Achromatization of a diffractive optical element (DOE) is achieved by a doublet of two holograms etched into different substrates. We show that for optimal results, it is not sufficient to just maximize the diffraction index difference, but the dispersion must also be regarded. A simple but effective strategy is presented to select substrates which allow minimum etch depths for the holograms. We apply this strategy to design an achromatic DOE for the near-infrared range. The introduction of a corridor in which the DOE phase shift is allowed to vary increases the spectral range for which the figures of merit (diffraction efficiency, nonuniformity error) indicate excellent performance.
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