 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

 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 Fourier transform

 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 Hz, or 600,000,000,000,000 oscillations per second  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 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

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