Incoherent　digital　holographic　adaptive　optics　is　a　new　technology　of　wavefront　sensing　and　correction.　Combined　with　appropriate　numerical　algorithm,　wavefront　sensing　and　compensation　can　be　achieved　by　the　wavefront　recording　and　reconstruction　ability　of　the　holography.　Based　on　the　basic　principle　of　the　Fresnel　incoherent　correlation　holography　(FINCH),　the　incoherent　digital　holographic　adaptive　optics　is　investigated　through　theoretical　analysis　and　simulations.　Holograms　of　the　guide　star　and　the　distorted　object　are　recorded　respectively　using　a　modified　Michelson　interferometer.　Aberrations　in　the　distorted　hologram　can　be　compensated　digitally　by　using　the　complex　conjugate　of　the　guide　star　hologram.　The　effect　of　the　size　and　position　of　the　guide　star　on　the　wavefront　compensation　are　investigated　quantitatively　through　experiments.　The　aberrations　can　be　well　compensated　by　the　guide　star　chosen　from　a　suitable　area　which　is　measured　by　the　parameters　of　system.　Furthermore,　the　isoplanatic　region　of　the　system　is　demonstrated.　©,　2014,　Science　Press.　All　right　reserved.