Stokes Parameter Calculator
Stokes Parameter Calculator is a free, accurate, and scientifically validated online tool that instantly computes the four Stokes Parameters (S₀, S₁, S₂, S₃) from measured intensities through linear and circular polarizers. Widely used in optics, photonics, astronomy, remote sensing, and polarimetry research, this calculator helps researchers and students determine the complete polarization state of light, including Degree of Linear Polarization (DoLP), Degree of Circular Polarization (DoCP), and polarization ellipse orientation.
Stokes Parameter Calculator
Enter the six measured intensities (in the same arbitrary units):
About the Stokes Parameter Calculator
The Stokes Parameter Calculator implements the classical and universally accepted Stokes formalism introduced by Sir George Gabriel Stokes in 1852. The four Stokes parameters completely describe the polarization state of electromagnetic waves, including partially polarized and unpolarized light. This tool uses the standard six-measurement method recommended in modern polarimetry literature and followed by leading researchers worldwide.
Scientific Foundation and Formulas Used
All calculations are based on the original and peer-reviewed definitions:
| Parameter | Physical Meaning | Formula |
|---|---|---|
| S₀ | Total intensity | S₀ = I₀° + I₉₀° |
| S₁ | Difference between horizontal and vertical linear polarization | S₁ = I₀° − I₉₀° |
| S₂ | Difference between +45° and −45° linear polarization | S₂ = I₄₅° − I₁₃₅° |
| S₃ | Difference between right and left circular polarization | S₃ = I_R − I_L |
Additional derived quantities:
- Degree of Polarization (DoP) = √(S₁² + S₂² + S₃²) / S₀ × 100%
- Degree of Linear Polarization (DoLP) = √(S₁² + S₂²) / S₀ × 100%
- Degree of Circular Polarization (DoCP) = |S₃| / S₀ × 100%
- Polarization ellipse orientation ψ = (1/2) × arctan(S₂ / S₁)
- Ellipticity angle χ = (1/2) × arcsin(S₃ / S₀)
Why Use the Stokes Parameter Calculator?
In optics and photonics research, understanding the exact polarization state is crucial. Whether you are studying atmospheric scattering, biological tissue imaging, quantum optics, astronomical polarimetry, or developing polarization-based sensors, the Stokes parameters provide a complete, unambiguous description that the Jones vector cannot represent for partially polarized light.
Unlike simple polarizer experiments that only reveal linear polarization fraction, this Stokes Parameter Calculator gives you the full picture — including circular polarization content — which is essential in modern applications such as 3D cinema, optical communication, stress analysis in materials, and remote sensing of planets and vegetation.
When Should You Use This Tool?
- During polarimetry experiments in optics labs
- Analyzing Mueller matrix data
- Interpreting data from division-of-amplitude or division-of-wavefront polarimeters
- Validating results from commercial polarimeters
- Teaching polarization optics in universities
- Research in biomedical optics and cancer detection using polarized light
- Astronomical observation of synchrotron radiation or exoplanet atmospheres
User Guidelines for Accurate Results
- All six intensity measurements must be taken under identical illumination and exposure conditions.
- Use high-quality polarizers with known extinction ratios.
- Ensure the light beam fully covers the detector area in all configurations.
- Take multiple measurements and average to reduce noise.
- For unpolarized light calibration, all six values should be nearly equal.
Importance in Modern Science and Technology
Polarization carries information that intensity alone cannot provide. From detecting camouflaged objects in military applications to early diagnosis of retinal diseases and skin cancer, Stokes parameters form the foundation of advanced imaging systems. NASA, ESA, and leading research institutions rely on Stokes polarimetry for planetary exploration and Earth observation satellites.
This Stokes Parameter Calculator brings laboratory-grade accuracy to your browser, making advanced polarimetry accessible to students, educators, and researchers worldwide — completely free of charge.
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