Lensing shear (${\gamma }_1=({\psi }_{,11}-{\psi }_{,22})/2,{\gamma }_2={\psi }_{,12}$)

The trace-free part of the angular lensing-potential Hessian stretches an image anisotropically. The source-image Jacobian matrix has eigenvalues $1-\kappa \pm |\gamma |$. Thus a circular source becomes an ellipse in the local linear approximation; the orientation follows the shear axes.

The combination of lensing shear and lensing convergence governing the local shape distortion of background sources. Galaxy ellipticities estimate it statistically under a specified ellipticity convention and intrinsic-orientation model. It is invariant under the mass-sheet degeneracy, so shape information alone does not generally fix absolute projected mass normalization.

The shear-to-isotropic-focusing ratio inferred from background image shapes. The mass-sheet transformation rescales numerator and denominator equally, leaving this quantity unchanged.