the spectrum can be reconstructed using a Fourier transform of the temporal coherence of the light. Michelson spectrographs are capable of very high spectral resolution observations of very bright sources. The Michelson or Fourier-transform spectrograph was popular for infra-red applications at a time when infra-red astronomy only had single-pixel detectors. Imaging Michelson spectrometers are a possibility, but in general have been supplanted by imaging Fabry–Pérot instruments, which are easier to construct. Extracting the spectrum The intensity as a function of the path length difference (also denoted as retardation) in the interferometer and wavenumber is where is the spectrum to be determined. Note that it is not necessary for to be modulated by the sample before the interferometer. In fact, most FTIR spectrometers place the sample after the interferometer in the optical path. The total intensity at the detector is This is just a Fourier cosine transform. The inverse gives us our desired result in terms of the measured quantity : Pulsed Fourier-transform spectrometer A pulsed Fourier-transform spectrometer does not employ transmittance techniques. In the most general description of pulsed FT spectrometry, a sample is exposed to an energizing event which causes a periodic response. The frequency of the periodic response, as governed by the field conditions in the spectrometer, is indicative of the measured properties of the analyte. Examples of pulsed Fourier-transform spectrometry In magnetic spectroscopy (EPR, NMR), a microwave pulse (EPR) or a radio frequency pulse (NMR) in a strong ambient magnetic field is used as the energizing event. This turns the magnetic particles at an angle to the ambient field, resulting in gyration. The gyrating spins then induce a periodic current in a detector coil. Each spin exhibits a characteristic frequency of gyration (relative to the field strength) which reveals information about the analyte. In Fourier-transform mass spectrometry, the energizing event is the injection of the charged sample into the strong electromagnetic field of a cyclotron. These particles travel in circles, inducing a current in a fixed coil on one point in their circle. Each traveling particle exhibits a characteristic cyclotron frequency-field ratio revealing the masses in the sample. Free induction decay Pulsed FT spectrometry gives the advantage of requiring a single, time-dependent measurement which can easily deconvolute a set of similar but distinct signals. The resulting composite signal, is called a free induction decay, because typically the signal will decay due to inhomogeneities in sample frequency, or