We propose a model for coherence scanning interferometry using familiar Fourier optics methods and the spectrum of plane waves for the case where light source spectral bandwidth limits the fringe contrast as a function of optical path length. The model is straightforward to implement, is computationally efficient, and reveals many of the common error sources related to the optical filtering properties of the imaging system. We quantify the limits of applicability of the model related to the geometrical approximations for Fourier optics, particularly for high numerical apertures, and when using the fringe contrast for determining surface heights. These limitations can be overcome using a three-dimensional imaging model.