A basic imaging polarimeter. The notches on the plates indicate the orientation of the fast axis (waveplates) or the transmission axis (polarizers). In this case, the angles for the two delay plates and polarizer are 45°, 90°, and 45°, respectively.
Illustration of the Stokes vector on the Poincaré sphere. The (θ, ε) basis can be established by rotating the vector (1, 0, 0) by −2ε about the s 2 axis before rotating by 2θ about the s 3 axis. Alternatively, the (χ, δ) basis is established by rotating (1, 0, 0) by 2χ about the s 3 axis before rotating by δ about the s 1 axis.
(Left) Schematic of the MSE multiplet spectrum. The π components have greater separation than the central σ components. (Right) The corresponding interferogram fringe contrast showing the beating of the π interferograms and the resultant nett fringe contrast. For measurements on KSTAR, when operating with a toroidal magnetic field of 2.5 T and neutral deuterium beam energy of 80 keV, the Stark splitting between individual components of the multiplet will be Δλ S = 0.11 nm. The finite divergence of the neutral beam 8 causes each component of the multiplet to be Doppler broadened by approximately σλ, d = 0.04 nm and geometrical effects due to the finite size of the collecting lens contribute σλ, l = 0.02 nm. In this case, the optical delay that maximizes the contrast is approximately ϕ2 = 800 waves.
(Left) The dual-state hybrid imaging system. This system is sufficient to recover only the polarization orientation θ. The half-wave FLC waveplate can quickly switch its fast axis between the 45° (green – P 1) and 90° (red – P 2) orientations, while the displacer generates spatial heterodyne carrier fringes in the focal plane. (Right) To also obtain the ellipticity, the first quarter-waveplate is replaced with a quarter-wave FLC with states as shown. The 90° (both red – P 3) state provides the new information.
Example central regions of calibration images for the P 1 and P 2 states for θ ∼ 45° and ε = 0.
(Upper) Residual polarization angle θ image obtained from the frames P 1 and P 2 and (Lower) the residual δ angle image obtained from images P 3 and P 4 for calibration polarizer orientation angle θ ∼ 0° and ε = 0. The Newton's ring pattern is due to the calibration line interference filter. Systematic variations of ∼1° that are seen in the polarization angle image vary little with input polarization angle.
The deviation from the ideal θ measuring response of the polarimeter to polarized input light of variable orientation θ, and for five different values of ellipticity ε. The lines display the Mueller model calculation of the difference phase (g 1(θ, ε) − g 2(θ, ε))/4 − θ, while the dots represent the experimentally deduced angles obtained from the P 1 and P 2 frames of the three state system.
Polarization dependence of the Doppler phase image ϕ D for polarized input light of variable orientation θ, and for five different values of ellipticity ε. The lines display the Mueller model value of (g 1 + g 2)/2 and the dots represent the corresponding experimental value determined from the sum phase of the P 1 and P 2 states relative to a fixed carrier fringe position.
Variation of the phase angle δ for polarized input light of variable orientation θ, and for five different values of ellipticity ε. The lines display the Mueller model value of g 3 − (g 1 + g 2)/2 and the dots represent the corresponding experimental value deduced from the phase of the P 3 state with the approximate value of ϕ(y) subtracted (as determined from P 1 and P 2). Evidently, the ellipticity information is not unique about the intersection points near θ = 45° and 135°. In the ideal system, the results would be .
Ratio of fringe amplitudes in the P 3 and P 1 states for polarized input light of variable orientation θ, and for five different values of ellipticity ε. The lines display the Mueller model calculation of f 3/f 1 and the dots represent the experimentally deduced ratio. Evidently, the fringe amplitude is low in the P 3 state near θ = 45° and 135° when the ellipticity is small. In the ideal system, the results would be .
Showing the ray paths for a negative uniaxial birefringent displacer prism.
Alignments and birefringent phase shifts of the optical components.
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