  Mechanical vibrations of components of the optical system is one of the
sources of blurring of interference pattern in coherent imaging systems. The
problem is especially important in holography where the resolution of the
reconstructed objects depends on the effective size of the hologram, that is on
the extent of the interference pattern, and on the contrast of the interference
fringes. We discuss the mathematical relation between the vibrations, the
hologram contrast and the reconstructed object. We show how vibrations can be
post-filtered out from the hologram or from the reconstructed object assuming a
Gaussian distribution of the vibrations. We also provide a numerical example of
compensation for directional motion blur. We demonstrate our approach for light
optical and electron holograms, acquired with both, plane- as well as
spherical-waves. As a result of such hologram deblurring, the resolution of the
reconstructed objects is enhanced by almost a factor of 2. We believe that our
approach opens up a new venue of post-experimental resolution enhancement in
in-line holography by adapting the rich database/catalogue of motion deblurring
algorithms developed for photography and image restoration applications.
