  Thermal fluctuations cause the local normal vectors of fluid interfaces to
deviate from the vertical direction defined by the flat mean interface
position. This leads to a nonzero mean value of the corresponding polar tilt
angle which renders a characterization of the thermal state of an interface.
Based on the concept of an effective interface Hamiltonian we determine the
variances of the local interface position and of its lateral derivatives. This
leads to the probability distribution functions for the metric of the interface
and for the tilt angle which allows us to calculate its mean value and its mean
square deviation. We compare the temperature dependences of these quantities as
predicted by the simple capillary wave model, by an improved phenomenological
model, and by the microscopic effective interface Hamiltonian derived from
density functional theory. The mean tilt angle discriminates clearly between
these theoretical approaches and emphasizes the importance of the variation of
the surface tension at small wave lengths. Also the tilt angle two-point
correlation function is determined which renders an additional structural
characterization of interfacial fluctuations. Various experimental accesses to
measure the local orientational fluctuations are discussed.
