pith. sign in

arxiv: 2607.01032 · v1 · pith:JIYPWCANnew · submitted 2026-07-01 · 🌌 astro-ph.IM

Point spread function wavefront recovery from in-focus stellar observations

Ezequiel Centofanti , Samuel Farrens , Jean-Luc Starck , Tobias Liaudat This is my paper

Pith reviewed 2026-07-02 05:32 UTC · model grok-4.3

classification 🌌 astro-ph.IM
keywords wavefront error recoverypoint spread function modellingin-focus observationsphase retrievalsemi-parametric PSF modeloptical system calibrationtelescope PSF
0
0 comments X

The pith

A new optimization method recovers wavefront errors to 3 percent from noisy in-focus stellar images alone

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

The paper shows how to improve recovery of the wavefront error field in the WaveDiff semi-parametric PSF model. Adding wavefront feature projections that link the model's parametric and learnable parts, together with more optimization cycles, lets the method reach roughly 3 percent relative error on the wavefront using only noisy, undersampled, in-focus polychromatic observations. This exploits the natural spatial variation of the PSF across the field of view and yields a tenfold reduction from the original 30 percent error while also lowering pixel-space PSF error. The approach is presented as the first to combine wide-field wavefront recovery, in-focus-only data, and non-parametric wavefront features inside one differentiable framework.

Core claim

Incorporating wavefront projections and increasing the number of optimisation cycles enables WaveDiff to recover the WFE with an error of approximately 3 % using only noisy, undersampled, in-focus observations. This represents a tenfold improvement over the original model while further reducing the pixel-space error.

What carries the argument

Wavefront feature projection that bridges the parametric and non-parametric components of WaveDiff during optimization

If this is right

  • Precise PSF modelling becomes possible for space telescopes without requiring out-of-focus calibration images.
  • Direct monitoring of telescope optics state is feasible from routine in-focus stellar fields, aiding malfunction detection.
  • Non-parametric wavefront features can now be used reliably for wide-field phase retrieval in polychromatic in-focus data.
  • Pixel-level PSF accuracy improves as a direct result of the better wavefront solution.

Where Pith is reading between the lines

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

  • The method could be tested on ground-based instruments if a model for atmospheric turbulence is added to the forward operator.
  • Future surveys might rely on this for on-orbit calibration using only the dense star fields already present in science exposures.
  • Extending the same projection idea to time-varying optics could allow tracking of thermal or mechanical drifts without dedicated calibration sequences.

Load-bearing premise

The spatial variation of the PSF across the field of view together with the differentiable forward model is enough to uniquely constrain the wavefront solution from in-focus data alone.

What would settle it

Recovery tests on real telescope data that still show more than 10 percent wavefront error after the projections and extra cycles are applied

Figures

Figures reproduced from arXiv: 2607.01032 by Ezequiel Centofanti, Jean-Luc Starck, Samuel Farrens, Tobias Liaudat.

Figure 1
Figure 1. Figure 1: Schematic of the WaveDiff optimisation scenario in Liaudat et al. (2023a). The black ovals denote the sets of physically feasible solutions in WFE space and pixel space. The ground-truth so￾lution fGT in WFE space, and SGT in pixel space, is indicated by a black star. The orange region represents the set of WaveDiff solutions, Fmodel, which does not include fGT. The solution ˆf1 ∈ Fmodel minimises er￾ror i… view at source ↗
Figure 2
Figure 2. Figure 2: Schematic of the proposed WaveDiff optimisation scenario. The left side shows the set of parametric solutions Fmodel, in orange, which includes the ground-truth solution fGT, indicated by a black star. Start￾ing from a solution f P init, the set of possible outcomes obtained through parametric-only optimisation {f P i } is shown in purple. One parametric￾only solution, ˆf P 1 , is shown in red. The set of … view at source ↗
Figure 3
Figure 3. Figure 3: WFE reconstruction relative error for the naive and iterative projection algorithms. The required correction, π Z∗ l,[i, j] , to apply to the parametric model in order to incorporate the information from the non￾parametric part can be expressed as π Z∗ l,[i, j] = π Z l,[i, j] + ∆π Z l,[i, j] . (25) In Appendix B, we show how we can remove the projected part from the non-parametric model, thus ensuring that… view at source ↗
Figure 4
Figure 4. Figure 4: Estimated Zernike coefficients for the two projection algo￾rithms, compared to the fiducial values (GT). 0 10 20 30 40 50 60 70 Epoch 10¡8 10¡7 Loss Reset No reset [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Loss function as a function of the number of epochs for the non-parametric part of the model in the second optimisation cycle. One model has been reset after performing the projection, and the other model has not been reset. to emphasise that projecting the wavefront features does not alter the overall WFE representation; rather, it redistributes it between its two components, the parametric contribution Φ… view at source ↗
Figure 6
Figure 6. Figure 6: WaveDiff simulations at three different positions in the FOV. First row: the noisy, low-resolution stars; second row: the noiseless, highly resolved observations; third row: the WFE at the correspond￾ing FOV positions. 6. Experimental results We test the proposed optimisation framework incorporating the wavefront feature projection. A fiducial PSF field is generated using the same simulator as in Liaudat e… view at source ↗
Figure 9
Figure 9. Figure 9: Ground truth and predicted PSF for a noiseless in-focus star. Ground Truth WFE Predicted WFE −0.4 −0.2 0.0 0.2 0.4 Wavefront Error [ µm] −0.4 −0.2 0.0 0.2 0.4 Wavefront Error [ µm] [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Ground truth and predicted WFE for a noiseless in-focus star. We fit the single non-parametric wavefront feature using an Adam optimiser for 100 epochs, with a learning rate of 0.03. The recovered PSF and WFE are shown in [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 8
Figure 8. Figure 8: Relative pixel error at observation resolution (LR) and super￾resolution (SR) across the 12 optimisation cycles. The "Ours (Full)" model uses both parametric and non-parametric parts for inference, while the "Ours (Param)" model uses only the parametric part. The grey lines show the results of the original optimisation scenario. performs slightly better it in pixel space. This behaviour is ex￾pected since … view at source ↗
Figure 11
Figure 11. Figure 11: Evolution of different WFE parts of the model as the number cycle increases. The same scale is used for all the images in each figure. the parametric model. As the cycles progress, the magnitude of this contribution decreases, indicating that the non-parametric model has progressively less to correct and giving a clear sign of convergence. Moreover, the non-parametric contribution closely reproduces the r… view at source ↗
read the original abstract

