A High Precision Metacalibration Response Correction

In Metacalibration the shear response of a weak lensing measurement is estimated by applying an artificial shear to the image, but the shear operation imprints a spin-2 modulation on the image noise power, which biases the measured response. The standard fix adds a sheared noise field that symmetrizes the anisotropy, at the cost of doubling the noise variance ($\sqrt2$ in the noise). The fusion correction presented in this note reaches the same unbiased response while adding only the minimum power needed. It measures the noise power transfer by passing an impulse through the Metacal process, forms the common-level azimuthal deficit that equalizes the spin-2 ($m{=}2$) and spin-6 ($m{=}6$) modulations across the metacal types, and adds just that deficit by filtering the rotated noise field. The fusion correction raises the per-pixel noise by only $\sim2\%$ for a round PSF (versus $\sqrt2$ for the standard correction), rising toward the $\sqrt2$ level only for highly elliptical PSFs.