Polarization and polarimetry. What is polarization?

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1 Reote ensing ystes () Polarization and polarietry Questions to be answered: What is polarized light? What causes easurable polarization? What paraeters describe polarized light? How can interactions (reflections, scattering, etc.) of polarized light be described atheatically? How is a visible-band polarieter designed and built? Thanks to Nathan Pust for creating uch of the original version of this section of notes. Nathan did his Ph.D. research in the Optical Reote ensor Laboratory, ECE Departent, Montana tate University Bozean, working with Dr. J. haw on atospheric polarietric iaging research funded by the Air Force Office of cientific Research. Reote ensing ystes () What is polarization? Polarization describes the physical orientation of the electroagnetic field in space. Our eyes cannot see polarization directly. Electroagnetic Wave

2 Reote ensing ystes () What is polarization? Polarization is the preferred orientation of the electric field over tie. If the electric field fluctuates randoly, there is zero polarization. Electroagnetic Wave 3 Reote ensing ystes () Linear polarization vertical polarization horizontal polarization 45-degree polarization 4

3 Reote ensing ystes () Cobining Linear Polarization tates Phase difference = + = Phase difference = 9 + = Electroagnetic wave rotates in tie and space Note: circular polarization rarely occurs in nature 5 Reote ensing ystes () Elliptical Polarization Elliptical polarization is the ost general case of a polarized wave Think of it as a superposition of any horizontal aplitude with any vertical aplitude with any relative phase difference 6 3

4 Reote ensing ystes () Unpolarized light For theral sources (e.g., an incandescent light bulb), Unpolarized Light each photon is eitted with a fixed polarization, but this (ixture) polarization varies randoly in tie. Millions of these photons are intercepted over a typical easureent tie (~ s or s) Therefore, the tie-average easureent of this light appears unpolarized, even though each photon carries unique polarization (i.e., the light is polarized at each instant of tie, but with unpredictable orientation). 7 Reote ensing ystes () If natural light is unpolarized, what causes easurable polarization? Measurable polarization happens when a natural process selects a polarization. e.g., reflection fro a surface favors one linear polarization state. We will briefly overview two sources of polarization: Reflection fro a dielectric surface cattering by sall particles 8 4

5 Reote ensing ystes () 9 Reote ensing ystes () Total light 5

6 Reote ensing ystes () Light polarized parallel to the floor Reote ensing ystes () Light polarized perpendicular to the floor 6

7 Reote ensing ystes () Polarization by reflection or eission (transission through dielectric boundary) Polarization of the reflected and transitted waves depends on incidence angle and indices of refraction for the incident and reflecting edia. Glare is polarized in a direction parallel to the surface. Polarized sunglasses use vertical polarizers to reduce this glare. Further study: Fresnel equations Transittance and reflectance as a function of angle fro the scattering plane defined by ray fro source to scatterer and ray fro scatterer to observer. Incidence angles are defined relative to the surface noral. Graphs fro Hecht, Optics, pg. 3 Reote ensing ystes () Degree of Linear Polarization (DOLP) vs angle 7

8 Reote ensing ystes () Polarization by scattering Rayleigh scattering (sall particles) Particles that are sall with respect to the wavelength scatter according to Rayleigh scattering theory. When unpolarized light is scattered by a Rayleigh particle, the light scattered at 9 (relative to the original propagation direction) is % polarized. In the sky, visible light is scattered by air olecules according to Rayleigh scattering theory. Therefore, skylight at angles 9 fro the sun is highly polarized. (The / 4 wavelength dependence of Rayleigh scattering also is a priary reason a clean, clear sky is blue.) cattering by large particles (e.g. water droplets in clouds, aerosols in the air, etc.) Large-particle scattering (which can often be represented well with Mie scattering theory) polarizes light to a uch less easily predicted and often saller degree. 5 Reote ensing ystes () LWIR polarization iagery Polarization is a source of additional inforation for sensor systes that extends beyond the traditional brightness and color doain. Light can becoe partially polarized by scattering, reflection, and transission through birefringent edia (i.e. for which the refractive index varies with electricfield orientation). Polarization can enhance sensing in situations with norally low contrast (e.g., shadows, caouflage, or turbid edia). Visible color (iages courtesy Dr. David Chenault, Polaris ensors, Inc., Huntsville, AL, provided with perission of Huey Anderson, U.. Ary Res. Dev. & Eng. Coand, Restone Arsenal, AL). LWIR LWIR Pol. J.. Tyo, D. L. Goldstein, D. B. Chenault, J. A. haw, A review of passive iaging polarietry for reote sensing applications, Appl. Opt. 45, (6). 6 8

