The bitmap obtained by scanning a printed pattern depends on the exact
location of the scanning grid relative to the pattern. We consider id
eal sampling with a regular lattice of delta functions. The displaceme
nt of the lattice relative to the pattern is random and obeys a unifor
m probability density function defined over a unit cell of the lattice
. Random-phase sampling affects the edge-pixels of sampled patterns. T
he resulting number of distinct bitmaps and their relative frequencies
can be predicted from a mapping of the original pattern boundary to t
he unit cell (called a module-grid diagram). The theory is supported b
y both simulated and experimental results. The module-grid diagram may
be useful in helping to understand the effects of edge-pixel variatio
n on Optical Character Recognition.