Related papers: On the broken ray transform
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
Transformation optics offers an unconventional approach to the control of electromagnetic fields. A transformation optical structure is designed by first applying a form-invariant coordinate transform to Maxwell's equations, in which part…
This revisit gives a survey on the analytical methods for the inverse exponential Radon transform which has been investigated in the past three decades from both mathematical interests and medical applications such as nuclear medicine…
X-ray reflectivity and grazing incidence diffraction (XGID) from liquid surfaces are described.
Frustrated total internal reflection is analyzed from an unusual point of view Unlike most similar works, incident angles are used here as the scanning variable, instead of the tunneled film thickness. The theoretical framework is presented…
We consider the problem of developing a method to reconstruct a potential $q$ from the partial data Dirichlet-to-Neumann map for the Schr\"odinger equation $(-\Delta_g+q)u=0$ on a fixed admissible manifold $(M,g)$. If the part of the…
The X-ray transform on a compact symmetric space M is here inverted by means of an explicit inversion formula. The proof uses the conjugacy of the minimal closed geodesics in M and of the maximally curved totally geodesic spheres in M,…
In recent years, many types of elliptical Radon transforms that integrate functions over various sets of ellipses/ellipsoids have been considered, relating to studies in bistatic synthetic aperture radar, ultrasound reflection tomography,…
X-ray mirrors with high focusing performances are in use in both mirror modules for X-ray telescopes and in synchrotron and FEL (Free Electron Laser) beamlines. A degradation of the focus sharpness arises in general from geometrical…
Many known Radon-type transforms of symmetric (radial or zonal) functions are represented by one-dimensional Riemann-Liouville fractional integrals or their modifications. The present article contains new examples of such transforms in the…
A topology optimization method is presented and applied to a blazed diffraction grating in reflection under conical incidence. This type of gratings is meant to disperse the incident light on one particular diffraction order and this…
We show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective. This solves a long standing inverse problem in the two-dimensional case.
For the reconstruction problem, the universal representation of inverse Radon transforms implies the needed complexity of the direct Radon transforms which leads to the additional contributions. In the standard theory of generalized…
We establish results for the injectivity and injectivity modulo gauge of certain inverse source problems in transport on a simply connected domain with variable index of refraction inducing a 'simple geometry'. The model given by radiative…
We consider the problem of imaging extended reflectors in terminating waveguides. We form the image by back-propagating the array response matrix projected on the waveguide's non-evanescent modes. The projection is adequately defined for…
The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective…
X-ray diffraction tomography (XDT) resolves spatially-variant XRD profiles within macroscopic objects, and provides improved material contrast compared to the conventional transmission-based computed tomography (CT). However, due to the…
This article gives an analysis of the behavior of polarizing grids and reflecting polarizers by solving Maxwell's equations, for arbitrary angles of incidence and grid rotation, for cases where the excitation is provided by an incident…
We present a parabolic approximation that incorporates reflection. With this approximation, there is no need to solve the parabolic equation for a coupled pair of solutions consisting of the incident and reflected waves. Rather, this…
We study the geodesic X-ray transform $I_\Gamma$ of tensor fields on a compact Riemannian manifold $M$ with non-necessarily convex boundary and with possible conjugate points. We assume that $I_\Gamma$ is known for geodesics belonging to an…