Multi-harmonic reconstruction of photoelastic modulator-based Mueller polarimeters using the complex Q-matrix

Area of Science:

• Optical physics
• Metrology
• Data analysis

Background:

• Mueller matrix polarimetry data analysis has advanced with digital signal processing (DSP).
• Traditional methods use hardware or single-harmonic Fourier analysis of temporal data.
• DSP offers flexibility, but challenges like spectral leakage and phase recovery persist.

Purpose of the Study:

• To demonstrate DSP advancements for exploiting Mueller matrix polarimeter data more fully.
• To address spectral leakage and phase recovery issues in Fourier domain analysis.
• To enable automatic sign determination and improve precision using multi-harmonic analysis.

Main Methods:

• Numerical computation of Fourier integrals for temporal data analysis.
• Coherent combination of information from multiple harmonic channels.
• Complex Fourier domain analysis incorporating spectral phase information.

Main Results:

• Developed DSP techniques to address spectral leakage and phase recovery.
• Enabled numerical analysis in the complex Fourier domain for Mueller matrix recovery.
• Demonstrated that multi-harmonic analysis can theoretically improve instrumental precision by a factor of 1.3-1.7.

Conclusions:

• Advanced DSP, particularly multi-harmonic analysis, significantly enhances Mueller matrix polarimetry.
• Accurate phase recovery and spectral leakage mitigation are crucial for precise Mueller matrix element determination.
• Experimental results validate the theoretical precision improvements offered by the developed methods.