Search results for "GEOMETRICAL OPTICS"
showing 10 items of 27 documents
Spectral anomalies in focused waves of different Fresnel numbers
2004
Light propagation induces remarkable changes in the spectrum of focused diffracted beams. We show that spectral changes take place in the vicinity of phase singularities in the focal region of spatially coherent, polychromatic spherical waves of different Fresnel numbers. Instead of the Debye formulation, we use the Kirchhoff integral to evaluate the focal field accurately. We find that as a result of a decrease in the Fresnel number, some cylindrical spectral switches are geometrically transformed into conical spectral switches.
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…
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…
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…
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.
Retrieving leaf area index from multi-angular airborne data
2009
This work is aimed to demonstrate the feasibility of a methodology for retrieving bio-geophysical variables whilst at the same time fully accounting for additional information on directional anisotropy. A model-based approach has been developed to deconvolve the angular reflectance into single landcovers reflectances, attempting to solve the inconsistencies of 1D models and linear mixture approaches. The model combines the geometric optics of large scale canopy structure with principles of radiative transfer for volume scattering within individual crowns. The reliability of the model approach to retrieve LAI has been demonstrated using data from DAISEX- 99 campaign at Barrax, Spain. Airborn…
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…
On the scientific work of Victor Isakov
2022
Strictly convex corners scatter
2017
We prove the absence of non-scattering energies for potentials in the plane having a corner of angle smaller than $\pi$. This extends the earlier result of Bl{\aa}sten, P\"aiv\"arinta and Sylvester who considered rectangular corners. In three dimensions, we prove a similar result for any potential with a circular conic corner whose opening angle is outside a countable subset of $(0,\pi)$.