The bitmap obtained by scanning a printed pattern depends on the exact location of the scanning grid relative to the pattern. We consider ideal sampling with a regular lattice of delta functions. the displacement of the lattice relative to the pattern is random and obeys a uniform probability density function defined over a unit cell of the lattice. the resulting random-phase sampling noise affects the edge-pixels of scanned bitmaps. The number of distinct bitmaps and their relative frequencies can be predicted from a mapping of the original pattern boundary to the unit cell (called a modulo-grid-diagram).