相关论文: An artifact in fits to conic-based surfaces

We get new results (and rederive some know ones) on smooth surfaces in $\mathbb{R}^n$ by unifying several view points into a coherent general view. Namely, we show and use new relations of the evolute (caustic) with the curvature ellipse,…

The displacement of star images by atmospheric refraction observed by an Earth-bound telescope is dominated by a familiar term proportional to the product of the tangent of the zenith angle by the refractivity at the ground. The manuscript…

Optical prisms are made of glass and map temporal frequencies into spatial frequencies by decomposing incident white light into its constituent colors and refract them into different directions. Conventional prisms suffer from their…

In low dimensions, conformal anomaly has profound influence on the critical behavior of random surfaces with extrinsic curvature rigidity $1/\a$. We illustrate this by making a small $D$ expansion of rigid random surfaces, where a…

Atom optics demonstrates optical phenomena with coherent matter waves, providing a foundational connection between light and matter. Significant advances in optics have followed the realisation of structured light fields hosting complex…

We propose and study quantitative measures of smoothness which are adapted to anisotropic features such as edges in images or shocks in PDE's. These quantities govern the rate of approximation by adaptive finite elements, when no constraint…

The behavior of an elastic curve bound to a surface will reflect the geometry of its environment. This may occur in an obvious way: the curve may deform freely along directions tangent to the surface, but not along the surface normal.…

This is a survey of metric properties of non-Euclidean conics, mainly based on works of Chasles and Story. A spherical conic is the intersection of the sphere with a quadratic cone; similarly, a hyperbolic conic is the intersection of the…

With tangent angle perturbation approach the axial symmetry deformation of a spherical vesicle in large under the pressure changes is studied by the elasticity theory of Helfrich spontaneous curvature model.Three main results in axial…

We investigate geometric invariants of cuspidal edges on focal surfaces of regular surface. In particular, we shall clarify the sign of the singular curvature at a cuspidal edge on a focal surface using singularities of parallel surface of…

Three different periodic optical metasurfaces exhibiting Fano resonances are studied in mid-IR frequency range in the presence of a substrate. We develop a rigorous semi-analytical technique and calculate how the presence of a substrate…

A new type of confocal microscope is described which makes use of intensity correlations between spatially correlated beams of light. It is shown that this apparatus leads to significantly improved transverse resolution.

Recent investigations (e.g. Han et al. 2001) have shown that fitting the Hipparcos observations with an orbital model when the astrometric wobble caused by the companion is below the noise level can have rather unexpected consequences. With…

Self-assembly of colloidal particles is poised to become a powerful composite material fabrication technique, but remains challenged by a limited control over the ensuing structures. We develop a new breed of nematic colloids that are…

The parameterization of open and closed anatomical surfaces is of fundamental importance in many biomedical applications. Spherical harmonics, a set of basis functions defined on the unit sphere, are widely used for anatomical shape…

We find that the function that describes the surface of spherical aberration free lenses can be used for both positive and negative refractive index media. With the inclusion of negative index, this function assumes the form of all the…

The optically induced oscillatory response of a spherical two-component, shell-core structured, nanoparticle by nodeless elastic vibrations of soft peripheral shell against hard and dynamically immobile inner core is considered. The…

Light interacts differently with left and right handed three dimensional chiral objects, like helices, and this leads to the phenomenon known as optical activity. Here, by applying a polarization tomography, we show experimentally, for the…

We consider signals of photon-photon scattering in laser-based, low energy experiments. In particular, we consider the ellipticity induced on a probe beam by a strong background field, and compare it with a recent worldline expression for…

This paper introduces a new analytical method for the determination of the coverage area modeling the Earth as an oblate ellipsoid of rotation. Starting from the knowledge of the satellite's position vector and the direction of the…