Lenses in transmission or mirrors in reflection with a low ratio of focal length to diameter represent a problem in diffractive optics due to the high spatial frequencies involved. In this paper rigorous diffraction theory is used to calculate and to optimize focusing diffractive mirror arrays with a binary structure. Also metallic artificial dielectrics, which consist of binary sub-wavelength structures, are optimized. The initial design for the elements is carried out using approximate theory. The performance of the elements is evaluated using the criteria diffraction efficiency and wavefront quality.
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Haidner et al. (1997) studied this question.
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