Also known as spectromerty, 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 infra-red.
Spock ran a spectra analysis on the dead star Questar M-17, which revealed imploded matter. (TAS: "Beyond the Farthest Star")
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, amongst 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 IVin 2368 was the same creature that also devastated Omicron Theta in 2338. (TNG: "Silicon Avatar")
The USS Enterprise-D ran a spectrographic analysis on a Dyson sphere in 2369 to determine its structure and composition. (TNG: "Relics")