map often needs to use the weight of dozens or even hundreds of Zernike polynomials as the optimization independent variable. Second, in an actual optical system, the measurement of algorithm performance indicators will be disturbed by various noises such as camera readout noise, laser power fluctuation and mechanical vibration. Therefore, the selection of the superparameters of the SPGD algorithm needs an anti-interference automatic calibration method to ensure the convergence speed and stability of the algorithm during operation. SUMMARY

[0005] The technical problem to be solved by the present application is to overcome the shortcomings of the prior art, and to provide a dynamic beam shaping system and method based on a spatial light modulator.

[0006] The technical solution for solving the above technical problem is as follows: a dynamic beam shaping system based on a spatial light modulator, comprising a laser light source module, a beam expansion and collimation optical path, a beam modulator, a focusing optical assembly, a detection and feedback module and a control and optimization module connected in sequence.

[0007] The laser source module is arranged at an input surface of a system light path and is used for outputting a laser beam;

[0008] The beam expanding and collimating optical path is used for expanding and collimating the laser beam;

[0009] The beam modulator is used for modulating the laser beam after the shaping and collimating processing;

[0010] The focusing optical assembly is used for forming a target-shaped flat-top beam on a focal plane or a target surface after the modulating processing of the laser beam;

[0011] The detection and feedback module is arranged at an output surface of the system light path and is used for collecting a light spot intensity distribution image of the flat-top beam and transmitting the light spot intensity distribution image to the control and optimization module;

[0012] The control and optimization module is used for updating a phase distribution of the beam modulator in real time according to the light spot intensity distribution image, so as to correct the output flat-top beam.

[0013] The application further provides a dynamic beam shaping method based on a spatial light modulator.

[0014] A target intensity distribution image is generated according to parameters of a target flat-top light spot and a pixel size of an output surface camera An ideal beam shaping phase of the target flat-top light spot is calculated according to a coordinate system of an input surface and an output surface And an expression of an optimization phase of the beam modulator is constructed ;

[0015] A light spot intensity distribution image collected by an output surface detection and feedback module And a target intensity distribution image are used to construct an expression of a composite performance index

[0016] In each stage of the multi-stage SPGD algorithm, two groups of directionally random perturbation vectors are generated and the ideal beam shaping phase is updated respectively, two groups of new beam shaping phases are loaded to the beam modulator, and two new laser beams are generated;

[0017] Light spot intensity distribution images corresponding to the two new laser beams are collected, the composite performance index is calculated according to the expression of the composite performance index, target parameters in the expression of the optimization phase are optimized, and the laser beam is dynamically shaped by the beam modulator according to the optimized target parameters, so that a uniform flat-top beam is output from the focusing optical assembly.

[0018] On the basis of the above technical solution, the application can be further improved as follows:

[0019] Further: the ideal beam shaping phase of the target flat top spot is calculated according to the input plane and the output plane coordinate system , and the optimal phase of the beam modulator is constructed The expression of the formula specifically includes the following steps:

[0020] The shape, size and energy distribution range of the target flat top spot are set, and the corresponding target intensity image is generated in combination with the output plane camera pixel size ;

[0021] The ideal beam shaping phase of the target flat top spot is calculated in advance based on Fourier optics and standing phase method , wherein is the physical coordinate system of the input plane;

[0022] The Zernike polynomial is calculated , and the optimal phase of the beam modulator is constructed The expression is:

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] Wherein, p is the order number of the Zernike polynomial excluding the constant term (n=0, m=0), is the polar coordinate system of the input plane of the system light path, is the orthogonal normalized coefficient, n is the radial order of the Zernike polynomial, and m is the azimuthal frequency of the Zernike polynomial, is the radial polynomial of the Zernike polynomial, and the order is (n, m), is the target parameter of the Zernike polynomial to be optimized, is a vector composed of P Zernike polynomials.

[0030] Further: the light spot intensity distribution image collected by the output plane detection and feedback module and the target intensity distribution image The expression of the composite performance index is constructed and specifically includes the following steps:

[0031] The light spot intensity distribution image a normalized mean square error term between the target intensity distribution image , the calculation formula is:

[0032]

[0033] wherein, is a first balancing parameter for balancing the order of magnitude difference between the two images caused by measurement, F is the Frobenius norm, is the inner product of the two image matrices;

[0034] calculate the structural similarity between the spot intensity distribution image and the target intensity distribution image , the calculation formula is:

[0035]

[0036] wherein, is the covariance of the spot intensity distribution image and the target intensity distribution image , is the standard deviation of the spot intensity distribution image , is the standard deviation of the target intensity distribution image , is a small constant for avoiding calculation error caused by function division by 0;

[0037] According to the normalized mean square error term and the structural similarity , the composite performance index expression is constructed:

[0038]

[0039] wherein, is a second balancing parameter for balancing the order of magnitude difference between the normalized mean square error term and the structural similarity.

[0040] Further: the generation of two groups of direction random disturbance vectors and the update of the ideal beam shaping phase respectively specifically includes the following steps:

[0041] generating a group of positive and negative random but uniform size disturbance vectors :

[0042]

[0043] wherein, is a vector with length satisfying Rademacher distribution, is the amplitude of the disturbance of the s stage;​

[0044] According to a set of the disturbance vectors And the target parameter vector of the current stage Update the ideal beam shaping phase to obtain a new beam shaping phase in two opposite directions under disturbance :

[0045]

[0046] Wherein, The number of Zernike polynomials in the s-th stage, The target parameter of the p-th order and the t-th iteration in the s-th stage, The disturbance of the p-th order and the t-th iteration in the s-th stage, The p-th Zernike polynomial.

