The simplicity of the holographic stereogram (HS) makes it an attractive option in comparison to the more complex coherent computer generated hologram (CGH) methods. The cost of its simplicity is that the HS cannot accurately reconstruct deep scenes due to the lack of correct accommodation cues. The exact nature of the accommodation cues present in HSs, however, has not been investigated. In this paper, we provide analysis of the relation between the hologram sampling properties and the perceived accommodation response. The HS can be considered as a generator of a discrete light field (LF) and can thus be examined by considering the light ray oriented nature of the hologram diffracted light. We further support the analysis by employing a numerical reconstruction tool simulating the viewing process of the human eye. The simulation results demonstrate that HSs can provide accommodation cues depending on the choice of hologram segmentation size. It is further demonstrated that the accommodation response can be enhanced at the expense of loss in perceived spatial resolution.