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Pixelization effects in cosmic shear angular power spectra

T0 review · 1 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper gives the first derivation of the HEALPix pixel window function for spin-2 cosmic shear spectra from discrete galaxy catalogues, and supplies correction models that hold pixelization biases below one percent up to roughly the…

desk verdict A genuinely new spin-2 HEALPix window derivation, rigorously tested on Poisson sources, but its own §3.6 concedes the clustering assumptions that keep it from being directly survey-ready; still worth serious refereeing. read the letter →

arxiv 2501.08718 v2 pith:2WMAKEAR submitted 2025-01-15 astro-ph.CO

Alex Hall , Nicolas Tessore This is my paper · ORCID
classification astro-ph.CO
keywords cosmicshearweaklensingpseudo-CℓpowerspectraHEALPixpixelwindowfunctionaliasinggalaxysurveysystematicsspin-2fieldsparalleltransport
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Cosmic shear surveys turn millions of galaxy shape measurements into pixelized maps, then read cosmological parameters off the angular power spectra of those maps. This paper argues that the pixelization step injects several distinct biases — the pixel window smooths the signal, empty pixels behave like a stochastic mask, sub-pixel shear modes alias into the measured multipoles, and pixel shapes and sizes vary across the sky — and that these effects matter precisely on the small scales ($\ell \sim N_{\rm side}$ and above) where Stage-IV lensing surveys carry most of their information. Its central contribution is the first derivation of how the HEALPix pixel window function approximation arises for spin-2 fields sampled by discrete source catalogues on the curved sky, showing both when the standard multiplicative smoothing factor is justified and what it leaves behind. On that foundation the paper builds correction factors $f(\lambda)$, $g(\lambda)$, $h(\lambda)$ for empty pixels and weight stochasticity, tests the full model on 1000 mock shear catalogues, and proposes estimator changes — fixed source positions and weights, globally normalized maps, interlaced grids, footprint-adapted window functions — that hold residual biases at the sub-percent level for $\ell \lesssim N_{\rm side}$. If the models are right, these are exactly the corrections ongoing and forthcoming lensing surveys need before trusting their small-scale spectra.

What carries the argument

The load-bearing object is the pixel-averaged spin-weighted spherical harmonic $\pm2\Upsilon^p_{\ell m}$, obtained by integrating the shear over a pixel window weighted by the source catalogue. The argument rotates this integral into a frame aligned with the pixel centre, where axisymmetric pixels kill all but the $m=\pm 2$ azimuthal terms, so that the source-averaged pixel window reduces to $W^p_\ell = (2\pi/\Omega)\int_0^\pi d\theta\,\sin\theta\, W_p(\theta)\, d^\ell_{22}(\theta)$, and the sky average of $(W^p_\ell)^2$ is the familiar HEALPix window $W^2_\ell$. The same source-averaging procedure produces the occupancy functions $f(\lambda)$, $g(\lambda)$, $h(\lambda)$ that rescale signal, shot noise, and shape noise when pixels can be empty. Alongside this, the recommended estimator treats galaxy positions and weights as fixed, folding the binary occupancy map $\Theta(N_p)$ into the pseudo-$C_\ell$ mixing matrix, and the appendix on parallel transport supplies the phase factor $e^{-2i\beta}$ that must rotate each galaxy's shear to its pixel centre before averaging.

