Fig. 4. Relation between the noncalibrated raw signal of an IRD (raw units of a 12-bit analog to digital converter; abscissa) and the target position during fixation of that target. Each symbol corresponds to one fixation. The second set of data is separated from the first set by a time interval of 10 min. Solid lines indicate the fitted calibration curves (see text). Differences between the first and the second calibration are mainly due to relative movements between the IRD and the eye caused by slip of the head mount.

the mean squared distance between the IRIS signal during fixations and the fitted curve. The distance is measured along lines parallel to the abscissa of figure 4. The curvature of the calibration curve is more pronounced in the first data set (fig. 4; deviations from linearity: 4.5 ) than in the second data set (fig. 4; deviations from linearity: 2.8 ). This shows that using a nonlinear calibration is indeed profitable for accuracy. The difference between the two subsequent calibrations can largely vary between subjects and amounts up to 10 in the given example. We conclude that the calibration of an IRD can be substantially improved by considering temporal drifts of gain, offset, and nonlinearity.

Search Coil

The scleral search coil system measures the voltages in one or two coils induced by two or three rapidly oscillating magnetic fields. The coils are molded in a soft contact annulus that is attached to the eyeball. The magnetic fields are generated by three pairs of large coils, mounted in a cubic frame. The subject’s head is positioned in its center. The field coils should be large, because the homogeneity of the magnetic field is crucial for the precision of the measurement. With pairs of square-shaped coils, arranged in a cubic configuration, the inhomogeneity inside of a central test cube stays below 5% when the edge

magnetic fields can be objectively calibrated [45], i.e. their calibration does not rely on accurate fixation of targets at different positions, as most other recording techniques. The calibration method described by Bartl et al. [45] evaluates the gain matrix of the 3-D search coil system based on an objective measurement of the direction of the three magnetic fields. Only a single fixation target is needed in order to determine the orientation of the coil with respect to the eye.

Another important advantage of 3-field systems over 2-field systems is that the orientation of the coil vector can be determined without knowledge of the actual inductance of the scleral search coil. This is because changes in inductance will have the same proportional effect on all three voltages and can easily be eliminated by normalization.

With the search coil technique, the inherent system noise of horizontal and vertical eye position has been estimated to be on the order of 0.5 min of arc (0.0083 ) [29]. With a dual search coil and a 3-field system (Remmel Labs, Ashland, Mass., USA) using a 12-bit analog to digital converter, we measured a system noise of 0.007 for horizontal and vertical eye positions and 0.025 for torsional eye position. The system noise was defined as the standard deviation of the eye position signal from its mean when the coil was objectively fixed in space. Data were sampled at 1 kHz. The larger system noise of the torsional eye position is due to the smaller inductivity of the torsional coil (fig. 5). It should be noted that the actual resolution of the calibrated coil signal depends very much on the amplifier gain which should make optimal use of the dynamic range of the recording device (usually analog to digital converters). The system resolution is a very important parameter; it determines the smallest eye movement that can be detected. However, to compare the metrics of eye movements between different subjects or with a stimulusdefined requirement the accuracy is more important than the system noise. The system accuracy of search coils depends mainly on the quality of the calibration. Imai et al. [46] used an artificial eye to evaluate the coil accuracy. They obtained mean differences between coil measure and the set angle of the artificial eye of 0.458, 0.948, and 1.628 for horizontal, vertical, and torsional eye position, respectively. Measurement errors are mainly caused by instabilities of the current of the field coils, temperature dependences of the electronic circuits, and metallic parts in the neighborhood of the field coils. These difficulties, however, can be controlled by careful handling of the system.

Due to its large signal to noise ratio and reliability, the search coil technique has been the generally accepted reference standard for eye movement recordings for 30 years. However, the disadvantages, connected with the invasiveness of the method, have also been recognized. The search coil not only measures eye movements, but also affects them. Frens and van der Gest [47] found that saccades last longer (by about 8%) and become slower (by about 5%) when subjects wear search coils in both eyes than when they do not. When only

one search coil was applied, these effects did not reach significance within the tested population, because the differences between subjects were larger. At least in some subjects, wearing a search coil in one eye only also prolonged saccade duration and reduced saccade velocity. It was also shown that the eye torsion, when evaluated with the search coil, depends on the orientation of exit point of the connecting line from the search coil. With the nasal exiting orientation of a commercial eye coil (Skalar), Bergamin et al. [48] observed that ocular torsion depended more on eye elevation than with a modified exit point that minimized the contact between wire and eyelids. Changes in static torsion associated with 40 change in elevation were about 2 larger with the commercial search coil than with the modified eye coil. Differences in intrasaccadic torsion between the two different coils reached up to 5 . These results suggest that contact between eye lid and coil wire can lead to substantial changes of the coupling between gaze direction and ocular torsion.