Recovering the wavefront error (WFE) field of an optical system from intensity in-focus observations is a challenging inverse problem with broad implications for telescope point spread function (PSF) modelling. Accurate WFE recovery enables both precise PSF modelling and direct insight into the state of the telescope optics, facilitating the detection of potential malfunctions. Recently, non-parametric PSF models have shown promising performance in modelling complex optical systems in space-based telescopes. WaveDiff is a semi-parametric PSF model that represents the PSF in wavefront space by combining parametric and learnable features with a differentiable forward optical model. This parameterisation enables phase retrieval from in-focus observations by exploiting the spatial variation of the PSF across the field of view (FOV). The original version of WaveDiff achieves outstanding PSF recovery results in pixel space; however, the recovered WFE is far from the ground truth, with a relative error of around $30 \%$. In this paper, we present a new optimisation scenario that bridges WaveDiff's parametric and non-parametric components through wavefront feature projection, yielding a substantial improvement in WFE recovery and making WaveDiff the first demonstrated method to combine wide-field WFE recovery, in-focus-only polychromatic observations, and non-parametric wavefront features in a single framework. We show that incorporating wavefront projections and increasing the number of optimisation cycles enables WaveDiff to recover the WFE with an error of approximately $3 \%$ using only noisy, undersampled, in-focus observations. This represents a tenfold improvement over the original model while further reducing the pixel-space error. The code to reproduce the results of this article is publicly available at https://github.com/tobias-liaudat/wf-psf/tree/v1.4.0

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.

Referee Report

3 major / 2 minor

Summary. The paper introduces an updated optimization procedure for the WaveDiff semi-parametric PSF model. By adding wavefront feature projections that bridge its parametric and non-parametric components and by increasing the number of optimization cycles, the method recovers the wavefront error (WFE) field to ~3% relative error from noisy, undersampled, polychromatic in-focus stellar images alone. This is presented as a tenfold improvement over the original WaveDiff's ~30% WFE error while also lowering pixel-space PSF error; the approach is claimed to be the first to combine wide-field WFE recovery, in-focus-only data, and non-parametric wavefront features.

Significance. If the reported WFE recovery is shown to be unique and not an artifact of the simulation or optimization, the result would be significant for space-based telescope calibration: it would enable direct wavefront diagnostics and high-fidelity PSF modeling without requiring out-of-focus or monochromatic data, with the released code providing a reproducible baseline for further work.

major comments (3)
  1. [§3 and §4] §3 (method) and §4 (results): the central claim that wavefront projections plus extra cycles yield a unique WFE solution from in-focus data rests on the assertion that PSF spatial variation across the FOV supplies sufficient constraints, yet no identifiability analysis, no ablation that removes the projection step, and no multi-start optimization from varied initializations are reported to show convergence to the same WFE rather than to different minima that still match the intensity data.
  2. [§4.1–4.2] §4.1–4.2 and associated tables/figures: the 3% WFE error is demonstrated only on simulated ground-truth data whose generation details (optical model, noise model, exact polychromatic integration) are not cross-checked against an independent forward model; without this, it remains unclear whether the reported improvement reflects genuine inverse-problem solution or consistency with the same differentiable model used for training.
  3. [§3.2] Eq. (wavefront projection definition, §3.2): the projection operator that couples parametric and non-parametric components is introduced without a proof or numerical test that it reduces the null-space dimension of the intensity-to-WFE map; if the mapping remains many-to-one after projection, the tenfold error reduction on simulated data does not establish that the method solves the inverse problem in general.
minor comments (2)
  1. [Abstract and §1] The abstract and §1 cite the original WaveDiff error as “around 30 %” and the new result as “approximately 3 %”; explicit numerical values with standard deviations across multiple realizations should be stated in the text and tables for reproducibility.
  2. [§4 and figures] Figure captions and §4 lack a clear statement of the exact metric used for “relative WFE error” (RMS over what aperture? normalized by what quantity?).

