# Column calibration sensitivity and calibration scope — 2026-10-03

**Conclusion:** image calibration is not one scalar per CCD. An explicitly
imposed 1% error proportional to the reconstructed column correction produces
median/p95 0.177/0.679 ppm temporal RMS in the fixed 165-star relative-photometry
sample. That particular error is too small to explain the larger residual
histories. Its chosen amplitude is not a measured calibration uncertainty;
arbitrary column errors, gain drift and chromatic flat response remain open.
The original instrumental-systematics/photon-noise goal is not achieved.

Run: `/astro/armin/koji/syndiff/dev_runs/temporal_raw_epsf_20261001/`.
Code: local `codex/temporal-raw-epsf` in
`/home/kshukawa/syndiff_pipeline/dev/.worktrees/temporal-raw-epsf`.
Scripts: `temporal_raw_epsf/applied_column_sensitivity.py` and its standalone
`test_applied_column_sensitivity.py`. No push or production replacement.

## What “RAW” means here

The actual science inputs are unsubtracted SPOC-calibrated `_ffic` images in
electrons/second. Uncalibrated coadds are `_ffir` images in digital counts.
[MAST product definitions](https://archive.stsci.edu/missions-and-data/tess/data-products.html)
distinguish these products. “RAW” in this experiment is relative to template
subtraction, not relative to detector calibration.

| Calibration component | Spatial and temporal scope |
|---|---|
| Static black/bias reference | Two-dimensional CCD map |
| Time-dependent black/bias | Per-exposure row curve for each readout output, inferred from overclock columns |
| Gain and nonlinear response | Separate parameters for four readout outputs |
| Shutterless-readout smear | Per-column correction from virtual rows |
| Flat field | Pixel-dependent CCD response map, not a scalar |

See [NASA's product description](https://heasarc.gsfc.nasa.gov/docs/tess/data-products.html)
and [Instrument Handbook §§6.6.3, 9.5.1](https://archive.stsci.edu/files/live/sites/mast/files/home/missions-and-data/active-missions/tess/_documents/TESS_Instrument_Handbook_v0.1.pdf).
The documented laboratory flat uses 780 ±25 nm illumination; the handbook
explicitly notes that different sky/star colours prevent complete removal of
strap response with one flat. A static spatial error can become temporal as
the WCS or PSF changes. This is a physical possibility, not a detected cause
in this sample. The precise original per-step reference manifest is incomplete
in the FFI headers, so reproducing their transformation does not establish
detector-truth calibration accuracy.

![Actual image and output boundaries](/astro/armin/koji/syndiff/dev_runs/temporal_raw_epsf_20261001/results/calibration_provenance/calibration_layout.png)

![Existing matched channel histories before and after corrections](/astro/armin/koji/syndiff/dev_runs/temporal_raw_epsf_20261001/results/calibration_readout_followup/current_readout_trends.png)

![Individual histories underlying the last channel comparison](/astro/armin/koji/syndiff/dev_runs/temporal_raw_epsf_20261001/results/calibration_readout_followup/individual_readout_histories.png)

These medians are descriptive: they include astrophysics and shared-reference
covariance. A CCD-wide trend alone cannot identify gain, illumination,
PSF/aperture response or a reference-star error. One CCD-wide multiplicative
change is also largely degenerate with relative-photometry normalization.

## Exact imposed perturbation

Use the effective column term reconstructed in `APPLIED_CALIBRATION.md`,
separately for both complementary pixel halves, on the same 36 FFIs.

$$\delta C_{t,y,x}=-\epsilon\,s_{t,a,x}\,g_a/(\Delta t_t Q_{y,x}).$$

Here $\delta C$ is the hypothetical calibrated-pixel rate change in
electrons/second; $t$ is exposure, $y,x$ are full-FFI pixel coordinates, and
$a$ is the pixel's readout output. The inferred $s$ is the subtracted column
term in linearized ADU/readout; $g$ is the header gain in electrons/ADU;
$\Delta t$ is header exposure seconds divided by retained readout count;
$Q$ is the fixed dimensionless candidate flat. The dimensionless $\epsilon$
is explicitly chosen as −0.01 or +0.01, not estimated from the stars.

The shape-only control replaces $s$ with its departure from each output's
mean over columns supported by every fit/epoch. Full-term interpretation
depends on the declared row-mean gauge. Every actual science/reference
measurement pixel must have inferred column support; no unsupported column
is filled and no star is dropped.

The pixel differences pass through the actual archived profile measurement
operator for science stars and fixed r3 aperture/sky weights for references.
The same physical count restoration, WCS, ePSF, flat and reference-ensemble
weights remain fixed. Science and reference changes are combined through the
existing multiplicative relative-flux calculation. Per-source constant
offsets are removed only to report temporal sensitivity. All 354 predefined
groups are described; no new instrumental-attribution significance is inferred.

## Validation and results

Independent numerical checks compare against direct synthetic pixel
recalibration and cover output boundaries, units, sign reversal, zero error,
uniform-flat sky rejection and coupling through a varying flat. All pass.
The archived science-profile measurement is replayed to a maximum fractional
disagreement of 3.68e-8. Both inferred pixel halves agree. Negative-error
controls reverse the pixel signal; tiny flux-ratio nonlinearities remain
in the final relative photometry, as expected.

| Imposed +1% error, pixel half 0 | Median/p95 source RMS [ppm] | Maximum [ppm] | Ensemble RMS [ppm] |
|---|---:|---:|---:|
| Full column correction | 0.177 / 0.679 | 2.672 | 0.0407 |
| Column shape only | 0.175 / 0.735 | 2.669 | 0.0392 |

The two preselected 10/16-star groups change by 0.0647/0.0611 ppm RMS in
the full-term control. All 165 eligible science stars and 235 disjoint
references are retained. These are deterministic conditional sensitivities,
not uncertainty intervals or a guarantee about unknown calibration errors.

![Imposed column-error sensitivity by time, magnitude, colour and position](/astro/armin/koji/syndiff/dev_runs/temporal_raw_epsf_20261001/results/applied_calibration_sample/column_sensitivity/column_impact.png)

![Underlying endpoint pixel differences on a common scale](/astro/armin/koji/syndiff/dev_runs/temporal_raw_epsf_20261001/results/applied_calibration_sample/column_sensitivity/column_difference_stamps.png)

The actual differences are column-like and fractionally larger for fainter
sources, consistent with an additive perturbation. Both figures were
inspected before this interpretation. The fixed-support experiment does not
refit the ePSF or learn a new light-curve correction.

Frozen job: `condor/applied_column_sensitivity/`, cluster 1648 on plscience3,
two requested CPUs/4000 MB, exit 0 after 24 seconds on plscience15.
The job directory contains source hashes and exact commands. Products:
`results/applied_calibration_sample/column_sensitivity/`, with `summary.json`,
`predictions.npz`, `group_changes.csv`, figures and `DONE`.
Canvas: [existing private report](http://localhost:18888/temporal-raw-epsf/canvas/temporal_raw_epsf.html).

**Conclusion:** the specified proportional column error is a weak pathway
into this bright-star photometry and cannot explain its larger trends at the
tested 1% amplitude. This does not clear upstream calibration. Independent
gain stability and chromatic/spatial response constraints, the actual hp_d
missing-light repair, broader populations and the complete noise budget
remain required. No calibration or science candidate is promoted.