arxiv: 2605.03445 · v1 · submitted 2026-05-05 · 🌌 astro-ph.IM

Recognition: unknown

Mitigating effects of telescope jitter through differentiable forward-modeling

Max Charles , Louis Desdoigts , Benjamin Pope , Connor Langford , David Sweeney , Peter Tuthill

Authors on Pith no claims yet

Pith reviewed 2026-05-07 13:01 UTC · model grok-4.3

classification 🌌 astro-ph.IM

keywords telescope jitterforward modelingastrometrybinary star separationpointing instabilitiesmodel misspecificationfrequency regimesimage degradation

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The pith

Differentiable forward modeling of telescope jitter recovers accurate binary star separations except when one-dimensional models are applied to two-dimensional motion.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that a differentiable forward-modeling approach can simulate and mitigate the blurring effects of telescope pointing instabilities on images. A sympathetic reader would care because these instabilities limit the precision of key measurements such as angular separations between stars, which are needed for detecting Earth-analogue exoplanets. The work divides jitter into low-, medium-, and high-frequency regimes relative to camera frame rate and shows the models work well for the low- and high-frequency cases. It finds that model misspecification in the medium-frequency regime does not create systematic bias in the recovered separation of a binary star pair unless a one-dimensional jitter model is fitted to two-dimensional motion, in which case the recommendation is to use two-dimensional models instead.

Core claim

The central claim is that differentiable forward modeling of jitter effects, built from simple models of how instabilities appear on the detector, effectively handles low- and high-frequency jitter relative to frame rate while medium-frequency jitter risks misspecification due to its unpredictability. When applied to simulated data for measuring the angular separation of the Alpha Centauri AB binary, this misspecification produces no systematic bias on the recovered separation except in the specific case of fitting a one-dimensional jitter model to two-dimensional motion, leading to the explicit recommendation for two-dimensional models. The same forward-modeling method is presented as a way

What carries the argument

Differentiable forward modeling of jitter blurring on detector images, using frequency-regime-specific models of pointing instabilities.

If this is right

The approach generalizes to other telescope systems facing similar pointing challenges.
Two-dimensional jitter models prevent bias in astrometric measurements that one-dimensional models would introduce.
Higher precision on scientific observables such as binary separations becomes achievable as demands for accuracy increase.
The method supports missions that rely on fine astrometry for exoplanet detection by reducing the impact of image degradation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Real-world validation could compare model outputs against simultaneous telemetry of actual telescope pointing to check for unmodeled effects.
The same modeling strategy might address jitter in other high-precision imaging applications where frequency content of instabilities varies.
Extending the analysis from simulations to on-sky data would test whether Fisher information predictions hold when additional noise sources are present.

Load-bearing premise

That the simple models of jitter based on how it appears on the detector fully capture real telescope pointing instabilities in every frequency regime, so that results from simulated data will match unbiased performance on actual observations.

What would settle it

A direct test on real telescope observations that shows a statistically significant bias in recovered binary separation when a one-dimensional jitter model is used on two-dimensional motion, or when medium-frequency jitter produces larger errors than predicted by the forward models.

Figures

Figures reproduced from arXiv: 2605.03445 by Benjamin Pope, Connor Langford, David Sweeney, Louis Desdoigts, Max Charles, Peter Tuthill.

**Figure 1.** Figure 1: Left: the Fisher information matrix, and right: covariance matrix of the likelihood distribution of a ∂LuxToliman model. The model is of the TOLIMAN instrument observing the α Cen AB system without jitter. These two matrices have an inverse relationship, with the covariance matrix showing the CRLB of the system. The diagonal of the covariance matrix shows the parameter variances of the likelihood function … view at source ↗

**Figure 2.** Figure 2: Modelled TOLIMAN science frames observing α Cen with different jitter models. These depict exaggerated examples of jitter for visualization purposes. From left to right, the models are: a) no jitter; b) linear jitter with equally spaced summed images; c) simple harmonic jitter with equally spaced summed images which are weighted by Equation (13); and d) multivariate normal jitter or Gaussian jitter, where … view at source ↗

