Considering the Effect of Neural Adaptation in the Estimation of Haidinger's Brush Perceptual Threshold

Abstract

Purpose

This study aimed to investigate the role of neural adaptation in the perception of Haidinger's brushes, an entoptic phenomenon enabling the perception of polarization by the human visual system. The objective was to consider the rotational speed of the pattern in combination with the polarization level of the input light, to identify normal values in a cohort of healthy individuals.

Methods

An experimental setup was designed and assembled using two LED sources, one of which was filtered by a rotating linear polarizer with adjustable speed. The relative intensity of the LEDs could be changed to tune the polarization level. A cohort of 37 healthy individuals underwent monocular testing at seven polarization levels. For each value, descending and ascending limit tests were conducted to determine the rotational speed thresholds.

Results

The rotational speed threshold decreases linearly with the logarithm of the polarization level. All participants could perceive the pattern down to at least 20% polarization, with a dramatic drop in the number of subjects at 10% and 5% polarization levels. The estimated average polarization threshold was 9.7 ± 1.2%. Lower initial rotational thresholds at maximum contrast corresponded with lower polarization thresholds.

Conclusions

The study confirms the crucial role of rotational speed in the perception of Haidinger's brushes, especially at low polarization levels. As a normal pattern perception correlates with macular pigment distribution and density, those findings are essential for the development and calibration of screening devices based on Haidinger's brush perception for the early detection of maculopathy and other macular diseases.

Although common in many animal species,¹ the perception of polarization was long thought to be absent in humans until 1844, when Wilhelm von Haidinger first reported² the perception of a faint yellowish pattern when observing the sky in the directions of maximally polarized diffused light. The pattern, known as Haidinger's brushes, is visible as a 3-degree visual angle bow tie around the fixation point, and arises from the filtering of polarized light by a spatially variant dichroic structure embedded in the macula.^3–8 Indeed, a non-negligible fraction of lipophilic macular pigments, primarily lutein and zeaxanthin, is contained within the double lipidic membranes of the photoreceptor axons of Henle's fiber layer,^9–11 which are arranged radially as a consequence of the cones foveal migration during the ontogenesis of the eye.¹² Such molecules are dichroic, exhibiting stronger absorption of light polarized parallel to their long axis with a peak at approximately 460 nm,¹³ thereby protecting the retina and transforming the foveal region into a radial polarizer for blue light.¹⁴ Then, the perception of Haidinger's brushes is strongly wavelength dependent, the pattern being most visible at short wavelengths and appearing yellow under white light. Although this yellowish pattern can be observed in natural conditions under white light, laboratory studies use blue light to enhance contrast and optimize perception conditions. Recent studies revealed an unexpectedly high sensitivity to detect polarized light based on Haidinger's brush perception, with a typical threshold of approximately 16% under blue light¹⁵ and 55% for white light illumination.^15–17 Remarkably, the radial polarizer for blue light formed by the Henle's fibers also provides a natural tool for analyzing spatially varying polarization patterns,¹⁸ enabling the naked eye¹⁹ recognition of structured light beams, such as vector beams,²⁰ and offering the potential to extend the standard visual range through the use of multiring structured beams.²¹

However, the perceived pattern is too weak to enable the development of additional visual capabilities. Moreover, unless the polarization orientation changes over time, the stimulus is promptly eliminated by neural adaptation, that is, the adaptive capability of the visual system to filter out static retinal images to optimize neural processes and prioritize environmental changes.²² In particular, the efficiency and speed of neural adaptation in filtering images depend significantly on contrast: lower contrast leads to more rapid filtering of quasi-static images.²³ Thus, although humans can perceive Haidinger's brushes under polarized light, this perception is notably ephemeral without continuous stimulus change. Typically, when fixating on static images, the visual system uses microsaccades, tremors, and drifts—tiny, rapid, involuntary eye movements that help to prevent neural adaptation in the retina by constantly refreshing the stimulation of photoreceptors. However, in the case of Haidinger's brushes, these fixational eye movements prove ineffective at maintaining perception. This is because the dichroic lutein and zeaxanthin molecules responsible for the phenomenon are contained within the double lipidic membranes of the photoreceptor axons in Henle's fiber layer, moving in concert with the eye itself. Consequently, these tiny eye movements do not prevent the neural adaptation that typically occurs with stimuli external to the retinal layers. This unique characteristic necessitates an alternative approach to sustain the perception of Haidinger's brushes: the rotation of the polarization axis by using a rotating polarizer, which creates a continuous change in the stimulus pattern on the retina. Even under maximum contrast conditions with blue light, the brushes are inherently weak, and their contrast diminishes if the polarization level decreases. Consequently, as the polarization level decreases, the pattern becomes increasingly difficult to see, partly owing to more efficient neural adaptation. This suggests that a higher rotational speed is required to maintain visibility at low polarization levels. To date, the rotation speed has not been considered thoroughly. The value is usually fixed to make the pattern perceivable in conditions of maximum contrast and is commonly not reported among the experimental conditions.