What would settle it

Build mock shear catalogues from clustered source galaxies with known two-point clustering at Euclid-like depth, construct shear maps at $N_{\rm side} = 2048$ (mean occupancy $\lambda \approx 2$), and compare the measured $EE$ and $BB$ spectra against the model of Equation (3.28) including $f(\lambda)$, $g(\lambda)$, $h(\lambda)$. If the residuals exceed the claimed sub-percent level for $\ell < N_{\rm side}$, or if the predicted $B$-mode amplitude fails to track the data, the Poisson-source assumption carrying the derivation is falsified.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the HEALPix pixel window function for cosmic shear is a derived consequence rather than an assumed kernel: writing the pixelized spin-weighted spherical harmonics exactly, and then averaging over unclustered source positions while treating pixels as axisymmetric on average, collapses pixelization to a single scalar window $W_\ell$ multiplying each multipole, with the residual sub-pixel shear variance appearing as a renormalized white-noise term. Equation (3.23), built from the per-pixel window $W^p_\ell = (2\pi/\Omega)\int_0^\pi d\theta\,\sin\theta\, W_p(\theta)\, d^\ell_{22}(\theta)$ sky-averaged as $W^2_\ell$, is the first statement of this approximation for discrete spin-2 catalogues on the curved sky. The same machinery yields the occupancy corrections $f(\lambda)$, $g(\lambda)$, $h(\lambda)$ of Equation (3.29), which turn the empty-pixel effect into an effective sky fraction and a rescaled shot noise, and simulations with 1000 mock catalogues show the corrected model reproduces measured $E$- and $B$-mode spectra at the sub-percent level up to $\ell \approx N_{\rm side}$, with the residual dominated by aliasing. A further new result quantifies the bias from omitting the parallel-transport phase $e^{-2i\beta}$ when averaging shears within pixels, finding a spatially varying multiplicative and additive bias that is acceptable for Stage-IV requirements at $N_{\rm side} \geq 128$.

Load-bearing premise

Every quantitative correction in the paper assumes source galaxies are unclustered (Poisson-distributed) positions whose measurement weights are independent of the shear field and of source density; real catalogues violate both, and the paper itself defers a clustered-source treatment to a forthcoming work.

Editorial extensions

If this is right

  • Residual biases in standard pseudo-$C_\ell$ shear spectra can be modelled to the sub-percent level for $\ell \lesssim N_{\rm side}$, with the remaining bias from aliasing growing to several percent by $\ell \simeq 2N_{\rm side}$.
  • Dividing the shear map by the per-pixel weight sum is the main source of analytic difficulty; unnormalized or globally normalized maps make the leading empty-pixel bias exactly $\lambda^2$ and the noise bias a simple $\sigma^2_\gamma/2\bar{n}$ term on the full sky.
  • Holding source positions and weights fixed converts the empty-pixel effect into a mixing matrix that can be computed from the weight map, and this realization-dependent model performs at least as well as the ensemble-averaged one in the paper's tests.
  • Rotating the HEALPix grid by $\Delta\phi = \pi/4N_{\rm side}$ and averaging the two maps suppresses most of the aliasing bias for blue spectra such as $C_\ell \propto \ell^{-1}$, at the cost of oversmoothing redder spectra.
  • Averaging the pixel window over the survey footprint instead of the whole sky removes the percent-level window-function bias for band-limited spectra; for non-band-limited shear, aliasing must be mitigated first for this fix to pay off.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The Poisson-source assumption is the boundary of the paper's quantitative claims: with clustered galaxies the corrections acquire extra $\ell$-dependence and extra $B$-mode power, so a natural next test is whether the $f(\lambda)$, $g(\lambda)$, $h(\lambda)$ model still holds at $\lambda \approx 2$ for Euclid-like clustering — I would expect new scale-dependent terms to be required.
  • The interlacing scheme is inherently equatorial, because it exploits the constant azimuthal spacing of pixels within HEALPix rings; its benefit should therefore scale with the fraction of a survey's area in equatorial rings, a testable prediction for surveys with different footprints that the paper leaves implicit.
  • The fixed-source 'visibility map' viewpoint connects pixelization bias directly to source-lens clustering: the same mixing-matrix machinery that absorbs the occupancy map could in principle absorb the clustered-source terms the paper defers, so the promised follow-up work may be a direct extension of Equation (6.2).
  • The sub-pixel shear-gradient variance identified in appendix B injects white noise that depends on the cosmology through the shear spectrum; the distinction between noise estimators such as Equations (3.39) and (3.40) is therefore not merely practical, and getting this term into models will matter more as survey depth and resolution grow.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 4 minor

Summary. This paper analyzes biases in the standard pseudo-Cℓ estimator of cosmic shear power spectra, caused by pixelization of discrete galaxy catalogues into HEALPix maps. The authors derive analytic expressions for the action of pixelization on spin-2 shear fields, including the HEALPix pixel window approximation, the effects of finite pixel occupancy and shot noise, empty-pixel masks, and a phase factor from parallel transport. They validate their models against 1000 Gaussian shear simulations with Poisson-distributed source positions, and propose improvements: unnormalized or globally normalized shear maps, a fixed-source estimator, interlaced HEALPix grids, and footprint-adapted pixel window functions. The central claim is a first derivation of the HEALPix pixel window function approximation for discrete, spin-2 sources on the curved sky.

