The present invention provides an electromagnetic wave/particle beam spectroscopic instrument that is not easily deteriorated in spectroscopic capability, and is resistant to electromagnetic noise, vibrations, heavy sound, heat and specific particle beams of interest, particle beams other than electromagnetic waves, electric noise due to electromagnetic waves, mechanical destruction, and recoiling of solid constituent atoms and is also more resistant to radiation exposure on the detection means than the conventional energy resolving technologies. A spectroscopic instrument 10 includes a Laplace transform filter 11 that performs Laplace transform on the intensity of an incident spectrum, a detection element 15 that detects a transmitted intensity of the incident spectrum, and an arithmetic device 17 that performs inverse Laplace transform on the detected transmitted intensity of the incident spectrum, thereby calculating the incident intensity of the incident spectrum that has entered the Laplace transform filter 11.