We examine patterns of absorption intensity in two-mode systems with a 2:1 Fermi resonance in an intensity model based on the effective fitting Hamiltonian. We relate these patterns to the Fermi resonance phase space structure and catastrophe map. Each of the four zones of the catastrophe map has a phase sphere structure with a certain number of distinct regions. For each zone, we find that for every region on the sphere, there is a distinct region in the intensity pattern.