We present an improved method for remote eye-fixation detection, using a polarization-modulated approach to retinal birefringence scanning (RBS), without the need for individual calibration or separate background measurements and essentially independent of corneal birefringence. Polarization-modulated RBS detects polarization changes generated in modulated polarized light passing through a unique pattern of nerve fibers identifying and defining the retinal region where fixation occurs (the fovea). A proof-of-concept demonstration in human eyes suggests that polarization-modulated RBS has the potential to reliably detect true foveal fixation on a specified point with an accuracy of at least ± 0.75°, and that it can be applied to the general population, including individuals with sub-optimal eyes and young children, where early diagnosis of visual problems can be critical. As could be employed in an eye-controlled display or in other devices, polarization-modulated RBS also enables and paves the way for new and reliable eye-fixation-evoked human-machine interfaces.
© 2014 Optical Society of America
Demand for a reliable technology that remotely detects eye fixation (when an eye is fixating on a specified point) is rising in a variety of disciplines , including neuroscience, ophthalmology and vision research, psychology and psychiatry, and human–computer/machine interactions.
Although various eye-tracking or fixation-monitoring technologies have been developed [2–14], none can remotely detect the actual direction of an individual’s fixation (measured in degrees of visual angle) directly or with high accuracy (currently no better than about ± 2° of visual angle [4–6]). Current remote eye trackers detect external eye features such as corneal light reflexes, whose location is neither constant relative to the retinal region where fixation occurs (the fovea) nor from one eye to the next, and which are susceptible to head movement or changes in external conditions (such as reflections and illumination sources) . The actual fixation direction must be inferred using either inaccurate approximations  or eye-fixation calibration done on at least an eye-by-eye basis, which limits the applicability of these methods only to those subjects who are able and willing to complete the procedure. Thus, existing approaches are not only unreliable and non-robust (73% failure rate ), but they are also restricted in their usefulness.
To detect the true fixation direction of an eye, one must know the location of its fovea – the specialized, most sensitive region of the retina which is used to aim at an object of regard in order to examine it. The fovea is surrounded by a layer of birefringent Henle fibers arranged in a radial pattern [Fig. 1(a)]. This birefringence pattern can be measured using retinal birefringence scanning (RBS) to sense the projection into space of the center of the Henle fibers, which defines and identifies the fovea [16, 17], and therefore the actual point of the eye’s fixation (foveal fixation). The retina is scanned with polarized near-infrared light in a circle (subtending a visual angle of 3°). Polarization-related changes in the light that is reflected back from the inner lining of the eye (the ocular fundus) are analyzed via differential polarization detection using a dual-photodetector system [Fig. 1(b)], resulting in the measurement of Stokes parameter S1. Because of the radially-symmetric arrangement of the Henle fibers, a characteristic frequency appears in the resulting S1 signal (RBS signal) when the scan is centered on the fovea (central fixation) [Fig. 1(c)]. Thus, by determining the signal’s frequency components using a fast Fourier transform (FFT) [16, 17] or other techniques , true foveal fixation at the center of the scanned circle can be detected.
RBS detects monocular [17, 19–21] and binocular foveal fixation [22–26] reasonably well, but its performance is limited. Like all polarization-sensitive ophthalmic technologies, RBS is adversely affected by the birefringence of the cornea, which is the largest contributor to overall ocular birefringence. Corneal birefringence varies widely in both amount (corneal retardance, or CR) and orientation (corneal azimuth, or CA) from eye to eye [27–29] and from person to person, and this creates variability in RBS signal levels between subjects and even within the same subject. In addition, existing RBS technology [16–26] employs a dual-photodetector system  per eye for differential polarization detection [Fig. 1(b)], which has limitations. First, these systems require precise alignment and electronic balancing. Second, they use a double-pass non-polarizing beam splitter, which loses more than 75% of the light. Finally, less than 0.1% of the incoming light is reflected by the ocular fundus , while a large amount of light is reflected from internal optics, lids, sclera, and cornea, thus contaminating the RBS signal with noise, with signal-to-noise ratios (SNRs) with previous implementations [17, 19–26] being as low as 0.11. Therefore although in principle eye-fixation calibration is not required with RBS, in practice previous implementations of this technology [17, 19–26] required the subject to undergo a preliminary eyes-closed “background” measurement that had to be subtracted from subsequent eyes-open measurements in order to improve the SNR to acceptable levels.