[0047] Further: the optimization of the target parameters in the optimization phase expression specifically includes the following steps:

[0048] The numerical gradient of the composite performance index of the new spot intensity distribution image corresponding to the two new laser beams is estimated The calculation formula is:

[0049]

[0050] Wherein, The composite performance index of the new beam shaping phase corresponding to the spot intensity distribution image under the positive disturbance vector disturbance, The composite performance index of the new beam shaping phase corresponding to the spot intensity distribution image under the negative disturbance vector disturbance, The disturbance amplitude of the s-th stage, The p-th value of the direction vector .

[0051] Based on the numerical gradient The numerical gradient vector is composed of The target parameters in the optimization phase expression are optimized by using the Adam optimizer.

[0052] Further: the optimization of the target parameters in the optimization phase expression based on the numerical gradient vector Specifically includes the following steps:

[0053] Set the preheating iteration number When the current iteration number is less than or equal to the preheating iteration number The target parameters in the optimization phase expression are updated by using the gradient descent method, and the calculation formula is:

[0054]

[0055] wherein, is the target parameter vector at the t+1th iteration of the Sth stage, is the target parameter vector at the tth iteration, is the learning rate of the Sth stage, is the numerical gradient vector at the tth iteration;

[0056] when the current iteration number is greater than the preheating iteration number , the first-order momentum and the second-order momentum of the Adam optimizer at the tth iteration are used to update the target parameters in the optimization phase expression, and the calculation formula is as follows:

[0057]

[0058] wherein, are the decay coefficients of the Adam optimizer, respectively, is a constant, , are the normalized first-order momentum and second-order momentum of the Adam optimizer, respectively;

[0059] read the composite performance indicators of the last iteration numbers, and perform least squares fitting on the changes of the iteration numbers to calculate the slope of the fitting curve, and when the ratio of to the initial slope is less than a preset proportion threshold , enter the next stage, repeat the above steps until all stages are completed, and obtain the final target parameters.

[0060] Further: before starting each stage, the following steps are further included:

[0061] adaptively calibrate the disturbance amplitude and the learning rate of the last stage to obtain the optimal disturbance amplitude and the learning rate corresponding to each stage.

[0062] Further: the adaptive calibration of the disturbance amplitude and the learning rate of the last stage includes the following steps:

[0063] repeat the measurement of the composite performance indicator measurement value times under the same phase diagram , wherein ε is a zero-mean noise, and estimate the variance of the noise ;

[0064] According to the composite performance index measurement value The local linearity index LLI is calculated, and the calculation formula is as follows:

[0065]

[0066]

[0067]

[0068]

[0069] Wherein, The mth random direction vector The composite performance index measurement value corresponding to the positive and negative candidate disturbance amplitude of The initial target parameter used in the current optimization stage The mean value of the composite performance index measurement value obtained by M0 times of measurement corresponding to The measurement standard deviation of The median operation is taken The local linearity calculated by the mth composite performance index measurement value under the current disturbance amplitude The optimal disturbance amplitude is determined based on the local linearity index LLI

[0070] , and the learning rate is adaptively set based on .

[0071] Further: the optimal disturbance amplitude is determined based on the local linearity index LLI, and the learning rate is adaptively set based on . The steps include:

[0072] In the first stage of the multi-stage SPGD algorithm, the initial value of the disturbance amplitude , and in the subsequent stage, the initial value of the disturbance amplitude is set to the disturbance amplitude of the last stage.

[0073] Search for the local linearity index LLI under the current disturbance amplitude and whether it exceeds the threshold value , if it exceeds the threshold value, the local linearity index LLI under the current disturbance amplitude is reduced to 1 / 2 of the original value, otherwise the local linearity index LLI under the current disturbance amplitude is increased to 2 times of the original value, until a group of disturbance amplitudes are obtained, which are respectively above and below the threshold value and closest to the threshold value .​

[0074] Based on the disturbance amplitude The optimal disturbance amplitude was calculated. The calculation formula is:

[0075]

[0076] based on and optimal perturbation amplitude Adaptive learning rate setting The calculation formula is:

[0077]

[0078] in, For use in controlling the learning rate The corresponding target parameter update magnitude is a normal number within the expected range.

[0079] The dynamic beam shaping system and method based on a spatial light modulator according to the present application first generates a target intensity distribution image according to the parameters of a target flat-top light spot and the pixel size of an output plane camera, calculates the ideal beam shaping phase of the target flat-top light spot according to the input plane and output plane coordinate system, and constructs the expression of the optimized phase of the beam modulator, and then constructs a composite performance index expression by the light spot intensity distribution image collected by the output plane detection and feedback module and the target intensity distribution image; in each stage of the multi-stage SPGD algorithm, two groups of directionally random perturbation vectors are generated and the ideal beam shaping phase is updated respectively, two new beam shaping phases are obtained and loaded onto the beam modulator, and two new laser beams are generated; finally, the light spot intensity distribution images corresponding to the two new laser beams are collected, the composite performance indexes are calculated according to the composite performance index expression, the energy distribution and shape characteristics are taken into account, the target parameters in the optimized phase expression are optimized, and the laser beam is dynamically shaped by the beam modulator according to the optimized target parameters, and a uniform flat-top light beam is output from the focusing optical assembly. The present application can correct the uniformity of the output flat-top light beam by using the SPGD algorithm and Zernike polynomials as control variables, so it can better adapt to the light source, reduce the difficulty of flat-top light beam shaping, improve the robustness and engineering applicability of the system, and has higher freedom in beam shaping applications, can generate and shape various flat-top light beam patterns, has lower requirements for the quality of the light source beam, uses a multi-stage gradual improvement of the order of Zernike polynomials to speed up the correction process of the flat-top light beam, and uses the convergence trend of the composite performance index as the criterion for stage switching; in the super parameter selection aspect, a disturbance strategy and learning rate automatic selection scheme are designed to resist measurement noise, so that the algorithm can quickly and stably converge in actual application; in the optimizer application aspect, the Adam optimizer is used to speed up the entire optimization process, and the behavior of the optimizer is adjusted for the application of the multi-stage algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0080] Figure 1 FIG. 1 is a structural schematic diagram of a dynamic beam shaping system based on a spatial light modulator according to an embodiment of the present application;