**Figure 3.** Figure 3: Fisher analysis results for linear (left) and SHM (right) models of jitter. This plot shows how well the science signal can be constrained as increasing levels of jitter excursion – in units of arcseconds (lower axis) and pixels (upper axis) – are injected. Results are plotted for different orientations of jitter angle ϕ: 0° being parallel to the binary separation vector, 90° being perpendicular. The axis … view at source ↗

**Figure 4.** Figure 4: Results for a random jitter, modeled by an image convolution with a two-dimensional normal distribution parameterized by magnitude det Σ, shear η, and angle ϕ. The three rows show results for different shear η values. For each row, Left: results of Fisher analysis showing the separation error varying with increasing det Σ. The top axis shows the corresponding FWHM of the semi-major axis of the convolution… view at source ↗

**Figure 5.** Figure 5: Histograms of maximum likelihood estimates of binary separation over 10 000 different noise realizations (i.e. Poisson draws) of the simulated data. The columns correspond to which jitter model generated the simulated data, and the rows correspond to which jitter model was used to fit the simulated data. Two simulated datasets were generated with the multivariate normal model: one with shear η = 0.1 (rela… view at source ↗

**Figure 6.** Figure 6: Figure displaying the relevant spectra for the calculation of the total photon count of a single exposure. Top: individual spectra of each star in the binary pair α Cen AB and their sum, calculated using phoenix stellar atmosphere models27 in PySynPhot. 28 Middle: The TOLIMAN bandpass and its components: the filter, the glass plates, and the quantum efficiency of the detector. The filter will be sandwiched… view at source ↗

**Figure 7.** Figure 7: Normalized histogram of time samples generated from g(t) passed through x(t) given by Equation (12), plotted against the derived analytic form of f(x) given by Equation (18). The histogram closely matches the expected analytic form. This function is only defined on the interval (−A, A). To ensure it is defined over all real numbers we lastly write f(x) = ( 1 π √ A2−x2 for (−A, A), 0 otherwise. (18) This eq… view at source ↗

read the original abstract

Instabilities in telescope pointing, commonly referred to as jitter, introduce image degradation that can compromise the accuracy of critical scientific observables. This work presents a differentiable forward-modeling approach to both understand and mitigate the impact of jitter. We apply dLux -- a differentiable optical simulation framework built in the JAX numerical simulation framework -- to model the blurring effects of jitter on the final image. We categorize jitter into low-, medium-, and high-frequency regimes with respect to the camera frame rate and build simple jitter models based on its manifestation on the detector. The forward-model approach proves effective for low- and high-frequency regimes, but the inherent unpredictability of medium-frequency jitter may lead to model misspecification. As a test case we apply these models to the TOLIMAN mission, a forthcoming CubeSat telescope dedicated to detecting nearby Earth-analogue exoplanets through high-precision astrometry. Using Fisher information analysis, we quantify the effect of jitter on TOLIMAN's primary science observable -- the angular binary separation of the Alpha Centauri AB binary components. We find model misspecification does not introduce a systematic bias on the recovered binary separation except when fitting a one-dimensional jitter model to a two-dimensional motion, hence we recommend the use of a two-dimensional model. The forward-model approach offers a generalized method applicable to other telescope systems, including ongoing work with JWST's NIRISS instrument. This approach represents a significant step toward delivering higher accuracy measurements at modern observatories as demands on precision continue to rise.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper applies differentiable forward modeling to jitter in TOLIMAN astrometry and flags a 2D model need, but its no-bias claim rests on Fisher information that cannot confirm unbiased recovery under misspecification.

