CN110133845A - A Design Method of Freeform Surface Wavefront Compensation Element Used in Laser System - Google Patents
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Abstract
本发明公开了一种用于激光系统的自由曲面波前补偿元件的设计方法，其中，该方法包括：通过畸变波前探测器探测激光系统输出的畸变波前，并将测量得到畸变波前的离散斜率数据(Sx，Sy)传输至计算机；采用多参数优化设计方法，以数值化正交多项式为基函数，拟合离散斜率数据，利用模式法进行曲面重构，获得畸变波前表征多项式W；根据波前相位互补原理，计算补偿激光系统畸变波前所需的自由曲面波前补偿元件面形表征多项式W*，实现激光系统畸变波前的校正。所述方法可用于复杂形状波前，且拟合精度高，具有很好的热稳定性，适合大功率激光系统畸变波前补偿。
The invention discloses a design method for a free-form surface wavefront compensation element used in a laser system, wherein the method includes: detecting the distorted wavefront output by the laser system through a distorted wavefront detector, and obtaining the distorted wavefront from the measurement The discrete slope data (S x , S y ) is transmitted to the computer; the multi-parameter optimization design method is adopted, and the numerical orthogonal polynomial is used as the basis function to fit the discrete slope data, and the model method is used to reconstruct the surface to obtain the representation of the distorted wavefront Polynomial W; According to the principle of wavefront phase complementarity, calculate the free-form surface wavefront compensation element surface shape representation polynomial W* required to compensate the distorted wavefront of the laser system, and realize the correction of the distorted wavefront of the laser system. The method can be used for wavefronts with complex shapes, has high fitting precision, has good thermal stability, and is suitable for compensating the distorted wavefronts of high-power laser systems.
Description
技术领域technical field
本发明涉及高能固体激光系统波前畸变补偿技术领域，具体地说涉及一种用于高功率激光系统的自由曲面波前补偿元件的设计方法。The invention relates to the technical field of wavefront distortion compensation for high-energy solid-state laser systems, in particular to a design method for free-form surface wavefront compensation components used in high-power laser systems.
背景技术Background technique
高功率固体激光器由于其小体积、大能量输出、高稳定性等优点，在国家安全、重大装备、科学研究等重大领域具有极其广阔的应用前景。追逐更高效率、更高功率、更高光束品质、更高可靠性运行模式一直是高功率固体激光研究与发展的主要目标与趋势。但在高能固体激光系统中，系统本身的光学元件形变和装调精度引入的静态波前畸变和激光晶体的热效应引入的动态波前畸变等因素是造成输出光束质量降低的主要因素。Due to its small size, large energy output, and high stability, high-power solid-state lasers have extremely broad application prospects in major fields such as national security, major equipment, and scientific research. The pursuit of higher efficiency, higher power, higher beam quality, and higher reliability operating modes has always been the main goal and trend of high-power solid-state laser research and development. However, in the high-energy solid-state laser system, factors such as the static wavefront distortion introduced by the deformation of the optical components of the system itself and the adjustment accuracy, and the dynamic wavefront distortion introduced by the thermal effect of the laser crystal are the main factors that cause the degradation of the output beam quality.
