2.1.

THz Imaging System

THz imagery was acquired using a compact imaging system that employs a photoconductive switch pumped by a 780 nm mode-locked fiber laser [pulse width = 230 fs, pulse repetition frequency (PRF) = 20 MHz, average power = 7.5 mW] described in detail elsewhere.¹⁶ The emitted THz radiation is directed to the sample at an angle of 14 deg from vertical through a chain of off-axis parabolic mirrors and then detected by a zero-bias Shottky rectifier (Virginia Diodes, Charlottesville, Virginia). The net power spectrum of this configuration has a center frequency of 525 GHz and an effective bandwidth of 125 GHz, which is sufficient to overcome interference from standing waves while still providing good spatial resolution (∼1.2 mm, 10% to 90% spot size).¹⁷ The choice of center frequency of our system is motivated by the tradeoff between water concentration sensitivity, robustness to scattering, and spatial resolution, which are observed to be well balanced at 525 GHz.¹⁸ THz imagery of a 35 × 35 mm area can be obtained in 110 s.¹⁹

2.2.

THz Spectroscopy System

THz spectroscopy data was obtained using a commercial time domain spectroscopy system (TPS Spectra 3000 CF system, TeraView). This system uses a proprietary photoconductive transceiver pumped by a Ti:Sapphire mode-locked laser (pulse width = 90 fs, PRF = 80 MHz, average power = 280 mW). It has a reflection-mode module that is used to acquire reflection data from a sample with an incidence and reflection angle of 30 deg from the vertical. The reflected waveform from a target is obtained by optoelectronic sampling, which can acquire a spectrum in 1 s with a frequency resolution of 6 GHz.

2.3.

THz Imaging of Evaporative Drying in an Ex Vivo Porcine Cornea

The THz imaging system was first used to monitor the loss of water by evaporation in an ex-vivo porcine cornea. To isolate the water contrast from all other factors, the drying mount illustrated in Fig. 1 was constructed which pressed a hydrated cornea against a fixed, transparent quartz imaging window (Meller Optics, Providence, Rhode Island) and allowed images to be taken in this constrained geometry over the course of several hours. This apparatus removes the effects of many sources of variation unrelated to hydration change, including topology, curvature, and the standoff distance between sample and imaging head. A porcine cornea was dissected from an eye and soaked in deionized water for 1 h followed by drying and re-soaking. The cornea was then allowed to dry on a mass balance (ZSA 80, Scientech, Boulder, Colorado) at room temperature. At preset increments, the cornea was removed from the scale, mounted on the window, and imaged. The window was cleaned with acetone and methanol between each scan. The average (inhomogeneously distributed) water concentration was determined by mass measurement on the scale (accuracy ±1 mg, giving an error of <0.53% water concentration for the entire cornea set which had hydrated masses of 190 mg and above).

Fig. 1

Illustration of experimental geometry for THz imaging and spectroscopy of ex vivo corneal tissues.

2.4.

THz Sensitivity to Hydration in Corneal Tissues

In order to measure the nominal sensitivity of reflection-mode sensing in the THz band to water concentration in the cornea, reflection-mode spectroscopy of ex-vivo porcine corneas dissected by the same method as in Sec. 2.3 was performed on nine samples at different hydration levels. This experiment requires the water concentrations of the cornea samples to be homogeneous so they can be computed using a mass measurement without the kind of spatial variation seen in the previous experiment (see Fig. 2). Following the work of Meek,²⁰ nine corneas were soaked in a 0%, 3%, 5%, and 7% polyethylene glycol (PEG) solutions containing 0.15M NaCl for 3 days. The concentrations of these solutions produce different equilibrium water concentrations in the corneas that varied between 79.1% and 91.5%. The corneas were mounted on a window frame in a similar manner as illustrated in Fig. 1, with the quartz window replaced by a tightly-stretched 12.7-μm mylar film. Abutting the cornea against this thin film forced it into a flat, orthogonal geometry with respect to the THz optics. The mylar window produces little perturbation to the passing beam because the window is optically thin with respect to the wavelengths of inquiry (mylar index ≈1.67, thickness <λ/10 up to 1.4 THz).²¹ THz spectroscopy data was obtained using the TeraView time-domain system. The relation between water concentration and THz reflectivity was computed from this data, and the absolute sensitivity of our system was predicted.

