Optimal method for reconstructing polychromatic maps from broadband observations with an asymmetric antenna pattern

TL;DR

This paper presents an optimal linear method to reconstruct multi-wavelength maps from broadband telescope data with asymmetric beams, enabling separation of signals like the CMB from foregrounds.

Contribution

It introduces a novel eigenvector-based approach to determine the best wavelength combinations for high signal-to-noise map reconstruction, applicable to both full and partial sky scans.

Findings

Accurate multi-wavelength map reconstruction demonstrated in simulations.

Optimal wavelength combinations derived from eigenvectors improve signal separation.

Method applicable to various astrophysical mapping scenarios.

Abstract

Broadband time-ordered data obtained from telescopes with a wavelength-dependent, asymmetric beam pattern can be used to extract maps at multiple wavelengths from a single scan. This technique is especially useful when collecting data on cosmic phenomena such as the Cosmic Microwave Background (CMB) radiation, as it provides the ability to separate the CMB signal from foreground contaminants. We develop a method to determine the optimal linear combinations of wavelengths (``colors'') that can be reconstructed for a given telescope design and the number of colors that are measurable with high signal-to-noise ratio. The optimal colors are found as eigenvectors of a matrix derived from the inverse noise covariance matrix. When the telescope is able to scan the sky isotropically, it is useful to transform to a spherical harmonic basis, in which this matrix has a particularly simple form. We propose using the optimal colors determined from the isotropic case even when the actual scanning pattern is not isotropic (e.g., covers only part of the sky). We perform simulations showing that maps in multiple colors can be reconstructed accurately from both full-sky and partial-sky scans. Although the original motivation for this research comes from mapping the CMB, this method of polychromatic map-making will have broader applications throughout astrophysics.