Perceiving polarization with the naked eye: characterization of human polarization sensitivity

Radial polarisation patterns identify macular damage: a machine learning approach

CLINICAL RELEVANCE

Identifying polarisation-modulated patterns may be an effective method for both detecting and monitoring macular damage.

BACKGROUND

The aim of this work is to determine the effectiveness of polarisation-modulated patterns in identifying macular damage and foveolar involvement using a methodology that involved feature selection, Naïve Bayes supervised machine learning, cross validation, and use of an interpretable nomogram.

METHODS

A cross-sectional study involving 520 eyes was undertaken, encompassing both normal and abnormal cases, including those with age-related macular disease, diabetic retinopathy or epiretinal membrane. Macular damage and foveolar integrity were assessed using optical coherence tomography. Various polarisation-modulated geometrical and optotype patterns were employed, along with traditional methods for visual function measurement, to complete perceptual detection and identification measures. Other variables assessed included age, sex, eye (right, left) and ocular media (normal, pseudophakic, cataract). Redundant variables were removed using a Fast Correlation-Based Filter. The area under the receiver operating characteristic curve and Matthews correlation coefficient were calculated, following 5-fold stratified cross validation, for Naïve Bayes models describing the relationship between the selected predictors of macular damage and foveolar involvement.

RESULTS

Only radially structured polarisation-modulated patterns and age emerged as predictors of macular damage and foveolar involvement. All other variables, including traditional logMAR measures of visual acuity, were identified as redundant. Naïve Bayes, utilising the Fast Correlation-Based Filter selected features, provided a good prediction for macular damage and foveolar involvement, with an area under the receiver operating curve exceeding 0.7. Additionally, Matthews correlation coefficient showed a medium size effect for both conditions.

CONCLUSIONS

Radially structured polarisation-modulated geometric patterns outperform polarisation-modulated optotypes and standard logMAR acuity measures in predicting macular damage, regardless of foveolar involvement.

Measuring the visual angle of polarization-related entoptic phenomena using structured light

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.

P-MIRU, a Polarized Multispectral Imaging System, Reveals Reflection Information on the Biological Surface

Reflection light forms the core of our visual perception of the world. We can obtain vast information by examining reflection light from biological surfaces, including pigment composition and distribution, tissue structure and surface microstructure. However, because of the limitations in our visual system, the complete information in reflection light, which we term 'reflectome', cannot be fully exploited. For example, we may miss reflection light information outside our visible wavelengths. In addition, unlike insects, we have virtually no sensitivity to light polarization. We can detect non-chromatic information lurking in reflection light only with appropriate devices. Although previous studies have designed and developed systems for specialized uses supporting our visual systems, we still do not have a versatile, rapid, convenient and affordable system for analyzing broad aspects of reflection from biological surfaces. To overcome this situation, we developed P-MIRU, a novel multispectral and polarization imaging system for reflecting light from biological surfaces. The hardware and software of P-MIRU are open source and customizable and thus can be applied for virtually any research on biological surfaces. Furthermore, P-MIRU is a user-friendly system for biologists with no specialized programming or engineering knowledge. P-MIRU successfully visualized multispectral reflection in visible/non-visible wavelengths and simultaneously detected various surface phenotypes of spectral polarization. The P-MIRU system extends our visual ability and unveils information on biological surfaces.

Dynamic modeling of Haidinger's brush phenomenon and analysis of the cornea effect based on the model

Starting from the dynamic feature of the vision process and taking into account the time constants of the polarization-dependent process of cones, this study proposed a physical model that can mathematically describe the transient nature of Haidinger's brushes (HB). A saturated exponential growth function was proposed to describe the dynamic process, and the corresponding formulas were derived and discussed. The sensitivities of both static and rotating HB were considered in the model, and the visibility of HB was also investigated. Additionally, the impact of the cornea on the visions of HB was examined by using this model. Analytical results reveal that there exist two types of patterns in the rotating HB phenomenon. The visual perception of the rotating HB is related to the magnitude and interaction of these two patterns, as well as the corneal phase shift. The rotation orientation reversal at large corneal phase shifts observed by some researchers can also be explained by the model. The results are consistent with experimental observations and might help with the clinical diagnosis of macula disorders and corneal abnormalities.

