An understanding of the structure of ultrathin polymer films on solid substrates has scientific importance in applications as well as in fundamental studies of polymer diffusion or adsorption. We present studies of the organization of dewetted droplets of polymers on a silicon surface using a new neutron scattering technique, spin-echo resolved grazing incidence scattering (SERGIS), that has the potential to address at the same time the droplet-droplet correlations and the chemical configuration inside each droplet. For the seminal experiments, the polarized neutron reflectometer EVA at the Institut Laue-Langevin, Grenoble, France, was equipped with a spin-echo setup, and measurements were taken on surface structures previously characterized by different techniques. The dewetted polymers used in our studies were pure polystyrene, a mixture of polystyrene and polyparamethylstyrene, and a diblock copolymer of the two homopolymers. Even with a provisional setup SERGIS, we were able to determine the correlation between the droplets, providing results in excellent agreement with those obtained by atomic force microscopy and grazing incidence small-angle X-ray and neutron scattering. In addition, it was confirmed that the correlation function for diblock copolymer droplets is more complex than for polymer mixtures, exhibiting partial ordering of the copolymer within each droplet.