A MRI machine can generate 3D image of a human brain. A 3D image have three axis x (horizontal), y (vertical) and z (head-foot). First, a slice along z were selected using frequency encoding. Then, the slice (x, y plane) were imaged using phase encoding and frequency encoding and can be converted to human readable image using Fourier transformation. Finally, every slice along z-axis will be imaged to get the final 3D image.

So, "Frequency-encoding may be used to define location either: 1) within a slice, or 2) between slices." How can frequency encoding be used in two dimensions? How can they be distinguished? Why not be used in all three dimensions?


1 Answer 1


In a very general sense, all this measurement techniques are basically interferometry where you have two signals: one from a phase/frequency reference source and the other is the reflected wave that is (semi-)coherent* with the reference.

Because of their coherency these can be added and their interference be detected by an amplitude sensor. To measure distance one measures phase difference between these two signals, reference and echo. This is a very accurate method over a radial distance of one wavelength, the problem is the inherent $2\pi$ ambiguity of the phase measurement because the result is essentially independent of a range variation that is an integer multiple of the wavelength.

To resolve this inherent ambiguity one applies several wavelengths and either simultaneously (more difficult) or consecutively (much easier) one sends multiple frequency tones and measure their phase shits relative to their reference reference. The most common method is the linear chirp signal whose instantaneous frequency is a relatively slow linear function of time compared to the carrier frequency oscillation but there can be other modulation schemes as well.

*semi-coherent meaning that relative to the reference your echo signal partially decoheres because of noise, Doppler shift, multiple reflections, absorptions, etc.; all these will have to be compensated for in the signal processor.

  • $\begingroup$ Could you please explain how slices along z-axis were selected using frequency encoding? $\endgroup$
    – John Smith
    Mar 30, 2022 at 14:03
  • $\begingroup$ With a single frequency (wavelength) you can measure relative phase shift between the local reference and the received echo within a wavelength but this results in $n \lambda$ range ambiguity. Now repeat the phase measurement with several wavelengths and use 1 to resolve the ambiguity. $\endgroup$
    – hyportnex
    Mar 30, 2022 at 14:33

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