  The Casimir force $\cF = -\frac{\pi^2\hbar c}{240a^4}$, which attracts to
each other two perfectly conducting parallel plates separated by the distance
$a$ in vacuum, is one of the blueprints of the reality of vacuum fluctuations.
Following the recent conjecture, that quantum fields should be described in
terms of the fields depending on the resolution of measurement, rather than the
position alone (M.V.Altaisky, Phys. Rev. D 81(2010)125003), we derive the
correction to the Casimir energy depending on the ratio of the plate
displacement amplitude to the distance between plates.
