FTIR Imaging — Fourier-Transform Infrared Hyperspectral Microscopy L1-140
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
A broadband IR source is passed through a Michelson interferometer; the OPD-varying interferogram modulates light through the sample; a FPA detector records interferograms per pixel, FFT yields absorption spectrum A(r, nu) = -log10(I/I_0). Beer-Lambert linear absorbance of K species with known molar absorption coefficients epsilon_k(nu).
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- unique under Beer-Lambert linearity when c_k * l small
- Stability:
- conditional
- κ:
- 200
Linear Beer-Lambert inverse problem; conditioning depends on spectral-overlap of K species. Mismatch: Mie scattering induces resonant distortions (Kramers-Kronig-like baseline); water vapor spikes.
Solvability C
- Solver class:
- CLS, PLS, ME-EMSC (extended-multiplicative-scatter-correction), RMieS (resonant-Mie), MCR-ALS, learned (IR-UNet, FTIR-classifier)
- Convergence rate q:
- 2
- Complexity:
- CLS O(H*W*K*N_nu); RMieS O(H*W*iter*N_nu^2) for reference-spectrum update