= Exposure-averaged light curve
{title2=$\overline F_i$}
An <exposure-averaged light curve> models what a finite exposure measures. For a constant response during an exposure of duration $\Delta t_i>0$, centred at $t_i$, the expected mean brightness is
$$
\overline F_i=\frac{1}{\Delta t_i}\int_{t_i-\Delta t_i/2}^{t_i+\Delta t_i/2}F(t)\,dt.
$$
The <integral> has units of brightness times <time>; division restores the units of $F$. Observed points fluctuate around this mean. A response that changes during the exposure must instead be included inside the <integral>, as in the first figure's known drift. Exposure duration and the interval between samples are distinct: there may be dead time or missing exposures.
A short dip can be blurred even with perfectly noiseless measurements. For a toy rectangular dip of fractional depth $\delta$ and duration $T<\Delta t$, an exposure containing the whole dip has fractional depth $\delta T/\Delta t$: averaging hides part of its depth. A $1\%$ dip lasting ten minutes therefore appears only $0.333\%$ deep in a thirty-minute exposure. No <interpolation> recovers its shape from that single number without additional assumptions. Forward modelling should average the predicted <light curve> over each exposure before comparing it with the measurements. Kipping's analysis of <exoplanet transit photometry> demonstrates how ignoring this averaging biases inferred system parameters. https://arxiv.org/abs/1004.3741[Kipping (2010), Binning is sinning]{ref}.
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