Fourier Transform Techniques

a mathematical procedure developed by a French mathematician by the name of Fourier

converts complex waveforms into a combination of sine waves, which are distinguished by their intensity and frequency

What is a Fourier transform?

Wave 1

Wave 2

Combination

How it works (without any maths)

use a simple 3-line emission spectrum as example

the spectrum you are familiar with is known as a frequency domain spectrum – a graph of intensity vs freq./wavel’gth

this can also be expressed as a function of time – a time domain spectrum

a time domain sp. is no use for analysis

a FT can convert a time domain into a freq. domain spectrum

Wavelength

Time

Fouriertransform

it needs all frequencies to be combined no monochromator no scanning no delay instant spectrum

Time domain spectrum advantage

a time domain spectrum must have enough detail of the variation with time the detector needs to be able to respond quickly enough 500 nm green light has a frequency of 6 x 1014 Hz, or 600,000,000,000,000

oscillations per second no detector that will ever be made could respond this quickly

A problem

Most detectors have a response time of 100 milliseconds. This means they only see an average of what occurs each 100 ms.

a) How many oscillations will occur while the detector responds? 6 x 1013

b) What will be the output from the detector? a flat line

Exercise 7.1

in the late 1800s, Michelson and Morley, built a device which was intended to prove that light moved at different speeds in different directions

to show that a substance known as an ether existed, through which the waveform of light was transmitted

based on constructive and destructive interference known as an interferometer it didn’t work – light travels at the same speed in all directions

How to make the FT idea workable

An interferometer

Interferometer

beam splitter

Radiation Source

Detector

Fixed Mirror

Moveable Mirror

beam is split 50:50 towards

the two mirrors

when it recombinesit will only regain its

intensity if the two beams are

in phase; otherwise it will be less intense

the mirror moves steadily along a path of a few centimetres the intensity at the detector varies due to the varying interference, producing an

interferogram now comes the miracle! the interferogram is:

◦ an exact replica of the waveform of the radiation from the source◦ with a frequency that is directly proportional to the real frequency of the

radiation it does not matter what shape the incoming waveform is, the interferogram will

replicate it

How does this help?

this produces a waveform that can be detected it can processed by the FT calculation need a way of determining the relationship between the real and interferogram

frequencies related to the velocity of travel of the moving mirror this velocity must be known very accurately calibrated using a radiation source of exactly known frequency – a laser

need a sample cell this goes between the interferometer and detector (though all logic says it should

go between source and interf.) a lot of computing power to process all the frequencies used in IR, NMR, NIR, Raman and MS (don’t ask) far superior to scanning (dispersive) equivalents no (repeat no) disadvantages

Putting this in an instrument

a FT-based instrument is like a multi-channel instrument, except it is has only detector◦ speed – the only moving part in the instrument is the mirror,◦ wavelength accuracy – 0.01 cm-1

◦ greater sensitivity – fewer optics, more radiation is passing through the sample◦ better quantitative performance – combination of above two advantages: Abs

> 2 still linear

Advantages of FT

speed allows two possibilities: signal averaging and time-resolved spectra◦ multiple spectra to be run on the same sample◦ these are averaged◦ noise is random and gets averaged out, the peak is constant◦ improved S/N ratio for weak spectra

Advantages of FT

previous advantages have been improvements on dispersive instruments

the ability to run spectra so fast you see reactions occurring is not possible at all on them

spectra at 400 us intervals

Time-resolved spectra