Theoretical investigations of the spatio-temporal statistical properties of arrival angle of a spherical wavefront perturbed by atmospheric turbulence are presented. The motivation is to evaluate the practicality of a high accuracy and high bandwidth active alignment for a ring segmented telescope used an optical tip measurement. The effect of finite wavefront outer scale is considered for exploring the spatial coherence of arrival angle. The temporal cross-spectrum of arrival angle is also calculated for studying the temporal coherence. The mean square of measurement error for a single short-exposure is calculated numerically. While, the magnitude of suppressing the error by time integration is discussed. The control bandwidth is calculated for an accuracy requirement of 0.01″ in some different cases of turbulence environment.