Structured decomposition of a multi-snapshot nine-reconstructables Mueller matrix polarimeter

Area of Science:

• Optics and Photonics
• Polarimetry
• Image Science

Background:

• Snapshot channeled polarimeters modulate polarization in space or wavenumber, avoiding temporal modulation.
• Recent methodologies have been developed for describing channeled and partial polarimeters.

Purpose of the Study:

• To investigate the nine-reconstructables design for snapshot channeled polarimeters.
• To analyze the trade-offs between spatial, spectral, and temporal bandwidth, and system complexity.
• To optimize noise characteristics and system complexity through multi-snapshot structured decomposition.

Main Methods:

• Focus on a nine-reconstructables design to limit resolution loss by reducing carriers.
• Utilize multi-snapshot structured decomposition for analytical shaping of the measured space.
• Analyze two-, three-, and four-snapshot systems for their reconstructables, null space, and signal-to-noise ratio (SNR).

Main Results:

• A two-snapshot system can measure 14 reconstructables with improved SNR over single-snapshot systems.
• A three-snapshot system measures all 16 Mueller elements, offering significant bandwidth-SNR improvements (26.3% spectral, 50.4% spatial).
• Four-snapshot systems show diminishing returns but may offer implementation advantages.

Conclusions:

• The nine-reconstructables design in snapshot channeled polarimeters provides favorable trade-offs in bandwidth and SNR.
• Multi-snapshot approaches enable analytical optimization of measurement space for improved performance and reduced complexity.
• The number of snapshots dictates the achievable performance, with three snapshots offering a compelling balance for Mueller matrix polarimetry.