The black circle with radius \(R_s\) represents the event horizon of the black hole.
Photons arrive from the right (\(x=+\infty\)
and \(y=b\)) in the same plane.
Each value of the impact parameter \(b\) gives a different deviation.
In dark blue deviation of \(\pi\over 2\), in light blue deviation of \(\pi\), in green deviation of \(3\pi\over 2\) and in yellow deviation of \(2\pi\) (full revolution).
After a numerical integration in \(\varphi\), the figure is plotted with Cartesian coordinates \(x=r\cos\varphi\) and \(y=r\sin\varphi\), considering a hypothetical black hole of the mass
of the sun \(M\odot\) that is, \(R_s=2 \ 953\ m\), \(b_{crit}=7\ 672.73\ m\)
and with \(b_{\pi\over 2} = 9\ 107\ m\), \(b_{\pi} = 7\ 910\ m\), \(b_{3\pi\over 2} = 7\ 720\ m\) and \(b_{2\pi} = 7\ 682\ m\).
Each value of \(b\) can be obtained by choosing the value of the final variation \(\Delta\varphi\) = deviation + \(\pi\) (target value in an Excel spreadsheet or input data in a Python script).
For a black hole with a different mass \(M\), the plots are kept by applying the scaling factor
\(\frac{M}{M\odot}\).
3D illustration
The black sphere is the event horizon
of the black hole, with radius \(R_s\)
and the light yellow sphere is the sphere
of photons, with radius\(\frac{3}{2}R_s\).
The figure is plotted in three dimensions
(90° and 360° deviations in an xy plane,
180° deviation in an xz plane
and 270° deviation in a yz plane).