  Self-affine rough interfaces are ubiquitous in experimental systems, and
display characteristic scaling properties as a signature of the nature of
disorder in their supporting medium, i.e. of the statistical features of its
heterogeneities. Different methods have been used to extract roughness
information from such self-affine structures, and in particular their scaling
exponents and associated prefactors. Notably, for an experimental
characterization of roughness features, it is of paramount importance to
properly assess sample-to-sample fluctuations of roughness parameters. Here, by
performing scaling analysis based on displacement correlation functions in real
and reciprocal space, we compute statistical properties of the roughness
parameters. As an ideal, artifact-free reference case study and particularly
targeting finite-size systems, we consider three cases of numerically simulated
one-dimensional interfaces: (i) elastic lines under thermal fluctuations and
free of disorder, (ii) directed polymers in equilibrium with a disordered
energy landscape, and (iii) elastic lines in the critical depinning state when
the external applied driving force equals the depinning force set by disorder.
Our results shows that sample-to-sample fluctuations are rather large when
measuring the roughness exponent. These fluctuations are also relevant for
roughness amplitudes. Therefore a minimum of independent interface realizations
(at least a few tens in our numerical simulations) should be used to guarantee
sufficient statistical averaging, an issue often overlooked in experimental
reports.