read the letter

The main takeaway is that this work uses dLux in JAX to forward-model jitter blurring across frequency regimes and applies it to simulated TOLIMAN binary separation measurements. It finds the approach works for low- and high-frequency cases and recommends a two-dimensional jitter model to avoid bias in the recovered separation. That is the concrete new piece: the regime categorization tied to detector manifestation plus the explicit 2D advice for this mission context. The use of an existing differentiable optics package is a practical choice that lets them simulate the effects cleanly and explore parameter sensitivity without custom code from scratch. Credit there for making the method accessible for other instruments like JWST NIRISS. The simulations are straightforward and the frequency split is a useful organizing idea for pointing stability problems. The soft spot is the central statistical claim. The abstract and analysis rely on Fisher information to argue that model misspecification does not introduce systematic bias on the separation except in the 1D-to-2D mismatch. Fisher information gives a variance bound assuming the model is correct and the estimator unbiased; it supplies no direct test for bias that appears precisely because the jitter model is wrong. The paper notes medium-frequency jitter is unpredictable and may cause misspecification, yet the reported results do not quantify how much that affects the science observable beyond the dimensionality case. All checks are on forward-simulated data with no real telescope observations or cross-check against independent methods, so the translation to actual measurements remains untested. This paper is for instrument teams and astrometry groups working on high-precision exoplanet missions or similar CubeSat projects. A reader already using differentiable modeling or dealing with pointing jitter would pick up the implementation details and the 2D recommendation. It is worth sending to peer review because the problem is real, the tool application is fresh for this use case, and the method is concrete enough that referees can check the simulations and statistical step directly. Expect questions on the bias analysis and on how the results hold once real data or more complex jitter enter the picture.

Referee Report

1 major / 1 minor

Summary. The paper introduces a differentiable forward-modeling method using the dLux framework in JAX to simulate and correct for telescope jitter effects on images. Jitter is divided into low-, medium-, and high-frequency categories based on camera frame rate, with models derived from detector manifestations. Applied to the TOLIMAN mission for measuring the angular separation of Alpha Centauri AB, Fisher information analysis on simulated data indicates that misspecification of the jitter model does not cause systematic bias in the separation estimate, except when using a 1D model for 2D jitter. The method is positioned as general for other telescopes including JWST NIRISS.

Significance. If substantiated, the differentiable forward-modeling approach could provide an efficient way to mitigate jitter-induced errors in high-precision astrometry, supporting exoplanet detection goals for missions like TOLIMAN. The JAX-based implementation enables gradient-based fitting and Fisher information calculations, which is a computational strength. The recommendation to use 2D jitter models to avoid bias is practical. However, the significance is limited by the absence of real-data validation and direct quantification of bias under misspecification.

major comments (1)

[Fisher information analysis] The central claim that Fisher information analysis shows model misspecification introduces no systematic bias on recovered binary separation (except in the 1D-to-2D case) is not supported by the analysis method. Fisher information supplies the Cramér-Rao bound assuming a correctly specified model and unbiased estimator; it provides no direct information on bias induced by misspecification (e.g., incorrect frequency regime or dimensionality). Direct Monte Carlo simulations fitting the misspecified model to data generated from the true jitter model, with reported bias values and uncertainties, are needed to substantiate the claim.

minor comments (1)

[Abstract] The abstract reports the absence of systematic bias but provides no quantitative values, error bars, or effect sizes for the bias or Fisher information results, which would aid assessment of practical impact.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed and constructive review. We address the single major comment below and will revise the manuscript to strengthen the central claim.

read point-by-point responses

Referee: The central claim that Fisher information analysis shows model misspecification introduces no systematic bias on recovered binary separation (except in the 1D-to-2D case) is not supported by the analysis method. Fisher information supplies the Cramér-Rao bound assuming a correctly specified model and unbiased estimator; it provides no direct information on bias induced by misspecification (e.g., incorrect frequency regime or dimensionality). Direct Monte Carlo simulations fitting the misspecified model to data generated from the true jitter model, with reported bias values and uncertainties, are needed to substantiate the claim.

