Frequency modulation atomic force microscopy is a method for imaging the surface of metals, semiconductors and insulators in ultrahigh vacuum with true atomic resolution. The imaging signal in this technique is the frequency shift Δf of an oscillating cantilever with eigenfrequency f0, spring constant k and amplitude A, which is subject to tip-sample forces Fts. Here, we present analytical results of Δf(f0,k,A) for several basic classes of Fts. With these results, a method to calculate images is derived and demonstrated with an example.