Steep aspheres and general complex optical surfaces are of great importance for many optical technologies and necessary for many high-technology applications where nanometer and sub-nanometer accuracy is indispensable. An example of such an application is lithography in the DUV, VUV or EUV region of the electromagnetic spectrum. The problem of measuring the topography with this high accuracy has not been solved in general. Recently, a particular measurement principle has been developed and investigated. It is referred to as high- resolution large-area curvature scanning, and the topography is determined by mathematical calculations on the basis of the information available about the curvature. It focuses on the principles of the traceability and the avoidance of error influences and is intended for determining the figure of steep aspheres and complex surfaces with ultra-precision. An uncertainty budget will be presented for the method and the facility. Special emphasis will be put on the different principles of intrinsic two-dimensional methods, in contrast to scanning methods, external references and their influences, errors of scanning stages and their influences, whole-body movements of artifact and their influences, the properties of the measurement signal, lateral and vertical resolution of the detector, long-term stability of the facility, etc.