# Matrix methods in geometric, wave, and statistical optics

## Tatiana Alieva, José A. Rodrigo, Óscar Martínez Matos, Martin J. Bastiaans, Alejandro Cámara, Ana Asenjo-García, and María Luisa Calvo

The objective of the educational project entitled "Matrix methods in geometric, wave, and statistical optics" is to treat in a matrix formalism different topics of optics, such as image formation systems, diffraction theory, spatial coherence, information processing, etc., which are included in the programs of undergraduate and Master courses at the Physical Faculty of Universidad Complutense de Madrid. Based on the knowledge obtained by the students from the courses on linear algebra, calculus, and classic mechanics, we explain the principal phenomena of paraxial geometric and wave optics, introducing the concept of phase space, which nowadays is widely used in coherence theory, quantum mechanics, signal processing, etc. Indeed, several books [see, for example, K. B. Wolf, Geometric Optics on Phase Space, Springer, NY (2004); W. P. Schleich, Quantum Optics in Phase Space, Wiley, London (2001); A. Torre, Linear Ray and Wave Optics in Phase Space, Elsevier, NY (2005); M. Testorf, B. Hennelly and J. Ojeda-Castaņeda, Phase-Space Optics, McGraw-Hill, NY (2009)], written on an advanced level, have been published recently and clearly demonstrate the advantages of a phase-space representation. In our project we tried to establish the basis for the understanding of the above-mentioned works.

The electronic book, which consists of 140 pages, 105 figures and 3 videos with corresponding interlinks, is written in Spanish and was published in the format of a CD by Editorial UCM (ISBN: 978-84-96703-25-4). It is multilevel (the degree of difficulty is marked by different colors) and multidisciplinary. Some parts of the book, which treat ray propagation, interference and diffraction in a matrix formalism, are accessible for undergraduate students; others, related to coherence state estimation, Wigner distribution, fractional Fourier transform, phase-space tomography, optical signal processing, etc., are oriented to Master students. The book also contains a list of problems and the description of two practical works: optical filtering and coherence control. The low prize of the book makes it affordable for students.

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To: Papers by Martin J. Bastiaans