  We study a CR analogue of the Ahlfors derivative for conformal immersions of
Stowe [23] that generalizes the CR Schwarzian derivative studied earlier by the
second-named author [21]. This notion possesses several important properties
similar to those of the conformal counterpart and provides a new invariant for
spherically equivalent CR maps from strictly pseudoconvex CR manifolds into a
sphere. The invariant is computable and distinguishes many well-known sphere
maps. In particular, it vanishes precisely when the map is spherically
equivalent to the linear embedding of spheres.
