Fig. 4 OD, OS shows that the greatest differences in judged gaze were between the centered pupil (BL PC) and the decentered pupil (BL PD) conditions, and Table 1 confirms that most of those differences were statistically significant. For OD, gaze from the decentered pupil was always judged to be to the right of gaze from the centered pupil, whereas for OS, gaze from the decentered pupil was always judged to be to the left of gaze from the centered pupil. In other words, decentration of the pupil caused the judged direction of monocular gaze to shift in the direction in which the pupil was displaced. Comparisons between the other iris types were not as consistently significant.
Fig. 4 shows that for OU exposure, the curves for all the iris conditions essentially overlapped, and the only significant difference being between BL NP and BL PD at −6 cm. For the binocular curves as a group, central gaze was judged fairly accurately, but their slope was greater than that of the monocular curves.
Only a few of the studies that have used live or photographed models to study the perceived direction of gaze have reported the iris characteristics (pale vs. dark, blue vs. brown, pupil centered vs. decentered). Yet, this study shows that the visibility of the pupil and whether it is centered or decentered has a large influence on the perceived direction of monocular gaze. Indeed, this may be the reason for some of the disagreement within the literature.13,14,15 It is urged that future studies report these iris features. Angle kappa, which is another parameter that has been shown to influence the perceived direction of gaze, has also been underreported.10
Cues to the Direction of Gaze
There are two main theories about what features of the eyeball and lids are used to determine the direction of gaze from a straight head. One cue is the location of the iris within the lid aperture, so that a shift of the irises to the left signifies gaze to the left and vice versa.16,17,18 The other cue is the direction in which the iris appears to be “pointing.”17,19 These theories are not incompatible, and it has been argued that both cues are variably important under different conditions.19
Because angle kappa varies between individuals, it adds a variable error to both of the above cues. How it does this requires an explanation of how angle kappa is measured. In a typical setup, the subject faces a small light source and views a target along the line of sight (LS), the line which connects the target to the center of the pupil (Fig. 5). When the light source, the target, and the viewer are co-aligned, the viewer usually sees the corneal reflection of the light source (X) as nasally displaced from the center of the pupil. Then, the fixation target is moved nasal to the light source and viewer, with the eye and its LS following it, until the corneal reflection of the light source is centered in the pupil. This establishes the pupillary axis (PA), which is the line that goes through the center of the pupil and the center of curvature of the cornea, and the angle that the eye has turned is called kappa (K).20 Angle kappa is usually greatest horizontally and because PA is typically temporal to LS, a significant angle kappa tends to make the eye look exotropic.11
According to the pointing theory, the eye should appear to gaze in the direction of the eye's anterior-posterior axis of rotational symmetry. An external estimate of this would be the line that goes through center of rotation and the center of the iris, which would be approximately perpendicular to the center of the iris (the iris axis, IA). Because, the pupil is usually nasally decentered,9 this would give a discrepancy between the PA and the IA because the fixation target would have to be moved farther nasally to place the corneal reflection in the center of the iris rather than in the center of the pupil (angle delta10 rather than angle kappa). Therefore, even a 0-angle kappa would leave a significant temporal deviation of the IA from straight gaze. Even though this pupil displacement may seem small, it would result in a large difference between angle delta and kappa. Therefore, the IA should be directed closer to the direction of gaze than the PA (especially in eyes with dark irises). This has been suggested previously, but it has not been adequately tested.10,21
For all iris conditions, straight binocular gaze (0.0 cm) was judged to be a few centimeters to the observers' right [Fig. 3 (A to D)]. This was probably because the model's head and lids were not perfectly left-right symmetrical, which gave an uncertainty to the straightness of the head and a consequent turn of the eyes in the opposite direction.
In a previous study, straight monocular gaze was judged to be abducted from its true direction, and it was suggested that this was, at least in part, because the models had large uncorrected positive angle kappas.10 However, the particular angle kappas for those models could not explain all of that difference, and it was argued that the discrepancy may have been because the IA (the line perpendicular to the center of the iris) was a better indicator of the perceived direction of gaze than the PA was.
