def alpha(self, theta_x, theta_y, kwargs_lens, k=None):
        """
        reduced deflection angle

        :param theta_x: angle in x-direction
        :param theta_y: angle in y-direction
        :param kwargs_lens: lens model kwargs
        :return:
        """
        beta_x, beta_y = self.ray_shooting(theta_x, theta_y, kwargs_lens)
        alpha_x = theta_x - beta_x
        alpha_y = theta_y - beta_y
        return alpha_x, alpha_y
reduced deflection angle

        :param theta_x: angle in x-direction
        :param theta_y: angle in y-direction
        :param kwargs_lens: lens model kwargs
        :return: