title: Celestial polarization patterns sufficient for Viking navigation with the naked eye: detectability of Haidinger's brushes on the sky versus meteorological conditions.
abstract: If a human looks at the clear blue sky from which light with high enough degree of polarizationdoriginates, 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 highdarcs 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, thedof the portion of the sky used must be greater than the viewer's degree of polarization thresholdd* for perception of Haidinger's brushes. We studied under which sky conditions the prerequisited>d* is satisfied. Using full-sky imaging polarimetry, we measured thed-pattern of skylight in the blue (450 nm) spectral range for 1296 different meteorological conditions with different solar elevation anglesθand per cent cloud coverρ. From the measuredd-patterns of a given sky we determined the proportionPof the sky for whichd>d*. We obtained thatPis the largest at low solar elevationsθ≈ 0° and under totally or nearly clear skies with cloud coverageρ= 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.
authors.affiliation: Environmental Optics Laboratory, Department of Biological Physics , Eötvös University , Pázmány sétány 1, 1117 Budapest , Hungary.
authors.forename: Gábor
authors.identifier: 0000-0002-9008-2411
authors.initials: G
authors.lastname: Horváth
authors.affiliation: Environmental Optics Laboratory, Department of Biological Physics , Eötvös University , Pázmány sétány 1, 1117 Budapest , Hungary.
authors.forename: Péter
authors.initials: P
authors.lastname: Takács
authors.affiliation: Environmental Optics Laboratory, Department of Biological Physics , Eötvös University , Pázmány sétány 1, 1117 Budapest , Hungary.
authors.forename: Balázs
authors.initials: B
authors.lastname: Kretzer
authors.affiliation: Environmental Optics Laboratory, Department of Biological Physics , Eötvös University , Pázmány sétány 1, 1117 Budapest , Hungary.
authors.forename: Szilvia
authors.initials: S
authors.lastname: Szilasi
authors.affiliation: Environmental Optics Laboratory, Department of Biological Physics , Eötvös University , Pázmány sétány 1, 1117 Budapest , Hungary.
authors.forename: Dénes
authors.initials: D
authors.lastname: Száz
authors.affiliation: Environmental Optics Laboratory, Department of Biological Physics, Eötvös University, Pázmány sétány 1, 1117 Budapest, Hungary; Danube Research Institute, MTA Centre for Ecological Research, 1113 Budapest, Karolina út 29-31, Hungary.
authors.forename: Alexandra
authors.initials: A
authors.lastname: Farkas
authors.affiliation: Environmental Optics Laboratory, Department of Biological Physics, Eötvös University, Pázmány sétány 1, 1117 Budapest, Hungary; Estrato Research and Development Ltd., Németvölgyi út 91/c, 1124 Budapest, Hungary.
authors.forename: András
authors.initials: A
authors.lastname: Barta
keywords: Haidinger's brushes; Viking navigation; human polarization vision; imaging polarimetry; sky polarization; sunstone