Formal Analysis of Optical Systems

Abstract

Optical systems are becoming increasingly important by resolving many bottlenecks in today’s communication, electronics, and biomedical systems. However, given the continuous nature of optics, the inability to efficiently analyze optical system models using traditional paper-and-pencil and computer simulation approaches sets limits especially in safety-critical applications. In order to overcome these limitations, we propose to employ higher-order-logic theorem proving as a complement to computational and numerical approaches to improve optical model analysis in a comprehensive framework. The proposed framework allows formal analysis of optical systems at four abstraction levels, i.e., ray, wave, electromagnetic, and quantum.

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Correspondence to Sanaz Khan-Afshar.

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Khan-Afshar, S., Siddique, U., Mahmoud, M.Y. et al. Formal Analysis of Optical Systems. Math.Comput.Sci. 8, 39–70 (2014). https://doi.org/10.1007/s11786-014-0175-z

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Keywords

  • Theorem proving
  • Computer algebra systems
  • Optical systems
  • Ray optics
  • Electromagnetic optics
  • Quantum optics

Mathematics Subject Classification (2010)

  • Primary 68T15
  • Secondary 78A05
  • 78A25
  • 81V80