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In NMR, the protons’ frequencies are affected by the magnet which makes them precess around its magnetic field so now all protons will have different frequencies according to their environment including shielding and de-shielding effects. As I read, the radio frequency pulses only change the resonance of protons and make their $ω$ angle change $180^{o}$ to be induced inside the coil and make signals that can be measured.

  • But if this true why do we have to use different gradient coils and phase encoding gradient coils in MRI, if the protons really have different frequencies?
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    $\begingroup$ The gradient coils allow the experiment to be sensitive to the position of the protons, which you need for imaging. They are not necessary for most chemical structure MRI algorithms. $\endgroup$ – CuriousOne Dec 26 '15 at 21:14
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First of all, try to imagine a simple MRI experiment with an perfectly homogeneous main magnetic field in the order of 1-3 T and an object to image that only contains protons of the same kind (i.e. the signal-baring protons are chemically all of the same kind in the object, i.e. there is only water in your object).

  • When the object is brought into the main magnetic field, the protons align their magnetic moments along this field (note: this is a classical description and it is the one to go to understand MRI). All the protons have the same resonance frequency, since they are all subject to the same main magnetic field.

  • The radio-frequency coils are built in a way that their magnetic field is perpendicular to the main magnetic field. You can achieve this with a simple solenoid coil, if you place its axis of symmetry perpendicular to the main magnetic field. More sophisticated designs are normally used nowadays (e.g. the bird-cage design that is the standard for clinical applications).

  • If a current is sent through the coil with the correct frequency (Larmor-frequency; dependent on the nucleus under investigation and the main magnetic field strength), the magnetic field of the coil will act upon the magnetic moment of the protons and tilt the magnetization vector away from its initial position. Note that the pulse parameters (e.g. its duration and its amplitude) determine how far the magnetization vector is deflected. This angle is called the flip angle and can in principle have arbitrary values. Especially it is not always 180° as you assumed in your question.

  • The RF pulse acted upon all protons, since no additional gradient field was applied during its irradiation. This is a common procedure for 3D imaging.

  • After the RF-pulse, all protons resonate on the same frequency and irradiate RF waves themselves while they precess and realign with the main magnetic field again. From this signal, no spatial information is available.

Here comes the spatial encoding part

To get the spatial distribution of the protons from the signal, the resonance frequency must vary in space. For this, additional (linear) gradient fields are switched on and off.

  • The deflected magnetization vectors of the protons experience slightly different magnetic fields when such a gradient field is applied. They therefore resonate on slightly different frequencies in the direction of the gradient field. All protons perpendicular to the axis of the gradient experience the same field and resonate on the same frequency. Therefore, your signal is basically the projection of the proton distribution along the direction of the gradient field.

You could repeat this process with gradient fields in all possible directions and use a 3D filtered back-projection to gain the distribution of the protons. However, today usually the linear gradient is kept constant (i.e. the frequency distribution along the direction of this gradient field is the same in each measurement step), and a second and a third, additional gradient field are applied after excitation and before the signal acquisition.

  • Those additional gradient fields to the same thing as the initially introduced gradient field, but they are applied for a short time only. Hence, they cause the protons to resonate on different frequencies along their directions for a short time. When these gradient fields are switched off, the protons resonate again on the same frequency, but have experienced a position-dependent change in their phase.

  • Those phase shifts are varied over and over again by applying the second and third gradient with different strengths. Therefore, each acquired signal is modulated from those gradients.

  • Finally, you can reconstruct your proton distribution by using a Fourier Transformation of your acquired signals. This works, because you use linear field gradients and (of course) choose the different gradient steps appropriately to fulfill certain criteria (basically the sampling theorem).

I hope this lengthy answer is of help to you, since I assume that you do confuse the roles of RF pulses and gradient fields somehow. It is a bit difficult in MRI with all the different fields and what they do.

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