目前对高功率激光系统的波前畸变采用压电陶瓷或伺服电机控制变形镜实现波前畸变补偿，其主要结构包括：动镜、变形镜、控制器和处理器、探测器。但是其存在自身限制：1.空间频率响应有限，不能有效校正高频噪声；2.针对促动单元增多，机械结构复杂，求解变形镜的变形性困难，算法复杂耗时；3.变形镜行程有限，难以校正PV值十几个波长以上的波前畸变。另外，一般常用泽尼克多项式或勒让德多项式进行自由曲面拟合，其中，泽尼克多项式针对圆域连续曲面拟合，但激光系统得到的是离散梯度数据；勒让德多项式主要针对方域波前拟合，而激光系统中圆域较为常见；两者对于自由曲面面形形状均不具有通用性，且拟合精度受到拟合多项式项数的影响。针对这些问题，且基于高能固体激光器工作时的波前分布相对稳定的特点，根据波前相位互补原理，提出利用自由曲面波前补偿元件对高能固体激光器产生的波前畸变进行补偿，采用以数值化正交多项式为基函数的模式法进行曲面重构实现提高输出光束质量，校正较大畸变波前的目标，不需要控制器单元，单独的自由曲面波前补偿元件实现高能激光系统畸变补偿。At present, the wavefront distortion of high-power laser systems is compensated by piezoelectric ceramics or servo motors to control deformable mirrors to realize wavefront distortion compensation. The main structure includes: moving mirror, deformable mirror, controller and processor, and detector. However, it has its own limitations: 1. The spatial frequency response is limited, and high-frequency noise cannot be effectively corrected; 2. Due to the increase in the number of actuating units, the mechanical structure is complex, it is difficult to solve the deformability of the deformable mirror, and the algorithm is complex and time-consuming; 3. The stroke of the deformable mirror Limited, it is difficult to correct wavefront distortion with a PV value above a dozen wavelengths. In addition, Zernike polynomials or Legendre polynomials are generally used for free-form surface fitting. Among them, Zernike polynomials are used for continuous surface fitting in circular domains, but the laser system obtains discrete gradient data; Legendre polynomials are mainly for square domain waves. Pre-fitting, while circular domains are more common in laser systems; neither of them is universal for free-form surface shapes, and the fitting accuracy is affected by the number of fitting polynomial terms. In view of these problems, and based on the relatively stable wavefront distribution of high-energy solid-state lasers, according to the principle of wavefront phase complementarity, a free-form surface wavefront compensation element is proposed to compensate the wavefront distortion generated by high-energy solid-state lasers. The pattern method of turning the orthogonal polynomial into the basis function performs surface reconstruction to improve the quality of the output beam and correct the target of a large distorted wavefront. No controller unit is required, and a separate free-form surface wavefront compensation element realizes distortion compensation of the high-energy laser system.
因此，利用自由曲面波前补偿元件可以实现高能固体激光器输出光束的波前畸变补偿。Therefore, the wavefront distortion compensation of the output beam of the high-energy solid-state laser can be realized by using the free-form surface wavefront compensation element.
发明内容Contents of the invention
本发明的目的在于克服上述现有技术的不足，提供一种用于高功率激光系统的自由曲面波前补偿元件的设计方法，利用测量得到的高能激光系统的畸变波前离散斜率数据(Sx,Sy)；采用多参数优化设计方法，以数值化正交多项式为基函数，拟合离散斜率数据，利用模式法进行曲面重构，获得畸变波前表征多项式W；根据波前相位互补原理，计算补偿激光系统畸变波前所需的自由曲面波前补偿元件面形表征多项式W*，实现激光系统畸变波前的校正。克服变形镜波前畸变补偿存在的不能有效校正高频噪声，机械结构复杂，变形镜行程有限的问题，以及一般表征多项式无法表征复杂元件面形的问题。The purpose of the present invention is to overcome the above-mentioned deficiencies in the prior art, provide a kind of design method for the free-form surface wave front compensating element of high power laser system, utilize the distortion wave front discrete slope data (S x ,S y ); using the multi-parameter optimization design method, using the numerical orthogonal polynomial as the basis function, fitting the discrete slope data, using the model method to reconstruct the surface, and obtaining the distortion wavefront representation polynomial W; according to the principle of wavefront phase complementarity , to calculate the free-form surface wavefront compensation element surface shape polynomial W* required to compensate the distorted wavefront of the laser system, and realize the correction of the distorted wavefront of the laser system. Overcome the problems of wavefront distortion compensation of deformable mirrors that cannot effectively correct high-frequency noise, complex mechanical structure, limited travel of deformable mirrors, and the inability of general characterization polynomials to characterize the surface shape of complex components.
