This study provides a comprehensive analysis of the directional reflectance properties of the cornea using OCT imaging. By modeling reflectance as a function of incidence angle and corneal depth, we developed detailed exponential models for both mean and 97th percentile reflectance profiles across different corneal layers. Our findings reveal distinct reflectance patterns and directionalities within these layers.
Reflectance values in the epithelium, stroma, and endothelium exhibited non-normal leptokurtic distributions with a right-tailed skew, necessitating the use of nonparametric techniques for percentile calculations. Approximately 3.6% of superpixel bins were normally distributed, likely because of statistical anomalies from the large number of bins tested. Most of these superpixels were at higher incidence angles where sample sizes are lower and data are subject to artifacts. At high incidence angles, the signal-to-noise ratio decreases, causing noise to overcome the signal and potentially leading to a more normal distribution.
Our results showed that the angular dependence of the mean reflectance of the middle and posterior epithelium is modeled by a single exponential function, indicating a less directional reflectance pattern. The half-reflectance angles were relatively large (26.58° and 15.85°), suggesting that reflectance decreases gradually with increasing incidence angle. This observation aligns with Rayleigh and Mie scattering theories, where small, randomly arranged scattering elements cause diffuse scattering with minimal dependence on the angle of incidence.
12,13 The epithelial cells and subcellular structures are comparable in size to the OCT wavelength (840 nm), resulting in uniform reflectance across varying angles.
In contrast, the stromal layers required two exponential components to model their mean reflectance, indicating the presence of multiple structural components, each with distinct angular dependence. The anterior and posterior stroma exhibited higher reflectance and more pronounced directionality compared to the middle stroma (
Table 1;
Figs. 2 and
3). The anterior stroma, with a half-reflectance angle of 0.17°, displayed the sharpest decrease in reflectance with increasing angle, indicating strong directionality. In comparison, the posterior and middle stroma had larger half-reflectance angles of 0.89° and 1.29°, respectively, reflecting a more gradual decline in reflectance and less pronounced directionality (
Table 1). However, the anterior stroma exhibited a less pronounced decrease in reflectance at lower incidence angles, indicating a flatter, less directional component compared to the middle and posterior stroma (
Fig. 3).
Two key structural factors that contribute to corneal transparency are the uniformity of collagen fibril diameters and the tight regulation of spacing between adjacent fibrils.
2 Our findings suggest differences in collagen fiber organization, lamellar spacing, and keratocyte density across the stromal depth.
14,15 Additionally, variations in tissue composition, such as the presence of a nerve plexus, may further contribute to these reflectance differences.
16,17 According to Ruberti et al. (2011), the organization of the corneal lamellae displays a narrowed weaving pattern in the anterior stroma, whereas in the posterior stroma, the organization transitions to a plane pattern with lamellae lying regularly in the plane of the cornea.
14 The intensity of reflectance is affected by refractive index variations within the tissue. Denser lamellae in the anterior stroma create more abrupt changes in refractive index, which can enhance reflectance intensity. The spacing between lamellae also influences reflectance; tightly packed lamellae can cause constructive interference of backscattered light, increasing reflectance, whereas regular spacing can promote destructive interference, contributing to corneal transparency.
2 Differences in lamellar density, regularity, and spacing between stromal layers may explain why the middle stroma mean reflectance is less pronounced compared to the anterior and posterior stroma.
An interesting observation in our study is the distinct patterns of magnitude and directionality between the mean and 97th percentile reflectance profiles. While the anterior and posterior stroma exhibited the highest mean reflectance, the 97th percentile reflectance was much higher in the middle and posterior stroma (
Figs. 4 and
5). Despite this, the less directional component of the anterior stroma at higher incidence angles, observed in the mean reflectance, remains present relative to the middle and posterior stroma in the 97th percentile profiles as well. Different reasons may explain such discrepancy such as differences in collagen organization within the stromal layers. The anterior stroma is known to have densely packed
18 and randomly directed
19 interwoven collagen fibers.
20 In contrast, the posterior stroma has a more lamellar organization with collagen fibers arranged parallel to the corneal surface.
2 Moreover, keratocytes, which are transparent except for their nuclei,
2 contribute up to 15% of the stromal volume
21 and are thought to limit backward scattering.
22 Studies have shown increased keratocyte density in the anterior stroma.
23,24
Wang et al.
25 further elaborated that the gradient of mean corneal densitometry values could be due to a combination of factors, including differences in refractive indices across the cornea, variations in hydration in the axial direction, differences in lamellar structure, and differences in the ratio of keratocytes. Thus corneal reflectance might result from the interplay of these factors. Our observations align with this perspective, suggesting that the structural differences between the anterior and posterior stroma contribute to the variations in reflectance profiles.
