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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White-Light Supercontinuum Generation with 60-ps Pump Pulses in a Photonic Crystal Fiber

The generation of a spatially single-mode white-light supercontinuum has been observed in a photonic crystal fiber pumped with 60-ps pulses of subkilowatt peak power. The spectral broadening is identified as being due to the combined action of stimulated Raman scattering and parametric four-wave-mixing generation, with a negligible contribution from the self-phase modulation of the pump pulses. The experimental results are in good agreement with detailed numerical simulations. These findings demonstrate that ultrafast femtosecond pulses are not needed for efficient supercontinuum generation in photonic crystal fibers. © 2001 Optical Society of America.