In this paper, we describe a new polarization-modulated approach to RBS that overcomes these issues and offers a significantly improved method of remote eye-fixation detection, a method that detects the foveal projection directly (that is, without the need for calibration or separate background measurements). The method has been optimized and simulated using an algorithm implemented in MATLAB (Mathworks, Inc., Natick, MA) and validated experimentally in human eyes using a prototype remote eye-fixation monitor that implements the optimized design.
2. The polarization-modulated RBS technique
Because of the strict radial symmetry of the Henle fibers about the eye’s fovea, RBS causes the polarization state of the light to change at whole multiples of the frequency of the circular scan, for example, at twice [16–26] or four times [Fig. 1(c)] the scanning frequency. By incorporating a spinning half wave plate (HWP), the axis of linear polarization of the light impinging on the eye can be continuously rotated, at twice the angle of HWP rotation, which causes modulation of the scan-generated (Henle-fiber-generated) frequency, with generation of new frequencies. When the HWP is spun at a specific fractional frequency — more precisely, at an odd multiple of 1/16th of the scanning frequency (f) — the polarization-related changes arising from the birefringent radial array of Henle fibers – the RBS signal – can be modulated such that they occur at a multiple of half the scan frequency [Fig. 2(a)].
The continuous change of polarization orientation by spinning the HWP also enables determination of different polarization states with a single analyzer/photodetector per eye, at different points in time [Fig. 2(b)]. This is because, on alternate 360° scans, the polarization state of the incident light striking a given patch of Henle fibers is rotated to a new azimuth. Use of a single photodetector (per eye) eases optical fabrication and alignment tolerances, as well as simplifies the electronics, as compared with conventional dual-photodetector RBS arrangements. In addition, this arrangement eliminates the need for a 50:50 non-polarizing beam splitter, greatly improving light throughput.
Thus with different polarization measurements being represented in the recorded RBS signal one scanning cycle apart, a differential polarization signal is obtained by shifting a copy of the recorded signal by one scanning period (360°) and subtracting it from the original signal (“360°-phase-shift subtraction”). This causes the desired signal components at half-multiples of the scan frequency to double in amplitude, and even quadruple in signal strength (FFT power). The amplitude doubling occurs because on alternate 360° scans the signal components with a frequency of a multiple of half the scan frequency differ by a 180° phase shift, so that when the alternate 360° scans are subtracted from one another, the amplitudes of these half-multiple frequency signal components double. Light that has been depolarized by reflection from the skin and/or the sclera is not affected by the spinning HWP, such that this source of optical background noise repeats over a single scanning cycle and will occur at a whole multiple of the scanning frequency. Any such signal component with a frequency of a whole multiple of the scanning frequency will be eliminated by the 360°-phase-shift subtraction because each whole-number frequency signal will be in phase with itself when shifted by 360° and will thus be eliminated on subtraction.
In addition to the spinning double-pass HWP, a fixed double-pass wave plate is used to enable detection of a differential RBS signal essentially independently of the amount and orientation of corneal birefringence, which varies from person to person and from eye to eye. To achieve this goal, the characteristics of both wave plates were optimized using an algorithm implemented in our RBS computer program in MATLAB, which was based on Müller-Stokes-matrix calculations and corneal-birefringence measurements from a data set of 322 human eyes. This data set is representative of the general population and includes 150 adult eyes  and 172 eyes from a recent study that included children . A detailed description of the optimization procedure is provided in the Methods section.
3.1 Determination of the optimal spinning frequency of the double-pass HWP
An algorithm was developed and implemented in our computer model in MATLAB  to find the HWP rotation speed (that is, the specific odd multiple of 1/16th of the scanning frequency, f) that statistically maximizes the RBS-signal strength (FFT power at particular half-multiples of the frequency) for the 322 eyes in the data set. Corneal birefringence is highly correlated between right and left eyes [27, 29] and is approximately symmetric about 90° CA. Thus, to derive a method that is essentially independent of right- and left-eye corneal birefringences, the mirror image of each eye (mirrored about 90° CA) was included in the assessment to yield a total of 644 “eyes.”