Significance. If correct, the paper fills a real gap in the weak-lensing literature: the standard HEALPix window function for spin-2 fields is widely applied but its derivation in the discrete-catalogue setting was not previously published. The analytic models are derived from first principles, with no parameters fitted to the simulation outcomes; the interlacing rotation is fixed by symmetry, and the HEALPix window is an external input. Validation with 1000 simulations gives sub-percent agreement to ℓ≈Nside for the occupation-number corrections. The paper is also honest about its limits: §3.6 explicitly defers clustered sources and source-lens clustering, and §7 cautions that interlacing is spectrum-dependent. These scoping statements are commendable and should be preserved in any revision.

major comments (1)
  1. [Abstract; §3.3; §3.6; §6.2] The abstract claims that the paper 'derive[s] models that can bring residual biases to the percent level on small scales', and §3.3 states that Eq. (3.23) provides 'for the first time' the HEALPix pixel window approximation for discrete sources and spin-2 fields. Both statements rest on Eq. (3.12), which replaces the weighted source density with its uniform per-pixel expectation and is exact only for unclustered (Poisson) sources with weights independent of position and of the shear. As the paper itself states in §3.6, clustered sources and source-lens clustering are deferred to a forthcoming work, and the fixed-source tests in §6.2 also use Poisson-distributed positions. The quantitative sub-percent claims in Figs. 6 and 8 are therefore not established for real survey catalogues, whose source positions are strongly clustered and correlated with the shear through source-lens clustering. I request an explicit scope statement in the abstract and in the introduction to §6.2, and a qualifier in §3.3 clarifying that the first derivation is for unclustered sources; with that qualification the derivation appears sound.
minor comments (4)
  1. [Figure 4 caption] The word 'prediciton' should be 'prediction'.
  2. [§3.4.2] The heading 'F ull sky , unit shear weights' contains stray spaces and should be 'Full sky, unit shear weights'.
  3. [Eq. (3.26)] The symbol γ is used both for the Euler–Mascheroni constant and for the lower incomplete Gamma function γ(α, x); please disambiguate this notation.
  4. [§8, Fig. 12] The legend entries 'HEALPix window' and 'masked window' are not self-explanatory; please state in the caption that 'masked window' is the footprint-averaged (bespoke) pixel window, i.e. Eq. (8.1) restricted to the equatorial or polar pixels.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the central derivations are self-contained and tested against independent simulations; self-citations are not load-bearing.

full rationale

I walked the claimed derivation chain and found no step in which a prediction reduces to its own input by construction. The core result, Eq. (3.23), follows from explicit first-principles steps: Eq. (3.12) averages the pixel window functions over Poisson-distributed source positions at fixed occupancy; axisymmetry then enforces m = ±2; Eq. (3.21) expresses the per-pixel spin-2 window as an integral over the Wigner d-function d^l_22; and Eq. (3.23) constructs the isotropic window as a sky average of these per-pixel windows. The HEALPix window function is used as an external comparison in Fig. 1 and as a benchmark, not as a parameter fitted to the simulations. The functions f(λ), g(λ), h(λ) in Eqs. (3.26)-(3.29) are closed-form averages over Poisson pixel occupancy, and Section 4 tests them against independent mock catalogues with a fiducial ΛCDM input spectrum, so the agreement is a genuine model test rather than a re-description of the fitted input. The fixed-source estimator model in Section 6 is explicitly introduced as a schematic ansatz, Eq. (6.2), and is validated against simulations; it is not derived from the source-averaged result by circular substitution. Similarly, the bespoke pixel windows of Section 8 are constructed from the survey footprint geometry and tested on band-limited simulations, so the improvement is not imposed by fitting the measured spectra. The paper does cite the companion Euclid paper, Ref. [20], whose authors overlap with the present paper, and it also cites Ref. [43], but these citations are used for context, implementation, and prior testing; none carries a load-bearing proof of the main derivations. The limitation acknowledged in Section 3.6, namely that clustered sources and source-lens clustering are deferred to future work, is an applicability caveat for real surveys rather than a circularity: it does not make the Poisson-source derivation equivalent to its output. Overall, I found no circular reduction of the kind where Eq. X equals Eq. Y by definition or where a fitted parameter is renamed as a prediction; the minor self-citations justify the non-zero but low circularity score.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central claims rely on standard spherical harmonic formalism and several domain assumptions that are stated in the text: Poisson (unclustered) sources for the main analytic bias model, shear weights uncorrelated with shear and density, axisymmetry of pixels on average, and Gaussianity of the shear field for numerical tests. No invented entities are introduced.

