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We investigated the question of how the perception of 3D information of digital holograms reconstructed numerically and presented on conventional displays depends on motion and stereoscopic presentation. Perceived depth in an adjustable random pattern stereogram was matched to the depth in holographic objects. The objects in holograms were a microscopic biological cell and a macroscopic coil. Stereoscopic presentation increased perceived depth substantially in comparison to non-stereoscopic presentation. When stereoscopic cues were weak or absent e.g. because of blur, motion increased perceived depth considerably. However, when stereoscopic cues were strong, the effect of motion was small. In conclusion, for the maximisation of perceived 3D information of holograms on conventional displays, it seems highly beneficial to use the combination of motion and stereoscopic presentation.