Measuring polarisation, spectrum, temporal dynamics, and spatial complex amplitude of optical beams is essential to studying phenomena in laser dynamics, telecommunications and nonlinear optics. Here, we harness principles of spatial state tomography to measure a complete description of an unknown beam as a set of spectrally, temporally, and polarisation resolved spatial state density matrices. Each density matrix slice resolves the spatial complex amplitude of multiple mutually incoherent fields, which over several slices reveals the spectral or temporal evolution of these fields even in scenarios when they spectrally or temporally overlap. We demonstrate these features by characterising the rich spatiotemporal and spatiospectral output of a vertical-cavity surface-emitting laser.
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