Methods for making rapid and accurate measurements and maps of the transverse relaxation time from a single free induction decay (FID) are proposed. The methods use a multi-echo sequence in combination with B1 insensitive (hyperbolic secant or BIREF2b) refocusing pulses and rapid echo-planar imaging techniques. The results were calibrated against a single spin echo echo-planar imaging sequence using a phantom containing a range of CuSO4 concentrations. The mean percentage absolute difference between the multi-echo and single-echo results was 3% for the multi-echo sequence using the hyperbolic secant refocusing pulse, and 7% for the multi-echo sequence using the BIREF2b refocusing pulse, compared to 13% for a multi-echo sequence using a nonselective sinc refocusing pulse. The use of the sequences in vivo has been demonstrated in studies of gastric function, i.e., the measurement of gastric dilution and monitoring of formation of a raft of alginate polysaccharide within the stomach.