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On the Formalization of Cardinal Points of Optical Systems

  • Umair SiddiqueEmail author
  • Sofiène Tahar
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 346)

Abstract

Optical systems are widely used in safety critical applications such as aerospace, telecommunication and biomedical systems. The verification of such systems is usually performed by informal techniques (e.g., numerical simulation and paper-and-pencil based proofs) which may result in erroneous designs. Interactive theorem proving has the potential to verify complex optical designs with better accuracy and soundness. However, existing formalizations of optics theories do not provide the facility to analyze optical imaging properties which are used to characterize the behavior of objects under observation (e.g., cancer cells, human eye or commercial camera lenses). In this paper, we present the formalization of cardinal points which are the most fundamental requirement to model imaging properties. We also present the formal verification of the cardinal points for an arbitrary optical system consisting of any number of optical components. In order to demonstrate the usefulness of our formalization, we present the formal analysis of an optical instrument used to compensate the ametropia of an eye.

Keywords

Theorem Proving HOL Light Optical Systems Cardinal Points 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringConcordia UniversityMontrealCanada

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