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Abstract
The ability to perceive polarization-related entoptic phenomena arises from the dichroism of macular pigments held in Henle’s fiber layer of the retina and can be inhibited by retinal diseases, such as age-related macular degeneration, which alters the structure of the macula. Structured light tools enable the direct probing of macular pigment density and retinal structure through the perception of polarization-dependent entoptic patterns. Here, we directly measure the visual angle of an entoptic pattern created through the illumination of the retina with a structured state of light and a perception task that is insensitive to corneal birefringence. The central region of the structured light stimuli was obstructed, with the size of the obstruction varying according to a psychophysical staircase. Two stimuli, one producing 11 azimuthal fringes and the other three azimuthal fringes, were presented to 24 healthy participants. The pattern with 11 azimuthal fringes produced an average visual angle threshold of 10° ± 1° and a 95% confidence interval (C.I.) of [6°, 14°]. For the pattern with three azimuthal fringes, a threshold extent of 3.6° ± 0.3° C.I. = [1.3°, 5.8°] was measured, a value similar to the published extent of Haidinger’s brush (4°). The increase in apparent size and clarity of entoptic phenomena produced by the presented structured light stimuli offers the potential to detect the early signs of macular disease over perception tasks using uniform polarization stimuli.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The human perception of polarized light has long been an area of active research, dating back to the identification of the Haidinger’s Brush phenomenon in 1844 [1], continuing with the Maxwell and Helmholtz models of human polarization perception [2,3], to modern investigations, motivated by the observation that human polarization perception is inhibited in patients with early-stage age-related macular degeneration (AMD) [4–6]. Despite this research interest, current clinical diagnosis of AMD does not utilize polarization perception, in part because existing polarization perception diagnostic tests show significant false-positive AMD detection, that is, healthy participants are not always able to perceive these polarization patterns [7,8]. AMD remains the leading cause of blindness in people over the age of 60 in the developed world [9], and a significant number of people over 60 show symptoms of AMD that are not detected in standard vision care [10].
Over the past five decades, the term “structured light” has evolved from referring to the generation of intensity patterns at a particular camera plane by diffractive optics to a wide variety of techniques for creating non-trivial phase patterns in coherent beams of light and other non-optical waves [11–13]. Recently, the field of structured light has become associated with orbital angular momentum (OAM) states which possess an azimuthal phase-ramp from $0$ to some multiple (also called the OAM number) of $2\pi$. The development of numerous components capable of generating the phase vortex indicative of OAM states has led to applications in information transmission, matter manipulating, and material science [14–21]. Furthermore, advancements in the generation of structured states of light have bridged the gap between structured light research and biological material characterization, including the study of biological tissue [22], and the study of human polarization perception [23–26].
Structured light tools enable the generation of polarization states which elicit entoptic profiles inaccessible with traditional forms of light [23,24]. Here, we present the first direct measurement of the visual angle of entoptic patterns through psychophysical perception tasks coupled with fundus images taken using a structured light illumination source. The extent of entoptic patterns generated by polarization-coupled OAM states was measured by obstructing the central region of the structured light state, with a variable diameter obstruction. A forced-choice 2-up/1-down staircase was used to vary the size of the obstruction to determine the apparent size of the entoptic pattern. This diameter could then be converted to degrees of visual angle with reference to retinal images taken with an imaging device using structured light illumination. By projecting the polarization-coupled state directly onto the retina, we remove the propagation effects seen in [23], namely the central region of low intensity [27], and enable the use of variable obstructions. Furthermore, we enable the generation of entoptic patterns selectively on particular regions of the retina. Leveraging these advantages, we report that the perceived entoptic pattern generated by an $\ell =13$ OAM state is $10^\circ \pm 1^\circ$ in diameter. The extent of the entopic pattern generated with $\ell =5$, containing three azimuthal fringes, was measured with the same apparatus to be $3.6^\circ \pm 0.3^\circ$ and found to be in agreement with the reported extent of Haidinger’s Brush, $4^\circ$ [6,28]. This increase in apparent entoptic pattern size and clarity suggests that structured states may provide significantly increased utility as a diagnostic tool over polarization perception methods utilizing Haidinger’s Brush.
