= Interferogram of an equally spaced spectral multiplet
{title2=$|g^{(1)}|=|\sin(N\Delta\omega\tau/2)/[N\sin(\Delta\omega\tau/2)]|$}
For $N$ equally intense spectral lines at $\omega_n=\omega_0+n\Delta\omega$, sum their delayed self-correlations as a <geometric series>. The result is
$$
g^{(1)}(\tau)=e^{-i[\omega_0+(N-1)\Delta\omega/2]\tau}
\frac{\sin(N\Delta\omega\tau/2)}{N\sin(\Delta\omega\tau/2)}.
$$
The <interferometric visibility> revives every $T=2\pi/\Delta\omega$. There are $N-1$ zeros between adjacent revivals, at $\tau=jT/N$ for $j=1,\ldots,N-1$. The removable singularity at a revival has unit modulus. Revival spacing fixes line spacing; the internal zero count fixes $N$ under the equal-intensity model. The interferogram alone does not establish a fixed relative phase between the source lines or prove the emission is a coherent pulse train.
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