An Overview of Lutein in the Lipid Membrane

Lutein, zeaxanthin, and meso-zeaxanthin (a steroisomer of zeaxanthin) are macular pigments. They modify the physical properties of the lipid bilayers in a manner similar to cholesterol. It is not clear if these pigments are directly present in the lipid phase of the membranes, or if they form complexes with specific membrane proteins that retain them in high amounts in the correct place in the retina. The high content of macular pigments in the Henle fiber layer indicates that a portion of the lutein and zeaxanthin should not only be bound to the specific proteins but also directly dissolved in the lipid membranes. This high concentration in the prereceptoral region of the retina is effective for blue-light filtration. Understanding the basic mechanisms of these actions is necessary to better understand the carotenoid-membrane interaction and how carotenoids affect membrane physical properties-such as fluidity, polarity, and order-in relation to membrane structure and membrane dynamics. This review focuses on the properties of lutein.

Structured light enhanced entoptic stimuli for vision science applications

The dichroic macular pigment in the Henle fiber layer in the fovea enables humans to perceive entoptic phenomena when viewing polarized blue light. In the standard case of linearly polarized stimuli, a faint bowtie-like pattern known as the Haidinger's brush appears in the central point of fixation. As the shape and clarity of the perceived signal is directly related to the health of the macula, Haidinger's brush has been used as a diagnostic marker in studies of early stage macular degeneration and central field visual dysfunction. However, due to the weak nature of the perceived signal the perception of the Haidinger's brush has not been integrated with modern clinical methods. Recent attempts have been made to increase the strength of the perceived signal by employing structured light with spatially varying polarization profiles. Here we review the advancements with the structured light stimuli and describe the current challenges and future prospects.

The Differential Contribution of Macular Pigments and Foveal Anatomy to the Perception of Maxwell's Spot and Haidinger's Brushes

The relationship of macular pigments and foveal anatomy to the perception of Maxwell's spot (MS) and Haidinger's brushes (HB) entoptic phenomena were investigated. Dual-wavelength-autofluorescence and OCT were used to define macular pigment density and foveal anatomy in 52 eyes. MS was generated by alternating unpolarized red/blue and red/green uniform field illumination. HB was generated by alternating the linear polarization axis of a uniform blue field. In Experiment 1, horizontal widths of MS and HB were measured using a micrometer system and compared with macular pigment densities and OCT-defined morphometry. MS radius (mean 1.4°) was significantly less than HB radius (mean 1.6°), with the spatial extent of both phenomena falling between the boundaries of the foveola and foveal pit. Multiple regression showed MS and HB radii to be significantly associated with the macular pigment spatial profile radius. HB radius, but not MS radius, was also significantly associated with foveolar morphometry. Experiment 2 compared perceptual profiles of MS with macular pigment distribution patterns and demonstrated close agreement. The size and appearance of MS is a direct indicator of macular pigment density and distribution. Measures of HB radii are less specific, with dependence on both macular pigment density and foveal structure.

Mathematical modeling and experimental verification of aging human eyes polarization sensitivity

The polarization perception sensitivity of the human eyes affects the perceived polarized image quality. In this paper, we used polarized spatiotemporal structured images to develop a spatiotemporal age mapping of the polarization perception of human eyes. We built an optical modulation transfer function mathematical model of the aging human eyes with spatiotemporal frequency domains and introduced the Stokes vector to analyze the polarized images. The proposed model provides a testing method based on a set of polarization images with spatiotemporal frequencies varying according to the perception of differently aged viewers. Then, we experimentally validated the proposed model by performing polarization perception tests on a group of volunteers. The test method has the diagnostic potential to confirm the health of human eyes and identify potential age-related macular diseases.

