A metal is a solid with a Fermi surface. It is known how to reconstruct the shape of the Fermi surface by immersing the metal in a magnetic field and measuring the period of field-induced oscillations of the magnetization/resistivity. I will show how to extract information about the quantum-mechanical wavefunction of the Fermi surface from measuring the phase offset of these same oscillations. In some metals, this information is robust against deformations of the Hamiltonian (describing the metal), and may therefore be viewed as a topological invariant.