In our RBS computer model , which simulates RBS in a double-pass system, every component of the eye is characterized by its own Müller matrix M. Because reflection from the ocular fundus exhibits a high degree of polarization preservation , and the detector field of view in our basically confocal systems is constrained to the small area of the fundus where the light spot is incident, the fundus is treated as a complete polarization-preserving ideal reflector, modeled by the Müller matrix of an ideal mirror. The cornea and the retina are considered to be birefringent media that affect the polarization state of light passing into and, upon fundus-reflection, back out of the eye (that is, a double-pass effect). More precisely, the cornea is modeled as a linear retarder with a specific CR and CA where the latter represents the fast axis. The retina (in this case, the Henle fiber layer) is modeled as a radially birefringent medium with the maximum single-pass retardance located approximately 1.5° from the foveal center  (the maximum retardance is considered to be 7° for consistency with the previously used value , whereas this value is closer to 8–9° [35, 36] for an operating wavelength of 785 nm as used in our current RBS systems). With the eye fixating properly on the central fixation point in the center of the 3° circular scan, the stack of Henle fibers at each point where the light strikes is about 1.5° from the foveal center. The Henle fiber layer therefore acts as a radially-disposed linear retarder with a retardance of approximately 7°. Thus during central fixation, the circular scan on the retina can be simulated as a spinning wave plate with a retardance δr = 7° and a fast-axis orientation θr rotating at f. Any small retardance that may arise from the coated scanning mirrors themselves, from tilting of the thin-film protective coating on their front surface, is neglected.
Similarly, the spinning HWP was modeled by the Müller matrix of a retarder with retardance δHWP = 180° and a fast-axis orientation θHWP. The latter changes continuously with time at an odd multiple of 1/16th of the scanning frequency or angular rotation of the 7° wave plate:
During simulated central fixation, a beam of initially vertically polarized light (before passage through the cornea), described by the Stokes vector, , was scanned on the retina (the superscript “T” represents vector transpose). This beam continuously changed the orientation of its linear polarization after passing through the spinning HWP. The outgoing Stokes vector, , determines the final polarization state:
Optimization was achieved by varying n from 0 to 7. For each HWP rotation frequency (fHWP = 1/16, 3/16, 5/16, …, 15/16 times f), the relevant half-multiple frequency components in the RBS signal (Stokes parameter S1) were determined. At each determined frequency component, the FFT power was computed for each of the representative CR and CA combinations in the data set. The sum of the RBS-signal strengths for the 644 “eyes” was calculated for a given frequency, and the HWP rotation frequency with the highest number (maximum sum) was chosen as the best rotation speed.
Spinning the HWP at (9/16th)f maximized the RBS-signal strength for the representative 644 “eyes.” At this particular rotation speed, the modulation caused by the HWP causes the polarization-related changes arising from the Henle fibers to occur predominantly at 2.5f (with a minor contribution at 6.5f for eyes with high CR). However, the full advantage of the single-photodetector RBS approach using a spinning HWP cannot be appreciated when the subject’s CR is low or close to zero. Figure 3 shows a three-dimensional (3D) plot of differential RBS-signal strength (FFT power) at 2.5f plus that at 6.5f as a function of CR and CA, during simulated central fixation. Superimposed on the 3D plot are the signal strengths for the representative 644 “eyes.” The 3D plot indicates that the RBS signal falls off with low values of CR and goes to zero when CR is zero. Thus artificial “corneal” birefringence might be added to the design in the form of a double-pass wave plate with specific orientation and retardance to make the distribution of signal strengths more uniform across the potential combinations of CR and CA.
3.2 Selection of the optimal double-pass wave plate
In order to select the optimal double-pass wave plate that, in combination with the double-pass HWP spinning at (9/16)f, will statistically maximize RBS-signal strength while minimizing the variability across corneal birefringences, a wave plate (WP) with unknown retardance, δWP, and fixed azimuth, θWP, was inserted into Eq. (2):
The solution was optimized by varying the properties of the wave plate from 0° to 180° retardance, and from 0° to 180° azimuth. To minimize processing time, both variables were first stepped through in increments of 10°, sufficient to localize the approximate best range of retardance and azimuth, and then in 1° steps within this suggested range. For each incremental step, the mean and standard deviation of the RBS-signal strengths for the 644 “eyes” in the data set were computed. The standard deviation was then divided by the mean to result in the normalized standard deviation for this particular retardance/azimuth combination of the wave plate. The retardance/azimuth combination with the minimum normalized standard deviation was chosen to identify the best wave plate to be added.
