Reflections from any pair of these four surfaces can cause interference effects. For example, reflections,
r _{1} and
r _{2}, from the boundaries of the PLTF, are seen to be in phase for the wavelength of
Figure 1A , causing constructive interference and hence a large amplitude for the combination of these two reflections. For a different wavelength, these two reflections can be out of phase (destructive interference) so that the combination of the two reflections would be relatively weak. Thus, a reflectance spectrum should show peaks at some wavelengths and troughs at other wavelengths corresponding to constructive and destructive interference, respectively. These peaks and troughs alternate, giving rise to spectral oscillations.
^{ 6 } ^{ 21 } ^{ 22 } For normal incidence, oscillations in reflectance corresponding to interference between reflections from surfaces
i and
j, can be fitted by:
where
and γ
_{ ij } is the contrast of the spectral oscillations,
t′ is the effective thickness between surfaces
i and
j based on refractive index of
n _{1} (i.e., tears),
t _{ k } is the thickness of layer
k, λ is the vacuum wavelength, and φ
_{ ij } and λ
_{ ij } are constants.
^{ 20 } The wavelength variation of refractive index (dispersion) of tears,
n _{1}, was assumed to equal that for water. The term cos(2
πt′α
+ φ) corresponds to the spectral oscillations, whereas the decay term exp(
−λ _{ ij } /1) is empiric, providing a better fit to the reflectance spectrum. It follows from
equation 2 that the effective thickness,
t′, is given by the frequency of the oscillations, when plotted as a function of α. In theory, contrast is given by
^{ 20 } where abs(2
r _{ i } r _{ j }) is the absolute value of 2
r _{ i } r _{ j }. In practice, the measured contrast can be reduced by any of the following conditions: If the two surfaces are not parallel, if there is an eye movement during the exposure that changes the thickness of the layer, if either surface (particularly the corneal surface, surface 4) is rough, if the microprojections (microvilli and microplicae) on the corneal surface act as an antireflective coating, or if the modulation transfer function of the spectrograph is less than unity. These factors presumably contribute to the decay term in
equation 2 .