  We investigate a method for the measurement and shaping of a perfect optical
vortex (POV) by using the cross-phase for the first time. Experimentally, we
propose a method to measure the topological charges +3 and +-5 of POVs with the
low-order cross-phase (LOCP) at the Fourier plane; we realize shaping intensity
distributions of POVs at the Fourier plane with the high-order cross-phase
(HOCP) and show the asymmetric modulation ability of the HOCP for an optical
field. Furthermore, we discuss the influence of parameters on the optical field
in the shaping process. On this basis, we propose a secondary energy control
method that combines the characteristics of the POV, which ensures flexible
control of the shape while reducing the impact on the orbital angular momentum
of the original POV. This work provides an alternative method to measure and
shape a POV, which facilitates applications in optical micro-manipulation.
