Virbhadra–Ellis lens equation

The Virbhadra–Ellis lens equation ^[1] relates angular positions of the unlensed source $\left(\beta\right)$, the image $\left(\theta\right)$, the Einstein bending angle of light $(\hat{\alpha})$, and the angular diameter lens-source $\left(D_{ds}\right)$ and observer-source $\left(D_s\right)$ distances.

$\tan \beta = \tan \theta - \frac{D_{ds}}{D_s} \left [\tan \theta + \tan \left (\hat{\alpha}-\theta\right ) \right ]$.

This lens equation is mainly useful for studying gravitational lensing in a strong gravitational field (see here for more information.)

References

1. K.S. Virbhadra and G. F.R. Ellis, Phys. Rev. D62, 084003 (2000).