Expression of the residual scintillation index of a received intensity from a rough target in atmospheric turbulence is derived by using the extended Huygens-Fresnel principle combined with the Rytov method. The formula is numerically evaluated in the cases of spherical wave and plane wave incidences, and the results agree with those obtained by the slip-step Fourier method, which proves the validity of the theory. The relationship between the residual scintillation index with the target size and the propagation distance is analyzed, which proves that the residual scintillation index is the scintillation index on the target plane averaged by the target aperture.