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

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