Abstract: We introduce a new interferometric imaging methodology that we term interferometry with coded mutual intensity, which allows selectively imaging photon paths based on attributes such as their length and endpoints. At the core of our methodology is a new technical result that shows that manipulating the spatial coherence properties of the light source used in an interferometric system is equivalent, through a Fourier transform, to implementing light path probing patterns. These patterns can be applied to either the coherent transmission matrix, or the incoherent light transport matrix describing the propagation of light in a scene. We test our theory by building a prototype inspired by the Michelson interferometer, extended to allow for programmable phase and amplitude modulation of the illumination injected in the interferometer. We use our prototype to perform experiments such as visualizing complex fields, capturing direct and global transport components, acquiring light transport matrices, and performing anisotropic descattering, both in steady-state imaging and, by combining our technique with optical coherence tomography, in transient imaging.