  We measure subnanometer displacements of thin samples vibrated by
piezotransducer. Samples contain $^{57}$Fe nuclei, which are exposed to 14.4
keV $\gamma$-radiation. Vibration produces sidebands from a single absorption
line of the sample. The sideband intensities depend on the vibration amplitude
and its distribution along the sample. We developed a model of this
distribution, which adequately describes the spectra of powder and stainless
steel (SS) absorbers. We propose to filter $\gamma$-radiation through a small
hole in the mask, placed before the absorber. In this case only a small spot of
the vibrated absorber is observed. We found for SS foil that nuclei, exposed to
$\gamma$-radiation in this small spot, vibrate with almost the same amplitudes
whose difference does not exceed a few picometers.
