Bounding the relative errors associated with a complete Stokes polarimeter.

Area of Science:

• Optics and Photonics
• Polarimetry
• Metrology

Background:

• Accurate determination of the Stokes vector is crucial for characterizing light polarization.
• Existing methods for error analysis in polarimetry often rely on specific assumptions about error sources.
• Quantifying relative errors in Stokes vector determination is essential for reliable optical measurements.

Purpose of the Study:

• To propose a robust criterion for bounding relative errors in Stokes vector determination.
• To develop a generalized figure of merit for optimizing polarimeters.
• To analyze the impact of analyzer configuration errors on polarization measurements.

Main Methods:

• Derivation of a novel error bounding criterion for Stokes vector determination.
• Identification of condition number and equally weighted variance as key optimization parameters.
• Introduction of a new parameter accounting for matrix errors in analyzer configurations.
• Development and application of a generalized figure of merit.

Main Results:

• A criterion is established for bounding relative errors in Stokes vector determination without prior error assumptions.
• Condition number and equally weighted variance emerge as intrinsic optimization parameters.
• A new optimization parameter is identified, incorporating errors from the analyzer configuration matrix.
• A generalized figure of merit is derived and successfully applied to optimize a known polarimeter.

Conclusions:

• The proposed criterion offers a general framework for error analysis in polarimetry.
• The derived figure of merit enhances the optimization of polarimetric instruments.
• This work provides a more comprehensive approach to understanding and mitigating errors in polarization measurements.