Metacalibration: Direct Self-Calibration of Biases in Shear Measurement

TL;DR

Weak-lensing studies require precise calibration of how the true reduced shear $g$ maps to observed galaxy ellipticities. The paper introduces metacalibration, a self-calibration method that perturbs real images with a known shear to measure the ensemble response of any per-object shape estimator, enabling direct estimation of multiplicative $m$ and additive $c$ biases without relying on external simulations. The method uses counterfactual images $I'({\mathbf{x}}|{\mathbf{g}})$ and an ensemble-responsivity inference based on histograms of shape measurements, with a per-field minimum-variance estimator for $g$. Validation on GREAT3 simulations shows substantial bias reductions across PSFs, morphologies, and estimators, including detrending of PSF-induced additive biases, suggesting practical applicability to upcoming surveys while noting real-data issues such as masking and blending. Metacalibration thus provides a principled, data-driven path to robust weak-lensing calibration.

Abstract

One of the primary limiting sources of systematic uncertainty in forthcoming weak lensing measurements is systematic uncertainty in the quantitative relationship between the distortions due to gravitational lensing and the measurable properties of galaxy images. We present a statistically principled, general solution to this problem. Our technique infers multiplicative shear calibration parameters by modifying the actual survey data to simulate the effects of a known shear. It can be applied to any shear estimation method based on weighted averages of galaxy shape measurements, which includes all methods used to date for shear estimation with real data. Use of the real images mitigates uncertainty due to unknown galaxy morphology, which is a serious concern for calibration of shear estimates based on image simulations. We test our results on simulated images from the GREAT3 challenge, and show that the method eliminates calibration biases for several different shape measurement techniques at the level of precision measurable with the GREAT3 simulations (a few tenths of a percent).

Figures (7)

• Figure 1: Left: Normalized distribution of metacalibration shear responsivities from regaussianization, on the Control-Ground-Constant branch of the GREAT3 simulations. Right: Distribution of metacalibration PSF ellipticity responsivities from regaussianization, on the Control-Ground-Constant branch of the GREAT3 simulations. A vertical red dashed line is drawn for reference at the expected responsivity for perfectly round objects, $R=2$, in the left panel.
• Figure 2: Shear calibration bias $m_1$before ( left) and afterright metacalibration for the regaussianization ( top), KSB ( middle), and Linear Moments ( bottom) algorithms on the CGC branch. The shaded region covers the same vertical range in each panel. Points excluded by the log-likelihood cut are marked with red squares.
• Figure 3: Effects of the metacalibration algorithm applied to PSF correction. Left panels show the relationship between measured shear and PSF ellipticity before correction, and right panels show the same trends afterwards. Note that the shaded horizontal band covers the same vertical range in each panel. Points rejected by our likelihood cut are shown with red boxes. Simulation branch/algorithm pairs shown in order from top to bottom are RGC-regauss, CGC-KSB, and CGC-moments. The combination of the metacalibration algorithm with our maximum-likelihood averaging procedure makes accurate corrections when the PSF ellipticities are small or comparable to the magnitude of the shear signal. It is clear that a large fraction of the trend remaining after correction is driven by remaining unmasked high-PSF-ellipticity outlier fields. While these were not rejected by our likelihood criterion, they would typically not pass the image quality requirements in a realistic experiment.
• Figure 4: Effects of introducting additional noise. Points with errors correspond to additive shear bias in the control-ground-constant branch when additional noise is added. The noise enhancement factor corresponds to the factor by which the noise in each galaxy image is increased relative to the fiducial GREAT3 simulations. The solid red line shows the expected power-law scaling resulting from correlated noise bias, with a normalization fixed to the measured additive biases.
• Figure 5: Calibration bias results. Each row shows muliplicative calibration bias $m_1$ (top) and $m_2$ (bottom) before and after metacalibration. Pre- and post-correction points are connected by gray arrows: in every case the procedure has reduced or eliminated the amplitude of detectable multiplicative calibration bias.