本发明的技术解决方案为：Technical solution of the present invention is:
一种用于激光系统的自由曲面波前补偿元件的设计方法，该设计方法包括如下步骤：A design method for a free-form surface wavefront compensation element used in a laser system, the design method comprising the steps of:
步骤1)通过畸变波前探测器探测激光系统输出的畸变波前，并将测量得到畸变波前的离散数据斜率(Sx,Sy)传输至计算机；Step 1) Detect the distorted wavefront output by the laser system through the distorted wavefront detector, and transmit the measured discrete data slope (S x , S y ) of the distorted wavefront to the computer;
步骤2)计算获得畸变波前表征多项式W；Step 2) Calculate and obtain the polynomial W representing the distortion wavefront;
步骤3)令补偿激光系统畸变波前所需的自由曲面波前补偿元件面形表征多项式W*满足如下关系：Step 3) Let the free-form surface wavefront compensation element surface shape characterization polynomial W* required to compensate the distorted wavefront of the laser system satisfy the following relationship:
当透射系统：满足W＝-W*；When the transmission system: satisfy W=-W*;
当反射系统：对于直射，满足W＝2W*，对于斜入射，满足W＝2W*·cosα，其中，α为入射角度。When the reflection system: for direct radiation, satisfy W=2W*, for oblique incidence, satisfy W=2W*·cosα, where α is the angle of incidence.
本发明中计算激光系统的畸变波前表征多项式W，具体计算过程如下：In the present invention, the distortion wavefront representation polynomial W of the laser system is calculated, and the specific calculation process is as follows:
步骤2.1)将畸变波前探测器测量得到的N个离散斜率数据(Sx,Sy)表示为并令波前探测器测得的光强最强点和最弱点的数据点斜率(Sx,Sy)置为零，以确保重构波面平滑无局部凸点；Step 2.1) Express the N discrete slope data (S x ,S y ) measured by the distorted wavefront detector as And set the data point slope (S x , S y ) of the strongest point and the weakest point of light intensity measured by the wavefront detector to zero, so as to ensure that the reconstructed wavefront is smooth and has no local convex points;
步骤2.2)对QTQ/N＝PTP进行乔利斯基分解，得到中间矩阵P，计算获得数值化正交多项式F的变换矩阵M，公式为M＝(PT)-1,其中，Q为正交基函数，数值化正交多项式F＝QMT Step 2.2) Carry out Cholesky decomposition to Q T Q/N=P T P, obtain the intermediate matrix P, calculate and obtain the transformation matrix M of the numericalized orthogonal polynomial F , the formula is M=(PT) -1 , wherein , Q is an orthogonal basis function, and the numerical orthogonal polynomial F=QM T
对进行乔利斯基分解，得到中间矩阵R，计算获得数值化正交梯度多项式的变换矩阵D，公式为D＝(RT)-1，其中，为数值化正交梯度多项式，公式为 right Carry out Cholesky decomposition to obtain the intermediate matrix R, and calculate and obtain the transformation matrix D of the numerical orthogonal gradient polynomial, the formula is D=(R T ) -1 , where, is the numerical orthogonal gradient polynomial, the formula is
步骤2.3)利用模式化法进行曲面构建，得到畸变波前表征多项式W，公式如下：Step 2.3) Use the modeling method to construct the curved surface to obtain the polynomial W representing the distortion wavefront, the formula is as follows:
式中，α为数值化正交梯度多项式的权重， In the formula, α is the numerical orthogonal gradient polynomial the weight of,
本发明与现有技术相比，显著优点在于：Compared with the prior art, the present invention has significant advantages in that:
(1)由于光学自由曲面是一种具有超高自由度的曲面，能够校正系统像差，简化结构，具有很好的热稳定性，适应大功率激光的光学系统，且大大降低成本的优点。(1) Since the optical free-form surface is a surface with an ultra-high degree of freedom, it can correct system aberrations, simplify the structure, have good thermal stability, adapt to the optical system of high-power lasers, and greatly reduce the cost.
