Is the spatially averaged spectrum equal to the global spectrum?

Near-field optical spectroscopy and microscopy give access to excitations that cannot be revealed in the far zone. In order to investigate these remarkable differences, we present a theoretical analysis of the local optical properties of semiconductor quantum wells including the effects of disorder arising from interface fluctuations. The far-field absorption spectrum is compared with spatially averaged absorption spectra calculated at different spatial resolutions. We find that summing up local optical spectra does not reproduce the global spectrum in contrast to findings at diffraction-limited resolutions.