Polarization transition between sunlit and moonlit skies with possible implications for animal orientation and Viking navigation: anomalous celestial twilight polarization at partial moon

Ultraviolet bionic compass method based on non-ideality correction and statistical guidance in twilight conditions

Bionic polarization compass is a fascinating subject in the navigation domain. However, the polarization navigation accuracy is severely degraded by the influence of city glow at dusk. Therefore, we proposed an ultraviolet bionic compass method based on non-ideality correction and statistical guidance. A non-ideal polarization imaging model was established to correct the system detection error. A meridian extraction algorithm based on the statistical properties of solar direction vectors was proposed for accurate heading calculation. The proposed algorithm was demonstrated experimentally and reduced the heading error to approximately 1°, which shows strong anti-interference performance against urban glare.

Better, not more, lighting: Policies in urban areas towards environmentally-sound illumination of historical stone buildings that also halts biological colonization

Anthropogenic or Artificial light at night (ALAN) pollution, or more simply light pollution, is an issue of increasing concern to the general public, as well as to scientists and politicians. However, although advances have been made in terms of scientific knowledge, these advances have not been fully transferred to or considered by politicians. In addition, illumination of stone monuments in urban areas is an emerging contribution to ALAN pollution that has scarcely been considered to date. This paper presents a literature review of the topic of light pollution and related policies, including a bibliometric analysis of studies published between 2020 and 2022. The prevailing legislation in Europe regarding the regulation of outdoor lighting, which emphasises the complexity of controlling light pollution, is summarised and the regulation of monumental lighting in Spain is discussed. Findings concerning the impact of ALAN on biodiversity in urban areas, and the promising biostatic effect of ornamental lighting (halting biological colonization on stone monuments, mainly caused by algae and cyanobacteria) are described. Finally, trends in monument illumination and policymaking towards environmentally sustainable management are considered.

Biomimetic Polarized Light Navigation Sensor: A Review

A polarized light sensor is applied to the front-end detection of a biomimetic polarized light navigation system, which is an important part of analyzing the atmospheric polarization mode and realizing biomimetic polarized light navigation, having received extensive attention in recent years. In this paper, biomimetic polarized light navigation in nature, the mechanism of polarized light navigation, point source sensor, imaging sensor, and a sensor based on micro nano machining technology are compared and analyzed, which provides a basis for the optimal selection of different polarized light sensors. The comparison results show that the point source sensor can be divided into basic point source sensor with simple structure and a point source sensor applied to integrated navigation. The imaging sensor can be divided into a simple time-sharing imaging sensor, a real-time amplitude splitting sensor that can detect images of multi-directional polarization angles, a real-time aperture splitting sensor that uses a light field camera, and a real-time focal plane light splitting sensor with high integration. In recent years, with the development of micro and nano machining technology, polarized light sensors are developing towards miniaturization and integration. In view of this, this paper also summarizes the latest progress of polarized light sensors based on micro and nano machining technology. Finally, this paper summarizes the possible future prospects and current challenges of polarized light sensor design, providing a reference for the feasibility selection of different polarized light sensors.

Sensitivity and robustness of sky-polarimetric Viking navigation: Sailing success is most sensitive to night sailing, navigation periodicity and sailing date, but robust against weather conditions

Although Viking sailors did not have a magnetic compass, they could successfully navigate with a sun-compass under a sunny sky. Under cloudy/foggy conditions, they might have applied the sky-polarimetric Viking navigation (SPVN), the high success of which has been demonstrated with computer simulations using the following input data: sky polarization patterns measured with full-sky imaging polarimetry, and error functions of the navigation steps measured in psychophysical laboratory and planetarium experiments. As a continuation of the earlier studies, in this work we investigate the sensitivity of the success of SPVN to the following relevant sailing, meteorological and navigational parameters: sunstone type, sailing date, navigation periodicity, night sailing, dominance of strongly, medium or weakly cloudy skies, and changeability of cloudiness. Randomly varying these parameters in the simulation of Viking voyages along the latitude 60° 21’ 55’’ N from Norway to Greenland, we determined those parameters which had strong and weak influences on the success of SPVN. The following intrinsic parameters of the simulation were also randomly changed: sailing speed, visibility distance of Greenland’s southeast coastline and start time of diurnal sailing. Our results show that the sailing success is sensitive to the night sailing, navigation periodicity and sailing date, while it is robust against the sunstone type, dominance of strongly, medium or weakly cloudy skies, and changing cloudiness.

