The ring fit reported the SCATTER of its measurements (rms, and the beam-centre
standard error that follows from it) but nothing about how well the fit pinned
each parameter. Those two part company exactly where a calibration is worth
doubting: as the rings run out, the tilt and the beam centre stop being
separable - both displace a ring's radius as cos(phi) and only the way that
amplitude scales with radius tells them apart - so the fit can sit tightly on
the few points it has while being free to spend tens of pixels of beam centre
on a tilt the data do not support.
Take the covariance of the converged problem from Ceres and report it. Measured
on a LaB6 distance series, the fitted tilt is 50 sigma at 110 mm and 0.1 sigma
at 500 mm, where only two rings reach the detector; at 500 mm the fit quotes its
own beam centre to +-180 px and its tilt to +-2.9 deg on a 0.35 deg value, and
the correlation between them is 1.000. Nothing acts on this yet - it is printed
so the next change can gate on it.
Ceres returns the bare (J'J)^-1 of an unweighted problem, so it is scaled by
chi2 per degree of freedom; that leaves the sigmas in pixels, mm and radians
whatever unit the residual is stated in. Cost is one 5x5 SVD per run, below the
noise of the surrounding I/O.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NfuDvf5ipV3Hi8TiCUKD27
leonarski_fandClaude Opus 5
fba5435c38