The source of the reduction in the zero-order intensity in binary Damm
ann gratings is described as an error in the areas in the phase areas
within the unit cell of the grating. Equations for determining the amo
unt of error required to produce a specific reduction ratio are given.
A two-dimensional, N = 1, Dammann grating that creates a 3 x 3 beam f
an-out with a 24% reduction of the zero order provides an example of s
uch an effect. The calculation shows agreement with the measured error
.