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Fractal dimension (D) is an effective parameter to represent the irregularityand fragmental property of a self-affine surface, which is common in physicalvapor deposited thin films. D could be evaluated through the scalingperformance of surface roughness by using atomic force microscopy (AFM)measurements, but lots of AFM images with different scales (L) are needed. Inthis study, a surface roughness prediction (SRP) method was proposed toevaluate D values of a single AFM image, in which the roughness at smaller Lwas estimated by image segmentation with flatten modification. Firstly, aseries of artificial fractal surfaces with ideal dimension (Di) values rangingfrom 2.1 to 2.9 were generated through Weierstrass-Mandelbrot (W-M) function,in order to compare SRP method with traditional methods such as box countingmethod and power spectral density method. The calculated dimension (Dc) by SRPmethod was much closer to Di than the other methods, with a mean relative errorof only 0.64%. Secondly, SRP method was utilized to deal with real surfaces,which were AFM images of amorphous alumina thin films with L of 1-70 {\mu}m. Dcobtained by SRP method based on a single AFM image was also close to the resultin our previous study by multi-image analysis at L above 10 {\mu}m, while thelarger Dc at smaller L was consisted with the actual surface feature. Thevalidity of SRP method and the physics nature of real surfaces were discussed,which might be helpful to obtain more understandings of fractal geometry.

Accurate evaluation of the fractal dimension based on a single morphological image