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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 (

Fiddler crabs process intensity and polarization information independently and in parallel to enhance visual contrast., Many crustaceans are sensitive to the polarization of light and use this information for object-based visually guided behaviors. For these tasks, it is unknown whether polarization and intensity information are integrated into a single-contrast channel, whereby polarization directly contributes to perceived intensity, or whether they are processed separately and in parallel. Using a novel type of visual display that allowed polarization and intensity properties of visual stimuli to be adjusted independently and simultaneously, we conducted behavioral experiments with fiddler crabs to test which of these two models of visual processing occurs. We found that, for a loom detection task, fiddler crabs process polarization and intensity information independently and in parallel. The crab’s response depended on whichever contrast was the most salient. By contributing independent measures of visual contrast, polarization and intensity provide a greater range of detectable contrast information for the receiver, increasing the chance of detecting a potential threat.

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 (r 2 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.

Gaze stabilization is an almost ubiquitous animal behaviour, one that is required to see the world clearly and without blur. Stomatopods, however, only fix their eyes on scenes or objects of interest occasionally. Almost uniquely among animals they explore their visual environment with a series pitch, yaw and torsional (roll) rotations of their eyes, where each eye may also move largely independently of the other. In this work, we demonstrate that the torsional rotations are used to actively enhance their ability to see the polarization of light. Both Gonodactylus smithii and Odontodactylus scyllarus rotate their eyes to align particular photoreceptors relative to the angle of polarization of a linearly polarized visual stimulus, thereby maximizing the polarization contrast between an object of interest and its background. This is the first documented example of any animal displaying dynamic polarization vision, in which the polarization information is actively maximized through rotational eye movements., Mantis shrimps are known to display large pitch, yaw and torsional eye rotations. Here, the authors show that these eye movements allow mantis shrimp to orientate particular photoreceptors in order to better discriminate the polarization of light.

Many animals use structural coloration to create bright and conspicuous visual signals. Selection of the size and shape of the optical structures animals use defines both the colour and intensity of the light reflected. The material used to create these reflectors is also important; however, animals are restricted to a limited number of materials: commonly chitin, guanine and the protein, reflectin. In this work we highlight that a particular set of material properties can also be under selection in order to increase the optical functionality of structural reflectors. Specifically, polarization properties, such as birefringence (the difference between the refractive indices of a material) and chirality (which relates to molecular asymmetry) are both under selection to create enhanced structural reflectivity. We demonstrate that the structural coloration of the gold beetle Chrysina resplendens and silvery reflective sides of the Atlantic herring, Clupea harengus are two examples of this phenomenon. Importantly, these polarization properties are not selected to control the polarization of the reflected light as a source of visual information per se. Instead, by creating higher levels of reflectivity than are otherwise possible, such internal polarization properties improve intensity-matching camouflage. This article is part of the themed issue ‘Animal coloration: production, perception, function and application’.

In this paper, we present recent work on bioinspired polarization imaging sensors and their applications in biomedicine. In particular, we focus on three different aspects of these sensors. First, we describe the electro–optical challenges in realizing a bioinspired polarization imager, and in particular, we provide a detailed description of a recent low-power complementary metal–oxide–semiconductor (CMOS) polarization imager. Second, we focus on signal processing algorithms tailored for this new class of bioinspired polarization imaging sensors, such as calibration and interpolation. Third, the emergence of these sensors has enabled rapid progress in characterizing polarization signals and environmental parameters in nature, as well as several biomedical areas, such as label-free optical neural recording, dynamic tissue strength analysis, and early diagnosis of flat cancerous lesions in a murine colorectal tumor model. We highlight results obtained from these three areas and discuss future applications for these sensors.

