Degree of Polarization
Calculate DoP from Stokes parameters, decompose into polarized and unpolarized components.
Stokes Parameters
Results
Decomposition
Key Formulas
DoP = √(S₁² + S₂² + S₃²) / S₀
I_pol = √(S₁² + S₂² + S₃²) I_unpol = S₀ − I_pol
Orientation: ψ = ½ · atan2(S₂, S₁)
Ellipticity angle: χ = ½ · asin(S₃ / I_pol)
Ellipticity: e = tan(χ)
Spectral: ⟨S⟩ = ⟨M(λ)⟩ · S, Γ(λ) = 2π m λ₀/λ
Convention (Goldstein): RCP = [1, i]/√2 turns clockwise as seen by the receiver; S₃ > 0 is right-handed.
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
DOP = √(S₁² + S₂² + S₃²)/S₀, ψ = ½ atan2(S₂, S₁), χ = ½ asin(S₃/I_p) for physical vectors. Spectral mode: a fixed-Δn retarder at 45°, light flat in wavelength, Stokes vectors averaged over the band.
- 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