TESS pointing jitter: evidence and processing treatments

The main finding

Track mean motion and within-exposure motion separately. Registration can remove a positional offset. It cannot undo the blur accumulated during an exposure, recover flux discarded onboard, or separate a changing neighbour from the target by itself.

The literature supports a layered treatment: inspect quality and engineering data, model the background, solve image geometry, allow the stellar image shape to change, then correct residual photometric correlations with signal-preservation tests. This is a synthesis of the methods below, not a single published universal recipe.

Established

Centroid is not enough

HR 858 shows flux systematics associated with within-exposure pointing scatter and PSF width. Dispersion information can matter even when the mean location is nearly unchanged. [hr858]

Established mechanism

Onboard processing matters

The handbook explains how rejecting high/low pixel samples can couple to moving starlight. The resulting flux error need not behave like a flux-conserving blur. [handbook]

Limited case evidence

Fast-cadence noise can change

A 2025 study finds high-frequency excess and time-dependent flux–position relationships in selected fast light curves. Its proposed subpixel-sensitivity explanation remains a hypothesis. [fast]

Scope: spacecraft pointing jitter and its photometric consequences. A fitted “jitter” variance in a transit likelihood and stellar radial-velocity jitter are different concepts. This is a broad, targeted review with citation chaining, not a claim to have exhaustively retrieved every TESS paper. The bibliography marks how deeply each source was inspected.

Separate the mechanisms before choosing a correction

Effect	Observable clue	What helps
Mean pointing drift / displacement	Field-star positions move; subtraction has dipoles	Per-exposure astrometry; registration or evaluate the model on native pixels
Within-exposure jitter	Quaternion dispersion, image width or ellipticity changes	Temporal PSF/ePSF or matching kernel; dispersion regressors
Motion × detector response / finite aperture	Flux correlates with subpixel phase or aperture choice	Better extraction; regularized centroid / pixel-based correction
Motion × onboard rejection	Residual flux changes with jitter despite registration	Empirical correction or rejection of poor exposures; cannot reconstruct discarded samples exactly
Thermal focus / background / blends	Shape change without corresponding attitude change; background structure; neighbour dependence	Independent shape, sky and scene modeling; avoid attributing all correlations to jitter

Synthetic reference and shifted, broadened and dimmed images, with their signed residuals on shared scales — Original schematic, not a TESS measurement. Top: image intensities on one scale. Bottom: differences on one signed scale. A shift makes a dipole; directional blur produces a central deficit and wing excess; simple flux loss has one sign. Real PSFs, background errors and blends can mix these patterns, so morphology alone does not identify the cause. The flux-loss example illustrates normalization only, not a simulation of onboard rejection.

Physical model and why a centroid correction misses blur

The following is an explanatory derivation for a locally shift-invariant, linear detector, not a fitted TESS result:

$$P_t(\mathbf{x})=\int P_0(\mathbf{x}-\mathbf{u})J_t(\mathbf{u})\,d^2\mathbf{u},\qquad \int J_t(\mathbf{u})\,d^2\mathbf{u}=1.$$

Here $t$ labels an exposure; $\mathbf{x}$ and $\mathbf{u}$ are detector position and displacement in pixels; $P_0$ is a normalized static point-spread function (PSF), in pixel$^{-2}$; $P_t$ is its exposure-averaged form, in the same units; and $J_t$ is the normalized displacement distribution, in pixel$^{-2}$, estimated from pointing samples or constrained by stellar images. A PSF describes the image of a point source; an effective PSF also includes the detector response.

$$\boldsymbol\mu_t=\mathbb E_{J_t}[\mathbf{u}],\qquad C_t=\mathbb E_{J_t}[(\mathbf{u}-\boldsymbol\mu_t)(\mathbf{u}-\boldsymbol\mu_t)^\mathsf T].$$

$\boldsymbol\mu_t$ is the measured mean displacement in pixels; $C_t$ is the measured displacement covariance in pixel$^2$; $\mathbb E_{J_t}$ denotes an exposure-weighted expectation. Mean alignment removes $\boldsymbol\mu_t$, not $C_t$.

$$P_{t,\mathrm{aligned}}-P_0\simeq\tfrac12\sum_{i,j}C_{t,ij}\,\partial_i\partial_jP_0.$$

Indices $i,j$ refer to the two detector axes; $\partial_i$ is a spatial derivative per pixel. This small-motion Taylor approximation shows why zero-mean jitter changes curvature, width and ellipticity. It neglects higher displacement moments, changing optics, saturation and nonlinear rejection. A real reference image is already blurred; matching it involves differences in blur, not convolution with the absolute jitter covariance a second time.