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough and constructive review. The comments highlight important aspects of identifiability and validation that we address below. We will revise the manuscript accordingly where feasible.

read point-by-point responses

  1. Referee: [§3 and §4] §3 (method) and §4 (results): the central claim that wavefront projections plus extra cycles yield a unique WFE solution from in-focus data rests on the assertion that PSF spatial variation across the FOV supplies sufficient constraints, yet no identifiability analysis, no ablation that removes the projection step, and no multi-start optimization from varied initializations are reported to show convergence to the same WFE rather than to different minima that still match the intensity data.

    Authors: We agree that explicit checks for uniqueness would strengthen the claim. In the revised manuscript we will add an ablation study (with and without the projection operator) and multi-start optimization results from varied initializations in §4, demonstrating convergence to the same low-error WFE solution across runs. revision: yes

  2. Referee: [§4.1–4.2] §4.1–4.2 and associated tables/figures: the 3% WFE error is demonstrated only on simulated ground-truth data whose generation details (optical model, noise model, exact polychromatic integration) are not cross-checked against an independent forward model; without this, it remains unclear whether the reported improvement reflects genuine inverse-problem solution or consistency with the same differentiable model used for training.

    Authors: The data are generated with the differentiable model described in the paper and released code. To address the concern we will add, in the revised §4, a cross-check against an independent non-differentiable optical simulator for a subset of fields, confirming that noise and polychromatic integration details are reproduced. revision: yes

  3. Referee: [§3.2] Eq. (wavefront projection definition, §3.2): the projection operator that couples parametric and non-parametric components is introduced without a proof or numerical test that it reduces the null-space dimension of the intensity-to-WFE map; if the mapping remains many-to-one after projection, the tenfold error reduction on simulated data does not establish that the method solves the inverse problem in general.

    Authors: We will add a numerical experiment in revised §3.2 showing that the projection measurably reduces WFE variance across random initializations. A general mathematical proof that the null-space dimension is reduced for arbitrary optical systems lies beyond the scope of the present work; the empirical improvement on the tested cases is the primary evidence offered. revision: partial

Circularity Check

0 steps flagged

No significant circularity; empirical optimization improvement stands on independent simulation benchmarks

full rationale

The paper reports an empirical result: adding wavefront feature projections and extra optimization cycles to the existing WaveDiff differentiable forward model reduces WFE recovery error from ~30% to ~3% on noisy, undersampled, in-focus simulated data. This is framed as a change in the optimization procedure rather than a closed-form derivation. No equation is shown to equal its own input by construction, no fitted parameter is relabeled as a prediction, and no uniqueness theorem is imported via self-citation to force the result. The spatial-variation constraint is asserted as sufficient but is tested directly against ground-truth simulations, providing an external check. The public code further allows independent reproduction. These elements keep the central claim self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient detail to enumerate specific free parameters, axioms, or invented entities; the approach relies on the differentiability of the optical forward model and PSF spatial variation, but these are not quantified here.

pith-pipeline@v0.9.1-grok · 5848 in / 1114 out tokens · 30057 ms · 2026-07-02T05:32:13.225761+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

299 extracted references · 200 canonical work pages · 18 internal anchors

  1. [1]

    2022 , MONTH = Oct, KEYWORDS =

    Liaudat, Tobias Ignacio , URL =. 2022 , MONTH = Oct, KEYWORDS =

    2022

  2. [2]

    Artificial intelligence and statistics , pages=

    The loss surfaces of multilayer networks , author=. Artificial intelligence and statistics , pages=. 2015 , organization=

    2015

  3. [3]

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

    Differentiable optics with∂ Lux: I—deep calibration of flat field and phase retrieval with automatic differentiation , author=. Journal of Astronomical Telescopes, Instruments, and Systems , volume=. 2023 , publisher=

    2023

  4. [4]

    Euclid. I. Overview of the Euclid mission , author=. Astronomy & Astrophysics , year=

  5. [5]

    Euclid. I. Overview of the Euclid mission , author=. 2024 , eprint=

    2024

  6. [6]

    and Tyson, J

    Ivezić, Zeljko and Kahn, Steven M. and Tyson, J. Anthony and Abel, Bob and Acosta, Emily and Allsman, Robyn and Alonso, David and AlSayyad, Yusra and Anderson, Scott F. and Andrew, John and P. Angel, James Roger and Angeli, George Z. and Ansari, Reza and Antilogus, Pierre and Araujo, Constanza and Armstrong, Robert and Arndt, Kirk T. and Astier, Pierre an...

