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HIGH RESOLUTION FOURIER TRANSFORM
SPECTROSCOPY
H. Buijs, H. Gush
To cite this version:
JOURNAL DE PHYSIQUE Colloque C 2, suppliment au no 3-4, Tome 28, mars avril1967, page C 2
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105HIGH RESOLUTION FOURIER TRANSFORM SPECTRO SCOPY
H. L. BUIJS and H. P. GUSH
The Department of Physics, The University of Toronto, Canada
RBsume.
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Un interfkrometre B deux ondes a Ctk construit pour servir de spectrometre infra- rouge dans la region de 1 a 8 p. L'analyse spectrale, qui est une transformation de Fourier de l'interfkrogramme est faite par un calculateur digital. L'ktat d'interfkrence dans l'interfkrometre est independant de petites rotations du miroir mobile, et une diffkrence demarche allant jusqu'a un metre peut &tre obtenue. L'instrument est utilisC presentement pour mesurer, avec un pouvoir de rksolution ClevC, le spectre de vibration de l'hydrogene gazeux induit par un champ Clectrique intense.Abstract. - A two beam interferometer has been constructed for use as an infrared spectro- meter in the spectral region 1.0 to 8.0 microns ; the spectral analysis, which consists of a Fourier analysis of the interferogram, is carried out by a digital computer. The state of interference in the interferometer is independent of small rotations of the moving mirror and a path difference of up to one metre may be introduced. The instrument is currently being used to measure at high resolution the vibrational spectrum of gaseous hydrogen induced by a strong electric field.
Introduction. - There are a number of problems in molecular spectroscopy which demand for their solution the measurement of spectra at a limit of resolution of 0.1 cm-' or better. To attack such problems we have constructed a two-beam interfero- meter capable of 1 meter path difference, which is used as a Fourier transform spectrometer. At present the instrument may be used in a wavelength region which extends from the visible to 8 microns, the latter limit being imposed by the calcium fluoride beam- splitting plate. Spectra are being measured on a routine basis at a limit of resolution of 0.1 cm-' in a study of spectral line broadening by molecular collisions. The interferometer is capable of much higher resolution than this, but for the specific pro- blem under investigation 0.1 cm-' resolution is ade- quate. The absolute frequencies of the spectral lines in question are of considerable importance ; a specific advantage of the Fourier transform method of spec- troscopy is that each spectrum is automatically cali- brated in frequency provided that a wavelength stan- dard is used to monitor the path difference in the interferometer.
Description of the Apparatus. - A schematic diagram of the optical components of the interfero- meter is shown in figure 1. The light first strikes the b e a n splitting surface where it divides. The beam
FIG. 1.
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Schematic diagram of interferometer showing light path.which travels to the right passes through the com- pensating plate (a corner of which is shown by a dotted line) and is then deflected by a corner mirror to a pair of reflecting prisms ; the light returns to the beam splitting plate via the corner mirror and the compensating plate. The returning beam is spatially separated from the incoming beam because of the lateral displacement at the reflecting prism. The beam which travels to the left is reflected first from one of a pair of flat mirrors ; it is then returned to the other flat mirror by reflection from the prisms, and
H. L. BUIJS AND H. P. GUSH
OUTPUT 4 J OUTPUT 2 l REFLECTING PRISMS ON CARRIAGE
PARATING PLATE COMFENSATING PIATE
INVAR BASE
FIG. 2. -Scale drawing of interferom~ter ; slideway length 17 inches.
recombines with the first beam at the beam splitting
plate. The path difference is changed by displacing MONOCHROM.
the prisms parallel to the light path, the increase in path difference being four times the displacement. Small rotations of the prism pair have no effect on the state of interference. Two output beams are acces- sible for detection, and two input channels are avai- lable for the source.
The mechanical design of the interferometer is shown in figure 2.
The experimental arrangement for studying absorp- tion spectra is shown in figure 3. It is important to restrict the band width of the light falling on the interferometer to strictly the region of interest to avoid saturating the infrared detector with radiation
FIG. 3.
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Overall schematic of experiment.which does not contain useful information. This is accomplished in our system by means of a small grating monochromator between the tungsten filament source and the interferometer. The detector signal, after amplification, is measured by an analog-digital converter associated with a small computer. The path difference in the interferometer is monitored by means of monochromatic fringes produced by the green line of a Hgxg8 isotope lamp. The fringes are converted to a train of pulses which command the A-D converter.
It is essential in the analysis to know accurately the zero path difference location of the infrared inter-
HIGH RESOLUTION FOURIER TRANSFORM SPECTROSCOPY C 2,
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107to define the spectrum in the range of interest; the number of points is reduced to the minimum imposed
by the finite bandwidth of the spectrum by a numerical __-I
filtering performed in real time by the 1 620 IBM computei. This filtering is a convolution of the measu-
red interferogram with the pulse response of a narrow I TABLE OC COSINES lrT HARMONIC
IS ADEQUATE FORTHE
band filter centred on the desired frequency. The F.T. CALCULATION. filtered interferogram is recorded on punched cards. THE SAMECOSINES ,--
The Fourier transformation is carried out by a ARE USED F o a u c H
7094 IBM computer. The most rapid program which HARMONIC BUT I N
DIFFERENTSEQUENCE
we have developed until now consists in the calcula- tion of a cosine table which contains all the cosines necessary to define the complete spectrum. These cosines are used over and over again as is indicated in figure 4. A very simple calculation is adequate to locate in the table the cosine to be associated with a particular point on the interferogram, being given the frequency. However only harmonics of the interfe- rogram are calculated by this procedure ; to facilitate drawing the spectrum it is convenient to interpolate between harmonics by performing a convolution with the instrumental line shape function. The cal- culating time is approximately 0.080 seconds per spectral point per thousand input points.
FIG. 4. -Showing the principle of an harmonic anzlysis.
Results. -The instrument has been used to mea- sure the so-called field induced rotation-vibration spectrum in hydrogen. Because hydrogen is homo- nuclear it has no dipole infrared spectrum ; however, in a strong electric field the molecule is polarized and the fundamental frequency of vibration becomes infrared active. Our interest in this spectrum is in a
C 2 - 108 H. L. BUIJS AND H. P. GUSH
precise measurement of the vibrational frequency and its shift with pressure. In figure 5 is shown the hydrogen spectrum at a pressure of 50 atmospheres. Two spectra are shown, one with hydrogen gas in the cell, but with no electric field, the other with the field applied. (Note : the path length is 10 cm, the field strength is about lo5 volts/cm.) Also, the logarithm of the ratio of the two spectra is plotted. The spectra appear to be noisy, but in fact the irregularities are real structure and disappear when the ratio is taken; the absorption coefficient shows very little noise and it is possible to assign a central frequency for the two
lines to within
