You recall vibrations IR spectrometers detect in the range of $4000\dots\pu{800 cm^{-1}}$ typically are either fundamental vibrations and combinations. Tuning for shorter wavelengths / higher wavenumbers however renders recording absorptions about overtones instead of fundamentals more likely. On occasion, you may encounter this part of the electromagnetic spectrum accessed by the larger UV-Vis-NIR spectrometers (e.g., PerkinElmer Lambda series) with a spectral range from $175\dots\pu{3300 nm}$); here, NIR is the label about near infrared.
The typical overtone is less probable than the fundamental, thus -- in parlance of Beer-Lambert's law, $\mbox{Abs} = \varepsilon \cdot c \cdot d$ -- the molecular absorption coefficient $\varepsilon$ is smaller. While this may appear on first sight as a drawback (at same analyte concentration $c$ and pathlength $d$, this lowers $\mbox{Abs}$ recorded), it very well may become an advantage if you want to record absorption bands about matter in high concentration, e.g., to check the quality of grain and crops in general where NIR spectroscopy is used as such.
IR spectroscopy has a long tradition of chemometrics, e.g. in the on-line process control of petroleum fractions where whole spectra are used to determine concentrations of components (e.g., keyword principal component analysis) allowing to map a sample for its chemical composition as tool in histology (a review). Again, tuning the senors to record NIR instead of the range of $4000\dots\pu{800 cm^{-1}}$ allows to see some things literally in a different light (e.g., Landsat satellites, farming).
(credit)
