Differential polarization imaging. IV. Images in higher Born approximations

The theory of differential polarization imaging developed previously within the framework of the first Born approximation is extended to higher Born approximations, taking into account interactions among the polarizable groups in the object. Several properties of differential polarization images, originally described using first Born approximation are modified when higher Born approximations are used. In particular, (a) when the polarizable groups are spherically symmetric, the off-diagonal Mueller elements Mij (i not equal to j) in bright field do not vanish in higher Born approximations, as they do in the first Born approximation case. (b) In higher Born approximations, the dark field Mi4 and M4i (i = 1, 2, 3) images do not vanish as in the first Born approximation, due to the anisotropy induced by the interactions among the groups. (c) When the polarizability tensor of each group is symmetric and real, the bright field M14 and M41 images always vanish in the first Born approximation. In higher Born approximations, these terms do not vanish if the groups bear a chiral relationship to each other. Quantitative criteria for the validity of the first Born approximation in differential polarization imaging are explicitly derived for three different types of media: (a) linearly anisotropic, (b) circularly anisotropic, and (c) linearly and circularly anisotropic (medium displaying linear birefringence and circular birefringence). These criteria define the limits of thickness and the degree of anisotropy of optically thin media. Finally, the possibility to perform optical sectioning in differential polarization imaging in the presence and absence of group interactions is discussed.