We extend the work of photon sieves to spiral photon sieves (SPSs) for the generation of a hard-x-ray vortex. A robust digital prolate spheroidal window, which has an optimal energy concentration at low frequencies, was used to adjust the number of pinholes on each ring of the SPS. It was demonstrated that an SPS has better spatial resolution and lower background than a spiral zone plate using the specified smallest structures condition. The intensity at the center of the dark core is difficult to damp to true zero, primarily owing to current limitations of high-aspect-ratio metal nanostructures. The diameter of the dark core increases as the charge value increases. However, the FWHM of the doughnut-shaped ring and background will also increase. Our results pave the way toward the design of high-performance SPSs for the generation of a hard-x-ray vortex.
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