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Photon-budget allocation for a Raman gain ratio distributes measurement effort among the channels entering a ratio. For four large independent Poisson photoelectron counts with means ${\mu }_i$, the shot-noise precision of a Raman gain ratio has approximate relative variance $V={\sum }_{i}1/{\mu }_i$. With a freely allocatable fixed total expected count $N$, the minimum is $16/N$ at equal counts. The constraint matters: fixed total exposure time is a different optimization problem.

Suppose channel $i$ has known photoelectron rate $r_i>0$ and an independently adjustable exposure $t_i>0$. Estimate the optical ratios from exposure-normalized rates, so the known exposure factors are included. Then ${\mu }_i=r_i{t}_i$ and a total time budget ${\sum }_i{t}_i=T$ givesThe Cauchy-Schwarz inequality, or differentiation with a constraint multiplier, givesThis exposure-time allocation for a Raman gain ratio spends longer on weak channels without necessarily equalizing their final counts.

For an original one-second budget, let two rates be $4\times 10^6$ and two be $10^6$ photoelectrons per second. The optimal exposures are $1/6$ second for each bright channel and $1/3$ second for each weak channel. Expected counts are about $666667$ and $333333$ respectively, with relative standard uncertainty $0.0030$. Four equal exposures would give about $0.003162$ instead. The gain comes from allocating the stated resource more efficiently, not creating additional information by normalizing counts.

The primary FSRS detector records probe and reference spectra together and alternates pump-on/off exposures.^[ref] Such linked channels cannot have four independently chosen exposure times; the appropriate grouped constraints must replace the ideal model above. Read noise, dark uncertainty, saturation and sample change can alter the optimum as well.

Readout overhead in Raman exposure allocation is the detector time that consumes the acquisition budget without collecting useful probe/reference photons. For $n$ pump-on/off exposure pairs, let each frame require a fixed closed-shutter readout duration $d$. A wall-clock budget $W$ leaves total live timeUnder the stationary-rate, independent shot noise model of exposure-time allocation for a Raman gain ratio, its minimum approximate relative variance at fixed $n$ isReadout changes the available live time, but not this optimum ratio when the overhead is fixed and independent of the on/off allocation. The live-time formula itself ceases to describe all constraints when exposures hit saturation limits or the number of pairs is variable.

The 2003 primary stimulated-Raman experiment used 97 ms exposures and 10 ms detector readout with the exposure shutter closed. The pump shutter switched state during readout, giving successive on/off measurements.^[ref] These reported settings give an idealized two-frame cycle of $2(97+10)=214\mathrm{ms}$, containing $194\mathrm{ms}$ live time. The paper describes the practical full cycle as approximately 220 ms, so the two-duration sum need not include every system delay.

For an original comparison at fixed wall time, the 214 ms idealization has live fraction $194/214\approx 0.9065$. Relative to a hypothetical zero-overhead detector at the same rates and on/off allocation, the shot-noise variance is multiplied by $214/194\approx 1.1031$, and its standard deviation by about $1.0503$. Using 10 ms rather than 97 ms exposures with the same 10 ms readout would give a live fraction $1/2$ and a variance penalty of two.

Longer frames reduce the fractional overhead but cannot be extended without limit. A maximum-exposure constraint in paired Raman acquisition can arise from saturation, while drift rejection can require frequent on/off alternation. Thus minimizing readout count alone is not a complete acquisition design; the applicable frame limits and switching cadence belong in the optimization.