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基于靶面温度分布测量反演激光强度时空分布的重构表达式中,被积函数包含的奇异阿贝尔核函数导致了求解积分表达式的病态和解的不稳定。为了解决这一积分求解问题,基于广义函数理论和正则变换方法,对积分函数进行了重新构造,获得了基于靶面温度时空分布测量反演入射激光强度分布的重构算法,并分析了重构结果对温度测量误差的敏感性。借助数值模拟方法对重构算法进行了验证,数值计算给出了重构强度误差与靶板厚度和辐照时间的关系。验证结果表明,两种背光面边界条件下反演获得的激光束时空分布,不仅与原始模型激光束达到了较好的一致,而且不受薄板条件的限制。算法对强激光辐照效应的靶面激光参量监测有实用性。
In the reconstruction expression of the spatiotemporal distribution of laser intensity, which is measured by the temperature distribution of the target surface, the singular Abelian kernel function included in the integrand function leads to the instability of solving the ill-posed solution of the integral expression. In order to solve this problem of integral solution, the integral function was reconstructed based on the generalized function theory and the regular transformation method, and a reconstruction algorithm based on the spatiotemporal distribution of the target surface temperature to obtain the incident laser intensity was obtained. Sensitivity of results to temperature measurement errors. The reconstruction algorithm was verified by means of numerical simulation. The relationship between reconstruction intensity error and target plate thickness and irradiation time was given by numerical calculation. The verification results show that the space-time distribution of the laser beam obtained by the two backlight boundary conditions is not only consistent with the laser beam of the original model, but also not limited by the sheet condition. The algorithm has the practicability to monitor the laser surface parameters of the laser irradiated by strong laser.