The diffraction problem for the Fresnel half-period zone plate is solved. The zone plate behaves as a lens with marked chromatism which can be taken advantage of for use in a spectrometer. The multiplicity of foci associated with the zone plate are examined in detail, and it is shown that the spectral range that can be focused without overlap is min≥λmax. The wavelength resolution is λ/Δλ ≈ (m+1)/0.445, where m is the number of transparent half-period zones. For m = 300, this corresponds to a 34-wave number resolution at 20 microns. The intensity at the focus is given approximately by 4I (m+1)2, where I is the intensity at the zone plate. The transmitted power that falls within the airy disk is proportional to the area of the zone plate.

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