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Determination of index profiles by time domain reflectometry
No full textInternational audienceA numerical approach of the reconstruction of an inhomogeneous slab is described, the relative permittivity or the index of which are unknown. This one-dimensional dielectric medium is assumed to be linear, isotropic and non-magnetic, its conductivity being known, generally equal to zero. Its frequency independent permittivity arbitrarily varies, normally to its interfaces. A TEM plane wave of arbitrary causal time dependence illuminates this slab. A solution of this inverse problem is based upon a space-time discretization of a field integral formulation, in time-domain. A checked iterative process makes it possible to determine the index profile step by step. Some examples are given to illustrate the main features of this reconstruction method; simulation of experimental errors is considered with a special attention
Photoelectron Shot Noise
No full textInternational audienceThe instants of time emission of photoelectrons generated by a detector immersed in an optical field constitute a point compound Poisson process. A complete definition of such a process is introduced to calculate some average values of the distribution. The shot noise due to this point process is also considered and we study the difference .between the deterministic and the random shot noises. They are completely defined by the set of their characteristic functions. We consider also the asymptotic properties of the shot noise and we show that for large mean density of the point process the fluctuations are not described by a Gaussian, but by a Gaussian compound random function. Thus the central limit theorem is not strictly valid. An experimental setup to obtain these fluctuations is described and some statistical properties of the asymptotic shot noise are presented
Spherically Invariant and Compound Gaussian Stochastic Processes
No full textInternational audienceThis paper discusses the comparison between the class of spherically invariant processes and a particular class of Gaussian compound processes. We give a simple expression for the probability distribution and calculate some expectation values. The comparison shows that spherically invariant processes are slightly more general