• Bayesian design;
  • Cluster design;
  • D-optimality;
  • Laser–surface chemistry;
  • Non-linear regression;
  • Poisson regression

Summary.  The design of experiments for generalized non-linear models is investigated and applied to an optical process for characterizing interfaces which is widely used in the physical and natural sciences. Design strategies for overcoming the dependence of a D-optimal design on the values of the model parameters are explored, including the use of Bayesian designs. Designs for the accurate estimation of model parameters are presented and compared, as are designs for the estimation of a set of ratios of parameters which is of particular importance in the motivating example. The effectiveness of various design methods is studied, and the benefits of well-designed experiments are demonstrated.