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This work describes a novel radiation algorithm designed to capture the three-dimensional, space-time resolved electromagnetic field structure emitted by large ensembles of charged particles. % in particle-in-cell (PIC) codes. The algorithm retains the full set of degrees of freedom that characterize electromagnetic waves by employing the Li\'enard-Wiechert fields to retrieve radiation emission. Emitted electric and magnetic fields are deposited in a virtual detector using a temporal interpolation scheme. This feature is essential to accurately predict field amplitudes and preserve the continuous character of radiation emission, even though particle dynamics is known only in a discrete set of temporal steps. Our algorithm retains and accurately captures, by design, full spatial and temporal coherence effects. We demonstrate that our numerical approach recovers well known theoretical radiated spectra in standard scenarios of radiation emission. We show that the algorithm is computationally efficient by computing the full spatiotemporal radiation features of High Harmonic Generation through a plasma mirror in a Particle-In-Cell (PIC) simulation.