Related papers: Analysis of ellipsometric data obtained from curve…
This paper gives a detailed derivation of the surface of a tri-axial ellipsoid. The general result is in terms of the elliptic integrals of the first and second kind. It is in checked for all special cases included and the corresponding…
We present a geometric framework to model the optical effects of deformations of planar holographic optical elements (HOE) into curved surfaces, such as sphere segments. In particular, we consider deformations which do not preserve the…
With systems for acquiring 3D surface data being evermore commonplace, it has become important to reliably extract specific shapes from the acquired data. In the presence of noise and occlusions, this can be done through the use of…
We introduce a new method for studying stochastic homogenization of elliptic equations in nondivergence form. The main application is an algebraic error estimate, asserting that deviations from the homogenized limit are at most proportional…
We study negative curves on surfaces obtained by blowing up special configurations of points in the complex projective palne. Our main results concern the following configurations: very general points on a cubic, 3-torsion points on an…
In spectroscopic ellipsometry, the optical properties of materials are obtained indirectly by generally assuming dielectric function and optical models. This ellipsometry analysis, which typically requires numerous model parameters, has…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
We learn parameterized nonlinear elasticity on curved surfaces using a physics-informed neural network that enforces governing equations and boundary conditions directly through the loss function, enabling a single trained model to…
We survey some aspects of the theory of elliptic surfaces and give some results aimed at determining the Picard number of such a surface. For the surfaces considered, this will be equivalent to determining the Mordell-Weil rank of an…
We propose a multiscale approach for a nonlinear Helmholtz problem with possible oscillations in the Kerr coefficient, the refractive index, and the diffusion coefficient. The method does not rely on structural assumptions on the…
We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection…
The multi-beam measurement system plays a crucial role in ocean mapping and underwater terrain detection. By simultaneously transmitting multiple beams, the system can accurately receive sound waves reflected from the seabed, providing more…
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…
Atomic-scale mapping of the chemical elements in materials is now possible using aberration-corrected electron microscopes but delocalization and multiple scattering can confound image interpretation. Here we report atomic-resolution…
In this work we consider the inverse problem of reconstructing the optical properties of a layered medium from an elastography measurement where optical coherence tomography is used as the imaging method. We hereby model the sample as a…
Galaxy lenses are frequently modeled as an elliptical mass distribution with external shear and isothermal spheres to account for secondary and line-of-sight galaxies. There is statistical evidence that some fraction of observed quads are…
This paper presents a method for mathematical modelling of surfaces conditioned on empirical data. It is based on solving a discrete biharmonic equation over a domain with given inner point and inner curve data. The inner curve data is used…
Characterising the noise of an airborne electromagnetic (AEM) system is critical in correctly imaging the earth's subsurface conductivity. Deterministic and probabilistic geophysical inversion algorithms require foreknowledge of the system…
Ellipsometry techniques allow to measure polarization information of materials, requiring precise rotations of optical components with different configurations of lights and sensors. This results in cumbersome capture devices, carefully…
In this paper, we consider the problem of estimating the covariance kernel and its eigenvalues and eigenfunctions from sparse, irregularly observed, noise corrupted and (possibly) correlated functional data. We present a method based on…