free parameters (1)
  • Interlacing rotation angle Δφ = π/(4Nside)
    Chosen by hand in Section 7 as half the azimuthal spacing of HEALPix pixels in the equatorial ring. It is not fitted to data but is an ad hoc parameter of the proposed interlacing scheme.
assumptions (5)
  • domain assumption Source galaxies are unclustered (Poisson) in the analytic bias model.
    Equations (3.26) to (3.29) and the f(λ), g(λ), h(λ) corrections assume Poisson statistics for pixel occupancy; real sources are clustered, which the paper acknowledges in Section 3.6 and defers to future work.
  • domain assumption Shear weights are statistically independent of the shear field and of source density.
    Stated at the start of Section 3.4; this allows the factorization of weight averages from shear averages. In practice weights depend on galaxy properties and PSF, so this is an idealization.
  • domain assumption HEALPix pixels are axisymmetric on average, so source-averaged pixel window functions factor as in Equation (3.19).
    Section 3.3 uses this to derive the isotropic HEALPix window function; pixel shapes vary by up to about 10% (Figure 2), so this is an approximation.
  • domain assumption The shear field is Gaussian in the simulation tests.
    Section 4 draws Gaussian realizations from a fiducial power spectrum; the analytic derivations themselves do not assume Gaussianity, but the quantitative tests do.
  • standard math Spin-weighted spherical harmonic and Wigner D matrix formalism is valid and is used without proof.
    Used throughout, for example Equations (3.6) to (3.9) and Appendix A, as standard mathematics.

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Cite this review

Pith. "Pith review of Pixelization effects in cosmic shear angular power spectra." pith.science (2026). https://pith.science/paper/2WMAKEAR

@misc{pith2026250108718,
  author       = {Pith},
  title        = {Pith review of: Pixelization effects in cosmic shear angular power spectra},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2WMAKEAR}},
  note         = {Machine review of arXiv:2501.08718}
}
abstract

We conduct a comprehensive study into the impact of pixelization on cosmic shear, uncovering several sources of bias in standard pseudo-$C_\ell$ estimators based on discrete catalogues. We derive models that can bring residual biases to the percent level on small scales. We elucidate the impact of aliasing and the varying shape of HEALPix pixels on power spectra and show how the HEALPix pixel window function approximation is made in the discrete spin-2 setting. We propose several improvements to the standard estimator and its modelling, based on the principle that source positions and weights are to be considered fixed. We show how empty pixels can be accounted for either by modifying the mixing matrices or applying correction factors that we derive. We introduce an approximate interlacing scheme for the HEALPix grid and show that it can mitigate the effects of aliasing. We introduce bespoke pixel window functions adapted to the survey footprint and show that, for band-limited spectra, biases from using an isotropic window function can be effectively reduced to zero. This work partly intends to serve as a useful reference for pixel-related effects in angular power spectra, which are of relevance for ongoing and forthcoming lensing and clustering surveys.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Analytical covariances for catalogue-based pseudo-$C_\ell$s

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    A new analytic method computes disconnected covariance matrices for catalogue-based pseudo-Cℓ power spectra by smoothing source positions and treating self-pair shot noise exactly.

