Interpretation of measured 3×3 partial depolarizing Mueller matrices.

Area of Science:

• Optics and Photonics
• Materials Science
• Data Science

Background:

• Mueller polarimetry is vital for analyzing light-matter interactions.
• Instrumental limitations often result in incomplete 3x3 Mueller matrices.
• Zero-padding incomplete matrices leads to physically inconsistent results.

Purpose of the Study:

• To present a systematic procedure for completing 3x3 Mueller matrices into physically consistent 4x4 matrices.
• To ensure accurate polarimetric data reconstruction despite instrumental constraints.

Main Methods:

• Utilizing the covariance matrix formalism.
• Employing a maximal polarimetric purity criterion to select the most deterministic completion.
• Developing a generalizable procedure applicable to any partial Mueller matrix data.

Main Results:

• A reliable method for reconstructing complete 4x4 Mueller matrices from incomplete 3x3 measurements.
• The completed matrices are physically consistent for both nondepolarizing and depolarizing systems.
• The method identifies the most deterministic two-component model consistent with the data.

Conclusions:

• The developed procedure offers a physically grounded solution for incomplete Mueller matrix data.
• This enhances the reliability of Mueller polarimetry in diverse scientific fields.
• It provides a crucial tool for advanced polarimetric imaging and materials characterization.