  The self-energy $\Sigma({\bf k},\omega)$, the fundamental function which
describes the effects of many-body interactions on an electron in a solid, is
usually difficult to obtain directly from experimental data. In this paper, we
show that by making certain reasonable assumptions, the self-energy can be
directly determined from angle resolved photoemission data. We demonstrate this
method on data for the high temperature superconductor $Bi_2Sr_2CaCu_2O_{8+x}$
(Bi2212) in the normal, superconducting, and pseudogap phases.