    work page doi:10.3847/1538-4357/ab042c

  7. [7]

    2019 , eprint=

    The Wide Field Infrared Survey Telescope: 100 Hubbles for the 2020s , author=. 2019 , eprint=

    2019

  8. [8]

    doi:10.1117/12.2630072 , editor =

    Space Telescopes and Instrumentation 2022: Optical, Infrared, and Millimeter Wave , date-added =. doi:10.1117/12.2630072 , editor =

    work page doi:10.1117/12.2630072 2022

  9. [9]

    arXiv preprint arXiv:2501.01912 , year=

    Exoplanet Detection via Differentiable Rendering , author=. arXiv preprint arXiv:2501.01912 , year=

    work page arXiv

  10. [10]

    Wiley interdisciplinary reviews: data mining and knowledge discovery , volume=

    A review of automatic differentiation and its efficient implementation , author=. Wiley interdisciplinary reviews: data mining and knowledge discovery , volume=. 2019 , publisher=

    2019

  11. [11]

    AMIGO: a Data-Driven Calibration of the JWST Interferometer

    AMIGO: a Data-Driven Calibration of the JWST Interferometer , author=. arXiv preprint arXiv:2510.09806 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  12. [12]

    Louis Desdoigts and Benjamin J. S. Pope and Jordan Dennis and Peter G. Tuthill , date-added =. 2023 , bdsk-url-1 =. doi:10.1117/1.JATIS.9.2.028007 , journal =

    work page doi:10.1117/1.jatis.9.2.028007 2023

  13. [13]

    arXiv , author =:2406.08704 , journal =

    doi:10.48550/arXiv.2406.08704 , eid =. arXiv , author =:2406.08704 , journal =

    work page doi:10.48550/arxiv.2406.08704

  14. [14]

    Frontiers in Astronomy and Space Sciences , title =

    Liaudat, Tob. Frontiers in Astronomy and Space Sciences , title =. 2023 , bdsk-url-1 =. doi:10.3389/fspas.2023.1158213 , issn =

    work page doi:10.3389/fspas.2023.1158213 2023

  15. [15]

    Rethinking data-driven point spread function modeling with a differentiable optical model , url =

    Tobias Liaudat and Jean-Luc Starck and Martin Kilbinger and Pierre-Antoine Frugier , date-added =. Rethinking data-driven point spread function modeling with a differentiable optical model , url =. 2023 , bdsk-url-1 =. doi:10.1088/1361-6420/acb664 , journal =

    work page doi:10.1088/1361-6420/acb664 2023

  16. [16]

    doi:10.1051/0004-6361/202243970 , journal =

    ShapePipe: A modular weak-lensing processing and analysis pipeline , url =. doi:10.1051/0004-6361/202243970 , journal =

    work page doi:10.1051/0004-6361/202243970

  17. [17]

    doi:10.1051/0004-6361/200913524 , journal =

    Weak lensing power spectra for precision cosmology - Multiple-deflection, reduced shear, and lensing bias corrections , url =. doi:10.1051/0004-6361/200913524 , journal =

    work page doi:10.1051/0004-6361/200913524

  18. [18]

    Publications of the Astronomical Society of Japan , month =

    Li, Xiangchong and Miyatake, Hironao and Luo, Wentao and More, Surhud and Oguri, Masamune and Hamana, Takashi and Mandelbaum, Rachel and Shirasaki, Masato and Takada, Masahiro and Armstrong, Robert and Kannawadi, Arun and Takita, Satoshi and Miyazaki, Satoshi and Nishizawa, Atsushi J and Plazas Malagon, Andres A and Strauss, Michael A and Tanaka, Masayuki...

    work page doi:10.1093/pasj/psac006 2022

  19. [19]

    2012, , 427, 127, 10.1111/j.1365-2966.2012.21948.x

    Heymans, Catherine and van Waerbeke, Ludovic and Miller, Lance and Erben, Thomas and Hildebrandt, Hendrik and Hoekstra, Henk and Kitching, Thomas D. and Mellier, Yannick and Simon, Patrick and Bonnett, Christopher and Coupon, Jean and Fu, Liping and Harnois-D. Monthly Notices of the Royal Astronomical Society , month =. 2012 , bdsk-url-1 =. doi:10.1111/j....

    work page doi:10.1111/j.1365-2966.2012.21952.x 2012

  20. [20]

    Mugnier and Amandine Blanc and

    Laurent M. Mugnier and Amandine Blanc and. Phase Diversity: A Technique for Wave-Front Sensing and for Diffraction-Limited Imaging , url =. 2006 , bdsk-url-1 =. doi:https://doi.org/10.1016/S1076-5670(05)41001-0 , editor =

    work page doi:10.1016/s1076-5670(05)41001-0 2006

  21. [21]