Flux caveat: normalized convolution conserves total flux on an infinite uniform detector. Aperture truncation, imperfect sensitivity calibration, crowding and nonlinear onboard operations break the simple inference that conserved model flux means unchanged measured photometry. A Gaussian blur is a useful baseline, not proof that all motion distributions or residuals are Gaussian.

What the spacecraft history tells us

Early attitude-control changes followed noisy wheel-speed measurements; the handbook describes improved pointing after an algorithm change. This is historical context, not a present-day jitter amplitude. [handbook] Later mission operations place momentum management differently; use the actual observation and dump tables instead of hard-coding the early cadence. [ops]

There is no single jitter-to-ppm conversion valid for every star. The coupling depends on the stellar image, detector position, brightness, neighbours, aperture and cadence. The often quoted mission noise requirement is not a measured universal residual floor. [instrument]

How people treat it in processing

Method	Supported use	Main limitation / check
Quality and engineering cuts [fausnaugh]	Exclude loss of pointing, anomalous excursions and unreliable epochs. Fausnaugh bins both offsets and their scatter to FFI windows.	Flag definitions and reprocessing versions matter. A clean flag does not prove clean photometry; document retained duty cycle.
Aperture design [condensed]	Capture moving flux and saturated bleed; compare several apertures. Mission reprocessing enlarged some bright-star apertures to reduce losses.	Larger apertures also collect more background and contaminating stars. A time-varying aperture needs its own throughput validation.
Centroid decorrelation [eleanor]	Fit flux dependence on image position, with low-order terms or a regularized response surface.	Does not measure motion inside an exposure. Target centroids can themselves move during genuine variability in a blend.
Quaternion decorrelation [hr858]	Use exposure-binned attitude statistics, especially scatter; combine with selected common trends.	Camera coordinates, missing samples and time alignment must be handled. Telemetry does not encode all local optical effects.
Registration + subtraction [reduce]	Effective when relative shifts dominate and cutouts do not constrain a flexible kernel well.	Residual shape changes remain; interpolation correlates pixel noise. Avoid blindly smoothing across pointing discontinuities.
Kernel-matched subtraction [dia] [cdips]	Match image shapes as well as positions; crowded-field surveys demonstrate practical use.	Kernel freedom competes with background, flux and transient signal. Reference choice and stellar support determine stability.
Empirical PSF / ePSF scene fits [tglc] [pathos]	Model neighbours and allow local image shape to change with time.	Catalogue errors, variable neighbours and an unconstrained PSF can bias flux. A better residual image alone is insufficient.
CBV / ensemble detrending [tda_corr] [spoc]	Fit common instrumental trends from other stars, with regularization and science-dependent settings.	Real variability can overlap the nuisance basis. Transit and asteroseismic objectives need different preservation tests.
Pixel regression / PLD / causal pixel model [unpopular] [pld] [pldtut]	Model shared pixel signals; distant-pixel predictors and held-out fitting can preserve slow transients.	Background dominance, contamination and predictor leakage matter. TESS Lightkurve defaults differ from K2.
PSF-shape components [wasp76]	Image autocorrelation/PCA can expose changes missed by centroids; demonstrated in a TESS application.	Shape is not uniquely jitter: focus and blends also change images. Select components with validation and an astrophysical model.
Joint GP / astrophysical fit [k2sc] [sff] [everest]	Separate position dependence from time-dependent astrophysics rather than removing all smooth variations first.	Identifiability is weak when instrument and source vary together. K2 evidence does not establish TESS performance.

