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.spherical coordinate, sound field separation, spherical wave spectrum transform, wave-number domain filter As a method for source identification and visualization in vibro-acoustic problems, nearfield acoustic holography (NAH) is widely used in many areas nowadays. In this technique, by the measured acoustic pressure on the holographic surface which is located in the near field of the sources, such acoustic quantities as acoustic pressure, particle velocity, acoustic intensity, far-field directivity and total radiated power in three-dimension acoustic field can be calculated successfully [1][2][3][4][5][6][7][8] . So far, the algorithms to realize the NAH mainly include FFT [1][2][3][4][5] and boundary element method (BEM) [6][7][8] . The first approach has high calculation speed, but only can be applied in separable coordinates. The other can be used for any coordinate, but it is more complicated, and has low calculation speed.The research on the scattered field is very important in underwater acoustics [9][10][11] . Because the sound field is composed of the scattered and incident fields, the scattered field cannot be meas-