Related papers: Making geometrical optics exact
The geometric concept of geodesic completeness depends on the choice of the metric field or "metric frame". We develop a frame-invariant concept of "generalised geodesic completeness" or "time completeness". It is based on the notion of…
Transformation equations for physical quantities that characterize plane electromagnetic wave propagation in transparent optical media are presented. The Doppler effect, and measurements performed by an observer moving with the wave are…
The promise of perfect imaging in the optical domain, where light can be imaged without aberrations and with ultra-high resolution, could revolutionize technology and nanofabrication [1, 2, 3, 4, 5, 6]. Recently it has been shown…
In this paper, we present a new method for computing approximate geodesic distances. We introduce the wave method for approximating geodesic distances from a point on a manifold mesh. Our method involves the solution of two linear systems…
A general linear gauge-invariant equation for dispersive gravitational waves (GWs) propagating in matter is derived. This equation describes, on the same footing, both the usual tensor modes and the gravitational modes strongly coupled with…
In this paper we present and analyse a high accuracy method for computing wave directions defined in the geometrical optics ansatz of Helmholtz equation with variable wave number. Then we define an "adaptive" plane wave space with small…
Precise modelling of the (off-axis) point spread function (PSF) to identify geometrical and polarization aberrations is important for many optical systems. In order to characterise the PSF of the system in all Stokes parameters, an…
We investigate the identification of the time-dependent source term in the diffusion equation using boundary measurements. This facilitates tracing back the origins of environmental pollutants. Employing the concept of dynamic complex…
Gravitational waves propagate along null geodesics like light rays in the geometrical optics approximation, and they may have a chance to suffer from gravitational lensing by intervening objects, as is the case for electromagnetic waves.…
We discuss an approach to gravitational waves based on Geometric Algebra and Gauge Theory Gravity. After a brief introduction to Geometric Algebra (GA), we consider Gauge Theory Gravity, which uses symmetries expressed within the GA of flat…
The mechanism of wavefront reconstruction by a geometric-optical reflection of reconstructing light from surfaces with constant phase differences between the object and reference waves used to record the interference fringe structure in the…
Using exact solutions, we show that it is in principle possible to regard waves and particles as representations of the same underlying geometry, thereby resolving the problem of wave-particle duality.
In this paper, we describe a method designed to add precision to radiation simulations in the adaptive mesh refinement cosmological hydrodynamics code ENZO. We build upon the geometric correction factor described in \textit{ENZO+MORAY:…
Gravitational waves travel through the distributions of matter and dark energy during propagation. For this reason, gravitational waves emitted from binary compact objects serve as a useful tool especially to probe the nature of dark…
A two-dimensional water wave model based on conformal mapping is presented. The model is exact in the sense that it does not rely on truncated series expansions, nor suffer any numerical diffusion. Additionally, it is computationally highly…
End-to-end optimization, which simultaneously optimizes optics and algorithms, has emerged as a powerful data-driven method for computational imaging system design. This method achieves joint optimization through backpropagation by…
When propagating through periodically structured media, i. e. photonic crystals, optical waves will be modulated with the periodicity. As a result, the dispersion of waves will no longer behave as in a free space, and so called frequency…
The generation of accurate 3D molecular conformations is a pivotal challenge in computational chemistry and drug discovery. Recently, diffusion and flow matching models have achieved remarkable success. However, there is a critical…
In this paper, we propose a novel gradient-free and dimensionality-independent sampler, the Geometric Optics Approximation Sampling (GOAS), based on a near-field reflector system. The key idea involves constructing a reflecting surface that…
In this study, the authors employ the analogy between continuum mechanics and general relativity to investigate, from the perspective of elasticity and crystal plasticity, the deformations of space measured by LIGO/VIRGO interferometers…