The most informative evidence — and its boundaries

HR 858: dispersion is actionable

Vanderburg et al. used quaternion dispersion and fast-timescale cotrending vectors for the more affected sector, while clipping broad-image outliers in another. Their reduction masked transits when refining the correction. The result is a concrete precedent, not a universal choice of regressors. [hr858]

Inspect the original Fig. 2 and §2.1 →

Fast data: a nonstationary relationship

Kálmán et al. analyze WASP-167 in Sector 64 and report related behavior in some other fast light curves, but not all. Simple position correction reduces the high-frequency feature; different intervals show different relationships. Do not infer a fixed all-sector correction or equate this with the onboard-rejection mechanism. [fast]

Inspect original Fig. 1 →

TESSreduce: model complexity can hurt

In its SN 2020fqv cutout comparison, shifts gave cleaner subtraction than the tested discrete-kernel fit. This supports checking whether the data constrain a kernel. It does not demonstrate that PSF changes are absent in every field or that all kernel methods fail. [reduce]

Inspect original Fig. 12 / Appendix A →

TGLC: fit the effective stellar image

Han & Brandt fit local ePSFs independently for each frame and use Gaia to constrain the scene. This provides a direct alternative to correcting extracted flux afterward. It does not uniquely decompose jitter, optical focus and detector response. [tglc]

Inspect model and residual figures in §III →

Published images behind two key comparisons

Original TESSreduce comparison: observed image, shift-subtracted image and kernel-subtracted image — Ridden-Harper et al., TESSreduce, Fig. 12 (original figure, served by arXiv). The observed field is shown beside both subtraction results; the tested kernel leaves stronger structure around the host. This is a particular cutout and kernel implementation, not a universal method ranking. Source and full caption.

Original WASP-167 light curve, flux-position relationships and power spectra before and after centroid correction — Kálmán et al. (2025), Fig. 1 (CC BY 4.0; original figure served by arXiv). Time-domain measurements and position dependence accompany the power spectra. The case motivates testing nonstationary corrections; the causal detector explanation remains tentative. Source and full caption. In the original figure, Φ denotes normalized flux; δ is centroid distance in pixels; f is frequency in Hz; PSD is power spectral density, shown logarithmically in dB; γ is its fitted spectral index; BJD is barycentric Julian date. External figures require access to arXiv.

Recent developments worth keeping

The 2024 WASP-76 b analysis combines engineering detrending with image-shape components. The 2026 QLP release adopts TGLC photometry from Sector 94, demonstrating continuing movement toward catalogue-assisted extraction. Neither result establishes a universal jitter-only improvement factor. [wasp76] [qlp2026]

What remains unsettled: the relative contribution of intra-pixel response, aperture leakage, onboard rejection and imperfect scene modeling for a given target; whether telemetry alone predicts its residual image; and whether a more flexible correction preserves the astrophysical signal. The studies use different targets, cadences, baselines and noise metrics, so their published precision values should not be ranked as a controlled comparison.

A practical processing plan for SynDiff

Recommendations inferred from this review. No SynDiff run was modified, no new TESS dataset was fitted, and no improvement is claimed for your current pipeline.

Build an exposure-level diagnostic table. Record sector, camera, CCD, cadence, processing version, exposure start/stop, quality flags, quaternion coverage and dispersion, background, fitted field-star shifts and PSF shape. Keep full-FFI and crop-local coordinates explicit.
Make telemetry and images share a time basis. Bin engineering samples over the actual exposure window; reconcile spacecraft time with target-dependent barycentric correction. Use camera metadata and sample counts. Missing telemetry is missing information, not zero jitter. [vectors]
Separate geometry, shape and background. Measure shifts from many stable stars. Validate across the CCD rather than at only the target. Solve an additive background independently enough that gradients do not masquerade as shape or shift. Inspect residual stamps before choosing more parameters.
Compare nested models on identical data. Start with background + geometry, add a constrained temporal shape model or kernel, then add telemetry-based residual correction. Use the same exposures, masks, stars and evaluation pixels in every comparison. Preserve a separate untouched baseline.
Test a physically constrained temporal ePSF. A starting hypothesis is a static local ePSF plus zero-centroid, flux-normalized shape changes related to projected jitter covariance. Compare against an empirical shape model and focus indicators. Quaternion components require a calibrated projection into detector coordinates; they are not pixel shifts directly.
Correct residual flux only with protected signal. Fit a small regularized nuisance basis, mask known transits/events or fit astrophysics jointly, and allow justified segment changes. Retain raw, image-corrected and detrended flux products so the correction is auditable.
Accept only an improvement on held-out data. Hold out stars and contiguous time blocks. Require better residual images and flux statistics, reduced telemetry correlation, and successful injection recovery. Include quiet and disturbed epochs; report rejected-exposure fractions rather than improving scatter by silently removing difficult data.

