  We study dense and highly polydisperse emulsions at droplet volume fractions
\phi >= 0.65. We apply oscillatory shear and observe droplet motion using
confocal microscopy. The presence of droplets with sizes several times the mean
size dramatically changes the motion of smaller droplets. Both affine and
nonaffine droplet motions are observed, with the more nonaffine motion
exhibited by the smaller droplets which are pushed around by the larger
droplets. Droplet motions are correlated over length scales from one to four
times the mean droplet diameter, with larger length scales corresponding to
higher strain amplitudes (up to strains of about 6%).
