在X射线荧光光谱(EDXRF)测试中, 由于探测器分辨率的影响, 谱线会有不同程度的展宽, 多元素存在时谱线还会有一定的重叠。 获得纯净的谱线强度, 并保证准确测试结果的过程, 通常被称为EDXRF解谱。 传统的解谱方法包括感兴趣区加和、 纯元素谱线剥离以及干扰系数法等, 但这些方法在解决EDXRF解谱问题时都有不同程度的局限性。 最优化算法本质上是一种多自变量求极值的方法, 首先列出具有多个自变量参数并能够描述真实物理学过程的目标方程, 然后设定参数初值和边界条件, 通过数学(如共轭梯度法)的运算, 得到最优化的目标方程解。 将最优化计算的思想应用于EDXRF解谱过程中, 假设EDXRF谱图是一系列理想高斯峰的叠加, 可以列出其与原始谱图残差的目标方程, 根据物理学现象对这些高斯峰的高度、 位置和宽度三个参数分别进行估计, 此时目标方程的值通常较大, 通过设定所有参数各自的边界条件, 用共轭梯度法不断调整, 做最优化计算, 直至该值达到极小, 此时多峰叠加的结果与实测谱最为贴合, 解谱精度大大提高。 利用这种方法研究开发了能用于商业化EDXRF仪器的软件程序。 对最优化计算用于EDXRF解谱的方法进行了介绍, 并以Pr和Nd混合液的L系EDXRF谱图的解析举例, 这段谱线由11个谱峰组成, 通过设定33个高斯峰参数的初始值, 用共轭梯度法执行33个自变量的最优化计算, 运行于普通计算机, 经过580 ms的计算, 拟合谱与实测谱的残差从37.645减小为1.699 4, 二者在对比谱图上也极为吻合, 从而说明这是一种比较有效的谱线拟合方法。 通过对结果的分析还发现, 部分谱线的宽度发生了变化, 真实地反映了该条谱线是由多条相邻谱线构成的事实。 研究创新性在于, 将数学中的最优化计算原理应用于EDXRF谱图解析过程中, 获得了较好的效果, 并以较为复杂的Pr和Nd双稀土元素的L系谱线解析为例进行了说明。

With the restriction of detector resolution in EDXRF, the peaks will be widened, and the overlapping of several peaks cannot be neglected especially in multi elements sample. The process of achieving the intensity of pure peaks, named spectrum unfolding is difficult. There are three unfolding methods traditionally, ROI integration, pure element peeling, and the coefficient method. Both of the methods cannot unfold the complex EDXRF spectrum perfect. In this work, we introduce an optimized algorithm to EDXRF spectrum unfolding process. Pure peaks, processed by applying the smooth and debackground operation to raw spectrum, can be considered as the sum of several Gaussian peaks, which can be formulated by Gaussian functions with 3 parameters each, height, width and position. By alternating the values of the 3N parameters within certain boundary conditions, the error between theory function and raw spectrum can be smaller and smaller. In mathematics, this alternating process can be finished by Optimize algorithm. When we developed the algorithm by 3N parameters Conjugate Gradient Method and coding the program, an EDXRF spectrum of Pr/Nd solution was studied. Sum of 11 Gaussian peaks with 33 parameters was very well closed to the raw spectrum composed of 11 L-series peaks of Pr and Nd, and the error calculated changed from 37.645 to 1.699 4. The innovative of this paper is the application of optimized method in complex EDXRF spectrum unfolding process.