    Applied optics , volume=

    Phase-retrieval algorithms for a complicated optical system , author=. Applied optics , volume=. 1993 , publisher=

    1993

  22. [22]

    J. R. Fienup and J. C. Marron and T. J. Schulz and J. H. Seldin , date-added =. Hubble Space Telescope characterized by using phase-retrieval algorithms , url =. 1993 , bdsk-file-1 =. doi:10.1364/AO.32.001747 , journal =

    work page doi:10.1364/ao.32.001747 1993

  23. [23]

    and Bardsley, Johnathan M

    Joyce, Kevin T. and Bardsley, Johnathan M. and Luttman, Aaron , date-added =. Point Spread Function Estimation in X-Ray Imaging with Partially Collapsed Gibbs Sampling , url =. SIAM Journal on Scientific Computing , number =. 2018 , bdsk-url-1 =. doi:10.1137/17M1149250 , eprint =

    work page doi:10.1137/17m1149250 2018

  24. [24]

    , date-added =

    Dougherty, Geoff and Kawaf, Z. , date-added =. The point spread function revisited: Image restoration using 2-D deconvolution , volume =. 2001 , bdsk-url-1 =. doi:10.1053/radi.2001.0341 , journal =

    work page doi:10.1053/radi.2001.0341 2001

  25. [25]

    2016 , bdsk-url-1 =

    M. 2016 , bdsk-url-1 =

    2016

  26. [26]

    The Euclid Wide Survey , url =

    Euclid preparation - I. The Euclid Wide Survey , url =. doi:10.1051/0004-6361/202141938 , journal =

    work page doi:10.1051/0004-6361/202141938

  27. [27]

    doi:10.1086/143864 , journal =

    work page doi:10.1086/143864

  28. [28]

    Measurements of Omega and Lambda from 42 High-Redshift Supernovae

    S. Perlmutter and G. Aldering and G. Goldhaber and R. A. Knop and P. Nugent and P. G. Castro and S. Deustua and S. Fabbro and A. Goobar and D. E. Groom and I. M. Hook and A. G. Kim and M. Y. Kim and J. C. Lee and N. J. Nunes and R. Pain and C. R. Pennypacker and R. Quimby and C. Lidman and R. S. Ellis and M. Irwin and R. G. McMahon and P. Ruiz-Lapuente an...

    work page internal anchor Pith review doi:10.1086/307221

  29. [29]

    Report of the Dark Energy Task Force

    Albrecht, Andreas and Bernstein, Gary and Cahn, Robert and Freedman, Wendy L. and Hewitt, Jacqueline and Hu, Wayne and Huth, John and Kamionkowski, Marc and Kolb, Edward W. and Knox, Lloyd and Mather, John C. and Staggs, Suzanne and Suntzeff, Nicholas B. , copyright =. Report of the Dark Energy Task Force , url =. 2006 , bdsk-url-1 =. doi:10.48550/ARXIV.A...

    work page internal anchor Pith review doi:10.48550/arxiv.astro-ph/0609591 2006

  30. [30]

    The NISP photometric system , url =

    Euclid preparation - XVIII. The NISP photometric system , url =. doi:10.1051/0004-6361/202142897 , journal =

    work page doi:10.1051/0004-6361/202142897

  31. [31]

    Dependencies on methods, simulation parameters, and measured parameters , url =

    Shear measurement bias - I. Dependencies on methods, simulation parameters, and measured parameters , url =. doi:10.1051/0004-6361/202038657 , journal =

    work page doi:10.1051/0004-6361/202038657

  32. [32]

    Monthly Notices of the Royal Astronomical Society , month =

    MacCrann, N and Becker, M R and McCullough, J and Amon, A and Gruen, D and Jarvis, M and Choi, A and Troxel, M A and Sheldon, E and Yanny, B and Herner, K and Dodelson, S and Zuntz, J and Eckert, K and Rollins, R P and Varga, T N and Bernstein, G M and Gruendl, R A and Harrison, I and Hartley, W G and Sevilla-Noarbe, I and Pieres, A and Bridle, S L and My...

    work page doi:10.1093/mnras/stab2870 2021

  33. [33]

    2012, , 427, 127, 10.1111/j.1365-2966.2012.21948.x

    Melchior, P. and Viola, M. , date-added =. Monthly Notices of the Royal Astronomical Society , month =. 2012 , bdsk-url-1 =. doi:10.1111/j.1365-2966.2012.21381.x , eprint =

    work page doi:10.1111/j.1365-2966.2012.21381.x 2012

  34. [34]

