  Quantum projection synthesis can be used for phase-probability-distribution
measurement, optical-state truncation and preparation. The method relies on
interfering optical lights, which is a major challenge in experiments performed
by pulsed light sources. In the pulsed regime, the time frequency overlap of
the interfering lights plays a crucial role on the efficiency of the method
when they have different mode structures. In this paper, the pulsed mode
projection synthesis is developed, the mode structure of interfering lights are
characterized and the effect of this overlap (or mode match) on the fidelity of
optical-state truncation and preparation is investigated. By introducing the
positive-operator-valued measure (POVM) for the detection events in the scheme,
the effect of mode mismatch between the photon-counting detectors and the
incident lights are also presented.
