Formal Analysis of Geometrical Optics using Theorem Proving

Geometrical optics is a classical theory of Physics which describes the light propagation in the form of rays and beams. One of its main advantages is efficient and scalable formalism for the modeling and analysis of a variety of optical systems which are used in ubiquitous applications including telecommunication, medicine and biomedical devices. Traditionally, the modeling and analysis of optical systems have been carried out by paper-and-pencil based proofs and numerical algorithms. However, these techniques cannot provide perfectly accurate results due to the risk of human error and inherent incompleteness of numerical algorithms. In this thesis, we propose a higher-order logic theorem proving based framework to analyze optical systems. The main advantages of this framework are the expressiveness of higher-order logic and the soundness of theorem proving systems which provide unrivaled analysis accuracy. In particular, this thesis provides the higher-order logic formalization of geometrical optics including the notion of light rays, beams and optical systems. This allows us to develop a comprehensive analysis support for optical resonators, optical imaging and Quasi-optical systems. This thesis also facilitates the verification of some of the most interesting optical system properties like stability, chaotic map generation, beam transformation and mode analysis. We use this infrastructure to build a library of commonly used optical components such as lenses, mirrors and optical cavities. In order to demonstrate the effectiveness of our proposed approach, we conduct the formal analysis of some real-world optical systems, e.g., an ophthalmic device for eye, a Fabry-P\'{e}rot resonator, an optical phase-conjugated ring resonator and a receiver module of the APEX telescope. All the above mentioned work is carried out in the HOL Light theorem prover

Formal Analysis of Quantum Optics

At the beginning of the last century, the theory of quantum optics arose and led to a revolution in physics, since it allowed the interpretation of many unknown phenomena and the development of numerous powerful, cutting edge engineering applications, such as high precision laser technology. The analysis and verification of such applications and systems, however, are very complicated. Moreover, traditional analysis tools, e.g., simulation, numerical methods, computer algebra systems, and paper-and-pencil approaches are not well suited for quantum systems. In the last decade, a new emerging verification technique, called formal methods, became common among engineering domains, and has proven to be effective as an analysis tool. Formal methods consist in the development of mathematical models of the system subject for analysis, and deriving computer-aided mathematical proofs. In this thesis, we propose a framework for the analysis of quantum optics based on formal methods, in particular theorem proving. The framework aims at implementing necessary quantum mechanics and optics concepts and theorems that facilitate the modelling of quantum optical devices and circuits, and then reason about them formally. To this end, the framework consists of three major libraries: 1) Mathematical foundations, which mainly contain the theory of complex-valued-function linear spaces, 2) Quantum mechanics, which develops the general rules of quantum physics, and 3) Quantum Optics, which specializes these rules for light beams and implements all related concepts, e.g., light coherence which is typically emitted by laser sources. On top of these theoretical foundations, we build a library of formal models of a number of optical devices commonly used in quantum circuits, including, beam splitters, light displacers, and light phase shifters. Using the proposed framework, we have been able to formally verify common quantum optical computing circuits, namely the Flip gate, CNOT gate, and Mach-Zehnder interferometer

UV Imaging of the Galaxy Cluster CL0939+4713 (Abell 851) at z=0.41

The first UV F300W and F218W WFPC2 observations of the rich galaxy cluster CL0939+4713 at z=0.41 are presented and discussed. UV/optical two-color and c-m diagrams of the sources detected in the F300W waveband are constructed. Thanks to pre-existing HST optical images of the same field a morphological classification for the majority of these objects is also provided. Moreover, taking advantage of recent redshift surveys along CL0939+4713 line of sight, separate diagrams comparing the properties of galaxies belonging to the cluster and to its close projected field are presented. Possible evolutionary effects in the UV from z~0.4 to present time are investigated by comparing the restframe [mid-UV-Optical] colors of galaxies in CL0939+4713 with balloon-borne data of the Coma cluster, as well as by resorting to suitable galaxy evolution models. Finally, current attempts to constrain the epoch of the UV-upturn onset in evolved populations by means of HST UV observations are discussed.Comment: 20 pages, LaTeX, with 6 PostScript figures, Submitted to The Astrophysical Journal, Figures 1 and 2 have lower resolution than the ApJ submitted versio

