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Generation and characterization of focused helical x-ray beams

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Science Advances  14 Feb 2020:
Vol. 6, no. 7, eaax8836
DOI: 10.1126/sciadv.aax8836
  • Fig. 1 Experimental setup and fabricated ZPs.

    (A) Scanning electron microscopy (SEM) image of fabricated ZP1. (A′) and (A″) show the simulated beam intensities in and 1000 μm downstream the focal plane, respectively, of ZP1. (B) SEM image of the fabricated ZP2. Because of the large ratio between ZP2’s diameter and feature sizes, only partial SEM views are shown for clarity. (B′) and (B″) show the simulated beam intensities in and 1000 μm downstream the focal plane, respectively, of ZP2. The arrows in the insets in all panels show vortex locations in the original beam design that were converted into pitchfork-shaped structures via binary thresholding. (C) UE46-PGM2 beamline and MAXYMUS scanning microscope at the BESSY II synchrotron facility. OSA, order sorting aperture; CCD, charge-coupled device.

  • Fig. 2 Ptychographic reconstructions.

    (A) SEM image of resolution test target. (B) PCDI reconstruction of the sample in (A). (C to F) PCDI reconstructed beam intensities at 250, 500, 750, and 1000 μm downstream sample in (A). (G) SEM image of integrated circuit. (H) PCDI reconstruction of the sample in (G). (I to L) PCDI reconstructed beam intensities at the same distances downstream the sample in (G) as in (C) to (F). In (B) and (H), brightness and hue correspond to the transmissivity and phase shift of the specimens, respectively.

  • Fig. 3 3D rotating soft x-ray beam profile and vorticity.

    (A) Central lobes of helical beam intensity along propagation direction as produced by ZP1. (B to G) Numerically propagated beam intensities from z = − 1 mm to z = + 1 mm around the focal plane. (H to M) Vorticity for the beams in (B) to (G). (B) to (G) and (H) to (M) share the same spatial dimensions as indicated by the scale bars in (G) and (M). The color bar in (H) indicates the polarity of the vorticity.

  • Fig. 4 Coherent mode structure of rotating soft x-ray beam.

    (A) Coherent mode structure of the beam produced by ZP2 and an exit slit opening of 100 μm × 100 μm: The white ellipsoids show regions containing coherence simplices (hue and brightness represent phase and amplitude, respectively). (B) Beam intensity in OSA plane. (C) Normalized mutual intensity γ(Δx) computed along the colored lines in (B). The black dotted line shows the average over all coherence curves with 1 SD indicated by the shaded region. (D) Relative mode energy versus mode number. The mode numbers in (D) correspond to the numbers (#) indicated in (A). HWHM, half width at half maximum.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/7/eaax8836/DC1

    Table S1. Summary of ZP parameters.

    Fig. S1. Binary ZP design.

    Fig. S2. Mode transfer in binary ZPs.

    Fig. S3. Spatial resolution analysis.

    Movie S1. Propagation of beam from ZP1.

    Movie S2. Propagation of beam from ZP2.

  • Supplementary Materials

    The PDF file includes:

    • Table S1. Summary of ZP parameters.
    • Fig. S1. Binary ZP design.
    • Fig. S2. Mode transfer in binary ZPs.
    • Fig. S3. Spatial resolution analysis.
    • Legends for movies S1 and S2

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.avi format). Propagation of beam from ZP1.
    • Movie S2 (.avi format). Propagation of beam from ZP2.

    Files in this Data Supplement:

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