Neutral point detection using the AOP of polarized skylight patterns

The neutral points are one of the most significant characteristics of the polarized skylight pattern in the whole sky. At present, detection of the neutral points mostly utilizes ellipse fitting of the degree of polarization. However, because the degree of polarization distribution characteristics of a polarized skylight pattern is easily affected by the environment, the robustness of the detection is unstable. Aiming at the problem, we analyzed the angle of polarization distribution characteristics of polarized skylight patterns in the region around the neutral point by measurement experiments. Based on this, we proposed an automatic detection method of neutral points using the angle of polarization of the polarized skylight pattern. The experimental results of different times in a continuous period of time show that compared with ellipse fitting of the degree of polarization, the detection accuracy of the proposed method is almost the same, but the robustness is better. It provides a novel method for the position detecting of the neutral point, which is in favor of the measurement applications of polarization technology.

Improved Models of Imaging of Skylight Polarization Through a Fisheye Lens

Researchers have found that some animals can use the skylight polarization pattern for navigation. It is also expected to use the skylight polarization pattern for human navigating in the near future. However, the challenge is that the need for a more accurate and efficient model of the imaging of skylight polarization is always felt. In this paper, three improved models of imaging of skylight polarization are proposed. The proposed models utilize the analysis of the distribution of the skylight polarization pattern after the polarization imaging system. Given that the skylight polarization pattern after the polarization imaging system is distorted, the focus of this paper is on the degree of distortion of the skylight polarization pattern in these imaging models. Experiments in clear weather conditions demonstrate that the proposed model operates close to the actual acquired skylight polarization pattern.

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.

Study on skylight polarization patterns over the ocean for polarized light navigation application

Polarized skylight navigation has excellent navigation performance with no error accumulation over time and low susceptibility to interference. The skylight polarization distribution contains rich directional information, such as the solar meridian, the neutral point, and the polarization angle, which plays a key role in the polarization navigation. But up to now the polarizations of both sunlit and moonlit skies have been investigated mainly over the land. In this work, the polarization distribution patterns of the skylight over the East China Sea and the Yellow Sea were studied. The polarization patterns were captured continuously during daytime and nighttime by using a full-sky imaging polarimetry system and then compared with the simulation results using the libRadtran radiative transfer software package. The result shows that the skylight polarization distribution over the sea has almost the same pattern as that on the land. The accuracy of the angle of polarization and the degree of polarization dropped significantly under the cloudy sky. It was found that when the ship sailed on the sea, the direction of the real meridian was close to the solar azimuth during the daytime and close to the lunar azimuth during the nighttime. It was also found that the nautical twilight polarization distribution was affected by both the solar polarization and the lunar polarization, but the solar polarization was dominant. The experiments show that the skylight polarization distribution pattern over the sea can still be applied in the field of polarization navigation. Thus, it is feasible for ships and unmanned aerial vehicles to use the polarized skylight to navigate and orient on the sea.

It's Not a Bug, It's a Feature: Functional Materials in Insects

Over the course of their wildly successful proliferation across the earth, the insects as a taxon have evolved enviable adaptations to their diverse habitats, which include adhesives, locomotor systems, hydrophobic surfaces, and sensors and actuators that transduce mechanical, acoustic, optical, thermal, and chemical signals. Insect-inspired designs currently appear in a range of contexts, including antireflective coatings, optical displays, and computing algorithms. However, as over one million distinct and highly specialized species of insects have colonized nearly all habitable regions on the planet, they still provide a largely untapped pool of unique problem-solving strategies. With the intent of providing materials scientists and engineers with a muse for the next generation of bioinspired materials, here, a selection of some of the most spectacular adaptations that insects have evolved is assembled and organized by function. The insects presented display dazzling optical properties as a result of natural photonic crystals, precise hierarchical patterns that span length scales from nanometers to millimeters, and formidable defense mechanisms that deploy an arsenal of chemical weaponry. Successful mimicry of these adaptations may facilitate technological solutions to as wide a range of problems as they solve in the insects that originated them.

