In the electron-beam fabrication of interferogram-typo 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 β 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 β. It is found, e.g., that the maximum local phase error must be as large asπ/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. # 1997 Optical Society of America
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