Colour width plan · step 0 · 2026-09-25

Does the colour-dependent PSF width survive colour model #14?

Single-FFI scene fits, F1 = S24 C2K2 and F2 = S20 C3K3 (difference images). All four models are the matched runs from sffi_rawgauge_20260924. They share the same stage-2 start and 1500 stage-3 steps, and were rasterised with dev main 65a8ac9, which renders the raw gauge and the extra terms exactly.

Old 8-term: mean gauge (R0).
8-term raw gauge (R1).
#14: raw gauge plus dilation d0 + d1·r. This is the current default.
#15: #14 plus axis astigmatism a0 + a1·r.

Width terms are Δσ²/2 in 1e-3 px², where negative means sharper, fitted to stacked residual/flux.

Gate result

Yes. The colour width survives #14 almost unchanged, so step 1 is justified. Its targets should shift.

#14 compared with the 8-term raw gauge. #14 does essentially nothing to the colour width: the curves lie on top of each other. The regional χ² against zero stays at 190–580 over 9 regions.

#15. It removes part of the radial/tangential anisotropy (rms 7.6→6.1 on F1, 3.8→2.1 on F2). It leaves the 45° component and the round part untouched.

Anisotropy. The anisotropy (cxx−cyy) is the same under both gauges. It is present in bright stars (T8–10, which dominate the fit) as well as faint ones, so it is not a weighting artefact.

Round part and curvature. The round part flips sign between the mean and raw gauges, so it is partly a gauge choice. With the raw gauge, the colour dependence is mostly linear, and the "curvature" seen before came largely from the mean gauge.

Planes. Planes in (x, y) still beat every axis-based form in 8 of 8 lanes. Even so, they leave χ²/dof ≈ 10 on F1 and ≈ 5 on F2, so planes alone will not reach the χ²/dof ≲ 2 target.

Summary numbers

run	red−blue cxx	cyy	cxy	round χ²/9 (rms)	radial−tangential χ²/9 (rms)	45° χ²/9 (rms)
F1 old 8-term	−4.80	+0.78	+6.54	256 (2.96)	626 (7.09)	407 (4.78)
F1 8-term raw	−0.39	+5.72	+7.24	272 (2.31)	532 (7.75)	492 (4.98)
F1 #14	−0.21	+5.67	+6.84	234 (2.99)	584 (7.59)	503 (4.96)
F1 #15	−0.65	+5.33	+5.23	198 (2.60)	349 (6.10)	459 (4.89)
F2 old 8-term	−3.60	−2.28	−3.05	477 (3.70)	286 (2.95)	107 (1.83)
F2 8-term raw	+1.21	+3.08	−3.85	249 (1.81)	502 (4.00)	155 (2.10)
F2 #14	+1.04	+2.84	−3.73	189 (1.71)	407 (3.83)	137 (2.10)
F2 #15	+1.14	+3.03	−2.04	205 (1.85)	140 (2.08)	104 (1.84)

Red = BP−RP > 1.25, blue < 0.75, T10–13, whole CCD. The χ² is against zero over 3×3 regions with 20-bootstrap errors (floor 0.05). These errors are probably somewhat underestimated, so read the χ² as relative between models.

Red minus blue stacks and width terms against colour for four colour models on two CCDs — **Width against colour.** R1, #14 and #15 (orange, red and blue) coincide in every panel: the dilation term changes nothing measurable. Compared with the old gauge (grey), the raw gauge moves the colour trend from cxx (curved, −6 at BP−RP 1.6) into cyy (linear, −5 → +3.4 on F1). cxy is linear and large (−3.5 → +7 on F1, +1.7 → −4 on F2), and #15 only trims its red end. The red−blue stacks on the left keep a strong quadrupole under #14 and #15. On F2 there is also a vertical dipole, a leftover colour shift that the width fit absorbs through its shift terms.

Width against colour for bright and faint stars, old gauge and #14 — **Bright (red) against faint (blue) stars.** Under #14 (solid), the bright stars that dominate the loss show the same cyy slope (F1 −2.4 → +2.0 against −3.8 → +2.5) and the same sign of cxy, with about half the F1 cxy slope. So the model is not simply fitting bright stars and leaving faint ones. The faint-star slope is steeper, which overlaps with the magnitude-width term, but the colour effect exists at both brightnesses.

Three by three region maps of round, radial-tangential and 45 degree colour width for each model — **Region maps (columns: old 8-term, raw 8-term, #14, #15; rows per CCD: round, radial−tangential, 45°).** The radial−tangential maps are what #15 targets. It lightens them (F2 is now mostly within ±1 except the left column), but F1 still reaches −11 in the centre-right cell. The 45° maps are identical across all four models (F1 −9 bottom-left, F2 +4.6 bottom-right). The round maps change sign from old to raw gauge (F1 −4.6 → about 0 in the centre, but +4.6/+5.3 bottom right). A free global d0 still leaves a nearly uniform +1.5–2 on F2, so the fitted round term and this measured round width are not the same quantity.

Orientation histograms of the colour anisotropy — **Orientation, 8 step-0 lanes.** 75% of the significant anisotropy amplitude lies within ±22.5° of radial/tangential, against 18% for rows/columns (50% if uniform). This is the same optics-like result as on C5. The magnitude difference has no significant anisotropy (1 region).

Chi-squared per dof for planes versus axis-based forms per lane — **Spatial form of what remains.** Planes (P, 9 params) win BIC in 8/8 lanes, including the #15 lanes. P still leaves χ²/dof ≈ 10 (F1) and ≈ 5 (F2). Either the regional errors are too small or the field needs more than a plane (F1's centre-right cell is an outlier in every model).

What this changes in the step-1 plan

Keep: the q1/q2 anisotropy planes. This is the main, gauge-independent, bright-and-faint signal, and #15 fixes only part of it.
Lower priority: the δ² colour-curvature terms. With the raw gauge the trends are mostly linear; only F1 cxx bends at the red end.
Check first: the round-width plane. The measured round width depends on the gauge, and the free d0 does not absorb a uniform offset. Before adding dil_x/dil_y, the round part needs a like-for-like comparison between what the dilation/blur/kurtosis generators produce in my Δσ² estimator and what is measured.
Evaluation: use ≥100 bootstraps, because χ²/dof ≈ 5–10 even for the best form.

Step 1 (code on branch chroma-width-planes) has not started and waits for your approval.

Outputs: /astro/armin/koji/syndiff/dev_runs/colourwidth_step0_20260925/: an/*/raster_res_model.npz, lanes/*.json, step0_compare.json, step0_bright_vs_faint.json, and the scripts. Worktree: dev/.claude/worktrees/colour-step0 (detached at 65a8ac9).