Success of sky-polarimetric Viking navigation: revealing the chance Viking sailors could reach Greenland from Norway

According to a famous hypothesis, Viking sailors could navigate along the latitude between Norway and Greenland by means of sky polarization in cloudy weather using a sun compass and sunstone crystals. Using data measured in earlier atmospheric optical and psychophysical experiments, here we determine the success rate of this sky-polarimetric Viking navigation. Simulating 1000 voyages between Norway and Greenland with varying cloudiness at summer solstice and spring equinox, we revealed the chance with which Viking sailors could reach Greenland under the varying weather conditions of a 3-week-long journey as a function of the navigation periodicity Δt if they analysed sky polarization with calcite, cordierite or tourmaline sunstones. Examples of voyage routes are also presented. Our results show that the sky-polarimetric navigation is surprisingly successful on both days of the spring equinox and summer solstice even under cloudy conditions if the navigator determined the north direction periodically at least once in every 3 h, independently of the type of sunstone used for the analysis of sky polarization. This explains why the Vikings could rule the Atlantic Ocean for 300 years and could reach North America without a magnetic compass. Our findings suggest that it is not only the navigation periodicity in itself that is important for higher navigation success rates, but also the distribution of times when the navigation procedure carried out is as symmetrical as possible with respect to the time point of real noon.

Accuracy of the hypothetical sky-polarimetric Viking navigation versus sky conditions: revealing solar elevations and cloudinesses favourable for this navigation method

According to Thorkild Ramskou's theory proposed in 1967, under overcast and foggy skies, Viking seafarers might have used skylight polarization analysed with special crystals called sunstones to determine the position of the invisible Sun. After finding the occluded Sun with sunstones, its elevation angle had to be measured and its shadow had to be projected onto the horizontal surface of a sun compass. According to Ramskou's theory, these sunstones might have been birefringent calcite or dichroic cordierite or tourmaline crystals working as polarizers. It has frequently been claimed that this method might have been suitable for navigation even in cloudy weather. This hypothesis has been accepted and frequently cited for decades without any experimental support. In this work, we determined the accuracy of this hypothetical sky-polarimetric Viking navigation for 1080 different sky situations characterized by solar elevation θ and cloudiness ρ, the sky polarization patterns of which were measured by full-sky imaging polarimetry. We used the earlier measured uncertainty functions of the navigation steps 1, 2 and 3 for calcite, cordierite and tourmaline sunstone crystals, respectively, and the newly measured uncertainty function of step 4 presented here. As a result, we revealed the meteorological conditions under which Vikings could have used this hypothetical navigation method. We determined the solar elevations at which the navigation uncertainties are minimal at summer solstice and spring equinox for all three sunstone types. On average, calcite sunstone ensures a more accurate sky-polarimetric navigation than tourmaline and cordierite. However, in some special cases (generally at 35° ≤ θ ≤ 40°, 1 okta ≤ ρ ≤ 6 oktas for summer solstice, and at 20° ≤ θ ≤ 25°, 0 okta ≤ ρ ≤ 4 oktas for spring equinox), the use of tourmaline and cordierite results in smaller navigation uncertainties than that of calcite. Generally, under clear or less cloudy skies, the sky-polarimetric navigation is more accurate, but at low solar elevations its accuracy remains relatively large even at high cloudiness. For a given ρ, the absolute value of averaged peak North uncertainties dramatically decreases with increasing θ until the sign (±) change of these uncertainties. For a given θ, this absolute value can either decrease or increase with increasing ρ. The most advantageous sky situations for this navigation method are at summer solstice when the solar elevation and cloudiness are 35° ≤ θ ≤ 40° and 2 oktas ≤ ρ ≤ 3 oktas.

