Abstract <p>The process of detection of Unruh radiation by a screened pointlike monopole detector with a narrow directivity pattern is considered for massive and massless scalar fields in (3+1)D space-time. The corresponding stationary energy-angular dependencies of the screened detector responses to the Unruh radiation are calculated numerically for massive and massless particles and are estimated analytically for massless particles. It is shown that in all cases the response is significantly anisotropic, and its energy profile strongly depends on the shape of the screening function. The corresponding brightness temperature of the observed Unruh radiation may exceed the Unruh temperature by orders of magnitude for a directivity pattern narrow enough. These points confirm that the Unruh radiation cannot be considered as thermal (equilibrium) radiation. The generation of the Unruh radiation is a pair production process that is symmetric and implies the existence of counterpart radiation going to infinity. The spectrum of this outgoing counterpart radiation also depends on the accelerated detector properties and, in principle, can be observed by detectors at rest in an initial Minkowski frame. This may allow one to detect and identify the counterpart radiation in particle accelerators in the future. The interaction of the Unruh radiation with an accelerated screened detector should lead to the emergence of a reaction force acting on this detector.</p>