The frequencies of the half-multiple frequency components within the RBS signal that indicate central fixation are determined by the interaction of the spinning HWP with the radial, birefringent Henle fiber layer. These frequencies are 2.5f and 6.5f when the HWP is spun at (9/16)f. Another half-multiple frequency component (4.5f) occurs in the signal whose frequency is determined by the fractional frequency of the HWP alone. This 4.5f signal is thus inherently independent of the fixation condition of the eye and will be referred to as the “spin-generated frequency” from here on. When the system is configured such that the spin-generated frequency is also relatively independent of corneal birefringence, the spin-generated frequency can be used to great advantage for normalization purposes. This normalization is necessary to compensate for variations in fundus reflectivity, pupil sizes, light levels, and dust that gathers on the optics over time.
The minimal normalized standard deviation of RBS-signal strengths was thus calculated at the central frequencies 2.5f and 6.5f, and also at the spin-generated frequency 4.5f, for each retardance/azimuth combination. The minimum product of normalized standard deviations was chosen to identify the best retardance/azimuth combination for the fixed wave plate as follows:
3.3 Simulation of spatial dependency of the RBS signal
With the scanning circle decentered from the foveal center (paracentral fixation), the retina can no longer be considered a rotating wave plate with the same amount of retardance at each scanning position and an azimuth of foveal birefringence that rotates through 360°. Both foveal retardance and fast-axis orientation change depending on the momentary scanning position. δr specifically depends on the distance from the foveal center and increases from zero in the very center to a maximum at about 1.5° from the foveal center, as mentioned above. From that position, the retardance subsequently tapers off with increasing distance from the foveal center [19, 32]:32]:
4.1 Optimization results
The optimization results are presented in Fig. 4. With an incremental resolution of 10°, the optimization algorithm [Eq. (4)] measured an absolute minimum with a fixed wave plate having a retardance of 70° and an azimuth of 90°. According to the requirements of minimizing the variability of RBS-signal strengths across eyes, which basically means to make the surface of distributed RBS-signal strengths in the 3D plot as symmetric as possible about 90° CA, an azimuth of 90° was favored as the best fast-axis orientation of the double-pass wave plate. Thus the fast-axis orientation was kept constant at 90° while the algorithm was re-applied, varying the retardance of the wave plate from 50° to 90°, in increments of 1°, covering the area adjacent to the absolute minimum.
Foveal fixation detection was optimized, with the HWP spinning at (9/16)f, when the fixed wave plate had a retardance of 74° and fast axis vertical at 90°. Essentially equivalent results were obtained with a 106° retardance and fast axis horizontal at 0° (or 180°), which falls within another local area of minimal standard deviation as shown in Fig. 4. In fact, for retardance/azimuth combinations that fall within the annotated “0.0035” contour (where the product of the normalized standard deviations is below 0.0035), the results are reasonably comparable. At (9/16)f, the modulation produced by the HWP causes the polarization-related changes that arise from the retina’s Henle fibers during central fixation (that is, with the scanned circle of light centered on the fovea) to occur at 2.5f and 6.5f. Another half-multiple frequency component (4.5f) occurs in the signal of high amplitude and at a frequency that is determined solely by the HWP rotation speed. This spin-generated frequency is thus inherently independent of the eye’s direction of fixation [Fig. 5(f)].
4.2 Simulated results using the polarization-modulated technique
Figure 5 shows the simulated results obtained using the optimized design with the HWP spinning at (9/16)f and a fixed 74° wave plate at 90°. Figures 5(a)–5(d) shows a three-dimensional (3D) plot of differential RBS-signal strength (FFT power) at the frequencies of interest (2.5f, 6.5f, 4.5f) as a function of CR and CA, during simulated central fixation. Superimposed on the 3D plot are the signal strengths for the representative eyes from the data set. The data indicate that when both central fixation frequencies, 2.5f [Fig. 5(a)] and 6.5f [Fig. 5(b)], are combined in the analysis [Fig. 5(c)], strong and essentially uniform differential RBS signals are obtained over the entire known range of corneal birefringence for both eyes. Extremely high and relatively uniform signals are also obtained at a frequency of 4.5f [Fig. 5(d)].
