Polygon approximation of the fringes of diffractive elements.

In the electron-beam fabrication of interferogram-type diffractive elements, such as diffractive lenses, continuous fringes are often approximated by polygons to reduce the data volume. Local wave-front errors are then generated that scatter light and give rise to background noise. A roughness parameter beta is introduced to quantify local phase errors in polygon-encoded diffractive structures. An efficient numerical method is developed to compute the Fresnel diffraction pattern of a polygon aperture. Polygon-approximated diffractive axicons and lenses are then investigated to determine the dependence of the signal fidelity on beta. It is found, e.g., that the maximum local phase error must be as large as pi/6 rad before the Strehl ratio S of a paraxial diffractive lens reduces below S = 0.9. However, much smaller errors can noticeably break the circular symmetry of the diffraction pattern.