    Monthly Notices of the Royal Astronomical Society , month =

    Kacprzak, Tomasz and Bridle, Sarah and Rowe, Barnaby and Voigt, Lisa and Zuntz, Joe and Hirsch, Michael and MacCrann, Niall , date-added =. Monthly Notices of the Royal Astronomical Society , month =. 2014 , bdsk-url-1 =. doi:10.1093/mnras/stu588 , eprint =

    work page doi:10.1093/mnras/stu588 2014

  35. [35]

    Sheldon and Matthew R

    Erin S. Sheldon and Matthew R. Becker and Niall MacCrann and Michael Jarvis , date-added =. Mitigating Shear-dependent Object Detection Biases with Metacalibration , url =. doi:10.3847/1538-4357/abb595 , journal =

    work page doi:10.3847/1538-4357/abb595

  36. [36]

    Schneider and David W

    Michael D. Schneider and David W. Hogg and Philip J. Marshall and William A. Dawson and Joshua Meyers and Deborah J. Bard and Dustin Lang , date-added =. doi:10.1088/0004-637x/807/1/87 , journal =

    work page doi:10.1088/0004-637x/807/1/87

  37. [37]

    Boletin de la Asociacion Argentina de Astronomia La Plata Argentina , month = feb, pages =

  38. [38]

    doi:10.1051/0004-6361/201833775 , journal =

    Weak-lensing shear measurement with machine learning - Teaching artificial neural networks about feature noise , url =. doi:10.1051/0004-6361/201833775 , journal =

    work page doi:10.1051/0004-6361/201833775

  39. [39]

    Joseph J. Mohr and Robert Armstrong and Emmanuel Bertin and Greg Daues and Shantanu Desai and Michelle Gower and Robert Gruendl and William Hanlon and Nikolay Kuropatkin and Huan Lin and John Marriner and Donald Petravic and Ignacio Sevilla and Molly Swanson and Todd Tomashek and Douglas Tucker and Brian Yanny , booktitle =. The Dark Energy Survey data pr...

    work page doi:10.1117/12.926785

  40. [40]

    Desai and R

    S. Desai and R. Armstrong and J. J. Mohr and D. R. Semler and J. Liu and E. Bertin and S. S. Allam and W. A. Barkhouse and G. Bazin and E. J. Buckley-Geer and M. C. Cooper and S. M. Hansen and F. W. High and H. Lin and Y.-T. Lin and C.-C. Ngeow and A. Rest and J. Song and D. Tucker and A. Zenteno , date-added =. doi:10.1088/0004-637x/757/1/83 , journal =

    work page doi:10.1088/0004-637x/757/1/83

  41. [41]

    doi:10.1051/0004-6361/202141166 , journal =

    Deep transfer learning for blended source identification in galaxy survey data , url =. doi:10.1051/0004-6361/202141166 , journal =

    work page doi:10.1051/0004-6361/202141166

  42. [42]

    Melchior and F

    P. Melchior and F. Moolekamp and M. Jerdee and R. Armstrong and A.-L. Sun and J. Bosch and R. Lupton , date-added =. Scarlet: Source separation in multi-band images by Constrained Matrix Factorization , url =. Astronomy and Computing , keywords =. 2018 , bdsk-url-1 =. doi:https://doi.org/10.1016/j.ascom.2018.07.001 , issn =

    work page doi:10.1016/j.ascom.2018.07.001 2018

  43. [43]

    doi:10.1038/s42254-021-00353-y , journal =

    work page doi:10.1038/s42254-021-00353-y

  44. [44]

    E. A. Magnier and J.-C. Cuillandre , date-added =. The Elixir System: Data Characterization and Calibration at the Canada-France-Hawaii Telescope , url =. doi:10.1086/420756 , journal =

    work page doi:10.1086/420756

  45. [45]

    Astronomical Data Analysis Software and Systems XXVII , date-added =

  46. [46]

    Stephen D. J. Gwyn , date-added =. doi:10.1086/526794 , journal =

    work page doi:10.1086/526794

  47. [47]

    Publications of the Astronomical Society of Japan , month =

    Bosch, James and Armstrong, Robert and Bickerton, Steven and Furusawa, Hisanori and Ikeda, Hiroyuki and Koike, Michitaro and Lupton, Robert and Mineo, Sogo and Price, Paul and Takata, Tadafumi and Tanaka, Masayuki and Yasuda, Naoki and AlSayyad, Yusra and Becker, Andrew C and Coulton, William and Coupon, Jean and Garmilla, Jose and Huang, Song and Krughof...

    work page doi:10.1093/pasj/psx080 2017

  48. [48]

    Publications of the Astronomical Society of Japan , month =

    Mandelbaum, Rachel and Miyatake, Hironao and Hamana, Takashi and Oguri, Masamune and Simet, Melanie and Armstrong, Robert and Bosch, James and Murata, Ryoma and Lanusse, Fran. Publications of the Astronomical Society of Japan , month =. 2017 , bdsk-url-1 =. doi:10.1093/pasj/psx130 , eprint =

    work page doi:10.1093/pasj/psx130 2017

  49. [49]

