Optically monitoring and controlling nanoscale topography

Methods and apparatus for method for characterizing a height profile of a scattering surface relative to a fiducial plane. The scattering surface, which may be an interface between distinct solid, liquid, gaseous or plasma phases, is illuminated with substantially spatially coherent light, and light scattered by the scattering surface is collected and dispersed, such as by a grating, into zeroth- and first-order beams. A spatial Fourier transform of the zeroth- and first-order beams is created, and one of the beams is low-pass filtered. The beams are interfered at a focal plane detector to generate an interferogram, which is transformed to retrieve a spatially resolved quantitative phase image and/or an amplitude image of the scattering surface. Imaging may be performed during an etching process, and may be used to adaptively control a photoetching process in a feedback loop.