PURPOSE: We present a theory and a corresponding method to compute high-resolution field maps over a large dynamic range.
THEORY AND METHODS: We derive a closed-form expression for the error in the field map value when computed from two echoes. We formulate an optimization problem to choose three echo times which result in a pair of maximally distinct error distributions. We use standard field mapping sequences at the prescribed echo times. We then design a corresponding estimation algorithm which takes advantage of the optimized echo times to disambiguate the field offset value.
RESULTS: We validate our method using high-resolution images of a phantom at 7T. The resulting field maps demonstrate robust mapping over both a large dynamic range, and in low SNR regions. We also present high-resolution offset maps in vivo using both, GRE and multiecho gradient echo sequences. Even though the proposed echo time spacings are larger than the well known phase aliasing cutoff, the resulting field maps exhibit a large dynamic range without the use of phase unwrapping or spatial regularization techniques.
CONCLUSION: We demonstrate a novel three-echo field map estimation method which overcomes the traditional noise-dynamic range trade-off.