= Time-corrected electropherogram peak area
{title2=$A_p/t_m$}
A \b[<time-corrected electropherogram peak area>] is a raw <electropherogram peak area> divided by its migration time,
$$
A_{\rm corr}=\frac{A_p}{t_m}.
$$
It compensates for the longer passage time of a slower band through a concentration-sensitive detector in <capillary electrophoresis>. The first-party processing documentation defines this quantity explicitly and computes a percentage by dividing each corrected area by the sum of corrected areas.<Processing Methods - CE data by Waters>[Procedure, Step 5, items 4–5]{ref}
The transport model explains the correction. If the baseline-subtracted detector <signal> is $kc(t)$, internal capillary <area> is $S$ and band speed through the window is constant $v$, then
$$
A_p=k\int c(t)\,dt,\qquad n=Sv\int c(t)\,dt.
$$
With detector distance $L_d$ and $v=L_d/t_m$,
$$
\boxed{n=\frac{SL_d}{k}\,A_{\rm corr}.}
$$
Thus dividing the time integral by migration time removes one speed dependence. It does not determine the response coefficient $k$, injected sample amount or chemical identity.
For an original example, two peaks have raw areas 90 and 150 signal-seconds and migration times 150 and 300 s. Their corrected areas are 0.60 and 0.50 signal units. With equal detector response coefficients, their modeled relative amounts are $6:5$, giving $54.55\%$ and $45.45\%$ of the corrected total. Raw-area normalization would instead give $37.5\%$ and $62.5\%$.
Species-dependent detector response remains important. If the first coefficient is twice the second, amounts are proportional to $0.60/2$ and $0.50/1$, giving $37.5\%$ and $62.5\%$ instead. Equal normalized corrected areas therefore need not mean equal amounts when the detector responds differently to the species. A <measurement calibration> must match the response and sample conditions being interpreted.
The reduction also assumes each band travels at a representative constant speed. If the <electric field> or <electroosmotic flow> changes substantially during a run, $L_d/t_m$ is an overall migration speed and need not equal the speed during detection. Baseline error, unresolved neighbors and nonlinear detector response are likewise not repaired merely by dividing by time. The software's chosen migration-time definition is part of the calculation: its CE mode uses the peak apex, while its CIA mode uses the midpoint of the start and end times.<Processing Methods - CE data by Waters>[Procedure, Step 1, migration-time definitions]{ref}
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