Abstract: Regular fractal has ideal scale-invariance.But the probability distribution curve and the range of scale-invariance of random fractal (for example thin film growth) are related to the calculation method.The scale-invariance is not good and the multifractal spectrum is not smooth when the probability is calculated by variance from average height.The range of scale-invariance can be extend to 3 orders of magnitude and the multifractal spectrum is smooth when the probability is calculated by height based on the bottom of the film.An extending method is here used to correct the deviation of gray level setting-up so as to improve the multifractal spectrum.The effect of the range of the moment order q is discussed as well.

Key words: multifractal spectra, scale-invariant, the moment order