  Ferroic domain walls are known to display the characteristic scaling
properties of self-affine rough interfaces. Different methods have been used to
extract roughness information in ferroelectric and ferromagnetic materials.
Here, we review these different approaches, comparing roughness scaling
analysis based on displacement autocorrelation functions in real space, both
locally and globally, to reciprocal space methods. This allows us to address
important practical issues such as the necessity of a sufficient statistical
averaging. As an ideal, artifact-free reference case and particularly targeting
finite-size systems, we consider two cases of numerically simulated interfaces,
one in equilibrium with a disordered energy landscape and one corresponding to
the critical depinning state when the external applied driving force equals the
depinning force. We find that the use of the reciprocal space methods based on
the structure factor allows the most robust extraction of the roughness
exponent when enough statistics is available, while real space analysis based
on the roughness function allows the most efficient exploitation of a dataset
containing only a limited number of interfaces of variable length. This
information is thus important for properly quantifying roughness exponents in
ferroic materials.
