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 . The wavelength resolution is , where is the number of transparent half-period zones. For , this corresponds to a -wave number resolution at 20 microns. The intensity at the focus is given approximately by , where 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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July 01 1969
Solution to the Fresnel Zone Plate Problem
H. Malcolm Childers;
H. Malcolm Childers, David E. Stone; Solution to the Fresnel Zone Plate Problem. Am. J. Phys. 1 July 1969; 37 (7): 721–726. https://doi.org/10.1119/1.1975785
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