Tilt scanning interferometry: a 3D k-space representation for depth-resolved structure and displacement measurement in scattering materials

Abstract

Tilt Scanning Interferometry (TSI) has been recently developed as an experimental method to measure multi-component displacement fields inside the volume of semitransparent scattering materials. It can be considered as an extension of speckle interferometry in 3D, in which the illumination angle is tilted to provide depth information, or as an optical diffraction tomography technique with phase detection. It relies on phase measurements to extract the displacement information, as in the usual 2D counterparts. A numerical model to simulate the speckle fields recorded in TSI has been recently developed to enable the study on how the phase and amplitude are affected by factors such as refraction, absorption, scattering, dispersion, stress-optic coupling and spatial variations of the refractive index, all of which may lead to spurious displacements. In order to extract depth-resolved structure and phase information from TSI data, the approach had been to use Fourier Transformation of the intensity modulation signal along the illumination angle axis. However, it turns out that a more complete description of the imaging properties of the system for tomographic optical diffraction can be achieved using a 3D representation of the transfer function in k-space. According to this formalism, TSI is presented as a linear filtering operation. In this paper we describe the transfer function of TSI in 3D k-space, evaluate the 3D point spread function and present simulated results.