Authors: We agree that the Fisher information matrix yields the Cramér-Rao lower bound only under the assumption of a correctly specified model and therefore cannot by itself demonstrate the presence or absence of bias when the model is misspecified. In the manuscript we used the Fisher matrix to quantify how different jitter-model assumptions affect the expected uncertainty on the binary separation parameter, and we compared the resulting covariance structures across models. This comparison led us to conclude that misspecification does not shift the recovered separation except in the 1D-to-2D case; however, we acknowledge that this inference is indirect. To address the referee’s concern directly, we will add Monte Carlo experiments to the revised manuscript. These will consist of (i) generating large ensembles of images from the true two-dimensional jitter model, (ii) fitting each realization with the misspecified models (wrong frequency regime or one-dimensional jitter), and (iii) reporting the mean recovered separation, its standard deviation, and the empirical bias relative to the known truth. The results will either confirm the original claim or allow us to qualify it with quantitative bias values. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's core analysis relies on forward-modeling jitter effects via dLux simulations followed by Fisher information calculations on those simulated datasets to quantify impacts on binary separation recovery. These steps use standard statistical tools on externally generated test cases rather than reducing any reported bias or precision result to a fitted parameter or self-referential definition by construction. No load-bearing self-citations, ansatzes smuggled via prior work, or renaming of known results appear in the provided abstract and claims; the derivation remains self-contained against the simulated benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that jitter manifests as simple, categorizable blurring on the detector that can be forward-modeled differentiably; no new physical entities are introduced, but several modeling choices function as free parameters.

free parameters (1)

jitter frequency cutoffs and amplitudes
Simple jitter models for low-, medium-, and high-frequency regimes are built from detector manifestation; these require choices or fits for cutoff frequencies and motion amplitudes.

axioms (1)

domain assumption Jitter can be adequately represented by frequency-regime-specific blurring kernels on the detector
Invoked when categorizing jitter and building the forward models used for both simulation and Fisher analysis.

pith-pipeline@v0.9.0 · 5581 in / 1528 out tokens · 103336 ms · 2026-05-07T13:01:25.233830+00:00 · methodology

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Reference graph

Works this paper leans on

45 extracted references · 16 canonical work pages

[1]

Probability 2003-04 , author=

Transforming Density Functions , url=. Probability 2003-04 , author=

2003
[2]

Google , publisher=

Pichai, Sundar , year=. Google , publisher=
[3]

GitHub , author=

SHM Jitter , howpublished=. GitHub , author=
[4]

MultiMedia LLC , title =
[5]

arXiv e-prints , keywords =

Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro. arXiv e-prints , keywords =
[6]

James Bradbury and Roy Frostig and Peter Hawkins and Matthew James Johnson and Chris Leary and Dougal Maclaurin and Skye Wanderman-Milne , title =
[7]

Matteo Hessel and David Budden and Fabio Viola and Mihaela Rosca and Eren Sezener and Tom Hennigan , title =
[8]

2021 , journal=

Patrick Kidger and Cristian Garcia , title=. 2021 , journal=

2021
[9]

and Granger, B

P\'erez, Fernando and Granger, Brian E. , Title =. Computing in Science and Engineering , Volume =. doi:10.1109/MCSE.2007.53 , publisher =

work page doi:10.1109/mcse.2007.53 2007
[10]

and Oliphant, T

Jones, E. and Oliphant, T. and Peterson, P. and Others , year =
[11]

Hunter, J. D. , Title =. Computing In Science & Engineering , Volume =
[12]

and Millman, K

Harris, Charles R. and Millman, K. Jarrod and van der Walt, St. Array programming with. Nature , Number =
[13]

2019 , publisher =

Brandon Dube , title =. 2019 , publisher =. doi:10.21105/joss.01352 , url =

work page doi:10.21105/joss.01352 2019
[14]

