Basically the title, the concept is simple, but I`m having a hard time trying to9 find an explicit solution.

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  • have you done some preliminary calculations or given some thoughts to this problem, or do you just want a formula? – ZeroTheHero Dec 8 at 20:02

The Stokes signal intensity $I_S \propto n+1$, while the anti-Stokes intensity $I_A \propto n$, where $n$ is the phonon population following the Bose-Einstein distribution, and the constants of proportionality are the same. $$ n = \frac{1}{e^{\epsilon/kT}-1} $$ Here, $\epsilon$ is the energy of the phonon (= $h c$ times measured wavenumber), and $k$ is the Boltzmann constant. I will leave it as an exercise for the reader to determine $T$ from $I_S/I_A$.

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