Fig. 2

(a) Optical and THz image of a hydrated ex vivo cornea. (b) THz image of an ex vivo porcine cornea at (upper-left to lower-right) 84.74%, 78.64%, 75.27%, 70.25%, and 66.06% water content by mass.

2.5.

Simulation of THz-Corneal Tissue Interaction and the Penetration Depth in Corneal Tissues

The reflectivity spectrum of a hydrated corneal tissue can be simulated using a Bruggeman effective media model which combines the basic constituents of the cornea. The details of Bruggeman analysis and its application to biological tissue are discussed elsewhere.²² A useful model of the cornea system is a binary mixture of water and biological background material. The dielectric function of both of these materials is known from the literature. The double-Debye model of water describes the dielectric response of the water in the cornea,²³ and the refractive index of corneal tissue with the water removed was measured as approximately 1.55.²⁴ Following the analysis in Bennett,²² the reflection from a homogeneous mixture of corneal tissue and water behind a 12.7-μm mylar window is computed for the cornea which is hydrated to a water concentration of 79.1% by mass, which approximately matches the physiological norm in vivo. ²⁵ This model will assume that the PEG solution preparation successfully prepares the corneal tissue to a homogeneous water concentration, and so the tissue can be approximated as having a uniform water concentration. This assumption will be verified by imaging one of the corneas.

This model is compared to the measured spectrum, and then used to compute the penetration depth of THz radiation in cornea tissue. For a wave traveling through a medium of complex dielectric function ε_r in the z-direction, the electric field and intensity can be written in the form:

These figures are discussed below in terms of the severity and affected tissue regions of several corneal disease processes to assess the usefulness of THz imaging for diagnosis and monitoring of corneal disease.

3.1.

THz Imaging of Evaporative Drying in a Porcine Cornea

The results of the corneal drying experiment are shown in Fig. 2, with the cornea represented by the entire oval-shaped area centered in the window. The corneal tissue is fully hydrated in the initial scan, and therefore appears bright across the entire image. Clear preferential drying from the outer edges is then seen in the images that follow, as the dark “dry” border closes further inwards toward the center with each subsequent frame. The colorbar scale is inverted with respect to the other images in this study because the refractive index of a hydrated cornea is much larger than that of a dehydrated cornea, and when both are viewed through quartz (n = 2.11),²⁷ the larger mismatch exists between the quartz and the dehydrated cornea. The reflection through quartz is therefore stronger for a dry cornea (smaller index) than a hydrated one (larger index) because the reflection strength depends on the magnitude of the difference. When both corneas are viewed through air (n = 1), the larger air/hydrated-cornea mismatch provides the larger reflection. The remainder of the images will be acquired through an optically small mylar window in free space, for which hydrated tissue reflects the most strongly.

The lateral edges of the cornea sample suffer evaporative loss from exposure to air in addition to losses from the epithelial and endothelial surfaces. The progression of drying from the outside–inward is the expected result of the faster diffusion in the lateral directions relative to the thickness direction.^{10, 28} This is also in accordance with observations from a previous preliminary study in which a single cornea was imaged at a one point in time without constraining its geometry.²⁹

3.2.

THz Sensitivity to Corneal Hydration

The corneas prepared in the PEG solutions reached water concentrations of 78.8%, 79.1%, 81.0%, 82.4%, 86.9%, 88.7%, 89.0%, 90.0%, and 91.5%. A THz image of one of these corneas is shown in Fig. 3, with the cornea on the right and a piece of microscope cover glass on the left as a reference. Fresnel's equations predict a 13% reflectivity at a 30 deg incidence angle for glass and this is a near match for the predicted THz reflectivity of a 78% hydrated cornea using the Bruggeman model.^{27, 30, 31} In this image, the entire cornea shows a uniform intensity, indicating that the THz reflectivity and the water concentration that it reflects is uniform across the entire cornea. This demonstrates the effectiveness of the PEG technique in yielding samples of high spatial uniformity with respect to hydration.

Fig. 3

Image of porcine cornea (right) prepared by soaking in a PEG solution and a glass square for calibration (left) affixed with glue (tall dark spot on left edge).

The spectroscopy results from scanning the cornea samples using the TeraView system are shown in Fig. 4. A clear decrease in reflected intensity is seen in the corneas with reduced amounts of absorbed water at all frequencies. This THz spectrum was observed to be constant as the beam was moved around on the surface of the cornea, again indicating that the equilibration process was successful in uniformly distributing the water throughout the cornea.

