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The surge of massive antenna arrays in wireless networks calls for the adoption of analog/hybrid array solutions, where multiple antenna elements are driven by a common radio front end to form a beam along a specific angle in order to maximize the beamforming gain. Many heuristics have been proposed to sample the angular domain by trading off between sampling step size and overhead, where arbitrarily small angular step size is only attainable with infinite sampling overhead. We show that, for uniform linear and rectangular arrays, lossless reconstruction of the array's angular responses at arbitrary angular precision is possible using a finite number of samples without resorting to assumptions of angular sparsity. The proposed method, sampling and reconstructing angular domain (SARA), defines how many and which angles to be sampled and the corresponding reconstruction. This general solution to scan the angular domain can therefore be applied not only to beam acquisition and channel estimation, but also to radio imaging techniques, making it a candidate for future integrated sensing and communications (ISAC). Extensive simulation results for target detection and radio imaging have demonstrated clear advantages of SARA versus other considered baselines, both in terms of angular reconstruction performance and computational complexity.