The Third Gravitational Lensing Accuracy Testing (GREAT3) Challenge Handbook

1. INTRODUCTION

• Systematic shape-measurement errors must fall by factors of 5–10 as coherent lensing distortions (~1%) are smaller than intrinsic ellipticities (~0.3) and PSF distortions.Removing PSF effects for moderately resolved, limited-signal-to-noise galaxies remains a demanding statistical problem for upcoming surveys.Source: §1 · p. 2

1.1. Previous challenges and the context for GREAT3

• GREAT08 and GREAT10 increased simulation complexity and each improved weak-lensing shape-measurement accuracy by factors of 2–3 (Bridle et al. 2009, 2010; Kitching et al. 2011, 2012, 2013).GREAT08 used known PSFs, simple galaxy models, and constant shear; GREAT10 added cosmologically varying shear fields, broader galaxy and observing-condition variation, and a standalone PSF-modelling Star Challenge.Source: §1.1 · p. 2
• GREAT3 targets unresolved shear-measurement issues using realistic galaxy-image and physically motivated PSF simulations, and releases documented open-source GalSim while blinding challenge parameters.The simulations use real galaxy images from the Hubble Space Telescope; the open-source code is intended to support improvement of existing methods and development of new ones.Source: §1.1 · p. 2
• GREAT3 simulations are statistically matched to the largest upcoming weak-lensing surveys, and participants can enter any subset of branches addressing different field issues and observation types.The goal is to keep systematic errors below statistical errors so systematics do not dominate the error budget.Source: §1.1 · p. 3

2.1. Lensing shear

• Shear and convergence describe the locally linear lensing transformation: shear stretches galaxy images, while positive convergence makes them appear larger and brighter.Because the convergence term is often not estimated, the observed stretching is commonly described by reduced shear, g = γ/(1 − κ); in many cosmological applications g ≃ γ.Source: §2.1 · p. 3

2.2. Shear fields

• Galaxy and cluster lensing use approximately constant tangential shear around foreground objects, while shear correlations across angular scales test cosmological models.These measurements can constrain how visible matter traces underlying mass and inform models of dark matter, dark energy, and modified gravity.Source: §2.2 · p. 4

2.3. Measuring shear fields

• Shear-field studies use individual-galaxy estimates to map mass or measure spatial correlations that probe the growth of cosmic structure.GREAT3 uses a correlation-function metric for simulations with variable shear, which can also probe contamination from variable and constant PSFs.Source: §2.3 · p. 5

2.4. Variable PSF

• The PSF convolves and alters galaxy images: circular blurring dilutes shape, while coherent anisotropy can leak into galaxy shapes and mimic lensing.Stars serve as PSF measurements, which must be interpolated to galaxy positions.Source: §2.4 · pp. 5–6

2.5. Summary of effects

• Lensing images are further affected by the atmosphere, telescope optics, detector pixelation, noise, and detector effects, making sub-percent nuisance-effect removal necessary for upcoming large datasets.Noise can bias the nonlinear estimation of the original shear.Source: §2.5 · p. 6

3.1. Realistic galaxy morphologies

• Only ~20% of HST galaxies are perfectly fit by simple models, nearly half show additional substructure, and ~30% are irregulars, motivating GREAT3’s test of morphology-driven underfitting bias.Shear couples second moments to higher-order moments, while realistic models may require many parameters that are impractical at typical S/N ∼10–20.Source: §3.1 · p. 6, Figure 3 · p. 6

3.2. Variable PSFs

• GREAT3 tests both realistic complex PSF profiles supplied to participants and spatially varying PSFs they must infer, judging the latter by shear-field recovery rather than PSF reconstruction accuracy.Sparse high-S/N stars make high-frequency spatial modes difficult to track, and different PSF residual patterns can affect recovered shear differently even at the same RMS accuracy.Source: §3.2 · p. 7

3.3. Combination of multiple exposures

• GREAT3 tests multi-exposure image combination, especially for non-Nyquist-sampled images that require subpixel-dithered exposures for critical sampling.The challenge provides a basic test rather than addressing complications such as data holes; methods might also benefit from up-weighting higher-resolution exposures when PSFs differ.Source: §3.3 · p. 7

