I understand that in an atomic clock there is a microwave signal that is locked to the frequency of the atomic rotation. However, if one wants to extract time ticks from the microwave signal (shown below):
$$v(t)=V_0[1+\alpha(t)]\cos[2\pi \nu_0 t+\phi(t)]$$
it would seem that we need to assign a tick of our clock as either when the signal crosses some threshold or when the signal reaches a peak (dv/dt=0). However, in choosing one of these, your ticks will be susceptible to amplitude or phase fluctuations respectively. So, what is the standard that is used in atomic clocks (or more generally if there is a more general standard), and why (i.e. maybe amplitude fluctuations are smaller than phase fluctuations or vice-versa)?