# The Problem of Phase

In high resolution NMR we need to see our peaks as narrow and symmetric as possible. This is equivalent to say that the signals in the FID must be in phase with the instrument receiver. This is not possible, so two steps are taken: 1) the FID is acquired in two channels, in quadrature detection. 2) Phase is corrected computationally afterwards, just remixing these two channels. There is a further complication: each signal has its own phase. So we need to separate signals according to their frequency first. This is exactly what the Fourier Transfom does. Then we can perform phase correction.

The above discussion holds for directly acquired dimensions.
Multi-dimensional spectra also have indirect dimensions. Here the phase shifts
are completely determined by the pulse sequence program, so they can be accurately
predicted. Still each signal requires its own correction, so you still have to
wait until after FT, to apply the correction. From the user's point of view there is
a great difference in phasing a direct dimension or an indirect dimension.

In the former case the user should rely on its eye only. In the latter, he should rely on its
memory first.

While there is only one way, computationally, to apply phase correction, there are two distinct ways to choose the coefficient parameters: either they come from the user or they are guessed by the program. The latter approach is certainly faster, while the former is certainly more accurate. The best solution is to follow both ways: first an automatic, computer driven, correction which brings quite near to the solution in a fraction of second. Then a patient, slow, eye-driven refinement, the manual correction.

As we stated above, phase correction is frequency dependent. For example, in a 1-D experiment, it can be expressed by a function like:

phase = Z + F * frequency.where Z is called the zero-order term, F is called the first-order term. More complicated equations are not used, although in theory they are more accurate. The result, the phase, is the weight to give to the imaginary component when mixing it with the real component. A spectrum has just one real component, but as many imaginary components as axes. Because of this, an n-dimensional spectrum has n equations like the above. Summing things up, a spectrum with n dimensions requires n corrections, and each correction requires two parameters.