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On the Formal Analysis of Geometrical Optics in HOL

  • Conference paper
Automated Deduction in Geometry (ADG 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7993))

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Abstract

Geometrical optics, in which light is characterized as rays, provides an efficient and scalable formalism for the modeling and analysis of optical and laser systems. The main applications of geometrical optics are in stability analysis of optical resonators, laser mode locking and micro opto-electro-mechanical systems. Traditionally, the analysis of such applications has been carried out by informal techniques like paper-and-pencil proof methods, simulation and computer algebra systems. These traditional techniques cannot provide accurate results and thus cannot be recommended for safety-critical applications, such as corneal surgery, process industry and inertial confinement fusion. On the other hand, higher-order logic theorem proving does not exhibit the above limitations, thus we propose a higher-order logic formalization of geometrical optics. Our formalization is mainly based on existing theories of multivariate analysis in the HOL Light theorem prover. In order to demonstrate the practical effectiveness of our formalization, we present the modeling and stability analysis of some optical resonators in HOL Light.

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Concordia University, Montreal, Canada

    Umair Siddique, Vincent Aravantinos & Sofiène Tahar

Authors
  1. Umair Siddique
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  2. Vincent Aravantinos
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  3. Sofiène Tahar
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Editor information

Editors and Affiliations

  1. Department of Computer Science, 1006, Laboratory of Advanced Research, University of Tsukuba, 305-8573, Tsukuba, Japan

    Tetsuo Ida

  2. School of Informatics, Informatics Forum, University of Edinburgh, 10 Crichton Street, EH8 9AB, Edinburgh, UK

    Jacques Fleuriot

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Siddique, U., Aravantinos, V., Tahar, S. (2013). On the Formal Analysis of Geometrical Optics in HOL. In: Ida, T., Fleuriot, J. (eds) Automated Deduction in Geometry. ADG 2012. Lecture Notes in Computer Science(), vol 7993. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40672-0_11

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  • DOI: https://doi.org/10.1007/978-3-642-40672-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40671-3

  • Online ISBN: 978-3-642-40672-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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