Other disadvantages of the scleral search coil are that wearing the coil may lead to drying, and temporal deformations of the cornea, and reduced visual acuity in the eye with the search coil. Therefore, the manufacturer of the search coil limits wearing time to 30 min. Irving et al. [49] observed corneal deformations of more than 3 dpt in 2 of 6 subjects and visual acuity (Snellen) of less than 6/9 in 2 subjects. These effects appeared as early as 15 min after coil insertion and dissipated after coil removal. As the number of subjects in this study was small, it is possible that the frequency of occurrence of such effects is less across the population. However, in eye movement experiments involving visual tasks, particularly with binocular search coil recordings, visual acuity should be checked. Even though most authors feel confident that the safety risks of the search coil are relatively minor [49, 50], the discomfort induced by wearing eye coils makes it more difficult to work with untrained volunteers. Irving et al. [49] asked subjects to rate the coil-induced discomfort on a scale between none (1) and ‘extreme discomfort’ (5). The mean subject rating on this scale was 3.0 0.3 at the point of maximum discomfort (immediately before coil removal).

Video-Oculography

Video-based eye movement recordings have become more and more popular because of the rapid progress made in electronic data processing. The devices have become affordable, the robustness of the algorithms improved, and the range of applications expanded. Nowadays, commercial companies produce VOG devices that can be used in an fMRI scanner (MeyeTrack, SMI, Berlin, Germany). Most fundamental VOG techniques, as defined above, are based on tracking of the position of eye-fixed markers in a 2-D image. These positions have to be expressed in head-fixed coordinates. Since head-fixed markers are difficult to obtain with high precision, one strategy of VOG systems is to attach

the video camera as firmly as possible to the head. As long as the system is not compensated for relative translation between camera and head, the accuracy of VOG has a problem very similar to that of the IRD. A translation of 1 mm will result in an error of about 5 . Head-fixed devices cause a problem under headfree conditions, because the stability of the head mount is not sufficient. Because of this problem, actual VOG systems can make highly accurate measurements of eye position, only as long as the head is fixed in space.

Karmali and Shelhamer [51] compared algorithms to compensate for camera translation by tracking specific landmarks in the surrounding of the eyes that are supposed to move little with respect to the head. Karmali and Shelhamer

[51]were especially interested in the differences in vertical translation between the cameras of the left and the right eye. In this study, the best results were obtained when the upper eyelid was localized using a template matching algorithm together with 20% outlier rejection. On average, the estimate of head translation differed by less than 1.5 pixels from a manual estimate of head position. Another method of compensating for head translation uses the relative position of the corneal reflex of an infrared LED (Eyelink II, SR Research, Osgode, Canada). One difficulty with this method is that using the corneal reflection adds more noise. For eye movements of about 12–15 the reflection reaches the edge of the cornea, and can no longer be used for compensation. Moreover, this approach relies on the topography of the cornea, which varies between subjects. Therefore, it seems to be useful when compensating for large translations, but may be unable to provide very high accuracy.

Since the pupil position is detected and evaluated in image coordinates, the nonlinearity of the VOG systems (in contrast to IRDs) is well defined by the geometry of the image projection. With parallel projection, the angular eccentricity of the eye can be approximated by the inverse sinus of the ratio of the eccentricity of the pupil center and the eye radius, both expressed in image coordinates. The main aim of the VOG calibration is therefore to determine the location of the center of rotation of the eye and the radius of the eyeball.

Up to now, no objective method has been established to determine these parameters. This is due to the following difficulties. (1) Pure rotation is an insufficient mathematical model to describe the actual movement of the eyeball

[52]during large changes of vergence. (2) The pupil is viewed through the cornea and therefore, the detected pupil center is subject to refractive errors. Systems that track the limbus position [53] avoid this problem, because the limbus is closer to the eye surface than the pupil. Usual calibration methods do not explicitly compensate for these effects but use 2-D interpolating functions to transform the image coordinates of the pupil to 2-D eye position. The parameters of these functions are computed by minimizing the mean squared error in a similar manner as for the IRD (see above). Van der Geest and Frens [54] used

Fig. 6. Simultaneous recordings of an oblique saccade with a search coil and VOG. Data from Van der Geest and Frens [54].

such a calibration (biquadratic interpolating function) for a 2-D VOG system (Eyelink version 2.04, SR Research) and compared it with a simultaneous recording of a 2-D coil system (fig. 6). This VOG system neither tracked the corneal reflex nor tried to compensate for relative translation between camera and head. While fixating targets between 20 horizontal and vertical eccentricity, the standard deviation of the difference of gaze position between both systems was 0.98 for the horizontal errors and 1.05 for the vertical errors. Since the accuracy of the 2-D search coil was estimated at about 0.5 [46; see above], Van der Geest and Frens [54] concluded that the ‘…video system should be treated with care when the accuracy of fixation position is required to be smaller than 1 deg’. This statement can be generalized for any eye movement recording system using calibrations based on fixation data because the standard deviation of the eye position across repeated fixation of the same target position in healthy subjects is on the order of 1–2 (fig. 4). The accuracy of a calibration based on fixations is not better than the standard error of the fixation. For example, nine fixations with a standard deviation of 1.8 lead to a calibration accuracy of 0.6 . The resolution of the 2-D VOG defined by the standard deviation of system noise measured with an artificial eye is about 0.01 (details provided by SR research). This system noise is typical and is also reached by other modern VOG devices [55]. Since these values were obtained with artificial eyes under optimal lighting conditions, system noise should be about 2–5 times higher with human eyes under natural conditions.

Table 1. Summary of the main features of EOG, IRD, scleral search coil and VOG