Narrowing the Gravitational Sight Cone

How does occur narrowing of the gravitational sight cone?
Photon beams are bent by gravity. Only the photon whose emitter is in a line with the center of the star reaches the eye undeflected. Therefore, almost all visible light travels along curved lines.

The image appears magnified; a curved surface appears to be stretched out like a disk. With strong gravity, only a small amount of light comes from the targeted center. However, one can even see the sides that would be obscured in a straight line.
How are the deflection angles of the hyperbolas of light calculated?
One could use Einstein's formula for the deflection of light. To do this, one would have to extend the presumed asymptote until it intersects the radius. Even if this point lies within the star, the entire mass of the star is included in the calculation. The integral then only needs to be evaluated up to the luminous point.

Ludwig Resch