9 Reote ensing ystes () Polarization iagers The following are exaples of the various ethods for easuring polarization. Choosing a polarization easureent ethod typically involves tradeoffs of spatial or teporal resolution. Division of tie (variable or rotating eleent) A rotating or electronically variable retarder (VR) operates in front of a fixed linear polarizer (P). + siple - can be slow VR P caera Division of aplitude Light is split into 3 separate beas with bea splitters (B), each with its own detector array (D) and polarization optics (PO), such as waveplates and linear polarizers at different orientations. + fast - coplex - difficult to align lens PO B B D PO3 D3 PO D 7 Reote ensing ystes () Polarization iagers () Division of aperture Iage is re-iaged onto four separate portions of the focal plane array through different sets polarization optics. + siultaneous acquisition + pixel registration - lower spatial resolution - additional reiaging optics required Re-iaging optics 4 copies of iage in 4 polarization states Division of focal plane Micro-polarizer array on focal plane array cobines four different polarization-sensitive pixels into one super pixel. + siultaneous acquisition - pixel registration errors - pixel-pixel cross talk - lower spatial resolution 8 9

10 Reote ensing ystes () Quantifying polarization A tokes vector of four tokes paraeters fully characterizes the polarization state of light. 3 Total irradiance Vertical (or horizontal) coponent I(9 ) I( ) 45 or 35 coponent I(35 ) I(45 ) Circular coponent Other polarization paraeters: Degree of polarization = DoP Degree of Linear Polarization = DoLP 3 Degree of circular polarization = DoCP 3 9 Reote ensing ystes () tokes vector exaples Horizontal 45 deg 45 deg Right Circular.9 9% Vertical Unpolarized

11 Reote ensing ystes () Alteration of stokes vectors How do we describe the change undergone by a tokes vector during reflection, transission, or scattering? Reote ensing ystes () Mueller atrix Introduction The polarizing effect of optical devices, subsystes, systes, and even propagation can be described with a 4 4 real Mueller atrix. ' ' ' ' Output Light 3 Input Light

12 Reote ensing ystes () What can Mueller atrices describe? Atospheric scattering Refraction and reflection Effect of lenses Reflection fro water Polarization devices Polarizers Retarders Depolarizers Note: in any cases (especially with wide-fields of view), each ray path ust be described by a different Mueller atrix 3 Reote ensing ystes () Mueller atrix exaples Transission in a vacuu Horizontal Linear Polarizer Quarter Wave Plate with Fast Axis Vertical * 4

13 Reote ensing ystes () Using Mueller atrices Right-hand circular Polarization Quarter Wave Plate 45º with Fast Axis Vertical light Light that is initially linearly polarized at 45 is converted into right-hand circular polarization after transission through a quarter-wave plate (/4). 5 Reote ensing ystes () Using Mueller atrices vertical polarizer horizontal polarizer unpolarized light Light is copletely extinguished by the polarizers. No light is passed through crossed linear polarizers. Notice how Mueller Matrices are chained. This ethod can be used to describe a light path in a syste. Transission through an optical syste, atospheric transission, and reflection off of a surface can be explained using chained Mueller atrices. 6 3

14 Reote ensing ystes () Using Mueller atrices vertical polarizer 45 polarizer horizontal polarizer unpolarized light / 8 / 8 Introducing the 45 polarizer between the vertical and horizontal polarizers allows soe light to coe through! 7 Reote ensing ystes () Chaining Mueller atrices yste Propagation Model for a Polarieter ' ' M Polarizer M retarder M Lens ' '