Haidinger's brushes: Psychophysical analysis of an entoptic phenomenon

Entoptic phenomena are visual artifacts arising from the interaction of light with the specific anatomic structure of the human eye. While they are usually too subtle to actually enable additional visual abilities, their perception can provide indirect information on the physiological conditions of the visual system. Among the most famous ones, Haidinger's brushes consist in the appearance of a yellowish bow tie perceived in the presence of linearly polarized white light and originate from the particular spatial distribution of dichroic carotenoid molecules forming a sort of embedded radial polarizer in the foveal region. In this work, we develop a compact and versatile optical setup for the psychophysical analysis of the perceptual threshold of such entoptic effect. The tests performed on a group of 113 healthy individuals under conditions of maximum contrast (blue light) reveal the capability to perceive an average polarization degree around 16%. The developed prototype outlines a new optical platform to train the users in the perception of the phenomenon and infer information on the polarization-degree sensitivity of the human visual system.

Human psychophysical discrimination of spatially dependant Pancharatnam-Berry phases in optical spin-orbit states

We tested the ability of human observers to discriminate distinct profiles of spatially dependant geometric phases when directly viewing stationary structured light beams. Participants viewed polarization coupled orbital angular momentum (OAM) states, or "spin-orbit" states, in which the OAM was induced through Pancharatnam-Berry phases. The coupling between polarization and OAM in these beams manifests as spatially dependant polarization. Regions of uniform polarization are perceived as specifically oriented Haidinger's brushes, and study participants discriminated between two spin-orbit states based on the rotational symmetry in the spatial orientations of these brushes. Participants used self-generated eye movements to prevent adaptation to the visual stimuli. After initial training, the participants were able to correctly discriminate between two spin-orbit states, differentiated by OAM [Formula: see text], with an average success probability of [Formula: see text] ([Formula: see text], [Formula: see text]). These results support our previous observation that human observers can directly perceive spin-orbit states, and extend this finding to non-rotating beams, OAM modes induced via Pancharatnam-Berry phases, and the discrimination of states that are differentiated by OAM.

The Effect of Age-Related Macular Degeneration on Polarization Pattern Perception

Purpose

The purpose of this study was to determine if a battery of polarization-modulated stimuli, quantified as a single metric, is effective in identifying macular disease in the presence/absence of cataract or pseudophakia.

Methods

Using a modified liquid crystal display, polarization pattern perception (PPP) for a formulated battery of geometric and logMAR stimuli was evaluated in participants that had either no eye pathology (healthy participants) or were grouped according to the presence of cataract, pseudophakia, and/or age-related macular degeneration (AMD). PPP was quantified as response frequencies to individual stimuli, and as a novel monocular polarization sensitivity score (Ps) based on perception of the stimulus battery set.

Results

Stimulus response frequencies were pattern-dependent and, compared with healthy participants, reduced for cataract and AMD groups but not for subjects with pseudophakia. Compared with healthy eyes (n = 47, median Ps = 17), Ps was significantly reduced by AMD (n = 59, median Ps = 1, P < 0.001) and, to a lesser extent, by cataracts (n = 80, median Ps = 6, P < 0.001). There was no significant difference between Ps for healthy and pseudophakic eyes (n = 47, median Ps = 13, P = 0.323). There was no significant correlation between Ps and logMAR visual acuity.

Conclusions

In the absence of significant cataract, or in pseudophakia, a set of polarization-modulated visual stimuli, quantified as the Ps score, distinguishes AMD from healthy maculae.

Translational Relevance

Perception of polarization-modulated stimuli, previously shown to be macula-dependent in a laboratory setting, is effective as a test of macular function in health and disease in a clinic setting.

