Every manufacturer of large mirrors is familiar with the fact that the polishing process may not only lead to large-area surface errors, such as astigmatism or spherical aberration, but also to short-period errors. In particular, this applies to aspherical surfaces because they require polishing tools of small dimensions, as compared with the mirror diameter. These errors are not entirely irregular and may therefore not be treated as statistical errors; nor are they sufficiently regular to be described in terms of amplitudes of ZERNIKE polynomials as it is now ussually done in the case of large-area aberrations (F.FRANZA e. a. 1977). Unfortunately this still is true if very high radial and tangential orders are involved, e.g.in D. ANDERSON e.a.1982. The reason is quite obvious: The description by means of ZERNIKE polynomials is based on the assumption of a two-dimensional regularity which simply does not exist in practice.