A new approach for the verification of optical systems

Umair Siddique; Vincent Aravantinos; Sofiène Tahar

doi:10.1117/12.2024860

10 September 2013 A new approach for the verification of optical systems

Umair Siddique, Vincent Aravantinos, Sofiène Tahar

Proceedings Volume 8844, Optical System Alignment, Tolerancing, and Verification VII; 88440G (2013) https://doi.org/10.1117/12.2024860
Event: SPIE Optical Engineering + Applications, 2013, San Diego, California, United States

Abstract

Optical systems are increasingly used in microsystems, telecommunication, aerospace and laser industry. Due to the complexity and sensitivity of optical systems, their verification poses many challenges to engineers. Traditionally, the analysis of such systems has been carried out by paper-and-pencil based proofs and numerical computations. However, these techniques cannot provide perfectly accurate results due to the risk of human error and inherent approximations of numerical algorithms. In order to overcome these limitations, we propose to use theorem proving (i.e., a computer-based technique that allows to express mathematical expressions and reason about them by taking into account all the details of mathematical reasoning) as an alternative to computational and numerical approaches to improve optical system analysis in a comprehensive framework. In particular, this paper provides a higher-order logic (a language used to express mathematical theories) formalization of ray optics in the HOL Light theorem prover. Based on the multivariate analysis library of HOL Light, we formalize the notion of light ray and optical system (by defining medium interfaces, mirrors, lenses, etc.), i.e., we express these notions mathematically in the software. This allows us to derive general theorems about the behavior of light in such optical systems. In order to demonstrate the practical effectiveness, we present the stability analysis of a Fabry-Perot resonator.

Citation Download Citation

Umair Siddique, Vincent Aravantinos, and Sofiène Tahar "A new approach for the verification of optical systems", Proc. SPIE 8844, Optical System Alignment, Tolerancing, and Verification VII, 88440G (10 September 2013); https://doi.org/10.1117/12.2024860

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available