  Spatial resolution of most imaging devices is fundamentally restricted by
diffraction. This limitation is manifested in the loss of high spatial
frequency information contained in evanescent waves. As a result, conventional
far-field optics yields no information about an object's subwavelength
features. Here we propose a novel approach to recovering evanescent waves in
the far field, thereby enabling subwavelength-resolved imaging and spatial
spectroscopy. Our approach relies on shifting the frequency and the wave vector
of near-field components via scattering on acoustic phonons. This process
effectively removes the spatial frequency cut-off for unambiguous far field
detection. A straightforward extension of this technique, which we call spatial
Fourier transform infrared spectroscopy, allows to preserve phase information,
making it possible to perform 3D subwavelength imaging. We discuss the
implementation of such a system in the mid-IR and THz bands, with possible
extension to other spectral regions.