[0081] Figure 2 FIG. 3 is a structural schematic diagram of a simulation optical system according to an embodiment of the present application;

[0082] Figure 3A FIG. 5 is a comparison diagram of simulation results of single-stage and multi-stage SPGD algorithms according to an embodiment of the present application;

[0083] Figure 3B FIG. 6 is a comparison diagram of simulation convergence curves of single-stage and multi-stage SPGD algorithms according to an embodiment of the present application;

[0084] Figure 4AA spot diagram formed by a laser beam emitted by a laser source module in a dynamic beam shaping system based on a spatial light modulator according to an embodiment of the present application;

[0085] Figure 4B A comparison diagram of flat-top beam uniformity before and after dynamic beam shaping according to an embodiment of the present application. DETAILED DESCRIPTION

[0086] The principles and features of the present application are described below in conjunction with the accompanying drawings, which are only used to explain the present application and not intended to limit the scope of the present application.

[0087] As shown in Figure 1 A dynamic beam shaping system based on a spatial light modulator, comprising a laser source module, a beam expander and collimator, a beam modulator, a focusing optical assembly, a detection and feedback module, and a control and optimization module connected in sequence in an optical path;

[0088] The laser source module is arranged at an input surface of the optical path of the system and is configured to output a laser beam;

[0089] Here, the laser source module can output a beam with a near-Gaussian distribution, an elliptical Gaussian distribution, or other complex amplitude distribution, and can allow a beam center offset and a beam waist diameter error.

[0090] The beam expander and collimator is configured to expand and collimate the laser beam;

[0091] In an embodiment of the present application, the beam expander and collimator comprises an expander, a polarizer, and a mirror, and is configured to expand and collimate the laser beam.

[0092] The beam modulator is configured to modulate the laser beam after shaping and collimation;

[0093] Optionally, in one or more embodiments of the present application, the beam modulator is a phase-type spatial light modulator (SLM).

[0094] The focusing optical assembly is configured to form a flat-top beam with a target shape on a focal plane or a target surface after modulation of the laser beam;

[0095] In an embodiment of the present application, the focusing optical assembly comprises a 4f system and one or a group of objective lenses and lenses, the 4f system functions as a filter for 0-order light of the SLM and a beam reducer, and then the objective lens is used for beam shaping, and the objective lens and a lens before the camera of the detection and feedback module together form a magnification optical path for observing the shaped spot. The focusing optical assembly can form a flat-top beam with a target shape on a focal plane or a target surface after modulation of the SLM.

[0096] The detection and feedback module is arranged at an output surface of a system light path, and is configured to collect a light spot intensity distribution image of the flat top light beam and transmit the light spot intensity distribution image to the control and optimization module.

[0097] In the embodiment of the present application, the detection and feedback module includes a CCD, a CMOS camera or the like, and the collected light spot intensity distribution image is transmitted to the control and optimization module.

[0098] The control and optimization module is configured to update a phase distribution of the light beam modulator in real time according to the light spot intensity distribution image, so as to correct the output flat top light beam.

[0099] In the embodiment of the present application, the control and optimization module is realized by a computer or an embedded processor, and a multi-stage SPGD algorithm module is built-in, and the phase distribution of the SLM is updated in real time according to the collected pattern.

[0100] The present application also provides a dynamic light beam shaping method based on a spatial light modulator.

[0101] S1: generating a target intensity distribution image according to parameters of a target flat top light spot and pixel sizes of an output surface camera calculating an ideal light beam shaping phase of the target flat top light spot according to input surface and output surface coordinate systems and constructing an expression of an optimization phase of a light beam modulator ;

[0102] S2: constructing a composite performance index expression according to a light spot intensity distribution image collected by an output surface detection and feedback module and a target intensity distribution image ;

[0103] S3: in each stage of a multi-stage SPGD algorithm, generating two groups of directionally random perturbation vectors and updating the ideal light beam shaping phase respectively, loading two groups of new light beam shaping phases obtained to the light beam modulator, and generating two new laser beams

[0104] S4: collecting light spot intensity distribution images corresponding to the two new laser beams, calculating composite performance indexes of the light spot intensity distribution images according to the composite performance index expression respectively, optimizing target parameters in the optimization phase expression, and dynamically shaping the laser beams according to the optimized target parameters by the light beam modulator, so as to output a uniform flat top light beam from a focusing optical assembly.

[0105] In one or more embodiments of the present application, the ideal light beam shaping phase of the target flat top light spot is calculated according to input surface and output surface coordinate systems And construct the optimization phase of the beam modulator The expression of the target intensity image specifically includes the following steps:

[0106] S11: Set the shape, size and energy distribution range of the target flat-top spot, and generate the corresponding target intensity image combined with the pixel size of the output surface camera ;

[0107] For example, a square with a side length of 2R, the light intensity inside the edge range is set to be the same, then the target intensity image is:

[0108]

[0109] S12: Pre-calculate the ideal beam shaping phase to achieve the target flat-top spot based on Fourier optics and standing phase method , where is the physical coordinate system of the input plane;

[0110] Here, for one-dimensional case, the ideal flat-top spot generation phase is:

[0111] ,

[0112]

[0113] where is the waist radius of the incident Gaussian beam, R is the radius of the target uniform distribution. λ is the wavelength of the incident light, f is the focal length of the lens. If the target pattern is a one-dimensional separable pattern (such as a square), superimpose the corresponding two one-dimensional beam shaping phases in the vertical direction, and the generation phase of the two-dimensional flat-top beam .

