Depth-resolved Imaging and Displacement Measurement Techniques Viewed as Linear Filtering Operations

The last 5 years have seen the emergence of a family of optical interferometric techniques that provide deformation measurements throughout three-dimensional (3-D) weakly scattering materials. They include wavelength scanning interferometry (WSI), tilt scanning interferometry (TSI), phase contrast spectral optical coherence tomography (PC SOCT) and hyperspectral interferometry (HSI) and can be thought of as a marriage between the phase sensing capabilities of Phase Shifting Interferometry and the depth-sensing capabilities of Optical Coherence Tomography. It was recently shown that some closely related 3-D optical imaging techniques can be treated as shift-invariant linear filtering operations. In this paper, we extend that work to include WSI, TSI, PC SOCT and HSI as spatial filtering operations and also relate the properties of their transfer functions in the spatial frequency domain to their spatial resolution and phase sensitivity, for depth-resolved displacement measurements.