Millimeter-Resolution Cosmic-Ray Imaging via Projection-Shifted Muon Transmission Tomography

TL;DR

This work addresses the challenge of achieving millimeter-resolution in cosmic-ray muon imaging, a task hampered by PoCA-based scattering methods and limited transmission approaches. It introduces the Projection-shifted MUon transMission tomogrAphy (P$\mu$MA) framework, which jointly uses straight transmission tracks and projection shifts from material scattering to form high-resolution images, with two- and four-detector variants (P$\mu$MA2, P$\mu$MA4, and P$\mu$MA4C) that also exploit scattering-angle selection to boost contrast. Simulations show knife-edge widths around $w\approx$ 1.2–2.1 mm and spatial resolutions near $\text{MTF}_{10}\approx$ 2.3–2.8 mm, while experiments image 2 mm copper structures within 2–12 days, outperforming conventional MST under matched conditions. This approach reduces detector and electronics costs, increases muon acceptance, and enables practical millimeter-scale muography, with potential applicability to accelerator- or laser-generated muon beams for even higher resolution.

Abstract

Cosmic-ray muon imaging provides a non-destructive inspection technique, yet achieving millimeter-resolution imaging within practical timeframes remains challenging. Here we introduce Projection-shifted MUon transMission tomogrAghy (P$μ$MA), a hybrid framework that seamlessly integrates transmission and scattering information to enable high-resolution imaging. Unlike conventional approaches that rely on scattering-angle measurements to locate scattering points, P$μ$MA constructs transmission tracks by connecting hit positions in upstream and downstream detectors. The material-induced angular deflection is then projected as a detectable shift in an imaging plane. This approach allows millimeter-resolution cosmic-ray imaging with as few as two detectors, significantly increasing acceptance and usable muon events, and substantially lowering detector and electronics costs. We also present multi-detector variants that incorporate scattering-angle selection to enhance contrast. Simulations of a 30 mm thick lead block demonstrate a knife-edge width of 1.196 mm. Experiments resolve 2 mm copper sheets within 2 days, surpassing conventional methods under matched conditions.

Figures (4)

• Figure 1: a, Schematic diagram of the P$\mu$MA2 method. b, Schematic diagram of the P$\mu$MA4 method.
• Figure 2: a, Schematic diagram of simulated knife-edge sample placement. The area framed by the red line is the sampling area for the edge spread functions (ESFs). b, d, f, h, The imaging result of MSTC, P$\mu$MA2, P$\mu$MA4, and P$\mu$MA4C within the region where -70 mm $<$ x $<$ 70 mm and -70 mm $<$ y $<$ 70 mm. The imaging plane for P$\mu$MA methods is at z = -49.3 mm. c, e, g, i, The edge spread function obtained by MSTC, P$\mu$MA2, P$\mu$MA4, and P$\mu$MA4C.
• Figure 3: a, Schematic diagram of the experimental imaging sample. b, The imaging result of MSTC in about 12 days. c, f, i, The imaging results of P$\mu$MA2 in about 2, 3, and 8 days. (TR is normalized.) d, g, j, The imaging results of P$\mu$MA4 in about 3, 5, and 12 days. e, h, k, The imaging results of P$\mu$MA4C in about 3, 5 and 12 days.
• Figure 4: a, Schematic of the sample composed of nine materials. Each block measures 40 mm × 40 mm × 40 mm. The central block (No. 5) is located at (x, y, z) = (0, 0, –49.3 mm), and the coordinate system is indicated in the diagram. b, Transmission ratio (TR) values of the nine materials obtained with the P$\mu$MA4 and P$\mu$MA4C methods, normalized to the air TR (set to 1). c, Simulated reconstruction using the P$\mu$MA4 method. d, Simulated reconstruction using the P$\mu$MA4C method.