  The detection of spatial or temporal variations in very thin samples has
important applications in the biological sciences. For example, cellular
membranes exhibit changes in lipid composition and order, which in turn
modulate their function in space and time. Simultaneous measurement of
thickness and refractive index would be one way to observe these variations,
yet doing it noninvasively remains an elusive goal. Here we present a
microscopic-imaging technique to simultaneously measure the thickness and
refractive index of thin layers in a spatially resolved manner using
reflectometry. The heterodyne-detected interference between a light field
reflected by the sample and a reference field allows measurement of the
amplitude and phase of the reflected field and thus determination of the
complex reflection coefficient. Comparing the results with the simulated
reflection of a thin layer under coherent illumination of high numerical
aperture by the microscope objective, the refractive index and thickness of the
layer can be determined. We present results on a layer of polyvinylacetate
(PVA) with a thickness of approximately 80~nm. These results have a precision
better than 10\% in the thickness and better than 1\% in the refractive index
and are consistent within error with measurements by quantitative differential
interference contrast (qDIC) and literature values. We discuss the significance
of these results, and the possibility of performing accurate measurements on
nanometric layers. Notably, the shot-noise limit of the technique is below
0.5~nm in thickness and 0.0005 in refractive index for millisecond measurement
times.
