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 Quote by George Jones Are you interested in what an observer would see with his eyes, or in plotting the trajectory of a photon on a coordinate map, or maybe both? The first thing is somewhat hard, and the second thing is easier. Let me use an example to illustrate what I mean. Suppose a ship makes a long ocean voyage. The voyage could be watched from a telescope on a satellite in geosynchronous orbit, or the voyage could be plotted as a moving, glowing dot on a map.
My end goal will be to render what an observer would see , but for now I would like to simply plot the trajectory of several photons on a coordinate map.

I've been studying geodesics (not with much luck) and reading up on equations for the impact parameter and deflection angle in the schwarzschild metric which I have as :
$$\Delta\phi = \int^{r_{observed}}_{r_{omitted}} \stackrel{dr}{r\sqrt{r^{2}/b^{2} - 1 + R_{s}/r}}$$