Thresholds of polarization vision in octopuses

Polarization vision is widespread in nature, mainly among invertebrates, and is used for a range of tasks including navigation, habitat localization and communication. In marine environments, some species such as those from the Crustacea and Cephalopoda that are principally monochromatic, have evolved to use this adaptation to discriminate objects across the whole visual field, an ability similar to our own use of colour vision. The performance of these polarization vision systems varies, and the few cephalopod species tested so far have notably acute thresholds of discrimination. However, most studies to date have used artificial sources of polarized light that produce levels of polarization much higher than found in nature. In this study, the ability of octopuses to detect polarization contrasts varying in angle of polarization (AoP) was investigated over a range of different degrees of linear polarization (DoLP) to better judge their visual ability in more ecologically relevant conditions. The ‘just-noticeable-differences’ (JND) of AoP contrasts varied consistently with DoLP. These JND thresholds could be largely explained by their ‘polarization distance’, a neurophysical model that effectively calculates the level of activity in opposing horizontally and vertically oriented polarization channels in the cephalopod visual system. Imaging polarimetry from the animals’ natural environment was then used to illustrate the functional advantage that these polarization thresholds may confer in behaviourally relevant contexts.

Summary: Octopuses are highly sensitive to small changes in the angle of polarization (<1 deg contrast), even when the degree of polarization is low, which may confer a functional advantage in behaviourally relevant contexts.

Circularly polarized lanthanide luminescence for advanced security inks

Authenticating products and documents with security inks is vital to global commerce, security and health. Lanthanide complexes are widely used in luminescent security inks owing to their unique and robust photophysical properties. Lanthanide complexes can also be engineered to undergo circularly polarized luminescence (CPL), which encodes chiral molecular fingerprints in luminescence spectra that cannot be decoded by conventional optical measurements. However, chiral CPL signals have not yet been exploited as an extra security layer in advanced security inks. This Review introduces CPL and related concepts that are necessary to appreciate the challenges and potential of lanthanide-based, CPL-active security inks. We describe recent advances in CPL analysis and read-out technologies that have expedited CPL-active security ink applications. Further, we provide a systematic meta-analysis of strongly CPL-active Euⁱⁱⁱ, Tbⁱⁱⁱ, Smⁱⁱⁱ, Ybⁱⁱⁱ, Cmⁱⁱⁱ, Dyⁱⁱⁱ and Crⁱⁱⁱ complexes, discussing the suitability of their photophysical properties and highlighting promising candidates. We conclude by providing key recommendations for the development and advancement of the field.

Neural processing of linearly and circularly polarized light signal in a mantis shrimp Haptosquilla pulchella

Stomatopods, or mantis shrimp, are the only animal group known to possess circular polarization vision along with linear polarization vision. By using the rhabdomere of a distally located photoreceptor as a wave retarder, the eyes of mantis shrimp are able to convert circularly polarized light into linearly polarized light. As a result, their circular polarization vision is based on the linearly polarized light-sensitive photoreceptors commonly found in many arthropods. To investigate how linearly and circularly polarized light signals might be processed, we presented a dynamic polarized light stimulus while recording from photoreceptors or lamina neurons in intact mantis shrimp Haptosquilla pulchella The results indicate that all the circularly polarized light-sensitive photoreceptors also showed differential responses to the changing e-vector angle of linearly polarized light. When stimulated with linearly polarized light of varying e-vector angle, most photoreceptors produced a concordant sinusoidal response. In contrast, some lamina neurons doubled the response frequency in reacting to linearly polarized light. These responses resembled a rectified sum of two-channel linear polarization-sensitive photoreceptors, indicating that polarization visual signals are processed at or before the first optic lobe. Noticeably, within the lamina, there was one type of neuron that showed a steady depolarization response to all stimuli except right-handed circularly polarized light. Together, our findings suggest that, between the photoreceptors and lamina neurons, linearly and circularly polarized light may be processed in parallel and differently from one another.

The Clinical Application of Polarization Pattern Perception

Purpose

Determine the repeatability of and optimum stimulus parameters for testing polarization pattern perception in a real-world clinical population, and assess the ability of polarization perception to distinguish normal from abnormal eyes.

Methods

Polarization perception was evaluated in staff and patients attending ophthalmology clinics at Warwick Hospital, UK. A series of visual stimuli were presented in pseudorandom order using a liquid-crystal-display-based polarization pattern generator. Stimuli included geometric patterns, gratings, checkerboards, and optotypes. Participants had one or both eyes diagnosed as normal or abnormal following ophthalmic examination, optical coherence tomography, and measures of visual acuity. Measurement scores were assigned to the eye(s) of each participant depending on the total number of stimuli perceived or identified.

