Abstract
Purpose: :
To develop a matrix mathematical approach to simultaneous tear film lipid and aqueous layer thickness and anterior corneal surface refractive index calculations from interferometry measurements.
Methods: :
An optical interferometer of the type developed by King-Smith et al. was utilized. The tear film was modeled as a stack of 2 homogeneous films, the lipid and aqueous layers, between air and the corneal epithelium as a semi-infinite substrate. The film stack is treated with conventional matrix mathematics wherein the resultant system characteristic matrix is calculated by multiplication of the individual matrices of the layers. The expanded matrix equation for reflectance, R, was then multiplied by 2 empirical terms, noted "bb" and exp(-cc.*(1000./).^1.0). The bb term accounts for the difference between measured relative reflectance and absolute reflectance, and the exp(-cc.*(1000./).^1.0) term accounts for non-Gaussian corneal surface roughness. Interferometry spectra with a wavelength range of 559 - 1085 nm were measured from baseline tear film measurements from 25 participants, M/F, who reported dry eye symptoms. IRB approval was obtained (RCRC IRB). Spectra were fit to the equation for R using the Gauss-Newton method to find optimal values for the refractive index of the corneal epithelial surface, thicknesses of the aqueous and lipid layers and "bb" and "cc" parameters.
Results: :
Lipid and aqueous layer thickness values are consistent with literature, where lipid thickness range = 34 - 119 nm, mean = 74 nm, stdev = 23 nm and aqueous thickness range = 1546 - 3870 nm, mean = 2639 nm and stdev = 403 nm. Corneal surface refractive index range = 1.3288 - 1.3386, mean = 1.3328 and stdev = 0.0024. Intrasubject refractive index stdev for 6 subjects, n≥5 measurements, were: 0.0010, 0.0009, 0.0006, 0.0009, 0.0010 and 0.0027. Refractive index distribution was bimodal, with peaks at 1.3300 - 1.3310 and 1.3350 - 1.3360, wherein 15 out of 25 subjects had mean values lower than a low reported value of 1.3346 for the tear film.
Conclusions: :
A matrix mathematics approach has been successfully applied to interferometry measurements to simultaneously calculate tear film lipid and aqueous layer thicknesses and anterior corneal surface refractive index. Refractive index measurements confirm a prior hypothesis of comparable refractive index to that of the aqueous tear. Refractive index values lower than those of the aqueous tear were also obtained.
Keywords: cornea: tears/tear film/dry eye • cornea: basic science • cornea: epithelium