Digital Holography (off-axis and in-line intensity holograms) L1-071
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 coherent reference wave R interferes with the object wave O at the sensor, yielding intensity I = |O|^2 + |R|^2 + O*R + OR*. In off-axis holography a tilted reference shifts the object term to an isolated Fourier quadrant; in in-line holography (phase-shifting or Gabor) a sequence of phase-shifted reference states isolates the complex object term algebraically.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 1200
Off-axis single-shot: ill-posed without spatial bandwidth separation (tilt must exceed twice max object spatial frequency). In-line phase-shifting: well-posed with N >= 3 phase steps; stability dominated by reference-phase calibration error and wavelength drift.
Solvability C
- Solver class:
- Fourier demodulation (off-axis), phase-shifting algorithm (in-line), Gerchberg-Saxton, TV-ADMM for joint denoising, deep-hologram (DH-Net)
- Convergence rate q:
- 2
- Complexity:
- O(H * W * log(H*W)) per frame (2D FFT)