(2)模式法具有一般性，与该孔径内有效测试数据点的数量和位置有关，与测试对象的孔径形状无关，从而可实现激光系统中不同形状的波前曲面重构。(2) The mode method is general, it is related to the number and position of effective test data points in the aperture, and has nothing to do with the aperture shape of the test object, so it can realize the wavefront surface reconstruction of different shapes in the laser system.
(3)数值化正交多项式对离散数据点具有正交性，使各项系数互不影响，拟合精度高。(3) The numerical orthogonal polynomial has orthogonality to the discrete data points, so that the coefficients do not affect each other and the fitting accuracy is high.
附图说明Description of drawings
图1为本发明用于激光系统的自由曲面波前补偿元件的设计方法流程图Fig. 1 is the flow chart of the design method for the freeform surface wavefront compensation element of the present invention for laser system
图2为根据波前相位共轭原理，对应的透射系统补偿原理图，Figure 2 is a schematic diagram of the corresponding transmission system compensation based on the principle of wavefront phase conjugation,
具体实施方式Detailed ways
下面结合附图对本发明作进一步详细描述，但不应限制本发明的保护范围The present invention will be described in further detail below in conjunction with accompanying drawing, but protection scope of the present invention should not be limited
用于激光系统的自由曲面波前补偿元件的设计方法，包括下列步骤：A design method for a free-form surface wavefront compensation element used in a laser system, comprising the following steps:
步骤1)通过畸变波前探测器探测激光系统输出的畸变波前，并将测量得到畸变波前的离散数据斜率(Sx,Sy)传输至计算机；Step 1) Detect the distorted wavefront output by the laser system through the distorted wavefront detector, and transmit the measured discrete data slope (S x , S y ) of the distorted wavefront to the computer;
步骤2)计算获得畸变波前表征多项式W；Step 2) Calculate and obtain the polynomial W representing the distortion wavefront;
步骤3)令补偿激光系统畸变波前所需的自由曲面波前补偿元件面形表征多项式W*满足如下关系：Step 3) Let the free-form surface wavefront compensation element surface shape characterization polynomial W* required to compensate the distorted wavefront of the laser system satisfy the following relationship:
如图2所示，当透射系统：满足W＝-W*；As shown in Figure 2, when the transmission system: satisfies W=-W*;
当反射系统：对于直射，满足W＝2W*，对于斜入射，满足W＝2W*·cosα，其中，α为入射角度。When the reflection system: for direct radiation, satisfy W=2W*, for oblique incidence, satisfy W=2W*·cosα, where α is the angle of incidence.
