object and image plane wavenumbers takes the form This is another way of writing the Abbe sine condition, which simply reflects the classical uncertainty principle for Fourier transform pairs, namely that as the spatial extent of any function is expanded (by the magnification factor, M), the spectral extent contracts by the same factor, M, so that the space-bandwidth product remains constant. See also Lagrange invariant Smith-Helmholtz invariant Herschel's condition References Geometrical optics Microscopes Glass physics Trigonometry