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.

Mayflies are least attracted to vertical polarization: A polarotactic reaction helping to avoid unsuitable habitats

Like other aquatic insects, mayflies are positively polarotactic and locate water surfaces by means of the horizontal polarization of water-reflected light. However, may vertically polarized light also have implications for the swarming behaviour of mayflies? To answer this question, we studied in four field experiments the behavioural responses of Ephoron virgo and Caenis robusta mayflies to lamps emitting horizontally and vertically polarized and unpolarized light. In both species, unpolarized light induces positive phototaxis, horizontally polarized light elicits positive photo- and polarotaxis, horizontally polarized light is much more attractive than unpolarized light, and vertically polarized light is the least attractive if the stimulus intensities and spectra are the same. Vertically polarized light was the most attractive for C. robusta if its intensity was about two and five times higher than that of the unpolarized and horizontally polarized stimuli, respectively. We suggest that the mayfly behaviour observed in our experiments may facilitate the stability of swarming above water surfaces. Beside the open water surface reflecting horizontally polarized light, the shadow and mirror image of riparian vegetation at the edge of the water surface reflect weakly and non-horizontally (mainly vertically) polarized light. Due to their positive polarotaxis, flying mayflies remain continuously above the water surface, because they keep away from the unpolarized or non-horizontally polarizing edge regions (water surface and coast line) of water bodies. We also discuss how our findings can explain the regulation of mayfly colonization.

North error estimation based on solar elevation errors in the third step of sky-polarimetric Viking navigation

The theory of sky-polarimetric Viking navigation has been widely accepted for decades without any information about the accuracy of this method. Previously, we have measured the accuracy of the first and second steps of this navigation method in psychophysical laboratory and planetarium experiments. Now, we have tested the accuracy of the third step in a planetarium experiment, assuming that the first and second steps are errorless. Using the fists of their outstretched arms, 10 test persons had to estimate the elevation angles (measured in numbers of fists and fingers) of black dots (representing the position of the occluded Sun) projected onto the planetarium dome. The test persons performed 2400 elevation estimations, 48% of which were more accurate than ±1°. We selected three test persons with the (i) largest and (ii) smallest elevation errors and (iii) highest standard deviation of the elevation error. From the errors of these three persons, we calculated their error function, from which the North errors (the angles with which they deviated from the geographical North) were determined for summer solstice and spring equinox, two specific dates of the Viking sailing period. The range of possible North errors ΔωN was the lowest and highest at low and high solar elevations, respectively. At high elevations, the maximal ΔωN was 35.6° and 73.7° at summer solstice and 23.8° and 43.9° at spring equinox for the best and worst test person (navigator), respectively. Thus, the best navigator was twice as good as the worst one. At solstice and equinox, high elevations occur the most frequently during the day, thus high North errors could occur more frequently than expected before. According to our findings, the ideal periods for sky-polarimetric Viking navigation are immediately after sunrise and before sunset, because the North errors are the lowest at low solar elevations.

Adjustment errors of sunstones in the first step of sky-polarimetric Viking navigation: studies with dichroic cordierite/ tourmaline and birefringent calcite crystals

