Surface brightness measurements of the diffuse intracluster light (ICL) in centrally concentrated, relaxed clusters have demonstrated that stars bound only to the cluster potential can contain anywhere from 5 to 50% of the total cluster flux. These stars are a by-product of the evolution of galaxies in clusters, and can be used to constrain models for the structure and evolution of clusters and their member galaxies. The ICL will be an important test of cosmological models as it is a baryonic component of clusters that is likely to evolve with redshift. To learn about these processes we are undertaking a program to measure the characteristics of the ICL (total flux, color, and substructure) as a function of cluster mass, morphology, and redshift. We have obtained data for a sample of 10 clusters at low and moderate redshifts. We discuss here our preliminary results for one cluster in that sample, A3888. With 4-5 hour integration times on-source per filter (V & gunn-r), we reach a 1 sigma surface brightness limit of 29.9 mag/arcsec$^{2}$ in the V band. We have identified an intracluster light component that is $\sim10\%$ of total cluster light, extends to 600 kpc from the center of the cluster, and is redder in color than the cluster galaxies ($V-r = 0.4$ near the center, increasing to $V-r = 0.8$ at r = 500 kpc). In addition we find 3 low surface brightness features which are blue ($V-r \simeq 0$), and in total are equivalent to one $m_V = 20.8$ mag galaxy.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html