[0114] S13: Calculate the Zernike polynomial And construct the optimization phase of the beam modulator Expression:

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121] wherein p is the Noll order number of the Zernike polynomial excluding the constant term (n=0, m=0), is the polar coordinate system of the input surface of the system light path, is the orthogonal normalized coefficient, n is the radial order of the Zernike polynomial, and m is the azimuthal frequency of the Zernike polynomial, is the radial polynomial of the Zernike polynomial, whose order is (n, m), is the target parameter of the Zernike polynomial to be optimized, is the vector composed of P Zernike polynomials.

[0122] Here, the order of the Zernike polynomial is determined by the radial order n and the azimuthal frequency m. p is the Noll order number of the Zernike polynomial excluding the constant term (n=0, m=0).

[0123] It should be additionally pointed out that in step S1, the optimization independent variable distribution mode of the multi-stage SPGD algorithm also needs to be preset. If the multi-stage SPGD algorithm has K stages in total, the number of Zernike polynomials used in each stage satisfies , for example , which means that the first stage only uses the first 14 orders of Zernike polynomials for optimization, the second stage extends to 65, the third stage extends to 135, and so on.

[0124] In one or more embodiments of the present application, the light spot intensity distribution image collected by the output surface detection and feedback module and the target intensity distribution image The construction of the composite performance index expression specifically includes the following steps:

[0125] S21: Calculate the normalized mean square error term between the light spot intensity distribution image and the target intensity distribution image , and the calculation formula is:

[0126]

[0127] wherein is the first balancing parameter used to balance the order of magnitude difference between the two images caused by measurement, F is the Frobenius norm, and for a matrix, the F norm is defined as the square root of the sum of the squares of each element in the matrix, is the inner product of the two image matrices;

[0128] Here, the normalized mean square error term is used to compare the light spot intensity distribution image collected by the output surface detection and feedback module and the target image ​The difference between each pixel is balanced by α to balance the order of magnitude difference between the two images caused by the measurement.

[0129] S22: Calculate the structural similarity between the spot intensity distribution image and the target intensity distribution image The calculation formula is:

[0130]

[0131] Wherein, is the spot intensity distribution image and the target intensity distribution image , is the standard deviation of the spot intensity distribution image , is the standard deviation of the target intensity distribution image , is a small constant used to avoid calculation error caused by function division by 0;

[0132] In this embodiment, the structural similarity is used to compare the structural difference between the two images, and is not sensitive to brightness, contrast and the difference between single pixels.

[0133] S23: According to the normalized mean square error term and the structural similarity , the composite performance index expression is constructed:

[0134]

[0135] Wherein, is a second balancing parameter used to balance the order of magnitude difference between the normalized mean square error term and the structural similarity, which can be set by simulation or pre-experiment.

[0136] Next, taking the s-th stage (using the first P s Zernike polynomials) in the multi-stage SPGD algorithm as an example, the flow of the multi-stage SPGD algorithm is introduced in detail.

[0137] In one or more embodiments of the application, the generating two groups of direction random disturbance vectors and updating the ideal beam shaping phase respectively specifically includes the following steps:

[0138] S31: Generate a group of positive and negative random but uniform size disturbance vectors :

[0139]

[0140] Wherein, is a length of Vectors that satisfy the Rademacher distribution This is the amplitude of the disturbance in stage s, which is also a parameter that needs to be automatically calibrated before the start of each subsequent stage.

[0141] S32: Based on a set of the aforementioned perturbation vectors and the target parameter vector of the current stage The ideal beam shaping phase is updated to obtain new beam shaping phases with two opposite directions under perturbation. :

[0142]

[0143] in, Let be the number of Zernike polynomials in the s-th stage. Let p be the target parameter with sorting index p and iteration number t in stage s. Let p be the perturbation with sorting index p and iteration number t in stage s. Let p be the p-th Zernikal polynomial.

[0144] Because of the added perturbation, the ideal beam-shaping phase will change; therefore, this is addressed here by using the perturbation vector. and the target parameter vector of the current stage The ideal beam shaping phase is updated, allowing the output of the beam modulator to be adjusted based on the updated beam shaping phase, and the corresponding output beam spot to be acquired. and And calculate the corresponding composite performance index according to step S23 above. and .

[0145] In one or more embodiments of the present invention, optimizing the target parameter in the optimized phase expression specifically includes the following steps:

[0146] S41: Estimate the numerical gradient using the composite performance index of the spot intensity distribution images corresponding to the two new laser beams. The calculation formula is:

[0147]

[0148] in, It is a composite performance index of the spot intensity distribution image corresponding to the new beam shaping phase under positive perturbation vector perturbation. It is a composite performance index of the spot intensity distribution image corresponding to the new beam shaping phase under negative perturbation vector perturbation. Let be the disturbance amplitude in stage s. Direction vector The p-th value;

[0149] S42: Based on the numerical gradient Composition of numerical gradient vector The Adam optimizer is used to optimize the target parameters in the optimized phase expression.

