Stokes vector imaging of the polarized sky-dome

Skylight Polarization Pattern Simulator Based on a Virtual-Real-Fusion Framework for Urban Bionic Polarization Navigation

In a data-driven context, bionic polarization navigation requires a mass of skylight polarization pattern data with diversity, complete ground truth, and scene information. However, acquiring such data in urban environments, where bionic polarization navigation is widely utilized, remains challenging. In this paper, we proposed a virtual-real-fusion framework of the skylight polarization pattern simulator and provided a data preparation method complementing the existing pure simulation or measurement method. The framework consists of a virtual part simulating the ground truth of skylight polarization pattern, a real part measuring scene information, and a fusion part fusing information of the first two parts according to the imaging projection relationship. To illustrate the framework, we constructed a simulator instance adapted to the urban environment and clear weather and verified it in 174 urban scenes. The results showed that the simulator can provide a mass of diverse urban skylight polarization pattern data with scene information and complete ground truth based on a few practical measurements. Moreover, we released a dataset based on the results and opened our code to facilitate researchers preparing and adapting their datasets to their research targets.

Self-calibration algorithm for installation angle deviation of bionic polarization compound eyes

A self-calibration algorithm based on unsupervised optimization for polarizer installation angle deviation is proposed and used in a multi-aperture bionic polarization compound eye system. To simplify calibration operation, under the condition that the calibration-polarized light information is unknown, this algorithm fully exploits redundancy and random polarization information in the scene, and uses a non-convex multi-objective discrete parameter sorting optimization method to achieve angle self-calibration. Compared with ordinary calibration procedures, the algorithm requires less stringent conditions, achieves online calibration and is more accurate. It also can be applied to camera polarization arrays, division-of-focal-plane polarization cameras, and other polarization devices.

Adaptive method for estimating information from a polarized skylight

The acquisition and processing of skylight polarization information forms the cornerstone in modern navigation systems that are developed by imitating certain biological mechanisms. The accuracy of skylight polarization mode information plays a major part in improving the accuracy of polarized light navigation. This paper mainly focuses on developing a methodology that can avoid the error caused by the inaccurate rotation of the polarizer and manual readings from non-electrical equipment, when the time-sequence polarization measurement system is used to obtain the skylight polarization mode information. We propose an adaptive algorithm that can obtain the pictures of angle of polarization and degree of polarization with sets of random rotation angles with no need for precise readings for the rotation angle of the polarizer. By allocating initial random values to rotation angles, a simple iterative estimation method like the Gaussian-Newton method can be used to converge calculated angle of polarization and degree of polarization values to their respective real values. The experiment results show that the proposed method can be used to estimate polarization information with high accuracy and universality under various experiment settings including both sunny and cloudy weathers. Meanwhile, the time efficiency of the proposed method is comparable to traditional methods.

Electromagnetic phase coherence gratings for atmospheric applications

We propose using electromagnetic phase coherence gratings (EMPCGs) for fine spatial segregation in polarimetric components of stationary beams on their propagation in atmospheric turbulence. Unlike for other beams, e.g., non-uniformly correlated EM beams, the off-axis shifts occurring in polarimetric components of EMPCGs are shown to be invariant with respect to the local turbulence strength. This effect may lead to implementation of novel techniques for direct energy, imaging, and wireless optical communication systems operating in the presence of turbulent air.

Digital all-sky polarization imaging of the total solar eclipse on 21 August 2017 in Rexburg, Idaho, USA

All-sky polarization images were measured from sunrise to sunset and during a cloud-free totality on 21 August 2017 in Rexburg, Idaho using two digital three-camera all-sky polarimeters and a time-sequential liquid-crystal-based all-sky polarimeter. Twenty-five polarimetric images were recorded during totality, revealing a highly dynamic evolution of the distribution of skylight polarization, with the degree of linear polarization becoming nearly zenith-symmetric by the end of totality. The surrounding environment was characterized with an infrared cloud imager that confirmed the complete absence of clouds during totality, an AERONET solar radiometer that measured aerosol properties, a portable weather station, and a hand-held spectrometer with satellite images that measured surface reflectance at and near the observation site. These observations confirm that previously observed totality patterns are general and not unique to those specific eclipses. The high temporal image resolution revealed a transition of a neutral point from the zenith in totality to the normal Babinet point just above the Sun after third contact, providing the first indication that the transition between totality and normal daytime polarization patterns occurs over of a time period of approximately 13 s.

