Differential polarization imaging. IV. Images in higher Born approximations

Area of Science:

• Optical imaging
• Electromagnetism
• Materials science

Background:

• Differential polarization imaging (DPI) theory was previously established within the first Born approximation.
• Interactions among polarizable groups within an object were not fully accounted for in earlier models.

Purpose of the Study:

• To extend DPI theory to higher Born approximations, incorporating interactions between polarizable groups.
• To analyze modifications in differential polarization images arising from these interactions.
• To derive quantitative criteria for the validity of the first Born approximation in various anisotropic media.

Main Methods:

• Theoretical extension of DPI to higher Born approximations.
• Analysis of Mueller matrix elements (Mij) under different approximation levels.
• Derivation of validity criteria for the first Born approximation.

Main Results:

• Higher Born approximations reveal non-vanishing off-diagonal Mueller elements (Mij) for symmetric groups and non-vanishing dark field images (Mi4, M4i) due to induced anisotropy.
• Chiral relationships between groups lead to non-vanishing bright field images (M14, M41) in higher approximations.
• Quantitative criteria for first Born approximation validity were derived for linearly, circularly, and combined anisotropic media.

Conclusions:

• Interactions among polarizable groups significantly alter DPI characteristics beyond the first Born approximation.
• The derived criteria define the limits for applying the first Born approximation in optically thin anisotropic media.
• The study discusses the potential for optical sectioning in DPI with and without group interactions.