Results

Stimuli covered the range of spatial scales resolvable within polarization perception by normal and abnormal eyes. Different stimuli had different saliencies. For each stimulus type, polarization perception in the abnormal group was significantly reduced compared with normal eyes (P < 0.001). Relative stimulus salience was broadly similar for normal-eye and abnormal-eye viewing groups, being greatest for radially symmetric patterns and least for optotypes. Checkerboard pattern salience had an inverse logarithmic relationship with check fundamental spatial frequency. A devised metric covering the dynamic range of polarization perception was repeatable, and the score derived from the metric was reduced in the abnormal group compared with the normal group (P < 0.001).

Conclusions

Clinically useful metrics of polarization perception distinguish between normal and abnormal eyes.

Translational Relevance

Perception of spatial patterns formed of non-uniform polarization fields has potential as a quantitative clinical diagnostic measurement.

The electrophysiological response to polarization-modulated patterned visual stimuli

Recent reports indicate that the subjective ability of humans to discriminate between polarization E-vector orientations approaches that of many invertebrates. Here, we show that polarization-modulated patterned stimuli generate an objectively recordable electrophysiological response in humans with normal vision. We investigated visual evoked potential (VEP) and electroretinographic (ERG) responses to checkerboard patterns defined solely by their polarization E-vector orientation alternating between ± 45°. Correcting for multiple comparisons, paired-samples t-tests were conducted to assess the significance of post-stimulus deflections from baseline measures of noise. Using standard check pattern sizes for clinical electrophysiology, and a pattern-reversal protocol, participants showed a VEP response to polarization-modulated patterns (PolVEP) with a prominent and consistent positive component near 150 ms (p < 0.01), followed by more variable negative components near 200 ms and 300 ms. The effect was unrecordable with visible wavelengths >550 nm. Further, pseudo-depolarization negated the responses, while control studies provided confirmatory evidence that the PolVEP response was not the product of luminance artefacts. Polarization-modulated patterns did not elicit a recordable ERG response. The possible origins of the PolVEP signals, and the absence of recordable ERG signals, are discussed. We conclude that evoked cortical responses to polarization-modulated patterns provide an objective measure of foveal function, suitable for both humans and non-human primates with equivalent macular anatomy.

Polarization perception in humans: on the origin of and relationship between Maxwell's spot and Haidinger's brushes

Under specific conditions of illumination and polarization, differential absorption of light by macular pigments is perceived as the entoptic phenomena of Maxwell’s spot (MS) or Haidinger’s brushes (HB). To simulate MS and HB, an existing computational model of polarization-dependent properties of the human macula was extended by incorporating neuronal adaptation to stabilized retinal images. The model predicted that polarized light modifies the appearance of MS leading to the perception of a novel phenomenon. The model also predicted a correlation between the observed diameters of MS and HB. Predictions were tested psychophysically in human observers, whose measured differences in the diameters of each entoptic phenomenon generated with depolarized and linearly polarized light were consistent with the model simulations. These findings support a common origin of each phenomenon, and are relevant to the clinical use of polarization stimuli in detecting and monitoring human eye disorders, including macular degeneration. We conclude: (i) MS and HB both result from differential light absorption through a radial diattenuator, compatible with the arrangement of macular pigments in Henle fibres; (ii) the morphology of MS is dependent on the degree of linear polarization; (iii) perceptual differences between MS and HB result from different states of neural adaptation.

