Abstract Interpolation is a key ingredient in many imaging routines. In this note, we present
a thorough evaluation of an interpolation method based on exponential splines in tension. They are
based on so-called tension parameters, which allow for a tuning of their properties. As it turns
out, these interpolants have very many nice features, which are, however, not born out in the
literature. We intend to close this gap. We present for the first time an analytic
representation of their kernel which enables one to come up with a space and frequency
domain analysis. It is shown that the exponential splines in tension, as a function of the tension
parameter, bridging the gap between linear and cubic B-Spline interpolation. For example, with a
certain tension parameter, one is able to suppress ringing artefacts in the interpolant. On the
other hand, the analysis in the frequency domain shows that one derives a superior signal
reconstruction quality as known from the cubic B-Spline interpolation, which, however, suffers from
ringing artifacts. With the ability to offer a trade-off between opposing features of interpolation
methods we advocate the use of the exponential spline in tension from a practical point of view and
use the new kernel representation to qualify the trade-off.