[0150] Specifically, in one or more embodiments of the present invention, the step based on the numerical gradient vector The optimization of the target parameters in the optimized phase expression using the Adam optimizer specifically includes the following steps:

[0151] S421: Set the number of preheating iterations When the current iteration number is less than or equal to the preheating iteration number Then, the objective parameters in the optimized phase expression are updated using the gradient descent method, and the calculation formula is as follows:

[0152]

[0153] in, Let be the target parameter vector at the (t+1)th iteration in the S-th stage. Let be the target parameter vector at the t-th iteration. The learning rate for stage S. Let be the numerical gradient vector at the t-th iteration;

[0154] Here, to avoid slow convergence due to Adam's suppression of large gradient calculations in the first stage (s=1), this invention sets the number of preheating iterations. During warm-up (i.e., the number of iterations) At this point, the parameters are updated using simple gradient descent.

[0155] S422: When the current iteration number is greater than the preheating iteration number At that time, the first-order momentum at the t-th iteration of the Adam optimizer is used. With second momentum The target parameters in the optimized phase expression are updated using the following formula:

[0156]

[0157] in, These are the decay coefficients for the Adam optimizer, initially set to 0.9 and 0.99, respectively. It is a constant, taking the value 10. -8 To prevent the occurrence of extremely small values ​​when divided by 0, , These are the first and second momentum of the normalized Adam optimizer, respectively, to prevent excessive errors in gradient estimation during initialization; this ensures convergence stability in the initial stage while improving convergence speed in later stages.

[0158] S423: Read the most recent The composite performance index is calculated based on the number of iterations, and the change in the number of iterations is fitted using least squares. The slope of the fitted curve is then calculated. As iterations continue, the curve gradually converges, and... The ratio of the initial slope to the initial slope is less than a preset proportional threshold. (In this embodiment, the value is 0.3) When the value is reached, proceed to the next stage, repeat the above steps, until all K stages are completed, and the final target parameter is obtained. Here, the most recent value is read. When calculating the composite performance index for the number of iterations, the composite performance index from the previous stage is not included. Furthermore, when switching stages, the dimension of the variable parameters is first expanded to... The newly added parameters can be initialized to 0, and the second-order momentum of the Adam optimizer will be reset to 0 to enhance its adaptability to the new dimensions.

[0159] Preferably, in one or more embodiments of the present invention, the following steps are further included before the start of each stage:

[0160] S420: Regarding the disturbance amplitude mentioned in the previous stage and learning rate Adaptive calibration is performed to obtain the optimal perturbation amplitude for each stage. and learning rate This approach balances noise robustness with the local linear approximation of numerical gradient estimation.

[0161] Specifically, in one or more embodiments of the present invention, the disturbance amplitude of the previous stage and learning rate Adaptive calibration includes the following steps:

[0162] S4201: Repeat measurements under the same phase diagram Subcomposite performance index measurement value , where ε is zero-mean noise, and the variance of the noise is estimated. ;

[0163] Here, we assume the performance index measurement value is , where ε is zero-mean noise. The variance of the noise. This can be achieved by repeatedly acquiring data under the same phase map. Sub-performance index estimation. The larger the disturbance amplitude, the greater the change in the evaluation index, and the higher the signal-to-noise ratio.

[0164] S4202: Based on the measured values ​​of the composite performance indicators Calculate the local linearity index (Local Linearity Index, LLI), calculated using the following formula:

[0165]

[0166]

[0167]

[0168]

[0169] in, These are the m-th random direction vectors. The measured values ​​of the composite performance index corresponding to the positive and negative candidate perturbation amplitudes. These are the initial target parameters used in the current optimization phase. The mean value of the composite performance index obtained from the corresponding M0 measurements is used for local linearity estimation. for The standard deviation of measurement To calculate the standard deviation of the system's detection noise, For the median operation, This refers to the local linearity calculated using the m-th composite performance index measurement value under the current disturbance amplitude;

[0170] First, set M random direction vectors. For each candidate perturbation amplitude Measured M times and obtained a set of evaluation indicators , for The measurement standard deviation can be obtained from the results of the previous measurement using the error propagation theorem. LLI represents the final assessment of local linearity under the current perturbation size. A larger LLI indicates poorer local linearity and less reliable numerical gradient estimation under the current perturbation, requiring a reduction in the perturbation amplitude. However, due to measurement noise, LLI evaluation may be inaccurate, leading to very large LLI measurements even under small perturbations. Therefore, an additional factor is added to the denominator of the LLI measurement formula. It can achieve a 95% confidence level under the noise estimation conditions of the Gaussian model to avoid the denominator of LLI approaching 0.

[0171] The local linearity index (LLI) measures the nonlinearity of performance index J, and this index changes with the amplitude of the disturbance. The increase of [variable name] leads to an increase in [variable name]. During gradient estimation, the smaller the perturbation amplitude, the more accurate the gradient estimate in that region. In the formula for calculating the Local Linearity Index (LLI), the numerator corresponds to [variable name] in the current [variable name]. The second-order remainder of the Taylor expansion nearby, the denominator This is a first-order difference term.

[0172] S4203: Determine the optimal disturbance amplitude based on the local linearity index LLI. and based on Adaptively set the learning rate.

[0173] The selection of perturbation amplitude in the SPGD algorithm needs to consider both signal-to-noise ratio and local linearity. Therefore, a bisection method is designed to automatically search for the optimal perturbation amplitude.

