High-resolution x-ray scanning with a diffuse, Huffman-patterned probe to minimise radiation damage

TL;DR

This work tackles radiation damage in high-resolution x-ray imaging by introducing broad, diffuse probes encoded with 2D Huffman-like arrays whose aperiodic autocorrelation approaches a delta function, enabling sharp reconstruction through deconvolution. The authors develop theory and numerical methods to design, compress, and realize these masks, including non-negative P/N decompositions and multiple optimization schemes (Iterative down-scaling, Bernasconi/HRMC Monte Carlo) to maintain delta-like autocorrelation within a practical ±3 intensity range. They fabricate Ta-based binary and quaternary masks (11×11 to 86×86) on SiO$_2$ wafers, validate them at synchrotron beamlines, and demonstrate reconstructive accuracy on pinhole and simple gray-scale objects using bucket signals. This approach reduces local energy deposition while preserving image fidelity, with potential applications in low-dose XRF, ptychography, and coded-aperture imaging, and it opens avenues for 3D Huffman-like mask design and optical-beam shaping.

Abstract

Scanning objects with a more tightly focused beam (for example of photons or electrons) can provide higher-resolution images. However the stronger localisation of energy deposition can damage tissues in organic samples or may rearrange the chemical structure or physical properties of inorganic materials. Scanning an object with a broad beam can deliver an equivalent probe energy but spreads it over a much wider footprint. Sharp images can be reconstructed from the diffuse implanted signal when a decoding step can recover a delta-like impulse response. Huffman sequences, by design, have the optimal delta-like autocorrelation for aperiodic (non-cyclic) convolution and are well-conditioned. Here we adapt 1D Huffman sequences to design 2D Huffman-like discrete arrays that have spatially broad, relatively thin and uniform intensity profiles that retain excellent aperiodic autocorrelation metrics. Examples of broad shaped diffuse beams were developed for the case of x-ray imaging. A variety of masks were fabricated by the deposition of finely structured layers of tantalum on a silicon oxide wafer. The layers form a pattern of discrete pixels that modify the shape of an incident uniform beam of low energy x-rays as it passes through the mask. The intensity profiles of the x-ray beams after transmission through these masks were validated, first by acquiring direct-detector x-ray images of the masks, and second by raster scanning a pinhole over each mask pattern, pixel-by-pixel, collecting "bucket" signals as applied in traditional ghost imaging. The masks were then used to raster scan the shaped x-ray beam over several simple binary and "gray" test objects, again producing bucket signals, from which sharp reconstructed object images were obtained by deconvolving their bucket images.

Figures (28)

• Figure 1: (a) One of the fabricated 2cm $\times$ 2cm substrates containing 12 binary Huffman-like masks. Optical images of (b) a $PN$ pair of the fabricated $32\times32$ binary Huffman-like mask with 8 $\mu$m resolution, (c) a fabricated $11\times11$ binary Huffman-like mask with 15 $\mu$m resolution, and (d) a fabricated $15\times15$ binary Huffman-like mask with 10 $\mu$m resolution. The scale bar shown in b) also applies for the (c) and (d) images. The streak artefact in the image are residue from photoresist, which are transparent under x-rays.
• Figure 2: (a) design and (b) optical image of the fabricated $15\times15$ quaternary Huffman-like mask. L0, L1, L2, and L3 represent level 0, 1, 2, and 3 of the mask respectively.
• Figure 3: Detector images of the (a) positive ($P$) and (b) negative ($N$) $15 \times 15$ pixel Huffman-like mask generated using $3 \times 3$ binary pixels of pitch 15$\mu$m. (c) the signed mask, re-generated as $P-N$. (d) shows the histogram of image (c). The three peaks show the distribution of the measured x-ray illumination intensities that passed through the $-1, 0, +1$ sections of the fabricated mask, respectively. The vertical axis in (d) is counts, the horizontal axis displays the relative signal intensity.
• Figure 4: (a) Image of an ideal $32\times 32$$\pm 3$ gray-level Huffman-like mask, (b) Image of x-ray transmission through the fabricated mask with 20 $\mu$m pixel size, presented as $P - N$. (c) The histogram of graylevels in the ideal mask, image (a) (shown in orange), registered with the histogram of (b) the intensity of the x-rays transmitted through the fabricated mask (shown in blue). Both image histograms show five closely-matched peaks, representing the relative x-ray transmission intensities for mask levels $-2, -1, 0, +1, +2$ . The vertical scale is counts, the horizontal axis is relative intensity.
• Figure 5: (a) Image of x-ray transmission through the $[P,N / N,P]$ fabricated $15\times15$ gray-level masks with (a) $10$$\mu$m pixels and (b) $20$$\mu$m pixels.