在激光聚变研究中, 存在大量具有陡峭不连续界面特性的靶丸等离子体诊断问题, 需要借助Abel反演方法对结果进行分析。 提出了一种基于基函数展开处理不连续径向分布的Abel反演方法, 采用带约束的Landweber迭代法求得优化结果。利用该算法可以对不连续阶跃分布进行比较准确的反演, 获得阶跃结构特征。在理想情况下, 针对不连续阶跃分布的反演方差好于10-4, 即使在存在一定噪声的情况下也仍然可以获得较好的结果。该方法可用于对激光聚变研究中压缩过程中球壳的背光照相、自发光成像、光谱测量等诊断结果的数据分析。

Diagnostics of fusion capsule plasma which usually has a discontinuous radial distribution is a basic problem in laser fusion plasma researches. An Abel inversion method based on basis set expansion was proposed to handle this discontinuous Abel inverse problem. This method expands the radial distribution on a set of basis functions, and then the measurement data can be approximated by a linear combination of Abel transforms of the basis functions. The weighted coefficients of the basis functions were obtained by projected Landweber iteration method. Numerical simulations demonstrate that the proposed method is sufficiently accurate to reconstruct discontinuous radial distribution, and variance of reconstructed result can reach 10-4 for ideal signal. Although some noise were added in measurement data, the inversion result can still reflect discontinuous property of radial distribution accurately.