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

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.