Search results for "Geometrical optics"
showing 7 items of 27 documents
WIGNER TRANSFORM METHODS IN INCLUSIVE ELECTRON SCATTERING FROM NUCLEI
1984
A multiple scattering series for deep inelastic leptoninduced reactions is derived by using semiclassical Wigner transform methods. In contrast to the usual Glauber theory there is no limitation for the energy loss since a time-dependent formulation is used throughout. A simple parametrization of the generalized profile function yields a closed analytical expression for the longitudinal and transverse response function of p-shell nuclei. Comparison is made with the Saclay data for -'• C. I Introduction It is common knowledge that geometrical optics is valid if the wavelength of the scattering wave is small compared to the dimensions of the scatterer. Under these conditions the phase-space d…
Three-dimensional field distribution in the focal region of low-Fresnel-number axicons.
2006
Three-dimensional intensity and phase distributions generated by microaxicons are evaluated in the low-Fresnel-number regime. Apertured and nonapertured conical wavefronts may generate transverse patterns with notable deviations from the expected nondiffracting Bessel beam. First-order analytical expressions are proposed for the evaluation of the wave field produced by axicons of different Fresnel number in the focal region.
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 $(0,\pi)$.
The stenopaeic slit: an analytical expression to quantify its optical effects in front of an astigmatic eye.
2001
The stenopaeic slit is a trial case accessory used in subjective refraction, especially when high astigmatism is present. In spite of its simplicity, the effect of the slit when it is not oriented along one of the principal meridians of the examined eye is difficult to predict, even in terms of classical geometrical optics. In this paper, the optical principles of the slit are considered with full details in the theoretical framework of the dioptric power space. An analytical expression to obtain the residual refractive error when a stenopaeic slit is placed in front of an astigmatic eye at any orientation is deduced. In the light of these results, some aspects of the clinical procedure are…
Off-axis focal shift for rotationally nonsymmetric screens
2009
We report on an analytical formulation for evaluating the amplitude distribution along any line directed toward the geometrical focus of a spherical wave front that passes through a rotationally nonsymmetric diffracting screen. Our formula consists of two factors. The first factor involves the one-dimensional Fourier transform of the projection of the screen function onto the off-axis line. The second factor depends on the inverse distance to the screen and permits us to recognize the existence of focal shift along off-axis lines.
On some partial data Calderón type problems with mixed boundary conditions
2021
In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal Calderón type problems. We prove two main results on these type of problems: On the one hand, we derive simultaneous bulk and boundary Runge approximation results. Building on these, we deduce uniqueness for localized bulk and boundary potentials. On the other hand, we construct a family of CGO solutions associated with the corresponding equations. These allow us to deduce uniqueness results for arbitrary bounded, not necessarily localized bulk and boundary potentials. T…