Effect of spectral resolution

No matter what type of spectrometer is used, a measured spectrum is always slightly different from the true spectrum because of the measurement process, and it is important to recognize that instrumental effects often determine how well Beer s law is obeyed for any chemical system. For example, when a monochromator is used to measure a spectrum, the true spectrum is convolved with the spectrometer s slit function. The effect of this convolution is to decrease the intensity and increase the width of all bands in the spectrum. The convolution of Lorentzian absorption bands with a triangular slit function was reported over 50 years ago in a classic paper by Ramsay [1]. Ramsay defined a resolution parameter, p, as the ratio of the full width at half-height (FWHH) of the slit function to the true FWHH of the band. He showed how the measured, or apparent, absorbance, A, at the peak of a Lorentzian band varied as a function of the true peak absorbance, peak resolution parameter. Not surprisingly, Ramsay showed that as 

Fourier Transform Infrared Spectrometry, Second Edition, by Peter R. Griffiths and James A. de Haseth Copyright 2007 John Wiley Sons, Inc. 

Anderson and Griffiths [2] examined the corresponding behavior for Lorentzian bands measured with a FT-IR spectrometer. They defined the nominal resolution of the spectrometer as the reciprocal of the maximum retardation, so that in this case p is equal to the reciprocal of the product of the maximum retardation, max. and the true FWHH of the band. Plots of log Ap versus log Ap for spectra 

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Andrews, R. W. and Richardson, H. Effect of spectral resolution, detector linearity and chromatographic resolution on peak purity calculations. J. Chromatogr. 683 3-8, 1994. 

In designing a nonscanning spectroscopic monitoring system, two effects have to be considered. In addition to resolution, the number of detector elements also infiuenced the spectra and the predictions. The effect of spectral resolution on the spectra is shown in Figure 21.9, whereas the... 

FIGURE 3.3 The effect of digital resolution on the appearance of NMR spectral features. On the left is a portion of a spectrum with sufficient digital resolution. Successive moves to the right show the effect of reducing the digital resolution. 

Several approaches are possible to minimize the effects of spectral band-spectral line overlap. One method is to use a high resolution spectrometer with narrow slit widths. This method frequently resolves the band into its separate components, thus permitting better separation of spectral line and spectral band components. Another method is to determine if another line is available for use in a different spectral region. For example, there is less OH band interference with the copper 3274.0 A line than with the copper line at 3247.0 A. Cobalt at 2873.1 A is in a region of strong CH band interference, while the cobalt line at 3453.5 A is not. 

In order to understand the theoretical limitations of spectral resolution in classical spectroscopy. Chap. 3 treats the different causes of the broadening of spectral lines and the information drawn from measurements of line profiles. Numerical examples at the end of each section illustrate the order of magnitude of the different effects. 

Similarly, the number of photons detected can be increased by modestly increasing the spectral bandwidth on the emission side. However, again this will have a corresponding effect on spectral resolution. In the most sensitive of instruments the detector, invariably a photomultiplier tube, is cooled to reduce noise and thus improve the signal-to-noise levels. 

Besides the main instrumental effects, finite spectral resolution, and random noise, other modifications of the true spectrum occur. For example, the recorded data cover only certain, often very small parts of the total spectmm. Other spectral regions may offer the opportunity to provide redundant information. Simultaneous analysis of redundant regions is often desirable in order to gain confidence in the deduced conclusions. Radiometric instruments are also subject to systematic errors. Depending on the quality of the on-board calibration system, such errors can be kept within tolerable limits however, the tme magnitude of systematic errors is often difficult to estimate. 

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