Also known as spectrometry, a spectrographic analysis is a process where chemical elements are determined by measuring the wavelengths or spectral line intensity of a sample of matter. The wavelength or spectral line can be obtained by a form of excitation such as infrared.
When Geordi La Forge tried to find out what caused the mysterious disappearance of his former crewmates of the USS Victory on Tarchannen III, he ran a spectrographic analysis, among other things. The analysis however was without results. (TNG: "Identity Crisis")
A full spectrographic analysis, run by Data, revealed that the Crystalline Entity that destroyed Melona IV in 2368 was the same creature that also devastated Omicron Theta in 2338. (TNG: "Silicon Avatar")