Gravitational-lensing time delay ($\Delta t=(D_{\Delta t}/c)\Delta [\frac{1}{2}|\theta -\beta {|}^2-\psi ]$)

For a thin lens, relative arrival times follow the difference of $\frac{1}{2}|\theta -\beta {|}^2-\psi (\theta )$ between images, multiplied by $(1+z_l)D_l{D}_s/(c{D}_{ls})$. Both geometry and gravitational potential contribute; an additive delay common to all images is unobservable.

The distance combination $D_{\Delta t}=(1+z_l)D_l{D}_s/D_{ls}$ converts a dimensionless thin-lens delay difference into an observed time delay. Inference from a variable lensed source also requires a mass model and control of external convergence.