LensFactory.Lenses.init_PlummerLens — Typeinit_PlummerLens(D_d::Real=NaN, x_c::Real=0.0, y_c::Real=0.0, mass::Real=NaN, x_s::Real=NaN)Initialize a Plummer lens with the given parameters.
LensFactory.Lenses.PlummerLens.potential! — Functionpotential!(ψ::T, θx::T, θy::T, Dol::RV, θxc::RV, θyc::RV, mass::RV, θs::RV) where T <: ROA\[ψ(\pmb{θ}) = \frac{4{\rm G}M}{{\rm c}^2} \frac{1}{D_d} \ln \left( \sqrt{θ_s^2 + |\pmb{θ} - \pmb{θ}_c|^2} \right)\]
LensFactory.Lenses.PlummerLens.deflection! — Functiondeflection!(ψx::T, ψy::T, θx::T, θy::T, Dol::RV, θxc::RV, θyc::RV, mass::RV, θs::RV) where T <: ROA\[\pmb{\hat{α}} (\pmb{θ}) = \frac{4{\rm G}M}{{\rm c}^2} \frac{1}{D_d} \frac{\pmb{θ} - \pmb{θ}_c}{θ_s^2 + |\pmb{θ} - \pmb{θ}_c|^2}\]
LensFactory.Lenses.PlummerLens.jacobian! — Functionjacobian!(ψxx::T, ψyy::T, ψxy::T, θx::T, θy::T, Dol::RV, θxc::RV, θyc::RV, mass::RV, θs::RV) where T <: ROA\[\begin{align*} ψ_{xx} (\pmb{θ}) &= \frac{4{\rm G}M}{{\rm c}^2} \frac{1}{D_d} \frac{θ_s^2 - (\pmb{θ}_x - \pmb{θ}_{xc})^2 + (\pmb{θ}_y - \pmb{θ}_{yc})^2}{\left( θ_s^2 + |\pmb{θ} - \pmb{θ}_c|^2 \right)^2} \\[5pt] ψ_{yy} (\pmb{θ}) &= \frac{4{\rm G}M}{{\rm c}^2} \frac{1}{D_d} \frac{θ_s^2 + (\pmb{θ}_x - \pmb{θ}_{xc})^2 - (\pmb{θ}_y - \pmb{θ}_{yc})^2}{\left( θ_s^2 + |\pmb{θ} - \pmb{θ}_c|^2 \right)^2} \\[5pt] ψ_{xy} (\pmb{θ}) &= \frac{4{\rm G}M}{{\rm c}^2} \frac{1}{D_d} \frac{-2 \: (\pmb{θ}_x - \pmb{θ}_{xc}) \: (\pmb{θ}_y - \pmb{θ}_{yc})}{\left( θ_s^2 + |\pmb{θ} - \pmb{θ}_c|^2 \right)^2} \end{align*}\]
LensFactory.Lenses.PlummerLens.einstein_angle — Functioneinstein_angle(Dol::RV, Dls::RV, Dos::RV, mass::RV, θs::RV)::RV\[θ_E = \sqrt{\frac{4{\rm G} M}{c^2} \frac{D_{ds}}{D_{d}D_{s}} - θ_s^2}\]