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Both of gloss and gloss unevenness are important quality for printing paper. In addition, it is assumed that these optical refl ection characteristics are caused by paper surface topography. Therefore, it is important to build the mathematical model of paper surface topography to evaluate gloss and gloss unevenness. However, it is diffi cult to measure paper surface topography. Furthermore, it is diffi cult to make the mathematical model because it is irregular. In this paper, we propose a new method of mathematical modeling of paper surface topography based on the Perlin noise. To estimate paper surface topography, we assume that surface topography is expressed as the Perlin noise. The Perlin noise is a computer graphics drawing technique in recent years. It can generate irregular phenomena of natural world such as clouds, fl ames and water surface. These images are generated with a sense of natural by adjusting parameters. It is assumed that these optical refl ection characteristics are caused by paper surface topography. The parameters which decide about the Perlin noise model is derived from the measured statistical optical refl ection properties of paper. The statistical property of the surface normal distribution, that is BRDF (Bidirectional Refl ectance Distribution Function), is acquired by the collimator optical system. The spatial frequency property of the unevenness is acquired by the telecentric optical system. We estimate the surface topography with this method and verify the validity of the proposed model. The optical refl ection characteristics of the surface topography generated by the proposed Perlin noise model were close to the actual optical refl ection characteristic of paper. It was confi rmed that it can explain the paper gloss phenomena well.

Mathematical Model of Paper Surface Topography by Perlin Noise Derived from Optical Reflection Characteristics