= Solution
<Temporal coherence> measures <correlation> between an optical field and a delayed copy. For a stationary scalar complex field with carrier convention $e^{-i\omega t}$,
$$
\Gamma(\tau)=\langle E^*(t)E(t+\tau)\rangle,\qquad
g^{(1)}(\tau)=\frac{\Gamma(\tau)}{\Gamma(0)}.
$$
The <power spectrum> $S(\omega)\ge0$ and the field <autocorrelation> form a <Fourier transform> pair, the <Wiener-Khinchin theorem>:
$$
g^{(1)}(\tau)=\frac{\int S(\omega)e^{-i\omega\tau}\,d\omega}{\int S(\omega)\,d\omega}.
$$
A <Michelson interferometer> supplies delay $\tau=\Delta L/c$. With equal arm <intensities> and matched <polarization>, its <interferometric visibility> is $|g^{(1)}(\tau)|$; unequal <intensities> or mode mismatch lower visibility independently of <temporal coherence>. The relevant spectrum is the optical field spectrum, not the low-frequency spectrum of detector <intensity> fluctuations.
For a single Lorentzian optical line of angular-frequency <full width at half maximum> $\Delta\omega$, use the narrow-line detuning model
$$
\frac{S(\omega)}{\int S\,d\omega}=\frac{\Delta\omega/(2\pi)}{(\omega-\omega_0)^2+(\Delta\omega/2)^2},\qquad
\boxed{g^{(1)}(\tau)=e^{-i\omega_0\tau}e^{-\Delta\omega|\tau|/2}.}
$$
Such a model describes a phase-diffusing monochromatic source. An $e^{-1}$ <correlation> time is $2/\Delta\omega$, and its <coherence length> is $2c/\Delta\omega$. The Lorentzian extension over all detunings approximates a narrow optical line with $\Delta\omega\ll\omega_0$.
For two equal, mutually incoherent ideal monochromatic spectral lines,
$$
S\propto\delta(\omega-\omega_1)+\delta(\omega-\omega_2),\qquad
\boxed{g^{(1)}(\tau)=e^{-i\bar\omega\tau}\cos(\Delta\omega_{12}\tau/2).}
$$
Here $\bar\omega=(\omega_1+\omega_2)/2$ and $\Delta\omega_{12}=\omega_2-\omega_1$. Visibility has zeros and revivals, so the overall spectral span alone does not determine a unique decay time. Giving each line a common finite Lorentzian linewidth multiplies this beating <correlation> by the corresponding exponential envelope.
\Image[/past-exam-of-the-optics-and-electrodynamics-course-of-the-university-of-cambridge/2012/paper-1-oe2012-coherence-spectra.png]
{title=Original spectrum–coherence examples: a Lorentzian line and a doublet with visibility revivals}
These two examples distinguish irreversible envelope decay from cancellation and revival of discrete spectral components. The line profiles are explicit models, not claimed measurements of a particular source.
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