On the Formal Analysis of Geometrical Optics in HOL

Siddique, Umair; Aravantinos, Vincent; Tahar, Sofiène

doi:10.1007/978-3-642-40672-0_11

Cited by 9 publications

(12 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1. Finally, we can recursively apply these predicates to define the behavior of a ray going through a series of optical components in an arbitrary optical system where more details can be found in [SAT13b].…”

Section: Definition 410 (Behavior Of a Ray At Given Interface)mentioning

confidence: 99%

“…The main scope of this project includes the higher-order logic (HOL) [Har09a] formalization of different theories of optics which provides the basis to conduct more accurate analysis than traditional paper-and-pencil based proofs [KL66,NKST98,Moo01], numerical simulation [reZ15, SXS + 11, LAS15] and computer algebra systems (CAS) [Opt15]. So far, the formalization of ray optics [SAT13b,SAT13a], electromagnetic optics [KAHT14] and quantum optics [MT14] has been implemented in the HOL light [Har09b] proof assistant. Recently, an extension of process calculus has been reported for the verification of linear optical quantum circuits [FAGP13].…”

Section: Introductionmentioning

confidence: 99%

“…We build upon our preliminary work about the formalization of ray optics [SAT13b]. In particular, we formalize the notion of optical systems and Gaussian beams in higher-order logic.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the formal analysis of Gaussian optical systems in HOL

Siddique

Tahar

2016

Form. Asp. Comput.

Self Cite

View full text Add to dashboard Cite

Optics technology is being increasingly used in mainstream industrial and research domains such as terrestrial telescopes, biomedical imaging and optical communication. One of the most widely used modeling approaches for such systems is Gaussian optics, which describes light as a beam. In this paper, we propose to use higher-order-logic theorem proving for the analysis of Gaussian optical systems. In particular, we present the formalization of Gaussian beams and verify the corresponding properties such as beam transformation, beam waist radius and location. Consequently, we build formal reasoning support for the analysis of quasi-optical systems. In order to demonstrate the effectiveness of our approach, we present a case study about the receiver module of a real-world Atacama Pathfinder Experiment (APEX) telescope.

show abstract

Section: Definition 410 (Behavior Of a Ray At Given Interface)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the formal analysis of Gaussian optical systems in HOL

Siddique

Tahar

2016

Form. Asp. Comput.

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, the authors considered the electromagnetic field equations of the planar waveguide as real functions, which make the formal definition of electromagnetic fields not general enough to address many applications. The next significant work on formal analysis of optics, done by Siddique et al, 9,10 focused on formal analysis of geometrical optics addressing the stability analysis of resonators. However, the accuracy of geometrical optics is limited to find basic properties of optical systems, such as approximate image and object positions and magnifications, when the wavelength is small compared to other geometrical features of the optical system.…”

Section: Introductionmentioning

confidence: 99%

“…The formal analysis of optical systems has gained some interest from the community recently (e.g., [8][9][10] ). For the first time, in 2009, Hasan et al 8 presented the idea of formalizing optics using theorem proving by formal analysis of a planar waveguide.…”

Section: Introductionmentioning

confidence: 99%

Formal analysis of electromagnetic optics

Khan-Afshar¹,

Hasan²,

Tahar³

2014

SPIE Proceedings

Self Cite

View full text Add to dashboard Cite

Optical systems are increasingly being used in safety-critical applications. Due to the complexity and sensitivity of optical systems, their verification raises many challenges for 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 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 their correctness by taking into account all the details of mathematical reasoning) as a complementary approach to improve optical system analysis. This paper provides a higher-order logic (a language used to express mathematical theories) formalization of electromagnetic optics in the HOL Light theorem prover. In order to demonstrate the practical effectiveness of our approach, we present the analysis of resonant cavity enhanced photonic devices.

show abstract

A Framework for Formal Reasoning about Geometrical Optics

Siddique

Tahar

2014

Lecture Notes in Computer Science

View full text Add to dashboard Cite

On the Formal Analysis of Geometrical Optics in HOL

Cited by 9 publications

References 17 publications

On the formal analysis of Gaussian optical systems in HOL

On the formal analysis of Gaussian optical systems in HOL

Formal analysis of electromagnetic optics

A Framework for Formal Reasoning about Geometrical Optics

Contact Info

Product

Resources

About