CALC-102
Ambiguity crossover, metrology requirement, synthetic wavelength
What this is
This is the project's own arithmetic, published in full so it can be checked rather than taken on trust. It is not a source. Every input it uses is cited to a record, and the conclusion it reaches only carries as far as those inputs do.
Inputs. lambda = 122.364 mm at 2.45 GHz, k = 51.348 rad/m. Accuracy cap on the
interpolation residual 2.955 mm (CALC-085). Ambiguity cap on detector deviation lambda/2 =
61.18 mm, divided by the unwrap headroom in sigmas.
Crossover. Equal binding when sqrt(g(D/Lc)) = 2.955 mm / ((lambda/2)/n_sigma), with
g(t) = 1.5 - 2.exp(-(t/2)^2) + exp(-t^2)/2 from CLM-0897. Solved by bisection:
| n_sigma | sigma_s cap | D/Lc | attenuation |
|---|---|---|---|
| 1 | 61.18 mm | 0.338 | 20.7x |
| 2 | 30.59 mm | 0.484 | 10.4x |
| 3 | 20.39 mm | 0.600 | 6.9x |
At D = 50 m: ambiguity binds for Lc > 147.9 m (1 sigma), Lc > 83.3 m (3 sigma).
Metrology. Resolve the integer: 61.18 mm / 204.1 ps at 1 sigma, 20.39 mm / 68.0 ps at 3. Replace the pilot: 2.955 mm / 9.86 ps.
Synthetic wavelength. c/df, and required per-tone phase precision (lambda/2)/(c/df):
1 MHz gives 299.8 m and 0.073 deg; 20 MHz gives 15.0 m and 1.469 deg; 100 MHz gives 3.0 m and
7.347 deg.
Provenance. cassiopeia-ambiguity.py. Standard library only. Run
2026-09-13, Python 3.14.0.
What this does not establish. Which side of the crossover any real design sits on, since no structural correlation length is held. Nor that any CASSIOPeiA design uses a multi-tone pilot.
Cite this
energyaperture.com/calc/calc-102
CALC-102. The working above, not a source document.