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1 From the College of Optometry, the Ohio State University, Columbus, Ohio; and 2 School of Optometry, Indiana University, Bloomington, Indiana.
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Abstract |
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METHODS. Reflectance spectra from the human cornea were measured at normal incidence. These spectra show oscillations whose maxima correspond to constructive interference between light reflected from the air surface and from some deeper surface. The frequency of these spectral oscillations is proportional to the thickness of the layer between the air surface and the second surface. Therefore, Fourier analysis of reflectance spectra can be used to determine the thickness of layers of the tear film and cornea. In the main experiment, 36 low-resolution spectra were obtained from six normal eyes for measuring thickness up to 100 µm. Control experiments included measurements of the time course of thickness changes and high-resolution spectra for measuring thickness up to 1000 µm.
RESULTS. For the main experiment, in the thickness range 1 to 100 µm, the strongest peak in the Fourier transform was near 3 µm (range, 1.5–4.7 µm) beneath the air surface. In the range 20 to 100 µm, the strongest peak was near 55 µm (range, 50–59 µm) for all 36 spectra; none were in Prydal’s range near 40 µm. This 55-µm peak is consistent with a reflection from the basement membrane of the epithelium. Time course measurements after a blink show that the 3-µm peak is not an artifact. High-resolution spectra gave a peak near 510 µm, corresponding to the complete thickness of the cornea (plus tear film). This peak had a contrast similar to that of the 3-µm peak.
CONCLUSIONS. These studies did not confirm Prydal’s estimate of approximately 40 µm. Nor were there prominent peaks near Danjo’s value of approximately 11 µm, except in cases of probable reflex tears. Because the reflection at the aqueous–mucus boundary would be expected to be weaker than that from the epithelial surface, the 3-µm peak is unlikely to correspond to the aqueous layer (rather than the complete tear film). The proposal that the 3-µm peak corresponds to a reflection from the front of the cornea is supported by the demonstration of a peak of similar contrast from the back of the cornea. Thus, the current evidence consistently supports a value of approximately 3 µm for the thickness of the human precorneal tear film.
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Introduction |
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The first measurements of tear film thickness used methods that potentially disturbed the tear film, such as placing glass fibers against the cornea,7 measuring fluorescence after instilling fluorescein,5 7 or applying absorbent paper to the cornea.8 Such invasive methods have produced thickness estimates for the human tear film between 4 µm5 and 8 µm.8 A limitation of these methods is that the invasive nature of the procedure may alter the thickness of the tear film. This could be avoided by using noninvasive methods such as microscopy and interferometry. However, microscopy has not yet been applied with much success to the human tear film; Prydal et al.6 reported thickness values of 41 to 46 µm using confocal microscopy but noted that images were not sufficiently clear to identify the tear layer with certainty.
The most promising noninvasive method is interferometry.9 In this method, the intensity of light reflected from the air surface of the tears is modified by interference from light reflected from a deeper surface, such as the corneal surface. (The air surface reflects much more light than other surfaces, and so it is generally one of the two surfaces involved in interference effects.) Maxima and minima of reflected intensity occur when the two reflections are in phase or out of phase, respectively. The tear film thickness can be derived from observation of these maxima and minima (bright and dark fringes) in the reflected light.9 Interferometric methods are potentially accurate; for example, corneal thickness can be measured by "partial coherence interferometry" with a SD of less than 0.1%.10 Interferometric measurement of the tear film can be rapid enough to permit video photography.11
For the tear film, whose refractive index is intermediate between that
of the surrounding air and cornea, maxima of reflectance
occur9
12
when
 | (1) |
where m is called the order of the maximum,
n is the refractive index of the film, t is its
thickness, 
' is the angle of refraction in the film, 
is the
vacuum wavelength, and 
= 1/ is wave number. Thus,
interference fringes depend on three main factors, namely,
t, ', and . Interference effects can be studied by
varying any one of these three factors; correspondingly, the thickness
of the tear film has been studied by three methods, which have been
called "thickness-dependent fringes," "angle-dependent
fringes," and "wavelength-dependent fringes,"
respectively.9
Ideally, for any of these methods, one
factor is varied while the other two are held constant.9
An advantage of thickness-dependent fringes is that they provide a
two-dimensional "map" of the thickness of the tear
film.11
13
For the pre (contact) lens tear
film, bright and dark fringes are seen in front of the lens, which
represent contours of tear film thickness. Each cycle corresponds to a
thickness difference of /2n. Tear film thickness at any
location can be derived by counting the fringes between a dry spot and
that location. For the precorneal tear film, the observed
interference effects correspond to the thin, outer lipid
layer.11
13
Fringes corresponding to complete tear film
thickness have not been detected; probably their contrast is too low
and is masked by interference effects from the lipid layer.