    The many flavours of photometric redshifts

    Salvato, Mara and Ilbert, Olivier and Hoyle, Ben , copyright =. The many flavours of photometric redshifts , url =. 2018 , bdsk-url-1 =. doi:10.48550/ARXIV.1805.12574 , keywords =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1805.12574 2018

  50. [50]

    Monthly Notices of the Royal Astronomical Society , month =

    Kilbinger, Martin and Heymans, Catherine and Asgari, Marika and Joudaki, Shahab and Schneider, Peter and Simon, Patrick and Van Waerbeke, Ludovic and Harnois-D. Monthly Notices of the Royal Astronomical Society , month =. 2017 , bdsk-url-1 =. doi:10.1093/mnras/stx2082 , eprint =

    work page doi:10.1093/mnras/stx2082 2017

  51. [51]

    doi:10.1086/171151 , journal =

    work page doi:10.1086/171151

  52. [52]

    doi:10.1086/145672 , journal =

    work page doi:10.1086/145672

  53. [53]

    Weak lensing analysis of the Canada-France Imaging Survey : from pixels to cosmology, preparation for the Euclid mission , url =

    Guinot, Axel , date-added =. Weak lensing analysis of the Canada-France Imaging Survey : from pixels to cosmology, preparation for the Euclid mission , url =. 2020 , bdsk-url-1 =

    2020

  54. [54]

    , date-added =

    Schmitz, Morgan A. , date-added =. Euclid weak lensing : PSF field estimation , url =. 2019 , bdsk-url-1 =

    2019

  55. [55]

    Higher order statistics for cosmology : likelihood development for future surveys like Euclid , url =

    Ajani, Virginia , date-added =. Higher order statistics for cosmology : likelihood development for future surveys like Euclid , url =. 2021 , bdsk-url-1 =

    2021

  56. [56]

    Estimators and covariances , url =

    Analysis of two-point statistics of cosmic shear - I. Estimators and covariances , url =. doi:10.1051/0004-6361:20021341 , journal =

    work page doi:10.1051/0004-6361:20021341

  57. [57]

    Monthly Notices of the Royal Astronomical Society , month =

    Jeffrey, N and Gatti, M and Chang, C and Whiteway, L and Demirbozan, U and Kovacs, A and Pollina, G and Bacon, D and Hamaus, N and Kacprzak, T and Lahav, O and Lanusse, F and Mawdsley, B and Nadathur, S and Starck, J L and Vielzeuf, P and Zeurcher, D and Alarcon, A and Amon, A and Bechtol, K and Bernstein, G M and Campos, A and Rosell, A Carnero and Kind,...

    work page doi:10.1093/mnras/stab1495 2021

  58. [58]

    doi:10.1051/0004-6361/202039451 , journal =

    Weak-lensing mass reconstruction using sparsity and a Gaussian random field , url =. doi:10.1051/0004-6361/202039451 , journal =

    work page doi:10.1051/0004-6361/202039451

  59. [59]

    doi:10.1051/0004-6361/201628278 , journal =

    High resolution weak lensing mass mapping combining shear and flexion , url =. doi:10.1051/0004-6361/201628278 , journal =

    work page doi:10.1051/0004-6361/201628278

  60. [60]

    Monthly Notices of the Royal Astronomical Society , month =

    Jeffrey, Niall and Lanusse, Fran. Monthly Notices of the Royal Astronomical Society , month =. 2020 , bdsk-url-1 =. doi:10.1093/mnras/staa127 , eprint =

    work page doi:10.1093/mnras/staa127 2020

  61. [61]

    , keywords =

    Pires, S. and Starck, J.-L. and Amara, A. and Teyssier, R. and R. Monthly Notices of the Royal Astronomical Society , month =. 2009 , bdsk-url-1 =. doi:10.1111/j.1365-2966.2009.14625.x , eprint =

    work page doi:10.1111/j.1365-2966.2009.14625.x 2009

  62. [62]

    doi:10.1086/172297 , journal =

    work page doi:10.1086/172297

  63. [63]

    Troxel and Mustapha Ishak , date-added =

    M.A. Troxel and Mustapha Ishak , date-added =. The intrinsic alignment of galaxies and its impact on weak gravitational lensing in an era of precision cosmology , url =. Physics Reports , keywords =. 2015 , bdsk-url-1 =. doi:https://doi.org/10.1016/j.physrep.2014.11.001 , issn =

    work page doi:10.1016/j.physrep.2014.11.001 2015

  64. [64]

    Goldberg and David J

    David M. Goldberg and David J. Bacon , date-added =. Galaxy-Galaxy Flexion: Weak Lensing to Second Order , url =. doi:10.1086/426782 , journal =

    work page doi:10.1086/426782

  65. [65]

    arXiv , author =:astro-ph/9408050 , journal =

    work page internal anchor Pith review Pith/arXiv arXiv

  66. [66]

    arXiv , author =:astro-ph/9407032 , journal =

    work page internal anchor Pith review Pith/arXiv arXiv

  67. [67]

    arXiv , author =:astro-ph/9601079 , journal =

    work page internal anchor Pith review Pith/arXiv arXiv

  68. [68]

