Exposure-averaged light curve (${\overline{F}}_i$)

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 isThe 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. ^[ref].