Empirical modelling of the BLASTPol achromatic half-wave plate for precision submillimetre polarimetry

TL;DR

This paper presents the design, testing, and empirical modeling of a broad-band cryogenic achromatic half-wave plate for submillimetre polarimetry, enabling improved polarization measurements in astronomical observations.

Contribution

It introduces a novel empirical model for the HWP's frequency response, including a method to quantify non-idealities affecting polarization accuracy.

Findings

Successfully characterized the HWP at room and cryogenic temperatures.

Developed an empirical model to recover the HWP Mueller matrix and phase shift.

Demonstrated improved polarization angle measurement accuracy.

Abstract

A cryogenic achromatic half-wave plate (HWP) for submillimetre astronomical polarimetry has been designed, manufactured, tested, and deployed in the Balloon-borne Large-Aperture Submillimeter Telescope for Polarimetry (BLASTPol). The design is based on the five-slab Pancharatnam recipe and it works in the wavelength range 200-600 micron, making it the broadest-band HWP built to date at (sub)millimetre wavelengths. The frequency behaviour of the HWP has been fully characterised at room and cryogenic temperatures with incoherent radiation from a polarising Fourier transform spectrometer. We develop a novel empirical model, complementary to the physical and analytical ones available in the literature, that allows us to recover the HWP Mueller matrix and phase shift as a function of frequency and extrapolated to 4K. We show that most of the HWP non-idealities can be modelled by quantifying one wavelength-dependent parameter, the position of the HWP equivalent axes, which is then readily implemented in a map-making algorithm. We derive this parameter for a range of spectral signatures of input astronomical sources relevant to BLASTPol, and provide a benchmark example of how our method can yield improved accuracy on measurements of the polarisation angle on the sky at submillimetre wavelengths.