Cycle degree: another characteristic of the vortex phase distribution

A new characteristic of the distribution of the vortex phase, called the cycle degree, is introduced. It is calculated by averaging the phase derivative over the Lp norm for the order p≤1. For p=1, we have a standard definition of the topological charge. It is shown that for p≤1, the cycle degree is no greater than the topological charge and is equal to it for a uniform phase distribution.