The Journal of Open Source Software , year = 2016, month = aug, volume = 1, eid =

ChainConsumer. The Journal of Open Source Software , year = 2016, month = aug, volume = 1, eid =. doi:10.21105/joss.00045 , adsurl =

work page doi:10.21105/joss.00045 2016
[16]

Space Telescopes and Instrumentation 2022: Optical, Infrared, and Millimeter Wave , year = 2022, editor =

Optical design, analysis, and calibration using Lux. Space Telescopes and Instrumentation 2022: Optical, Infrared, and Millimeter Wave , year = 2022, editor =. doi:10.1117/12.2629774 , adsurl =

work page doi:10.1117/12.2629774 2022
[17]

Diffractive Pupil Astrometry in the Toliman Space Telescope: PSF as local 2D Ruler , author=
[18]

IEEE Transactions on Image Processing , year = 2004, month = sep, volume =

Fundamental Performance Limits in Image Registration. IEEE Transactions on Image Processing , year = 2004, month = sep, volume =. doi:10.1109/TIP.2004.832923 , adsurl =

work page doi:10.1109/tip.2004.832923 2004
[19]

2019 , url=

A SURVEY OF THE SPACECRAFT LINE-OF-SIGHT JITTER PROBLEM , author=. 2019 , url=

2019
[20]

Bely and Olivia L

Pierre Y. Bely and Olivia L. Lupie and John L. Hershey , title =. Space Astronomical Telescopes and Instruments II , editor =. 1993 , doi =

1993
[21]

Pong , title =

Christopher M. Pong , title =. 32nd Annual AIAA/USU Conference on Small Satellites , location =. 2018 , month =

2018
[22]

2024 , eprint=

Differentiable Optics with dLux II: Optical Design Maximising Fisher Information , author=. 2024 , eprint=

2024
[23]

Journal of Astronomical Telescopes, Instruments, and Systems , keywords =

Differentiable optics with Lux: I deep calibration of flat field and phase retrieval with automatic differentiation. Journal of Astronomical Telescopes, Instruments, and Systems , keywords =. doi:10.1117/1.JATIS.9.2.028007 , archivePrefix =. 2406.08703 , primaryClass =

work page doi:10.1117/1.jatis.9.2.028007
[24]

James Bradbury and Roy Frostig and Peter Hawkins and Matthew James Johnson and Chris Leary and Dougal Maclaurin and George Necula and Adam Paszke and Jake Vander
[25]

Margossian, Charles C. , year=. A review of automatic differentiation and its efficient implementation , volume=. WIREs Data Mining and Knowledge Discovery , publisher=. doi:10.1002/widm.1305 , number=

work page doi:10.1002/widm.1305
[26]

Optical and Infrared Interferometry and Imaging VI , year = 2018, editor =

The TOLIMAN space telescope. Optical and Infrared Interferometry and Imaging VI , year = 2018, editor =. doi:10.1117/12.2313269 , adsurl =

work page doi:10.1117/12.2313269 2018
[27]

Space Telescopes and Instrumentation 2018: Optical, Infrared, and Millimeter Wave , year = 2018, editor =

Precision astrometry mission for exoplanet detection around binary stars. Space Telescopes and Instrumentation 2018: Optical, Infrared, and Millimeter Wave , year = 2018, editor =. doi:10.1117/12.2313919 , adsurl =

work page doi:10.1117/12.2313919 2018
[28]

Space Telescopes and Instrumentation 2024: Optical, Infrared, and Millimeter Wave , year = 2024, editor =

Getting to know the neighbours: Earth analogues in Alpha Centauri with the TOLIMAN space telescope. Space Telescopes and Instrumentation 2024: Optical, Infrared, and Millimeter Wave , year = 2024, editor =. doi:10.1117/12.3019256 , adsurl =

work page doi:10.1117/12.3019256 2024
[29]

