Superresolution: an ill-posed problem in Fourier optics

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On the regularization of linear inverse problems in Fourier optics

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Resolution beyond the diffraction limit for regularized object restoration

We propose a new formulation of Miller's regularization theory, which is particularly suitable for object restoration problems. By means of simple geometrical arguments, we obtain upper and lower bounds for the errors on regularized solutions. This leads to distinguish between ' Holder continuity ' which is quite good for practical computations and ` logarithmic continuity ' which is very poor. However, in the latter case, one can reconstruct local weighted averages of the solution. This procedure allows for precise valuations of the resolution attainable in a given problem. Numerical computations, made for object restoration beyond the diffraction limit in Fourier optics, show that, when logarithmic continuity holds, the resolution is practically independent of the data noise level. © 1980 Taylor & Francis Group, LLC.

Mapping 2-D defects in a conductive half-space by eigenfunction expansions in K-space of Fourier-Laplace transforms

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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.

Applied Inverse Problems in Optics

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FANTASIO: a versatile experimental set-up to investigate jet-cooled molecules

The design of a new apparatus, named FANTASIO, for studying jet-cooled molecules is described. It includes, around the same supersonic expansion cell, a high resolution Fourier transform spectrometer with single or multipass optics, a tunable diode laser spectrometer with optional cavity ring-down facilities, and a quadrupole mass spectrometer. Performance and operational procedures are illustrated.

New high-resolution analysis of the ν7 and ν9 fundamental bands of trans-formic acid by IR Fourier transform and millimeterwave spectroscopies

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Laboratory Fourier transform spectroscopy of the water absorption continuum from 2500 to 22500 cm-1

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Nonuniform Depth Distribution Selection with Discrete Fourier Transform

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