To quantify the effect of decoherence in quantum measurements, it isdesirable to measure not merely the square modulus of the spatial wavefunction,but the entire density matrix, whose phases carry information about momentumand how pure the state is. An experimental setup is presented which can measurethe density matrix (or equivalently, the Wigner function) of a beam ofidentically prepared charged particles to an arbitrary accuracy, limited onlyby count statistics and detector resolution. The particles enter into anelectric field causing simple harmonic oscillation in the transverse direction.This corresponds to rotating the Wigner function in phase space. With aslidable detector, the marginal distribution of the Wigner function can bemeasured from all angles. Thus the phase-space tomography formalism can be usedto recover the Wigner function by the standard inversion of the Radontransform. By applying this technique to for instance double-slit experimentswith various degrees of environment-induced decoherence, it should be possibleto make our understanding of decoherence and apparent wave-function collapseless qualitative and more quantitative.
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