Deep-Field Analytical Calibration

Abstract

The next generation of imaging surveys, including the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), Euclid, and the Nancy Grace Roman Space Telescope, will place unprecedented constraints on cosmology using weak gravitational lensing. To fully exploit their statistical power, shear measurement methods must achieve sub-percent accuracy while mitigating systematic biases from noise, the point-spread function (PSF), blending, and shear-dependent detection. The analytical calibration framework (\texttt{AnaCal}) has demonstrated such accuracy but requires adding noise to images, reducing their effective depth. We introduce Deep-Field Analytical Calibration (\textsc{deep-field~}\texttt{AnaCal}), an extension of \texttt{AnaCal} that leverages deep-field images to compute shear responses while preserving wide-field statistical power. We validate the method on isolated and blended galaxy simulations with LSST-like seeing and noise, showing it meets the stringent requirement of multiplicative bias $|m| < 3\times10^{-3}$ at 99.7% confidence. Relative to standard \texttt{AnaCal} on wide-field images, this method improves effective galaxy number density from $17$ to $30$ arcmin$^{-2}$ for simulated 10-year LSST data. Assuming deep fields with $10\times$ the exposure of wide fields, we find the pixel noise variance in shear estimation is reduced by $30%$ and the overall shear uncertainty by $\sim 25%$. Finally, we assess sample variance impacts using the LSST Deep Drilling Fields strategy, finding an equivalent calibration uncertainty of $\lesssim 0.3%$. These results establish \textsc{deep-field~}\texttt{AnaCal} as a promising approach for shear calibration in upcoming weak lensing surveys.