A spatial representation of RBS-signal strengths at 2.5f and 6.5f for a typical right eye (CR = 39 nm, CA = 70°; statistical average of right eyes from the data set) is depicted in Fig. 5(e). As expected, a definite signal maximum can be seen at the foveal center (0,0) that falls off away from the center. The full-width of the distribution at half-maximum (FWHM) is approximately ± 0.75°. In contrast, the spatial distribution of the RBS signal at 4.5f is essentially uniform with decentration [Fig. 5(f)]. Because this spin-generated frequency is independent of both corneal birefringence and fixation direction, it can be used to perform normalization across different ocular reflectivities, pupil sizes, and other parameters. These results show that eye fixation can be detected by computing the combined powers at 2.5f and 6.5f normalized by the power at 4.5f.
Fourier analysis of the RBS signal revealed that other frequencies (3.5f and 5.5f) exhibit trends during simulated paracentral fixation (that is, with the scanned circle of light decentered from the fovea) [Fig. 5(g)]. These data indicate that although the overall RBS-signal strength at these paracentral fixation frequencies is also essentially independent of corneal birefringence, it is somewhat lower than the RBS-signal strength at 2.5f and 6.5f during simulated central fixation [Fig. 5(c)].
4.3 Experimental validation and proof-of-concept demonstration with human eyes
To enable validation of the remote eye-fixation detection method, we built a binocular eye-fixation monitor [Fig. 6], implementing the computer-model-optimized, polarization-modulated RBS technique (with the HWP spinning at (9/16)f and a fixed 106° wave plate at 0°; f = 30 Hz). In Fig. 6, the main 785-nm laser diode (LD1) provides a substantially point source of near infrared light that is linearly polarized vertically. This light is imaged by lenses through a polarizing beam splitter (PBS) and a spinning HWP to an aerial point image, wherefrom the light diverges to fill the binocular exit pupils located substantially at the pupillary plane of the eyes of a subject. Large exit pupils (40 mm x 40mm) are necessary in our system to allow relative freedom of the subject’s head and thus facilitate application to less cooperative subjects such as young children. The exit pupils of the portable instrument are kept aligned with the subject’s eyes using a low-power triangulated laser pointer rangefinder. The plane containing the eyes has been rotated 90 degrees about the optical axis for clarity of illustration. After passing through the HWP that is spun at 9/16 of the scan frequency, the beam of continuously rotating, linearly-polarized light enters the scanning unit, which consists of two rigidly fixed gold-plated mirrors (M1 and M2). The scanning unit is continuously rotated about the optical axis, at 30 Hz, by conventional mechanical means not shown. This process keeps the beam of light aimed toward the eyes but scans the apparent point source in a circle. Light from the outer scanning mirror (M2) travels toward the eyes through a 106° retarder (WP) with its fast axis oriented horizontally (0° azimuth). A blinking red light generated by a 690-nm laser diode (LD2) is positioned optically conjugate to LD1 and appears to be in the center of the scanning circle. While the subject’s eyes fixate on the blinking light, the retina of each of the eyes is scanned by the spot of laser light in a circle subtending a visual angle of 3° in diameter. The small portions of light reflected from the ocular fundi are re-imaged by the auto-conjugacy of the optical system along the same path from where they came. The unchanged portion of the returning light (that is, the portion with the same polarization as the original plane of polarization) is transmitted through the PBS and back toward the light source; thus, this light does not reach the detection unit. In contrast, the changed portion of the returning light is reflected by the PBS through converging lenses and a narrow-band optical filter centered at 785 nm, which is sandwiched between the lenses, to be reflected by a knife-edge reflecting prism (P) toward the photodetector assembly, which consists of two 2-mm photodetectors (PD1 and PD2), one for each eye. The 2 mm diameter active area is not much larger than the typical best-focus double-pass image of the point light source. The vertical plane containing the photodetectors has been rotated 90 degrees about the vertical axis for clarity of illustration. Signals from the photodetectors are amplified, filtered, and subsequently transmitted to a computer for analog-to-digital conversion, signal processing, and analysis.
