<div>Infrared chemical microscopy through mechanical probing of light-matter interactions by atomic force microscopy (AFM) bypasses the diffraction limit. One increasingly popular technique is photo-induced force microscopy (PiFM), which utilizes the mechanical heterodyne signal detection between cantilever mechanical resonant oscillations and the photo induced force from light-matter interaction. So far, photo induced force microscopy has been operated in only one heterodyne configuration. In this article, we generalize heterodyne configurations of photoinduced force microscopy by introducing two new schemes: harmonic heterodyne detection and sequential heterodyne detection. In harmonic heterodyne detection, the laser repetition rate matches integer fractions of the difference between the two mechanical resonant modes of the AFM cantilever. The high harmonic of the beating from the photothermal expansion mixes with the AFM cantilever oscillation to provide PiFM signal. In sequential heterodyne detection, the combination of the repetition rate of laser pulses and polarization modulation frequency matches the difference between two AFM mechanical modes, leading to detectable PiFM signals. These two generalized heterodyne configurations for photo induced force microscopy deliver new avenues for chemical imaging and broadband spectroscopy at ~10 nm spatial resolution. They are suitable for a wide range of heterogeneous materials across various disciplines: from structured polymer film, polaritonic boron nitride materials, to isolated bacterial peptidoglycan cell walls. The generalized heterodyne configurations introduce flexibility for the implementation of PiFM and related tapping mode AFM-IR, and provide possibilities for additional modulation channel in PiFM for targeted signal extraction with nanoscale spatial resolution.</div>
