Non-dispersive spectroscopy

It is also possible to use interference effects to measure spectral energy distributions instead of a dispersing element. The Fabry-Perot is an example of such a type of instrument, although it does not record all wavelengths simultaneously.

Another instrument which uses interference to infer spectroscopy information is the Fourier Transform Spectrometer (FTS), which is basically a scanning Michaelson interferometer. The light from the source is split into two parts using a beamsplitter. One part of light is reflected off a fixed flat mirror and the other is reflected off a mirror which can be moved laterally. The two images are combined to form fringes. The fringe pattern changes as the path length of the second beam is changed. The intensity modulation for a given wavelength ($\lambda$) or wavenumber ( $k=2\pi/\lambda$) is given by:

$$T(k,\Delta x) = {T_{max}\over 2} [a + \cos(2k\Delta x)]$$

and the flux after integrating over all wavelengths is:

$$F(\Delta x) = C \int I(k) T(k,\Delta x) dk = C \int I(k) cos(2k\Delta x) dk$$

where $I(k)$ is the input spectrum. Consequently it is possible to recover the input spectrum by taking the Fourier cosine transform of the recorded intensity. In practice, a discrete Fourier transform is used.

The FTS requires scanning in path spacing. But unlike the Fabry-Perot, it yields information on intensity at all wavelengths simultaneously.