We address the problem of computing IMSE-optimal designs for random fields interpolation models. A spectral representation of the IMSE criterion is obtained from the eigendecomposition of the integral operator defined by the random field covariance kernel and the integration measure considered. The IMSE can this way be approximated by spectral truncation and bounds on the error induced by truncation are given. We then illustrate how the IMSE and truncated-IMSE can be easily computed when a quadrature rule is used to approximate the integrated MSE and the design space is restricted to subset of quadrature points. Numerical experiments are carried out and indicate (i) that retaining a small number of eigenpairs (in regards of the quadrature size) is often sufficient to tightly approximate IMSE optimal quadrature-designs when optimizing the truncated criterion and (ii) that optimal quadrature-designs generally give efficient approximations of the true optimal designs for the quadrature approximation of the IMSE.