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The inverse problem in optics, which is closely related to the classical question of the resolving power, is reconsidered as a communication channel problem. The main result is the evaluation of the maximum number $M_epsilon$ of $epsilon$-distinguishable messages ($epsilon$ being a bound on the noise of the image) which can be conveyed back from the image to reconstruct the object. We study the case of coherent illumination. By using the concept of Kolmogorovs $epsilon$-capacity, we obtain: $M_epsilon ~ 2^{S log(1/epsilon)} to infty$ as $epsilon to 0$, where S is the Shannon number. Moreover, we show that the $epsilon$-capacity in inverse optical imaging is nearly equal to the amount of information on the object which is contained in the image. We thus compare the results obtained through the classical information theory, which is based on the probability theory, with those derived from a form of topological information theory, based on Kolmogorovs $epsilon$-entropy and $epsilon$-capacity, which are concepts related to the evaluation of the massiveness of compact sets.
We present an optimization framework based on Lagrange duality and the scattering $mathbb{T}$ operator of electromagnetism to construct limits on the possible features that may be imparted to a collection of output fields from a collection of input f
Aperture based scanning near field optical microscopes are important instruments to study light at the nanoscale and to understand the optical functionality of photonic nanostructures. In general, a detected image is affected by both, the transverse
The present status of the coupled-channel inverse-scattering method with supersymmetric transformations is reviewed. We first revisit in a pedagogical way the single-channel case, where the supersymmetric approach is shown to provide a complete solut
Modern reconstruction methods for magnetic resonance imaging (MRI) exploit the spatially varying sensitivity profiles of receive-coil arrays as additional source of information. This allows to reduce the number of time-consuming Fourier-encoding step
We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a part