According to an old but still unproven theory, Viking navigators analysed the skylight polarization with dichroic cordierite or tourmaline, or birefringent calcite sunstones in cloudy/foggy weather. Combining these sunstones with their sun-dial, they could determine the position of the occluded sun, from which the geographical northern direction could be guessed. In psychophysical laboratory experiments, we studied the accuracy of the first step of this sky-polarimetric Viking navigation. We measured the adjustment error e of rotatable cordierite, tourmaline and calcite crystals when the task was to determine the direction of polarization of white light as a function of the degree of linear polarization p. From the obtained error functions e(p), the thresholds p* above which the first step can still function (i.e. when the intensity change seen through the rotating analyser can be sensed) were derived. Cordierite is about twice as reliable as tourmaline. Calcite sunstones have smaller adjustment errors if the navigator looks for that orientation of the crystal where the intensity difference between the two spots seen in the crystal is maximal, rather than minimal. For higher p (greater than p crit) of incident light, the adjustment errors of calcite are larger than those of the dichroic cordierite (p crit=20%) and tourmaline (p crit=45%), while for lower p (less than p crit) calcite usually has lower adjustment errors than dichroic sunstones. We showed that real calcite crystals are not as ideal sunstones as it was believed earlier, because they usually contain scratches, impurities and crystal defects which increase considerably their adjustment errors. Thus, cordierite and tourmaline can also be at least as good sunstones as calcite. Using the psychophysical e(p) functions and the patterns of the degree of skylight polarization measured by full-sky imaging polarimetry, we computed how accurately the northern direction can be determined with the use of the Viking sun-dial under 10 different sky conditions at 61° latitude, which was one of the main Viking sailing routes. According to our expermiments, under clear skies, using calcite or cordierite or tourmaline sunstones, Viking sailors could navigate with net orientation errors [Formula: see text]. Under overcast conditions, their net navigation error depends on the sunstone type: [Formula: see text], [Formula: see text] and [Formula: see text].

Sky light polarization detection with linear polarizer triplet in light field camera inspired by insect vision

Stable information of a sky light polarization pattern can be used for navigation with various advantages such as better performance of anti-interference, no "error cumulative effect," and so on. But the existing method of sky light polarization measurement is weak in real-time performance or with a complex system. Inspired by the navigational capability of a Cataglyphis with its compound eyes, we introduce a new approach to acquire the all-sky image under different polarization directions with one camera and without a rotating polarizer, so as to detect the polarization pattern across the full sky in a single snapshot. Our system is based on a handheld light field camera with a wide-angle lens and a triplet linear polarizer placed over its aperture stop. Experimental results agree with the theoretical predictions. Not only real-time detection but simple and costless architecture demonstrates the superiority of the approach proposed in this paper.

Testing a polarimetric cloud imager aboard research vessel Polarstern: comparison of color-based and polarimetric cloud detection algorithms

Cloud cover estimation is an important part of routine meteorological observations. Cloudiness measurements are used in climate model evaluation, nowcasting solar radiation, parameterizing the fluctuations of sea surface insolation, and building energy transfer models of the atmosphere. Currently, the most widespread ground-based method to measure cloudiness is based on analyzing the unpolarized intensity and color distribution of the sky obtained by digital cameras. As a new approach, we propose that cloud detection can be aided by the additional use of skylight polarization measured by 180° field-of-view imaging polarimetry. In the fall of 2010, we tested such a novel polarimetric cloud detector aboard the research vessel Polarstern during expedition ANT-XXVII/1. One of our goals was to test the durability of the measurement hardware under the extreme conditions of a trans-Atlantic cruise. Here, we describe the instrument and compare the results of several different cloud detection algorithms, some conventional and some newly developed. We also discuss the weaknesses of our design and its possible improvements. The comparison with cloud detection algorithms developed for traditional nonpolarimetric full-sky imagers allowed us to evaluate the added value of polarimetric quantities. We found that (1) neural-network-based algorithms perform the best among the investigated schemes and (2) global information (the mean and variance of intensity), nonoptical information (e.g., sun-view geometry), and polarimetric information (e.g., the degree of polarization) improve the accuracy of cloud detection, albeit slightly.

Measurements of skylight polarization: a case study in urban region with high-loading aerosol

We investigate skylight polarization patterns in an urban region using our developed full-Stokes imaging polarimeter. A detailed description of our imaging polarimeter and its calibration are given, then, we measure skylight polarization patterns at wavelength λ=488  nm and at solar elevation between -05°10' and +35°42' in the city of Hefei, China. We show that in an urban region with high-loading aerosols: (1) the measured degree of linear polarization reaches the maximum near sunset, and large areas of unpolarized sky exist in the forward sunlight direction close to the Sun; (2) the position of neural points shifts from the local meridian plane and, if compared with a clear sky, alters the symmetrical characteristics of celestial polarization pattern; and (3) the observed circular polarization component is negligible.