The far-field propagation model of annular plane beam through Kolmogorov atmospheric turbulence is presented and the nonlinear response characterization, such as so called "dead zone" and nonlinear saturation effect of CCD sensor are considered as well, the theoretical far-filed irradiance profiles of annular beam with obscuring ratio 0.5 under different turbulence strengths and their corresponding measurement results with CCD are calculated. The parameters of peak Strhel ratio RS, beam quality factor β and encircled energy ratio Ree are taken as evaluating far-field spot quality. The influence of dead zone and nonlinear saturation effect of CCD on measurement results of far-field spot profile and beam quality are analyzed, and the approaches to eliminate the measurement errors are discussed.