Reference graph

Works this paper leans on

58 extracted references · 15 canonical work pages · cited by 1 Pith paper

  1. [20]

    Tessore, B

    Euclid Collaboration, N. Tessore, B. Joachimi, A. Loureiro, A. Hall, G. Ca˜ nas-Herrera et al., Euclid preparation. Angular power spectra from discrete observations,arXiv e-prints(2024) arXiv:2408.16903 [2408.16903]

    arXiv 2024

  2. [1]

    Mellier, Abdurro’uf, J.A

    Euclid Collaboration, Y. Mellier, Abdurro’uf, J.A. Acevedo Barroso, A. Ach´ ucarro, J. Adamek et al.,Euclid. I. Overview of the Euclid mission,arXiv e-prints(2024) arXiv:2405.13491 [2405.13491]

    arXiv 2024

  3. [2]

    Ivezi´ c, S.M

    ˇZ. Ivezi´ c, S.M. Kahn, J.A. Tyson, B. Abel, E. Acosta, R. Allsman et al.,LSST: From Science Drivers to Reference Design and Anticipated Data Products, ApJ873(2019) 111 [0805.2366]

    arXiv 2019

  4. [3]

    Theory and Statistics of Weak Lensing from Large-Scale Mass Inhomogeneities

    M. Kamionkowski, A. Babul, C.M. Cress and A. Refregier,Theory and statistics of weak lensing from large-scale mass inhomogeneities, MNRAS301(1998) 1064 [astro-ph/9712030]

    work page Pith review arXiv 1998

  5. [4]

    Crittenden, P

    R.G. Crittenden, P. Natarajan, U.-L. Pen and T. Theuns,Discriminating Weak Lensing from Intrinsic Spin Correlations Using the Curl-Gradient Decomposition, ApJ568(2002) 20 [astro-ph/0012336]

    arXiv 2002

  6. [5]

    Schneider, L

    P. Schneider, L. van Waerbeke, M. Kilbinger and Y. Mellier,Analysis of two-point statistics of cosmic shear. I. Estimators and covariances, A&A396(2002) 1 [astro-ph/0206182]. – 35 –

    arXiv 2002

  7. [6]

    Asgari, C.-A

    M. Asgari, C.-A. Lin, B. Joachimi, B. Giblin, C. Heymans, H. Hildebrandt et al.,KiDS-1000 cosmology: Cosmic shear constraints and comparison between two point statistics, A&A645 (2021) A104 [2007.15633]

    arXiv 2021

  8. [7]

    Secco, S

    L.F. Secco, S. Samuroff, E. Krause, B. Jain, J. Blazek, M. Raveri et al.,Dark Energy Survey Year 3 results: Cosmology from cosmic shear and robustness to modeling uncertainty, Phys. Rev. D105(2022) 023515 [2105.13544]

    arXiv 2022

Show all 58 references
  1. [8]

    A. Amon, D. Gruen, M.A. Troxel, N. MacCrann, S. Dodelson, A. Choi et al.,Dark Energy Survey Year 3 results: Cosmology from cosmic shear and robustness to data calibration, Phys. Rev. D105(2022) 023514 [2105.13543]

    2022

  2. [9]

    X. Li, T. Zhang, S. Sugiyama, R. Dalal, R. Terasawa, M.M. Rau et al.,Hyper Suprime-Cam Year 3 results: Cosmology from cosmic shear two-point correlation functions, Phys. Rev. D108 (2023) 123518 [2304.00702]

    2023 arXiv

  3. [10]

    Brown, A.N

    M.L. Brown, A.N. Taylor, D.J. Bacon, M.E. Gray, S. Dye, K. Meisenheimer et al.,The shear power spectrum from the COMBO-17 survey, MNRAS341(2003) 100 [astro-ph/0210213]

    2003 arXiv

  4. [11]

    Hikage, M

    C. Hikage, M. Takada, T. Hamana and D. Spergel,Shear power spectrum reconstruction using the pseudo-spectrum method, MNRAS412(2011) 65 [1004.3542]

    2011 arXiv

  5. [12]

    Asgari, A

    M. Asgari, A. Taylor, B. Joachimi and T.D. Kitching,Flat-SkyPseudo-Cls analysis for weak gravitational lensing, MNRAS479(2018) 454 [1612.04664]

    2018 arXiv

  6. [13]

    Alonso, J

    D. Alonso, J. Sanchez, A. Slosar and LSST Dark Energy Science Collaboration,A unified pseudo-Cℓ framework, MNRAS484(2019) 4127 [1809.09603]

    2019 arXiv

  7. [14]

    Nicola, C

    A. Nicola, C. Garc ´ ıa-Garc ´ ıa, D. Alonso, J. Dunkley, P.G. Ferreira, A. Slosar et al.,Cosmic shear power spectra in practice, J. Cosmology Astropart. Phys.2021(2021) 067 [2010.09717]

