Optical Diffraction Tomography (ODT) — 3D refractive-index imaging L1-073
Unclaimed Principle — open for contribution
This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.
To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.
Forward model E
U_s(k_x, k_y; theta) = i \cdot k / (2 \cdot \sqrt{k^2 - |k_perp|^2)) \cdot F{n(r) - n_0}(k_perp, k_z(theta)) + n_noiseODT illuminates a weakly scattering 3D object with coherent plane waves at multiple angles; for each angle the complex scattered field is measured holographically. Under first Born / Rytov approximations, each scattered field is a 2D slice of the 3D Fourier transform of the refractive-index contrast on a cap of the Ewald sphere. Rotating the illumination fills the 3D k-space volume (up to the missing cone).
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 6000
Ill-posed along the missing-cone axis (cone of k-space unreachable by finite-NA illumination). Regularized inversion (TV, deep priors) fills the cone with smoothness assumptions. Non-linear Beyond-Born solvers (LS-LT, SEAGLE) handle multiple scattering but become strongly non-convex.
Solvability C
- Solver class:
- FBP-ODT (filtered backprojection over Ewald cap), Rytov inversion, TV-regularized ADMM, Multi-slice (beam-propagation), DeepODT / UNet-ODT
- Convergence rate q:
- 2
- Complexity:
- O(K * H * W * log(H*W)) for linear Born-Rytov; O(K * H * W * D) per iteration for multi-slice non-linear