Estimation of curl in paper using a combination of shape measurement and least-squares modelling

Curl is a quality problem that makes paper less suitable for printing. A paper sheet that has structural variations in its thickness such as gradients of "bre orientation, density and "ller content, will curl and hence assume a cylindrical shape when its humidity content is changed. We propose a method to measure curl that can be used for automated analysis of the paper quality. The shape of the curled paper is measured using a stereoscopic camera system, which is capable of viewing a random pattern that is projected onto the specimen. The shape of the object is found by calculating the perspective di!erence in the camera set-up using digital image correlation. The quality parameters that are searched for are the magnitude of curl, which is de"ned as the inverse of the radius of curvature and the orientation of the curled paper. These parameters are estimated by performing a least-squares "t of a cylindrical shape to the three-dimensional measurement data. The least-squares model is non-linear and an iterative technique based on the Gauss}Newton algorithm is used. 2001 Elsevier Science Ltd. All rights reserved.