**Fourier-transformed spectroscopy**

*abbr.,*FT spectroscopy (rus. Фурье-спектроскопия) — Optical spectroscopy method that allows to collect the spectrum as a result of inverse Fourier transform of the interference pattern of radiation under analysis, which depends on the difference of optical paths of two rays and is a Fourier-transformed spectrum (a distribution function of emitted energy by frequency).

### Description

The equipment that performs these operations is called a Fourier Spectrometer (FS). It usually consists of a two-beam interferometer, an illuminator, radiation detector, amplifier, analogue-digital converter and a computer.

The interferometer consists of two mutually perpendicular mirrors, fixed and moving, and a semi-transparent beam-splitting plate at the intersection of the incident beams and the beams reflected from both mirrors. A radiation beam from the source, when reaching the plate is divided into two. One of them goes to a fixed mirror, the second goes to a moving mirror, and then both beams are reflected from the mirrors and go through a beam splitter out of the interferometer in the same direction. Further, the radiation is focused on the sample and goes to the radiation detector. The two beams differ in the optical path difference, which varies depending on the position of the moving mirror. As a result of the beam interference, the resulting light flow intensity is periodically changing (is modulated). The modulation frequency is a function of the incident radiation frequency and the moving mirror displacement speed.

Since Fourier spectrometers are much more sophisticated than conventional spectrometers, they have several advantages over other spectral instruments.

1. The entire spectrum can be registered at the same time using FSs. Because interferometers can have a larger inlet than the slit of the spectral dispersion element devices with the same resolution, Fourier spectrometers surpass conventional spectrometers in luminosity, which allows you to:

- reduce the time to record the spectra;

- increase the signal to noise ratio;

- increase the resolution;

- reduce the size of the device.

2. FSs win in the accuracy of wavelength measuring, as diffraction devices measure the wavelength only in indirect ways, and the FS interferogram measures the wavelength directly.

Most often, FSs are used in those studies where other methods are not efficient or applicable. In particular, the most widespread are the infra-red Fourier spectrometers which allow to obtain the vibration spectra in the infra-red region of radiation.

The interferometer consists of two mutually perpendicular mirrors, fixed and moving, and a semi-transparent beam-splitting plate at the intersection of the incident beams and the beams reflected from both mirrors. A radiation beam from the source, when reaching the plate is divided into two. One of them goes to a fixed mirror, the second goes to a moving mirror, and then both beams are reflected from the mirrors and go through a beam splitter out of the interferometer in the same direction. Further, the radiation is focused on the sample and goes to the radiation detector. The two beams differ in the optical path difference, which varies depending on the position of the moving mirror. As a result of the beam interference, the resulting light flow intensity is periodically changing (is modulated). The modulation frequency is a function of the incident radiation frequency and the moving mirror displacement speed.

Since Fourier spectrometers are much more sophisticated than conventional spectrometers, they have several advantages over other spectral instruments.

1. The entire spectrum can be registered at the same time using FSs. Because interferometers can have a larger inlet than the slit of the spectral dispersion element devices with the same resolution, Fourier spectrometers surpass conventional spectrometers in luminosity, which allows you to:

- reduce the time to record the spectra;

- increase the signal to noise ratio;

- increase the resolution;

- reduce the size of the device.

2. FSs win in the accuracy of wavelength measuring, as diffraction devices measure the wavelength only in indirect ways, and the FS interferogram measures the wavelength directly.

Most often, FSs are used in those studies where other methods are not efficient or applicable. In particular, the most widespread are the infra-red Fourier spectrometers which allow to obtain the vibration spectra in the infra-red region of radiation.

#### Authors

- Lourie Sergey
- Veresov Alexander G.

#### Sources

- Fourier transform spectroscopy // Wikipedia, the free encyclopedia. — http://en.wikipedia.org/wiki/Fourier_transform_spectroscopy (reference date: 12.12.2011).
- Fourier( transform) spectroscopy (in Russian) // Physical Encyclopedic Dictionary. — http://dic.academic.ru/dic.nsf/enc_physics/2337/Фурье (reference date: 12.12.2011).