Phase correction zero-order

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 antiphase doublet (Fig. 6.14(c)) is dispersive because /-coupling evolution to the antiphase state moves the vectors by 90°, from the +x axis to the +/ and —/ axes. This dispersive antiphase doublet can be phase corrected by moving the reference axis from the +x axis to the +/ axis (90° zero-order phase correction). Now the C = a peak is positive absorptive and the C = ft peak is negative absorptive (Fig. 6.15) and the central 12CH3l peak is pure dispersive because the vector is on the -hx/ axis and the reference axis is now +y (90° phase error). 

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... 

Such a correction is called a frequency independent or zero order phase correction as it is the same for all peaks in the spectrum, regardless of their offset. 

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. 

Step 2 With the cursor in the spectrum window click the right mouse button. The button panel changes to the layout shown on the left and at the same time a cursor appears at the top of the spectrum window designating the reference peak to be used for the zero-order phase adjustment. By default the cursor is set on the maximum signal (Big Point), clicking the Cursor button allows the reference peak to be set manually. Click on the Correct the Phase button to continue with the zero-order phase correction. 

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 . 

Zero-order phase correction is even easier to understand. It lines up the phase of the receiver with the phase of the transmitter so that a resonance that is exactly on resonance will appear purely absorptive—i.e., with no dispersive character. Zero-order phase correction affects every resonance in the entire frequency spectrum by the same amount. 

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