Haidinger's brushes elicited at varying degrees of polarization rapidly and easily assesses total macular pigmentation

Macular pigments (MPs), by absorbing potentially toxic short-wavelength (400-500 nm) visible light, provide protection against photo-chemical damage thought to be relevant in the pathogenesis of age-related macular degeneration (AMD). A method of screening for low levels of MPs could be part of a prevention strategy for helping people to delay the onset of AMD. We introduce a new method for assessing MP density that takes advantage of the polarization-dependent absorption of blue light by MPs, which results in the entoptic phenomenon called Haidinger's brushes (HB). Subjects were asked to identify the direction of rotation of HB when presented with a circular stimulus illuminated with an even intensity of polarized white light in which the electric field vector was rotating either clockwise or anti-clockwise. By reducing the degree of polarization of the stimulus light, a threshold for perceiving HB (degree of polarization threshold) was determined and correlated (r²=0.66) to macular pigment optical density assessed using dual-wavelength fundus autofluoresence. The speed and ease of measurement of degree of polarization threshold makes it well suited for large-scale screening of macular pigmentation.

Computational simulation of human perception of spatially dependent patterns modulated by degree and angle of linear polarization

Recent studies on polarization perception have shown that humans are sensitive to patterned stimuli modulated by either angle of linear polarization (AoP) or degree of polarization (DoP). Here, we present a model of human polarization sensitivity that incorporates both AoP and DoP as spatially dependent input variables. Applying the model to both sinusoidal- and square-wave-modulated DoP and AoP inputs, we demonstrate the theoretical similarities and differences generated by such inputs. Our model indicates the following: (i) edge boundaries between two adjacent areas of different linear polarization are preserved for both AoP- and DoP-modulated stimuli; and (ii) compared with DoP stimuli, AoP stimuli generate greater luminance changes at the photoreceptor level, suggesting that AoP-modulated patterns are potentially more salient than DoP patterns. The computational model is supported experimentally with an optical test of the model comprising a radial diattenuating polarizing filter and modified liquid crystal displays generating DoP- and AoP-modulated outputs. Psychophysical measures of human sensitivity confirm the increased salience of AoP- relative to DoP-modulated stimuli. These findings have practical application to the selection of DoP- and AoP-modulated stimuli for the investigation of macular function and macular pigment density in healthy and diseased eyes.

Polarisation signals: a new currency for communication

Most polarisation vision studies reveal elegant examples of how animals, mainly the invertebrates, use polarised light cues for navigation, course-control or habitat selection. Within the past two decades it has been recognised that polarised light, reflected, blocked or transmitted by some animal and plant tissues, may also provide signals that are received or sent between or within species. Much as animals use colour and colour signalling in behaviour and survival, other species additionally make use of polarisation signalling, or indeed may rely on polarisation-based signals instead. It is possible that the degree (or percentage) of polarisation provides a more reliable currency of information than the angle or orientation of the polarised light electric vector (e-vector). Alternatively, signals with specific e-vector angles may be important for some behaviours. Mixed messages, making use of polarisation and colour signals, also exist. While our knowledge of the physics of polarised reflections and sensory systems has increased, the observational and behavioural biology side of the story needs more (and more careful) attention. This Review aims to critically examine recent ideas and findings, and suggests ways forward to reveal the use of light that we cannot see.

Orienting to polarized light at night - matching lunar skylight to performance in a nocturnal beetle

For polarized light to inform behaviour, the typical range of degrees of polarization observable in the animal's natural environment must be above the threshold for detection and interpretation. Here, we present the first investigation of the degree of linear polarization threshold for orientation behaviour in a nocturnal species, with specific reference to the range of degrees of polarization measured in the night sky. An effect of lunar phase on the degree of polarization of skylight was found, with smaller illuminated fractions of the moon's surface corresponding to lower degrees of polarization in the night sky. We found that the South African dung beetle Escarabaeus satyrus can orient to polarized light for a range of degrees of polarization similar to that observed in diurnal insects, reaching a lower threshold between 0.04 and 0.32, possibly as low as 0.11. For degrees of polarization lower than 0.23, as measured on a crescent moon night, orientation performance was considerably weaker than that observed for completely linearly polarized stimuli, but was nonetheless stronger than in the absence of polarized light.

