Polarimetry Basics
Explore Stokes parameters, Poincaré sphere representation, and analyzer measurements for polarization state characterization.
S = [S₀, S₁, S₂, S₃]ᵀ
DOP = √(S₁² + S₂² + S₃²) / S₀
ψ = ½atan2(S₂, S₁), χ = ½asin(S₃/|S|)
Convention (Goldstein): RCP = [1, i]/√2 turns clockwise as seen by the receiver; S₃ > 0 is right-handed.
Transmitted intensity
0.750
DOP
61.6%
DOLP
58.3%
DOCP (S₃/S₀, + = right)
20.0%
Orientation ψ / Ellipticity χ
15.5° / 9.5°
Poincaré Sphere
Analyzer Transmission
Stokes Vector
S₀
1.000
S₁
0.500
S₂
0.300
S₃
0.200
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
Stokes analysis of a physical vector (DOP, DOLP, DOCP, ψ, χ) and an ideal linear analyzer, I(θ) = ½(S₀ + S₁ cos 2θ + S₂ sin 2θ). Not modelled: analyzer extinction, measurement noise.
- Goldstein D. H. (2011). Polarized Light, 3rd ed., chs. The Polarization Ellipse, pp. 49–58, and Stokes Polarization Parameters, pp. 59–91. CRC Press. doi:10.1201/b10436
- Collett E. (2005). Field Guide to Polarization, SPIE Field Guides FG05: the Stokes parameters and the Poincaré sphere. SPIE Press. doi:10.1117/3.626141