  Disordered packings of colloidal spheres show angle-independent structural
color when the particles are on the scale of the wavelength of visible light.
Previous work has shown that the positions of the peaks in the reflectance
spectra can be predicted accurately from a single-scattering model that
accounts for the effective refractive index of the material. This agreement
shows that the main color peak arises from short-range correlations between
particles. However, the single-scattering model does not quantitatively
reproduce the observed color: the main peak in the reflectance spectrum is much
broader and the reflectance at low wavelengths is much larger than predicted by
the model. We use a combination of experiment and theory to understand these
features. We find that one significant contribution to the breadth of the main
peak is light that is scattered, totally internally reflected from the boundary
of the sample, and then scattered again. The high reflectance at low
wavelengths also results from multiple scattering but can be traced to the
increase in the scattering cross-section of individual particles with
decreasing wavelength. Both of these effects tend to reduce the saturation of
the structural color, which limits the use of these materials in applications.
We show that while the single-scattering model cannot reproduce the observed
saturations, it can be used to design materials in which multiple scattering is
suppressed and the color saturated, even in the absence of absorbing
components.