In this study, the role of the rotational speed has been considered in depth for the first time, introducing a new parameter in the perception of Haidinger's brushes. In particular, the objective was to investigate this even unexplored degree of freedom in combination with the polarization level of the input light, to identify normal values in a cohort of healthy individuals. The interest extends beyond just gaining a deeper understanding of the entoptic phenomenon itself, because the knowledge of normal values is crucial for obtaining a calibration curve to design and optimize optical devices for the rapid, economical, and noninvasive screening of macular pigment density based on the perceptual threshold of Haidinger's brushes. Optical screening of macular pigments represents an essential approach for the early detection of macula dysfunction and the prevention of progressive visual impairment. A reduction in pigment density has been associated with an increased risk of developing age-related maculopathy and other retinal pathologies. At the same time, macular anomalies can affect retinal integrity before the late onset of visual symptoms. In this context, assessing the perception of Haidinger's brushes offers a valuable, noninvasive psychophysical method for indirectly evaluating macular pigment conditions. Because the correct perception of the pattern is correlated with normal density and conditions of macular pigments^24,25 and Henle's fiber structure,²⁶ the entoptic phenomenon can establish a practical and rapid screening tool for detecting early macular changes, complementing conventional imaging or optical measurements in both clinical and preventive settings.

Methods

Experimental Setup

The assembled setup (Fig. 1) comprises two RGB LED sources (RND 135-00193 - THT 5 mm, emission peaks at 468, 520, 632 nm), controlled in terms of intensity and color via a programmed electronic board (Arduino UNO Rev3). The two sources are collimated using 1-inch biconvex lenses with focal length f = 35 mm (LB1811-ML, Thorlabs, Newton, NJ, USA) and combined using a 50:50 beam splitter (CCM1-BS013/M, Thorlabs) placed in front of the ocular. One of the two sources (LED1) is filtered using a 1-inch linear polarizer (LPVISE100-A, Thorlabs) mounted on a 1-inch ball bearing actuated by an electric stepper motor (NEMA17) via a transmission belt mechanism. In this study, only the blue terminals of the RGB LEDs were addressed to investigate the perception dynamics under conditions of maximum contrast (blue light). By adjusting the relative intensity of the two LEDs while maintaining a constant total intensity, it is possible to tune the polarization level p. An initial calibration was required to find the proper attenuation factor η for LED2 in the nonpolarized arm. By indicating with s₁ the 8-bit value sent to LED1, then the value sent to LED2 is:

$$\begin{array}{c}\hfill s_2=\eta \left(255-s_1\right).\end{array}$$ (1)

Figure 1.

(a) Scheme of the experimental setup (not in scale). Two RGB LEDs controlled via an Arduino board are collimated with biconvex lenses (L) and combined with a 50:50 beam splitter (BS). One of the two arms is polarized using a linear polarizer (P), rotating with custom speed via a stepper motor (NEMA 17) with a controller. The intensity of the two LEDs can be adjusted using a potentiometer (knob) connected to the Arduino board, which is programmed to maintain a constant total intensity. The polarization level can be read on the display D1. The rotational speed is reported in revolutions per minute on display D2. The linear polarization is filtered by the Henle's fiber layer (b) in the retina of the subject's eye,¹⁷ and the characteristic bow-tie pattern of Haidinger's brushes (c) can be perceived. To elude neural adaptation and keep the pattern perceivable, the polarizer is rotated. The rotational speed must be increased when the polarization level decreases. The phenomenological experience is of a rotating bow-tie pattern (Haidinger's brushes) rather than a flickering stimulus, because the polarizer’s continuous rotation creates a smoothly rotating entoptic image. The perceived luminance at any local position within the brushes modulates at twice the rotational speed of the polarizer.

