Unlike holograms of real objects, holographic stereograms(HS) are made using a relatively small number of synthesized 2D images. The influence of aliasing artifacts caused by insufficient or improper sampling is presented, and a new sampling theory is proposed, which is used to making holographic stereograms. Also, the optical system for extension of viewing distance and viewing zone is proposed. Results of this analysis can be applied to design normal holographic stereograms and computer based holographic stereograms.