Subtraction artifacts

FIGURE 3.4 Bottom A sample spectrum of a mixture two polymers. Note that there are polystyrene and unknown bands overlapped with each other. Top A subtraction result. The polystyrene peaks have been removed and the unknown peaks are now more clearly visible. 

FIGURE 3.5 A comparison of a reference and a result spectrum reveals an unsubtracted reference band due to liquid water. 

FIGURE 3.6 An illustration of how subtracting two peaks that are not at the same wave-number can lead to derivative-shaped bands in the subtraction result. 

Despite the problems listed here, spectral subtraction, if used properly, is a legitimate way of simplifying mixture spectra, and making them easier to interpret. 

---

Avoid having moving metal objects near the magnet when carrying out nOe difference experiments, to prevent random variations in frequency. A small line-broadening ( 2 Hz) can also be applied to the spectra before or after subtraction, to reduce subtraction artifacts. 

The simplest and most popular experimental method is the well known one-dimensional (ID) NOE difference procedure [3], which is very easily implemented in any spectrometer and which can be routinely set up even by novice spectrometer operators. However, this difference method is based on subtraction of the unperturbed spectrum from the NOE-containing one, both separately recorded, and therefore the required difference information contributes only a small part of the recorded signal. Furthermore, the difference spectrum is very sensitive to subtraction errors, as well as pulse imperfections or missettings, or other spectrometer instabilities, all of which often result in prominent phase distortions or other subtraction artifacts which prevent the accurate measurement of the desired NOE values. Therefore the reliable measurement (or even detection) of enhancements below 1 % is not generally available using this difference method. 

In any difference spectrum, the conditions (temperature, RF power, sensitivity, magnetic field, and vibration) must be identical in the two experiments in order to get perfect subtraction of the signals that are not affected. This subtraction is always imperfect as the two spectra are recorded at different times, so there are always big subtraction artifacts in the difference spectrum. 

Figures 10.2 and 10.3 demonstrate the value of frequent calibration for the case of an unstable laser. An unstabilized single-mode diode laser exhibited mode hops over several hours, causing a laser frequency shift of 13 cm . If the Raman shift axis was not recalibrated after a mode hop, the apparent Raman shift also changes by 13 cm. Spectra before and after a mode hop are shown in Figures 10.2A and 10.2B, along with their difference. The mode hop caused a severe subtraction artifact due to the imprecise Raman shifts. Figure 10.3 shows spectra before and after the mode hop, but with the laser and...

It is not always the case that the minuend and the subtrahend will have the same lineshapes, in that the spectra may have been calculated with different apodization functions (something that should be avoided whenever possible), or the same line-shape may be distorted because of different concentrations. Differences in line-shape will often be exhibited as differences in bandwidth. If the minuend spectrum has bands that are broader than the subtrahend, even when the peak absorbances are matched, the difference spectrum will contain small doublets. The existence of these doublets is often taken as evidence of a minor component in the minuend, but in reality these are rarely more than subtraction artifacts. This phenomenon is generally more apparent when broad bands are subtracted. 

A problem with subtraction results is they are generally noisier than the sample and reference spectra from which they are calculated. Thus the SNR of spectra to be subtracted must be high to begin with to obtain usable subtraction results. Another problem encountered with subtraction results are artifacts, i.e., unwanted spectral features. An unsubtracted reference band, a type of subtraction artifact, is shown in Figure 3.5. 

Recall that large peaks frequently do not subtract completely because they may have a nonlinear absorbance/concentration relationship. These peaks are present in subtraction results and are a form of subtraction artifact. Comparison of the reference spectrum and result can help spot these artifacts any features common to both are unsubtracted reference peaks. This type of comparison is illustrated in Figure 3.5 where an unsubtracted reference peak from liquid water was spotted by comparing the reference to the result. There is nothing we can do to force a particular peak to follow Beer s Law. Hence there is nothing that can be done about unsubtracted reference bands except to learn to recognize them and ignore them. 

For the measurement of homonuclear NOE it is normal to switch off the decoupler just before measurement, in order to reduce artifacts. Small NOE s on sensitive nuclei such as H are conveniently identified by computer subtraction of the enhanced and unenhanced spectra, i.e., by NOE difference spectroscopy. As this subtraction is rarely perfect, it is wise to check for the presence of an overall peak integral to confirm that an apparent residual resonance is not merely a subtraction artifact. The percentage NOE of a peak is readily calculated by comparison of its area with the (negative) area of the large peak which will always arise from saturation at the position of irradiation. Irradiation sufficient for such spectroscopy can be specific within a typical range of +40 Hz. 

---