Roughness of the Corneal Surface Studied by Interferometry

Abstract

Purpose:: The contrast of interference fringes from the pre-corneal tear film, PCTF, varies inversely with wave number (1/wavelength). We test the proposal that this is due to the roughness of the corneal surface, and study the characteristics of this roughness.

Methods:: Reflection spectra from the PCTF show oscillations caused by interference between reflections from the front and back of the tear film. 840 reflection spectra over the wavelength range 912 to 1712 nm were recorded from the central cornea of each of 20 subjects (mean age 28, 12 females). Measurement area was nominally 25 x 33 microns and exposure time was 0.095 s. Mean contrast, C_m, was calculated from Fourier analysis of the spectral oscillations. Additionally, contrast, C, as a function of wave number, x, was fitted either by an exponential decay, C(x)=C_eexp(-K_ex), or by a gaussian decay, C(x)=C_gexp(-K_gx²), where C_e, K_e, C_g and K_g are constants. K_e and K_g are determined by surface roughness. C_e and C_g correspond to the contrast expected from a smooth surface, which is determined by the refractive indices of the tear film and epithelium.

Results:: As expected, contrast of the spectral oscillations varied inversely with wave number. Based on median values for each subject, C_m was negatively and strongly correlated with K_e (r=-0.938, P<0.001) and K_g (r=-0.942, P<0.001) showing that mean contrast is determined much more by surface roughness than by contrast at zero wave number, C_e or C_g. C_e was strongly correlated with K_e (r=0.943, P<0.001) but C_g was not correlated with K_g (r=-0.015, P>0.05).

Conclusions:: Because C_e and C_g depend on refractive indices and K_e and K_g depend on surface roughness, one might expect the correct model to show independence between C_e and K_e, or between C_g and K_g. The results therefore are consistent with the gaussian decay model. It can be shown that this model implies that the probability distribution of tear thickness is gaussian with a standard deviation of 0.134 ± 0.010 (SD between subjects) microns. As the front surface of the tear film is relatively smooth, this variability indicates a corresponding roughness of the corneal epithelium.

Keywords: cornea: epithelium • cornea: basic science • cornea: tears/tear film/dry eye