Mathematical moire models and their limitations

In a previous recent paper we discussed the limitations of the Fourier-based model in the prediction of visible moire effects. Here, we extend the discussion to other mathematical models that are also being used in the moire theory: the classical indicial equations method for modelling the moire fringes between periodic or curvilinear gratings, and two methods that are used to model different facets of the moire effects between correlated aperiodic layers. We discuss the limitations of each model, explain their significance, and suggest possible ways to overcome them.