Four　derivatives-based　autofocus　criteria　functions　are　proposed　through　bringing　several　applicable　computational　methods　of　derivatives　into　the　study　of　autofocus　algorithms　for　the　digital　holographic　imaging.　By　analyzing　the　transfer　of　noise　produced　during　recording　in　phase　shifting　digital　holography,　the　impact　of　noise　on　the　derivatives-based　autofocus　algorithms　is　investigated.　The　results　from　the　simulation　and　experiment　indicate　Prewitt　gradient　(PRG)　and　Tenebaum　gradient　(TEG)　criteria　functions,　together　with　the　angular　spectrum　reconstruction　routine　can　form　two　types　of　efficient　and　reliable　autofocus　algorithms.