Manuscript En01-B@2 · En01-B-v2.tex · section · f226d1eb

Calibration–control trade-offs

Calibration–control trade-offs · lines 2363–2419

En01-B@2#tab:tradeoff

Regime	Established result	Required next certificate
Proportional quadratic responses, $λ A_{r_{c}} c \leq Δ b$	Exact interferometer-family overlap	Joint external calibration may remove the match
Full response close to matched quadratic dynamics	Near-obstruction with bound $ζ$	Domain, aperture, sensing and residual errors
Nonquadratic response survives nuisance cancellation	Signed contrast margin $m_{C}$	Visibility-response confidence or complete-histogram gap
Broad residual spectral nuisance	Exact absorption if its spectrum admits the gravity addition	Independent constraints excluding that spectrum

negative and constructive results have compatible but different hypotheses. No row is an apparatus-specific experimental verdict.

The calibration width can be large while an ideal log contrast still cancels the quadratic nuisance. Nevertheless, larger attenuation lowers $V_{m i n}$ and increases the required sample count. Cancellation of a nuisance coefficient is not cancellation of its cost to visibility.

Additional settings help only when their validated response is transverse to the admitted nuisance templates. A time-only scan of

Y_{s} = a t_{s} + λ b_{G} t_{s}

has proportional derivatives and cannot distinguish the two coefficients. A separation scan likewise fails in a purely quadratic model. The three-setting construction exploits the exact sphere's nonquadratic response, not the number of settings alone.

If each setting admits a free offset $β_{0, i}$ , choose $β_{0, i}^{(0)} = β_{0, i}^{(1)} + λ t Γ_{r_{c}} (d_{i})$ . This matches all diagnostic visibilities and eliminates the proposed positive identification. Likewise a flat response $κ_{i} = 0$ eliminates visibility information at the detector even when the underlying contrast is nonzero.

Displayed formulas in this passage

unlabeled · line 2403
$Y_{s} = a t_{s} + λ b_{G} t_{s}$