[0174] In one or more embodiments of the present invention, the optimal perturbation amplitude is determined based on the Local Linearity Index (LLI), and based on... Adaptive learning rate setting specifically includes the following steps:

[0175] S42031: Initial value of the perturbation amplitude in the first stage of the multi-stage SPGD algorithm. And in subsequent stages, the initial value of the disturbance amplitude will be... Set to the disturbance amplitude of the previous stage ;

[0176] S42032: Search for the local linearity index (LLI) under the current perturbation amplitude and whether it exceeds the threshold. (In this embodiment, the value is 0.1). If the threshold is exceeded, the local linearity index (LLI) under the current disturbance amplitude is reduced to half of its original value; conversely, the local linearity index (LLI) under the current disturbance amplitude is increased to twice its original value, until a set of values ​​at the threshold is obtained. Up and down and closest to the threshold Disturbance amplitude ;

[0177] S42033: Based on the disturbance amplitude The optimal disturbance amplitude was calculated. The calculation formula is:

[0178]

[0179] based on and optimal perturbation amplitude Adaptive learning rate setting The calculation formula is:

[0180]

[0181] in, For use in controlling the learning rate The corresponding target parameter update magnitude is a normal number within the expected range.

[0182] The dynamic beam shaping system and method based on a spatial light modulator of the present invention has the following advantages:

[0183] a) This system does not rely on wavefront sensors; it only measures the intensity distribution of the output surface through a camera and constructs scalar performance indicators to achieve wavefront sensor-independent closed-loop beam shaping.

[0184] b) Multi-stage Zernikal polynomial expansion strategy. By controlling the order of the Zernikal polynomials involved in the optimization in stages, a small number of low-order optimizations are used to guide the rapid convergence of high-dimensional independent variables.

[0185] c) A multi-stage SPGD algorithm combining stochastic parallel gradients and Adam momentum. This algorithm uses stochastic perturbations to estimate gradients and is simple to implement in hardware. By introducing optimizer warm-up in the first stage and second-order momentum reset during stage switching, the convergence efficiency and algorithm robustness are improved.

[0186] d) Adaptive calibration mechanism for perturbation amplitude and learning rate. The LLI index is systematically introduced to quantitatively characterize the degree of nonlinearity at a given perturbation amplitude. A bisection search strategy is employed to automatically measure the perturbation amplitude and learning rate, avoiding empirical parameter tuning and enabling the algorithm to exhibit good adaptability under different target patterns and noise levels.

[0187] e) A composite performance index was designed, which combines the normalized mean square error with structural similarity. This constrains the overall energy distribution while emphasizing the overall shape similarity, making it more global than a single energy error constraint.

[0188] f) Automatic stage switching strategy driven by stage convergence trend. The slope of the fitted line of the performance index is used as an evaluation of the convergence trend to determine whether to switch to the next stage. Compared with optimization with a fixed number of iterations, this avoids wasting convergence times or premature termination.

[0189] g) The versatility and scalability of the device structure. The wavefront controller can be an SLM or a digital micromirror device (DMD), etc.

[0190] The following examples illustrate the dynamic beam shaping system and method based on spatial light modulators of this invention:

[0191] Example 1:

[0192] 1. Simulation Model Description:

[0193] Simulated optical systems are as follows Figure 2The optical path is shown. The pixel width of the input surface is set to 12.5 μm, and the lens parameters are set to focal length f = 10 mm and numerical aperture NA = 0.45. It is assumed that the laser beam at the input surface is a non-ideal elliptic Gaussian beam, such as... Figure 3A As shown: The elliptic Gaussian beam has an ellipticity of 0.6, an effective Gaussian radius of r0 = 2.1 mm, and a wavefront phase with aberrations randomly composed of the first 12 Zernike modes. The desired output is a square flat-top beam with a half-width of R = 0.1 mm, and the initial phase can be simulated. Light intensity distribution on the output surface, such as Figure 3A The initial values ​​are shown.

[0194] 2. Algorithm parameter settings:

[0195] This example compares a single-stage optimization strategy (S-ASPGD) using the Adam optimizer with the multi-stage optimization strategy (M-ASPGD) proposed in this invention. To ensure a fair comparison of the optimization processes, the Adam preheating startup method is also adopted in the S-ASPGD scheme. And the same hyperparameter selection strategy as M-ASPGD, M=8.

[0196] Other settings for the M-ASPGD algorithm: Evaluation metric: downward trend; Evaluation range: W = 40; Zernike polynomial order used in each stage. .

[0197] The S-ASPGD algorithm uses a P = 65 Zernike polynomial in a single operation.

[0198] 3. Performance Indicators and Comparison Results:

[0199] like Figure 3B As shown, the performance index of the M-ASPGD algorithm is close to convergence when the number of Zernike polynomials is increased to 65 in the third stage. However, the S-ASPGD algorithm is still being optimized at this time, and its performance index is worse than that of M-ASPGD.

[0200] The uniformity of the output flat-top beam is evaluated by the following two metrics:

[0201] Peak-valley values:

[0202]

[0203] And the flat-top uniformity as defined in ISO standard 13694:

[0204]

[0205] in and These are the maximum and minimum light intensity values ​​within the flat-top profile. The energy density histogram N(I) represents the energy density histogram. x,y ) middle The full width at half maximum (FWHM) of the nearest dominant peak. Output energy is represented by the measured intensity I, while N(I) x,y ) is an energy density of I x,y The number of image pixels. A perfectly uniform flat-top beam of U... p =0.

[0206] like Figure 3A As shown, S-ASPGD and M-ASPGD performed PV=0.62 and U for the same correction task. p =0.07 and PV=0.33, U p =0.05.

