Fold the Detector

You can't wrap flat tiles around a cylinder without a compromise

Detectors that surround a particle collision are built like a barrel. Their sensors are silicon, and silicon is brittle: it cannot bend through a sharp crease. So the barrel is tiled with flat modules.

No prior work bends the tiling pattern itself using origami creases. That is the gap this project addresses.

Keep the silicon flat. Put the creases between the tiles.

Origami turns a flat sheet into a curved shape using only straight creases. We tested three well-known cylindrical fold patterns against an ordinary flat-tiled barrel. Use the viewer at the top of the page to rotate each one.

Schematic crease patterns, not to scale. Solid = fold one way, dashed = the other.

Every flat face carries a rigid silicon sensor (300 µm thick). Underneath runs one continuous layer of flexible Kapton (50 µm). The Kapton is what lets the creases exist without cracking the silicon. This pairing is why these fold patterns are a realistic design direction.

Acceptance and material budget

Two terms carry the whole paper, and both sound like something else.

The main problem. A fold can catch more tracks, but every fold also adds a facet a track can cross at a shallow angle, or a seam where sensor overlaps sensor. Both add path length. You cannot raise acceptance without asking what happened to material.

A fair test changes one thing

The control barrel uses 141 tile columns so it is almost a smooth cylinder. A coarser 24-column barrel, on its own, shifted acceptance by +0.51 pp. That is why the baseline was fixed rather than chosen loosely.

1. Build each shape from its formulas in Python.
2. Export it as watertight triangular solids for Geant4: rigid silicon facets plus a continuous Kapton backing.
3. Fire 500,000 particles per shape in Geant4, from a 3 mm blob at the centre, in every direction.
4. Record hits, path length through material, and the angle each particle meets the surface.
5. Repeat five times per shape with different random seeds, and compare with standard statistics.

Try it yourself

This is a simplified version of the simulation. Pick a shape and fire particles from the centre. Amber lines hit a facet. Grey ones escape. A few hundred will not reproduce 500,000, so turn the beam on and watch the number settle.

Every fold catches more. Every fold costs material.

The dashed line is the frontier: barrel, Miura-ori and Kresling each improve on at least one axis over the last. Yoshimura sits below and to the right of Kresling, so it is worse on both. It is the only shape that is strictly beaten.

All six pairwise comparisons are statistically significant (p < 10⁻⁷, corrected for multiple comparisons). Run-to-run standard deviation is at most 0.05 pp, about ten times smaller than the smallest gap between shapes (0.49 pp).

The middle is identical. The ends are where folds win.

Physicists describe direction with |η|: 0 is straight out sideways, and larger values are closer to the beam line. We split all directions into a central belt (|η| ≤ 0.8, 66% of directions) and the ends.

A flat barrel has a finite length. Tracks that skim toward its open ends run out of barrel. Folded end facets are angled inward and keep intercepting them. Folding adds nothing in the middle, and costs nothing there either.

Five checks, and one puzzle

The puzzle

We checked how much the simulated particles scatter against a standard formula (Highland). The first check gave a result with no obvious explanation. A bug in the pipeline, or the wrong statistical model? Press the buttons to see what changed.

It depends on what limits your detector

The paper does not crown a best fold. It finds a trade-off frontier, and the practical choice narrows to two shapes. Scroll through each one. The 3D shapes are the Geant4 geometry files used in the simulation.

A simulation result, not a finished detector

On ALICE ITS3. With 50 µm silicon, folded geometries sit 0.010–0.016 pp (X/X₀) above ITS3's silicon-only figure, because flat facets meet particles at angles. The silicon-plus-Kapton stack falls below ITS3's 0.09% full-layer figure, but that is not a like-for-like comparison: ITS3's number includes carbon-foam supports, glue and cooling that this model leaves out. The results do not say folded detectors beat ITS3 on material.

An independent project, checked by outsiders

The idea, the simulation pipeline and the analysis were developed independently, with no lab or supervising group. Four physicists gave feedback at different stages: Prof. Biplob Bhattacharjee and Prof. Sudhir Vempati (IISc, early concept), Prof. Mei Dongming (University of South Dakota) and Prof. Daniel Marlow (Princeton), on the finished manuscript.

None of them endorse this project's conclusions, and none were involved in its design or execution. The idea, the methods, and any mistakes are the author's alone.

Claude (Anthropic) was used as an auxiliary tool for debugging and troubleshooting code during development of the simulation and analysis pipeline.

Read it, share it, rerun it

The slide deck explains the study without assuming a physics background. Your browser will ask before saving it.

Cite

@misc{sharma2026origami,
  author    = {Sharma, Kanishk},
  title     = {Origami-Folded Sensor Geometries for Cylindrical Tracking Detectors: A Geant4 Comparison},
  year      = {2026},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.22775533},
  note      = {Preprint; under review}
}