In the specific setup we used, η = 0.44. Then, the polarization level is given by p = s₁/255. The total power at the ocular, measured using a power meter (PM100D, sensor S120C, Thorlabs), was approximately 23 µW. All the optical components are mounted using a 30-mm cage system and fixed over a platform mounted using optical posts on a 30-cm × 30-cm portable optical breadboard. An adjustable chinrest has been integrated into the platform to ensure the stability of the participant during the test. The optical system can be translated along optical rails present on the breadboard to align the ocular with the eye under test. Two display systems have been incorporated to enhance precision and facilitate data collection: one dedicated to showing the degree of polarization p (OLED I2C SSD1306) and another integrated within the motor control driver (ZK-SMC01) to provide real-time readouts of the rotational velocity in revolutions per minute. Then, the read values require rescaling based on the ratio ρ between the radii of the two pulleys used in the experimental setup. To this aim, during the calibration stage, a second (fixed) polarizer was mounted after the first one, and a CCD camera was placed in correspondence with the ocular. When the first polarizer rotates, the intensity collected by the camera varies as the cosine square of the angle formed by the two polarizers, according to Malus’ law.²⁷ Then, the effective rotational speed can be calculated precisely and compared with the value read from the motor driver. A linear fit provides the scaling factor ρ = 0.453 to convert the values displayed in revolutions per minute of the motor into the effective number of revolutions per minute done by the polarizer.

Psychophysical Protocol

The study involved a cohort of 37 healthy individuals (15 males and 22 females) with a mean age of 26.0 ± 1.5 years. The research was approved by the ethical committee of the Department of General Psychology at Padova University (protocol 630-a). Informed consent was obtained from every participant in accordance with the Declaration of Helsinki. The study used a monocular testing protocol on both eyes, with subjects using their habitual correction. Seven levels of polarization (100%, 75%, 50%, 30%, 20%, 10%, and 5%) were examined. For each level, both descending and ascending limit tests were conducted to determine the threshold, calculated as the mean of the two limits. In the descending limit test, the initial rotation speed was set high (3.3 rev/s) and continuously decreased (precision of 0.008 rev/s) until the pattern became imperceptible. The procedure was repeated, starting from completely polarized light and diminishing the polarization degree according to the selected levels. Conversely, the ascending limit test began with a low rotation speed, incrementally increasing until the pattern became perceivable or the maximum rotation speed of 3.3 rev/s was reached. The polarization level increased from the minimum value of 5% to completely polarized light. There was unlimited response time, but participants typically responded within the first 3 to 5 seconds, with a pause interval between stimuli during which the device was turned off for approximately 5 seconds while the experimenter recorded the answer. After that, the rotation speed was changed by the experimenter, who turned on the device and a new trial started. Motion after-effect was never reported by the participants. As expected, the threshold for the ascending limit tests results were typically higher than the value of the descending limit tests, owing to response biases and sensory adaptation, considering that the average between the two thresholds is a common solution to reduce bias in one direction or the other. More tests were performed for each eye, resulting in a total testing time of approximately 40 minutes per participant. The phenomenological experience is to see a rotating bow-tie pattern (Haidinger's brushes) rather than a flickering stimulus, because the polarizer's continuous rotation creates a smoothly rotating entoptic image. The brush pattern, being a result of polarization filtering, exhibits a periodicity of π radians (180°) with respect to the polarizer rotation. Consequently, the perceived modulation frequency of luminance at any point within the brushes pattern is twice the number of revolutions per second of the polarizer. In the subsequent sections of this article, unless explicitly stated otherwise, all references to rotational speed pertain specifically to the angular velocity of the polarizer and signify a value for the luminance modulation frequency at any point of the brushes that is double. This convention has been adopted for practical and methodological reasons, because it directly corresponds with the experimentally controlled variable in our apparatus, that is, the polarizer rotational speed. The setup exhibits a good test–retest reliability, as shown in Supplementary Figures S1 and S2.

