  The possibility of spatially resolving the optical properties of atomically
thin materials is especially appealing as they can be modulated at the micro-
and nanoscale by reducing their thickness, changing the doping level or
applying a mechanical deformation. Therefore, optical spectroscopy techniques
with high spatial resolution are necessary to get a deeper insight into the
properties of two-dimensional materials. Here we study the optical absorption
of single- and few-layer molybdenum disulfide (MoS2) in the spectral range from
1.24 eV to 3.22 eV (385 nm to 1000 nm) by developing a hyperspectral imaging
technique that allows one to probe the optical properties with diffraction
limited spatial resolution. We find hyperspectral imaging very suited to study
indirect bandgap semiconductors, unlike photoluminescence that only provides
high luminescence yield for direct gap semiconductors. Moreover, this work
opens the door to study the spatial variation of the optical properties of
other two-dimensional systems, including non-semiconducting materials where
scanning photoluminescence cannot be employed.