2. Theory
While several physiological mechanisms through which humans perceive polarized light have been proposed [29], recent consensus is that axons located in Henle’s fiber layer of the retina cause this effect [30,31]. These axons contain pigment molecules, such as lutein, with an average orientation radial to the central axis of the fiber [32]. Within the macula, these axons lie parallel to the surface of the retina and are oriented radially [33]. The dichroic properties of lutein lead to Henle’s fiber layer acting as a radially oriented dichroic optical element in the region of the retina where these fibers lie parallel to the retinal surface [34]. A model for the macular pigment optical density (MPOD) [35], is
where these parameters have been measured to be $A_1 = 0.31\pm 0.12$, $A_2 = 0.11\pm 0.08$, $\rho _1 = 0.32(^\circ )^{-1}\pm 0.24(^\circ )^{-1}$, $\rho _2 = 1.2(^\circ )^{-2} \pm 1.1(^\circ )^{-2}$, and $\alpha _2 = 0.70^\circ \pm 0.66^\circ$ [35]. This MPOD, along with the uniformity with which Henle’s fiber layer is oriented in the macula, leads to the polarizing effect of the macula and therefore alters the entoptic pattern a person perceives. The macula can be modeled by a partially polarizing optical element of the form,
Fig. 1. (a) Simulation of the entoptic pattern generated by a $\ell =13$ spin-coupled OAM state, as shown in Eq. (3). The intensity of this entoptic pattern was generated using the macular pigment optical density (MPOD) model shown in Eq. (1). The state viewed by participants has a red guide light at the center of the orbital angular momentum state. The size of the central circular obstruction is shown here as $c$. (b) Monochromatic light from a 450 nm diode laser is prepared in a circularly polarized state, followed by a polarizer and quarter waveplate, each mounted on separate rotation stages. Following this, the beam is prepared in a polarization state which is orthogonal to the optic axis of the spatial light modulator (SLM). Light can then be prepared in the polarization-coupled OAM state described in Eq. (3). A two-lens imaging system is used to expand the beam for viewing through a Volk 20D Binocular Indirect Ophthalmoscopy lens. Retinal imaging is enabled by the translation stage mounted plate beamsplitter placed before the Volk lens. When placed in the beam, this plate beamsplitter directs reflected light from the retina through a linear polarizer to the camera-lens imaging system. The structured light imaging microscope enables the measurement of structured light pattern dimensions directly on a participant’s retina.
The human cornea has been shown to possess birefringence, oriented about a roughly horizontal axis [37]. In the special case of a uniformly polarized beam, $\ell =0$, the two azimuthal fringes of Haidinger’s Brush are visible, but the rotation direction of the pattern is reversed for large corneal birefringence values. With the $\ell =5$ and $\ell = 13$ OAM states, the perceived rotation direction of the entoptic phenomenon is insensitive to corneal birefringence. In the most extreme case, corneal birefringence will cause the $|{R}\rangle$ polarization state to become $|{L}\rangle$ (and vice-versa). This will, as described in [23], cause the number of azimuthal fringes a person perceives to change from $N = |\ell -2|$ to $N = |\ell + 2|$. For the case of a uniform polarization state ($\ell =0$) this will produce $2$ azimuthal fringes but with a difference in sign that causes the rotation direction to reverse. For OAM values greater than $\ell = 3$, this is not the case, and the entoptic pattern will rotate in the same direction regardless of corneal birefringence value. See the Supplementary Material for a detailed derivation.
It has been observed that the visibility of entoptic patterns created by polarized light structures that are stationary on the retina will reduce over time due to visual adaptation [1–3]. Therefore, any polarization pattern projected onto the retina must vary with time to be continuously perceived. This can be accomplished using a rotating linear polarizer that will modify the phase, $\theta$ in Eq. (3), and cause the polarization-coupled OAM state to rotate. Using the ability to control the polarization structure projected on the retina, limited only by the resolution of the SLM, we can measure the apparent size of this entoptic phenomenon through a perception task.
A schematic of the device used in this experiment is shown in Fig. 1(b). The polarization-coupled OAM-state is created with a 450 nm wavelength fiber-coupled diode laser, attenuated to 150 nW at the location of the pupil. After exiting the coupler, the light is prepared in a circularly polarized state, followed by a rotating polarizer and quarter waveplate combination which allows for any polarization state orthogonal to the horizontal axis to be prepared at equal intensity. This light is then reflected from an SLM, whose optical axis is aligned horizontally. The SLM is placed at one output of a beamsplitter while a red laser and pinhole, creating a fixation target light for participants, are placed at the other output port. Both the SLM screen and pinhole are then imaged and expanded by a $4f$-imaging system. A 20D Volk lens, placed in front of the user, is then used to map the image created by the $4f$-imaging system directly onto a participant’s retina. This direct projection of the polarization-coupled OAM state onto the retina removes the effects of state propagation seen in [23] and enables the use of a variable obstruction on the SLM screen. Real-time in-vivo imaging is enabled by an 80R/20T plate beamsplitter and a linear polarizer, both of which can be moved into the beam via translation stages. Light reflected off a participant’s retina then passes through an analyzer, anti-aligned to the movable polarizer placed before the beamsplitter, which eliminates corneal reflections from the image. Finally, the retina is imaged with the ZWO camera shown in Fig. 1(b).
