Tear film interferometry and corneal surface roughness

Abstract

Purpose: Previous studies of optical interference from the whole thickness of the precorneal tear film showed much lower contrast than from the pre-contact lens tear film. It is hypothesized that the recorded low contrast is related to roughness of the corneal surface compared with the smooth contact lens surface. This hypothesis is tested, and characteristics of this roughness are studied.

Methods: Reflectance spectra were recorded from 20 healthy individuals using a silicon-based sensor used in previous studies (wavelength range, 562-1030 nm) and an indium-gallium-arsenide (InGaAs) sensor responding at longer wavelengths (912-1712 nm). Interference from the whole thickness of the precorneal tear film caused oscillations in the reflectance spectra.

Results: Spectral oscillations recorded with the InGaAs sensor were found to decay as a Gaussian function of wave number (1/wavelength). This is consistent with a rough corneal surface, whose distribution of surface height is also a Gaussian function. Contrast of spectral oscillations for the InGaAs sensor was, on average, approximately four times greater than that for the silicon sensor.

Conclusions: For the Gaussian roughness model based on InGaAs spectra, the corneal surface was characterized by a surface height SD of 0.129 μm. Spectral oscillations recorded with a silicon-based camera can have higher contrast than expected from this Gaussian roughness model, indicating some reflectance from a smoother or more compact surface. The results also indicate that InGaAs cameras could provide whole-thickness interference images of higher contrast than silicon-based cameras.

Keywords: corneal epithelium; corneal surface; infrared spectroscopy; interference; tears.

Figure 1

Processing of a reflectance spectrum from a 25-year-old white female recorded with the InGaAs spectrometer. The calculated precorneal tear film thickness was 2.62 μm. (A) The solid line is measured reflectance as a function of wave number (1/wavelength), and the dashed line is the fitted sloping baseline (Equation 7). (B) Reflectance divided by the sloping baseline in (A). Solid black line corresponds to measured value. Blue curve (partly obscured by the magenta curve) gives fitted reflectance based on Gaussian decay of amplitude reflectance from the posterior tear surface (Equation 8). The magenta curve gives fitted reflectance based on exponential decay of amplitude reflectance from the posterior tear surface (Equation 9). (C) Blue and magenta solid curves show in-phase amplitude reflectance of the posterior tear surface for Gaussian and exponential decay models, respectively. Dashed curves show corresponding amplitude reflectance. (D) Extrapolation of (C) to zero wave number.

Figure 2

Amplitude reflectance as a function of wave number for all 20 individuals. (A) Gaussian model (Equation 8). (B) Exponential decay model (Equation 9).

Figure 3

The relation between amplitude reflectance at zero wave number and decay constants. (A) Gaussian model (Equation 8). (B) Exponential decay model (Equation 9).