Inverse-phase composite zone plate providing deeper focus than the normal diffraction-limited depth of X-ray microbeams

Abstract

A novel type of zone plate (ZP), termed an inverse-phase composite ZP, is proposed to gain a deeper focus than the standard diffraction-limited depth of focus, with little reduction in spatial resolution. The structure is a combination of an inner ZP functioning as a conventional phase ZP and an outer ZP functioning with third-order diffraction with opposite phase to the inner ZP. Two-dimensional complex amplitude distributions neighboring the focal point were calculated using a wave-optical approach of diffraction integration with a monochromatic plane-wave illumination, where one dimension is the radial direction and the other dimension is the optical-axis direction. The depth of focus and the spatial resolution were examined as the main focusing properties. Two characteristic promising cases regarding the depth of focus were found: a pit-intensity focus with the deepest depth of focus, and a flat-intensity focus with deeper depth of focus than usual ZPs. It was found that twice the depth of focus could be expected with little reduction in the spatial resolution for 10 keV X-ray energy, tantalum zone material, 84 nm minimum fabrication zone width, and zone thickness of 2.645 µm. It was also found that the depth of focus and the spatial resolution were almost unchanged in the photon energy range from 8 to 12 keV. The inverse-phase composite ZP has high potential for use in analysis of practical thick samples in X-ray microbeam applications.

Keywords: depth of focus; diffraction limit; microbeam; spatial resolution; zone plate.

Figure 1

(a) Positive ZP, (b) negative ZP, (c) composite ZP and (d) inverse-phase composite ZP (IP-CZP). The gray color of the zones indicates that ZPs function as a phase zone plate. The white dotted circle in (d) is the boundary of the iZP and oZP.

Figure 2

Definition of the main design parameters of the IP-CZP. (a) IP-CZP front view and (b) section; (c) outer ZP front view and (d) section.

Figure 3

Optical system for diffraction integration with a monochromatic plane-wave illumination. (ρ, φ) and (x ₀, y ₀) are coordinates in the IP-CZP plane, and (r, θ) and (x, y) are those in the observation plane at a distance z (= f + Δz) from the IP-CZP. l is the distance from a point Q in the IP-CZP plane to a point P in the observation plane.

Figure 4

Calculated two-dimensional intensity distributions: (a) ZP-A, (b) ZP-B and (c) iZP-only. The intensity is a normalized value by the peak intensity of iZP-only. The black dashed lines denote contours of 80% intensity relative to self-peak intensity.

Figure 5

(a) Calculated point spread functions at Δz = 0 and (b) intensity distributions along the optical axis, Δz, at r = 0. The ordinate is a normalized value by the peak intensity of iZP-only. Δ_res of ZP-A, ZP-B and iZP-only are 110 nm, 109 nm and 102 nm, respectively. DoFs of ZP-A, ZP-B and iZP-only are 461 µm, 412 µm and 231 µm, respectively.

Figure 6

Calculated point spread functions at Δz = 0 at several photon energies: (a) ZP-A and (b) ZP-B. The ordinate is a relative value to the peak intensity of iZP-only at the photon energy of 10 keV.

Figure 7

Calculated intensity distributions along the optical axis, Δz, at r = 0 at several photon energies: (a) ZP-A and (b) ZP-B. The ordinate is a relative value to the peak intensity of iZP-only at the photon energy of 10 keV. The abscissa, Δz, is a distance from a focus position of each photon energy.

Figure 8

(a) Calculated intensity changes at Δz = 0 and r = 0, and (b) DoF (left) and DoF/f (right) at several photon energies. The ordinate of (a) is a relative value to the peak intensity of iZP-only at the photon energy of 10 keV. In (b), the solid and dotted lines correspond to DoF and DoF/f, respectively. L-absorption edges of tantalum are indicated.