Finite-distance corrections to the gravitational bending angle of light
  in the strong deflection limit
  Continuing work initiated in an earlier publication [Ishihara, Suzuki, Ono,
Kitamura, Asada, Phys. Rev. D {\bf 94}, 084015 (2016) ], we discuss a method of
calculating the bending angle of light in a static, spherically symmetric and
asymptotically flat spacetime, especially by taking account of the finite
distance from a lens object to a light source and a receiver. For this purpose,
we use the Gauss-Bonnet theorem to define the bending angle of light, such that
the definition can be valid also in the strong deflection limit. Finally, this
method is applied to Schwarzschild spacetime in order to discuss also possible
observational implications. The proposed corrections for Sgr A$^{\ast}$ for
instance are able to amount to $\sim 10^{-5}$ arcseconds for some parameter
range, which may be within the capability of near-future astronomy, while also
the correction for the Sun in the weak field limit is $\sim 10^{-5}$
arcseconds.
