Search results for "GEOMETRICAL OPTICS"
showing 10 items of 27 documents
Determining an unbounded potential from Cauchy data in admissible geometries
2011
In [4 Dos Santos Ferreira , D. , Kenig , C.E. , Salo , M. , Uhlmann , G. ( 2009 ). Limiting Carleman weights and anisotropic inverse problems . Invent. Math. 178 : 119 – 171 . [Crossref], [Web of Science ®], [Google Scholar] ] anisotropic inverse problems were considered in certain admissible geometries, that is, on compact Riemannian manifolds with boundary which are conformally embedded in a product of the Euclidean line and a simple manifold. In particular, it was proved that a bounded smooth potential in a Schrödinger equation was uniquely determined by the Dirichlet-to-Neumann map in dimensions n ≥ 3. In this article we extend this result to the case of unbounded potentials, namely tho…
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…
Single cigar-shaped nanopores functionalized with amphoteric amino acid chains: experimental and theoretical characterization.
2012
We present an experimental and theoretical characterization of single cigar-shaped nanopores with pH-responsive carboxylic acid and lysine chains functionalized on the pore surface. The nanopore characterization includes (i) optical images of the nanostructure obtained by FESEM; (ii) different chemical procedures for the nanopore preparation (etching time and functionalizations; pH and electrolyte concentration of the external solution) allowing externally tunable nanopore responses monitored by the current-voltage (I-V) curves; and (iii) transport simulations obtained with a multilayer nanopore model. We show that a single, approximately symmetric nanopore can be operated as a reconfigurab…
Meeting the Discipline-Culture Framework of Physics Knowledge: A Teaching Experience in Italian Secondary School
2014
The paper deals with physics teaching/learning in high school. An investigation in three upper secondary school classes in Italy explored the reactions of students to a structuring lecture on optics within the discipline-culture (DC) framework that organises physics knowledge around four interrelated fundamental theories of light. The lecture presented optics as an unfolding conceptual discourse of physicists regarding the nature of light. Along with the knowledge constructed in a school course of a scientific lyceum, the students provided epistemological comments, displaying their perception of physics knowledge presented in the classroom. Students’ views and knowledge were investigated by…
A perfect Fresnel acoustic reflector implemented by a Fano-resonant metascreen
2018
We propose a perfectly reflecting acoustic metasurface which is designed by replacing the curved segments of the traditional Fresnel reflector by flat Fano-resonant sub-wavelength unit cells. To preserve the original Fresnel focusing mechanism, the unit cell phase follows a specific phase profile which is obtained by applying the generalized Snell's law and Fermat's principle. The reflected curved phase fronts are thus created at the air-metasurface boundary by tailoring the metasurface dispersion as dictated by Huygens' principle. Since the unit cells are implemented by sub-wavelength double slit-shaped cavity resonators, the impinging sound waves are perfectly reflected producing acoustic…
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.
White-light Fourier transformer with low chromatic aberration.
1992
A simple Fourier transformation system working with broadband parallel illumination is presented. The proposed setup, consisting of two on-axis zone plates and an achromatic objective, allows us to obtain the achromatic Fourier transform representation of the input at a finite distance with a low chromatic aberration. The discussion of the system, using the Fresnel diffraction theory, leads to an analytical expression to evaluate the transversal and longitudinal chromatic aberrations. It is shown that the resulting chromatic aberrations for typical values of the involved parameters are less than 1% over the entire visible spectrum.
Focal squeeze in axicons
2005
The on-axis irradiance distribution of a truncated conical wavefront is evaluated in terms of the Fresnel number of the focusing geometry. In agreement with geometrical optics, a focal line of increasing intensity is generated for extremely high Fresnel numbers. Otherwise clear deviations may be observed for the position of the maximum irradiance along the optical axis. A remarkable focal squeeze appears and, for decreasing Fresnel numbers, this effect manifests stronger. An analytical formula is provided for the fast evaluation of the focal squeeze.
Focal-shift formula in apodized nontelecentric focusing systems
2007
A single analytical formulation for evaluating the focal shift in any apodized nontelecentric focusing setup is reported. The formulation is also useful in the case of imaged paraxial beams. We show explicitly that the magnitude of the focal shift is determined by only one parameter that depends on the effective width of the pupil filter and its axial position. To illustrate our approach we examine different focusing setups.
Exploring Gravitational Lensing
2019
In this article, we discuss the idea of gravitational lensing, from a systematic, historical and didactic point of view. We show how the basic lensing equation together with the concepts of geometrical optics opens a space of implications that can be explored along different dimensions. We argue that Einstein explored the idea along different pathways in this space of implication, and that these explorations are documented by different calculational manuscripts. The conceptualization of the idea of gravitational lensing as a space of exploration also shows the feasibility of discussing the idea in the classroom using some of Einstein's manuscripts.