The Stokes Parameters in .NET

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4 The Stokes Parameters
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from the plane when looking back into the source, then the re ected light is leftelliptically polarized The result holds for any metal and any angle of incidence see Appendix A Right-handed polarization is denoted in Serkowski s paper as negative (see Figure 45b); for an observer facing the star, it corresponds to the E-vector rotating clockwise in a plane projected on the celestial sphere Serkowski compares his results with those of Gehrels noting that the latter worker describes righthanded polarization as being positive The convention of Gnedin & Shulov (1971) was based on a ve sign corresponding to a clockwise rotation of E, as seen by the observer looking at the star To the contrary, Avery, Michalsky & Stokes (1973) used a Cve sign such that, for an observer facing the source, the rotation of the electric vector in a xed plane was clockwise They commented that this convention is the opposite to that used by Kemp In Martin s (1972) analysis of the behaviour of interstellar grains, positive angles are measured counterclockwise on the sky and positive values of V correspond to right-handed polarization with a counterclockwise rotation of the electric vector (see Figure 45c) In their observations of Zeeman effects in newly discovered X-ray stars, Kemp & Wolstencroft (1973) considered circular polarization to be positive for counterclockwise rotations of the electric vector as seen by the observer For the measurements of AM Her, Tapia (1977) used the convention that the sign for handedness is determined according to the angular momentum convention The handedness is positive when the optical electric vector carries positive angular momentum to the observer Michalsky, Swedlund, Stokes, et al (1974) changed their convention to follow the sign convention adopted by the IAU Colloquium No 23; positive polarization is taken to mean that for an observer facing the source the electric vector s rotation in a xed plane is counterclockwise At the IAU General Assembly in Sydney in 1973, Commissions 25 and 40 proposed the adoption of the following terminology in polarimetry:
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The frame of reference for the Stokes parameters is that of Right Ascension and Declination with the position angle of electric vector maximum, , starting from North and increasing through East Elliptical polarization is de ned in conformity with the definitions of the Institute of Electrical and Electronics Engineers (IEEE Standard, 211, 1969) This means that the polarization of incoming radiation, for which the position angle, , of the electric vector, measured as a xed point in space, increases with time, is described as right-handed and positive
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As seen by an observer, the rotation of the E-vector for such right-handed polarizations is counterclockwise, i e is increasing continually The relevant de nition from IEEE Standard 211 relates to left-handed polarization and is
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Left-Handed (Counterclockwise) Polarized Wave An elliptically polarized electromagnetic wave in which the rotation of the electric eld vector with time is counterclockwise for a stationary observer
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Stellar P larimetry
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Fig 46 The IAU preferred de nitions for the description of polarization show the direction of vibration set at an angle, , North through East For circular polarization with the E-vector rotating with increasing , the form is described as right-handed with a C sign also applied
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looking in the direction of the wave normal (Note: For an observer looking from a receiver toward the apparent source of the wave, the direction of rotation is reversed)
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Careful consideration of this latter de nition of left-handed polarization shows that the angle de ning the direction of vibration is decreasing in the right-handed frame of celestial coordinates, i e East through North For right-handed polarization, the E-vector would be seen against the reference frame as rotating in the opposite direction, i e anti-clockwise or from North through East, with continuously increasing (see Figure 46) With such de nitions, it turns out that sense of the helix that is associated with the radiation itself has the opposite convention, i e right-handed polarization comprises left-handed helical disturbances which travel without rotation along the direction of propagation Relevant to radio astronomy, it may be noted that according to the IEEE de nition, left-handed polarization would be best received by a lefthanded helical antenna rather than by one of opposite sense Thus the de nition appears to be guided by the readily identi able physical form of the receiving equipment rather than the physical behaviour within the radiation For radio astronomy, a convention based on the unique handedness of helical antennae has been adopted (IRE, 1942, and Kraus, 1986) The largest reaction from a helical antenna occurs when it receives radiation carrying helical forms of the opposite sense So, for example, a left-handed antenna has maximum response when the radiation received is in the form of radiation travelling as a right-handed helix and the radiation would be referred to as being left-handed Obviously it is preferable to accept some convention that everyone is familiar with and one which for any new instrument can be readily checked out Whether it is the most logical one or not, the IAU de nition should be followed
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