An instrument and method is for characterizing the optical properties of an optical system, such as a lens, another optical device or the human eye, over an optical surface of the optical system. In one example, an incident beam is scanned over the surface of a lens to generate an emergent beam that is divided by a beam-splitter into two portions that are directed to respective two-dimensional detector arrays located at different optical distances from the lens. The detector arrays output the lateral coordinates of the points of incidence of the respective emergent beam portions so that the angle of emergent beam with respect to the optical axis or incident beam can be accurately determined. Determining the variation in the angle of the emergent beam over the surface of the lens allows many important optical characteristics of the lens to be characterized and mapped onto to the surface of the lens.