Distinguishing f(R) theories from general relativity by gravitational
  lensing effect
  The post-Newtonian formulation of a general class of f(R) theories is set up
to 3rd order approximation. It turns out that the information of a specific
form of f(R) gravity is encoded in the Yukawa potential, which is contained in
the perturbative expansion of the metric components. Although the Yukawa
potential is canceled in the 2nd order expression of the effective refraction
index of light, detailed analysis shows that the difference of the lensing
effect between the f(R) gravity and general relativity does appear at the 3rd
order when $\sqrt{f''(0)/f'(0)}$ is larger than the distance $d_0$ to the
gravitational source. However, the difference between these two kinds of
theories will disappear in the axially symmetric spacetime region. Therefore
only in very rare case the f(R) theories are distinguishable from general
relativity by gravitational lensing effect at the 3rd order post-Newtonian
approximation.