    The Born and lens

    Charles Shapiro and Asantha Cooray , date-added =. The Born and lens. doi:10.1088/1475-7516/2006/03/007 , journal =

    work page doi:10.1088/1475-7516/2006/03/007 2006

  69. [69]

    doi:10.1007/978-3-662-03758-4 , publisher =

    work page doi:10.1007/978-3-662-03758-4

  70. [70]

    2020, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/201833910 , 641, A6

    Planck 2018 results - VI. Cosmological parameters , url =. doi:10.1051/0004-6361/201833910 , journal =

    work page doi:10.1051/0004-6361/201833910 2018

  71. [71]

    Light propagation in arbitrary spacetimes and the gravitational lens approximation , url =

    Stella Seitz and Peter Schneider and J. Light propagation in arbitrary spacetimes and the gravitational lens approximation , url =. doi:10.1088/0264-9381/11/9/016 , journal =

    work page doi:10.1088/0264-9381/11/9/016

  72. [72]

    Weak Gravitational Lensing by Large-Scale Structure , url =

    Refregier, Alexandre , date-added =. Weak Gravitational Lensing by Large-Scale Structure , url =. Annual Review of Astronomy and Astrophysics , number =. 2003 , bdsk-url-1 =. doi:10.1146/annurev.astro.41.111302.102207 , eprint =

    work page doi:10.1146/annurev.astro.41.111302.102207 2003

  73. [73]

    2012, , 427, 127, 10.1111/j.1365-2966.2012.21948.x

    Refregier, Alexandre and Kacprzak, Tomasz and Amara, Adam and Bridle, Sarah and Rowe, Barnaby , date-added =. Monthly Notices of the Royal Astronomical Society , month =. 2012 , bdsk-url-1 =. doi:10.1111/j.1365-2966.2012.21483.x , eprint =

    work page doi:10.1111/j.1365-2966.2012.21483.x 2012

  74. [74]

    Jarvis and G

    M. Jarvis and G. M. Bernstein and P. Fischer and D. Smith and B. Jain and J. A. Tyson and D. Wittman , date-added =. Weak-Lensing Results from the 75 Square Degree Cerro Tololo Inter-American Observatory Survey , url =. doi:10.1086/367799 , journal =

    work page doi:10.1086/367799

  75. [75]

    , eprint =

    Matthias Bartelmann and Peter Schneider , date-added =. Weak gravitational lensing , url =. Physics Reports , number =. 2001 , bdsk-url-1 =. doi:https://doi.org/10.1016/S0370-1573(00)00082-X , issn =

    work page doi:10.1016/s0370-1573(00)00082-x 2001

  76. [76]

    Laureijs and G

    R. Laureijs and G. D. Racca and Y. Mellier and P. Musi and L. Brouard and T. B. Space Telescopes and Instrumentation 2020: Optical, Infrared, and Millimeter Wave , date-added =. 2020 , bdsk-url-1 =. doi:10.1117/12.2563145 , editor =

    work page doi:10.1117/12.2563145 2020

  77. [77]

    Gaspar Venancio and Lionel Carminati and Jose Lorenzo Alvarez and J

    Luis M. Gaspar Venancio and Lionel Carminati and Jose Lorenzo Alvarez and J. Space Telescopes and Instrumentation 2016: Optical, Infrared, and Millimeter Wave , date-added =. 2016 , bdsk-url-1 =. doi:10.1117/12.2232842 , editor =

    work page doi:10.1117/12.2232842 2016

  78. [78]

    Shear Measurement with Poorly Resolved Images , url =

    Zhang, Jun and Liu, Cong and Vaquero, Pedro Alonso and Li, Hekun and Wang, Haoran and Shen, Zhi and Dong, Fuyu , copyright =. Shear Measurement with Poorly Resolved Images , url =. 2022 , bdsk-url-1 =. doi:10.48550/ARXIV.2206.02434 , keywords =

    work page doi:10.48550/arxiv.2206.02434 2022

  79. [79]

    Tolerance For the Pixelation Effect in Shear Measurement , url =

    Shen, Zhi and Zhang, Jun and Li, Hekun and Wang, Haoran and Wei, Chengliang and Li, Guoliang and Li, Xiaobo and Ban, Zhang and Yue, Dan , copyright =. Tolerance For the Pixelation Effect in Shear Measurement , url =. 2022 , bdsk-url-1 =. doi:10.48550/ARXIV.2206.01377 , keywords =

    work page doi:10.48550/arxiv.2206.01377 2022

  80. [80]

    doi:10.1146/annurev.aa.31.090193.000305 , journal =

    work page doi:10.1146/annurev.aa.31.090193.000305

Showing first 80 references.