Since the sound pressures are measured on the holographic plane with a finite size, there are windowing effects and wraparound errors in the planar near_field acoustical holography (NAH) based on spatial fast Fouries transform (FFT)_based planar NAH). In order to overcome the windowing effects and wraparound errors, statistically optimal planar near_field acoustical holography (SOPNAH) is used. The sound field superposition theory is used to prove the formulas for the SOPNAH. A simple and effective method for choosing the wave number vector is proposed by means of limiting the spatial wavenumber in the kx,ky directions and discretizing the wavenumber space plane demarcated by the maximum and minimum of kx,ky. To overcome the limitation, that sound field on one side of the holographic plane must be free, in the application of the normal SOPNAH, the sound field separation technique with double holographic planes is proposed. Some results of experiment and numerical simulation are presented to demonstrate the validity of the formulas.