Optimal distribution of integration time for intensity measurements in Stokes polarimetry

We consider the typical Stokes polarimetry system, which performs four intensity measurements to estimate a Stokes vector. We show that if the total integration time of intensity measurements is fixed, the variance of the Stokes vector estimator depends on the distribution of the integration time at four intensity measurements. Therefore, by optimizing the distribution of integration time, the variance of the Stokes vector estimator can be decreased. In this paper, we obtain the closed-form solution of the optimal distribution of integration time by employing Lagrange multiplier method. According to the theoretical analysis and real-world experiment, it is shown that the total variance of the Stokes vector estimator can be significantly decreased about 40% in the case discussed in this paper. The method proposed in this paper can effectively decrease the measurement variance and thus statistically improves the measurement accuracy of the polarimetric system.

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

Using full-sky imaging polarimetry, we measured the celestial distribution of polarization during sunset and sunrise at partial (78% and 72%) and full (100%) moon in the red (650 nm), green (550 nm), and blue (450 nm) parts of the spectrum. We investigated the temporal change of the patterns of degree p and angle α of linear polarization of sunlit and moonlit skies at dusk and dawn. We describe here the position change of the neutral points of sky polarization, and present video clips about the celestial polarization transition at moonlit twilight. We found that at partial moon and at a medium latitude (47° 15.481' N) during this transition there is a relatively short (10-20 min) period when (i) the maximum of p of skylight decreases, and (ii) from the celestial α pattern neither the solar-antisolar nor the lunar-antilunar meridian can be unambiguously determined. These meridians can serve as reference directions of animal orientation and Viking navigation based on sky polarization. The possible influence of these atmospheric optical phenomena during the polarization transition between sunlit and moonlit skies on the orientation of polarization-sensitive crepuscular/nocturnal animals and the hypothesized navigation of sunstone-aided Viking seafarers is discussed.

Ground-based full-sky imaging polarimeter based on liquid crystal variable retarders

A ground-based full-sky imaging polarimeter based on liquid crystal variable retarders (LCVRs) is proposed in this paper. Our proposed method can be used to realize the rapid detection of the skylight polarization information with hemisphere field-of-view for the visual band. The characteristics of the incidence angle of light on the LCVR are investigated, based on the electrically controlled birefringence. Then, the imaging polarimeter with hemisphere field-of-view is designed. Furthermore, the polarization calibration method with the field-of-view multiplexing and piecewise linear fitting is proposed, based on the rotation symmetry of the polarimeter. The polarization calibration of the polarimeter is implemented with the hemisphere field-of-view. This imaging polarimeter is investigated by the experiment of detecting the skylight image. The consistency between the obtained experimental distribution of polarization angle with that due to Rayleigh scattering model is 90%, which confirms the effectivity of our proposed imaging polarimeter.

On the performance of the physicality-constrained maximum-likelihood estimation of Stokes vector

We address the estimation of the Stokes vectors taking into account the physical realizability constraint. We propose a fast method for computing the constrained maximum-likelihood (CML) estimator for any measurement matrix, and we compare its performance with the classical empirical physicality-constrained estimator. We show that when the measurement matrix is based on four polarization states spanning a regular tetrahedron on the Poincaré sphere, the two estimators are very similar, but the CML provides a better estimation of the intensity. For an arbitrary measurement matrix, the CML estimator does not always yield better estimation performance than the empirical one: their comparative performances depend on the measurement matrix, the actual Stokes vector and the signal-to-noise ratio.

Spectral polarization of clear and hazy coastal skies

Linear polarization of the clear daytime sky has often been measured as a spectrally integrated or quasi-monochromatic variable, but seldom as a spectral one. So we use a hyperspectral imaging system to measure skylight polarization at high spectral and angular resolutions for clear and hazy skies at our coastal site. The resulting polarization maps and spectra exhibit both commonalities and differences that seem unexplained by an existing polarized radiative transfer model. Comparing the measured polarization spectra with those predicted by aerosol single scattering suggests some basic verisimilitude tests for improving such models.

An instrument to measure the downwelling polarized radiance distribution in the ocean

We have built a new camera system to measure the downwelling polarized radiance distribution in the ocean. This system uses 4 fisheye lenses and coherent fiber bundles behind each image to transmit all 4 fisheye images onto a single camera image. This allows simultaneous images to be collected with 4 unique polarization states, and thus the full Stokes vector of the rapidly changing downwelling light field.

Effects of surface reflectance on skylight polarization measurements at the Mauna Loa Observatory

An all-sky imaging polarimeter was deployed in summer 2008 to the Mauna Loa Observatory in Hawaii to study clear-sky atmospheric skylight polarization. The imager operates in five wavebands in the visible and near infrared spectrum and has a fisheye lens for all-sky viewing. This paper describes the deployment and presents comparisons of the degree of skylight polarization observed to similar data observed by Coulson with a principal-plane scanning polarimeter in the late 1970s. In general, the results compared favorably to those of Coulson. In addition, we present quantitative results correlating a variation of the maximum degree of polarization over a range of 70-85% to fluctuation in underlying surface reflectance and upwelling radiance data from the GOES satellite.

