In recent years, new optical systems have been developed with the ability to collect light at very high angles of emission, exceeding the critical angle of total internal reflection. Prominent examples are solid-immersion lenses and paraboloid collectors. These systems achieve high efficiencies in fluorescence detection which is an important issue for sensitive applications in analytical chemistry and biochemical assays. The exclusive collection of supercritical angle fluorescence (SAF) allows for the detection of evanescent modes and thus to confine the detection volume within one wavelength to an interface. For conventional optical systems with high numerical aperture a precise wave-optical theory of imaging was developed by Richards and Wolf in the fifties of the last century. However, their theory is not directly applicable to non-imaging, strongly aberratic light collection systems systems that collect a significant part of light above the critical angle. Here, we extend the theory to describe the optical properties of such systems.