A different view: sensory drive in the polarized-light realm

Sensory drive, the concept that sensory systems primarily evolve under the influence of environmental features and that animal signals are evolutionarily shaped and tuned by these previously existing sensory systems, has been thoroughly studied regarding visual signals across many animals. Much of this work has focused on spectral aspects of vision and signals. Here, I review work on polarized-light signals of animals and relate these to what is known of polarization visual systems, polarized-light aspects of visual scenes, and polarization-related behavior (e.g., orientation, habitat-finding, contrast enhancement). Other than the broad patterns of scattered polarized light in the sky, most polarization in both terrestrial and aquatic environments results from either reflection or scattering in the horizontal plane. With overhead illumination, horizontal features such as the surfaces of many leaves or of air: water interfaces reflect horizontal polarization, and water scatters horizontally polarized light under most conditions. Several animal species have been demonstrated to use horizontally polarized light fields or features in critical aspects of their biology. Significantly, most biological signals are also horizontally polarized. Here, I present relevant polarization-related behavior and discuss the hypothesis that sensory drive has evolutionarily influenced the structure of polarization signals. The paper also considers the evolutionary origin of circular polarization vision and circularly polarized signals. It appears that this class of signals did not evolve under the influence of sensory drive. The study of signals based on polarized light is becoming a mature field of research.

Computational simulation of Haidinger's brushes

Haidinger's brushes (HB) are entoptic phenomena resulting from differential absorption of linear polarized light by the human macula. Computational models have assisted in understanding the behavior of these subjective phenomena but have been limited in their application. This study presents a revised computational model that incorporates known determinants of the form and behavior of HB. The model generates both static and animated simulations of HB that can be quantified by their density, contrast, and radial/circumferential extent. Measured physiological parameters are used to demonstrate the dependency of HB on macular pigment (MP) density, MP distribution, and ocular retardation. Physiological variations in these parameters explain the reported variations in the perception of HB.

Polarisation vision: overcoming challenges of working with a property of light we barely see

In recent years, the study of polarisation vision in animals has seen numerous breakthroughs, not just in terms of what is known about the function of this sensory ability, but also in the experimental methods by which polarisation can be controlled, presented and measured. Once thought to be limited to only a few animal species, polarisation sensitivity is now known to be widespread across many taxonomic groups, and advances in experimental techniques are, in part, responsible for these discoveries. Nevertheless, its study remains challenging, perhaps because of our own poor sensitivity to the polarisation of light, but equally as a result of the slow spread of new practices and methodological innovations within the field. In this review, we introduce the most important steps in designing and calibrating polarised stimuli, within the broader context of areas of current research and the applications of new techniques to key questions. Our aim is to provide a constructive guide to help researchers, particularly those with no background in the physics of polarisation, to design robust experiments that are free from confounding factors.

Noise creates polarization artefacts

The accuracy of calculations of both the degree and angle of polarization depend strongly on the noise in the measurements used. The noise in the measurements recorded by both camera based systems and spectrometers can lead to significant artefacts and incorrect conclusions about high degrees of polarization when in fact none exist. Three approaches are taken in this work: firstly, the absolute error introduced as a function of the signal to noise ratio for polarization measurements is quantified in detail. An important finding here is the reason for why several studies incorrectly suggest that black (low reflectivity) objects are highly polarized. The high degree of polarization is only an artefact of the noise in the calculation. Secondly, several simple steps to avoid such errors are suggested. Thirdly, if these points can not be followed, two methods are presented for mitigating the effects of noise: a maximum likelihood estimation method and a new denoising algorithm to best calculate the degree of polarization of natural polarization information.