Results

The boxplots in Figure 2 show the distribution of rotational speed thresholds (in revolutions per second) as a function of the polarization level. The distribution shows positive skewness and is more accurately represented by a log-normal rather than a Gaussian distribution (Supplementary Figs. S3, S4), implying that the logarithm of the variable is normally distributed. Accordingly, the geometric mean, computed as the exponential of the arithmetic mean of the logarithms, serves as a suitable central estimate.²⁸ Typical rotational thresholds increase, as expected, as the degree of polarization decreases (Fig. 3a), showing a linear trend with the logarithm of the polarization level (Fig. 3b). As a result of the linear fit in Figure 3b, we can estimate an approximate increase of 0.7 rev/s for each order of magnitude reduction in polarization. The threshold ranges from an average of 0.1 rev/s for fully polarized light to about 0.7 rev/s at a 10% polarization level. The boxplot clearly demonstrates how the distribution broadens and shifts towards higher rotation speeds as the polarization level decreases. Figure 2a shows the distribution of the threshold for the different polarization levels. As the degree of polarization diminishes, the number of subjects able to discern the pattern decreases (Fig. 2b). Variations may occur in the threshold between the two eyes of the same subject. That had already been noticed in previous studies, attributable to natural variations in macular pigment density, corneal birefringence, or learning mechanisms.^15,16,29 As shown in Figure 4, the differences are generally distributed around zero, with the dispersion increasing while the polarization level decreases. The difference distribution is analysed in more detail using Bland–Altman plots in Supplementary Figures S5 and S6. Compared with the same treatment for test–retest data reported in Supplementary Figures S1 and S2, it is worth noting how the SD of the threshold difference between the two eyes is very close to or lower than that for test–retest data at the same polarization level.

Figure 2.

(a) Boxplots referring to the distribution of the rotational speed threshold (RST) (b) in revolutions per second as a function of the polarization degree for the selected set of polarization levels. On each boxplot, marks refer to the 25th, 50th, and 75th percentiles, and whiskers show the whole variation interval.

Figure 3.

Typical rotational speed thresholds (RST) in revolutions per second as a function of the polarization level (PL) (a) and of its logarithm (b), linear regression: r² = 0.97, RPT = −0.71 log(PL) + 0.03. Assuming a log-normal distribution, for each polarization level the values are calculated as the geometric mean: $\langle RST\rangle =\sqrt[n]{{\prod }_i{x}_i}=exp\left({\sum }_{i}log{x}_i/n\right)$, being n the number of eyes able to perceived the pattern. Errors in (b) are given by $\pm \langle RST\rangle \sqrt{\left(e^{\pm s^2}-1\right)/n}$, where s is the SD of the logarithms.²⁸

Figure 4.

(a) Boxplots referring to the distributions (b) of the difference in the rotational speed thresholds (RST) between left and right eyes for the participants as a function of the polarization degree for the selected set of polarization levels. On each boxplot, marks refer to the 25th, 50th, and 75th percentiles, and whiskers show the whole variation interval.

Notably, all participants could perceive the pattern down to at least 20% polarization, in accordance with previous studies.¹⁵ At 10% and 5% polarization levels, a significant drop in the number of subjects capable of perceiving the pattern occurs (Fig. 5), accompanied by a marked increase in measurement dispersion (Figs. 2, 4).

Figure 5.

Number of participants able to perceive the entoptic pattern as a function of the polarization level in the selected set of values, and fit with the log-normal cumulative distribution function in (Equation 2).