Many insects use the pattern of polarized light in the sky as a navigational cue. In this study, we use this sensory ability as a source of inspiration to create a computational orientation model based on an artificial neural network (POL-ANN). After a training phase using numerically generated sky polarization patterns, stable and convergent networks are obtained. We undertook a series of verification tests using four typical but different sky conditions and showed that the post-trained networks were able to make an accurate prediction of the direction of the sun. Comparisons between the proposed models and models based on the convolutional neural network (CNN) structure revealed the merits of the bio-inspired architecture. We further investigated the accuracy of the models based on two different (locust-like, broader; Drosophila-like, narrower) visual fields of the sky. We find that the accuracy of the computations depends on the overhead visual scene, specifically that wider fields of view perform better when information about the overhead polarization pattern is missing.

Many biophotonic structures have their spectral properties of reflection ‘tuned’ using the (zeroth-order) Bragg criteria for phase constructive interference. This is associated with a periodicity, or distribution of periodicities, parallel to the direction of illumination. The polarization properties of these reflections are, however, typically constrained by the dimensional symmetry and intrinsic dielectric properties of the biological materials. Here we report a linearly polarizing reflector in a stomatopod crustacean that consists of 6–8 layers of hollow, ovoid vesicles with principal axes of ~550 nm, ~250 nm and ~150 nm. The reflection of unpolarized normally incident light is blue/green in colour with maximum reflectance wavelength of 520 nm and a degree of polarization greater than 0.6 over most of the visible spectrum. We demonstrate that the polarizing reflection can be explained by a resonant coupling with the first-order, in-plane, Bragg harmonics. These harmonics are associated with a distribution of periodicities perpendicular to the direction of illumination, and, due to the shape-anisotropy of the vesicles, are different for each linear polarization mode. This control and tuning of the polarization of the reflection using shape-anisotropic hollow scatterers is unlike any optical structure previously described and could provide a new design pathway for polarization-tunability in man-made photonic devices.

Dielectric multilayer reflectors that are non-polarizing are an important class of optical device and have numerous applications within optical fibres1, dielectric waveguides2 and light-emitting diodes3. Here, we report analyses of a biological non-polarizing optical mechanism found in the broadband guanine-cytoplasm ‘silver’ multilayer reflectors of three species of fish. Present in the fish stratum argenteum are two populations of birefringent guanine crystal, with their optical axes either parallel to the long axis of the crystal or perpendicular to the plane of the crystal, respectively. This arrangement neutralizes the polarization of reflection as a result of the different interfacial Brewster's angles of each population. The fish reflective mechanism is distinct from existing non-polarizing mirror designs4,5,6,7 in that, importantly, there is no refractive index contrast between the low-index layers in the reflector and the external environment. This mechanism could be readily manufactured and exploited in synthetic optical devices. The mechanism by which various species of silvery fish produce almost perfect broadband, polarization-neutral reflections is revealed. The answer lies with the use of multilayers composed of two types of birefringent guanine crystals, which each have their extraordinary and ordinary refractive indices orientated in different directions.

Aquatic habitats are rich in polarized patterns that could provide valuable information about the environment to an animal with a visual system sensitive to polarization of light. Both cephalopods and fishes have been shown to behaviourally respond to polarized light cues, suggesting that polarization sensitivity (PS) may play a role in improving target detection and/or navigation/orientation. However, while there is general agreement concerning the presence of PS in cephalopods and some fish species, its functional significance remains uncertain. Testing the role of PS in predator or prey detection seems an excellent paradigm with which to study the contribution of PS to the sensory assets of both groups, because such behaviours are critical to survival. We developed a novel experimental set-up to deliver computer-generated, controllable, polarized stimuli to free-swimming cephalopods and fishes with which we tested the behavioural relevance of PS using stimuli that evoke innate responses (such as an escape response from a looming stimulus and a pursuing behaviour of a small prey-like stimulus). We report consistent responses of cephalopods to looming stimuli presented in polarization and luminance contrast; however, none of the fishes tested responded to either the looming or the prey-like stimuli when presented in polarization contrast.

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 simplesteps to avoid such errors are suggested. Thirdly, if these points can’t 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.

