  Differential Interferometry allows to obtain the differential visibility and
phase, in addition to the spectrum. The differential phase contains important
information about the structure and motion of stellar photosphere such as
stellar spots and non-radial pulsations, and particularly the rotation. Thus,
this interferometric observable strongly helps to constrain the stellar
fundamental parameters of fast rotators. The spectro-astrometry mainly uses the
photocentre displacements, which is a first approximation of the differential
phase, and is applicable only for unresolved or marginally objects. We study
here the sensitivity of relevant stellar parameters to the simulated
photocentres using the SCIROCCO code: a semi-analytical algorithm dedicated to
fast rotators, applied to two theoretical modeling stars based on Achernar and
Regulus, in order to classify the importance of these parameters and their
impact on the modeling. We compare our simulations with published VLTI/AMBER
data. This current work sets the limits of application of photocentre
displacements to fast rotators, and under which conditions we can use the
photocentres and/or the differential phase, through a pre-established physical
criterion. To validate our theoretical study, we apply our method of analysis
on observed data of the edge-on fast rotator Regulus. For unresolved targets,
with a visibility $V\sim 1$, the photocentre can constrain the main stellar
fundamental parameters of fast rotators, whereas from marginally resolved
objects ($0.8 \leq V < 1$), mainly the rotation axis position angle ($\rm
PA_{\rm rot}$) can be directly deduced from the vectorial photocentre
displacement, which is very important for young cluster studies.
