Phase correction first-order

By taking into account the scaling factor in the pulse sequence, the linear BSPS can be effectively removed. Additionally, this linear BSPS can also be corrected by a first-order phase correction. 

In reality the individual lines obtained after the Fourier transformation are composed of both absorptive A(f) and dispersive D(f) components. This non-ideality arises because of a phase shift between the phase of the radiofrequency pulses and the phase of the receiver, PHCO, and because signal detection is not started immediately after the excitation pulse but after a short delay period A. Whereas the effect of the former is the same for all lines in a spectrum and can be corrected by a zero-order phase correction PHCO, the latter depends linearly on the line frequency and can be compensated for by a first-order phase correction PHCl. Both corrections use the separately stored real and imaginary parts of the spectrum to recalculate a pure absorptive spectrum. 

The zero and first-order phase correction parameters may be modified manually either by entering numerical values in a dialog box (Numerical button), or in an interactive way, using the Zero Order and First Order buttons and their corresponding slider box. With the Automatic button a fast and rough phase correction is performed which speeds up the subsequent manual fine adjustments. This automatic phase correction is not the same as the fully automatic (and more time consuming) phase correction mentioned above. 

Attention With spectra measured on spectrometers equipped with digital filters (DMX, DRX spectrometers), the automatically performed phase correction (DMX Phase Corr.) will be applied twice when the newly created FID is Fourier transformed again. This will introduce the baseline roll characteristic for the data of these type of spectrometers. A first order phase correction must then be performed manually by setting the PHCl value close to -22000 for the data available in the NMR data base. 

Varian parameter Ip, Bruker parameter PHC1) to zero and start over using manual phase correction. This time adjust the first-order phase correction by looking at a peak that is close to the pivot peak, and then move to peaks farther and farther away. 

Fig. 2. Theoretical 2H MAS NMR spectra calculated with quadrupolar coupling constant Cq = 200 kHz, asymmetry parameter r Q = 0.10, rotation frequency = 5.0 kHz (left) and uT = 10.0 kHz (right). The spectra represent (a) ideal RF irradiation conditions with RF field strength i/Rf = 100 kHz and optimum pulse length Tp = 2.25 fis, and (b, c) nonideal RF irradiation conditions with i rf = 25 kHz and tp = 4.25 fjbs. The phase distortion effects are illustrated in (b), while (c) demonstrates the result of performing a first-order phase correction. (Adapted from Kristensen et alP with permission.)...

A phase difference between the carrier frequency and the pulse leads to a phase shift which is almost the same for all resonance frequencies (u)). This effect is compensated for by the so-called zero-order phase correction, which produces a linear combination of the real and imaginary parts in the above equation with p = po- The finite length of the excitation pulse and the unavoidable delay before the start of the acquisition (dead time delay) leads to a phase error varying linearly with frequency. This effect can be compensated for by the frequency-dependent, first-order phase correction p = Po + Pi((o - (Oo), where the factor p is frequency dependent. Electronic filters may also lead to phase errors which are also almost linearly frequency-dependent. 

It has already been mentioned in Section 3.2 that the phase of a spectrum needs correcting following Fourier transformation because the receiver reference phase does not exactly match the initial phase of the magnetisation vectors. This error is constant for all vectors and since it is independent of resonance frequencies it is referred to as the zero-order phase correction (Fig. 3.38). Practical limitations also impose the need for a frequency-dependent or first-order phase correction. Consider events immediately after the... 

Luckily, it is often the case that the phase correction needed is directly proportional to the offset - called a linear or first order phase correction. Such a variation in phase with offset is shown in Fig. 4.8 (b). All we have to do is to vary the rate of change of phase with frequency (the slope of the line) until the spectrum appears to be phased as with the zero-order phase correction the computer software usually makes it easy for us to do this by turning a knob or pushing the mouse. In practice, to phase the spectrum correctly usually requires some iteration of the zero- and first-order phase corrections. 

In real experiments after Fourier transformed the lineshapes are mixtures of absorptive and dispersive signals and are related to the delayed FID acquisition (first-order phase error). The delayed acquisition is a consequence of the minimum time required to change the spectrometer from transmit to receive mode, during this delay the magnetization vectors process according to their chemical shift frequencies. The zero-order phase error arises because of the phase difference between the magnetization vectors and the receiver. In NMR-SIM the delayed acquisition is not necessary because the ideal spectrometer approach does not require any switching time and the first order phase correction is normally zero if no other sources of phase deviations are present. 

Step 3 The Zero Order correction is automatically selected, the phase of the reference signal is adjusted using the horizontal slider button in a similar manner to phasing a ID spectrum. Clicking on the First Order button switches to the first-order phase correction which is performed in an analogous way. When the spectrum is correctly phased the phase correction is started using the Accept button. 

A phase correction has to be applied for two reasons The zero-order phase correction PHCO arises because of the phase difference between the receiver and the detection pulse. Additional frequency dependent phase deviations arising from chemical shift evolution in the short delay between the last pulse and the signal detection can be compensated by a first-order phase correction PHCl . 

First-order phase correction. Syn. first-order phasing. The variation in the proportion of ampiitude data taken from two orthogonai arrays (or matrices) wherein the proportion varies iineariy as a function of the distance from the pivot point. 

First-order phase correction has one insidious effect, baseline distortion. A frequency-dependent phase shift cannot make up for the data that were lost during d the baseline error is just the DFT of the missing data. However, provided d is small compared to A, this baseline curvature can easily be corrected during postprocessing of the spectrum. In 2D... 

Figure 5 75.4 Mhz proton -decoupled 13c spectra of 30% menthol in deuteriochloroform, (A)b before and (B) after zero- and first-order phase correction.

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