3.4. Challenge philosophy

• GREAT3 uses realistic parameter distributions in controlled experiments across ground- and space-based, constant- and variable-shear datasets, isolating priority issues while omitting lower-priority complications.Participants can choose either or both data types; the challenge is more complex than GREAT08 and GREAT10 while retaining controlled tests of morphology, PSFs, PSF variation, and multiple-exposure combination.Source: §3 · p. 6, §3.4 · pp. 7–8

4.1. Branch structure

• Five experiments—one control, three testing individual effects, and one combining all three—crossed with four data types to create 20 branches.Each experiment includes constant and variable shear, each observed from ground and space; the control omits the three effects but still tests methods on galaxies spanning size and signal-to-noise.Source: §4.1 · p. 8

4.2. Overall information

• The estimated dataset totals 3.2 TB, participants can download selected branches, and submissions are ranked on branch-specific and overall leaderboards.Public code provides tools to prepare shear-correlation submissions and was planned to include example analysis scripts.Source: §4.2 · p. 8

4.3. Timeline

• A beta release of 12 of 20 branches began the six-month challenge in October 2013; remaining simulations followed in December, with the challenge ending April 30, 2014.A final meeting was scheduled for the end of May 2014.Source: §4.3 · p. 8

4.4. Evaluation of submissions

• Branch evaluation uses shear-dependent metrics selected through simulated bias tests for maximal sensitivity to multiplicative and additive systematic errors.Source: §4.4 · p. 8

4.4.1. Constant shear

• For constant shear, regression of submitted estimates against known shears measures multiplicative and additive biases; Qc uses targets mtarget = 2×10^-3 and ctarget = 2×10^-4.Estimates are evaluated in a frame aligned with mean PSF ellipticity; for constant-shear branches with variable PSF, additive-systematic sensitivity is reduced when mean PSF ellipticity is zero.Source: §4.4.1 · p. 9

4.4.2. Variable shear

• The variable-shear metric uses shear correlation functions rather than GREAT10’s power spectrum, avoiding shot-noise subtraction and allowing method-independent E/B separation.The correlation-function approach also provides greater sensitivity to additive systematics when the PSF is constant.Source: §4.4.2 · p. 10
• Variable-shear submissions report E-mode aperture-mass dispersion estimates for each of 10 fields, combining all 20 subfields in a field to span spatial scales.The submitted estimates are calculated across logarithmically spaced galaxy-pair separation bins.Source: §4.4.2 · p. 10
• Tested alternatives to Qv, including relative-difference and inverse-variance metrics, were less sensitive to multiplicative and additive shear biases.Qv itself is less sensitive than the constant-shear metric Qc, particularly to multiplicative biases, because variable-shear signals are smaller and its bias estimates rely on noisier higher-order combinations.Source: §4.4.2 · p. 11

5. SIMULATIONS

• GalSim, a fast modular C++ and Python tool, produces all challenge simulations; the simulations target realistic galaxy populations and PSF properties to test issues raised earlier in the paper.The paper points to Appendix D for evidence that GalSim accurately simulates galaxies with applied shear.Source: §5 · p. 11

5.1. Galaxies

• GREAT3 uses HST data for realistic galaxy size and magnitude distributions, actual deconvolved images in morphology tests, and Sersic fits otherwise to test underfitting bias.Resolution cuts exclude nearly unresolved galaxies and use precomputed adaptive second-moment resolution factors to avoid selection bias correlated with PSF ellipticity or shear.Source: §5.1 · pp. 11–12

5.2. Point-Spread Functions (PSFs)

• Variable-PSF branches tile large images and provide star fields for PSF estimation, with one star field per subfield.The tiled PSF model is shared across subfields within a field, with a provided position shift; constant-PSF branches instead select one PSF per subfield.Source: §5.2 · p. 12, §5.2.3 · p. 15

5.2.1. Optical PSFs

• The optical PSF model incorporates pupil shape, aberrations, pointing jitter, and detector response; spatially varying aberrations require instrument-specific models in variable-PSF branches.For constant-PSF branches, the models are simplified variants.Source: §5.2.1 · p. 13

5.2.2. Atmospheric PSFs

• Atmospheric PSF anisotropy correlations exceed lensing-shear correlations across nearly all relevant grid scales; optical anisotropy matters mainly at small scales and can matter at large scales after field tiling.The model uses PhoSim turbulence and Gaussian random fields for spatially varying PSF size and ellipticity, with a sheared Kolmogorov profile that omits higher-order distortions.Source: §5.2.2 · pp. 13–15, Figure 9 · p. 15

