 Raman pump-on pump-off gain ratio

A Raman pump-on pump-off gain ratio compares the probe spectrum with and without the narrowband Raman pump, after correcting detector background and normalizing by a reference. For positive dark-corrected probe values $S$ and reference values $R$,Unity denotes no pump-induced change in this model; $G-1$ is the fractional gain. The primary FSRS experiment explicitly performs dark subtraction, reference normalization and the on/off division.^[ref] These operations define a measured optical gain observable, not a direct count of Raman photons alone.

An original offset example has true probe readings $100000$ with pump off and $102000$ with pump on, with an unchanged reference ratio. The true gain is $1.02$. A common unremoved detector offset of $50000$ changes the raw ratio toReference normalization does not automatically remove an additive detector background. Uncertain subtraction also contributes uncertainty to the corrected ratio.

The shot-noise precision of a Raman gain ratio gives a separate statistical limit. If the four inputs are independent Poisson photoelectron counts with large means, first-order propagation givesFor weak gain and all four means approximately $N$, $u(G)\simeq 2/\sqrt{N}$. At $N=250000$, that is about $0.004$: a one-percent gain is only about2.5times this standard uncertainty. These are chosen photoelectron-count assumptions, not an uncertainty specification for arbitrary digitized detector counts.

Shared laser fluctuations, read noise, uncertain references and non-Raman nonlinear effects require their own covariance and response model. The ratio can reveal a weak band only when the acquisition and background control justify its precision. The parent femtosecond stimulated Raman spectroscopy article explains the pump/probe apparatus and supplies a distinct reference-fluctuation example.