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Problem 9 - Optical Compass Team Brazil – University of Campinas Problem 9 - Optical Compass Maria Carolina Volpato and Denise Christovam 1 Team Brazil – University of Campinas Problem Statement Bees locate themselves in space using their eyes’ sensitivity to light polarization. Design an inexpensive optical compass using polarization effects to obtain the best accuracy. How would the presence of clouds in the sky change this accuracy? 2 Team Brazil – University of Campinas Visualization of the phenomenon Problem 9- Optical Compass 3 Team Brazil – University of Campinas Light Scattering Incident Scattered Backward Forward scattering scattering Scattered Light Incoming Light 4 Problem 9- Optical Compass Particle Team Brazil – University of Campinas Light Scattering Rayleigh Scattering Mie Scattering Conditions to Rayleigh scattering are satisfied! Problem 9- Optical Compass 5 Team Brazil – University of Campinas Linear Polarization ➔ For the observer at PMP polarization plane collapses into a line ➔ 90o from the source of light Problem 9- Optical Compass 6 Team Brazil – University of Campinas Mapping the sky ➔ Rayleigh sky model describes how the maximally polarized light stripe varies with rotation Degree of polarization at sunset or sunrise. https://en.wikipedia.org/wiki/Rayleigh_sky_model Problem 9- Optical Compass 7 Team Brazil – University of Campinas Materials and design ➔ Polarizing sheets ➔ Guillotine Paper Cutting Machine ➔ Adhesive tape ~ R$ 30.00 ($6.00) ➔ Cardboard A4 (120 g/m²) o 12 petals – 30 72 petals – 5o 18 petals – 20o Problem 9- Optical Compass 8 Team Brazil – University of Campinas Angular Resolution - Malus Law Angular Resolution ~ 20º χ Polarization Direction Problem 9- Optical Compass 9 Team Brazil – University of Campinas Setup- Vertical and Horizontal Mapping Vertical Horizontal Problem 9- Optical Compass 10 Team Brazil – University of Campinas Vertical Angle χ Φ= 335º Ө 0º 40º 80º 120º Problem 9- Optical Compass 11 Team Brazil – University of Campinas Horizontal Angle Φ Ө ~ 10º 0º 60º 120º 180º 240º 300º Problem 9- Optical Compass 12 Team Brazil – University of Campinas Temporal evolution of the shadow ➔ Angle in relation to the ground Ө= 25±1º ➔ Approximate geographical position: ◆ Latitude: 23º 00’ 21” S ◆ Longitude: 46º 50’ 20” W ➔ Window facing SSW (276º form north) ➔ Total time of acquisition 266 min ( from 12 PM to sunset) ➔ Performed at 09/24/2019 https://www.timeanddate.com/sun/@3460598?month=9&year Problem 9- Optical Compass =2019 13 Team Brazil – University of Campinas Temporal evolution of the shadow Problem 9- Optical Compass 14 Team Brazil – University of Campinas Presence of clouds Clear sky Partly Cloudy Cloudy Typical radius of the droplets ~ 10² nm ~ λ Mie Scattering dominates Problem 9- Optical Compass 15 Team Brazil – University of Campinas Conclusions ➔ It is possible to build a cheap device R$ 30.00 - $ 6.00 ➔ It indicates N-S direction Rayleigh Scattering ➔ Clouds reduces the accuracy Mie Scattering Problem 9- Optical Compass 16 Team Brazil – University of Campinas Thank You! 17 Team Brazil – University of Campinas How do bees locate themselves? https://www.beeculture.com/bees-see-matters/ Problem 9- Optical Compass 18 Team Brazil – University of Campinas A model for radiation The electric fields propagate radially Time-averaged Poynting vector: “p” wave Total time-averaged power radiated: David J. Griffiths, Introduction to Electrodynamics, Prentice Hall, 1999 Problem 9- Optical Compass 19 Team Brazil – University of Campinas Rayleigh x Mie If α≪λ : Rayleigh Angular dependence Distance between Same dependence particle and with frequency observer We recover dipole radiation! If α is close to λ: Mie Distortion of the radiation in one direction Problem 9- Optical Compass 20 Team Brazil – University of Campinas Rayleigh x Mie Recovering the toroidal profile of dipole radiation: dipole z y Light scatters at xy plane – polarization depends on our position in relation to the Sun 21 Team Brazil – University of Campinas Atmospheric Conditions % Kinetic Diameter (nm) N2 78 0.364 O2 21 0.346 Conditions to Rayleigh scattering are satisfied! CO2 0.03 0.330 H2O 3 0.265 Ar 0.9 0.340 Problem 9- Optical Compass 22 Team Brazil – University of Campinas Linear polarization At PMP, the polarization Plane: L L L Plane the observer sees Observer’s Plane of view polarization At B, the observer sees E⊥ : Sunbeam L Observer Plane the observer sees 23 Problem 9- Optical Compass Team Brazil – University of Campinas Degree of polarization At B, the observer sees E⊥ : Sunbeam L Observer Plane the observer sees As sunlight is unpolarized at first We can define the degree of polarization P(γ): 24 Problem 9- Optical Compass Team Brazil – University of Campinas Navigation Scattering Angle Sun Observation point We always need some other info, like the time of the day (or measure for extended periods of time) y (W) z (N) Problem 9- Optical Compass 25 Team Brazil – University of Campinas Analyse the data ➔ ImageJ Problem 9- Optical Compass 26 Team Brazil – University of Campinas Defining angular resolution Problem 9- Optical Compass 27 Team Brazil – University of Campinas Angular resolution - Malus Law Deviation from Malus Law Intrinsic width of shadow: Limited due to small ~20o in 180o (“efficiency” of misalignments/anisotropies compass: ~89%) resolution Problem 9- Optical Compass 28 Team Brazil – University of Campinas Temporal evolution of the shadow ➔ Angle in relation to the ground Ө= 25±1º ➔ Approximate geographical position: ◆ Latitude: 23º 00’ 21” S ◆ Longitude: 46º 50’ 20” W ➔ Window facing SSW (276º form north) ➔ Total time of acquisition 266 min ( from 12 PM to sunset) ➔ Performed at 09/24/2019 Setup Problem 9- Optical Compass 29 Gaussian – Calibration Deviation from Malus Law due to small misalignments/ anisotropies Calibration curve for degree of polarization and sun 72 petals – 5o Intrinsic width of shadow: position ~20o in 180o (“efficiency” of compass: ~89%) Limited resolution 30 Timelapse – T0 = 1 PM 31 Timelapse – T0 = 5:26 PM 32 Temporal evolution of the shadow • Shadow sharpens • Strip rotates indicating solar position 33 Team Brazil – University of Campinas Accuracy Problem 9- Optical Compass 34 Team Brazil – University of Campinas Error Analysis - Intensity Problem 9- Optical Compass 35 Team Brazil – University of Campinas Error Analysis - Position 土5º Problem 9- Optical Compass 土8º 36 Team Brazil – University of Campinas Error Analysis - Position Problem 9- Optical Compass 37 Team Brazil – University of Campinas Atmospheric conditions - Cloudy weather Conditions to Rayleigh scattering are not satisfied Mie Scattering dominates Typical radius of the ~ λ droplets ~ 10² nm No pattern formed Problem 9- Optical Compass 38 Team Brazil – University of Campinas References Wehner, R.D., 1976. Polarized-light navigation by insects. Scientific American, 235(1), pp.106-115. Rossel, S., 1993. Navigation by bees using polarized skylight. Comparative Biochemistry and Physiology Part A: Physiology, 104(4), pp.695-708. 39.
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