Evaluation of the orientation distribution of fibers from reflection images of fibrous samples

¹ Department of Physics, University of Jyväskylä, P.O. Box 35, 40014 Jyväskylä, Finland
² Nanoscience Center, University of Jyväskylä, P.O. Box 35, 40014 Jyväskylä, Finland
³ Department of Mathematics and Physics, Lappeenranta University of Technology, P.O. Box 20, 53851 Lappeenranta, Finland
⁴ Department of Automation Science and Engineering, Tampere University of Technology, P.O. Box 527, 33101 Tampere, Finland
⁵ Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014 Helsinki, Finland

^a e-mail: jouni.j.takalo@jyu.fi

Received: 9 October 2013
Revised: 26 November 2013
Accepted: 18 December 2013
Published online: 27 January 2014

Abstract

We consider illumination systems and mathematical algorithms for determination of the anisotropy and topographical features of an illuminated surface from its reflection images. As a particular example we study determination of the fiber orientation of paper surface. We also consider illumination systems with multiple light sources, and introduce optimization algorithms that exploit different spectral bands of these light sources. We show that a system of three light sources, e.g., a blue, green and red LED placed in a regular triangular form, efficiently prevents distortion of the above features. It is also easy to implement in applications, e.g., of the paper industry. We furthermore show that a pentagonal illumination system would be even better. However, in this case a five-colour photographic system and the corresponding light sources would be needed.