Assuming a log-normal distribution of the thresholds as shown by Mottes et al.,¹⁵ the points in Figure 5 can be fitted by the corresponding cumulative distribution function:

$$\begin{array}{c}\hfill F\left(p\right)=\frac{1}{2}\left[1+\mathit{erf}\left(\frac{lnp-\mu }{\sigma \sqrt{2}}\right)\right],\end{array}$$ (2)

where erf is the Gauss error function and µ and σ are the parameters of the distribution. Then, an estimate of the average threshold of the polarization degree is given by the average:

$$\begin{array}{c}\hfill 〈p〉=e^{\mu +\frac{{\sigma }^2}{2}},\end{array}$$ (3)

with an error given by

$$\begin{array}{c}\hfill {\sigma }_{〈p〉}=〈p〉\sqrt{\frac{e^{{\sigma }^2}-1}{N}},\end{array}$$ (4)

where N is the total number of subjects. From the fit, we obtain that the estimated polarization threshold is 〈p〉 = 9.7 ± 1.2%. The value is slightly lower than the 15% found in a previous study¹⁵ using a similar setup. However, in that case, the polarizer was rotated by only one revolution using a piezoelectric rotor (ELL14K, Thorlabs), providing a fixed maximum speed of 430°/s (1.2 rev/s). Then, higher values of rotation speed, such as those achievable with the present setup, together with continuous rotation of the brushes, could enable the perception of the pattern also in people who were insensitive in the previous study at very low polarization levels. It is worth noting that a low rotational threshold at maximal contrast (p = 1.0) corresponds with a lower threshold for decreasing polarization levels as well (Fig. 6a). In addition, the probability of perceiving the pattern at low polarization levels is correlated with low values of initial rotational thresholds, as shown in Figure 6b. The figure reports the frequency of participants able to perceive the pattern as a function of the polarization levels for an initial threshold above or below the median value of 0.085 rev/s at p = 1.0 (Fig. 2a). Fitting the curves with (Equation 2) and using (Equations 3) and (4) we obtain an average polarization threshold of 〈p〉 = 7.2 ± 0.8% for the subjects in the first and second quartiles. The polarization threshold increases to 〈p〉 = 12.0 ± 1.0% for participants with an initial rotational threshold above the median value.

Figure 6.

(a) Rotational speed thresholds (RST) (rev/s) for the polarization levels PL = 0.2 (red points) and PL = 0.3 (blue points) as a function of the rotational speed threshold at PL = 1.0, and regression lines (r² = 0.79 and r² = 0.73, respectively). (b) Frequency of eyes able to perceive the pattern as a function of the polarization level, for initial rotational thresholds above (in red) and below (in blue) the median value (0.085 rps), and fit with the log-normal cumulative distribution function in (Equation 2).

Discussion

This study further investigates human sensitivity to light polarization, a phenomenon attributed to the anisotropic redistribution of macular pigments that occurs during foveal development. The radial configuration of Henle's fibers in the central macula, combined with the dichroic behavior of carotenoid pigments, provides a radial filter for blue light, resulting in the perception of a weak bow tie oriented almost perpendicular to the polarization axis of the input light. Unlike with external visual stimuli, where fixational eye movements (microsaccades, tremors, and drifts) typically prevent neural adaptation by constantly refreshing the stimulation of photoreceptors, these mechanisms are ineffective for Haidinger's brushes. Because the dichroic molecules responsible for the phenomenon are embedded within the retinal structure itself, they move in concert with the eye, rendering natural fixational movements ineffective at maintaining perception. This unique characteristic explains why the figure is cancelled soon, unless the pattern rotates around the fixation point, highlighting for the first time the critical importance of rotational speed as a parameter in the study of this entoptic phenomenon when analyzing the perceptual threshold in combination with the polarization degree.

Our findings confirm that decreasing the polarization level reduces contrast, fostering neural adaptation and signal elimination. This necessitates higher rotational speeds, establishing a new functional parameter in addition to the polarization level in the perception of the phenomenon. The nonlinear relationship between these factors provides a quantitative framework for assessing macular function, because accurate pattern perception correlates with macular pigments presence and density. In particular, the rotational speed threshold decreases linearly with the logarithm of the polarization level. As discussed elsewhere,¹⁵ this finding could be supported by the well-known Weber–Fechner law, proposing a logarithmic relationship between the perception of a sensory stimulus and its actual intensity. Because a change in the perception of Haidinger's brushes is related to differences in luminance, and the pattern can be recognized only when there is sufficient contrast, those assumptions could account for the logarithmic trend of the adaptation mechanism and the log-normal distribution assumed for the cumulative function of the subjects in Figures 5 and 6.

