VCD spectra obtained via FT-IR possesses the high S/N required to exploit this method of resolution en- hancement. VCD spectra, and difference spectra in gen- eral, are very susceptible to errors in interpretation due to cancellation of subtle spectral details caused by pos- itive and negative features lying in close proximity. Use of FSD, however, can retrieve much of this obscured information. This is accomplished without the introduc- tion of artifacts, as was demonstrated with (+)-3-meth- ylcyclohexanone. The spectrum of (+)-limonene was then used to show the dramatic improvement possible when spectral overlap is quite severe. The successful ap- plication of FSD to VCD spectroscopy has important implications for theoretical developments since the pro- gress made to date has occurred despite the badly over- lapped and low resolution spectra provided by most measurements. The principles established in this paper for VCD spectroscopy are also applicable to other types of difference spectroscopy where bandwidth changes be- tween the parent absorptions are not large. ACKNOWLEDGMENTS The authors gratefully thank Dr. David Cameron for his guidance and suggestions during the initial stages of this work. This work was supported by a grant from the National Science Foundation (CHE 83- 02416). 1. J. K. Kauppinen, D. J. Moffatt, H. H. Mantsch, and D. G. Cameron, Appl. Spectrosc. 35, 271 (1981). 2. J. K. Kauppinen, D. J. Moffatt, D. G. Cameron, and H. H. Mantsch, Appl. Opt. 20, 1866 (1981). 3. J. K. Kauppinen, D. J. Moffatt, H. H. Mantsch, and D. G. Cameron, Anal. Chem. 53, 1454 (1981). 4. J. K. Kauppinen, D. J. Moffatt, H. H. Mantsch, and D. G. Cameron, Appl. Opt. 21, 1866 (1982). 5. E. D. Lipp, C. G. Zimba, and L. A. Nafie, Chem. Phys. Lett. 90, 1 (1982). 6. E. D. Lipp and L. A. Nafie, Appl. Spectrosc., 38, 20 (1984). 7. J. I. Steinfeld, Molecules and Radiation (Harper and Row, New York, 1974), pp. 22-24. 8. D. Compton, private communication. Optimum Instrumental Resolution in Condensed Phase Infrared Spectroscopy JYRKI K. KAUPPINEN Department o[ Physics, University of Oulu, 90570 Oulu 67, Finland The optimum instrumental resolution is defined in the case where the instrumental profile width is smaller than the spectral band width. The formulae for the optimum condition are derived as a function of the signal-to-noise ratio with the use of sinc, sinc 2, triangular, and Gaussian shapes as instrumental functions. The results reveal the resolving power advantage of Fourier transform spectroscopy, which is emphasized and compared to grating spectroscopy. Index Headings: Instrumentation, infrared; Techniques, spectroscopic. INTRODUCTION In spectroscopy, the recorded spectrum E'(v) is the convolution of the instrumental function W(v) and the real spectrum E(u). Hence the recorded lineshape, Eo'(V), is given by Eo'(V) = W(v) * Eo(v) = [-oo W(v - v')E~(v') dr' J-co (i) where Eo(v) is the intrinsic line shape function. Received 30 November 1983; revision received 24 January 1984. We can distinguish three cases: 1. When W(v) is much narrower in width than Eo(v), then Eo'(v) ~ Eo(v). 2. When W(v) is much wider than Eo(v), then E0'(v) W(v). 3. When W(P) and Eo(v) are approximately equal in width, then Eo'(V) = W(v) * Eo(v). These three possibilities are illustrated in Fig. 1. In this work, we studied the situation illustrated in the upper row of Fig. 1. Our aim is to find an optimal res- olution, i.e., an optimal width of the instrumental func- tion W(P). On the other hand, there is no interest in doing this in cases where the resolution is limited by the instrumental function as shown in Fig. 1, B and C. In this paper we will outline that, in the case of Fig. 1A, there exists an optimal resolution depending only on Eo(v), W(v), and the S/N ratio of the spectrum. This optimum is simply the situation in which the maximum distortions of E'(v) due to the instrumental function W(v) are equal to the noise in E'(v). We also demonstrate that in the Fourier transform spectroscopy the optimum in- strumental resolution is the lowest possible. We would like to emphasize that this is an important advantage of 778 Volume 38, Number 6, 1984 O003-7028/S4/3SO6-077852,00/O APPLIED SPECTROSCOPY © 1984 Society for AppliedSpectroscopy