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Papermaking process consists in a succession of unit operations having for main objective the expression of water out of the wet paper pad. The three main stages are successively, the forming section, the press section and finally the drying section. Furthermore, another operation (calendering) may be used to improve the surface smoothness. Forming, pressing and drying are not on the scope of this paper, but the influence of formation and calendering on surface roughness is analyzed. The main objective is to characterize the materials and specially its superficial structure. The proposed model is described in order to analyze this topographical aspect. Some experimental results are presented in order to illustrate the interest of this method to better understand physical properties. This work is therefore dedicated to the description of the proposed model: the studied surface is measured at a microscopic scale using for example, a classical stylus profilometry method. Then the obtained surface is transformed using a conformal mapping that retains the surface orientations. Due to the anisotropy of the fiber distribution in the plane of the sheet, the resulting surface is often not isotropic. Hence, the micro facets that identify the interfaces between pores and solid (fibers in the studied case) at the micro level are transformed into a macroscopic equivalent structure. Furthermore, an ellipsoid may be fit to the experimental data in order to obtain a simple model. The ellipticities are proved to be linked for paper to both fiber orientation (through other optical methods) and roughness. These parameters (ellipticities) are shown to be very significant for different end-use properties. Indeed, they shown to be correlated to printing or optical properties, such as gloss for example. We present in a first part the method to obtain a macroscopic description from physical microscopic measurements. Then measurements carried on different paper samples, using a classical profilometry methods, illustrate the proposed methodology. Some comparisons with conventional roughness indexes are presented. Finally, some applications, and more precisely end use properties, are shown to underline the interest of the proposed method. These geometrical characteristics may be deduced from experimental results whatever the microscopic size is.
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