Abstract
The detection of spatial or temporal variations in very thin samples has\nimportant applications in the biological sciences. For example, cellular\nmembranes exhibit changes in lipid composition and order, which in turn\nmodulate their function in space and time. Simultaneous measurement of\nthickness and refractive index would be one way to observe these variations,\nyet doing it noninvasively remains an elusive goal. Here we present a\nmicroscopic-imaging technique to simultaneously measure the thickness and\nrefractive index of thin layers in a spatially resolved manner using\nreflectometry. The heterodyne-detected interference between a light field\nreflected by the sample and a reference field allows measurement of the\namplitude and phase of the reflected field and thus determination of the\ncomplex reflection coefficient. Comparing the results with the simulated\nreflection of a thin layer under coherent illumination of high numerical\naperture by the microscope objective, the refractive index and thickness of the\nlayer can be determined. We present results on a layer of polyvinylacetate\n(PVA) with a thickness of approximately 80~nm. These results have a precision\nbetter than 10\\% in the thickness and better than 1\\% in the refractive index\nand are consistent within error with measurements by quantitative differential\ninterference contrast (qDIC) and literature values. We discuss the significance\nof these results, and the possibility of performing accurate measurements on\nnanometric layers. Notably, the shot-noise limit of the technique is below\n0.5~nm in thickness and 0.0005 in refractive index for millisecond measurement\ntimes.\n
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