  Water, in its three phases, is ubiquitous, and the surface properties of ice
is important to clarifying the process of melting, as well as to various other
fields, including geophysics. As such, the subject has been studied both
theoretically and experimentally, for over a hundred years, while being an
active field of research today. It has been established that surface melting,
or premelting, exists below the melting point, and a `liquid-like layer' (LLL)
exists on the surface of ice. Here, we use the surface thermal fluctuation
spectra to study the properties of LLL, including its thickness, for pure ice,
and for ice with impurities. We find that the properties of LLL are consistent
with those of bulk liquid water, and for layers thicker than 10\,nm, their
properties are experimentally indistinguishable from those of liquid water.
Measured thicknesses are found to be much smaller than the previous
experimental measurements close to the bulk melting temperature. We find that
the additions of impurities at ppm levels cause LLL to be thicker, as well to
be quite inhomogeneous, with properties depending on the dopant. This is
revealed by scanning the surface at $\mu$m level resolution, and can contribute
to the slipperiness of ice in natural settings.
