  We analyze the continuous monitoring of a qudit coupled to a cavity using
both phase-preserving and phase-sensitive amplification. The quantum
trajectories of the system are described by a stochastic master equation, for
which we derive the appropriate Lindblad operators. The measurement back-action
causes spiraling in the state coordinates during collapse, which increases as
the system levels become less distinguishable. We discuss two examples: a
two-level system and an $N$-dimensional system and meter with rotational
symmetry in the quadrature space. We also provide a comparison of the effects
of phase-preserving and phase-sensitive detection on the master equation, and
show that the average behavior is the same in both cases, but individual
trajectories collapse at different rates depending on the measurement axis in
the quadrature plane.
