焦斑分布对连续相位板面形特性影响分析

Influence of Focal Spot Distribution on Characteristics of Continuous Phase Plates

基于近场与远场的传输关系研究波前梯度分布与远场焦斑分布的关系,根据靶构型和光束入射角度的不同将焦斑分为圆形焦斑、椭圆焦斑和偏心焦斑,采用统计学的方法量化分析三类焦斑对应的面形及随机波前在不同特征参数下的分布规律。结果表明:近场面形梯度直方图与远场焦斑不同半径光强占比直方图分布趋势一致,焦斑半径和能量分布会改变面形梯度分布。能量均匀分布的圆形焦斑和椭圆焦斑的一维梯度呈正态分布,焦斑尺寸决定梯度分布范围;椭圆焦斑的二维梯度随椭圆离心率的增大而偏向梯度小值;偏心焦斑的二维梯度峰值偏向梯度大值,偏心分布会增加实际加工难度,但直方图分布受偏心率影响较小。该研究可用于元件加工误差和检测性能的预估及波前检测领域。

Objective Inertial confinement fusion(ICF)requires uniform incident light distribution,and the continuous phase plate(CPP)modulates the incident wavefront distribution by employing the phase fluctuation on the surface,which can realize the shaping and smoothing of focal spots and improve target light uniformity.However,the actual processing ability and detection accuracy of CPP are limited by the surface gradient,which is related to the shaping and smoothing requirements of the farfield focal spot.The researchers studied the relationship between the surface gradient and the farfield focal spot size by geometric optics,but it is necessary to control the size and energy distribution of the focal spot with the requirement improvement in laser focal spot uniformity and energy distribution in high energy density physical experiments.The different focal spot distributions further increase the complexity of the surface gradient distribution and reduce the processing and detection accuracy of the components.Therefore,it is necessary to study and analyze the influence of focal spot size and energy distribution on gradient distribution,and to obtain the surface shape distribution characteristics to predict the processing performance of CPP.Methods Based on the theory of the nearfield and farfield transmission relationship of the beams,we derive the relationship between surface gradient distribution and farfield focal spot energy distribution,and statistically analyze the relationship between the focal spot energy distribution and gradient distribution.Firstly,the focal spots are divided into three types according to the distribution of different target types and the relationship between the light field distribution of the back focal plane and the target plane,including circular focal spots,elliptical focal spots,and eccentric focal spots,with the GS(GaussSeidel)iterative algorithm adopted to design CPP.Secondly,the characteristic parameters of the focal spots,such as elliptic eccentricity and asymmetry,are proposed to characterize the characteristics of the focal spots,and the influence of the gradient characteristics is evaluated by the characteristic parameters.Then we analyze the distribution relationship between the energy distribution of the three types of focal spots and the corresponding surface gradients by histogram statistical and quantitative analysis.Finally,the relationship between random wavefront distribution and farfield energy distribution is employed to verify the universality of the relationship,and the distribution characteristics of surface periods and amplitude are analyzed.Results and Discussions The results show that the histogram of surface depth gradient distribution is consistent with that of light intensity proportion under different radii of focal spots,and the radius of focal spots determines the gradient distribution range.Meanwhile,the energy distribution of focal spots determines the proportion of gradient distribution,and the theoretical analysis is in accordance with the numerical simulation results.The onedimensional gradient of circular or elliptical focal spots with uniform energy distribution is normally distributed,the mean gradient is close to zero(Fig.3),and the gradient variance positively correlates with the focal spot radius(Fig.4).The gradient value corresponding to the peak CPP twodimensional gradient of the elliptical focal spot decreases with the increasing eccentricity(Fig.6),and the gradient corresponding to the peak gradient proportion of CPP with eccentric focal spots rises(Fig.7).Additionally,the relationship between the random wavefront gradient distribution and its farfield focal spot distribution(Fig.9)is verified,and the minimum spatial period of CPP positively correlates with the surface depth when the target focal spot is determined(Table 2).Conclusions The relationship between the surface gradient distribution and farfield focal spot energy distribution is obtained based on the light field transmission theory,and the histogram of the surface depth gradient distribution is consistent with that of the light intensity under different radii of the focal spot.Meanwhile,the radius of the focal spot determines the gradient distribution range,and the energy distribution of the focal spot determines the proportion of the gradient distribution,with the theoretical analysis consistent with the numerical simulation results.The mean gradient is close to zero and the gradient variance positively correlates with the focal spot radius when the energy is uniformly distributed.The smaller elliptical eccentricity of the focal spot leads to a greater proportion of the large gradient value.Eccentric focal spots also increase the proportion of large gradient values.Additionally,the random wavefront is adopted to verify the generality.In conclusion,the relationship between the surface gradient distribution and farfield focal spot energy distribution is determined,and the research results can help estimate the surface distribution and machining error of CPP,thus providing a new idea for wavefront detection.