Deriving Amplification of Images in Schwartzschild Metric

[directbydirecct]

In the paper Strong field limit of black hole gravitational lensing, the amplification of images in the Schwartzschild metric was given by

$$
\frac{1}{\beta}\sqrt{\frac{2\,D_{LS}}{D_{OL}D_{OS}}}
$$However the authors did not derive this expression or explain its origin. Does anyone know how to derive this expression or knows where the author got it from?

Any help is appreciated.

Thanks in advance.

 

[robphy]

I'm not well versed in gravitational lensing... I'm just looking at the form of the equations and googling some of the paper's references.

Using the paper, it seems that this equation (30) looks like it is related to equation (2) since 4GM/c^2=2(2GM/c^2).
But I have no intuition with these quantities $\beta$, $\theta$, $\mu$, etc...

Possibly useful:
http://astro.psu.edu/users/rbc/a504/gravitational_lens.pdf
...apparently extracted from the paper's first reference [Schneider, Ehlers, Falco].