Third order spectroscopy, sometimes revered to as Aspnes's third-derivative, is a technique used to enhance the resolution of a spectroscopy measurement. This technique was first used by D.E. Aspnes to study electroreflectance in 1971. Using 3rd order derivatives can sharpen the peak of a function (see figure). Especially in spectroscopy, where the wave is never measured on one specific wavelength, but always on a band, it is use full to sharpen the peak, and thus narrow the band.
Another advantage of derivatives is that baseline shifts are eliminated since derivatives get rid of shifts. These shifts in spectra can for example be caused by sample handling, lamp or detector instabilities. This way, you can eliminate some of the background noise of measurements.