2D Muon Scattering Tomography: POCA Reconstruction

Hidden Object Material

Beam & Detector

Muon flux 60 /s

Mean muon momentum p 4.0 GeV/c

Reconstruction

Muons recorded

Localized scatters

θ₀ for this material (typical path)

0 mrad

How it works

This is the genuinely 2D counterpart of the 3D muon scanner: instead of a single mid-plane binning trick, each muon here crosses four real tracking planes — two above the hidden object and two below — exactly like a real cosmic-ray muon tomography rig. Two hits above fix the muon's straight incoming line; two hits below fix its outgoing line. If the muon scattered inside the object, those two lines no longer coincide — extending each and finding where they intersect (the 2D reduction of the real "point of closest approach" algorithm used in actual muon trackers) pinpoints exactly where inside the volume the scattering happened. The image is built by accumulating the squared scattering angle at every reconstructed intersection point.

Highland RMS scattering angle (unchanged physics):
θ₀ = (13.6 MeV / βcp) · √(x/X₀) · [1 + 0.038·ln(x/X₀)]

Built here as a random walk: the path through the object is
split into 12 sub-steps, each with variance θ₀²/12, so the
summed kink's variance converges to the same θ₀² — verified
numerically (see report), not just assumed.

Track intersection (2D POCA):
incoming: x = m_in·y + b_in   outgoing: x = m_out·y + b_out
y_scatter = (b_out − b_in) / (m_in − m_out)

Material buttons — set the hidden block's radiation length X₀; denser/higher-Z materials give a much larger θ₀ for the same thickness.
New Hidden Object — randomises the block's size and position; try to spot it in the reconstructed image before revealing it.
Flux — muons simulated per second; a real detector needs minutes to hours because natural muon flux is low.
Momentum — higher-momentum muons scatter less (θ₀ ∝ 1/p) and their tracks localize more precisely.
Muons that pass through empty space give two collinear tracks (no intersection to bin) — only genuine scatters light up the image, the same limitation real scattering-tomography has.

Scattered track Straight track Tracking planes