Phase structure function, residual phase structure function and long-exposure optical transfer function (OTF) of an adaptive optical system used as low-order modes correction are deduced by introducing the generalized phase spatial spectrum when low-order modes are corrected. Numerical results of long-exposure OTF, Strehl ratio and FWHM for different ρ0, which shows the state of atmospheric turbulence, and different β, which is the power-law exponent of phase power spectrum, are presented.