Overview
The MGE potential works for spherical profiles but fails for elliptical (4% for Sersic, 1100% for Gaussian). The circular E1 formula with sigma rescaling doesn't capture the elliptical potential correctly. Fix by implementing the Shajib (2019) line integral approach using the existing Faddeeva-based sigma function, matching the Jax-Lensing-Profiles (Herculens) implementation.
Plan
- Add sigma_function method to MGEDecomposer (wrapping existing wofz)
- Replace the E1-based potential with Gauss-Legendre quadrature of the sigma function line integral
- Keep the E1 formula as fallback for spherical profiles (faster, exact)
- Validate against Isothermal/PowerLaw analytic potentials for both spherical and elliptical
Overview
The MGE potential works for spherical profiles but fails for elliptical (4% for Sersic, 1100% for Gaussian). The circular E1 formula with sigma rescaling doesn't capture the elliptical potential correctly. Fix by implementing the Shajib (2019) line integral approach using the existing Faddeeva-based sigma function, matching the Jax-Lensing-Profiles (Herculens) implementation.
Plan