  We investigate the effect of exciton coupling on the optical absorption
spectrum of polymer molecules under conditions of strong inhomogeneous
broadening. We demonstrate that the dependence of the maximum in the rescaled
absorption spectrum on the number of monomers is determined by the average
monomer excitation energies and their resonant coupling and insensitive to the
inhomogeneous broadening. Thus the absorption spectrum can be used to determine
optical interactions between monomers. The results are applied to the
absorption spectra of poly-A poly-T DNA hairpins and used to interpret the
dependence of the absorption spectrum on the number of monomers. We also
discuss exciton localization in these hairpins.
