Mariangela Baggio

Terahertz spectroscopy is a promising method to diagnose ocular diseases, where the cornea is typically imaged by Gaussian beams. However, the beam’s mismatch with the cornea’s spherical surface produces a 5-10 % error in analysis. We investigate cornea spectroscopy with wavefront-modified vector beams, reducing the original analysis error to less than 0.5 %. Vector beams are synthesized by our developed 3D Angular Spectrum Method expanded to vector spherical harmonic presentation, allowing wavefront modification and scattering analysis from 100-layer cornea models. We show that wavefront-modified spherical vector beams possess increased accuracy and non-sensitive focusing on cornea spectroscopy compared to the Gaussian beams. Additionally, we investigate wavefront-modified cylindrical vector beams, which show frequency-dependent scattering power arising from s- and p-polarizations. As a result, these beams are unsuitable for cornea spectroscopy, although they have potential for optical force applications. Wavefront-modified vector beams can be applied to spherical target spectroscopy and optical force applications, such as medicine, medical imaging, and optical tweezers.

The feasibility of a 220 - 330 GHz zero order axicon generated Bessel beam for corneal water content was explored. Simulation and experimental data from the 25-degree cone angle hyperbolic-axicon lens illuminating metallic spherical targets demonstrate a monotonically decreasing, band integrated, backscatter intensity for increasing radius of curvature from 7 - 11 mm, when lens reflector and optical axis are aligned. Further, for radii >= 9.5 mm, maximum signal was obtained with a 1 mm transverse displacement between lens and reflector optical axes arising from spatial correlation between main lobe and out of phase side lobes. Thickness and permittivity parameter estimation experiments were performed on an 8 mm radius of curvature, 1 mm thick fused quartz dome over a 10 mm axial span. Extracted thickness and permittivity varied by less than ~ 25 $\mu$m and 0.2 respectively after correction for superluminal velocity. Estimated water permittivity and thickness of water backed gelatin phantoms showed significantly more variation due to a time varying radius of curvature.

The feasibility of a 220 - 330 GHz zero order axicon generated Bessel beam for corneal water content was explored. Simulation and experimental data from the 25-degree cone angle hyperbolic-axicon lens illuminating metallic spherical targets demonstrate a monotonically decreasing, band integrated, backscatter intensity for increasing radius of curvature from 7 – 11 mm, when lens reflector and optical axis are aligned. Further, for radii > = 9.5 mm, maximum signal was obtained with a 1 mm transverse displacement between lens and reflector optical axes arising from spatial correlation between main lobe and out of phase side lobes. Thickness and permittivity parameter estimation experiments were performed on an 8 mm radius of curvature, 1 mm thick fused quartz dome over a 10 mm axial span. Extracted thickness and permittivity varied by less than ∼ 25 μm and 0.2 respectively after correction for superluminal velocity. Estimated water permittivity and thickness of water backed gelatin phantoms showed significantly more variation due to a time varying radius of curvature. To the best of our knowledge, this is the first work that describes axicon generated Bessel beam measurements of layered spheres with varying radii of curvature, in the submillimeter range.

A system concept for online alignment verification of millimeter-wave, corneal reflectometry is presented. The system utilizes beam scanning to generate magnitude-only reflectivity maps of the cornea at 650 GHz and compares these images to a precomputed/measured template map to confirm/reject sufficient alignment. A system utilizing five off-axis parabolic mirrors, a thin film beam splitter, and two-axis galvanometric mirror was designed, simulated, and evaluated with geometric and physical optics. Simulation results informed the construction of a demonstrator system which was tested with a reference reflector. Similarity metrics computed with the aligned template and 26 misaligned positions, distributed on a 0.5 mm x 0.5 mm x 0.5 mm mesh, demonstrated sufficient misalignment detection sensitivity in 23 out of 26 positions. The results show that positional accuracy on the order of 0.5 mm is possible using 0.462 mm wavelength radiation due to the perturbation of coupling efficiency via beam distortion and beam walk-off.

Absolute thickness and free water content gradients in gelatin-based corneal phantoms with physiologically accurate radii of curvature, and aqueous backing were extracted via coherent submillimeter wave reflectometry at 220 330 GHz. Fourier-domain based calibration methods, utilizing temporal and spatial gating, were developed and yielded peak-to-peak amplitude and phase clutter of 10-3 and 0.1, respectively for signal to noise ratios between 40 dB and 50 dB. Twelve phantoms were fabricated. Calibration methods enabled quantification of target sphericity that strongly correlated with optical coherence tomography-based sphericity metrics via image segmentation. Extracted free water volume fraction varied less than 5 % in the 5 phantoms whose fabrication yielded the most spherical geometry. Submillimeter wave-based thickness accuracy was better than 111 m (~/9) with average of 65 m (~/17) and standard deviation of 44 m (~/25) for phantoms with physiologically relevant geometry. Monte Carlo simulations of measurement noise and uncertainty limits agree with experimental data analysis and indicates a lower thickness accuracy limit of 33 m, and water content sensitivities of 0.5 % and 11.8 % for the anterior and posterior segments respectively. Numerical analysis suggests measurement fidelity was SNR limited and identified optical path length ambiguities within the cornea where a continuum of thickness/water gradient pairs produce statistically insignificant differences in complex reflection coefficient for finite SNR. This is the first known submillimeter-wave measurement technique able to extract both the thickness and water content gradients from a soft-tissue phantom, with a water backing, without the need for ancillary measurements.

This paper presents measurements of the permittivity of gelatin hydrogels between 220 and 330 GHz. Hydrated gelatin was treated as a binary mixture of free water and a compound consisting of water bound to collagen. Submillimeter-wave reflectometry was used to estimate the hydrated gelatin permittivity, hydrated gelatin density, and free-water volume fraction in phantoms composed of 62, 67, 72, and 77% water by weight. A hydrated dry/wet density ratio of 0.335 was validated with optical-coherence tomography. A constant non-freezing bound-water mass of 0.6 g/g was observed and confirmed with differential-scanning calorimetry. Good agreement between results from different modalities supports the dielectric spectroscopy methods and data analysis. Depending on the hydrodynamics at the sample/air interface, measurements indicate a bound-water compound permittivity of 3.77 - j2.52 to 3.95 - j2.49 contrasting the pure-water average permittivity of 5.16 j5.63. The loss related to bound water was much higher than anticipated and characterization will help reduce uncertainty in measurements of gelatin hydrogel-based tissue phantoms; particularly corneal phantoms where adjacent free water creates complex hydration gradients. This is the first known, submillimeter-wave, frequency domain measurement of complex permittivity of the bound-water component in solid, proteinaceous matter.

THz-reflection spectroscopy was used to extract time-varying water gradients in drying paper targets mounted on electrically thick dielectric substrates. The data showed a pronounced and prolonged drop below dry reflectivity when the water content that peaks at low weight (∼10%). A binomial distribution fitted to the acquired data confirms the existence of the time-varying water content gradient and suggests aqueous thin film hydration can be quantified even when the contrast between the film and backing material is low.