A Lattice Model for Computing the Transmissivity of the Cornea and Sclera

Abstract

The method of photonic band structure is used to calculate the frequencies of light that propagate in lattice models of the cornea and sclera of the mammalian eye, providing an explanation for transparency in the cornea that first properly accounts for multiple scattering of light. Each eye tissue is modeled as an ordered array of collagen rods, and photonic band structure methods are used to solve Maxwell's equations exactly for these models, a procedure that automatically effectively includes all orders of multiple scattering. These calculations show that the dispersion relation for the cornea is linear in the visible range, implying that the cornea is transparent. We show that the transmissivity is approximately 97% by using an effective medium approximation derived from the photonic band structure results and applicable in the visible region. In contrast, the dispersion relation for the model in the sclera is not linear in the visible region, and there are band gaps in this region that could play an important role in the transmission of light in the sclera.

Corneal collagen—its role in maintaining corneal shape and transparency

“…In these structures, only certain frequencies of light are transmitted or reflected by a medium that consists of an array of two components with different dielectric constants, as is the case for the collagen fibrils and ground substance in the cornea. Photonic methods have been applied to the cornea (Ameen et al 1998) but on the basis of a hexagonal arrangement of the collagen fibrils. Preliminary data suggest that the collagen fibrils in the cornea may be arranged as a photonic quasicrystal which shows long-range order but is predicted to display the same diffraction and light transmission properties as seen in the cornea (J. Doutch and KM Meek, unpublished).…”

Averaged Spacing and 2-D Organization of Collagen Fibrils in the Posterior Cornea of the Rabbit Eye Assessed by Transmission Electron Microscopy

“…Maurice considered that the ordered arrays of collagen fibrils within the corneal stroma provided a rational basis for transparency of the tissue based on non-destructive interference of light rays. 2 Maurice, and others, 3,37,42 provide schematic diagrams to illustrate the possible arrangement of collagen fibrils in such a Averaged Spacing of Collagen Fibrils in Cornea 337 transparent cornea. The overall pattern shown in the overlay in Figure 3(B) clearly deviates from such an idealized arrangement yet, at the same time, shows several features indicating some remarkable organization.…”

Research Background and Motivation

“…These indicated strong redistribution of photon density of states in the porous plane with a decrease of density; and an increase of density for the pore channel direction [111]. Mammalian eye cornea has a similar porous structure as anodic porous alumina [112], and due to the same reasons above the porous structure removes reflection at the air/cornea interface and provides superior transmission of light into the eye [111]. In this way, Lutich et al [111] proposed that porous materials like anodic porous alumina can be used in focusing and spatial concentration of waves based on the anisotropic scattering of incident light.…”