ABSTRACT.  Product quality in the paper‐making industry can be assessed by opacity of a linear trace through continuous production sheets, summarized in spectral form. We adopt a class of non‐Gaussian stochastic models for continuous spatial variation to describe data of this type. The model has flexible covariance structure, physically interpretable parameters and allows several scales of variation for the underlying process. We derive the spectral properties of the model, and develop methods of parameter estimation based on maximum likelihood in the frequency domain. The methods are illustrated using sample data from a UK mill.