Let's say we have a monochromatic source of unknown frequency (say, a laser) and some device/sensor that measures the total photon energy absorbed over a fixed time interval (essentially, irradiance).
Since photon counting follows Poisson statistics, we can determine the light frequency via repeat measurements,
$$\langle E\rangle = \langle N \rangle h\nu \\ {\sigma_{E}}^2 = \langle N \rangle h^2 \nu^2$$
where $\langle E\rangle$ is the mean total photon energy across measurements, ${\sigma_{E}}^2$ is the variance, $\langle N \rangle$ is the mean number of photons absorbed across measurements, and $\nu$ is the frequency.
We can find the frequency,
$$ \nu = \frac{{\sigma_{E}}^2}{h \langle E\rangle} $$
This is interesting because you determine the frequency from the variance-to-mean ratio alone without any real calibration required (assuming you can accurately measure the total photon energy).
Has this been meaningfully used in practice or actual research?
My intuition says you could do this at microwave frequencies (with bolometers used to measure total energy). Could you measure a laboratory hydrogen maser this way?
This is probably a terrible estimator compared to just doing spectroscopy - but it's interesting how simple it is (in terms of how few variables it depends on).