[0207] Example 2:

[0208] 1. Optical system structure:

[0209] The optical setup for this experiment is shown in the diagram below. Figure 1 As shown, it consists of an SLM with a pixel size of 12.5 μm × 12.5 μm and a continuous-wave laser with a wavelength of λ = 532 nm. Figure 4A The image shows the laser spot, which is an elliptic Gaussian beam with an ellipticity of 0.8 and a maximum diameter d along its major axis. max = 1.48 mm, minimum diameter in the minor axis direction is d min = 1.19 mm. The beam is first filtered by a linear polarizer, then expanded by a 3x beam expander, and subsequently modulated by an SLM. To suppress the 0th order of the SLM, a 4th order grating phase is superimposed on each beam-shaping phase. The SLM-modulated beam is imaged by a 4f system, and the 0th order component is blocked at the Fourier plane by an aperture stop; simultaneously, the 4f system reduces the beam to a factor of 0.5 to fit the entrance pupil of the objective lens. After passing through the 4f system, the beam is split at a beam splitter and fed into the objective lens (numerical aperture NA = 0.25, focal length f1 = 16.5 mm). A mirror is placed at the focal plane of the objective lens, and the reflected light is magnified by the objective lens and a lens (focal length f2 = 100 mm) before being detected by a camera with a pixel size of 2.4 μm × 2.4 μm.

[0210] 2. Algorithm parameter settings:

[0211] Noise estimation related parameter M0=20, other hyperparameters are selected the same as in simulation M=8, W warm =W=40.

[0212] The phased strategy of the M-ASPGD algorithm is as follows: .

[0213] 3. Experimental phenomena and results:

[0214] like Figure 4B As shown, the target pattern is set as a square flat-top beam with a half-width of R=0.05 mm. Before dynamic shaping, PV=0.94, U p =0.38, the uniformity after dynamic shaping is PV=0.56, U p =0.29, average time taken: 20 minutes.

[0215] The above experimental results demonstrate that the dynamic beam shaping method based on a spatial light modulator of this invention...

[0216] a) The convergence speed is faster than traditional single-stage SPGD or single-stage multi-stage SPGD algorithms using the Adam optimizer. This invention employs staged expansion of the independent variable dimension, pre-startup of the optimizer, and staged second-order momentum reset, resulting in a significant improvement in convergence speed with the same number of iterations.

[0217] b) By using noise estimation and local linearity index, the perturbation amplitude and learning rate parameters in the multi-stage SPGD algorithm can be adaptively selected, which improves the robustness to noise and environmental perturbations.

[0218] c) No wavefront sensor required, system is simple and energy-efficient. This invention relies solely on a camera to measure light intensity distribution. The absence of an additional wavefront sensor and beam splitter allows for a more compact system layout and easier debugging.

[0219] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A dynamic beam shaping system based on a spatial light modulator, characterized by: The laser light source module, the beam expander and collimator, the beam modulator, the focusing optical assembly, the detection and feedback module and the control and optimization module are sequentially connected by optical paths. The laser light source module is arranged at an input surface of a system optical path and is configured to output a laser beam. The beam expander and collimator is configured to perform beam expansion and collimation on the laser beam. The beam modulator is configured to perform modulation on the laser beam after the shaping and collimation. The focusing optical assembly is configured to form a flat-top beam with a target shape on a focal plane or a target surface. The detection and feedback module is arranged at an output surface of the system optical path and is configured to acquire a light spot intensity distribution image of the flat-top beam and transmit the image to the control and optimization module. The control and optimization module is configured to update a phase distribution of the beam modulator in real time according to the light spot intensity distribution image to correct the output flat-top beam.

2. A dynamic beam shaping method based on a spatial light modulator, using the dynamic beam shaping system based on a spatial light modulator of claim 1, characterized in that, The method comprises the following steps: generating a target intensity distribution image according to parameters of a target flat-top spot and an output face camera pixel size calculating an ideal beam shaping phase of the target flat-top spot according to input face and output face coordinate systems and constructing an expression of an optimized phase of a beam modulator ​ The light spot intensity distribution image collected by the output surface detection and feedback module The target intensity distribution image Construct a composite performance index expression; In each stage of the multi-stage SPGD algorithm, two groups of directionally random perturbation vectors are generated to update the ideal beam shaping phase, and two new groups of beam shaping phases are loaded to the beam modulator to generate two new laser beams. The light spot intensity distribution images corresponding to the two new laser beams are acquired, and the composite performance index is calculated according to the composite performance index expression, the target parameters in the optimization phase expression are optimized, and the laser beam is dynamically shaped by the beam modulator according to the optimized target parameters to output a uniform flat-top beam from the focusing optical assembly.

3. The spatial light modulator based dynamic beam shaping method of claim 2, wherein: calculating the ideal beam shaping phase of the target flat top spot according to the input plane and output plane coordinate systems and constructing an optimized phase of the beam modulator The expression of the ideal beam shaping phase of the target flat top spot according to the input plane and output plane coordinate systems specifically includes the following steps: Setting the shape, size and energy distribution range of the target flat-top spot, combined with the pixel size of the output surface camera to generate a corresponding target intensity image ; Optical shaping phase for achieving target flat-top beam based on Fourier optics and stationary phase method wherein is the physical coordinate system of the input plane; Computing zernike polynomials and constructing an optimized phase for a beam modulator Expression: ； ； ； ； ； ； Wherein, p is the order number of Zernike polynomial excluding constant term (n=0, m=0), The polar coordinate system of the input surface of the system light path, The orthogonal normalization coefficient, n is the radial order of Zernike polynomial, and m is the azimuthal frequency of Zernike polynomial, The radial polynomial of Zernike polynomial, whose order is (n, m), The target parameter of the Zernike polynomial to be optimized, The vector composed of P Zernike polynomials.

