The invention is directed to methods and apparatus for detecting sequences of optical signals from parallel reactions on an array of nanostructures, such as nanopores, nanowells, or nanoparticles. In accordance with the invention, an array of nanostructures is provided, each nanostructure comprising a reaction site and each capable of confining a reaction that generates a sequence of optical signals, and the nanostructures of the array being arranged in clusters each comprising a number of nanostructures. Each different cluster is disposed within a different resolution limited area and the number of nanostructures in each cluster is either greater than one or a random variable with an average value greater than zero. Optical signals from reactions in the nanostructures are detected by an optical system operatively associated with the array.