Adapting a student Michelson interferometer to function as a Fourier transform spectrometer

Abstract

The theoretical work of Jacquinot and Fellgett, followed by the experimental demonstrations by Connes and Connes led to a survival of interest in Fourier Transform Spectroscopy in the period 1970 - 1980. Two kinds of Fourier transform spectrometers were discussed: (a) The Diffraction Grating Spectrometer outputs the Fourier transform of the amplitude function of a set of apertures, with the square of the Fourier transform representing directly the spectrum of the source; (b) The Michelson Interferometer in which the output is the result of interference effects between the two beams as the optical path difference is changed. This "interferogram", which is a measure of the variation in intensity at the centre of the fringe pattern with optical path difference, bears no resemblance to the source spectrum. The source spectrum can be obtained as the Fourier transform of the interferogram. A derivation of the integral equation which relates the interferogram to the spectrum was given. The prevention of "aliasing" and methods of reducing noise by apodization were described. A manually-operated student Michelson interferometer was adapted to operate as a Fourier Transform Spectrometer. The standard Michelson interferometer was first used to view circular fringes located at infinity. Then the set-up was converted to Twyman-Green mode, with a collimated input beam and an output beam focused on a solid-state detector. Using a stepper motor to move the translating mirror over small intervals, the resulting interferogram was displayed on an oscilloscope in analogue form. An analogue-to-digital converter sent the data to a PC hard disk. Using Microsoft Excel, the Fourier transform of the data was performed and the spectrum plotted. Scans were taken with different sources: Hg lamp, solid state laser, Na lamp and filament lamp. Scans with unfiltered and filtered sources were taken, using yellow, green and violet filters. Some scans were apodized using triangle and Gaussian functions; a scan intended to show the effects of aliasing was also taken. The results were discussed and further work suggested.