Fig. 1.

The figure is a graphical depiction of equation (2) and shows how the field ${\omega }_i$ for any volume i is approximated by a linear combination of a measured field ${\omega }_0$ and the derivative of that field with respect to θ (rotation around the x-axis) and ϕ (rotation around the y-axis). The weights for the derivative fields are given by the estimated movement parameters where $\text{Δ}{\theta }_i$ denotes the rotation around the x-axis of volume i relative the orientation that ${\omega }_0$ was acquired in (and correspondingly for $\text{Δ}{\varphi }_i$). The maps in the figure are estimated from our simulations and the grey-scales are −40 to 100 Hz for the $w_i$ fields and −5 to 5 Hz/degree for the $\partial \omega /\partial \theta$ and $\partial \omega /\partial \varphi$ fields. An intuitive description of the $\partial \omega /\partial \theta$ field is “How much the field changes if one nods forward (looks down) one degree”. The corresponding description for $\partial \omega /\partial \varphi$ would be “How much the field changes if one tilts one's head to the right (in the direction of the dark part of the field) one degree.