Physica A 432 (2015) 1–8 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Tsallis threshold analysis of digital speckle patterns generated by rough surfaces H.C. Soares a , J.B. Meireles b , A.O. Castro Junior b , J.A.O. Huguenin b , A.G.M. Schmidt b , L. da Silva a,b,∗ a Programa de Pós-Graduação em Engenharia Metalúrgica, Escola de Engenharia Industrial Metalúrgica de Volta Redonda, Universidade Federal Fluminense, Volta Redonda, RJ, Brazil b Departamento de Física, Instituto de Ciências Exatas, Universidade Federal Fluminense, 27.213-145, Volta Redonda, RJ, Brazil highlights • We use entropic segmentation on digital speckle pattern images acquired in the diffraction plane. • We relate threshold values obtained with Tsallis entropic segmentation with the surface roughness of metallic samples. • We propose a new method for characterizing rough surfaces with Tsallis entropic segmentation. article info Article history: Received 29 September 2014 Received in revised form 19 February 2015 Available online 18 March 2015 Keywords: Tsallis entropy Entropic threshold Speckle pattern Roughness Image processing abstract In this work we report on a study of entropic threshold of digital speckle patterns images produced by rough surfaces using Tsallis entropy. The speckle pattern images were obtained in the diffraction plane at the normal direction and they are the outcome of the incidence of a laser beam in the rough metallic surfaces. The speckle pattern images were segmented in order to verify the sensitivity of the optimal Tsallis entropic threshold value as a function of the surface roughness. We show that the surface roughness can be sensed and tuned by this method. © 2015 Elsevier B.V. All rights reserved. 1. Introduction Tsallis entropy [1] has been widely used as a successful approach to a great variety of systems and questions [2]. It has been a nice way to deal with non-extensive systems, as for instance physical systems with long-range interactions and long- time memory, such as stellar polytropes [3], anomalous diffusion [4,5], turbulence [6], earthquakes [7], among others [2]. It has also been applied to various fields of science optimization [8] and image processing [9]. The Tsallis proposal was introduced as a generalization of the Boltzmann–Gibbs–Shannon entropy S =− W  i=1 p i ln p i , (1) ∗ Correspondence to: Rua Desembargador Ellis Hermydio Figueira 783, Aterrado, Volta Redonda, 27.213-145, RJ, Brazil. E-mail address: ladario@puvr.uff.br (L. da Silva). http://dx.doi.org/10.1016/j.physa.2015.02.100 0378-4371/© 2015 Elsevier B.V. All rights reserved.