Mitigating the Noise-source Coupling Effect in Shear Measurement

Abstract

Subpercent level accuracy in shear measurement is required by the Stage-IV weak lensing surveys. One important challenge is suppressing the shear bias on source images of low signal-to-noise ratios (S/N ≲ 10). Previously, it has been demonstrated that the shear estimators defined in the Fourier_Quad (FQ) method can achieve subpercent accuracy at the very faint end (S/N ≲ 5) through ensemble averaging. Later, it was found that we can approach the minimum statistical error (the Cramer–Rao Bound) by symmetrizing the full probability distribution function (PDF) of the FQ shear estimators (the PDF_SYM approach), instead of taking ensemble averages. Recently, with a large amount of mock galaxy images, we were able to identify some small amount of shear biases in the PDF_SYM approach at the faint end. The multiplicative bias goes up to (1–2) × 10−2 at S/N ≲ 10, and the anisotropy of the point-spread function causes an additive bias that can reach a few times 10−4. We find that these biases originate from the noise-source coupling in the galaxy power spectrum. It turns out that this problem can be largely fixed by adding additional terms to the FQ shear estimators. The resulting multiplicative and additive biases can be significantly suppressed to the level of 10−3 and 10−5, respectively. These corrections substantially extend the available S/N range for accurate shear measurement with the PDF_SYM approach.

Weak gravitational lensing shear measurement with FPFS: analytical mitigation of noise bias and selection bias

“…We test the FPFS shear estimators by running them on mock astronomical images that have been sheared by a known amount. Our mock data are very similar to sample 2 of Mandelbaum et al (2018b), replicating the image quality and observing conditions of the Hyper-Suprime Cam (HSC) survey on the 8 m ground-based Subaru telescope, whose deep coadded 𝑖-band images of the extragalactic sky resolve ∼20 galaxies per arcminute 2 brighter than 𝑖 = 24.5 (Mandelbaum et al 2018a;Li et al 2021). The pixel scale is 0.…”

“…Across a galaxy population, the expectation value of residual noise is zero, 𝜖 𝒌 = 0. For any individual galaxy, the residual noise power includes contributions from the individual realisation of noise, and any correlation between that noise and the galaxy flux (see also Li & Zhang 2021). Combining equations ( 14) and ( 16), the two-point correlation function of the residual noise power is…”

“…The galaxy shapes are approximated with the best-fitting parametric (de Vaucouleurs 1948or Sérsic 1963 profile, sheared, convolved with a model of the HSC PSF, then rendered in 64×64 pixel postage stamp images (including a border around the 32 × 32 pixel region used for shear measurement). The pixel values are finally are multiplied by 2.587 to rescale the units, so their 𝑖 = 27 photometric zeropoint matches that of real HSC pipeline data (Li et al 2021).…”

“…A practical shear measurement method must overcome many challenges to work on real astronomical imaging: including the detection and selection of distant galaxies, correction of detector effects and the ★ mr.superonion@hotmail.com 1 Vera C. Rubin Observatory's Legacy Survey of Space and Time: http: //www.lsst.org/ 2 Euclid satellite mission: http://sci.esa.int/euclid/ 3 Nancy Grace Roman Space Telescope: http://roman.gsfc.nasa.gov/ wavelength-dependent point-spread function (PSF), and the combination of noisy pixellated data (for a review, see Mandelbaum 2018). Some methods (Mandelbaum et al 2018b;Kannawadi et al 2019;Li et al 2021;Hoekstra 2021) advocate empirical calibration of shear estimators such as reGauss (Hirata & Seljak 2003) and lensfit (Miller et al 2007;Fenech Conti et al 2017) using simulated images. That merely shifts the challenge to one of accurate simulation.…”

“…Several other existing methods also meet the Stage IV weak-lensing surveys' requirement on systematics control for isolated galaxies, including METACALIBRATION (Huff & Mandelbaum 2017;Sheldon & Huff 2017), Fourier_Quad (Zhang et al 2017;Li & Zhang 2021), BFD (Bernstein & Armstrong 2014;Bernstein et al 2016) without relying on calibration using external image simulations. Continuing to develop several methods simultaneously remains a useful mitigation of risk.…”