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# What is a Fourier transform spectrometer?

A Fourier transform spectrometer is an adaption of the Michelson interferometer. A collimated beam from a light source is divided into two by a beamsplitter and sent to two mirrors. These mirrors reflect the beams back along the same paths to the beamsplitter, where they interfere. The signal recorded at the output depends on the wavelength of the light and the optical path difference between the beamsplitter and each of the two  mirrors. If the optical path difference between the two beams is zero or  a multiple of the wavelength of the light then the output will be bright, but if the optical path difference is an odd multiple of half the wavelength of the light then the output will be dark.

In the Fourier transform spectrometer, one of the mirrors is scanned in the direction parallel to the light beam. This changes the path difference between the two arms of the interferometer, hence the output alternates between bright and dark fringes. If the light source is monochromatic, then the signal recorded at the output will be modulated by a cosine wave; if it is not monochromatic then the output signal will be the Fourier transform of the spectrum of the input beam.  The spectrum can then be recovered by performing a Fourier transform of the output signal.

In our Fourier transform spectrometer, the two mirrors are replaced by cat's-eye retroreflectors. These always reflect the beam back antiparallel to the axis of the incoming beam, regardless of the angle the beam entered the cat's-eye. Since the reflected beam is displaced from the incoming beam, they have the added advantage that they add a second output to the interferometer.

## Parameters of the NIST FT spectrometer

• Maximum path difference = 2 meters.
• Maximum resolution = 0.0025 cm-1    (0.025 pm at 1 µm; 0.625  pm at 5 µm).
• Maximum resolving power  4 x 106
• Current wavelength range: 200 nm to 5.5 µm (50000 cm-1 to 550  cm-1).
• Beamsplitters:
Fused silica: 200 nm to 2.5 µm      (50 000 cm-1 to 4000  cm-1).
Calcium Fluoride: 1 µm to 10 µm      (10 000 cm-1 to 1000  cm-1).
• Detectors:
Silicon photodiodes: 200 nm to 1.5 µm      (50 000 cm-1 to 6700  cm-1)
Indium antimonide: 1 µm to 5.5 µm      (10 000 cm-1 to 1800  cm-1)