Cataract Lens Protein Aggregation & Light Scattering (2D)

Cataract Progression

Crystallin aggregation 0%

Light wavelength 550 nm

Lens path length 4.0 mm

Photons in flight 70

Live Readouts

Mean aggregate radius

5.0 nm

Theory transmission T

99.99%

Turbidity (τL)

0.00

MC transmitted (n=0)

–

How it works (2D method)

This is the 2D-native counterpart to the 3D cataract simulator. Instead of orbiting instanced spheres inside a rendered lens ellipsoid, it draws three genuine 2D diagrams that all read the same underlying physics live:

Coagulation view — a real 2D Brownian-dynamics population of crystallin aggregates, diffusing and reflecting inside a lens cross-section disc. Their count and radius are set from the exact same volume-conserving coarsening law as the 3D model; drag to pan, scroll to zoom.
Photon Monte Carlo transport — every photon independently samples its own free path from the exact exponential (Beer–Lambert) distribution, ℓ = −ln(u)/μ with u~Uniform(0,1), then either scatters out before crossing the lens or survives to the far edge. The running fraction that survives is an independent statistical estimate of transmission — watch it converge to the closed-form curve as more photons fly.
Transmission spectrum — T(λ) plotted directly from the closed-form model across the visible range, with the current wavelength marked.

Rayleigh cross-section (dipole, radius a ≪ λ), capped near geometric limit:
  σ(a,λ) = [ 1/σ_Rayleigh + 1/σ_geom ]⁻¹
  σ_Rayleigh = (8π/3)·(2π/λ)⁴·a⁶·((m²−1)/(m²+2))²,   σ_geom = πa²

Volume-conserving coarsening:  N(a) = N₀·(a₀/a)³
Attenuation coefficient:       μ = N(a)·σ(a,λ)·κ      (per nm)
Beer–Lambert:                  τ = μ·L,   T = exp(−τ)
Photon free path (exact MC sampling of the same law):
  ℓ_scatter = −ln(u)/μ,   survives if ℓ_scatter > L

Aggregation slider — advances mean aggregate radius a from ~5 nm toward ~140 nm.

Wavelength slider — σ ∝ λ⁻⁴ in the Rayleigh regime, so blue scatters far more than red.

Lens path length — the physical thickness the light crosses; longer paths accumulate more optical depth for the same haze.

Photons in flight — how many independent Monte Carlo photon packets are sampled at once; more photons make the running MC estimate converge tighter to the theory curve.

Refractive indices, protein volume fraction and the calibration constant κ are identical to the 3D model, so every slider still traces the same physical lens — only the representation is genuinely 2D.

Crystallin aggregates (2D Brownian dynamics) Transmitted photon packet Scattered-out photon packet

drag to pan · scroll to zoom (coagulation view)