Optical and Infrared Interferometry and Imaging IX , year = 2024, editor =

Differentiable modelling and data analysis for the JWST aperture masking interferometer. Optical and Infrared Interferometry and Imaging IX , year = 2024, editor =. doi:10.1117/12.3020303 , adsurl =

work page doi:10.1117/12.3020303 2024
[30]

Mathematical proceedings of the Cambridge philosophical society , volume=

Theory of statistical estimation , author=. Mathematical proceedings of the Cambridge philosophical society , volume=. 1925 , organization=

1925
[31]

Proceedings of the Royal Society of London

Two new properties of mathematical likelihood , author=. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character , volume=. 1934 , publisher=

1934
[32]

Biometrika , volume=

Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information , author=. Biometrika , volume=. 1978 , publisher=

1978
[33]

Automatic Control in Aerospace 1992 , pages=

The pointing stability of the Hubble Space Telescope and proposed concepts for the pointing control of the Next Generation Space Telescope (NGST) , author=. Automatic Control in Aerospace 1992 , pages=. 1993 , publisher=

1992
[34]

2021 , institution=

Spacecraft line-of-sight jitter management and mitigation lessons learned and engineering best practices , author=. 2021 , institution=

2021
[35]

Composable effects for flexible and acceler- ated probabilistic programming in numpyro.arXiv preprint arXiv:1912.11554, 2019

Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro , author=. arXiv preprint arXiv:1912.11554 , year=

work page arXiv 1912
[36]

Exoplanets , year = 2010, editor =

Exoplanet Transits and Occultations. Exoplanets , year = 2010, editor =. doi:10.48550/arXiv.1001.2010 , adsurl =

work page doi:10.48550/arxiv.1001.2010 2010
[37]

2016 , rating =

State of the Field: Extreme Precision Radial Velocities. Publications of the Astronomical Society of the Pacific , keywords =. doi:10.1088/1538-3873/128/964/066001 , archivePrefix =. 1602.07939 , primaryClass =

work page doi:10.1088/1538-3873/128/964/066001
[38]

, title =

Tuthill, Peter and Betters, Christopher and Charles, Max and Crous, Fred and Deagan, Conaire and Desdoigts, Louis and Doelman, David and George, Mark and Grattan, Kyran and Guyon, Olivier and Holland, Thomas and Klupa, Peter and Langford, Connor and Langker, Milo and Larkin, Kieran and Luka, Clarissa and Montet, Ben and Nelson, Jack and Pope, Benjamin and...
[39]

Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation VI , year = 2024, editor =

Strategies to mitigate effects of pointing error for the TOLIMAN space telescope. Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation VI , year = 2024, editor =. doi:10.1117/12.3019548 , adsurl =

work page doi:10.1117/12.3019548 2024
[40]

pysynphot: Synthetic photometry software package
[41]

SF2A-2016: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics , year = 2016, editor =

The PHOENIX Model Atmosphere Grid for Stars. SF2A-2016: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics , year = 2016, editor =

2016
[42]

2026 , month = jan, note =

BFS-U3-200S6M-C USB 3.1 Blackfly S Monochrome Camera: EMVA and Specification Documentation , author =. 2026 , month = jan, note =

2026
[43]

2025 , eprint=

Image reconstruction with the JWST Interferometer , author=. 2025 , eprint=

2025
[44]

2025 , eprint=

AMIGO: a Data-Driven Calibration of the JWST Interferometer , author=. 2025 , eprint=

2025
[45]

arXiv e-prints , keywords =

Natural Gradient Methods: Perspectives, Efficient-Scalable Approximations, and Analysis. arXiv e-prints , keywords =. doi:10.48550/arXiv.2303.05473 , archivePrefix =. 2303.05473 , primaryClass =

work page doi:10.48550/arxiv.2303.05473
[46]

Journal of Machine Learning Research , volume=

New insights and perspectives on the natural gradient method , author=. Journal of Machine Learning Research , volume=