Matrix-based integral transformations for Stokes imaging with partially polarized and partially coherent light

Area of Science:

• Optics and Photonics
• Image Processing
• Mathematical Physics

Background:

• Polarization imaging is crucial for analyzing light-matter interactions.
• Partially polarized and partially coherent light present computational challenges in imaging.
• Existing methods often struggle to accurately model diffraction and aberrations.

Purpose of the Study:

• To develop a simplified framework for space- and frequency-domain calculations in polarization imaging.
• To introduce a generalized method for Stokes imaging under partially polarized and partially coherent illumination.
• To provide a unified approach for analyzing polarization-dependent imaging systems.

Main Methods:

• Utilized matrix convolution and matrix direct correlation for simplified calculations.
• Introduced a hypermatrix-based transmission cross-coefficient matrix.
• Developed generalized Stokes parameters and an apparent transfer matrix concept.

Main Results:

• Derived a simplified expression for polarization imaging calculations.
• Presented a formula for Stokes imaging incorporating diffraction and aberrations.
• Analyzed coherent and incoherent limits using the optical transfer matrix.

Conclusions:

• The proposed matrix-based methods offer a powerful tool for polarization imaging analysis.
• The transmission cross-coefficient matrix effectively models complex system effects.
• The generalized framework enhances the understanding of nonlinearities in polarization imaging.