An instrument and method 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 [Figure 1], an incident beam (16) is scanned over the surface of a lens (12) to generate an emergent beam (20) that is divided by a beam-splitter (22) into two portions (20a and 20b) that are directed to respective two-dimensional detector arrays (24 and 26) located at different optical distances from the lens (12). The detector arrays (24 and 26) output the lateral coordinates of the points of incidence of the respective emergent beam portions (20a and 20b) so that the angle of emergent beam (20) with respect to the optical axis (14) or incident beam (16) 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. Many novel variants of the instrument and methods are disclosed.