Chapter 2 Advanced Mueller Ellipsometry Instrumentation and Data Analysis Enric Garcia-Caurel, Razvigor Ossikovski, Martin Foldyna, Angelo Pierangelo, Bernard Drévillon and Antonello De Martino Abstract The main object of this chapter is to give an overview the possibilities offered by instruments capable of measuring full Mueller matrices in the field of optical characterization. We have chosen to call these instruments Mueller ellip- someters in order to highlight their close relation with instruments traditionally used in ellipsometry. We want to make clear to the reader the place that Mueller ellipsom- etry takes with respect to standard ellipsometry by showing the similarities but also the differences among these techniques, both in instrumentation and data treatment. To do so the chapter starts by a review of the optical formalisms used in standard and Mueller ellipsometry respectively. In order to highlight the particularities and the advantages brought by Mueller ellipsometry, a special section is devoted to the algebraic properties of Mueller matrices and to the description of different ways to decompose them. Matrix decompositions are used to unveil the basic polarimetric properties of a the sample when a precise model is not available. Then follows a description of the most common optical configurations used to build standard ellip- someters. Special attention is paid to show what can and what cannot be measured with them. On the basis of this knowledge it is shown the interest of measuring whole E. Garcia-Caurel (B ) · R. Ossikovski · M. Foldyna · A. Pierangelo · B. Drévillon · A. De Martino LPICM, CNRS-Ecole Polytechnique, Palaiseau, France e-mail: enric.garcia-caurel@polytechnique.edu R. Ossikovski e-mail: razvigor.ossikovski@polytechnique.edu M. Foldyna e-mail: martin.foldyna@polytechnique.edu A. Pierangelo e-mail: angelo.pierangelo@polytechnique.edu B. Drévillon e-mail: bernard.drevillon@polytechnique.edu A. De Martino e-mail: antonello.demartino@polytechnique.edu M. Losurdo and K. Hingerl (eds.), Ellipsometry at the Nanoscale, 31 DOI: 10.1007/978-3-642-33956-1_2, © Springer-Verlag Berlin Heidelberg 2013