An integrated laser tweezer and microphotometry device has been used to characterize in detail how individual, axially orientated goldfish photoreceptors absorb linearly polarized light. This work demonstrates that the mid-wavelength sensitive members of double cone photoreceptors display axial differential polarization sensitivity. The polarization contrast was measured to be 9.2±0.4%. By comparison, rod photoreceptors only exhibit isotropic absorbance. These data, combined with the square cone mosaic of double cones in the retina, suggest that intrinsic axial dichroism forms part of the underlying biophysical detection mechanism for polarization vision in this species.

We are constantly surprised by the ability of relatively simple animals to perform precise visually guided movements within complex visual scenes, often using eyes with limited resolution. Exceptional examples include the capture of airborne prey by dragonflies [1], the learning flights of bees and wasps [2], and the tracking of conspecifics by crabs on intertidal mudflats [3-5]. Most studies have focused on how animals do this using sensitivity to intensity or color. However, it is increasingly evident that a third ability, polarization vision, may contribute to such tasks. In many insects, polarization-sensitive photoreceptors are confined within an area of the eye known as the dorsal rim [6], which detects the polarized sky pattern specifically for navigation [7]. However, some animals, including fiddler crabs, are sensitive to the polarization of light across the majority of their image-forming eyes [8, 9], potentially allowing them to use polarization information to increase perceived contrast for general visual tasks [10-13]. Investigations into the use of polarization image-parsing by animals have largely been confined to laboratory settings under artificial lighting [10, 13-18]. This approach can occasionally mislead if the lighting conditions are different from natural [19]. This study presents the first behavioral evidence from the natural context for a function of polarization image parsing. Using experimental manipulations in wild populations of the fiddler crab Uca stenodactylus, we provide evidence that these animals use their polarization vision to enhance contrast in their visual environment, thereby increasing their ability to detect and respond to objects on the mudflat surface.

Polarization sensitivity (PS) is a common feature of invertebrate visual systems. In insects, PS is well known for its use in several different visually guided behaviours, particularly navigation and habitat search. Adult dragonflies use the polarization of light to find water but a role for PS in aquatic dragonfly larvae, a stage that inhabits a very different photic environment to the adults, has not been investigated. The optomotor response of the larvae of the Emperor dragonfly, Anax imperator, was used to determine whether these larvae use PS to enhance visual contrast underwater. Two different light scattering conditions were used to surround the larval animals: a naturalistic horizontally polarized light field and non-naturalistic weakly polarized light field. In both cases these scattering light fields obscured moving intensity stimuli that provoke an optokinetic response in the larvae. Animals were shown to track the movement of a square-wave grating more closely when it was viewed through the horizontally polarized light field, equivalent to a similar increase in tracking ability observed in response to an 8% increase in the intensity contrast of the stimuli. Our results suggest that larval PS enhances the intensity contrast of a visual scene under partially polarized lighting conditions that occur naturally in freshwater environments.

We have examined the vertebrate visual system from a liquid crystalline perspective, with the aim of understanding the mechanisms responsible for polarization vision in vertebrates. Using a technique called micro-spectrophotometry (MSP), we show that the different types of light-sensitive cells in the retina absorb polarized light differently. Based on these measured geometries of absorbance, analytic solutions to Maxwell's equations using a 4×4 matrix technique demonstrate the possibility of intrinsic linear dichroism under axial illumination in those photoreceptors sensitive to polarized light. This provides a new mechanism for axial polarization sensitivity in vertebrate photoreceptors.

We investigate the polarization dependence of localization length in alternating isotropic-birefringent stacks with uncorrelated thickness disorder. The birefringent layers can be positive uniaxial, negative uniaxial, or a mixture of both. Stacks which contain a mixture are shown to suppress the Brewster delocalization anomalies and, over all incident angles, exhibit $p$-polarization localization length maxima that are of similar magnitude to normal incidence. Furthermore, we propose a parameter set that enables the $p$-polarization localization length to monotonically decrease with angle of incidence. This investigation was inspired by weakly polarizing mirrors on the sides of silvery fish and provides a generic means to produce polarization-insensitive, broadband reflections from a random, all-dielectric layered medium.

