We study diffraction of twisted matter waves—electrons and light ions carrying orbital angular momentum $\ell /\hslash =0,\pm 1,\pm 2,...$—by circular and triangular apertures. Within the scalar Kirchhoff-Fresnel framework, circular apertures preserve cylindrical symmetry and produce ringlike far-field profiles whose radii and widths depend on $\left|\ell \right|$ but are insensitive to its sign. In contrast, equilateral triangles break axial symmetry and yield structured patterns that encode both the magnitude and the sign of $\ell$. A transparent Fraunhofer mapping links detector coordinates to the Fourier plane, explaining the $\left(\right|\ell |+1)$-lobe rule and the sign-dependent rotation of the pattern. We validate these results for both ideal Bessel beams and localized Laguerre-Gaussian packets, and we cross-check them by split-step Fourier propagation of the time-dependent Schrödinger equation. From these analyses we extract practical design rules—Fraunhofer distance, lattice pitch, and detector sampling—relevant to OAM diagnostics with moderately relativistic electrons of $E_{\text{kin}}\sim 0.1$–5 MeV and light ions of $E_{\text{kin}}\sim 0.1$–1 MeV/u. Our results establish triangular diffraction as a simple, passive, and robust method for reading out the OAM content of structured quantum beams.

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• Beam diagnostics
• Cold atoms & matter waves
• Structured light
• Electron diffraction
• Particle beams
• Particle sources & targets
• Schroedinger equation