The　lensless　Fourier　transform　digital　holography　has　been　widely　employed　in　microscopic　imaging.　It　enables　quantitative　phase　analysis　for　both　reflection　and　transmission　objects.　The　phase　image　is　obtained　in　the　numerical　reconstruction　procedure.　The　in-focus　reconstruction　distance　could　be　determined　according　to　the　extremum　of　the　autofocusing　criterion　function,　which　is　commonly　applied　in　finding　the　in-focus　amplitude　image　of　the　object.　Then　the　reconstruction　distance　for　the　phase　image　is　considered　to　be　equal　to　the　one　for　the　amplitude　image.　When　the　object　is　a　pure　phase　sample,　such　as　the　living　cell,　the　minimum　value　of　the　autofocusing　criterion　function　should　be　found　to　determine　the　in-focus　reconstruction　distance.　However,　in　the　experiment,　the　in-focus　amplitude　image　is　often　not　an　ideal　uniform　bright　field,　so　this　method　will　result　in　some　deviation.　In　this　contribution,　two　derivatives-based　criterion　functions　are　applied　to　the　phase　image　directly　to　accomplish　the　in-focus　phase　contrast　imaging,　which　is　more　intuitive　and　precise.　In　our　experiments,　the　set-up　of　the　lensless　Fourier　transform　digital　holography　is　established　firstly.　Then　the　living　cervical　carcinoma　cells　are　detected.　The　phase　aberration　is　corrected　by　two-step　algorithm.　The　final　autofocusing　results　verify　the　algorithm　proposed　in　this　paper.