Amplitude-Modulated Continuous-Wave Time-of-Flight (AMCW-ToF) Depth L1-095
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 NIR source is amplitude-modulated at frequency f_mod (10-100 MHz). Light reflected from the scene picks up a round-trip phase shift phi = 4*pi*f_mod*d/c. Four-bucket demodulation at the pixel extracts in-phase and quadrature components, from which phi and amplitude are computed. Depth d = c * phi / (4*pi*f_mod), with wrap ambiguity c/(2*f_mod). Multi-frequency captures resolve wraps.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 700
Well-posed with multi-frequency unwrap (3 f_mod sufficient for Chinese Remainder Theorem unwrap). Precision sigma_d ~ c / (4*pi*f_mod * sqrt(SNR)). Multipath interference (MPI) at concave corners and translucent surfaces biases depth; motion during 4-bucket integration causes phase artifacts.
Solvability C
- Solver class:
- four-bucket quadrature + CRT unwrap, MPI correction (sparse deconvolution, SRA, learned), deep ToF (ToF-DeepNet, ToF-FlowNet)
- Convergence rate q:
- 2
- Complexity:
- O(H * W * K) for bucket demod; O(H * W * N_freq) for multi-freq unwrap