15 Reote ensing ystes () Chaining Mueller atrices yste Propagation Model for a Polarieter ' ' M yste ' ' 3 3 This atrix describes the polarizer, retarders, and lenses in the instruent for one ray path. 9 Reote ensing ystes () Retrieval of tokes paraeters 3 yste Matrix Iage Iage Iage Iage 3 4 tokes paraeters are found by inverting the syste atrix and ultiplying by a vector coprising four independent easureents. 3 5

16 Reote ensing ystes () ky polarization with nearly pure Rayleigh scattering Mauna Loa, Hawaii (May June 8) 7 n DoLP J. A. haw photo Reote ensing ystes () Atospheric Polarization Iager syste overview Caera: Dalsa M3 Mpixel Mpixel, -bit, Pixels Retarders: Liquid Crystal Variable Retarders Quick change ~3 s between iages (Changes in the scene during the iage sequence can cause large errors) Optics: Nikon F-ount Narrow FOV: 3 Telephoto Full Field: 6 Fisheye Reduction Lens: 5 Micro Reduce the 35 iage to a 3 CCD 3 6

17 Reote ensing ystes () Optical design layout -- telephoto Field Lens bends light back toward the optical axis to prevent vignetting Field angles shown for to 4 degrees 33 Reote ensing ystes () Optical design layout -- fisheye Two field lenses needed for steeper angles 34 7

18 Reote ensing ystes () Exaple data Clear ky (45 n) 35 Reote ensing ystes () Exaple data Partially Cloudy ky (45 n) 36 8

19 Reote ensing ystes () Exaple data Clear ky (45 n) 37 Reote ensing ystes () Exaple data Clear ky (53 n) 38 9

20 Reote ensing ystes () Exaple Data Clear ky (7 n) 39 Reote ensing ystes () tress birefringence Iage of center of two lenses claped against each other between two crossed polarizers. The iage should be copletely dark. 4

21 Reote ensing ystes () References N. J. Pust and J. A. haw, Dual-field Iaging Polarieter using Liquid Crystal Variable Retarders, Appl. Opt. 45(), (6). J.. Tyo, D.L.Goldstein,D.B.Chenault, and J. A. haw, A Review of passive iaging polarietry for reote sensing applications, Appl. Opt. 45(), (6). N. J. Pust and J. A. haw, Digital all-sky polarization iaging of partly cloudy skies, Appl. Opt. 47, H9-H98 (8). Appendix The following notes describe how to use four independent easureents at different polarization states to deterine a syste atrix, which can be inverted to recover the tokes vector for the observed light. This technique is also described in the Tyo et al. (6) review paper included in the references. 4 Reote ensing ystes () Measuring tokes paraeters Changing the diattenuation or retardance inside the polarieter changes the Mueller atrix of the syste. Four iages taken at four different Mueller atrix states are used to reconstruct the tokes vector. everal ethods can be used to change the Mueller atrix of the syste: - rotating a polarizer - rotating a waveplate in front of a polarizer - changing the birefringence of a liquid crystal, etc. 4

22 Reote ensing ystes () Measuring tokes paraeters Only irradiance is easured by a detector (not field aplitude) Reote ensing ystes () Measuring tokes paraeters Iage 44

23 3 Reote ensing ystes () Retardance = 3 Retardance = How do you easure polarization? Measuring tokes paraeters Retardance Iage Reote ensing ystes () Retardance = 8 Retardance = 3 Measuring tokes paraeters Iage 3

24 Reote ensing ystes () Measuring tokes paraeters Retardance = 5 Retardance = Iage 4 47 Reote ensing ystes () The syste atrix Iage Iage Iage3 Iage

25 Reote ensing ystes () yste atrix Iage Iage Iage Iage 3 4 yste Matrix 3 49 Reote ensing ystes () Retrieval of tokes paraeters 3 yste Matrix Iage Iage Iage Iage 3 4 tokes paraeters are calculated by atrix inversion. 5 5