Measuring the influence of aerosols and albedo on sky polarization

All-sky distributions of the polarized radiance are measured using an automated fish-eye camera system with a rotating polarizer. For a large range of aerosol and surface albedo situations, the influence on the degree of polarization and sky radiance is investigated. The range of aerosol optical depth and albedo is 0.05-0.5 and 0.1-0.75, respectively. For this range of parameters, a reduction of the degree of polarization from about 0.7 to 0.4 was observed. The analysis is done for 90° scattering angle in the principal plane under clear sky conditions for a broadband channel of 450 ± 25 nm and solar zenith angles between 55° and 60°. Radiative transfer calculations considering three different aerosol mixtures are performed and and agree with the measurements within the statistical error.

All-sky imaging: a simple, versatile system for atmospheric research

A simple and inexpensive fully automated all-sky imaging system based on a commercial digital camera with a fish-eye lens and a rotating polarizer is presented. The system is characterized and two examples of applications in atmospheric physics are given: polarization maps and cloud detection. All-sky polarization maps are obtained by acquiring images at different polarizer angles and computing Stokes vectors. The polarization in the principal plane, a vertical cut through the sky containing the Sun, is compared to measurements of a well-characterized spectroradiometer with polarized radiance optics to validate the method. The images are further used for automated cloud detection using a simple color-ratio algorithm. The resulting cloud cover is validated against synoptic cloud observations. A Sun coverage parameter is introduced that shows, in combination with the total cloud cover, useful correlation with UV irradiance.

Spatiotemporal change of sky polarization during the total solar eclipse on 29 March 2006 in Turkey: polarization patterns of the eclipsed sky observed by full-sky imaging polarimetry

Using 180 degrees field-of-view (full-sky) imaging polarimetry, we measured the spatiotemporal change of the polarization of skylight during the total solar eclipse on 29 March 2006 in Turkey. We present our observations here on the temporal variation of the celestial patterns of the degree p and angle alpha of linear polarization of the eclipsed sky measured in the red (650 nm), green (550 nm), and blue (450 nm) parts of the spectrum. We also report on the temporal and spectral change of the positions of neutral (unpolarized, p = 0) points, and points with local minima or maxima of p of the eclipsed sky. Our results are compared with the observations performed by the same polarimetric technique during the total solar eclipse on 11 August 1999 in Hungary. Practically the same characteristics of celestial polarization were encountered during both eclipses. This shows that the observed polarization phenomena of the eclipsed sky may be general.

Polarization patterns of thick clouds: overcast skies have distribution of the angle of polarization similar to that of clear skies

The distribution of polarization in the overcast sky has been practically unknown. Earlier the polarization of light from heavily overcast skies (when the Sun's disc was invisible) has been measured only sporadically in some celestial points by point-source polarimetry. What kind of patterns of the degree p and angle alpha of linear polarization of light could develop after transmission through a thick layer of ice or water clouds? To answer this question, we measured the p and alpha patterns of numerous totally overcast skies on the Arctic Ocean and in Hungary by full-sky imaging polarimetry. We present here our finding that depending on the optical thickness of the cloud layer, the pattern of alpha of light transmitted through the ice or water clouds of totally overcast skies is qualitatively the same as the alpha pattern of the clear sky. Under overcast conditions the value of alpha is determined predominantly by scattering on cloud particles themselves. Nevertheless, the degrees of linear polarization of light from overcast skies were rather low (p<or=16%). Our results obtained under overcast conditions complete the earlier findings that the alpha pattern of the clear sky also appears in partly cloudy, foggy, and smoky skies. Our results show that the celestial distribution of the direction of polarization is a very robust pattern being qualitatively always the same under all possible sky conditions. This is of great importance for the orientation of polarization-sensitive animals based on sky polarization under conditions when the Sun is not visible.

Acousto-optic tunable filter imaging spectrometer with full Stokes polarimetric capability

Polarization is an important addition to spectral imaging in detecting and identifying objects of interest, and simple linear polarization measurements are often inadequate. Full polarization analysis can give additional information for discrimination where the polarization state is completely described by the Stokes parameters. An acousto-optic tunable filter (AOTF) imaging system was built incorporating two liquid-crystal variable retarders (LCVRs) that can provide complete spectral-polarimetric analysis, and it is believed to be the first demonstration of a full Stokes polarimetric AOTF spectral imaging system with no moving parts. It is also shown that a single LCVR cannot provide all the Stokes parameters.

