The　Rayleigh-Sommerfeld　formula(RS)　has　proved　accurate　for　evaluating　diffraction　of　the　optical　field　from　a　planar　aperture.　Thus　the　FFT　based　direct　integration　method　for　the　RS(FFT-DIRS)　can　provide　a　more　exact　reconstructed　image　from　sampling　points　of　the　diffraction　field　of　the　object　than　the　numerical　method　for　the　Fresnel　formula(FR)　that　is　an　approximation　of　the　RS.　Although　the　FFT-DIRS　has　been　proposed　and　studied　in　some　literatures,　an　important　problem　remains　to　be　solved,　that　is　the　effect　of　sampling　on　it.　Sampling　of　the　object　diffracted　field　leads　to　a　periodic　or　quasi　periodic　shifting　of　the　reconstructed　image.　If　these　spatial　replicas　overlap,　the　desired　image　can　not　be　recovered　without　the　aliasing　noise.　So　the　overlapping　period　plays　an　important　role　in　employing　the　FFTDIRS　for　the　practical　applications.　In　this　paper,　a　formula　of　this　overlapping　period　is　obtained　through　the　relationship　between　the　RS　and　the　FR.　Then　the　validity　of　this　formula　at　different　distances　is　investigated　by　the　experimental　results.　©　2009　SPIE.