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Exposure-time allocation for a Raman gain ratio must respect channels that are recorded together. The ideal photon-budget allocation for a Raman gain ratio permits four independently adjustable exposures. A probe/reference detector pair instead has a common pump-on exposure $T_{\mathrm{on}}$ and a common pump-off exposure $T_{\mathrm{off}}$.

Let the four positive photoelectron rates be $r_A,r_B$ during pump-on and $r_C,r_D$ during pump-off. Form the gain ratio from exposure-normalized rates. For independent large counts limited by shot noise, its approximate relative variance isWith a fixed live-time budget $T_{\mathrm{on}}+T_{\mathrm{off}}=T$, differentiation or the Cauchy-Schwarz inequality gives

For an original example, let both pump-on rates be $10^6{\mathrm{s}}^{-1}$ and both pump-off rates be $4\times 10^6{\mathrm{s}}^{-1}$. Then $\alpha =2\times 10^{-6}\mathrm{s}$, $\beta =0.5\times 10^{-6}\mathrm{s}$. A one-second live-time budget is best split into $2/3$ second on and $1/3$ second off. Its predicted relative standard deviation is $\sqrt{4.5\times 10^{-6}}\approx 0.002121$, compared with $\sqrt{5\times 10^{-6}}\approx 0.002236$ for equal times.

The 2003 primary stimulated-Raman apparatus recorded probe and reference spectra together, using 97 ms exposures followed by 10 ms readout with the detector-exposure shutter closed. The Raman-pump shutter changed state during readout.^[ref] These acquisition details motivate grouped exposure constraints and readout overhead in Raman exposure allocation. The optimization above uses live time, stationary rates and negligible read noise; a wall-clock budget, detector saturation or sample drift can change which exposures are feasible.

The shot-noise precision of a Raman gain ratio is the statistical precision expected from finite detected photoelectron numbers under a stated counting model. Write the Raman pump-on pump-off gain ratio as $G=AD/(BC)$, where $A,B$ are pump-on probe/reference counts and $C,D$ pump-off probe/reference counts. For large independent Poisson counts, applying first-order propagation to $\log G$ givesThe parent article derives the equal-count limit. Independence, large counts and a calibrated conversion from readout units to photoelectrons are assumptions, not consequences of taking a ratio.

An original imbalanced example has ${\mu }_A={\mu }_B={\mu }_C=10^6$ and ${\mu }_D=10^4$. The relative standard uncertainty is about $\sqrt{0.000103}=1.015\%$. Increasing the three bright channels tenfold only reduces it to about $1.0015\%$: the weakest count channel dominates. Multiplicative detector-gain corrections can make the mean ratio appropriate to the optical experiment, but they do not create additional photoelectrons.

A simple photon-budget allocation for a Raman gain ratio makes the trade-off explicit. If the four mean counts sum to $N_{\mathrm{tot}}$, the Cauchy-Schwarz inequality givesEquality in this ideal unconstrained budget requires equal counts. Near unity gain, four approximately equal means totalling $4\times 10^6$ give about $0.2\%$ relative precision. Actual optical ratios, reference splitting and exposure constraints may prevent exact equality.

The primary FSRS experiment explicitly compared its computed photoelectron shot-noise limit with observed baseline noise and found additional detector structure; it averaged repeated gain spectra and discussed pixel-dependent corrections.^[ref] A counting limit is therefore a useful benchmark, not a guarantee of achieved experimental sensitivity.