This paper provides a common mathematical framework for analyzing image fidelity losses in rectangularly and hexagonally sampled digital imaging systems. The fidelity losses considered are due to blurring during image formation, aliasing due to undersampling, and imperfect reconstruction. The analysis of the individual and combined effects of these losses is based upon an idealized, noiseless, continuous-discrete-continuous end-to-end digital imaging system model consisting of four independent system components: an input scene, an image gathering point spread function, a sampling function, and an image reconstruction function. The generalized sampling function encompasses both rectangular and hexagonal sampling lattices. Quantification of the image fidelity losses is accomplished via the mean-squared-error (MSE) metrics: imaging fidelity loss, sampling and reconstruction fidelity loss, and end-to-end fidelity loss. Shift-variant sampling effects are accounted for with an expected value analysis. This mathematical framework is used as the basis for a series of simulations comparing a regular rectangular (square) sampling grid to a regular hexagonal sampling grid for a variety of image formation and image reconstruction conditions.