Based　on　Fresnel　diffraction　theory,　the　point　spread　function　(PSF)　of　off-axis　lensless　Fourier　transform　digital　holographic　system　with　pre-magnification　is　deduced　for　the　first　time　to　the　best　of　our　knowledge.　The　lateral　resolution　limitation　of　digital　holographic　systems　with　and　without　pre-magnification　is　analyzed　in　detail.　For　lensless　Fourier　digital　holography,　the　expression　of　the　resolution　limitation　is　obtained　by　use　of　Rayleigh　resolution　criterion　and　the　PSF　of　this　system.　The　obtained　resolution　is　different　from　others　in　coefficient.　Moreover,　we　propose　new　recording　conditions　with　which　the　higher　resolution　can　be　achieved.　The　experimental　results　of　a　USAF　test　target　demonstrate　the　correctness　of　the　theoretical　analysis　about　the　lensless　Fourier　digital　holography.　For　digital　holography　with　pre-magnification,　the　resolution　limitation　is　also　analyzed　in　detail.　The　results　show　that　the　imaging　resolution　is　related　with　the　parameters　of　MO　and　CCD,　the　recording　condition　and　the　light　wavelength.　If　the　imaging　resolution　of　CCD　is　higher　than　that　of　MO,　the　resolution　of　the　whole　system　is　dependent　on　the　numerical　aperture　of　MO.　On　the　contrary,　the　resolution　is　dependent　on　the　imaging　resolution　of　the　CCD.　It　is　best　to　make　the　imaging　resolution　of　MO　approach　the　resolution　limitation　and　the　imaging　resolution　of　CCD　equal　to　or　higher　than　the　resolution　of　MO　slightly,　which　can　be　implemented　by　decreasing　the　distance　between　the　object　and　MO　and　decreasing　the　recording　distance　properly.　The　simulation　results　indicate　the　correctness　of　the　theoretical　analysis.