  We present a technique for optimal coaddition of image data for rapidly
varying sources, with specific application to gamma-ray burst (GRB) afterglows.
Unweighted coaddition of rapidly fading afterglow lightcurve data becomes
counterproductive relatively quickly. It is better to stop coaddition of the
data once noise dominates late exposures. A better alternative is to optimally
weight each exposure to maximize the signal-to-noise ratio (S/N) of the final
coadded image data. By using information about GRB lightcurves and image noise
characteristics, optimal image coaddition increases the probability of
afterglow detection and places the most stringent upper limits on
non-detections. For a temporal power law flux decay typical of GRB afterglows,
optimal coaddition has the greatest potential to improve the S/N of afterglow
imaging data (relative to unweighted coaddition), when the decay rate is high,
the source count rate is low, and the background rate is high. The optimal
coaddition technique is demonstrated with applications to Swift
Ultraviolet/Optical Telescope (UVOT) data of several GRBs, with and without
detected afterglows.