5.3. Noise model

• A 90°-rotated duplicate-galaxy scheme cuts shear errors by a factor of 3, equivalent to 9× simulation volume, with optimal S/N ≥20.With 5%, 10%, and 20% random omissions, errors rise by 8%, 30%, and 50%, respectively, versus 200% without cancellation; variable-shear runs put lensing in E modes and shape noise in B modes.Source: §5.3 · p. 15
• 10.0/12.0 (ground) and 11.7/13.2 (space) are the 99%/95% lower limits of SExtractor S/N despite an optimal S/N >20 simulation cut.The simulations use zero-mean Gaussian noise with constant variance within each subfield, use model fits as noise-free images for S/N calculations, and include only uncorrelated noise. Realistic-galaxy branches add only enough noise to reach the target noise correlation function.Source: §5.3 · p. 16

5.4. Image rendering

• GREAT3 uses discrete Fourier transform rendering in every branch because deconvolving the original PSF from real-galaxy images cannot be represented with photon shooting.The handbook reports comparing DFT and photon-shooting renderings in validation tests.Source: §5.4 · p. 16

5.5. Constant versus variable shear

• Half the branches use constant shear and half use variable shear fields, covering distinct lensing regimes and accommodating methods that may behave differently across them.Constant values are randomly drawn with random position angles; variable fields use a cosmological-shape power spectrum with slightly high amplitude and scale-dependent modifications of about 10%, then GalSim generates shear and convergence realizations used for reduced shear and magnification.Source: §5.5 · pp. 16–17

5.6. A note about physical scales

• GREAT3 uses 10×10 deg² grids of 100×100 galaxies for shear correlations, while variable-PSF branches sample PSF variation more densely across repeated subfields.The magnification treatment changes observed galaxy sizes and fluxes but omits magnification-induced number-density changes and scattering across flux and size cuts.Source: §5.6 · p. 17

5.7. Space versus ground

• Space-based simulations use smaller pixels to Nyquist-sample single-epoch images, while multi-epoch exposures remain undersampled until combined; ground images use 0.2″ pixels.Space pixel scales are 0.05″ for single-epoch and 0.1″ for multi-epoch data; the single-exposure choice avoids simulating co-addition effects such as correlated noise, while real combined space images may also exhibit aliasing.Source: §5.7 · p. 17

5.8. Deeper data

• Each branch adds five training-only images (2.5% of its volume), one magnitude deeper and 2.5 times higher in S/N, drawn from the same galaxy population and excluded from shear submissions.The effective deep-data fraction is 5–7.5%, with S/N >50; an I < 23.5 HST sample is adjusted in flux and radius to mimic observed S/N, size, and morphology for an I < 25 sample, but not its intrinsic redshift, luminosity, or size distributions.Source: §5.8 · pp. 17–18

• Grid-based galaxy placement avoids testing blends, while selection criteria that correlate galaxy inclusion with shear or PSF direction are also not tested.Weights that depend on shear or PSF can still produce a form of selection bias that appears in challenge results.Source: §6 · p. 18
• GREAT3 omits wavelength-dependent PSF effects from differing star and galaxy SEDs and galaxy color gradients, which may matter for upcoming surveys.Source: §6 · p. 18
• Instrument-specific effects—including cosmic rays, saturation, bad pixels or columns, scattered light, charge transfer inefficiency, and distortion—are omitted because they vary across instruments.Source: §6 · p. 18
• The challenge supplies separate galaxy and star fields, so it does not test star/galaxy separation or cross-contamination that can bias shear estimation.Source: §6 · p. 18
• GREAT3 images have the sky background essentially subtracted, leaving untested the effects of spatially varying backgrounds and residual gradients that can mimic shear.Its simple noise model also excludes Poisson noise from galaxy flux and processing-induced correlations between pixel noise levels.Source: §6 · p. 18
• GREAT3 excludes redshift-dependent shears and calibration, and assumes shear is constant across each galaxy, omitting higher-order distortions such as flexion.Source: §6 · p. 18