    2021 arXiv

  8. [15]

    Dalal, X

    R. Dalal, X. Li, A. Nicola, J. Zuntz, M.A. Strauss, S. Sugiyama et al.,Hyper Suprime-Cam Year 3 results: Cosmology from cosmic shear power spectra, Phys. Rev. D108(2023) 123519 [2304.00701]

    2023 arXiv

  9. [16]

    Schneider, T

    P. Schneider, T. Eifler and E. Krause,COSEBIs: Extracting the full E-/B-mode information from cosmic shear correlation functions, A&A520(2010) A116 [1002.2136]

    2010 arXiv

  10. [17]

    Asgari, P

    M. Asgari, P. Schneider and P. Simon,Cosmic shear tomography and efficient data compression using COSEBIs, A&A542(2012) A122 [1201.2669]

    2012 arXiv

  11. [18]

    Asgari, C

    M. Asgari, C. Heymans, H. Hildebrandt, L. Miller, P. Schneider, A. Amon et al.,Consistent cosmic shear in the face of systematics: a B-mode analysis of KiDS-450, DES-SV and CFHTLenS, A&A624(2019) A134 [1810.02353]

    2019 arXiv

  12. [19]

    C. Doux, C. Chang, B. Jain, J. Blazek, H. Camacho, X. Fang et al.,Consistency of cosmic shear analyses in harmonic and real space, MNRAS503(2021) 3796 [2011.06469]

    2021 arXiv

  13. [21]

    Efstathiou,Myths and truths concerning estimation of power spectra: the case for a hybrid estimator, MNRAS349(2004) 603 [astro-ph/0307515]

    G. Efstathiou,Myths and truths concerning estimation of power spectra: the case for a hybrid estimator, MNRAS349(2004) 603 [astro-ph/0307515]

    2004 arXiv

  14. [22]

    Hall and A

    A. Hall and A. Taylor,Non-Gaussian likelihood of weak lensing power spectra, Phys. Rev. D 105(2022) 123527 [2202.04095]

    2022 arXiv

  15. [23]

    Maraio, A

    A. Maraio, A. Hall and A. Taylor,Testing quadratic maximum likelihood estimators for forthcoming Stage-IV weak lensing surveys, MNRAS520(2023) 4836 [2207.10412]

    2023 arXiv

  16. [24]

    Sullivan, L.T

    R.M. Sullivan, L.T. Hergt and D. Scott,Methods for CMB map analysis,arXiv e-prints(2024) arXiv:2410.12951 [2410.12951]. – 36 –

    2024 arXiv

  17. [25]

    Garc ´ ıa-Garc ´ ıa, M

    C. Garc ´ ıa-Garc ´ ıa, M. Zennaro, G. Aric` o, D. Alonso and R.E. Angulo,Cosmic shear with small scales: Des-y3, kids-1000 and hsc-dr1,Journal of Cosmology and Astroparticle Physics2024 (2024) 024 [2403.13794]

    2024 arXiv

  18. [26]

    Lizancos and M

    A.B. Lizancos and M. White,Harmonic analysis of discrete tracers of large-scale structure, Journal of Cosmology and Astroparticle Physics2024(2024) 010

    2024

  19. [27]

    Belkner, A.J

    S. Belkner, A.J. Duivenvoorden, J. Carron, N. Schaeffer and M. Reinecke,cunuSHT: GPU accelerated spherical harmonic transforms on arbitrary pixelizations,RAS Techniques and Instruments3(2024) 711 [2406.14542]

    2024 arXiv

  20. [28]

    G´ orski, E

    K.M. G´ orski, E. Hivon, A.J. Banday, B.D. Wandelt, F.K. Hansen, M. Reinecke et al., HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere, ApJ622(2005) 759 [astro-ph/0409513]

    2005 arXiv

  21. [29]

    Garc ´ ıa-Garc ´ ıa, J

    C. Garc ´ ıa-Garc ´ ıa, J. Ruiz-Zapatero, D. Alonso, E. Bellini, P.G. Ferreira, E.-M. Mueller et al., The growth of density perturbations in the last 10 billion years from tomographic large-scale structure data, J. Cosmology Astropart. Phys.2021(2021) 030 [2105.12108]

    2021 arXiv

  22. [30]

