Gravitational lensing is one of the most impressive celestial phenomena, which has interesting behaviors in its strong field limit. Near such limit, Bozza finds that the deflection angle of light is well-approximated by a logarithmic term and a constant term. In this way he explicitly derived the analytic expressions of deflection angles for a few types of black holes. In this paper, we study the explicit calculation to two new types of metrics in the strong field limit: (i) the Schwarzschild metric extended with an additional $r^{-n}(n\ge 3)$ term in the metric function; (ii) the Reissner-Nordstrom metric extended with an additional $r^{-6}$ term in the metric function. With such types of metrics, Bozza's original way of choosing integration variables may lead to technical difficulties in explicitly expressing the deflection angles, and we use a slightly modified version of Bozza's method to circumvent the problem.

引力透镜是最令人印象深刻的天体现象之一，它在其强场极限下具有有趣的行为。在接近这个极限时，Bozza 发现光的偏转角可以通过对数项和常数项很好地近似。通过这种方式，他明确地推导出了几种类型黑洞偏转角的解析表达式。在本文中，我们研究了强场限制中两种新型度量的显式计算：（i）Schwarzschild 度量扩展了一个额外的$r^{-n}(n\ge 3)$度量函数中的项；(ii) Reissner-Nordstrom 度量扩展了一个额外的$r^{-6}$度量函数中的项。对于此类度量，Bozza 选择积分变量的原始方式可能会导致在明确表示偏转角方面存在技术困难，我们使用 Bozza 方法的稍微修改版本来规避该问题。