One can imagine a situation in which an apparatus performs some measurement on quantum systems, and determining what particular measurement is desired. The strategy is to send in systems of various known states, and use these states to estimate the outcomes of the unknown measurement. Also known as "quantum estimation", tomography techniques are increasingly important including those for quantum measurement tomography and the very similar quantum state tomography. Since a measurement can always be characterized by a set of POVM 's, the goal is to reconstruct the characterizing POVM 's Π Π l . The simplest approach is linear inversion. As in quantum state observation, use