Image formation and analysis in optical systems with polarization aberrations

This dissertation presents image formation and analysis in optical systems with polarization aberrations. The analysis is divided into two parts. The first part calculates the polarization state of a wavefront exiting an optical system with polarization aberrations via polarization aberration theory. The other part studies general image formation in polarizing optical systems with application to systems with polarization aberrations.; The polarization modifying properties of the class of optical systems composed of rotationally symmetric lenses and mirrors are described. Several significant extensions to polarization aberration theory are made including: the description of tilted and decentered elements, the use of exponential form of Jones, and fourth order aberrations calculations. An off-axis LIDAR system and an IR scan mirror system are used to demonstrate the aberrations of non-rotationally symmetric systems. The relationship between thin film, optical design, and instrumental polarization is examined using a magnetograph as an example.; The second part of the dissertation applies diffraction image formation and analysis to optical systems with polarization aberrations. This part derives the point spread function and optical transfer function for optical systems with polarization aberration, and explores how image formation depends on the coherence and polarization state of the source. It is shown that the scalar point spread function (PSF) of Fourier optics can be generalized in the presence of polarization aberration to a 4 x 4 point spread matrix (PSM) in Mueller matrix notation. A similar 4 x 4 optical transfer matrix (OTM) is shown to be an appropriate generalization of the optical transfer function (OTF). The PSM and OTM are associated with the optical system and are independent of the incident polarization state but dependent on the coherence of the illumination. Since an optical system with polarization aberrations will have a different point spread function and optical transfer function for different incident polarization states, the PSM and OTM act as filters with regard to the incident polarization state. The effect of the polarization aberrations on image field is investigated. The effect of spatial pseudodepolarizers on the point spread and optical transfer functions is examined.