本发明中计算激光系统的畸变波前表征多项式W，具体计算过程如下：In the present invention, the distortion wavefront representation polynomial W of the laser system is calculated, and the specific calculation process is as follows:
步骤2.1)将畸变波前探测器测量得到的N个离散斜率数据(Sx,Sy)表示为并令波前探测器测得的光强最强点和最弱点的数据点斜率(Sx,Sy)置为零，以确保重构波面平滑无局部凸点；Step 2.1) Express the N discrete slope data (S x ,S y ) measured by the distorted wavefront detector as And set the data point slope (S x , S y ) of the strongest point and the weakest point of light intensity measured by the wavefront detector to zero, so as to ensure that the reconstructed wavefront is smooth and has no local convex points;
步骤2.2)对QTQ/N＝PTP进行乔利斯基分解，得到中间矩阵P，计算获得数值化正交多项式F的变换矩阵M，公式为M＝(PT)-1,其中，Q为正交基函数，数值化正交多项式F＝QMT Step 2.2) Carry out Cholesky decomposition to Q T Q/N=P T P, obtain the intermediate matrix P, calculate and obtain the transformation matrix M of the numericalized orthogonal polynomial F , the formula is M=(PT) -1 , wherein , Q is an orthogonal basis function, and the numerical orthogonal polynomial F=QM T
对进行乔利斯基分解，得到中间矩阵R，计算获得数值化正交梯度多项式的变换矩阵D，公式为D＝(RT)-1，其中，为数值化正交梯度多项式，公式为 right Carry out Cholesky decomposition to obtain the intermediate matrix R, and calculate and obtain the transformation matrix D of the numerical orthogonal gradient polynomial, the formula is D=(R T ) -1 , where, is the numerical orthogonal gradient polynomial, the formula is
步骤2.3)利用模式化法进行曲面构建，得到畸变波前表征多项式W，公式如下：Step 2.3) Use the modeling method to construct the curved surface to obtain the polynomial W representing the distortion wavefront, the formula is as follows:
式中，α为数值化正交梯度多项式的权重， In the formula, α is the numerical orthogonal gradient polynomial the weight of,
本发明实施例可以适用于各种高能激光器的畸变波前校正和补偿，其中，畸变波前主要来源为：由于系统热效应的影响，光学镜片产生变形等产生的离焦像差；光学系统中较大口径的光学元件，由于直立安装重力的影响，或者镜框夹持力量不均匀，或者非平面元件装调上存在偏心或倾斜，产生的像散像差；系统中球面元件或者平面元件受到加工误差、镀膜应力的影响等产生的球差。The embodiment of the present invention can be applied to the distortion wavefront correction and compensation of various high-energy lasers, wherein the main source of the distortion wavefront is: the defocus aberration caused by the deformation of the optical lens due to the influence of the thermal effect of the system; For large-diameter optical components, due to the influence of gravity when installed upright, or the clamping force of the frame is uneven, or there is eccentricity or inclination in the installation of non-planar components, astigmatic aberrations are generated; spherical components or planar components in the system are subject to processing errors , The impact of coating stress and other spherical aberrations.
所述的畸变波前探测器为哈特曼-夏特波前探测器。The distorted wavefront detector is a Hartmann-Schatterer wavefront detector.
选择合适扩束准直镜参数，使激光系统出射光的光斑尺寸与哈特曼-夏特波前探测器中微透镜阵列尺寸相符。The parameters of the beam expander and collimator are selected appropriately so that the spot size of the outgoing light from the laser system is consistent with the size of the microlens array in the Hartmann-Schatter wavefront detector.
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| CN112629677A (en) * | 2020-12-01 | 2021-04-09 | 浙江大学 | Rapid large-dynamic-range wavefront detection device and detection method based on mode recovery |
| CN112905952A (en) * | 2021-02-09 | 2021-06-04 | 南京信息工程大学 | Wavefront gradient data reconstruction method for optical element with any aperture |
| CN114035310A (en) * | 2021-11-23 | 2022-02-11 | 四川中科朗星光电科技有限公司 | A hyperboloid secondary mirror using free-form surface instead of RC optical system |
| CN117977356A (en) * | 2024-04-01 | 2024-05-03 | 杭州翎贤科技有限公司 | Apparatus and method for improving beam quality of large aperture laser |
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| CN112629677B (en) * | 2020-12-01 | 2022-04-19 | 浙江大学 | Fast and large dynamic range wavefront detection device and detection method based on pattern recovery |
| CN112905952A (en) * | 2021-02-09 | 2021-06-04 | 南京信息工程大学 | Wavefront gradient data reconstruction method for optical element with any aperture |
| CN114035310A (en) * | 2021-11-23 | 2022-02-11 | 四川中科朗星光电科技有限公司 | A hyperboloid secondary mirror using free-form surface instead of RC optical system |
| CN117977356A (en) * | 2024-04-01 | 2024-05-03 | 杭州翎贤科技有限公司 | Apparatus and method for improving beam quality of large aperture laser |
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