One method for fabricating high resolution (≈.1μm) Fresnel zone plates suitable for focusing ultrasoft ≈3nm) x-rays is electron beam lithography. Present technology limits the device size to about 100μm. For a scanning microscope we need to produce a small focal spot free of background. This requires a central stop on the zone plate as well as a collimator to eliminate the zeroth order radiation. The apodized region is now a significant fraction of the zone plate area and the intensity in the focal plane is no longer the Airy pattern of an ideal amplitude zone plate. We have calculated the intensity distribu-tions of some feasible zone plates with 50 or fewer open zones. The results indicate that an acceptably small fraction of the first order radiation is shifted to the higher order lobes. In addition, we have calculated the wavelength bandpass and allowable off-axis tilt for zone plates and conclude that they should produce an intense nearly diffraction limited spot when used with suitably monochromatized synchrotron radiation.
"Optical Performance Of Apodized Zone Plates", Proc. SPIE 0316, High Resolution Soft X-Ray Optics, (24 March 1982); doi: 10.1117/12.933144; https://doi.org/10.1117/12.933144