This paper is concerned with a general mathematical framework for the modeling and analysis of pulsed radiation from an extended source distribution. The radiated field is expressed as a continuous superposition of pulsed beam (PB) propagators which emanate from all points in the source plan and in all directions and initiation times. This phase-space distribution of PB is matched rigorously to the given time-depended source distribution via the new 'local Radon transform', which extracts the local space-time spectral (directional) properties of the source distribution. The representation integral emphasizes a priori the local radiation properties of the source distribution, thereby improves numerical efficiency and enhances physical interpretation. The basic concepts have been introduced recently for two-dimensional configurations. The present paper extends the representation to three dimensions, derives expressions for relevant transforms and propagators and discusses the additional phenomena introduced by the three dimensionality. This phase- space formulation should be contrasted with the alternative Hermite pulsed beam expansion scheme presented elsewhere in this issue, which applies only for well collimated radiation.
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