Two human subjects were studied, including a 29-year-old individual with emmetropic eyes (no refractive error) and a 67-year-old presbyopic individual with essentially no remaining focusing ability and with mild nuclear sclerotic cataracts in both eyes. The study was approved by the Johns Hopkins University Institutional Review Board and adhered to the tenets of the Declaration of Helsinki. Special attention was paid to laser safety. The main 785-nm laser diode (LD1) is driven at continuous 50 mW (maximum) optical power. Theoretical considerations and experimental measurements show that our 50 mW non-collimated laser diode delivers less than 0.20 mW/cm2 at the subject’s pupil, being scanned in a circle on the subject’s retina. For the duration of ten measurements (10 s) and for the wavelength used, this irradiance is well below the threshold established by the American National Standards Institute (ANSI) Z-136 safety standard , of 0.46 mW/cm2 for a non-scanned, collimated, continuous wave laser for an indefinite period. The 690-nm laser diode (LD2) used as a target is driven in blinking mode at less than 35 mW optical power and delivers less than 0.14 mW/cm2 at the subject’s pupil, which is also well below the safety exposure limit of about 0.30 mW/cm2 for a collimated laser for 1000 s.
Results obtained using the binocular eye-fixation monitor are depicted in Fig. 7 and Fig. 8. The data in Fig. 7(a) are shown as FFT power spectra of the differential polarization signals (after 360°-phase-shift subtraction) from the 29-year-old’s emmetropic (no refractive error) left eye during central and paracentral fixation. This eye had CR = 37 nm and CA = 104°, measured separately with a GDx-VCC instrument (Carl Zeiss Meditec AG, Jena, Germany) [38, 39] as previously described [19, 29, 32]. As predicted, during central fixation (on a blinking target presented in the center of the scanned circle) and thus with the scanned circle of light centered on the fovea, the signal had a strong 195-Hz (6.5f) component, a strong 135-Hz (4.5f) component and a minor contribution at 75 Hz (2.5f). As expected, the signals at 195 Hz and 75 Hz essentially disappeared during paracentral fixation while the 135-Hz component remained. During paracentral fixation on the edge of the red scanning circle (1.5° away from the center), the signal had a predominant 165-Hz (5.5f) component and a 105-Hz (3.5f) component. In accordance with the modeling results, the combined power at these frequencies is lower than that of the 195-Hz (6.5f) and 75-Hz (2.5f) components observed during central fixation. These results confirm that the presence and absence, respectively, of the 2.5f and 6.5f frequency components indicate central and paracentral fixation, and that the 4.5f spin-generated frequency is suitable for normalization purposes. As a result, the combined powers at 2.5f and 6.5f, normalized by the power at 4.5f, [(FFT2.5f + FFT6.5 f)/FFT4.5f] can be used to assess foveal fixation of an eye.
Figure 7(b) shows the central fixation signal from the 29-year-old’s emmetropic right eye (CR = 34 nm, CA = 77°) with and without 360°-phase-shift subtraction. As expected, noise at whole multiples of the scanning frequency (harmonics of the 30-Hz scanning frequency) is eliminated when 360°-phase-shift subtraction is performed (note the disappearance of the 60-Hz signal), and the signals of interest at half-multiples of the scanning frequency (such as at 135 Hz and 195 Hz) are nearly quadrupled in strength. With eyes closed or with no subject in front of the system, very low noise levels at the frequencies of interest were measured [Fig. 7(c)], yielding a SNR in the order of 100 or more with the new technique. This confirms that, in contrast to previous RBS systems [17, 19–26] with SNRs as low as 0.11, preliminary eyes-closed “background” measurements are not required for our polarization-modulated RBS method.