The spectral, spatial and contrast sensitivity of human polarization pattern perception

It is generally believed that humans perceive linear polarized light following its conversion into a luminance signal by diattenuating macular structures. Measures of polarization sensitivity may therefore allow a targeted assessment of macular function. Our aim here was to quantify psychophysical characteristics of human polarization perception using grating and optotype stimuli defined solely by their state of linear polarization. We show: (i) sensitivity to polarization patterns follows the spectral sensitivity of macular pigment; (ii) the change in sensitivity across the central field follows macular pigment density; (iii) polarization patterns are identifiable across a range of contrasts and scales, and can be resolved with an acuity of 15.4 cycles/degree (0.29 logMAR); and (iv) the human eye can discriminate between areas of linear polarization differing in electric field vector orientation by as little as 4.4°. These findings, which support the macular diattenuator model of polarization sensitivity, are unique for vertebrates and approach those of some invertebrates with a well-developed polarization sense. We conclude that this sensory modality extends beyond Haidinger's brushes to the recognition of quantifiable spatial polarization-modulated patterns. Furthermore, the macular origin and sensitivity of human polarization pattern perception makes it potentially suitable for the detection and quantification of macular dysfunction.

Celestial polarization patterns sufficient for Viking navigation with the naked eye: detectability of Haidinger's brushes on the sky versus meteorological conditions

If a human looks at the clear blue sky from which light with high enough degree of polarization d originates, an 8-shaped bowtie-like figure, the yellow Haidinger's brush can be perceived, the long axis of which points towards the sun. A band of high d arcs across the sky at 90° from the sun. A person can pick two points on that band, observe the yellow brushes and triangulate the position of the sun based on the orientation of the two observed brushes. This method has been suggested to have been used on the open sea by Viking navigators to determine the position of the invisible sun occluded by cloud or fog. Furthermore, Haidinger's brushes can also be used to locate the sun when it is below the horizon or occluded by objects on the horizon. To determine the position of the sun using the celestial polarization pattern, the d of the portion of the sky used must be greater than the viewer's degree of polarization threshold d* for perception of Haidinger's brushes. We studied under which sky conditions the prerequisite d > d* is satisfied. Using full-sky imaging polarimetry, we measured the d-pattern of skylight in the blue (450 nm) spectral range for 1296 different meteorological conditions with different solar elevation angles θ and per cent cloud cover ρ. From the measured d-patterns of a given sky we determined the proportion P of the sky for which d > d*. We obtained that P is the largest at low solar elevations θ ≈ 0° and under totally or nearly clear skies with cloud coverage ρ = 0%, when the sun's position is already easily determined. If the sun is below the horizon (-5° ≤ θ < 0°) during twilight, P = 76.17 ± 4.18% for [Formula: see text] under clear sky conditions. Consequently, the sky-polarimetric Viking navigation based on Haidinger's brushes is most useful after sunset and prior to sunrise, when the sun is not visible and large sky regions are bright, clear and polarized enough for perception of Haidinger's brushes.

Intuitive representation of photopolarimetric data using the polarization ellipse

Photopolarimetry is the spatial characterization of light polarization. Unlike intensity or wavelength, we are largely insensitive to polarization and therefore find it hard to explore the multidimensional data that photopolarimetry produces (two spatial dimensions plus four polarization dimensions). Many different ways for presenting and exploring this modality of light have been suggested. Most of these ignore circular polarization, include multiple image panes that make correlating structure with polarization difficult, and obscure the main trends with overly detailed information and often misleading colour maps. Here, we suggest a novel way for presenting the main results from photopolarimetric analyses. By superimposing a grid of polarization ellipses onto the RGB image, the full polarization state of each cell is intuitively conveyed to the reader. This method presents linear and circular polarization as well as ellipticity in a graphical manner, does not require multiple panes, facilitates the correlation between structure and polarization, and requires the addition of only three novel colours. We demonstrate its usefulness in a biological context where we believe it would be most relevant.

Diffraction gratings generating orders with selective states of polarization

We propose specially designed double anisotropic polarization diffraction gratings capable of producing a selective number of diffraction orders and with selective different states of polarization. Different polarization diffraction gratings are demonstrated, including linear polarization with horizontal, vertical and ± 45° orientations, and circular R and L polarization outputs. When illuminated with an arbitrary state of polarization, the system acts as a complete polarimeter where the intensities of the diffraction orders allow measurement of the Stokes parameters with a single shot. Experimental proof-of-concept is presented using a parallel-aligned liquid crystal display operating in a double pass architecture.