Illustration of the different reference frames: the black-hole frame (in black) (x_bh,y_bh,z_bh) labeled in Kerr-Schild coordinates, where the z_bh-axis corresponds to the angular momentum-axis; the orbit frame (in blue) (x_orb,y_orb,z_orb); and finally, the observer frame (in green) (α,δ,z_obs). The angles i′ and Ω′ allow to recover the direction of the angular momentum of the black hole; they give the position of the black-hole frame relative to the observer frame. The point P on the orbit of the star denotes the pericenter.