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In our work we present new and consistent analytical theory of the spatial correlation properties of Bright squeezed vacuum light. To describe theoretically these states and their far-field spatial correlation features we developa generalized fully analytical approach, based on the concept of independent collective (Schmidt) modes and valid for the cases of both weak and strong nonlinear interaction. Such possibility is based on the known Schmidt decomposition procedure. In the frame of the Heisenberg representation we obtain the fully analytical solution for the spatial evolution of the photon-creation operators either for the induced new collective Schmidt modes or for the plane wave modes. Using the obtained solution we calculate analytically the angular distribution of non-linear signal as well as different correlation characteristics such as covariance, second-order correlation function, etc in terms of both Schmidt modes and initial angular modes for signal and idler beams. We present the comparison of our theoretical results with the properties of bright squeezed vacuum observed in experiments performed in the Max-Planck Institute and demonstrate a good agreement. Using the developed analytical theory we explain many new interesting physical effects observed experimentally in a different experimental setup including two separated nonlinear crystals. The possibility of predominant generation of only one lowest spatial Schmidt mode is demonstrated.