We propose a perturbative method to compute the deflection angle of both null and massive particles for source and detector at finite distance. This method applies universally to the motion of particles with general velocity in the equatorial plane of stationary axisymmetric spacetimes or static spherical symmetric spacetimes that are asymptotically flat. The resultant deflection angle automatically arranges into a quasi-inverse series form of the impact parameter, with coefficients depending on the metric functions, the signal velocity and the source and detector locations through the apparent angles. In the large impact parameter limit, the series coefficients are reduced to rational functions of sine/cosine functions of the zero order apparent angle.

中文翻译：

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有限距离和一般速度信号的微扰偏转角

我们提出了一种微扰方法来计算有限距离的源和探测器的零粒子和大质量粒子的偏转角。该方法普遍适用于具有一般速度的粒子在静止轴对称时空或渐近平坦的静止球对称时空赤道面上的运动。由此产生的偏转角自动排列成冲击参数的准逆系列形式，系数取决于度量函数、信号速度以及通过视角的源和探测器位置。在大冲击参数限制下，级数系数被简化为零阶视角的正弦/余弦函数的有理函数。