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A method for the correction of instrumental broadening of a littrow mount grating spectrometer
Infrared Physics, 1968, Vol. 8, pp. 197-198. Pergamon Press. Printed in Great Britain.
RESEARCH
NOTE
A Method for the Correction of Instrumental Broadening of a Littrow Mount Grating Spectrometer (Received 24 September 1967)
FOR the study of line breadths with a poor resolution
spectrometer, some suitable correction for instrumental broadening is of interest. The well known relationship between the observed intensity distribution,f(v), and the true intensity distribution,fr(r), is:
(1)
where: fs (V - v’) is the instrumental profile which is defined as the apparent normalized intensity detected by the spectrometer at frequency, Y’,for a monochromatic source of frequency, v’. During the investigation of the far-infrared spectrum of boron-doped silicon using a littrow mount grating spectrometer fitted with a grating blazed at 16~ in the first order, a suitable technique was developed to correct J-(V)for instrumental effects and to obtain fr(~). The essence of this correction method is presented here. As a first step to obtain fs (V- v’),a 0.6328 p He-Ne laser radiation was detected in the 25, 26 and 27 orders. In terms of the grating angle, 8, the normalized intensity profile, I(B), measured in all three observations was very nearly Gaussian: 1 I(8) = (qnFa exp - (8 - B’/a)2
where 0 and 0’ are related to h = c/vand h’ = 0.6328~, respectively, by the grating formula (mx = 2dc sin 0); and a depends only on the slit width. By assuming that the most important contributions to the instrumental broadening are due to : (a) wide entrance slits which allow the radiation to be incident on the grating with a non-zero angular spread, and (b) wide exit slits which accept radiation diffracted from the grating in a non-zero angular spread, fs (V - v’) can be obtained quite simply from Z (0) if the instrumental broadening of a single peak centered at frequency ~0, is considered. In this manner one can show that
where
Changing notation
,q (v) = Y [ (2 dc +n~)~ - 1 1)
f(v) -+ f0 (v) where D = ab
(VO)
equation (1) becomes (4) 197
198
Since (5) and
(0) 0,~where OSis that one sees that,pf (v) can be obtained by extrapolating,fD (Y) to 4 = 0, given fV (12)for 0 value of 4 corresponding to the slit widths used. It is noted that this technique is equally applicable to asymmetrical peak profiles as symmetrical profiles and can be employed quite effortlessly if a digital computer is used to analyse the data. Department of Physks The University of British Colrrmbiu Vancouver 8, B.C. Canada
RESEARCH
NOTE
A Method for the Correction of Instrumental Broadening of a Littrow Mount Grating Spectrometer (Received 24 September 1967)
FOR the study of line breadths with a poor resolution
spectrometer, some suitable correction for instrumental broadening is of interest. The well known relationship between the observed intensity distribution,f(v), and the true intensity distribution,fr(r), is:
(1)
where: fs (V - v’) is the instrumental profile which is defined as the apparent normalized intensity detected by the spectrometer at frequency, Y’,for a monochromatic source of frequency, v’. During the investigation of the far-infrared spectrum of boron-doped silicon using a littrow mount grating spectrometer fitted with a grating blazed at 16~ in the first order, a suitable technique was developed to correct J-(V)for instrumental effects and to obtain fr(~). The essence of this correction method is presented here. As a first step to obtain fs (V- v’),a 0.6328 p He-Ne laser radiation was detected in the 25, 26 and 27 orders. In terms of the grating angle, 8, the normalized intensity profile, I(B), measured in all three observations was very nearly Gaussian: 1 I(8) = (qnFa exp - (8 - B’/a)2
where 0 and 0’ are related to h = c/vand h’ = 0.6328~, respectively, by the grating formula (mx = 2dc sin 0); and a depends only on the slit width. By assuming that the most important contributions to the instrumental broadening are due to : (a) wide entrance slits which allow the radiation to be incident on the grating with a non-zero angular spread, and (b) wide exit slits which accept radiation diffracted from the grating in a non-zero angular spread, fs (V - v’) can be obtained quite simply from Z (0) if the instrumental broadening of a single peak centered at frequency ~0, is considered. In this manner one can show that
where
Changing notation
,q (v) = Y [ (2 dc +n~)~ - 1 1)
f(v) -+ f0 (v) where D = ab
(VO)
equation (1) becomes (4) 197
198
Since (5) and
(0) 0,~where OSis that one sees that,pf (v) can be obtained by extrapolating,fD (Y) to 4 = 0, given fV (12)for 0 value of 4 corresponding to the slit widths used. It is noted that this technique is equally applicable to asymmetrical peak profiles as symmetrical profiles and can be employed quite effortlessly if a digital computer is used to analyse the data. Department of Physks The University of British Colrrmbiu Vancouver 8, B.C. Canada