The　expressions　for　the　reconstructed　field　from　the　sample　of　the　diffracted　wave,　which　is　produced　by　illuminating　an　object,　are　found　by　use　of　different　diffraction　integrals　in　the　digital　holography.　The　numerical　reconstruction　methods　that　truncate　and　sample　this　field　are　compared　in　overlapping　quality,　accuracy,　pixel　resolution,　computation　window,　and　speed.　The　fast　Fourier　transform　(FFT)-based　direct　integration　method　for　the　Fresnel　integral　and　the　modified　FFT-based　direct　integration　method　for　the　Rayleigh-Sommerfeld　integral　have　similar　overlapping　quality　and　can　flexibly　control　pixel　resolution　and　computation　window　size.　Meanwhile,　the　FFT-based　angular　spectrum　method　is　superior　to　the　FFT-based　convolution　method　in　accuracy　and　speed.　The　experimental　results　are　presented　to　verify　these　consequences.　(C)　2009　Society　of　Photo-Optical　Instrumentation　Engineers.　[DOI:　10.1117/1.3251340]