Scleral search coil systems facilitate the estimation of eye orientation from either four or six observations, depending on whether there are two or three magnetic fields inducing current in the two scleral coils. The computation of rotation between observed orientations is of particular interest to those investigating the "Listing's law" hypothesis. An often-cited approach to the estimation of orientation from the coil observations arranges them in a 3x3 rotation matrix (Tweed et al., Vision Research, 30: 97-110). Eye rotation is estimated by taking the product of a pair of such matrices, which is transformed into a rotation quaternion for subsequent analysis.

The author has investigated the cumulative error in the above approach and found that it is greater than that of an alternative solution to a similar problem known in the domains of computer vision and inertial navigation systems (Horn, Journal of the Optical Society of America, 8(10): 629-642). This approach solves for the minimal four parameters of a quaternion directly. A sufficiently detailed explanation is given to facilitate reader implementation. An error analysis is provided for the cases of both four and six observations.

Apart from the algorithm used, a likely source of error is non-orthogonality of the magnetic fields. A variety of such error has been simulated and the resulting rotation distortion presented. Much of this distortion is similar to that which has been found by others and possibly erroneously-interpreted as naturally-occurring deviation from Listing's plane.

Finally, it is demonstrated how rotation deviations from a plane are more easily analysed when the quaternion elements are plotted in a spherical, rather than Cartesian, co-ordinate system.