The high refresh-rate SLM used to generate this state allows for the real-time control of an arbitrary polarization pattern that illuminates a participant’s retina directly. Therefore, we can obstruct the central region of a structured light state to determine the spatial extent of the entoptic pattern generated by said profile, as can be seen in Fig. 1(a). To ensure that participants are not able to distinguish the motion of the entoptic pattern from any other motion, the rotating polarizer used to generate rapid motion in the polarization profile is set to always rotate in the same direction. Distinct motion in the entoptic stimulus can be generated by changing the orientation of the quarter waveplate following the rotating polarizer. Note that this quarter waveplate remains stationary during a trial.
3. Experiment
Twenty-four participants, all with healthy retinas, were recruited to perform the discrimination task. All participants provided informed consent and were treated in accordance with the Declaration of Helsinki. All subjects received an ocular examination (medical and family history, unaided visual acuity test, subjective refraction, binocular vision test, ocular motility, slit-lamp biomicroscopy, indirect ophthalmoscopy, colour fundus photography) during their screening visit. Exclusion criteria included a previous diagnosis of ocular and systemic diseases, for example, macular degeneration, strabismus, ocular injury, diabetic retinopathy, arterial hypertension, neurological disorders, Alzheimer’s, and Huntington’s diseases. All research procedures received approval from the University of Waterloo Office of Research Ethics. The laser power incident on the retina was measured to be less than 10 nw mm−2, which is a factor 100 lower than the safety limits outlined for 450 nm wavelength laser illumination [38].
The retina of each participant was illuminated with a structured light state with OAM prepared on the right-circular polarization state. Two stimuli, the first with an OAM value of $\ell =5$ and the second with $\ell = 13$, were used to generate different numbers of azimuthal fringes in a participant’s vision. The $\ell = 5$ state produced $N = 3$ azimuthal fringes, a similar number to Haidinger’s Brush ($N = 2$), while the $\ell =13$ OAM state generated $N = 11$ azimuthal fringes, a pattern containing higher spatial frequencies which enables easier perception at larger visual angles. Aligned to the center of this OAM state was a $50\;\mathrm{\mu}\textrm{m}$ pinhole illuminated by a red laser, creating an approximately Gaussian guide light with a maximum visible extent of $1^\circ$ for participants to fixate on. Each trial consisted of 500 ms of an OAM state rotating either clockwise (CW) or counterclockwise (CCW). After the 500 ms presentation, the structured light pattern was blocked by a shutter, while the fixation target remained on, and the participant indicated the direction of pattern rotation. Each new trial began with the presentation of a stationary structured light state pattern to allow the participant to verify visibility, and the onset of the task rotation was participant-controlled.
In order to measure the eccentric extent of polarization sensitivity, a circular obstruction was centered on the fixation point, and the diameter was varied following the 2-up/1-down staircase method [39]. Two consecutive correct answers resulted in an increase in the diameter of the circular obstruction placed at the center of the structured light state, while one incorrect response resulted in a decrease in the diameter of the central obstruction. This procedure enables the calculation of an obstruction threshold corresponding to 70.7% performance accuracy, where a larger threshold indicates a larger eccentric range of polarization sensitivity. As the stimulus is focused to a point in front of the iris, the risk of polarization artifacts created by light reflected off the patient’s face or eyelids, as noted in [40], is minimized. There is, however, the possibility of stray reflections within the apparatus creating artifacts that indicate the entoptic pattern rotation direction. This is accounted for by the inclusion of pinholes between optical components, obstructing these reflections and ensuring only the polarization structure from the SLM reaches the retina. Furthermore, as described in the Supplementary Material, the rotating polarizer was designed to rotate in the same direction for both the clockwise and counter-clockwise rotating stimuli. This prevents participants from identifying the rotation direction of the stimulus through cues linked to the physical rotation of the polarizer, for example, dust or imperfections that might be present on the polarizer.
