Abstract: We describe a digital lock-in amplifier instrument which is designed to optimally extract the amplitude and phase of response at intermodulation product frequencies. This general purpose laboratory instrument has broad application in the analysis of nonlinear systems. A defining property of the intermodulation lock-in is, that the Fourier components of the drive waveform and the sampling frequency used to sample the response are all integer multiples, or close to integer multiples, of a fundamental base frequency ?f. We describe an implementation of the intermodulation lock-in with a field programmable gate array. Applications of the intermodulation lock-in are discussed, including its use in Atomic Force Microscopy.

Abstract: We have invented a method of sensing a surface by driving a resonator with two or more frequencies and exploiting the nonlinear phenomenon of intermodulation. When a resonator (for example an oscillating cantilever) with a sharp tip is brought close to a surface, the non-linear tip-surface interaction generates intermodulation response of the resonator. The measured frequency spectrum of intermodulation response contains much information about the material composition of the surface. When the resonator is scanned over the surface, the intermodulation spectrum can be used to make an image of the surface with enhanced contrast for different materials on the surface, or it can be used to extract the tip-surface interaction at every point on the surface.