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Based on canonical transforms, we develop the space-time cross covariance from incoherent fields emitted from distant objects. We simplify the results to stress the aspects qualitatively, thereby falling short of exact quantities. Specifically, we argue that fourth order field correlations in the detector plane (the Earth) can reveal the difference in axial velocities (Stellar objects) for two – or several – unresolvable objects. Besides, we derive the angular velocity for a rotating cloud of objects with rotational axes, pointing towards the observer, as can the spatial cross covariance for a single object rotating about a transverse axis. We neglect relativistic effects and the influence of optical turbulence. The analysis resembles the ones performed for objects illuminated with a coherent field, although here the spatial coherence arises due to the extreme distances between object and observer, and the temporal coherence is facilitated by spectral filtering augmented optionally by adjusting the detector separation.
The results are applicable for radiation in a broader spectrum including microwaves and gamma radiation.
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