Superresolution: an ill-posed problem in Fourier optics

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On the problems of object restoration and image extrapolation in optics

In this paper we consider the problems of object restoration and image extrapolation, according to the regularization theory of improperly posed problems. In order to take into account the stochastic nature of the noise and to introduce the main concepts of information theory, great attention is devoted to the probabilistic methods of regularization. The kind of the restored continuity is investigated in detail; in particular we prove that, while the image extrapolation presents a Hölder type stability, the object restoration has only a logarithmic continuity. © 1979 American Institute of Physics.

On the regularization of linear inverse problems in Fourier optics

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Applied Inverse Problems in Optics

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Experimental Studies of the Coherence of Microstructure-Fiber Supercontinuum

The phase coherence of supercontinuum generation in microstructure fiber is quantified by performing a Young's type interference experiment between independently generated supercontinua from two separate fiber segments. Analysis of the resulting interferogram yields the wavelength dependence of the magnitude of the mutual degree of coherence, and a comparison of experimental results with numerical simulations suggests that the primary source of coherence degradation is the technical noise-induced fluctuations in the injected peak power. © 2003 Optical Society of America.

Cross-correlation frequency resolved optical gating analysis of broadband continuum generation in photonic crystal fiber: Simulations and experiments

Numerical simulations are used to study the temporal and spectral characteristics of broadband supercontinua generated in photonic crystal fiber. In particular, the simulations are used to follow the evolution with propagation distance of the temporal intensity, the spectrum, and the cross-correlation frequency resolved optical gating (XFROG) trace. The simulations allow several important physical processes responsible for supercontinuum generation to be identified and, moreover, illustrate how the XFROG trace provides an intuitive means of interpreting correlated temporal and spectral features of the supercontinuum. Good qualitative agreement with preliminary XFROG measurements is observed. © 2002 Optical Society of America.