Search results for "Geometrical optics"

Ray optics for absorbing particles with application to ice crystals at near-infrared wavelengths

2018

Abstract Light scattering by particles large compared to the wavelength of incident light is traditionally solved using ray optics which considers absorption inside the particle approximately, along the ray paths. To study the effects rising from this simplification, we have updated the ray-optics code SIRIS to take into account the propagation of light as inhomogeneous plane waves inside an absorbing particle. We investigate the impact of this correction on traditional ray-optics computations in the example case of light scattering by ice crystals through the extended near-infrared (NIR) wavelength regime. In this spectral range, ice changes from nearly transparent to opaque, and therefore…

Fundamentals of 3D imaging and displays: a tutorial on integral imaging, light-field, and plenoptic systems

2018

There has been great interest in researching and implementing effective technologies for the capture, processing, and display of 3D images. This broad interest is evidenced by widespread international research and activities on 3D technologies. There is a large number of journal and conference papers on 3D systems, as well as research and development efforts in government, industry, and academia on this topic for broad applications including entertainment, manufacturing, security and defense, and biomedical applications. Among these technologies, integral imaging is a promising approach for its ability to work with polychromatic scenes and under incoherent or ambient light for scenarios fro…

Geometrical super resolved lensless imaging

2011

In the field of super resolution researchers are trying to overcome both the diffraction as well as the geometrical bounds of an imaging system. In this paper we present a recently developed approach that aims to overcome the geometrical bounds while using a unified spatial light modulator (SLM) based lensless configuration.

Fractional Fourier transforms, symmetrical lens systems, and their cardinal planes

2007

We study the relation between optical lens systems that perform a fractional Fourier transform (FRFT) with the geometrical cardinal planes. We demonstrate that lens systems symmetrical with respect to the central plane provide an exact FRFT link between the input and output planes. Moreover, we show that the fractional order of the transform has real values between 0 and 2 when light propagation is produced between principal planes and antiprincipal planes, respectively. Finally, we use this new point of view to design an optical lens system that provides FRFTs with variable fractional order in the range (0,2) without moving the input and output planes.

Effective Fresnel-number concept for evaluating the relative focal shift in focused beams

1998

We report on an analytical formulation, based on the concept of effective Fresnel number, to evaluate in a simple way the relative focal shift of rotationally nonsymmetric scalar fields that have geometrical focus and moderate Fresnel number. To illustrate our approach, certain previously known results and also some new focusing setups are analytically examined.

Fractional Fourier Transforms and Geometrical Optics

2010

Optical studies of laser-induced gray-tracking in KTP

1999

We have studied gray-tracking induced by a pulsed and polarized 532-nm laser beam in flux grown KTiOPO/sub 4/ (KTP) crystals. Transmission spectra measured under polarized light give different results: gray-tracking leads to an increase in the initial anisotropy of the linear optical properties of KTP, and the polar axis is the most sensitive to this process. The dynamics of relaxation of gray-tracking is anisotropic and depends on the wavelength under analysis. We show a possible induced modification of the crystal surface and also the existence of an intensity above which gray-tracking reaches the saturation point. We then measure the temperature above which gray-tracking no longer exists.

Inverse problems for elliptic equations with power type nonlinearities

2021

We introduce a method for solving Calder\'on type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not known. Assuming the knowledge of a nonlinear Dirichlet-to-Neumann map, we determine both a potential and a conformal manifold simultaneously in dimension $2$, and a potential on transversally anisotropic manifolds in dimensions $n \geq 3$. In the Euclidean case, we show that one can solve the Calder\'on problem for certain semilinear equations in a surprisingly simple way w…

The Calderon problem in transversally anisotropic geometries

2016

We consider the anisotropic Calderon problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier work \cite{DKSaU}, it was shown that a metric in a fixed conformal class is uniquely determined by boundary measurements under two conditions: (1) the metric is conformally transversally anisotropic (CTA), and (2) the transversal manifold is simple. In this paper we will consider geometries satisfying (1) but not (2). The first main result states that the boundary measurements uniquely determine a mixed Fourier transform / attenuated geodesic ray transform (or integral against a more general semiclassical…

Partial data inverse problems for the Hodge Laplacian

2017

We prove uniqueness results for a Calderon type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or absolute-to-relative boundary value maps uniquely determine a zeroth order potential. The method is based on Carleman estimates for the Hodge Laplacian with relative or absolute boundary conditions, and on the construction of complex geometric optics solutions which reduce the Calderon type problem to a tensor tomography problem for 2-tensors. The arguments in this paper allow to establish partial data results for elliptic systems that generalize the scalar resu…