I found this page on gravitational lensing:
The author claims that the standard lens calculations are wrong.
Take an extreme case: the lens is next to the source (star), the situation of the galactic center, where the observed orbiting stars and estimated a central mass of about 4 million solar masses.
What should be the angle of deflection here: zero or 1/2 of the full deflection (in accordance with the formula GR)?
, this is the full deflection when the light goes from the source at a distance behind the lens d_s, to the observer at a distance from the lens: d_o, and both of these distances are large compared to the parameter b: d_s >> b, and d_o >> b;
After resetting one of these distances, we get half the deflection or zero?
The deflection for the Sun in the direction of 90 degrees, we have: d_o = 0, and: b = 1AU, the stars are far away: d_s >> b:
Apparently, measured 0.004'', or rather half, not zero.
Thus, reversing the situation: from a distant star should measure shift of the Earth's image by the same angle, because the path of light rays in both directions is exactly the same, right?
It is hard to imagine a zero deflection of the image source next to the Sun: d_s = 0 and b = R_s, because then the light would need to run in a straight line, which is impossible in the immediate vicinity of the Sun.
Sun itself should be greater for these 1.7'' (1/2 * 1.7'' around).
Thus, the author is probably right, and those orbits of stars near Sagittarius A* should actually be very deformed (according to GR), but they are not - why?
I think the standard approximations apply only to a particular case: a source is far behind the lens. Then they are applied to all possible cases, and so we have a zero deflection alleged to sources close to the lens, instead of half.