Fig. 4

THz spectra of ex-vivo porcine corneas prepared to uniform hydrations using PEG solutions.

From this data, it is possible to calculate the intrinsic sensitivity of THz imaging systems to corneal hydration. Each frequency value along the x-axis intercepts the reflectivity curves from nine different corneas. These nine points can be plotted to describe the relation between THz reflectivity and corneal hydration at that frequency. This relationship is shown at five frequencies in Fig. 5. The relationships are approximately linear, and the slope of each linear trendline gives the THz reflectivity change characteristic of a unit change in the water concentration at that frequency. Both the reflectivity magnitude and the slope of these linear fits decrease with increasing frequency. This is an example of one of the key trade-offs in THz imaging of hydrated materials. Higher frequencies are capable of producing images with finer spatial resolution, but lower frequencies are more strongly reflected by water and therefore produce both higher reflected signal and more contrast to small water concentration changes.

Fig. 5

THz reflectivity versus cornea concentration at 0.25, 0.45, 0.65, 0.85, and 1.05 THz shown alongside linear fits.

The slope of the reflectivity-concentration relationship is plotted against frequency in Fig. 6. This curve describes the decreasing sensitivity of THz sensing to water content as frequency increases. For example, a THz reflection measurement at 200 GHz must be able to resolve a minimum of a 0.32% reflection change in order to detect a water concentration change of 1% in a sample. The same water concentration sensitivity would require 0.17% reflectivity resolution at 400 GHz, 0.11% resolution at 600 GHz, and 0.07% resolution at 800 GHz. Thus lower frequencies are more sensitive to corneal hydration changes than higher frequencies. These measurements can be combined with the noise parameters of a given THz imaging system to estimate the contrast that can be realized by any operational frequency band.

Fig. 6

Derivative of THz reflectivity with respect to water concentration, plotted against frequency.

To estimate the sensitivity of the imaging system used in this research, the THz beam from the imaging system was focused onto a 1-mm piece of microscope glass (n ∼ 2.11 at 300 and 900 GHz)³² and the reflected power was measured at 100 ms increments for 5 min. From the variance of this data, a noise-limited THz reflection sensitivity of ΔR = 0.0275% was computed. Therefore, the noise-equivalent water concentration change can be found by

3.3.

Simulation of THz–Corneal Tissue Interaction and the Penetration Depth of THz Radiation in Corneal Tissues

The dielectric function of the composite of water and dry corneal tissue was modeled as described above and the simulated reflectivity is plotted in Fig. 7 alongside the measured THz reflectivity of a cornea at 79.1% water concentration. The measured and modeled reflectivity trends correspond very closely (R ² = 0.977), validating our use of the Bruggeman model.

Fig. 7

(a) Measured and simulated reflectivity from a porcine cornea near physiological hydration. (b) Simulated half-value layer of THz radiation in corneal tissue.

The effective combined permittivity computed for the composite cornea model (the effective media combination of water and dry corneal tissue) in this analysis can also be used to predict the depth in the cornea that can be interrogated by this technique. The simulated half-value layer of corneal tissue at 79.1% water concentration is shown in the bottom plot of Fig. 7. For example, at the center frequency of our imaging system, δ_HVL ≈ 81 μm. Thus the THz imaging system is predicted to interrogate roughly a few hundred micrometers of tissue and contains little influence from material behind the cornea (i.e., aqueous humor), where the signal for a round trip would be attenuated by >40 dB.

This model also predicts that as the frequency falls below 50 GHz, the half-value layer rises above 255 μm and the round trip loss drops to ∼13 dB. Therefore, radiation in the microwave frequency bands below ∼ 50 GHz are likely to significantly interact with the aqueous humor, and are not well suited to the task of corneal imaging.

This estimate of the penetration depth of the THz radiation tissue is critical to the discussion of THz hydration sensing because robust sampling of the cornea requires that the radiation interacts primarily in the corneal stroma without overshooting into the aqueous humor. Further, some disease processes exhibit depth-dependant hydration changes, and successful detection of these will require the selection of a probe frequency that can adequately penetrate to the appropriate depth for each. Direct measurement of the penetration depth is challenging because the attenuation in corneal tissue is very strong and it is difficult to detect radiation transmitted through whole cornea at THz frequencies. Future research will attempt to directly measure the penetration depth through thin slices of corneal tissue prepared to uniform thicknesses with a microkeratome and scanned immediately after harvesting to minimize the loss of tissue hydration through evaporation.