In order to assess accuracy of the eye-fixation detection method, the subject was asked to fixate centrally on the blinking target and then to fixate paracentrally on various points on a projected grid that indicated displacements from 0.5° to 1.5° away from the center in 0.5° increments along eight half-meridians [as indicated in Fig. 7(e)]. The spatially-mapped distribution of the indicator of foveal fixation, [(FFT2.5f + FFT6.5 f)/FFT4.5f], obtained from the emmetropic right eye is shown in Figs. 7(d)–7(e). Each point represents the average of 10 one-second epochs of data collection. The interpolation on a regular grid of 0.01 degree was carried out by means of the GRIDDATA function of MATLAB, with the “cubic” parameter which employs a Delaunay triangulation. The curve’s peak is located very close to (0,0) with an FWHM of approximately ± 0.75°. This agrees with the predictions from our simulated results [Fig. 5(e)] and demonstrates that polarization-modulated RBS can detect eye fixation with an accuracy of at least ± 0.75°. The half-maximum was taken as the preliminary threshold setting to differentiate between central fixation and non-central fixation (as indicated by illumination of the upper indicator light [central fixation] or the lower indicator light [non-central fixation] in the upper right-hand corner of the displayed FFT power spectra [see Fig. 7(a)]) even in eyes expected to generate low-level signals, such as eyes with moderate refractive errors or media opacities. As an example and demonstration of the robustness of our method, Fig. 8 illustrates the successful detection of central fixation, with illumination of the upper indicator lights, in the 67-year-old presbyopic individual with essentially no remaining focusing ability and mild bilateral nuclear sclerotic cataracts who was measured through corrective lenses.
5. Discussion and conclusion
Polarization-modulated RBS provides unique advantages for eye-fixation detection. In contrast to the existing RBS technology [16–26], our approach employs just one detector per eye to measure a differential polarization signal. This simplifies both the optical and electronic design, with lower power consumption than conventional dual-photodetector RBS arrangements. Our approach also eliminates most of the background noise associated with conventional RBS [17, 19–26], typically improving the SNR by a factor of at least 100, and therefore avoids the need to perform an eyes-closed “background” measurement on each subject.
The polarization-modulated RBS approach described in this paper essentially achieves independence from binocular corneal birefringence. We had made preliminary attempts  to minimize interference from corneal birefringence – a challenge faced by all polarization-sensitive ophthalmic technologies – by incorporating a fixed wave plate in a monocular device , but results obtained using this “wave-plate-enhanced” approach were not independent of right- and left-eye corneal birefringence . The variable that was minimized in our optimization algorithm to find a solution that achieves maximal signal strength with the least variability across corneal birefringences was the normalized standard deviation (SD/mean) of RBS-signal strengths (as detailed in the Methods section). The minimized value for the polarization-modulated approach was (SD/mean = 0.019, considering the central frequencies only), which is about 15 times better than that of the fixed wave plate approach (SD/mean = 0.287).
In contrast to existing eye-tracking and fixation-monitoring technologies, which measure external eye features whose location is neither constant relative to the fovea nor from one eye to the next, the radial pattern of Henle fiber birefringence (that our method relies upon) defines the location of the fovea, and therefore our method can detect fixation on a specified point not only directly (that is, without the need for individual calibration or separate background measurements), but also accurately, within ± 0.75°. It should be noted that this measure of accuracy was derived from the full-width at the half-maximum of the spatially-mapped distribution of the indicator of foveal fixation, which was taken as the preliminary threshold setting. Future studies in more subjects will show whether this threshold can be set higher, yielding even better accuracy. Existing remote technology, under ideal conditions (that is, with the head stabilized and following at least one calibration procedure per eye) can detect eye fixation with accuracies between ± 0.4° and ± 1° [7, 8, 12, 13]. If polarization-modulated RBS were to be used under such ideal conditions (e.g., with a calibration map being obtained and using a high threshold setting) accuracies on the order of ± 0.1° might even be achieved.
The high uniformity and symmetry of the radial Henle fiber pattern which defines the fovea across eyes, independent of changes in external conditions and head motion, makes our approach also more robust, and in principle allows fixation detection in any eye with a fovea. The major source of inter-subject variability associated with previous RBS technology, corneal birefringence, is essentially eliminated in the polarization-modulated approach, and variations in pupil sizes and fundus reflectivities are accounted for by normalization via the spin-generated frequency signal. A study on robustness of an existing remote eye-tracking system, with a reported ideal accuracy of at least ± 1° , noted that 63% of individuals could not be tracked . Here, we have demonstrated that polarization-modulated RBS allows foveal fixation detection in eyes with mild media opacities and through corrective lenses. Because no calibration measurement is necessary, studies are also possible with less cooperative subjects, such as young children who are at risk for disorders for which eye-fixation abnormalities are early indicators.
