DTI to measure gradients
It is relatively easy to make an image of the static magnetic field itself, using two acquisitions with TE shifting. However, making an image of the gradient fields is harder, since the gradients themselves are what is used to make an image in the first place.
One method is to make an image of a fiducial object, something with some spatial structure that has been measured outside the scanner. Then take an image of this object: its distortions will map the gradient field nonlinearities.
Without such an object, another way is to use an internal reference: the diffusion tensor of pure water (OK, water doped with a T1 relaxation agent to make the signal brighter). This tensor has a known value. Now use a DTI sequence to make an image of this tensor. Its deviation from being a spatially constant multiple of the identity is a measure of the nonlinearity of the gradient fields. Noise is a problem, but since the gradient fields are smooth, we could fit them to the DTI data by an expansion in spherical harmonics.
The advantage of this method is that the only phantom required is a bottle of water, the plainer the better. It would be important to make sure the water was still, so the phantom should be placed in the scanner bed carefully and then left for a while (overnight?) to let internal currents damp out. To calibrate the gradients precisely, the temperature of the phantom should be uniform and known, as well. Details, details, details.
This would be a nice M.S. or postbac project, but is probably too small for a Ph.D. project (unless it can be tricked out with more wrinkles).