APPENDIX EXISTING APPROACHES TO SHEAR MEASUREMENT

• Early methods such as KSB corrected weighted galaxy-image moments for PSF smearing but assumed concentric isophotes and small intrinsic ellipticities.Later moment-based methods retained moment measurements while applying prescriptions to correct galaxy moments for the PSF.Source: APPENDIX EXISTING APPROACHES TO SHEAR… · p. 20
• Forward-modeling methods range from compact astrophysical galaxy-model fits to flexible orthonormal-basis decompositions, alongside Fourier-space and non-parametric approaches (Bernstein & Armstrong 2013).Basis decompositions require more parameters but allow greater flexibility for complex galaxies; image stacking also has potential for constant-shear measurements after success in GREAT08 (Lewis 2009; Bridle et al. 2010).Source: APPENDIX EXISTING APPROACHES TO SHEAR… · p. 20
• GREAT10 introduced methods using machine-learning and computer-science techniques, including neural-network and lookup-table training approaches.Earlier studies assessed limitations of existing methods and proposed compensations; the appendix refers readers to relevant papers and GREAT08/GREAT10 summaries for further detail.Source: APPENDIX EXISTING APPROACHES TO SHEAR… · p. 20

ESTIMATING THE SHEAR CORRELATION FUNCTION

• GREAT3 averages pairs of complex shear measurements to form two correlation functions, ξ+ and ξ−, for assessing variable-shear measurements.The actual cosmic shear field is non-Gaussian, so higher-order statistics such as three-point correlations can also be relevant.Source: ESTIMATING THE SHEAR CORRELATION… · pp. 20–21
• The public corr2 package uses a ball-tree algorithm to group galaxy pairs with similar separation vectors instead of calculating every pair individually.The passage points to Jarvis et al. (2004) for algorithm details.Source: ESTIMATING THE SHEAR CORRELATION… · p. 21
• Separating E- and B-modes removes much of the shape-noise contribution because simulated lensing shear is pure E-mode and intrinsic-shape noise is almost pure B-mode, reducing the galaxies needed for a given precision.Source: ESTIMATING THE SHEAR CORRELATION… · p. 21
• Because E/B separation formally needs correlations down to zero separation, GREAT3 substitutes true input correlations below the closest measurable galaxy pairs, making the correction small.Source: ESTIMATING THE SHEAR CORRELATION… · p. 21
• GREAT3 approximates logarithmically binned correlations as constant within each bin; although this can shift cosmological aperture masses by several percent, it applies the same procedure to inputs and submissions.Source: ESTIMATING THE SHEAR CORRELATION… · p. 21

CHALLENGE RULES

• The section describes rules related to participation in the challenge.Source: CHALLENGE RULES · p. 21

Teams

• Participants are encouraged to describe their methods during the challenge and, after it ends, to write results papers citing the official challenge paper.Participants will be asked to reveal their identities and contribute to a results paper; first- and second-place winners must identify themselves to receive prizes.Source: Teams · p. 22
• Teams may include any number of people, join multiple teams, and submit multiple methods, but only each team’s top-ranked method per branch appears on the leaderboard.Other submissions are retained for later reference and interpretation.Source: Teams · p. 22
• Different methods may earn rankings on different branches, but forming teams to submit essentially unchanged methods to displace others can lead to disqualification.Teams are limited to one submission per branch per day and may form through the public GitHub repository.Source: Teams · p. 22
• Teams with executive committee members are flagged: they appear on branch leaderboards but receive no official ranking and are excluded from the overall leaderboard.Committee members are responsible for identifying themselves when a team is formed, or notifying the challenge organizers if they join later.Source: Teams · p. 22

Overall leader board

• About 40% of winners submitted to 10 or fewer branches when scoring was limited to each team’s best five branches, versus 15% without that limit.Around 60% of simulated teams submitted to 10 or fewer branches.Source: Overall leader board · p. 22
• The leaderboard scores teams on their best-ranked five branches, awarding 1,000 points for fifth place up to 16,000 for first.Teams submitting to fewer than five branches are scored on those submissions; the team with the highest total wins.Source: Overall leader board · p. 22
• In 10,000 simulations, the ranking method did not strongly favor particular score distributions, though it slightly rewarded consistency across branches over specialization..Source: Overall leader board · p. 22
• Almost 60% of first-place teams did not place first in any individual branch.Source: Overall leader board · p. 22
• Ties are broken first by total points across all submitted branches, then by the earliest submission timestamp among branches in which tied teams placed in the top five.Source: Overall leader board · p. 22

Sersic shear accuracy

• m_DFT is a few × 10^-6 for n = 1.5 Sersic profiles and rises to ~1 × 10^-4 for n = 6.2, below the 2 × 10^-4 target.The GREAT3 profiles use n ≤ 6; the comparison is between DFT and photon-shooting renderings.Source: Figure 10 · p. 23, VALIDATION OF GALSIM SHEARING PRECISION · p. 23