A compact residual-flux model to test

$$f_t=m(t;\theta)+\mathbf{z}_t^\mathsf T\boldsymbol\beta+\epsilon_t.$$

$f_t$ is extracted relative flux (dimensionless); $m(t;\theta)$ is the astrophysical model with fitted physical parameters $\theta$; $\mathbf z_t$ is a measured, centered and standardized dimensionless nuisance vector; $\boldsymbol\beta$ is its fitted coefficient vector in relative-flux units; $\epsilon_t$ is residual measurement noise in those units. Candidate entries of $\mathbf z_t$ include mean shifts, within-exposure dispersion/covariance, image-shape measures, background and a small set of CBVs. These are alternatives to compare, not a recommendation to include all correlated features. Choose regularization on held-out blocks. A fitted extra white-noise term only inflates uncertainty; it does not correct the instrumental effect.

Required validation canvas for a future experiment

Question	Show this evidence
Did geometry improve?	Data/model/residual stamps plus residual centroid vectors across the CCD
Did blur modeling improve?	Low/high-jitter absolute stacks and their differences, shared scales, matched star populations
Did photometry improve?	Flux residuals against mean motion and dispersion; matched-cadence scatter, PSD and time-binned residuals
Did it preserve science?	Pixel/scene-level injected transits and slow transients recovered through extraction and detrending; amplitude/timing bias and completeness
Is it robust?	Held-out magnitude, colour, position and crowding bins; quiet/poor-pointing epochs; background and focus controls

For faint transients, prioritize scene/background fidelity and preservation of slow rises. For bright isolated stars, telemetry plus conservative extraction is a strong baseline. For crowded fields, compare catalogue-assisted PSF photometry with difference imaging. For fast cadence, also inspect the high-frequency spectrum and time-dependent coefficients. These are conditional recommendations, not measured rankings.

Where to get the information

Start with the sector/reprocessing release notes and engineering-product inventory, then use tessvectors when its cadence and camera coverage fit the task. Its exposure-binned products are convenient but do not replace checks on sampling and timestamps. [drn] [products] [vectors]

Compare existing light curves when available: TGLC, TASOC, eleanor, and the relevant SPOC products. Agreement across independent reductions is useful; disagreement should trigger inspection of apertures, neighbours, masks and filtering.

Annotated paper & resource library

Download the full collection as CSV, BibTeX, or JSON. PDFs link to the authors’ or archives’ copies; the report does not redistribute full papers. BibTeX entries are portable reading-list records, with publication/preprint dates retained in the notes.

SearchCategory

Mission documentation · 2018

TESS Instrument Handbook, v0.1

Vanderspek et al.

Read §§8.2 and 9.2.1 for attitude-control history and jitter coupling to onboard rejection. Historical hardware description; consult release notes for later operations.

Review depth: Full PDF; relevant sections read

The main finding

Centroid is not enough

Onboard processing matters

Fast-cadence noise can change

Separate the mechanisms before choosing a correction

What the spacecraft history tells us

How people treat it in processing

The most informative evidence — and its boundaries

HR 858: dispersion is actionable

Fast data: a nonstationary relationship

TESSreduce: model complexity can hurt

TGLC: fit the effective stellar image

Published images behind two key comparisons

Recent developments worth keeping

A practical processing plan for SynDiff

Required validation canvas for a future experiment

Where to get the information

Annotated paper & resource library

Search method and coverage

Conclusion