Optimal echo times for multi-gradient echo-based B0 field-mapping

B-0 field maps are used ubiquitously in neuroimaging, in disciplines ranging from magnetic resonance spectroscopy to temperature mapping and susceptibility-weighted imaging. Most B-0 maps are acquired using standard gradient-echo-based vendor-provided sequences, often comprised of two echoes spaced a few milliseconds apart. Herein, we analyze the optimal spacing of echo times, defined as those maximizing precision-minimizing the standard deviation-for a fixed total acquisition time. Field estimation is carried out using a weighted least squares estimator. The standard deviation is shown to be approximately inversely proportional to the total acquisition time, suggesting a law of diminishing returns, whereby substantial gains are obtained up to a certain point, with little improvement beyond that point. Validations are provided in a phantom and a group of volunteers. Multi-gradient echo sequences are readily available on all manufacturer platforms, making our recommendations straightforward to implement on any modern scanner.