Currently, the fundamental relationships which establish the limits to optical imaging appear useful only as comparative metrics for microlithographic applications. Furthermore, with the continual advances in optical lithography, the validity of such 'rules-of-thumb' become suspect. A set of universal equations would be useful but additional description and expansion beyond the Rayleigh definitions is needed for application to current technologies. Relationships which govern the limits of resolution and focal depth are presented here in order to develop a more complete description for various lithographic imaging situations. Expanded Rayleigh definitions can then allow for insight into fundamental limitations and scaling for conventional partially coherent imaging, imaging with off-axis illumination, and phase-shift masking. Depth of focus relationships are also expanded to describe the distribution of diffraction orders over the lens pupil and are modified to accommodate feature pitch and partial coherence. Such analysis can allow for a more thorough understanding and prediction of performance for a given lithographic technology.