Beyond these general trends in perception thresholds, the individual differences observed in rotational speed thresholds merit further consideration and likely reflect several factors. Although variations in macular pigment density and distribution, and the corneal birefringence, are the primary physiological factors of interest, we acknowledge that criterion differences in the adjustment procedure may contribute to some variation. Participants with more conservative criteria for what constitutes just visible might appear less sensitive across all polarization levels. Additionally, individual differences in sensitivity to rotational motion could potentially influence the results, although this factor would likely affect performance consistently across polarization levels. However, the strong correlation between thresholds at different polarization levels (Fig. 6a) suggests consistent within-subject performance, supporting the interpretation that these differences primarily reflect physiological rather than methodological factors.

Notwithstanding these factors mentioned, we believe that this subtle visual effect provides a noninvasive method for assessing macular integrity and function,¹⁷ and Haidinger's brushes have garnered increasing attention in clinical ophthalmology. Recent studies have explored the potential of polarization perception in screening for early-stage maculopathies, including AMD and diabetic maculopathy.^29–32 The sensitivity of the phenomenon to changes in macular pigment density and distribution makes it a promising tool for detecting subtle alterations in retinal health before conventional imaging techniques reveal structural changes after the late onset of visual symptoms. Furthermore, the method can be used for longitudinal monitoring of macular pigment optical density, enabling the evaluation of the efficacy of nutritional interventions, such as antioxidant supplements prescribed for patients with at least intermediate AMD.³³ That finding suggests that Haidinger's brushes could serve as a valuable adjunct to existing diagnostic methods, potentially enabling earlier intervention and improved patient outcomes in several macular disorders.

Therefore, of particular interest is the development of screening devices based on Haidinger's brush perception for noninvasive, economic, and rapid assessment of macular integrity. Preliminary studies on cohorts of healthy individuals are essential for estimating normal values of clinical parameters and for the accurate calibration of instruments. The study confirms how the rotational speed is a critical parameter to assess the capability of the subject to perceive the pattern for a given polarization level. With respect to previous studies, the possibility of increasing the rotational speed above the threshold has probably improved the perception of the pattern also at low contrast values, providing an estimate around 10% of the polarization perception threshold, which resulted in lower values than previous analyses.¹⁵ Therefore, in developing an effective screening protocol, it is crucial to consider both the degree of polarization and the rotational speed when defining the perceptual threshold. These two factors play a significant role in determining the visibility of Haidinger's brush and should be calibrated carefully to ensure accurate and reliable results. Moreover, research suggests an alternative and more practical screening method based on Haidinger's brushes perception using a simplified optical setup. In fact, instead of modulating the polarization degree with a fixed (high) rotational speed, one can perform the psychophysical test at the maximum polarization degree (100%) by acting on the polarizer rotation to find the rotational speed threshold. The optical architecture is simplified, because there is no need to control the polarization degree of the source, and the exploitation of high polarization level allows for increasing the precision of the measure with respect to the conditions of low polarization degree, which are characterized by a higher data dispersion. Concurrently, unusual rotational speed thresholds at high polarization levels may also be related to adaptation difficulties. Such anomalies could potentially signal underlying neural or cortical issues in parallel to anomalies in macular pigments density, warranting further investigation.

Future research should focus on improving the precision of threshold estimation by increasing the sample size of healthy participants and accounting for additional individual parameters, such as age. Although the influence of age on the perceptual threshold remains debated,^15,25 potentially owing to confounding factors such as lens opacification and reduced blue light transmission, the effect of aging on the rotational speed threshold may be non-negligible in older individuals, likely reflecting an age-related decline in neural processing efficiency. In parallel, applying the test to patients with early or moderate maculopathy could help establish a correlation between disease stage and perceptual threshold, thereby facilitating calibration and optimization of the screening protocol.

To conclude, the study of Haidinger's brushes not only enhances our comprehension of human visual perception, but also holds significant potential for ophthalmological diagnostics and preventive care. By bridging fundamental vision optics with potential clinical applications, this research paves the way for innovative approaches in the early detection and management of macular diseases.