Marilyn F. Bishop

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

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 Maxwells 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.

Calculations of scattered light from rigid polymers by Shifrin and Rayleigh-Debye approximations.

We show that the commonly used Rayleigh-Debye method for calculating light scattering can lead to significant errors when used for describing scattering from dilute solutions of long rigid polymers, errors that can be overcome by use of the easily applied Shifrin approximation. In order to show the extent of the discrepancies between the two methods, we have performed calculations at normal incidence both for polarized and unpolarized incident light with the scattering intensity determined as a function of polarization angle and of scattering angle, assuming that the incident light is in a spectral region where the absorption of hemoglobin is small. When the Shifrin method is used, the calculated intensities using either polarized or unpolarized scattered light give information about the alignment of polymers, a feature that is lost in the Rayleigh-Debye approximation because the effect of the asymmetric shape of the scatterer on the incoming polarized electric field is ignored. Using sickle hemoglobin polymers as an example, we have calculated the intensity of light scattering using both approaches and found that, for totally aligned polymers within parallel planes, the difference can be as large as 25%, when the incident electric field is perpendicular to the polymers, for near forward or near backward scattering (0 degrees or 180 degrees scattering angle), but becomes zero as the scattering angle approaches 90 degrees. For randomly oriented polymers within a plane, or for incident unpolarized light for either totally oriented or randomly oriented polymers, the difference between the two results for near forward or near backward scattering is approximately 15%.