Reduction of the zero-order intensity in binary Dammann gratings

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