  We show how the interface curvature autocorrelation function (ICAF) and
associated structure factor (ICSF), of relevance in non-equilibrium
pattern-formation problems where sharp interfaces are present, provide new and
interesting information on domain structure, as yet not visible via the
order-parameter structure factor (OPSF). This is done by discussing numerical
simulations of model A (non-conserved relaxational phase-ordering kinetics) in
two-dimensional systems. The ICAF is Gaussian over short distances and exhibits
dynamical scaling and $t^{1/2}$ power-law growth. We use it to show what the
typical length-scale in the model A dynamics corresponds to physically and how
it can be obtained uniquely, rather than simply within a multiplicative
constant. Experimental methods to measure the ICAF and/or ICSF are still needed
at this point.
