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 integrating 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 and for quadrature designs (i.e., designs composed of quadrature points), the truncated criterion yields a significant reduction of the computational cost for multiple IMSE criterion evaluations. We present numerical experiments which illustrate that retaining a small number of eigenpairs is often sufficient to obtain an IMSE-optimal quadrature design while optimizing the truncated criterion.