Extraction of Thickness and Water-Content Gradients in Hydrogel-Based Water-Backed Corneal Phantoms Via Submillimeter-Wave Reflectometry

Abstract

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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> and 0.1°, respectively, for signal-to-noise ratios (SNRs) between 40 and 50 dB. Total 12 phantoms were fabricated. Calibration methods enabled quantification of target sphericity that strongly correlated with optical-coherence tomography-based sphericity metrics via image segmentation. The extracted free-water volume fraction varied less than 5% in the five phantoms whose fabrication yielded the most spherical geometry. Submillimeter-wave-based thickness accuracy was better than 111 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> m (∼λ/9) with an average of 65 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> m (∼λ/17) and standard deviation of 44 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> m (∼λ/25) for phantoms with physiologically relevant geometry. Monte-Carlo simulations of measurement noise and uncertainty limits agree with the experimental data analysis and indicate a lower thickness accuracy limit of 33 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> m, and water-content sensitivities of 0.5% and 11.8% for the anterior and posterior segments, respectively. Numerical analysis suggests that the measurement fidelity was SNR limited and identified optical path length ambiguities within the cornea where a continuum of thickness/water gradient pairs produces statistically insignificant differences in complex reflection coefficient for finite SNR. This is the first known submillimeter-wave measurement technique, which is 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.