  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.
