# Basic FTIR theory(2) Interference of light waves,Interferogram, Fourier Transform and Single Beam spectrum

## Interference of light waves

In physics, interference is the phenomenon in which two waves superpose each other to form a resultant wave of greater or lower amplitude [Quoted from Wikipedia "Interference (wave propagation)"].

If optical path difference of two light waves ⊿ is 2n (n is integer) times of half wavelength, they will strengthen each other. In case, it is (2n＋1) times of half wavelength , the lights will weaken each other as shown in the following images.

[Optical path difference Δ is

2n times of have wave length]

[Optical path difference Δ is

(2n+1) times of have wave length]

In FT-IR spectroscopy, a device called "Interferometer" which has a fixed mirror and a moving mirror generates optical path difference and makes waves interfer in it.

When waves of each wave number emitted from an IR source enters an interferometer, they will be split by an optic called "beamspliter" which is set 45°oblique against the entrance of the beams to two directions to a fixed and a moving mirror.

Returning beams from two mirrors will join again at the beamsplitter(A beamsplitter also plays a role as a beam combiner) and go out the interferometer with an angle of emergence 90° against entrance beam, then travle through optical path of a spectrometer, and will reach an IR detector.

The feature of an interferometer is that it can make multiple waves given off an IR source at once.

Structure of Interferometer

## Interferogram

Waves of each wavelength will interfer each other and generate superimposed spectrum called "Interferogram" (See the bellow image). Information contained in an interferogram are critical in FT-IR measurement because it will be converted to other spectral file format as absorbance unit and single beam spectra.

In the above image, three cosine waves and their sum, offset by three signal units for clarity. An actual interferogram is more complex, with the amplitude decreasing with distance from the ZPD burst as shown bellow.

On dealing with a FT-IR spectrometer, an operater has to check whether he or she can get a good shaped interferogaram after turning on the spectrometer.

## Fourier Transform

We do not deal with detailed description of Fourlier Transform here because it will go beyond the scope of this page(We are now translating the Japanese page of "Application of Fourier Transform to IR spectroscopy").

In short, the Fourier transform is a mathematical operation that decomposes a time-domain, interferogram signal into its constituent frequencies based on the Fourier Series principle that complicated functions are written as the sum of simple waves mathematically represented by sines and cosines.

an and bn are Fourier factors;

Interferogram is got by plotting signals at each data point detected by IR sensor. He-Ne laser installed in a interferometer emits white color with a single sine curve generate each data points.

## Single Beam Spectrum

Contituent waves can be got by fourier-transforming an interferogram.

Plotting amplitudes of decomposed waves will form a spectrum over wide-range wavelength (In FTIR, the unit "wavenumber" is mainly used.) called "Single Beam spectrum".

Although interferogram has all required information for FTIR analysis, PCs can calculate them as they are. But, it is difficult for humans to read. So, there are usually single beam spectra prepared which are visually easy to understand so that we can know in which analytical regeion absorption occurs.

As we have seen, we will find that, in FTIR, spectral operation is done through PC, not through diffraction grating. And this property will give FTIR spectroscopy an advantage over other spectral technique as dispersive spectroscopy in cases as when we would like to get a spectrum over wide range of wavenumbers with a high resolution. This is called "multiplex advantage" or "Fellgett advantage".