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 criterion can hence be evaluated without explicitly integrate the MSE and spectral truncation naturally defines an approximated criterion. The approach is of particular interest when a quadrature rule is used to approximate the integral of the MSE. In this situation, both IMSE and truncated-IMSE optimal designs are supported by quadrature points. In addition, numerical experiments indicate that retaining a small number of eigenpairs is sufficient to obtain IMSE-optimal designs when optimizing the truncated criterion, resulting in a significant reduction of the optimization computational cost.