The staircase terminated after 14 reversals (that is, a change in hole-size progression from increasing to decreasing or vice versa) or after 90 total trials. The initial obstruction was 20 pixels in diameter, equal to the diameter of the red fixation point. The initial step size of the change in central obstruction visual angle was $2.70^\circ$, became $1.80^\circ$ after three reversals, then became $0.90^\circ$ after six reversals, and finally became $0.45^\circ$ after nine reversals. Each person’s eccentric obstruction threshold is calculated by taking the arithmetic mean of the final six reversal points. If the participant completed 90 trials, then the final point was treated as a reversal point. Example staircases and thresholds are shown in Fig. 2. At random intervals, with 10% probability, the participant may be shown an obstruction either $0.90^\circ$ or $2.70^\circ$ in diameter. The purpose of these random trials is to prevent a participant from learning the conditions by which hole size is changed, which may unconsciously bias the participant’s responses. Before performing the thresholding task, all participants performed an initial familiarization task. The initial obstruction size ($0.90^\circ$) was presented for several seconds 10 times, and all participants achieved at least 70${\% }$ discrimination accuracy. The duration of this familiarization period ranged significantly, with some participants requiring only 2 minutes while others required up to 30 minutes. Participants whose staircase results show more than 1 reversal point at the minimum obstruction diameter within the final 6 reversals are considered to have “failed” the perception task. Altogether, 15 out of 24 total participants (5M/19F, mean age = $21\pm 3$) successfully completed the task with a valid threshold for both $\ell =5$ and $\ell =13$ stimuli. While these “failed” participants correctly perceived the entoptic phenomenon rotation direction when presented for no less than 2 seconds, the stimulus presentation time of 500 ms inhibited these participants’ ability to discern a rotation direction. One participant produced a threshold visual angle that was 3.3 standard deviations beyond the mean value and was removed on the assumption that the participant’s vision was either not fixated on the central point or was moving eccentrically during the test.
Fig. 2. Select examples of participant staircase results. The final six reversal points, labeled as black dots, are averaged to determine the diameter at which the structured light stimulus is perceivable at 70.7% correct. Three example staircases are shown all using the $\ell =13$ stimulus.
4. Results
From each participant’s perception threshold in SLM pixel units, it is possible to calculate the threshold in degrees of visual angle. To achieve this, retinal images are taken using the described structured light device to determine the spatial extent of the central field obstruction on the retina through an image that shows both the optic disk and the structured light pattern. As a confirmation, retinal images are also taken using a Nidek MP-3 fundus camera and the size of the optic disk in degrees of visual angle can be compared between these two photos. An example of the image captured by the structured light imaging device can be seen in Fig. 3(a) and the corresponding image produced by the commercial retinal camera can be seen in Fig. 3(b).
Fig. 3. Two example retinal images from a single participant. (a) Retinal image taken with the structured light imaging device. The incident light is passed through a polarizer in order to display the radial pattern of the structured light state. By displaying structured light states limited to a set diameter, we can measure the size of these patterns relative to features on each participant’s retina. (b) Retinal image captured by a Nidek MP-3 fundus camera. The size of features in the optic nerve head can be used to relate the size of various structured light patterns. These two images allow us to verify the detection threshold diameter in degrees of visual angle, accounting for differences on an individual level.
The results for each participant, converted from pixel units into degrees of visual angle, are shown in Fig. 4, where the mean value is determined by the average of the final six reversal points and the error bars are given by the standard deviation of these reversal points. As can be seen in Fig. 4, the average threshold for eleven azimuthal fringes was $10^\circ \pm 1^\circ$ with a 95% confidence interval (C.I.) of [$6^\circ$, $14^\circ$], while the threshold extent for three azimuthal fringes was $3.6^\circ \pm 0.3^\circ$ C.I. = [$1.3^\circ$, $5.8^\circ$]. For all but two subjects, the measured extent of the entoptic pattern containing eleven azimuthal fringes was larger than the threshold extent for three azimuthal fringes.
Fig. 4. Threshold results from all participants who successfully complete the perception task, shown as blue points where empty circles show the results for three azimuthal fringes ($\ell =5$) and filled squares show the results for eleven azimuthal fringes ($\ell =13$). The threshold value was measured by averaging the final six reversal points from each participant’s staircase, with the standard deviation of the reversal points indicated as error bars. The threshold was converted to degrees of visual angle impinging on the retina by coregistering a structured light image of the retina with a commercial fundus image and calculating the size of landmarks. The average threshold visual angle was $10^\circ \pm 1^\circ$ for the $\ell =13$ stimulus and $3.6^\circ \pm 0.3^\circ$ for the $\ell =5$ stimulus. The mean of these threshold values is shown as black points on the right side of the plot, where the filled square shows the mean for $\ell =13$ stimulus thresholds and the empty circle shows the mean for $\ell =5$ stimulus thresholds.