    Loureiro, L

    A. Loureiro, L. Whittaker, A. Spurio Mancini, B. Joachimi, A. Cuceu, M. Asgari et al.,KiDS and Euclid: Cosmological implications of a pseudo angular power spectrum analysis of KiDS-1000 cosmic shear tomography, A&A665(2022) A56 [2110.06947]

    2022 arXiv

  23. [31]

    C. Doux, B. Jain, D. Zeurcher, J. Lee, X. Fang, R. Rosenfeld et al.,Dark energy survey year 3 results: cosmological constraints from the analysis of cosmic shear in harmonic space, MNRAS 515(2022) 1942 [2203.07128]

    2022 arXiv

  24. [32]

    McEwen and Y

    J.D. McEwen and Y. Wiaux,A Novel Sampling Theorem on the Sphere,IEEE Transactions on Signal Processing59(2011) 5876 [1110.6298]

    2011 arXiv

  25. [33]

    K. Wolz, D. Alonso and A. Nicola,Catalog-based pseudo-C ℓ s, J. Cosmology Astropart. Phys. 2025(2025) 028 [2407.21013]

    2025 arXiv

  26. [34]

    Challinor, P

    A. Challinor, P. Fosalba, D. Mortlock, M. Ashdown, B. Wandelt and K. G´ orski,All-sky convolution for polarimetry experiments, Phys. Rev. D62(2000) 123002 [astro-ph/0008228]

    2000 arXiv

  27. [35]

    Varshalovich, A.N

    D.A. Varshalovich, A.N. Moskalev and V.K. Khersonskii,Quantum Theory of Angular Momentum, World Scientific (1988), 10.1142/0270

    1988 doi

  28. [36]

    Duncan and M.L

    C.A.J. Duncan and M.L. Brown,Avoiding lensing bias in cosmic shear analysis,arXiv e-prints (2024) arXiv:2411.15063 [2411.15063]

    2024 arXiv

  29. [37]

    Bernardeau,The effects of source clustering on weak lensing statistics, A&A338(1998) 375 [astro-ph/9712115]

    F. Bernardeau,The effects of source clustering on weak lensing statistics, A&A338(1998) 375 [astro-ph/9712115]

    1998 arXiv

  30. [38]

    Schneider, L

    P. Schneider, L. van Waerbeke and Y. Mellier,B-modes in cosmic shear from source redshift clustering, A&A389(2002) 729 [astro-ph/0112441]

    2002 arXiv

  31. [39]

    Linke, S

    L. Linke, S. Unruh, A. Wittje, T. Schrabback, S. Grandis, M. Asgari et al.,Euclid and KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear analyses,arXiv e-prints(2024) arXiv:2407.09810 [2407.09810]

    2024

  32. [40]

    A.J. Mead, S. Brieden, T. Tr¨ oster and C. Heymans,HMCODE-2020: improved modelling of non-linear cosmological power spectra with baryonic feedback, MNRAS502(2021) 1401 [2009.01858]

    2021 arXiv

  33. [41]

    Blanchard, S

    Euclid Collaboration, A. Blanchard, S. Camera, C. Carbone, V.F. Cardone, S. Casas et al., Euclid preparation. VII. Forecast validation for Euclid cosmological probes, A&A642(2020) A191 [1910.09273]

    2020 arXiv

  34. [42]

    Scaramella, J

    Euclid Collaboration, R. Scaramella, J. Amiaux, Y. Mellier, C. Burigana, C.S. Carvalho et al., Euclid preparation. I. The Euclid Wide Survey, A&A662(2022) A112 [2108.01201]. – 37 –

    2022 arXiv

  35. [43]

    von Wietersheim-Kramsta, K

    M. von Wietersheim-Kramsta, K. Lin, N. Tessore, B. Joachimi, A. Loureiro, R. Reischke et al., KiDS-SBI: Simulation-based inference analysis of KiDS-1000 cosmic shear, A&A694(2025) A223 [2404.15402]

    2025 arXiv

  36. [44]

    Singh, R

    S. Singh, R. Mandelbaum, U. Seljak, S. Rodr ´ ıguez-Torres and A. Slosar,Cosmological constraints from galaxy-lensing cross-correlations using BOSS galaxies with SDSS and CMB lensing, MNRAS491(2020) 51 [1811.06499]