Because this study simulated a 0-angle kappa, it provides direct evidence that kappa alone cannot explain why straight gaze is usually perceived to be exotropic. If the pupil were centered in the iris, angles kappa and delta would be identical, and equal gaze directions would be predicted whether the pupil was poorly visible (dark iris) or easily visible (light iris). However, because most pupils are decentered nasally, angle delta would usually be larger than angle kappa. Therefore, to the extent that the pupils are decentered, gaze from eyes with pale irises (usually blue) should more closely follow the PA, whereas gaze from eyes with dark irises should follow the IA so that blue eyes should be perceived to be looking less far to the side than brown eyes. Fig. 3 shows this result. Oddly, when the blue irises had no pupil or a centered pupil (Fig. 3B, C), the divergence was greater than for the brown iris (Fig. 3A). This may be because the decentered pupil within the brown iris was still somewhat visible (Fig. 1B).
Previous studies have disagreed on whether binocular gaze to the side gives the perception that the gazer is looking farther or less far to the side than he or she actually is.5,10,17,19,22,23 In this study, binocular side gaze was overestimated. This disagreement within the literature does not seem to be explained by differences in the distance of the model or the target from the observer, or by differences in the extent of side gaze that has been tested. It is possibly because of differences in the eyelid shapes of the models, which have been shown to influence the perceived amount of eye turn.3
Studies have more consistently reported that the judged direction of binocular gaze follows the judged direction of monocular gaze from the abducting eye.5,10,19 This study supports this. The judged direction of straight binocular gaze seemed to be based on the average of the curves for straight monocular gaze (0.0 cm), but, for side gaze, binocular gaze tended to follow the judged monocular gaze of the abducting eye.
For all the simulated irises, the binocular curves had a steeper slope than the monocular curves which, except for the one in which highly visible pupils were decentered, caused the monocular curves to roughly coincide with the binocular curves at the true gaze locations of −3 cm and +3 cm (Fig. 3A to C). Because these crossing points agree with the half distance between the centers of the average pair of eyes, the judgment that binocular gaze is toward one of the observer's eyes agrees with that of monocular gaze from the eye on the same side. This may have some functional significance. Because gaze in face-to-face encounters is usually directed toward one or the other of an observer's eyes, the monocular/binocular crossing point would minimize any conflict between the perceived directions of monocular and binocular gaze. Because the eye to the same side is relatively abducted compared with the opposite adducting eye, binocular gaze may follow the abducted eye for other gaze angles as well to be consistent. The above applies to all brown eyes that have poorly visible pupils and to pale eyes that have little or no pupil decentration.
The monocular curves from the highly visible decentered pupils essentially overlapped each other and joined the binocular curve at 0.0 cm (Fig. 3D), so they did not show the distinct crossing points with the binocular curve mentioned above. The fact that the irises with easily visible decentered pupils had a greater agreement between monocular and binocular gaze over the entire observer's face than the other irises did may, in part, be the reason why such eyes can have such a piercing stare.
It might be assumed that the perceived direction for binocular gaze is the average of the two directions for monocular gaze, but this only occurs when gaze is straight. For side gaze, the function must be more complex because, even though the monocular curves differed for the different iris configurations (Fig. 4 OD, OS), all the curves for binocular gaze overlaid one another regardless of iris configuration (Fig. 4 OU). It is possible that gaze perception may involve a process similar to face recognition, which has been shown to involve more than the sum of the individual facial features.24
Finally, we might note other consequences of a nasally displaced pupil. The displacement of the pupil from the average optical axis of the eye has been shown to introduce monochromatic aberrations, which would degrade the retinal image,25 although it is unclear how a positive angle kappa might interact with a nasal pupil decentration to affect those aberrations. However, a nasal pupil decentration in conjunction with a positive angle kappa has been shown to reduce the effect of chromatic difference of magnification, which would improve the retinal image.21 The fact that nasally decentered pupils appear to result in a more accurate assessment of another person's monocular gaze may add an additional benefit of decentered pupils to this list.
This study was supported by a Northeastern State University Faculty Research Council grant.
Roger W. West
Oklahoma College of Optometry
Northeastern State University
1001 North Grand Avenue
Tahlequah, Oklahoma 74464
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Keywords:© 2011 American Academy of Optometry
gaze; gaze perception; pupil; eye contact; angle kappa