We investigate a method for the generation and measurement of high-order optical vortices (OVs) by using the cross phase (CP), which is applied to implement interconversion between Laguerre-Gauss (LG) beams and Hermite-Gaussian beams in the far-field. Experimentally, we generate LG beams, which are a kind of typical OVs, with 20 radial nodes, and measure OVs with topological charges up to 200 via the CP. On this basis, we discuss the relationship between intensity distributions and the waist radius of initial light beams. This work provides an alternative method to generate and measure high-order OVs, which is useful in the fields of optical micro-manipulation, high-dimensional quantum entanglement, and remote sensing of the angular rotation of structured objects.