What is commonly called Fourier transform spectrometry1,2 is misnamed in as much as the name concentrates on an incidental at the expense of the essentials. The essential feature is multiplexing, and realizing this interferometrically confers some additional advantages, such as removing the need for any dispersing system. The Fourier transform is only an incidental means to these ends.3 It is important to correct these misconceptions, in the interests both of truth and accuracy, and of practical application, because a spectrometer may be Fourier but not multiplex, or multiplex but not Fourier.
I am indebted to Professor N. Sheppard FRS for encouraging me to provide an account of these matters. The text that follows is substantially what I prepared for him, together with some corrections and clarifications that he suggested and for which I am grateful.
The development of multiplex spectrometry was the culmination of a systematic logical process. I had shown4,5 that there is an ultimate limit to the sensitivity of radiation detectors set by fundamental fluctuations in the radiation which the detector exchanges with its surroundings. These fluctuations may be regarded as a combination of wave and particle statistics, the former being dominant in the radio region and the latter in the optical region. I was able to formulate a uniform theory predicting the fluctuations over the whole electromagnetic spectrum, and on comparing the predictions with the actual performance of existing radiation detectors at room temperature I found that they performed within a quite moderate factor of the ultimate limits. Because no major improvement in room-temperature sensitivity was therefore possible, the only way to achieve greatly enhanced performance was to use existing sensitivities more effectively.
I recognize that a major inefficiency in spectrometry in the infrared region, where highly multiple detectors such as photographic plates are not available, is that the available observing time has to be shared among all the observed spectral elements. This inefficiency can be overcome by multiplexing all spectral elements through a single detector; that is to say, imposing mutually orthogonal modulations on the separate elements, and sorting out their individual contributions in the final output. I illustrated the principle notionally2 by reference to the use of a dispersing system feeding a multi-zone mechanical chopper, but it was apparent that a two-beam interferometer scanned at a uniform rate in path difference imposed a sinusoidal modulation on each spectral element at a frequency characteristic of the wavelength, thus achieving what in communication technology is called frequency-division multiplexing; the contribution of the individual elements can then be separated by Fourier transformation.
I presented a practical illustration of this2 using a minimal interferometer comprising a wedge of air between two glass plates. With this I had determined low-resolution spectra of a filament lamp and a mercury discharge lamp.
There was of course nothing new in relating an interferogram to a spectrum. This relationship had been familiar to Michelson. What was new was the use of interferometry to achieve multiplexing and hence a signal-to-noise advantage. It is worthwhile to notice that the multiplexing of a million points by Connes et al.6 means that observations can be secured in one year, which using an otherwise similar non-multiplex spectrometer would have required more time than the human race has existed on Earth!
Michelson worked with line spectra and used fringe visibility, ignoring phases. Therefore he could have calculated only the autocorrelation function of the spectrum. Although Michelson writes as though he had determined spectra by direct Fourier transformation, there seems to be no evidence that he actually did this. His method was probably to guess the spectrum and adjust the guesses until the corresponding fringe visibility matched his observations, which of course is fairly easy with line spectra but virtually impossible with continuous spectra.
I demonstrated the multiplex method using a cube-corner interferometer (which some authors whose grasp of language is weak have misquoted as a corner-cube). First, this relaxes the requirement for the mirrors (as in a Michelson interferometer for example) to remain parallel to within a fraction of the wavelength of light as they are scanned. Second, it enables a lateral shift to be imposed on the go and return beams, so that the beam-splitting and recombining areas can be different. If a semi-reflecting coating is then placed on opposite sides of the substrate in these two areas, the refraction of the substrate is automatically cancelled and no separate compensating plate (as in the Michelson interferometer) is needed. Last, every interferometer must by reciprocity and conservation of energy have two input and two output ports, but these may (as in a Michelson interferometer) not all be accessible. The cube-corner configuration enables all four to be used, thus not only increasing the sensitivity but enabling compensation for (for example) sky background in astronomical observations. In the subsequent work by Connes et al.6 in conformity with the French tradition of fine optics, ‘Cat's eye’ retroreflectors were used for the same purpose.
Electronic digital computers were not available in the 1950s, and I initially performed Fourier transformation by hand with Lipson–Beavers strips, which had been developed for X-ray crystallography.7 At this time the fast Fourier transform algorithm had been forgotten. American authors in particular ascribe this to Cooley and Tukey,8 who certainly popularized it, but it had apparently been known to Gauss in 1805. It had also been known in the 1930s.9–11 The availability of this algorithm greatly increased the scope and applicability of the Fourier transform method.6 The speed and convenience of the fast Fourier transform is greatly enhanced by the fact that digital computers work in binary. Barton12 has shown that factors other than two may be used, but the housekeeping becomes so horrendous that much or all of the speed advantage is lost.
- © 2006 The Royal Society