To further illustrate these reflectance differences, an OCT B-scan of the cornea is shown in
Figure 6. The reflectance profile is non-homogeneous, as expected. The stroma exhibits distinct reflectance patterns, with higher intensity observed in the posterior stroma. At higher incidence angles, reflectance is more pronounced in the epithelium, anterior stroma, and endothelium, likely due to a lower directional component. The posterior stroma shows more organized fibrils, visible in
Figure 6A, contributing to a stronger and more directional reflectance. These reflectance differences between the anterior and posterior stroma are consistent with our model.
Previous studies have reported varying results regarding stromal reflectance profiles. Dhubhghaill et al.
26 and Ning et al.,
27 using Scheimpflug imaging, observed higher densitometry values in the anterior corneal layers compared to the middle and posterior layers. In contrast, Wang et al.,
25 using OCT imaging (wavelength = 850 nm), reported that normal corneas exhibited the highest backscatter in the epithelium and posterior stroma, with the anterior stroma showing lower backscatter.
Knighton et al.
6,7 used an ex vivo approach to study retinal nerve fiber layer reflectance, adjusting the camera and light source to observe directional changes. In contrast, we used an in vivo method using OCT, leveraging the natural curvature of the cornea to achieve variation in incidence angles. By assuming homogeneity in corneal properties across similar depths, our approach avoids the need for physical manipulation and allows for a more practical, clinically relevant analysis of reflectance patterns.
Our study extends the work of previous researchers by providing quantitative models that account for the angle of incidence in corneal reflectance, a factor not explored in earlier studies. Although Scheimpflug imaging has been used to assess corneal densitometry,
26,27 it suffers from poor axial resolution and inability to segment individual corneal layers. OCT provides higher resolution and layer-specific imaging capabilities, which we used to gain detailed insights into the optical behavior of each corneal layer.
Modeling corneal reflectance as a function of incidence angle holds significant clinical potential. Quantitative metrics derived from these models could improve the diagnostic capabilities of OCT by detecting early microstructural changes in the cornea, such as those seen in keratoconus, Fuchs' dystrophy, or corneal scarring.
8,9 Increased reflectance in specific stromal layers may indicate early stromal haze or scarring, allowing for earlier intervention.
28 Importantly, our findings suggest that nonparametric percentile analysis, such as evaluating the 97th percentile reflectance, should be favored over parametric mean-based models for detecting localized scattering events such as opacities, edema, or haze.
25,28,29 This is because parametric mean reflectance models do not account for normal variations in high-intensity scattering events, potentially misclassifying normal high reflectance as opacity, whereas percentile analysis is sensitive to these outliers. Additionally, exploring the relationship between reflectance and directionality patterns and specific corneal diseases could lead to new diagnostic criteria or monitoring tools.
In addition to our modeling, we performed a variance component analysis on the superpixel-level residuals—defined as the percentage deviation between the measured and model-predicted reflectance—to elucidate the sources of variability in our dataset. In the linear domain, the total normalized variance was 0.42 for the epithelium, 0.56 for the stroma, and 0.49 for the endothelium. Notably, the stroma exhibited the highest overall variability, likely reflecting its complex collagen architecture, whereas the epithelium showed relatively consistent reflectance. Further partitioning revealed that in the epithelium, 31.4% of the variance was attributable to between-patient differences, 6.3% to between-eye differences, and 62.3% to within-eye variability. Similar patterns were observed in the stroma and endothelium—with the endothelium displaying the highest between-patient variability (38.8%) and between-eye variability (10.5%)—suggesting that, in addition to local microstructural heterogeneity, inter-individual differences in the endothelium may be driven by factors such as variations in endothelial cell density or other patient-specific factors, possibly including subclinical endothelial dysfunction or age-related changes.
Moreover, both Pearson correlation and two-sample t-test analyses revealed no significant associations between patient age or gender and the normalized residual variance in any layer. It is noteworthy that variance estimates computed in the linear domain are higher than those that would be obtained in the logarithmic domain due to dynamic range compression.
Although our study is limited by its retrospective design, its limited sample size, and the exclusive inclusion of normal eyes, it establishes a robust framework for modeling corneal reflectance. Although previous studies have linked corneal densitometry to demographic factors,
26,27 our findings suggest that, when reflectance is quantified on OCT via our approach, such influences are minimal. Importantly, although our cohort was imaged using a single, calibrated OCT system, we believe that—with appropriate calibration and data conversion—the mathematical model presented here can be extended and applied across different OCT devices.
In summary, our work enhances the understanding of corneal optical properties by providing a detailed quantitative model of directional reflectance that accounts for depth incidence angle variability. This model holds significant potential for improving OCT-based diagnostics and lays the groundwork for future investigations into the complex interplay between corneal microstructure and optical behavior.