Original analysis and influence of the focal shift on the retro-reflected power of cat's eye effect

Focal shift is a critical factor that determines the retro-reflected power of the cat's eye effect. In order to study the rule how the focal shift affected the retro-reflected power of the cat's eye effect, a propagation model on the basis of geometrical optics was built. Then the expressions of the retro-reflected power and the equivalent center of the retro-reflected beam including focal shift were deduced. After that, the influence mechanism under different focal shift was analyzed, some experiments were also done. The results show that the retro-reflected beam can be equivalent to a pyramidal spherical wave when there is a focal shift. With the increase of the focal shift, the distance between the acceptance point and the center of spherical wave becomes larger, so the retro-reflected power decays. The center of spherical wave and the acceptance point are at the same side when the focal shift is positive, otherwise at the opposite sides. Therefore, under the same focal shift, the attenuation caused by the negative focal shift is much larger than the positive one. The experimental result is inline with the theoretical results.