5. Discussion
In this work, we have directly mapped a polarization-coupled OAM state onto the human retina. This negates propagation effects seen in [23], enabling the use of a variable obstruction on the SLM screen itself. Using this variable obstruction, we have directly measured the extent of the entoptic phenomenon created by a polarization-coupled OAM state. This, combined with retinal imaging using structured light illumination has allowed for the measurement of these entoptic phenomena in degrees of visual angle. Between participants, there is significant variation in the visual angle this entoptic pattern subtends.
No significant correlation is observed between perceived entoptic pattern size and refractive error, including spherical, cylindrical, and spherical equivalent refractive errors. The variation between participant thresholds may be attributable to individual differences in macular pigment density or retinal structure. No apparent relationship was observed between the measured extents of each entoptic pattern. The decreased variability of threshold values with the $3$ fringe stimulus may indicate a more uniform distribution of macular pigment densities in the central region of the macula between these participants. A combination of threshold extent measurements using structured light stimuli with macular pigment optical density measurements could isolate changes in perception caused by retinal structure from differences in macular pigment distribution. It should be noted that variations in pattern contrast due to corneal birefringence or eye movement during the test could also affect this result. While variations in patient gaze due to the size of the red fixation point are possible, the agreement between the threshold extent of the entoptic pattern with three azimuthal fringes and Haidinger’s Brush (two azimuthal fringes) suggests that this does not account for the increase in threshold extent measured here.
The mean apparent size of the entoptic pattern with $11$ azimuthal fringes, $10^\circ \pm 1^\circ$, exceeded the mean apparent size of the pattern containing three azimuthal fringes, $3.6^\circ \pm 0.3^\circ$. Furthermore, in 13 of 15 results, the measured extent of the pattern containing eleven fringes was smaller than the extent of the pattern containing three fringes, suggesting the increase in threshold extent from $3$ to $11$ azimuthal fringes observable from the mean thresholds is also present in the majority of participants. The mean apparent size of the pattern containing three fringes, $3.6^\circ \pm 0.3^\circ$, was similar to previously published results for the extent of Haidinger’s Brush, $4^\circ$ [6,28]. The threshold extent of the $11$ azimuthal fringe pattern, $10^\circ \pm 1^\circ$, and spatially resolved measurements of the macular pigment density profile [41,42] suggest that all entoptic patterns, including Haidinger’s Brush, may be visible to this extent. However, humans exhibit poor contrast sensitivity to the low spatial frequencies exhibited by Haidinger’s Brush at these eccentricities [43]. Specifically, the Haidinger’s Brush entoptic pattern has a spatial frequency of $0.06$ cycles per degree of visual angle (cpd) at an extent of $10^\circ$, while $11$ azimuthal fringes has a spatial frequency of $0.4$ cpd.
The diagnostic potential of Haidinger’s Brush perception tasks has previously been suggested [44,45], though clinical trials have not yet shown diagnostic utility. The significant increase in the apparent size and clarity of entoptic phenomenon produced by polarization-coupled OAM stimuli suggests a greater utility of structured light stimuli as a perception test to evaluate macular health. These advancements open new avenues of research whereby the extent of patterns created by structured light stimuli can be used to measure properties of the macula and spatially map changes in the macula through polarized light perception. Future studies will relate direct measurements of spatially-dependent changes in polarization perception to AMD and other retinal disorders, incorporating other methods of measuring macular pigment density to isolate changes in retinal structure.
Funding
Center for Eye and Vision Research; New Frontiers in Research Fund (NFRFE-2019-00446); Collaborative Research and Training Experience; Canada First Research Excellence Fund; Natural Sciences and Engineering Research Council of Canada (RGPIN-418579); Canada Excellence Research Chairs, Government of Canada (215284).
Acknowledgments
This work was also supported by the Hong Kong SAR government, and the InnoHK Centre for Eye and Vision Research (CEVR).
Disclosures
DP: Incoherent Vision, Inc. (P, S), DS: Incoherent Vision, Inc. (P, S), CK: Incoherent Vision, Inc. (P, S).
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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