  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
Kolmogorov's $\epsilon$-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
Kolmogorov's $\epsilon$-entropy and $\epsilon$-capacity, which are concepts
related to the evaluation of the massiveness of compact sets.