4. The spatial light modulator based dynamic beam shaping method of claim 2, wherein: The light spot intensity distribution image collected by the output surface detection and feedback module The target intensity distribution image The composite performance index expression construction specifically includes the following steps: Computing a light spot intensity profile image A normalized mean square error term between the target intensity profile image The formula is:​ ； wherein, is a first balancing parameter for balancing the order of magnitude difference between the two images resulting from the measurement, F is the Frobenius norm, is the inner product of the two image matrices; calculating a structural similarity between the light spot intensity distribution image and the target intensity distribution image , the calculation formula is: ； wherein, is the spot intensity profile image is the target intensity profile image is the covariance of the spot intensity profile image is the standard deviation of the spot intensity profile image is the standard deviation of the target intensity profile image is the standard deviation of the target intensity profile image is the standard deviation of the target intensity profile image is a small constant used to avoid computational errors resulting from division by zero of the function; According to the normalized mean square error term With structural similarity Constructing composite performance indicator expression: ； wherein is a second balancing parameter for balancing the order of magnitude difference between the normalized mean square error term and the structural similarity.

5. The spatial light modulator based dynamic beam shaping method of claim 2, wherein: The two groups of directionally random perturbation vectors are generated to update the ideal beam shaping phase, which comprises the following steps: Generating a set of random positive and negative perturbation vectors of uniform size : ； wherein is a vector of length , satisfying a Rademacher distribution, is the amplitude of the perturbation of the s-th phase; According to a set of the perturbation vectors and the target parameter vector of the current stage updating the ideal beam shaping phase to obtain new beam shaping phases in two opposite directions under perturbation : ； wherein, is the number of Zernike polynomials of the s-th stage, is the target parameter of the s-th stage with the ranking number p and the iteration number t, is the perturbation of the s-th stage with the ranking number p and the iteration number t, is the p-th Zernike polynomial.

6. The spatial light modulator based dynamic beam shaping method of claim 5, wherein: The target parameters in the optimization phase expression are optimized, which comprises the following steps: Numerical gradient estimated using composite performance index of the intensity distribution images of the two new laser beams. The calculation formula is: ； wherein, a composite performance indicator of the spot intensity distribution image corresponding to the new beam shaping phase under the positive perturbation vector perturbation, a composite performance indicator of the spot intensity distribution image corresponding to the new beam shaping phase under the negative perturbation vector perturbation, a perturbation amplitude of the s-th stage, a directional vector a p-th value of the directional vector. based on the numerical gradient composing a numerical gradient vector optimizing the target parameters in the optimized phase expression using an Adam optimizer.

7. The spatial light modulator based dynamic beam shaping method of claim 6, wherein: based on the numerical gradient vector optimizing the target parameters in the optimized phase expression with an Adam optimizer specifically includes the following steps: Setting the preheat iteration number When the current iteration number is less than or equal to the preheat iteration number The target parameter in the optimization phase expression is updated by using the gradient descent method, and the calculation formula is: ； wherein, is the target parameter vector at the t+1 iteration of the Sth stage, is the target parameter vector at the t iteration, is the learning rate of the Sth stage, is the numerical gradient vector at the t iteration. When the current iteration number is greater than the warm-up iteration number the first-order momentum of the Adam optimizer at the tth iteration and the second-order momentum updating the target parameters in the optimization phase expression, the calculation formula is as follows: ； wherein, are the decay coefficients of the Adam optimizer, respectively, is a constant, , are the normalized first and second moment of the Adam optimizer, respectively; Read recent The composite performance index of the number of iterations is fitted by least squares fitting, and the slope of the fitting curve is calculated And when The ratio of the initial slope is less than the preset proportion threshold Enter the next stage, repeat the above steps until all stages are completed, and get the final target parameter.

8. The spatial light modulator based dynamic beam shaping method of claim 7, wherein: Before the start of each stage, the following steps are further included: the disturbance amplitude of the previous stage and learning rate adaptive calibration is performed to obtain the optimal disturbance amplitude and learning rate corresponding to each stage and learning rate .

9. The spatial light modulator based dynamic beam shaping method of claim 8, wherein: said disturbance amplitude of the previous phase and learning rate adaptive calibration comprises the following steps: Repeating measurements under the same phase map Secondary composite performance indicator measurements where ε is the zero-mean noise and estimates the variance of the noise ; According to the composite performance index measurement value A local linearity index LLI is calculated, according to the following formula: ； ； ； ； in, These are the m-th random direction vectors. The measured values ​​of the composite performance index corresponding to the positive and negative candidate perturbation amplitudes. These are the initial target parameters used in the current optimization phase. The mean of the composite performance index measurements obtained from the corresponding M0 measurements, for The standard deviation of measurement For the median operation, This refers to the local linearity calculated using the m-th composite performance index measurement value under the current disturbance amplitude; based on the local linearity index determining an optimal perturbation amplitude and based on adaptively setting the learning rate.

10. The spatial light modulator based dynamic beam shaping method of claim 9, wherein: The local linearity index is determined based on the local linearity index determining an optimal perturbation amplitude, and setting the learning rate based on The adaptive setting of the learning rate specifically includes the following steps: In the first stage of the multi-stage SPGD algorithm, the initial value of the perturbation amplitude is set to be the perturbation amplitude of the previous stage in the subsequent stage ; searching for the local linearity index LLI at the current perturbation amplitude and whether it exceeds the threshold value , if it exceeds the threshold value, reducing the local linearity index LLI at the current perturbation amplitude to 1 / 2 of the original, otherwise increasing the local linearity index LLI at the current perturbation amplitude to 2 times the original, until a set of perturbation amplitudes are obtained which are respectively at the threshold value above and below and closest to the threshold value ;​ According to the disturbance amplitude The optimal disturbance amplitude is calculated The calculation formula is: ； based on and the optimal perturbation amplitude adaptively setting the learning rate , the calculation formula is: ； wherein, is a normal number corresponding to a target parameter update range expectation is a normal number corresponding to a target parameter update range expectation

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