I show that the difference in 'spin up' and 'spin down' angular intensities of electrons emitted from inner core levels of atoms in a magnetic crystal is a spin hologram. Its inverse 'pictures' the component of the spins in the neighborhood of the emitter in the direction that the detected electrons are spin analyzed. Measuring the spin difference in three orthogonal directions determines a vector hologram which gives an image of the atomic spin vectors. I develop the theory and illustrate the feasibility and potential of this novel technique by means of model calculations. Furthermore, I give a detailed treatment of the elastic scattering processes that are responsible for the spin holograms, and study the effect of multiple scattering and self-interference which could cause complications.