  THz time domain spectroscopy is a powerful technique enabling the
investigation of different materials in the far-infrared frequency range. Even
if nowadays this technique is well established, its application to very thin
films remains particularly difficult. We investigated the utilization of THz
spectroscopy on samples of micrometric thickness with the aim to disentangle
multiple reflections and to measure with high accuracy the absolute values of
the material parameters. We implemented an experimental and data analysis
procedure that can be applied to free-standing single-layers or multi-layers
samples. Specifically, we report on the experimental investigation by THz time
domain spectroscopy of two samples: a test sample made of two layers of known
thickness and materials; and a second sample, that is of a great interest for
cultural heritage studies, made of a thin film of ink layered on a thicker
support. Moreover, we describe in details the data analysis and fitting
procedures needed to extract the material parameters from the experimental
results.
