Related papers: A General Method for the Determination of Matrix C…
It has recently been shown that periodic layered media can reflect strongly for all incident angles and polarizations in a given frequency range. The standard treatment gets these band gaps from an eigenvalue equation for the Bloch factor…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
We present a generalized 4 $\times$ 4 matrix formalism for the description of light propagation in birefringent stratified media. In contrast to previous work, our algorithm is capable of treating arbitrarily anisotropic or isotropic,…
The rich information content of measurements in the molecular frame rather than the laboratory frame has motivated the development of several methods for aligning gas phase molecules in space. Even so, for asymmetric tops the problem of…
Recently, significant progress has been made in the study of methods for 3D reconstruction from multiple images using implicit neural representations, exemplified by the neural radiance field (NeRF) method. Such methods, which are based on…
We present a new mathematical framework for incorporating partial coherence effects into wave optics simulations through a comprehensive surface-to-detector approach. Unlike traditional ensemble averaging methods, our dual-component…
The efficient design of continuous freeform surfaces, which transform a given source into an arbitrary target intensity, remains a challenging problem. A popular approach are ray-mapping methods, where first a ray mapping between the…
Consider the task of matrix estimation in which a dataset $X \in \mathbb{R}^{n\times m}$ is observed with sparsity $p$, and we would like to estimate $\mathbb{E}[X]$, where $\mathbb{E}[X_{ui}] = f(\alpha_u, \beta_i)$ for some Holder smooth…
The Jacobi system with matrix-valued coefficients and with the spectral parameter depending on a matrix-valued weight factor is considered on the full-line lattice. The scattering from the full-line lattice is expressed in terms of the…
We present a ray-tracing technique for radiative transfer modeling of complex three-dimensional (3D) structures which include dense regions of high optical depth like in dense molecular clouds, circumstellar disks, envelopes of evolved…
We prove that the focal set generated by the reflection of a point source off a translation invariant surface consists of two sets: a curve and a surface. The focal curve lies in the plane orthogonal to the symmetry direction containing the…
A theorem of Mandel allows to determine the covector set of an oriented matroid from its set of topes by using the composition condition. We provide a generalization of that result, stating that the covector set of a conditional oriented…
We propose a new algorithm to compute the X-ray transform of an image represented by unit (pixel/voxel) basis functions. The fundamental issue is equivalently calculating the intersection lengths of the ray with associated units. For any…
The purpose of this report is a study of the algebraic approach possibilities to reconstruct images. This approach is reduced to solution of the large system of linear algebraic equations. We also point out some possible further…
The optical aberrations of a system can be described in terms of the wave aberrations, defined as the departure from the ideal spherical wavefront; or the ray aberrations, which are in turn the deviations from the paraxial ray intersection…
Unitary transformations are routinely modeled and implemented in the field of quantum optics. In contrast, nonunitary transformations that can involve loss and gain require a different approach. In this theory work, we present a universal…
This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided…
The displacement field in highly non uniformly strained crystals is obtained by addition of constraints to an iterative phase retrieval algorithm. These constraints include direct space density uniformity and also constraints to the sign…
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 consider the inverse problem of reconstructing the scattering coefficient of a simple radiative transport equation (RTE) used to model light propagation inside a scattering medium. To do so, we extract information from the second term in…