The effect of the single-particle constraint on the response of phase-Doppler instruments is determined for particle flows that are spatially nonuniform and time-dependent. Poisson statistics are applied to particle positions and arrival times within the phase-Doppler probe volume to determine the probability that a particle is measured successfully. It is shown that the single-particle constraint can be viewed as applying spatial and temporal filters to the particle flow. These filters have the same meaning as those that were defined previously for uniform, steady-state sprays [1], but in space-and time-dependent form. Criteria are developed for determining when a fully inhomogeneous analysis of a flow is required and when a quasi-steady analysis will suffice. A new bias due to particle arrival time displacement is identified, and the conditions under which it must be be considered are established. The present work provides the means to rigorously investigate the response of phase-Doppler measurement systems to transient sprays such as those that occur in diesel engines. To this end, the results are applied to a numerical simulation of a diesel spray. The calculated hypothetical response of the ideal instrument provides a quantiative demonstration of the regimes within which measurements can accurately be made in such sprays.