A higher-order discretization model for coded aperture-based spectral imaging (CASSI) systems is experimentally demonstrated. The analog light propagation phenomena as it transverses a compressive spectral imaging system is better approximated by analyzing the effects of non-linear dispersive elements. Using the higher-order discretization model for CASSI leads to a more accurate optical transfer function. The new model extracts enhanced measurements that in turn yields more precise spatial and spectral signal reconstructions. Experimental reconstructions confirm the improvements of the proposed model.