Changing polarization of foveal nerve fibers in the eye allows detection of central fixation
Identifying if and when a subject is visually fixating a given target is an important task with potential applications in different areas. Conventional eye trackers make this identification using the corneal light reflex or information from the pupil. But these tests monitor the position of the eye globe itself, not the actual visual axis or point of fixation.
When an individual looks at a target, that target is imaged on an area of the retina called the fovea. This foveal fixation correlates best with gaze direction. Previously, we developed instruments that used the optics of the eye in an auto-conjugate arrangement and employed a circular scanning system.1–3 When the eye fixated and focused on the target, the eye automatically focused the light reflected from the retina back to the source, where it was deflected by a beamsplitter and measured. But this method required a rapidly spinning motor, which added noise and vibration and which was generally of limited life.
Light reflected by the fovea creates a characteristic bow-tie pattern of polarization states. We have developed a new instrument (see Figure 1) that uses four spots of vertically linearly polarized light: two aligned with the ‘bright’ arms of the bow-tie pattern, and two aligned with the ‘dark’ arms. A single 780nm, 100mW laser diode produces the four spots using a multifaceted prism. A near-infrared wavelength was selected to minimize reflex pupillary constriction and thus loss of power. This wavelength also maximizes spectral reflectance compared with visible wavelengths. The fixation target is a small, translucent ‘smiley face’ that is rear-illuminated with a white LED, located in the center of a square whose corners are the four faintly red light spots seen by the test subject. Safe light levels were used at all times.
The light reflected from the fundus, the part of the eye opposite the pupil, travels through a quarter-wave plate and a polarizer. It is then imaged onto a four-quadrant photodetector of 8mm diameter (see Figures 1 and 2), whereby the circular polarization component of the polarization state of each reflected patch of light is measured. In the Stokes vector representation of the polarization state, S = S0,S1,S2,S3, S3 represents the differential measurement of the circular polarization component (right-handed circular polarization minus left-handed circular polarization). Our device measures the circular polarization component by first rotating the polarization states on the Poincaré sphere 90° by means of the quarter-wave plate, and then measuring the linear polarization along the S1 axis using a polarizer in front of the detector. We then mathematically obtain a spatial differential measurement by subtracting the signals from the patches in the ‘dark’ arms of the bow-tie pattern from the signals from the patches in the ‘bright’ arms. The four signals from the four photodetectors are amplified, filtered, and transmitted to a PC for analog-to-digital conversion and digital analysis.
If A,B,C, and D are the signals from the four-quadrant photodetector, counted in the clockwise direction and with A and C corresponding to the areas yielding higher intensities and B and D to lower intensities, then subtracting the signals of the anticipated lower intensity quadrants from those of the higher intensity quadrants yields a differential signal. Normalization is applied to eliminate the influence of individual differences in fundus reflectance:
The normalized differential signal ND is highest with central fixation, where A and C are at maximum positive and B and D are at maximum negative values. In Figure 3, ND was plotted in the X and Y directions away from the center of the bow-tie pattern in 0.25° (visual angle) increments and with interpolation. In addition, a mathematical model was used to simulate the distribution of the birefringence signal across the fundus as well as the signal detected by the four-quadrant photodetector. The model and measured signals agreed well.
We also studied the influence of double-pass corneal birefringence, which can interfere with this measurement by rotating the bow tie slightly away from the typical 45°. Based on measurements of corneal retardance performed by Knighton and Huang,4 and on a relatively small number of our own measurements on a GDx-VCC instrument (Carl Zeiss Meditec), we modeled the system using Stokes vector analysis and Mueller matrix multiplication. The cornea was modeled as a linear retarder, whereas the foveal area was modeled as a radially symmetric birefringent medium. The orientation of the bow tie was calculated as a function of corneal retardance and azimuth. Our calculations with the four-quadrant model showed that at orientations deviating from 45° by up to ±20°, the normalized difference still displays a positive maximum at central fixation, but loses up to about 25% of its value. Central fixation in such cases is still detectable, at the cost of a reduced threshold.
Our computer simulation and preliminary tests on human eyes demonstrate the feasibility of this type of fixation monitor. The device does not need calibration for each subject. The results of this study were published in detail by the Journal of Biomedical Optics.5