Brady et al . (Reports, 20 November 2015, p. 965) claimed that the silvery sides of certain fish are cryptic when viewed by animals with polarization sensitivity, which they termed “polarocrypsis.” After examining their evidence, we find this claim to be unsupported due to (i) pseudoreplication, (ii) confounding polarization contrast with intensity contrast, and (iii) measurements taken at very shallow depths.

We present a computationally inexpensive analytical model for simulating celestial polarization patterns in variable conditions. We combine both the singularity theory of Berry et al (2004 New J. Phys. 6 162) and the intensity model of Perez et al (1993 Sol. Energy 50 235–245) such that our single model describes three key sets of data: (1) the overhead distribution of the degree of polarization as well as the existence of neutral points in the sky; (2) the change in sky polarization as a function of the turbidity of the atmosphere; and (3) sky polarization patterns as a function of wavelength, calculated in this work from the ultra-violet to the near infra-red. To verify the performance of our model we generate accurate reference data using a numerical radiative transfer model and statistical comparisons between these two methods demonstrate no significant difference in almost all situations. The development of our analytical model provides a novel method for efficiently calculating the overhead skylight polarization pattern. This provides a new tool of particular relevance for our understanding of animals that use the celestial polarization pattern as a source of visual information.

Biological multilayer reflectors are common in nature and some are able to reflect light across a broad range of wavelengths with a low degree of polarization over all angles of incidence. This inspired us to examine theoretically possible mechanisms that would allow stacks of biological materials to produce broadband omnidirectional reflections. Through the application of anisotropic multilayer theory, we establish that the degree of polarization of light reflected from the structure can be neutralized by birefringent layers with variations in the orientation of their optics axis and random variations in their optical thickness. The degree of polarization of reflected light decreases with the number of crystal layers and can be made arbitrarily low to produce true omnidirectional reflection. We also show that systematic variation in orientation and layer thickness can produce the same effect. This reflective structure is distinct from existing omnidirectional mirrors and can produce omnidirectional reflection even if the refractive index of the external environment is same as the low index isotropic layers.

While color signals are well known as a form of animal communication, a number of animals communicate using signals based on patterns of polarized light reflected from specialized body parts or structures. Mantis shrimps, a group of marine crustaceans, have evolved a great diversity of such signals, several of which are based on photonic structures. These include resonant scattering devices, structures based on layered dichroic molecules, and structures that use birefringent layers to produce circular polarization. Such biological polarizers operate in different spectral regions ranging from the near-UV to medium wavelengths of visible light. In addition to the structures that are specialized for signal production, the eyes of many species of mantis shrimp are adapted to detect linearly polarized light in the ultraviolet and in the green, using specialized sets of photoreceptors with oriented, dichroic visual pigments. Finally, a few mantis shrimp species produce biophotonic retarders within their photoreceptors that permit the detection of circularly polarized light and are thus the only animals known to sense this form of polarization. Mantis shrimps use polarized light in species-specific signals related to mating and territorial defense, and their means of manipulating light's polarization can inspire designs for artificial polarizers and achromatic retarders.

Polarization microspectrophotometry recordings were made to investigate possible differences in the way different spectral classes of photoreceptors from coho salmon (Oncorhynchus kisutch) absorb linearly polarized light. The results strongly suggest that rods and cones absorb transversely illuminating polarized light differently. Cones were found to exhibit a tilted optical geometry in which the maximum absorbance occurred when the E-vector was at a small angle to the transverse axis of the outer segment. Solutions to Maxwell's equations were deduced to investigate the effect of this tilt under conditions of axial illumination. Calculations show an approximate 10% difference in the absorbance of orthogonal polarizations, suggesting the possibility of axial dichroism in the cones of this species.