半连续Ag纳米薄膜显微图像的多重分形谱研究

Study on Multifractal Spectrum of Microscope Image of Semi-Continuous Ag Nanoparticle Films

多重分形谱是分形理论中最基本的一个数学概念,也是分形理论应用中最重要的一个方面。在解决实际问题中多重分形谱主要用来描述物理量不均匀的随机概率分布,通过对半连续Ag纳米薄膜显微图像结构形貌的分析和处理,以及通过薄膜显微图像多灰度概率测度进行多重分形谱分析,用多重分形谱描述随薄膜厚度变化的Ag颗粒的空间分布的不均匀性。实验结果表明,多重分形谱是一种有意义的表征参数,能够从多分形角度对薄膜中Ag厚度的空间分布均匀性和尺寸分布进行定量化的分析和解释。

The multifractal spectrum is a basic mathematical conception in the fractal theory and it is one of the most important factors in the applications of the fractal theory. In engineering problems, the multifractal spectrum is mainly to describe the random probability distribution of physical phenomenon. In this paper the multifractal spectrum is calculated by multigray probability measures of the microscope image of semicontinuous Ag nanoparticle films. It is found that multifractal spectrum can characterize space distribution of Ag particles influence on nanoparticle film uniformity in different thickness films quantitatively. Experimental results show that the multifractal spectrum is an important characteristic parameter, which enables the quantitative analysis and explanation of the homogeneous space distribution and size distribution of Ag particles thickness of films from the multifractal issue.