Stokes Parameters Calculator

Compute polarization state from optical intensity measurements quickly. Choose linear or circular analyzer readings easily. Get Stokes values, degrees, and angles in seconds today.

Calculator

Choose an input method. Enter values in any consistent intensity units.

Results appear above after calculation.
Formula used

The Stokes vector S = (S0, S1, S2, S3) describes the polarization state of light using intensity-like quantities.

From analyzer intensities
S0 = I0 + I90
S1 = I0 − I90
S2 = I45 − I135
S3 = IR − IL
If IR and IL are missing, S3 is set to 0.
From field amplitudes and phase
S0 = Ex² + Ey²
S1 = Ex² − Ey²
S2 = 2 Ex Ey cos(δ)
S3 = 2 Ex Ey sin(δ)
Ex and Ey are real amplitudes; δ is the relative phase.

Derived metrics (with S0 > 0):

DoP = √(S1² + S2² + S3²) / S0
DoLP = √(S1² + S2²) / S0
DoCP = S3 / S0
ψ = ½ atan2(S2, S1)
χ = ½ atan2(S3, √(S1² + S2²))
How to use this calculator
  1. Select an input method: analyzer intensities or field amplitudes.
  2. Enter measurements in consistent units (arbitrary intensity units are fine).
  3. If you have circular analyzer readings, fill IR and IL for S3.
  4. Press Calculate to view results above the form.
  5. Use Download CSV or Download PDF for exports.
Example data table

These sample values illustrate typical inputs and outputs. Your instrumentation may use different scaling.

Input method Inputs Outputs (S0, S1, S2, S3) DoP
Analyzer intensities I0=1.00, I90=0.60, I45=0.90, I135=0.70, IR=0.85, IL=0.75 S0=1.60, S1=0.40, S2=0.20, S3=0.10 0.2958
Field amplitudes Ex=1.00, Ey=0.80, δ=30° S0=1.64, S1=0.36, S2=1.3856, S3=0.8000 0.9756

Stokes Parameters in Polarization Analysis

1) Output summary

Provide analyzer intensities and obtain S0–S3 with DoP, DoLP, and DoCP. S0 is total intensity; S1 and S2 describe linear polarization in two bases; S3 describes circular polarization. The approach supports partial polarization.

2) Stokes vector concept

The Stokes vector [S0,S1,S2,S3] is based on intensity averages, matching typical detector outputs. Normalized values s1=S1/S0, s2=S2/S0, s3=S3/S0 help compare polarization states.

3) H/V basis

S0 = IH + IV and S1 = IH − IV. Positive S1 indicates more horizontal content; negative S1 indicates more vertical. Keep units and gain consistent.

4) ±45° and circular bases

S2 = I45 − I135 and S3 = IR − IL. Record analyzer labeling and the circular convention so S3 signs remain comparable.

5) Polarization degrees

DoP = √(S1²+S2²+S3²)/S0, DoLP = √(S1²+S2²)/S0, DoCP = |S3|/S0. Near 1 is strongly polarized; near 0 is largely unpolarized.

6) Physical constraints

Valid states satisfy S0 ≥ 0 and S0² ≥ S1²+S2²+S3². If DoP exceeds 1, check offsets, alignment, extinction ratio, and detector linearity.

7) Numeric example

IH=0.62, IV=0.38, I45=0.55, I135=0.45, IR=0.50, IL=0.50 gives S0=1.00, S1=0.24, S2=0.10, S3=0.00, DoP≈0.26.

8) Engineering uses

Stokes parameters are used in fiber links, imaging polarimetry, remote sensing, and laser diagnostics. Reporting [S0,S1,S2,S3] with DoP/DoLP/DoCP supports consistent trending across instruments.

FAQs

1) What inputs do I need for a full Stokes calculation?

You need six intensity measurements: horizontal, vertical, +45°, −45° (or 135°), right-circular, and left-circular. They can be absolute power or relative counts, but all must be on the same scale.

2) Can I use normalized values instead of intensities?

Yes. If you already know S0 and the normalized components, select the normalized mode and enter s1, s2, and s3. The calculator reconstructs S1–S3 and recomputes DoP-based metrics.

3) Why does my DoP come out greater than 1?

DoP>1 usually indicates measurement error or inconsistent scaling. Common causes are un-subtracted dark offsets, detector saturation, misaligned optics, low extinction ratio, or waveplate retardance errors.

4) What does S3 = 0 mean?

S3 near zero means the measured circular components are balanced, so circular polarization is weak. The light may still be linearly polarized (nonzero S1 or S2) or largely unpolarized (small S1, S2, and S3).

5) Does the Stokes method work for unpolarized light?

Yes. For fully unpolarized light, S1≈S2≈S3≈0 while S0 remains positive. The calculator will report DoP near zero, which is the expected outcome.

6) How should I report results in a lab report?

Report the Stokes vector [S0,S1,S2,S3], the measurement basis definitions, the circular handedness convention, and DoP/DoLP/DoCP. Include uncertainty estimates if you repeated measurements.

7) What is the difference between DoLP and DoCP?

DoLP measures the linear fraction using S1 and S2, while DoCP measures the circular fraction using S3. Both are normalized by S0, so they compare polarization content independent of total intensity.

Related Calculators

root mean square speed calculatorraman shift calculatorrecoil velocity calculatorknudsen number calculatorponderomotive energy calculatorfret distance calculatorthermal de broglie wavelength calculatorconfocal pinhole size calculatorvacuum conductance calculatornumerical aperture calculator

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.