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We give a brief introduction to Hamiltonian optics and Lie algebraic methods. We use these methods to describe the operators governing light propagation, refraction and reflection in phase space. The method offers a systematic way to find…
The recent history of optical design saw a progressive trend of also designing without rotational symmetry, especially spectrometers due to the use of reflective and diffractive elements in their designs. A freeform hyperspectral imager…
Lie-integration is one of the most efficient algorithms for numerical integration of ordinary differential equations if high precision is needed for longer terms. The method is based on the computation of the Taylor-coefficients of the…
Lie group methods are used for the study of various issues related to symmetries and exact solutions of the barotropic vorticity equation. The Lie symmetries of the barotropic vorticity equations on the $f$- and $\beta$-planes, as well as…
Imaging systems are inherently prone to aberrations. We present an optimization method to design two-dimensional freeform reflectors that minimize aberrations for various parallel ray beams incident on the optical system. We iteratively…
We study a nonlinear system of partial differential equations which describe rotating shallow water with an arbitrary constant polytropic index $\gamma $ for the fluid. In our analysis we apply the theory of symmetries for differential…
In this paper, we give algorithms for determining the existence of isomorphism between two finite-dimensional Lie algebras and compute such an isomorphism in the affirrmative case. We also provide algorithms for determining algebraic…
This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with unbroken rays and for…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the diffraction problem of a plane wave on…
In this paper, a method for solving the initial structure of an off-axis multi-mirror system applied to extreme ultraviolet (EUV) lithography using a paraxial ray-tracing algorithm based on Seidel aberration theory is proposed. By tracing…
This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with ubroken rays and for…
Context. High accuracy astrometric instruments like Gaia aiming at an accuracy of 1 microarcsecond cannot be considered as point-like observers in the framework of relativistic modelling of observable quantities. Aims. Special-relativistic…
The non-linear transformations incurred by the rays in an optical system can be suitably described by matrices to any desired order of approximation. In systems composed of uniform refractive index elements, each individual ray refraction…
It is well-known that a Severi-Brauer surface has a rational point if and only if it is isomorphic to the projective plane. Given a Severi-Brauer surface, we study the problem to decide whether such an isomorphism to the projective plane,…
Do object part localization methods produce bilaterally symmetric results on mirror images? Surprisingly not, even though state of the art methods augment the training set with mirrored images. In this paper we take a closer look into this…
A general algorithm for calculating the reflection and refraction of nonuniform plane waves from an arbitrarily oriented and charged planar interface between two lossy isotropic media is proposed based on the decomposition of the complex…
The influence of the relativistic motion of the reference frame on the light reflection law is investigated. The method is based on applying the relativistic aberration affect for three light signals: incident, normal and reflected rays.…
This paper addresses the problem of mirror surface reconstruction, and proposes a solution based on observing the reflections of a moving reference plane on the mirror surface. Unlike previous approaches which require tedious calibration,…
If one has to attain high accuracy over long timescales during the numerical computation of the N-body problem, the method called Lie-integration is one of the most effective algorithms. In this paper we present a set of recurrence…
The increasing use of freeform optical surfaces raises the demand for optical design tools developed for generalized systems. In the design process surface-by-surface aberration contributions are of special interest. The expansion of the…