By the spherical wave spectrum transform, the sound pressures on the two spherical surfaces surrounding the scattering objects with arbitrarily-shaped surfaces are decomposed into spherical wave components that propagate in a known manner, the relationships between the spherical wave components of the same order on the two spherical surfaces are established by the wave field extrapolation theorem, and the formula of the separation theory in the spherical coordinate is established in the wave-number domain. After separating the scattered pressure,the total scattered field can be obtained by holographic reconstruction and prediction. In order to overcome the instability of acoustic inverse problem, a new wave-number domain filter technique is proposed. It is proved that, as long as the two holographic spherical surfaces are taken to be close enough, the singularity of the separation formula can be avoided. The results of numerical simulation demonstrate the feasibility and validity of the separation theory.