Galaxy-size accuracy

• The size-bias slopes are 4.7 ± 0.7 × 10^-5 for n = 1.5, −1.4 ± 3.6 × 10^-5 for n = 4.5, and −3.4 ± 8.1 × 10^-5 for n = 6.2.All three are below the 2 × 10^-4 multiplicative-bias target, supporting accurate simulation of galaxy sizes for magnification measurements.Source: VALIDATION OF GALSIM SHEARING PRECISION · p. 23

Realistic-galaxy shearing

• Interpolation biases for the two shear components are (−1.3 ± 0.5) × 10^-5 and (−0.2 ± 3) × 10^-5, while c_interp is of order 10^-10.These results use GalSim’s default interpolants and settings; the authors report both shear biases as below tolerance.Source: VALIDATION OF GALSIM SHEARING PRECISION · p. 24

Leakage checks

• Shear-component leakage terms m_(1,2)_interp are of order 1 × 10^-5.The section also checks leakage between magnification and shear.Source: VALIDATION OF GALSIM SHEARING PRECISION · p. 24

Reconvolution accuracy

• For reconvolution, ⟨m_reconv⟩ is consistent with zero and its standard deviation is 3 × 10^-5, below the 2 × 10^-4 target.The test used 270 training-sample galaxies and space-based and ground-based target PSFs.Source: VALIDATION OF GALSIM SHEARING PRECISION · p. 24

• The dataset is used to simulate a realistic galaxy population for GREAT3.Source: REAL GALAXY DATASET · p. 24

HST training sample

• COSMOS imaging combines 575 ACS Wide Field Channel pointings in a 1.64 degrees2 region, with shape-measurement-optimized co-adds at 0.03′′/pixel.The raw images are corrected for charge transfer inefficiency, and multidrizzle performs registration, distortion correction, sky subtraction, cosmic-ray rejection, and combination.Source: HST training sample · p. 24
• Catalog cuts require F814W < 25.2, MU CLASS = 1, CLEAN = 1, and GOOD ZPHOT SOURCE = 1; GREAT3 uses galaxies brighter than 23.5.The photometric-redshift requirement supports tests that the simulated population is representative of reality.Source: HST training sample · pp. 24–25
• For each galaxy, the procedure subtracts background, masks other objects with correlated noise, and uses Tiny Tim PSF models to remove COSMOS PSF effects.The models span primary/secondary separations, the main determinant of PSF ellipticity; they are considered close enough to reality for simulations despite imperfections at long wavelengths.Source: HST training sample · p. 25
• Because calibration targets a redshift-averaged population, large-scale-structure fluctuations in narrow redshift bins effectively cancel, so the sample receives no density-dependent weighting.The passage notes that intrinsic ellipticity distributions can differ between dense and underdense environments, affecting calibration in narrow redshift slices.Source: HST training sample · p. 25

Parametric fits

• Each galaxy was fit with a seven-parameter Sérsic profile and a ten-parameter de Vaucouleurs-bulge plus exponential-disk model, with constrained sizes and shapes.The Sérsic index is restricted to 0.1–6 and axis ratio to 0.05–1; bulge and disk share a centroid, and the bulge half-light radius must be smaller than the disk's. The fitting method follows Lackner & Gunn (2012).Source: Parametric fits · p. 25
• A 2-dimensional Levenberg–Marquardt fit minimizes weighted squared differences between each galaxy image and its PSF-convolved model.Weights use inverse pixel variance from sky and source-photon noise, although the method assumes uncorrelated pixels, unlike the HST postage stamps; exponential-profile fits provide initial values.Source: Parametric fits · p. 25
• Within 1 standard deviation, mean measured-minus-input offsets remain at S/N = 50 or higher.For B/T = 0.3–0.7, B/T errors range from 0.10 to 0.17 as S/N decreases from 100 to 50; bulge and disk half-light-radius errors are 25–44% and 10–30%, respectively. Single-component size uncertainties are 2–10%, and size errors are usually 3 times larger near Sérsic index 4 than for bulgeless exponential disks.Source: Parametric fits · pp. 25–26
• Two-component fits were retained for about one-third of the sample; edge cases or fits with higher MAD instead use single-Sérsic fits.Two-component fits are excluded when B/T is below 0.1 or above 0.9, component parameters reach fit limits, or their MAD is not lower than the single-component fit; unusual bulges at 0.1 < B/T < 0.2 were retained.Source: Parametric fits · p. 26
• Bulge and disk position angles in two-component fits show a significant tendency to align, while allowing non-negligible offsets in the simulations.The comparison is shown in Fig. 11, including for the control experiment.Source: Parametric fits · p. 26

