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David Attwood studies the use of diffraction for X-ray microscopy. With Janos Kirz, he authored the X-Ray Data Booklet's account of zone plates: concentric rings select contributions that interfere at a focus. Their treatment connects outer-zone width to spatial resolution and explains why an ideal opaque/transparent zone plate sends only $1/{\pi }^2$ of incident power into its first diffraction order. Resolving a small structure and collecting a useful fraction of the incident X-rays are therefore separate design constraints.^[ref]

Janos Kirz developed X-ray imaging methods using zone plates. His joint technical account with David Attwood explains how diffraction replaces ordinary refraction in a small focusing optic. Replacing absorbing zones by zones that shift the wave phase can raise the focusing efficiency. Their account also connects finite illumination bandwidth to chromatic blurring: many zones improve focusing only if the incident X-rays occupy a sufficiently narrow range of wavelengths.^[ref]

By Janos Kirz and David Attwood. Section 4.4 of the X-Ray Data Booklet, Lawrence Berkeley National Laboratory.

Official text: xdb.lbl.gov/Section4/Sec_4-4.html

The section specifies half-period-zone geometry and distinguishes focal resolution from first-order diffraction efficiency. Its ideal binary amplitude zone plate has first-order efficiency $1/{\pi }^2$.