The Mars polar layered deposits (PLD) likely hold an extensive record of recent climate during a period of high-amplitude orbit and obliquity cycles. Previous work has detected limited evidence for orbital signatures within PLD stratigraphy, but data from the High Resolution Imaging Science Experiment (HiRISE) permit renewed analysis of PLD stratigraphy at sub-meter scale. Topography derived from HiRISE images using stereogrammetry resolves beds previously detectable only as alternating light and dark bands in visible images. We utilize these data to measure the thickness of individual beds within the PLD, corrected for non-horizontal bed orientation. Stratigraphic columns and bed thickness profiles are presented for two sites within the NPLD, and show several sets of finely bedded units 1-2 m thick; isolated marker beds 3-4 m thick; and undifferentiated sections. Bed thickness measurements for three sites within the SPLD exhibit only one bed type based on albedo and morphology, and bed thicknesses have a larger mean and variance compared to measurements for the NPLD. Power spectra of brightness and slope derived along the measured stratigraphic sections confirm the regularity of NPLD fine bed thickness, and the lack of a dominant SPLD bed thickness. The regularity of fine bed thickness of the NPLD is consistent with quasiperiodic bed formation, albeit with unknown temporal period; the SPLD thickness measurements show no such regularity.