Mimicking a fainter sample

• The method uses a sample with robust two-component fits and simpler single-Sérsic properties, together with B/T, to reproduce observed properties that determine shear calibration.The target observables include S/N, apparent size, intrinsic ellipticity, and morphology.Source: Mimicking a fainter sample · p. 26
• 0.6 scaling of flux and size makes the < 23.5 sample statistically match the < 25.2 sample in apparent size, S/N, n, B/T, and ε, with fewer high-ellipticity objects.The authors note that the missing high-ellipticity objects may be consistent with noise in the faint sample, so their absence could be beneficial.Source: Mimicking a fainter sample · p. 26
• The authors have not confirmed that the transformation reproduces irregular-galaxy fractions, and it may under-represent irregulars and slightly underestimate realistic morphology.They consider this preferable to basing simulations on noisy galaxy images, which would make non-negligible noise part of the galaxies.Source: Mimicking a fainter sample · p. 26

OPTICAL PSF MODELS

• For space-based PSFs, GREAT3 interpolated a WFIRST-AFTA prototype’s Zernike wavefront model through order j = 11 and added aberrations with ensemble RMS wavefront error λ/13.The simulation substituted radial for the prototype’s six non-radial struts, modeled jitter and charge diffusion as Gaussian convolutions, and stretched the FOV to 0.5 × 0.5 deg2 tiles.Source: OPTICAL PSF MODELS · pp. 26–27
• For ground-based PSFs, GREAT3 used an interpolated DECam design-residual model with Zernike terms through order j = 11 and additional aberrations for misalignment and tilt.The model’s 1.56 × 1.56 deg2 FOV was stretched to 2 × 2 deg2, enabling 25 optical PSF tiles per 10 × 10 deg2 image.Source: OPTICAL PSF MODELS · p. 28

The PhoSim atmospheric model

• PhoSim’s atmospheric model represents the air column with seven frozen Kolmogorov screens at different altitudes, whose wind-driven motion perturbs photon paths and includes wavelength- and zenith-dependent dispersion.The screens use a three-dimensional von Karman spectrum split into three scale ranges, with smaller screens combined as photons hit them.Source: The PhoSim atmospheric model · pp. 28–29

Estimation of atmospheric PSF parameters

• Atmospheric ellipticity variance was typically 10−4 to 10−3, with substantial variation among realizations and shape coherence extending to large scales.The PSF size fluctuations were a few tenths of a percent; GREAT3 drew exposure times of 60–180s for the variable-PSF experiment.Source: Estimation of atmospheric PSF parameters · p. 30

GalSim implementation of the atmospheric PSF

• GalSim generated GREAT3 atmospheric PSFs by converting the modeled ellipticity correlation function to a power spectrum and simulating gridded shear with equal E- and B-mode power.The same field’s convergence values provided fractional PSF-size changes, and the simulated grid was extended to avoid correlation cutoffs at image edges.Source: GalSim implementation of the… · p. 30

B-MODE SHAPE NOISE

• Because the training sample fixes intrinsic ellipticity magnitudes, GREAT3 reduced B-mode shape-noise leakage by rank-matching galaxy shapes to target B-mode ellipticities and rotating them into alignment.This retained the sample’s ellipticity distribution rather than replacing it with a Gaussian distribution.Source: B-MODE SHAPE NOISE · p. 31
• Intrinsic-shape E-mode leakage was 7-8 times smaller in variance than expected shot noise, while the procedure preserved the training sample’s ellipticity distribution.The method assigns training galaxies to target pure B-mode ellipticities and rotates them to align their shapes.Source: B-MODE SHAPE NOISE · p. 31

SIMULATING SHEAR FIELDS ON FINITE GRIDS

• On finite grids, GREAT3 approximates the shear as a Gaussian random field sampled at fixed grid points, draws Fourier modes to match the target power spectrum, and applies an inverse DFT.The result approximates the desired shear field when the real-space and Fourier-space grid spacings are sufficiently small.Source: SIMULATING SHEAR FIELDS ON FINITE GRIDS · pp. 31–32