Symmetry between partially polarised light and partial polarisers in the vectorial Pauli algebraic formalism

Tudor, Tiberiu; Manea, V.

doi:10.1080/09500340.2011.575960

Cited by 15 publications

(7 citation statements)

References 19 publications

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“…There are many formalisms to describe polarized light: Stokes parameters [1,2], Jones calculus [3,4], Poincaré sphere [5], Mueller matrices [6], Pauli formalism [7][8][9], Jackson's complex vectors [10], complex numbers [11,12], and the more recent pure operatorial Pauli algebraic approach [13][14][15]. All these formalisms are dependent on each other, and there are fundamental textbooks [16,17] in polarization theory that establish the correspondences between them.…”

Section: Introductionmentioning

confidence: 99%

Polarization ellipse and Stokes parameters in geometric algebra

2011

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In this paper, we use geometric algebra to describe the polarization ellipse and Stokes parameters. We show that a solution to Maxwell's equation is a product of a complex basis vector in Jackson and a linear combination of plane wave functions. We convert both the amplitudes and the wave function arguments from complex scalars to complex vectors. This conversion allows us to separate the electric field vector and the imaginary magnetic field vector, because exponentials of imaginary scalars convert vectors to imaginary vectors and vice versa, while exponentials of imaginary vectors only rotate the vector or imaginary vector they are multiplied to. We convert this expression for polarized light into two other representations: the Cartesian representation and the rotated ellipse representation. We compute the conversion relations among the representation parameters and their corresponding Stokes parameters. And finally, we propose a set of geometric relations between the electric and magnetic fields that satisfy an equation similar to the Poincaré sphere equation.

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Section: Introductionmentioning

confidence: 99%

Polarization ellipse and Stokes parameters in geometric algebra

2011

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“…The incident skylight of the polarization sensor includes two components: unpolarized light and totally polarized light. The two respective gains [32] can be described as follows:leftgup=(τM+τm)/2=τtrue¯gtp=τMcos2θ+τmsin2θ, where g up represents the gain of unpolarized light; g tp is the gain of totally polarized light. τ M is the transmittance when the reference angle and main polarization angle of incident light are parallel.…”

Section: Calibration Methodsmentioning

confidence: 99%

A Bio-Inspired Polarization Sensor with High Outdoor Accuracy and Central-Symmetry Calibration Method with Integrating Sphere

Wang

Chu

Zhang

et al. 2019

Sensors

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A bio-inspired polarization sensor with lenses for navigation was evaluated in this study. Two new calibration methods are introduced, referred to as “central-symmetry calibration” (with an integrating sphere) and “noncontinuous calibration”. A comparison between the indoor calibration results obtained from different calibration methods shows that the two proposed calibration methods are more effective. The central-symmetry calibration method optimized the nonconstant calibration voltage deviations, caused by the off-axis feature of the integrating sphere, to be constant values which can be calibrated easily. The section algorithm proposed previously showed no experimental advantages until the central-symmetry calibration method was proposed. The outdoor experimental results indicated that the indoor calibration parameters did not perform very well in practice outdoor conditions. To establish the reason, four types of calibration parameters were analyzed using the replacement method. It can be concluded that three types can be easily calibrated or affect the sensor accuracy slightly. However, before the sensor is used outdoors every time, the last type must be replaced with the corresponding outdoor parameter, and the calculation needs a precise rotary table. This parameter, which is mainly affected by the spectrum of incident light, is the main factor determining the sensor accuracy. After calibration, the sensor reaches an indoor accuracy of ±0.009° and a static outdoor accuracy of ±0.05° under clear sky conditions. The dynamic outdoor experiment shows a ±0.5° heading deviation between the polarization sensor and the inertial navigation system with a ±0.06° angular accuracy.

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“…Due to an adequate parameterization, specific to the VPOPA approach, simple, physically expressive, and symmetric expressions are obtained for the gain and, implicitly, for the generalized Malus' law in the frame of this formalism [27].…”

Section: The Gain Of a Dichroic Device And The Generalized Malus' Lawmentioning

confidence: 99%

Vectorial pure operatorial Pauli algebraic approach in polarization optics: a theoretical survey and some applications

Tudor

2012

Appl. Opt.

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In the last decade we have elaborated a mathematical tool for the description of the interaction of polarized light with polarization devices, alternative to the standard matrix (Jones and Mueller) formalisms, namely a vectorial pure operatorial Pauli algebraic one. After a brief, coherent survey of this formalism, we present some applicative results obtained in this frame, referring to the gain and the modification of the state of polarization at the interaction of the polarized light with deterministic devices. Due to an adequate parameterization of the problem, specific to this method, symmetric expressions of the gain and of the generalized Malus' law are obtained. On the other hand, the equation of the ellipsoid in which a Poincaré sphere of a given degree of polarization is mapped by such a device can be established.

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Symmetry between partially polarised light and partial polarisers in the vectorial Pauli algebraic formalism

Cited by 15 publications

References 19 publications

Polarization ellipse and Stokes parameters in geometric algebra

Polarization ellipse and Stokes parameters in geometric algebra

A Bio-Inspired Polarization Sensor with High Outdoor Accuracy and Central-Symmetry Calibration Method with Integrating Sphere

Vectorial pure operatorial Pauli algebraic approach in polarization optics: a theoretical survey and some applications

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