For example, polarization-modulated RBS has the potential to screen infants and youngsters reliably and directly for strabismus (a misalignment of the eyes in which only one eye fixates on a target at a time), which is the most common cause of amblyopia (lazy eye), before it becomes clinically apparent. Amblyopia is the leading medical cause of decreased vision in childhood. The early and accurate detection of even small eye-fixation deviations (at least 0.75° or approximately 1.5 prism diopters) that is permitted by our method exceeds what is otherwise possible clinically (2-3 prism diopters) and would provide the opportunity to intervene optically (e.g., corrective eyeglasses or contact lenses) at an early stage and reduce or eliminate the need for subsequent strabismus surgery. In addition, early detection in such patients could enable the maintenance of high-grade binocularity, which is usually irretrievably lost from delays in diagnosis. Combining binocular polarization-modulated RBS with double-pass focus detection  in the same optical pathway (via substituting a bull’s eye focus detector for the RBS photodetector for each eye, conjugate to the original point source of light, to assess the size of the double-pass blur patch), can provide a robust and sensitive technique to screen young children automatically and reliably for both of the primary causes of amblyopia: strabismus and defocus.
Polarization-modulated RBS also has the potential to monitor eye fixation during visual field testing, laser eye surgery, optical coherence tomography, and other forms of diagnostic and therapeutic ophthalmic procedures.
Eye-fixation abnormalities have also been associated with a number of other medical conditions, such as autism and attention-deficit hyperactivity disorder (ADHD) . The accurate monitoring of characteristic fixation abnormalities, as well as small and otherwise imperceptible errors of fixation, offers the potential not only to improve diagnosis, but also to monitor progress objectively, and to guide interventional strategies.
Finally, the reliable and direct nature of polarization-modulated RBS brings out the intriguing and immediate potential of enabling new forms of human– (or animal–) machine interaction that rely on accurate, remote, eye-fixation-evoked machine control. For example, an array of emitter-sensor modules integrated into a display could allow selection of icons or keys through visual fixation only. Amongst numerous such applications, such interfaces could serve as a communication aid for individuals otherwise disabled or with limited mobility.
In conclusion, this paper presents a polarization-modulated approach to RBS that enables direct and reliable detection of true foveal fixation, without the need for individual calibration measurements or separate background measurements, immune to corneal birefringence, and with large exit pupils and with large exit pupils facilitating simultaneous binocular testing with remote instruments. Preliminary results in human eyes demonstrate accuracies of at least ± 0.75°. Polarization-modulated RBS has important implications and immediate practical relevance in a variety of disciplines, ranging from medical research and diagnostics to human-computer/machine interaction.
This work was supported in part by gifts from Robert and Maureen Feduniak, Dewey and Janet Gargiulo, David and Helen Leighton, Richard and Victoria Baks, Robert and Diane Levy, and by awards from The Hartwell Foundation (B.I.G., K.I.), Research to Prevent Blindness (D.L.G.), and the Knights Templar Eye Foundation (K.I.). Author contributions: K.I. wrote the original manuscript and coordinated revisions, carried out mathematical modeling and related analyses, derived the theoretic explanation for generation of RBS signals at half-multiples of the scan frequency, and developed the computer algorithms for optimization and simulations that resulted in the final polarization-modulated RBS design. D.L.G. historically conceived of RBS for foveal fixation detection, directed the current project, and conceived of the idea to use a spinning half wave plate in combination with 360°-phase-shift subtraction to determine a differential polarization signal with only one photodetector per eye. D.L.G., Y.-K.W., and B.I.G. determined that a fixed wave plate could be added to the design to make the distribution of signal strengths more uniform across the population range of corneal birefringence, and performed initial mathematical modeling prior to upgrade and final theoretic foundation, optimization, and verification by K.I. D.L.G. and K.I. jointly designed and built the opto-mechanical portions of the polarization-modulated RBS system based on the modeling results, with initial participation of Y.-K.W. B.I.G. designed, optimized, and fabricated the analog and digital electronics, optoelectronics (lasers and detectors), and the computer interface to the opto-mechanical system. B.I.G. wrote the software for data acquisition, visualization, signal processing, and archiving. K.I., B.I.G., and D.L.G. designed and conducted the validation experiments. All of the authors discussed the results, commented on the manuscript, and helped with the revisions.
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