  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 Combination Wave 1 Wave 2

     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 Fourier transform Time

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

    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 10 14 oscillations per second Hz, or 600,000,000,000,000 no detector that will ever be made could respond this quickly



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 10 13

b)



What will be the output from the detector?

a flat line

     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

beam is split 50:50 towards the two mirrors Radiation Source Fixed Mirror Moveable Mirror Detector beam splitter Interferometer when it recombines it 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

      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

 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

 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

   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