Spectral Imaging: Methods, Design, and Applications - Biomedical Optical Imaging Technologies: Design and Applications - page 136

Fig. 4.16 Michelson interferometer that can be used for Fourier spectroscopy. The light is split
by a beam splitter, and the two identical beams travel to two mirrors. Mirror M1 is fixed while
mirror M2 can be shifted with sub-micrometer resolution. The two reflected beams combine at
the detector and the resulted intensity depends on the phase difference that is created due to the
optical path difference that is created. b Sagnac interferometer results in a similar effect, but it is
a “common-path” interferometer. The beams are split by a beam splitter and reflected by mirrors
M1 and M2. The optical path difference is changed by rotating the elements in the observed gray
circle

4.4.4 Fourier-Based Spectral Imaging

Another method for measuring spectral images uses the principle of Fourier
spectroscopy [ 39 , 40 ]. In this technique, the dispersion is performed in the Fourier
domain, unlike all other methods that directly measure the wavelength.
Fourier spectroscopy, also known as Fourier transform spectroscopy, is based on
the use of an interferometer (Fig. 4.16 a).
In this method, there are no filters, grating, or prism and the spectrum is measured
by using the effect of interference of light. An interferometer (Fig. 4.16 a) is a
system that splits the light into two beams, creates an optical path difference (OPD)
which consequently forms a time delay between the traveling beams, and joins
the beams back again to interfere at the detector. The intensity at the detector is
measured at many different OPDs; the output I.OPD/ is called an interferogram
function. The interferogram is actually a representation of the tested spectrum and
by mathematical data transformation, the spectral information can be derived, as
shown below.
Figure 4.16 a shows a Michelson interferometer. It can certainly be used for
spectral imaging, but it is very sensitive to environmental variables such as
temperature changes. It results from the fact that the two splitted beams are traveling
to different mirrors, and every small change in the length will affect the measured
interference pattern and the interferogram.