What you’ll be able to do after this lesson

• Explain how one dimension is encoded during the readout and the other over many repetitions
• State why phase encoding, not frequency encoding, dominates scan time
• Explain why motion, wrap and flow artefacts propagate along the phase direction
• Decide when to swap the phase-encode direction, and what it costs

Two dimensions, two different tricks

Slice selection has reduced the problem from a body to a plane. Within that plane you still have to locate every signal in two dimensions, and the scanner uses a different method for each — not out of elegance, but out of necessity.

The reason is that a receiver coil measures one number at a time: the summed voltage from the entire excited slice. It has no idea where any part of that voltage came from. All spatial information must be written into the signal before it is received, using the only two properties a rotating vector has: its frequency and its phase.

Frequency encoding: the readout direction

During the readout — the window in which the echo is actually sampled — a gradient is switched on along one in-plane axis. This is the frequency-encoding or readout gradient.

While it is on, spins at different positions along that axis precess at different rates. The signal arriving at the coil is therefore not a single tone but a mixture: a chord containing every frequency present in the slice, each with an amplitude proportional to how much signal came from the corresponding position.

A Fourier transform decomposes that chord back into its component frequencies and their amplitudes — which, because frequency maps to position, is a profile of signal along the readout axis. One echo, one full row of spatial information, in a few milliseconds.

This is genuinely fast and essentially free. If you increase the readout matrix from 256 to 320 samples, you sample the same echo more finely; the readout lengthens somewhat but no extra repetitions are required. Frequency encoding costs almost no scan time.

Phase encoding: the slow direction

You cannot use the same trick twice. Turn on a second gradient along the other in-plane axis during readout and its frequencies would be indistinguishable from the first gradient’s — the coil would receive one merged chord with no way to separate the axes.

So the second dimension uses phase. Before the readout, a gradient is applied briefly along the remaining axis, then switched off. While it is on, spins along that axis precess at different rates and accumulate different amounts of phase. When it is switched off, they all return to the same frequency — but the phase difference they accumulated is retained. Position has been written into phase.

Here is the catch: a single measurement cannot separate phase from amplitude. A weak signal and a phase-shifted signal look alike in one sample. To resolve the phase axis you must repeat the whole excitation many times, each with a different phase-encoding gradient strength, and compare across repetitions. Only then can the Fourier transform disentangle position along that axis.

The scan-time equation follows immediately:

Scan time ≈ TR × number of phase-encode steps × NSA (÷ echo train length in FSE, ÷ acceleration factor in parallel imaging)

The number of phase-encode steps is the number of repetitions, and therefore the dominant cost of the scan. Readout resolution is nearly free; phase resolution is bought in TRs. This asymmetry underlies almost every speed-up in MRI: fast spin echo fills several phase lines per TR, partial Fourier skips half of them, parallel imaging skips every other one. All of them attack the phase direction, because that is where the time is.

Why artefacts live along phase

Frequency encoding samples one echo in a few milliseconds — a near-instantaneous snapshot along that axis. Phase encoding is assembled from measurements spread over the entire scan, seconds to minutes apart.

Anything that changes between those measurements corrupts the phase axis and only the phase axis:

• Motion — the patient breathes, swallows or shifts between phase steps, so different lines carry inconsistent phase. The Fourier transform disperses that inconsistency into discrete ghosts along the phase direction.
• Pulsatile flow — arterial blood has a different velocity, and therefore different phase, at each phase step. It produces the same ghosting, aligned with the vessel.
• Aliasing (wrap) — tissue outside the field of view along the phase direction is not distinguishable from tissue inside it, because phase repeats every 360°. It folds onto the opposite side. (Along the readout direction, modern systems oversample and digitally filter as a matter of course, which is why readout-direction wrap is rarely seen.)

This single fact — phase is the slow axis, so time-varying problems land on it — is the most useful troubleshooting rule on the scanner floor.

Swapping the phase direction

Because the artefacts are directional, moving the direction moves the artefacts. Swapping phase and frequency encoding does not reduce ghosting; it relocates it, and relocation is often all you need.

Two standard uses:

• Get ghosts off the anatomy. On an axial abdomen, respiratory ghosts run anteroposteriorly through the liver and kidneys. Swap to left–right and the ghosts run across the image where they overlie less critical tissue — at the cost of a wider body dimension along phase, which brings wrap into play unless oversampling is enabled.
• Get flow ghosts off a structure. On axial cervical spine, carotid pulsation ghosts can cross the cord. Swapping the direction, adding a saturation band over the vessel, or applying flow compensation are the three tools, and they are often used together.

The costs to weigh: the FOV along phase must cover the body part (or use oversampling, which spends time), and the object’s dimension along the new phase axis sets how many steps are needed for the same resolution. Swapping is a trade, not a free win.

At the console

An axial T2 of the abdomen returns with clear ghosting through the liver along the anteroposterior axis. Breath-holding was adequate; the patient is stable.

Reason from the physics rather than the artefact catalogue. Ghosts along phase mean something changed between phase-encode steps, and in the abdomen that is almost always respiration or vascular pulsation. Your options are (1) reduce the inconsistency — better breath-hold coaching, respiratory triggering, or a motion-robust radial acquisition; (2) suppress the source — a saturation band over the anterior abdominal wall to remove signal from the moving fat; or (3) relocate the result — swap phase to left–right so the ghosts no longer cross the liver, enabling phase oversampling to prevent wrap from the wider dimension. Most departments do a combination, and the reason each works is now visible to you.

Second case. A registrar asks why the sagittal spine sequence uses a 320 readout matrix but only 224 phase steps, and whether that “wastes resolution”. It does reduce resolution along phase — but the readout samples are nearly free while every phase step costs a full TR. Prescribing phase along the anteroposterior axis, where the body is narrow and fewer steps are needed for the same pixel size, and giving the readout the long head-to-foot axis, is exactly the right way to spend the budget. That choice is deliberate, not a compromise.

Check yourself

Explain in two sentences why doubling the readout matrix costs almost nothing while doubling the phase matrix roughly doubles the scan. Then: a colleague says swapping the phase direction “gets rid of the ghosts”. What is the more accurate description, and what new problem might the swap create?

This is a private prompt. Nothing you write is stored or assessed.

Key takeaways

• The coil measures one summed voltage. Position must be written into the signal beforehand, using frequency and phase.
• Frequency encoding happens during the readout: one echo yields a whole row after Fourier transform, at almost no time cost.
• Phase encoding requires a separate repetition per line, so the number of phase steps dominates scan time — and is what every acceleration technique attacks.
• Anything that varies over the scan corrupts the phase axis: motion, pulsatile flow and aliasing all propagate along phase.
• Swapping the phase direction relocates artefacts rather than removing them, and brings its own FOV and wrap considerations.

References

1. Edelstein WA, Hutchison JMS, Johnson G, Redpath T. Spin warp NMR imaging and applications to human whole-body imaging. Physics in Medicine and Biology. 1980;25(4):751–756 https://doi.org/10.1088/0031-9155/25/4/017
2. McRobbie DW, Moore EA, Graves MJ, Prince MR. MRI from Picture to Proton, 3rd ed. Cambridge University Press, 2017 — ch. 7
3. Bernstein MA, King KF, Zhou XJ. Handbook of MRI Pulse Sequences. Elsevier Academic Press, 2004 — §8.5, phase encoding gradients; §8.1, frequency encoding
4. Elster AD. Questions and Answers in MRI — ‘Frequency encoding’, ‘Phase encoding’ https://mriquestions.com/frequency-encoding.html