Dual-field imaging polarimeter using liquid crystal variable retarders

An imaging Stokes-vector polarimeter using liquid crystal variable retarders (LCVRs) has been built and calibrated. Operating in five bands from 450 to 700 nm, the polarimeter can be changed quickly between narrow (12 degrees ) and wide (approximately 160 degrees) fields of view. The instrument is designed for studying the effects of differing sky polarization upon the measured polarization of ground-based objects. LCVRs exhibit variations in retardance with ray incidence angle and ray position in the aperture. Therefore LCVR-based Stokes polarimeters exhibit unique calibration challenges not found in other systems. Careful design and calibration of the instrument has achieved errors within +/-1.5%. Clear-sky measurements agree well with previously published data and cloudy data provide opportunities to explore spatial and spectral variations in sky polarization.

Review of passive imaging polarimetry for remote sensing applications

Imaging polarimetry has emerged over the past three decades as a powerful tool to enhance the information available in a variety of remote sensing applications. We discuss the foundations of passive imaging polarimetry, the phenomenological reasons for designing a polarimetric sensor, and the primary architectures that have been exploited for developing imaging polarimeters. Considerations on imaging polarimeters such as calibration, optimization, and error performance are also discussed. We review many important sources and examples from the scientific literature.

How well does the Rayleigh model describe the E-vector distribution of skylight in clear and cloudy conditions? A full-sky polarimetric study

We present the first high-resolution maps of Rayleigh behavior in clear and cloudy sky conditions measured by full-sky imaging polarimetry at the wavelengths of 650 nm (red), 550 nm (green), and 450 nm (blue) versus the solar elevation angle thetas. Our maps display those celestial areas at which the deviation deltaalpha = /alphameas - alphaRyleigh/ is below the threshold alphathres = 5 degrees, where alphameas is the angle of polarization of skylight measured by full-sky imaging polarimetry, and alphaRayleigh is the celestial angle of polarization calculated on the basis of the single-scattering Rayleigh model. From these maps we derived the proportion r of the full sky for which the single-scattering Rayleigh model describes well (with an accuracy of deltaalpha = 5 degrees) the E-vector alignment of skylight. Depending on thetas, r is high for clear skies, especially for low solar elevations (40% < r < 70% for thetas < or = 13 degrees). Depending on the cloud cover and the solar illumination, r decreases more or less under cloudy conditions, but sometimes its value remains remarkably high, especially at low solar elevations (rmax = 69% for thetas = 0 degrees). The proportion r of the sky that follows the Rayleigh model is usually higher for shorter wavelengths under clear as well as cloudy sky conditions. This partly explains why the shorter wavelengths are generally preferred by animals navigating by means of the celestial polarization. We found that the celestial E-vector pattern generally follows the Rayleigh pattern well, which is a fundamental hypothesis in the studies of animal orientation and human navigation (e.g., in aircraft flying near the geomagnetic poles and using a polarization sky compass) with the use of the celestial alpha pattern.

Neutral points of skylight polarization observed during the total eclipse on 11 August 1999

We report here on the observation of unpolarized (neutral) points in the sky during the total solar eclipse on 11 August 1999. Near the zenith a neutral point was observed at 450 nm at two different points of time during totality. Around this celestial point the distribution of the angle of polarization was heterogeneous: The electric field vectors on the one side were approximately perpendicular to those on the other side. At another moment of totality, near the zenith a local minimum of the degree of linear polarization occurred at 550 nm. Near the antisolar meridian, at a low elevation another two neutral points occurred at 450 nm at a certain moment during totality. Approximately at the position of these neutral points, at another moment of totality a local minimum of the degree of polarization occurred at 550 nm, whereas at 450 nm a neutral point was observed, around which the angle-of-polarization pattern was homogeneous: The electric field vectors were approximately horizontal on both sides of the neutral point.

Ground-based full-sky imaging polarimetry of rapidly changing skies and its use for polarimetric cloud detection

For elimination of the shortcomings of imaging polarimeters that take the necessary three pictures sequentially through linear-polarization filters, a three-lens, three-camera, full-sky imaging polarimeter was designed that takes the required pictures simultaneously. With this polarimeter, celestial polarization patterns can be measured even if rapid temporal changes occur in the sky: under cloudy sky conditions, or immediately after sunrise or prior to sunset. One of the possible applications of our polarimeter is the ground-based detection of clouds. With use of the additional information of the degree and the angle of polarization patterns of cloudy skies measured in the red (650 nm), green (550 nm), and blue (450 nm) spectral ranges, improved algorithms of radiometric cloud detection can be offered. We present a combined radiometric and polarimetric algorithm that performs the detection of clouds more efficiently and reliably as compared with an exclusively radiometric cloud-detection algorithm. The advantages and the limits of three-lens, three-camera, full-sky imaging polarimeters as well as the possibilities of improving our polarimetric cloud detection method are discussed briefly.