Maunakea Spectroscopic Explorer Advancing from Conceptual Design

The Maunakea Spectroscopic Explorer (MSE) project has completed its Conceptual Design Phase. This paper is a status report of the MSE project regarding its technical and programmatic progress. The technical status includes its conceptual design and system performance, and highlights findings and recommendations from the System and various subsystems design reviews. The programmatic status includes the project organization and management plan for the Preliminary Design Phase. In addition, this paper provides the latest information related to the permitting process for Maunakea construction.Comment: 15 pages; Proceedings of SPIE Astronomical Telescopes + Instrumentation 2018; Ground-based and Airborne Telescopes VI

BeamOptics: a Symbolic Platform for Modeling and the Solution of Beam Optics System

BeamOptics [1] is a Mathematica-based computing platform devoted to the following objectives; · Structured representation and manipulation of particle beam optics systems with symbolic capabilities, · Analytical and numerical modeling of beam optics system behaviors, · Solution to specific beam optical or general accelerator system problems, in algebraic form in certain cases, through customized algorithms. Taking advantage of and conforming to the highly formal and self-contained structure of Mathematica, BeamOptics provides a unique platform for developing accelerator design and analysis programs. The feature of symbolic computation and the ability to manipulate the beam optics system at the programming language level enable the user to solve or optimize his system with considerably more efficiency, rigour and insight than can be easily achieved with passive modeling or numerical simulation methods. BeamOptics is developed with continuous evolution in mind. New features and algorithms from diverse sources can be incorporated without major modification, due to its formal and generic structure. In this report, a survey is given of the basic structure and methodology of BeamOptics, as well as a demonstration of some of its more specialized applications, and possible direction of evolution

A Search for Rapid Photometric Variability in Symbiotic Binaries

We report on our survey for rapid (time scale of minutes) photometric variability in symbiotic binaries. These binaries are becoming an increasingly important place to study accretion onto white dwarfs since they are candidate Type Ia supernovae progenitors. Unlike in most cataclysmic variables, the white dwarfs in symbiotics typically accrete from a wind, at rates greater than or equal to 10^{-9} solar masses per year. In order to elucidate the differences between symbiotics and other white dwarf accretors, as well as search for magnetism in symbiotic white dwarfs, we have studied 35 primarily northern symbiotic binaries via differential optical photometry. Our study is the most comprehensive to date of rapid variability in symbiotic binaries. We have found one magnetic accretor, Z And, previously reported by Sokoloski & Bildsten (1999). In four systems (EG And, BX Mon, CM Aql, and BF Cyg), some evidence for flickering at a low level (roughly 10 mmag) is seen for the first time. These detections are, however, marginal. For 25 systems, we place tight upper limits (order of mmag) on both aperiodic and periodic variability, highlighting a major difference between symbiotics and cataclysmic variables. The remaining five of the objects included in our sample (the 2 recurrent novae RS Oph and T CrB, plus CH Cyg, o Ceti, and MWC 560) had previous detections of large-amplitude optical flickering, and we present our extensive observations of these systems in a separate paper. We discuss the impact of our results on the ``standard'' picture of wind-fed accretion, and speculate on the possibility that in most symbiotics, light from quasi-steady nuclear burning on the surface of the white dwarf hides the fluctuating emission from accretion.Comment: 24 pages, 17 figures. Submitted to MNRAS (12/21/00), and revised in response to referee comments (3/30/01

Energy-transport systems for optical lattices: derivation, analysis, simulation

Energy-transport equations for the transport of fermions in optical lattices are formally derived from a Boltzmann transport equation with a periodic lattice potential in the diffusive limit. The limit model possesses a formal gradient-flow structure like in the case of the energy-transport equations for semiconductors. At the zeroth-order high temperature limit, the energy-transport equations reduce to the whole-space logarithmic diffusion equation which has some unphysical properties. Therefore, the first-order expansion is derived and analyzed. The existence of weak solutions to the time-discretized system for the particle and energy densities with periodic boundary conditions is proved. The difficulties are the nonstandard degeneracy and the quadratic gradient term. The main tool of the proof is a result on the strong convergence of the gradients of the approximate solutions. Numerical simulations in one space dimension show that the particle density converges to a constant steady state if the initial energy density is sufficiently large, otherwise the particle density converges to a nonconstant steady state