Related papers: Retrieving the Aerosol Complex Refractive Index us…
Research on photonics and metamaterials constantly challenges our intuitive understanding of the behaviour of light. In recent years we have seen negative refraction, focusing of light by a flat slab, a ``perfect'' prism, and an…
Many naturally-occuring models in the sciences are well-approximated by simplified models, using multiscale techniques. In such settings it is natural to ask about the relationship between inverse problems defined by the original problem…
The problem of reconstruction of an unknown refractive index $k(x)$ of an inhomogeneous solid $P$ is considered. The refractive index is assumed to be a piecewise-H\"{o}lder function The original boundary value problem for the Helmholtz…
We study the extinction efficiencies as well as scattering properties of particles of different porosity. Calculations are performed for porous pseudospheres with small size (Rayleigh) inclusions using the discrete dipole approximation.…
The high computational expense of simulating light through ray-tracing in large, sparsely instrumented particle detectors such as IceCube and Antares is a critical outstanding problem in particle physics. When the detector is sparsely…
We show that an arbitrary spatial distribution of complex refractive index inside an object can be exactly represented as a sum of two "monomorphous" complex distributions, i.e. the distributions with the ratios of the real part to the…
This report models the refractive index above a telescope site by an atmosphere with exponential decay of the refractive index (susceptibility) as a function of altitude. The air is represented as a spherical hull around the surface. We…
Motivated by non-destructive testing of optical fiber, we consider the problem of determining the index of refraction of a two-dimensional medium from magnitude of the total field resulting from known incident plane waves at a fixed…
We describe here how to apply the three dimensional imaging technique of refrecative index matched scanning to hydrogel spheres. Hydrogels are water based materials with a low refractive index, which allows for index matching with…
This paper investigates the formulation and implementation of Bayesian inverse problems to learn input parameters of partial differential equations (PDEs) defined on manifolds. Specifically, we study the inverse problem of determining the…
We performed high-resolution Fourier-transform infrared (FTIR) spectroscopy of a polymethyl methacrylate (PMMA) sphere of unknown size in the Mie scattering region. Apart from a slow, oscillatory structure (wiggles), which is due to an…
We propose a tomographic method to reconstruct the optical properties of a highly-scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes…
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…
The empirical law of Gladstone-Dale is insufficient for high-precision studies using the refractivity of a gas: this is not exactly proportional to its density, and the gas may not be properly described as perfect. An optical Mariotte…
With the advent of next generation high resolution telescopes, our understanding of how the magnetic field is organized in the internetwork (IN) photosphere is likely to advance.We aim to evaluate the extent to which we can retrieve…
This article investigates the unique determination of a radial refractive index n from spectral data. First, we demonstrate that for piecewise twice continuously differentiable functions, n is not uniquely determined by the special…
In this paper, we will try to explain the method of theoretical estimation of index of refraction of an assymetric organic Electro-Optic compound called MNA or 2,methyl,4,nitro-aniline. It is transparent in a wide range between 500nm-2000nm…
An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of…
A method is proposed which allows a complete determination of the complex reflection coefficient for any free unknown real potential (i.e., in the case where there is no effective absorption). In this method the unknown layer mounted on top…
This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…