Based　on　Fresnel　diffraction　formula,　the　spatial　frequency　distribution　of　the　holograms　recorded　with　plane　and　spherical　reference　wave　are　analyzed.　Using　the　sampling　theorem　and　the　condition　of　spectrum　separation,　the　general　recording　conditions　of　the　digital　hologram　are　deduced.　The　minimum　recording　distances　and　the　offsets　of　the　reference　wave　for　some　practical　recording　configurations　are　given.　The　deduced　recording　conditions　about　off-axis　Fresnel　hologram　are　different　from　others,　which　are　different　each　other.　The　separating　condition　of　the　frequency　spectrum　for　Fourier　transform　holography　is　applied　directly　in　their　derivation.　Moreover,　they　have　applied　different　other　approximations　in　their　derivation.　No　approximation　is　applied　to　our　deduction.　Therefore,　the　results　derived　from　our　proposed　method　are　accurate.　The　recording　conditions　of　digital　holography　with　general　spherical　reference　wave　are　presented　firstly　on　our　knowledge.　The　recording　conditions　of　in-line　and　off-axis　lensless　Fourier　can　be　gotten　directly　as　special　case.　The　simulations　and　the　experiments　demonstrate　that　the　method　and　the　results　are　valid.　The　results　also　show　that　only　the　sampling　and　separation　conditions　are　met　simultaneously,　the　reconstructed　image　with　high　quality　can　be　obtained.