Optical Interferometric Polarimetry. I. Foundation

Abstract

The theoretical response of long-baseline optical interferometers and Fourier transform spectrometers, including polarization effects, is derived. The formalism, employing the Jones and Mueller calculi as well as the relationship between them, was adapted from previous work in radio interferometry and tailored specifically for optical wavelengths. Expressions for Jones and Mueller matrices corresponding to specific optical components and effects are stated. It was determined that the system squared visibility depends on the instrument, atmosphere, and normalized intrinsic polarization of sources under observation. A sample algebraic calculation was performed to highlight the typical functional form for the instrumental system squared visibility, demonstrating that reductions from unity can be determined directly from differential measurements of polarization quantities between the arms. Monte Carlo simulations were performed using two trains of identical mirrors with random relative orientation offsets, yielding results consistent with the algebraic example. Four mathematical appendices are provided for reference.