    2020 arXiv

  37. [45]

    Joachimi, C.A

    B. Joachimi, C.A. Lin, M. Asgari, T. Tr¨ oster, C. Heymans, H. Hildebrandt et al.,KiDS-1000 methodology: Modelling and inference for joint weak gravitational lensing and spectroscopic galaxy clustering analysis, A&A646(2021) A129 [2007.01844]

    2021 arXiv

  38. [46]

    Friedrich, F

    O. Friedrich, F. Andrade-Oliveira, H. Camacho, O. Alves, R. Rosenfeld, J. Sanchez et al.,Dark Energy Survey year 3 results: covariance modelling and its impact on parameter estimation and quality of fit, MNRAS508(2021) 3125 [2012.08568]

    2021 arXiv

  39. [47]

    Reischke, S

    R. Reischke, S. Unruh, M. Asgari, A. Dvornik, H. Hildebrandt, B. Joachimi et al., KiDS-Legacy: Covariance validation and the unified OneCovariance framework for projected large-scale structure observables,arXiv e-prints(2024) arXiv:2410.06962 [2410.06962]

    2024

  40. [48]

    Deshpande, T

    Euclid Collaboration, A.C. Deshpande, T. Kitching, A. Hall, M.L. Brown, N. Aghanim et al., Euclid preparation. XXXVI. Modelling the weak lensing angular power spectrum, A&A684 (2024) A138 [2302.04507]

    2024 arXiv

  41. [49]

    Y. Yu, P. Zhang, W. Lin and W. Cui,The Source-lens Clustering Effect in the Context of Lensing Tomography and Its Self-calibration, ApJ803(2015) 46 [1402.7144]

    2015 arXiv

  42. [50]

    Brown, P.G

    M.L. Brown, P.G. Castro and A.N. Taylor,Cosmic microwave background temperature and polarization pseudo-Cl estimators and covariances, MNRAS360(2005) 1262 [astro-ph/0410394]

    2005 arXiv

  43. [51]

    Hockney and J.W

    R.W. Hockney and J.W. Eastwood,Computer simulation using particles, McGraw-Hill (1988)

    1988

  44. [52]

    Sefusatti, M

    E. Sefusatti, M. Crocce, R. Scoccimarro and H.M.P. Couchman,Accurate estimators of correlation functions in Fourier space, MNRAS460(2016) 3624 [1512.07295]

    2016 arXiv

  45. [53]

    Ruhl, P.A.R

    J.E. Ruhl, P.A.R. Ade, J.J. Bock, J.R. Bond, J. Borrill, A. Boscaleri et al.,Improved Measurement of the Angular Power Spectrum of Temperature Anisotropy in the Cosmic Microwave Background from Two New Analyses of BOOMERANG Observations, ApJ599 (2003) 786 [astro-ph/0212229]

    2003 arXiv

  46. [54]

    Zonca, L.P

    A. Zonca, L.P. Singer, D. Lenz, M. Reinecke, C. Rosset, E. Hivon et al.,healpy: equal area pixelization and spherical harmonics transforms for data on the sphere in python,Journal of Open Source Software4(2019) 1298

    2019

  47. [55]

    Massey, H

    R. Massey, H. Hoekstra, T. Kitching, J. Rhodes, M. Cropper, J. Amiaux et al.,Origins of weak lensing systematics, and requirements on future instrumentation (or knowledge of instrumentation), MNRAS429(2013) 661 [1210.7690]

    2013 arXiv

  48. [56]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, C. Armitage-Caplan, M. Arnaud, M. Ashdown et al.,Planck 2013 results. XVII. Gravitational lensing by large-scale structure, A&A571 (2014) A17 [1303.5077]

    2014 arXiv

  49. [57]

    Challinor and G

    A. Challinor and G. Chon,Geometry of weak lensing of CMB polarization, Phys. Rev. D66 (2002) 127301 [astro-ph/0301064]

    2002 arXiv

  50. [58]

    Planck 2015 beams

    Planck Collaboration, “Planck 2015 beams.” https://wiki.cosmos.esa.int/planckpla2015/index.php/Beams. – 38 – A Bias due to neglecting parallel transport of shear In this section we discuss in detail the bias in angular power spectra due to neglecting the phase factor required ...

    2015

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