A Novel Method for Calculating Deflection Angle with Finite-Distance Correction

In recent study in Ref.[7] (arXiv: 2401.12525), we have introduced a method aimed at calculating the weak-field asymptotic deflection angle. This method offers an efficient computational approach that avoids the complexities of integration and cumbersome iterative procedures typically associated with deflection angle calculations. In the present paper, we expand upon this method to encompass finite-distance deflection scenarios, wherein it is postulated that both the distances from the source to the lens and from the observer to the lens are finite. Importantly, this extension naturally encompasses the case of a lens in asymptotically non-flat spacetime. As an illustrative example, we apply this method to compute the gravitational deflection angle of massive particles in Kerr spacetime while accounting for the effects of finite distance.