# Field-of-View and Zooming In

Decreasing the FOV does produce a "zoomed in" image. But as you know, if the object under investigation extends outside the FOV, aliasing occurs. But what if we didn't care about aliasing, or if the object under investigation was is small (e.g. an *ex vivo* tissue sample)?

If we consider what actually changes when we change the FOV at the scanner console, we can understand a bit better what is going on. Decreasing the FOV is achieved by changing two things: gradient strength (G, units: mTm-1) and/or the receiver bandwith (rBW, units: kHz).

### Gradient Strength

The FOV is inversely proportional to the line spacing in k-space. This means that if we decrease the FOV, we're actually increasing the spacing between the lines in k-space. If the matrix size (number of lines) stays the same, this means the lines at the edges of k-space are pushed "further out" in k-space. This is what achieves a resolution increase. But hang on, can we manage to go further out into k-space? What does this demand of the scanner? Going further out into k-space means that we want to encode higher spatial frequencies (more fine detail), and this means that the gradient strength must be increased, to change the magnetic field enough at the edges of k-space so that those spatial frequencies are reached. Thus *we are limited by our maximum gradient strength*.

### Receiver Bandwidth

Bandwidth also affects the FOV. Whatever the gradient strength is, if we reduce the range of frequencies that we consider (a smaller range than that which the gradient has encoded), we narrow our interest to a smaller physical location within the scanner. This is what we want, isn't it? So it would seem that the *minimum limit of our receiver bandwidth* also affects our minimum FOV. What limits minimum receiver bandwidth? Well, nothing actually stops you using a smaller and smaller receiver bandwith. But for smaller and smaller bandwidths, the pixel size would also become so small (for a constant gradient), that the SNR would sink to below an acceptable level.

In fact,

FOV_{min} = rBW_{min} / ~~γ~~G_{max}

where ~~γ~~ = 42.56 MHz T^{-1}.

So we can't keep on "zooming in" even if we wanted to. And just pushing the scanner to its limits has other consequences which we may not desire. For example, decreasing rBW increases SNR if the gradient strength is allowed to vary, which is nice, but it also increases chemical shift artefact, increases geometric distortion and increases the shortest allowable TE.

Further reading on this topic:

Books: MRI From Picture to Proton p127-129, MRI The Basics p160-165