POLARIZATION ABERRATIONS (THIN FILMS).

Abstract

Polarization aberrations are the variations of amplitude, phase, polarization and retardance associated with ray paths through optical systems. This dissertation develops methods for calculating the polarization aberrations of radially symmetric systems of weak polarizers, systems like lenses, telescopes and microscopes. The instrumental polarization in these systems arises from weak polarization effects occurring near normal incidence at glass, metal and thin film coated interfaces. Polarized light and polarizers are treated using the Jones calculus. Weak polarizers, optical elements with small polarization effects, are treated by expanding the Fresnel equations and thin film equations into a Taylor series. Methods are given for calculating the Taylor series coefficients for a multilayer coated interface whose polarization performance is known, for example from a thin film design program. Equations are derived for the propagation of polarized light through optical systems. Weak polarizers are shown to be very weakly order dependent; this greatly facilitates the calculation of the effect of a sequence of weak polarizers. The dominant terms are order independent polarization terms which are readily calculated. The order dependent portion can be systematically evaluated as higher order terms. The instrumental polarization, being a function of angle of incidence, is different for different rays through the system. Thus an optical system is a spatially varying polarizer. The instrumental polarization associated with a single surface is often well approximated as a "parabolic" polarizer. The instrumental polarization function is calculated as a Taylor series Jones matrix about the optical axis as a function of object and pupil coordinates. The resulting spatial variations of the instrumental polarization function bear a strong resemblance to the wavefront aberrations, since both arise from fundamental geometrical considerations. In particular, there are terms in the weak linear polarization and in the weak retardance of radially symmetric systems which strongly resemble defocus, tilt and piston error. A polarization aberration expansion is defined to second order in the object and pupil coordinates. A method is derived for calculating the polarization aberration coefficients for a sequence of radially symmetric surfaces from the Taylor series representation of the polarization associated with the individual interfaces.