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Stokes Parameters

Analyze polarization state from Stokes vector components with sliders, presets, and Poincaré sphere visualization.

Model: Exact

Stokes Vector Input

1
0.1–2
0.5
-1–1
0.3
-1–1
0.2
-1–1
S = [1.00, 0.50, 0.30, 0.20]

Polarization Analysis

Degree of Polarization (DOP)0.6164
Degree of Linear Polarization (DOLP)0.5831
DOCP (S₃/S₀, + = right)0.2000
Orientation angle ψ15.48°
Ellipticity angle χ9.47°
Axis ratio b/a0.1667
HandednessRight-handed elliptical

Convention (Goldstein): RCP = [1, i]/√2 turns clockwise as seen by the receiver; S₃ > 0 is right-handed.

Poincaré Sphere

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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, DOLP, signed DOCP and the ellipse angles ψ = ½ atan2(U, Q), χ = ½ asin(V/I_p) of a physical Stokes vector, √(Q² + U² + V²) ≤ I. V > 0 is right-handed (Goldstein).

  1. 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
  2. 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
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