  We present a formalism for self-calibrating tomography of arbitrary
dimensional systems. Self-calibrating quantum state tomography was first
introduced in the context of qubits, and allows the reconstruction of the
density matrix of an unknown quantum state despite incomplete knowledge of the
unitary operations used to change the measurement basis. We show how this can
be generalized to qudits, i.e. d-level systems, and provide a specific example
for a V-type three-level atomic system whose transition dipole moments are not
known. We show that it is always possible to retrieve the unknown state and
process parameters, except for a set of zero measure in the state-parameter
space.
