Tilt scanning interferometry: a novel technique for mapping structure and three-dimensional displacement fields within optically scattering media

Abstract

We describe a novel technique that we call tilt scanning interferometry to measure depth-resolved structure and displacement fields within semi-transparent scattering materials. The method differs significantly from conventional optical coherence tomography, in that only one wavelength is used throughout the whole measurement process. Temporal sequences of speckle interferograms are recorded while the illumination angle is tilted at constant rate. Fourier transformation of the resulting three-dimensional intensity distribution along the time axis reconstructs the scattering potential within the medium. Repeating the measurements with the object wave at equal and opposite angles about the observation direction results in two three-dimensional phase-change volumes, the sum of which gives the out-of-plane-sensitive phase volume and the difference between which gives the in-plane phase volume. From these phase-change volumes the in-plane and out-of-plane depth-resolved displacement fields are obtained. The theoretical framework for the technique is explained in detail and a practical optical implementation is described. Finally, results from proof-of-principle experiments involving a semi-transparent beam undergoing bending are presented.

Identification of Materials Mechanical Properties from Full-Field Measurements: Latest Advances in the Virtual Fields Method

“…Joint projects between medical and engineering groups should be established in the near future to help solve these very important and challenging problems. A first application of the VFM in this area was published recently [25] and a project is presently underway with Loughborough University on the measurement of the stiffness variation of cornea in the throughthickness direction using optical coherence tomography-based techniques [26].…”

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

“…In TSI, depth-resolved displacements are measured by tilting the illumination angle during the acquisition of image sequences [3]. Figure 1 (c) shows a simplified schematic setup of this technique.…”

“…As in WSI, spectral analysis of the time-varying intensity signal at a given camera pixel provides depth-resolved information, the magnitude relating to the specimen structure and the phase relating to the optical path differences between the scatterers lying within the volume. Figure 2 shows the setup for bending beam experiments, and sample wrapped phase maps from the proof of principle experiments detailed in [3]. The top row shows the horizontal in-plane phasechange distribution for different slices within an epoxy resin beam measured relative to a reference surface at z = z 1 , starting at the object surface z -z 1 = 0 mm (left) in steps of 1.74 mm down to z -z 1 = 5.22 mm (right).…”

“…An alternative to the '2 spatial + time' axes, involves the acquisition of time independent data that allows phase volumes to be reconstructed along all three spatial coordinates. 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 3 Wavelength scanning interferometry [1,2], tilt scanning interferometry [3,4], phase contrast spectral optical coherence tomography [5,6] and hyperspectral interferometry [7] have been developed over the past five years and can be regarded as a combination of the depth-sensing capabilities of optical coherence tomography and the phasesensitive capabilities of traditional 2-D full-field interferometric techniques [1-3, 5, 6].…”

Simultaneous measurement of in-plane and out-of-plane displacement fields in scattering media using phase-contrast spectral optical coherence tomography

“…For oblique illumination in the plane yz at an angle θ to the z axis, the phase difference due to object deformation is [8]: …”