A Quantitative Model for Optical Coherence Tomography

K-Space Approach in Optical Coherence Tomography: Rigorous Digital Transformation of Arbitrary-Shape Beams, Aberration Elimination and Super-Refocusing beyond Conventional Phase Correction Procedures

For the most popular method of scan formation in Optical Coherence Tomography (OCT) based on plane-parallel scanning of the illuminating beam, we present a compact but rigorous K-space description in which the spectral representation is used to describe both the axial and lateral structure of the illuminating/received OCT signals. Along with the majority of descriptions of OCT-image formation, the discussed approach relies on the basic principle of OCT operation, in which ballistic backscattering of the illuminating light is assumed. This single-scattering assumption is the main limitation, whereas in other aspects, the presented approach is rather general. In particular, it is applicable to arbitrary beam shapes without the need for paraxial approximation or the assumption of Gaussian beams. The main result of this study is the use of the proposed K-space description to analytically derive a filtering function that allows one to digitally transform the initial 3D set of complex-valued OCT data into a desired (target) dataset of a rather general form. An essential feature of the proposed filtering procedures is the utilization of both phase and amplitude transformations, unlike conventionally discussed phase-only transformations. To illustrate the efficiency and generality of the proposed filtering function, the latter is applied to the mutual transformation of non-Gaussian beams and to the digital elimination of arbitrary aberrations at the illuminating/receiving aperture. As another example, in addition to the conventionally discussed digital refocusing enabling depth-independent lateral resolution the same as in the physical focus, we use the derived filtering function to perform digital "super-refocusing." The latter does not yet overcome the diffraction limit but readily enables lateral resolution several times better than in the initial physical focus.

Measured and simulated mechanical properties of additively manufactured matrix-inclusion multimaterials fabricated by material jetting

Modern additive manufacturing enables the simultaneous processing of different materials during the printing process. While multimaterial 3D printing allows greater freedom in part design, the prediction of the mix-material properties becomes challenging. One type of multimaterials are matrix-inclusion composites, where one material contains inclusions of another material. Aim of this study was to develop a method to predict the uniaxial Young's modulus and Poisson's ratio of material jetted matrix-inclusion composites by a combination of simulations and experimental data.Fifty samples from commercially available materials in their pure and matrix-inclusion mixed forms, with cubic inclusions, have been fabricated using material jetting and mechanically characterized by uniaxial tensile tests. Multiple simulation approaches have been assessed and compared to the measurement results in order to find and validate a method to predict the multimaterials' properties. Optical coherence tomography and microscopy was used to characterize the size and structure of the multimaterials, compared to the design.The materials exhibited Young's moduli in the range of 1.4 GPa to 2.5 GPa. The multimaterial mixtures were never as stiff as the weighted volume average of the primary materials (up to [Formula: see text] softer for 45% RGD8530-DM inclusions in VeroClear matrix). Experimental data could be predicted by finite element simulations by considering a non-ideal contact stiffness between matrix and inclusion ([Formula: see text] for RGD8530-DM, [Formula: see text] for RGD8430-DM), and geometries of the printed inclusions that deviated from the design (rounded edge radii of [Formula: see text]m). Not considering this would lead to a difference of the estimation result of up to [Formula: see text]MPa (44%), simulating an inclusion volume fraction of 45% RGD8530-DM.Prediction of matrix-inclusion composites fabricated by multimaterial jetting printing, is possible, however, requires a priori knowledge or additional measurements to characterize non-ideal contact stiffness between the components and effective printed geometries, precluding therefore a simple multimaterial modelling.