Angle-dependent fringes have been used to measure human corneal thickness by Green et al.,14 but they found that fringes from the precorneal tear film were of low contrast and were too thin to quantify; thickness was estimated to be 10 µm or less. However, Prydal’s group found tear thickness in the range 34 to 45 µm in six subjects,6 in reasonable agreement with their confocal microscopy. Application of 20% acetylcysteine, a mucolytic agent, thinned the tear film in one subject to 11 µm, which then returned to a thickness of approximately 40 µm over 40 minutes. They concluded that the precorneal tear film is approximately 40 µm thick and is mainly mucus.
In the method of wavelength-dependent fringes, which is used in this article, a reflection spectrum is measured for a small spot on the cornea at normal incidence. Interference gives rise to "spectral oscillations," maxima and minima in the reflection spectra that are analogous to the bright and dark fringes seen in thickness- and angle-dependent fringes. The thickness of the film is proportional to the frequency of these oscillations.15 16 Olsen15 used the principle of this method to interpret his observation that reflectance from the human eye is greater at 500 nm than at 700 nm. He concluded that this difference corresponds to part of a low-frequency spectral oscillation from the lipid layer, which he estimated to be 0.04 µm thick. Danjo et al.16 applied this method to measuring the complete thickness of the human precorneal tear film, which they found to be 12.0 and 10.3 µm in two subjects. We reported strong (up to 24% contrast) spectral oscillations from the prelens tear film,17 giving thickness values of up to 4.9 µm, in reasonable agreement with values (up to 4.4 µm) from thickness-dependent fringes.13 Weak spectral oscillations were recorded from the precorneal tear film of one subject, yielding a thickness of approximately 3 µm.
In this study, a modified version of Danjo’s method was used to study interference effects from the tear film and cornea. The purpose was to correlate the findings with the known structure and optical properties of the cornea and the optical properties of the tear film, with the aim of determining the most probable value of tear film thickness. A preliminary report of some of the present study has been made.18
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Methods |
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The spectrograph detector is an array of 1024 columns
(wavelengths) x 64 rows. In "array-mode," the photoelectric
charges from all 65,536 elements are read into the computer and stored
on disc; the shutter, Sh, was used in this mode. In "binning mode,"
the 64 charges of each column (wavelength) are "binned" (added
electrically) before being read; this mode is faster, but has a lower
signal-to-noise ratio. The shutter was removed for this mode.
Low-resolution spectra were obtained with a 300 grooves/mm
grating, giving a spectral range of 562 to 1030 nm. These spectra are
suitable for layers of up to 100 µm. The angular width of the
illuminating cone at the cornea should be limited because of the effect
of the cos(') term in Equation 1
. The diameter of
S2 was 10 mm, and the semi-angle of the
illuminating cone was 4.8o (focal length of
L2 was 60 mm). High-resolution spectra
used a 1200 grooves/mm grating with wavelength ranges of 760 to 836 nm
or 865 to 931 nm. The diameter of S2 was reduced
to 3.2 mm, giving a semi-angle of 1.5o at the
cornea. These spectra are suitable for layers of up to 1000 µm.
Data processing is illustrated in Figure 2
. Empirically, it was found that the following steps, incorporated into
a C program, provided satisfactory analysis. Step 1: Recorded spectra
from the eye and from the reference lens were read from disc, and, for
array-mode, the data from the 64 elements at each wavelength were
added. Wavelength was converted to its reciprocal: wave number,
. Figure 2A
shows typical recorded spectra from the eye,
V(), and from the reference lens,
VL(). Response units are
106 electrons per wavelength sample. Step 2:
Spectra were corrected for small nonlinearities of the photodetector at
each wavelength, giving corrected values V'() and
VL'(). Step 3: Figure 2B
illustrates the derivation of the reflectance spectrum of the eye,
 | (2) |
) is the reflectance
of the reference lens, which was derived from Fresnel’s
equation.12
Step 4: The sloping baseline of the
reflectance spectrum (due to the lipid layer9
15
) was fit
by the Marquardt19
method with the function
 | (3) |
), h() are
derived from changes in the reflection spectra from the reference lens,
with vertical and lateral displacement, respectively; their inclusion
in Equation 3
provides a modest improvement to the accuracy of fit. In
the fitting program, more weight was given to wavelengths with greater
photodetector response (Fig. 2A)
. The resulting fit, p(),
is shown by the dashed line in Figure 2B
. Step 5: The fractional
deviation of the reflectance from this fit, that is,
[r() - p()]/p() is
shown by the black curve in Figure 2C
. Step 6: This deviation was then
reexpressed as a function of 
= 2n, where
n is the refractive index of the layer of interest. The
refractive indices at 588 nm for tears20
and
cornea21
were taken as 1.337 and 1.376, respectively, and
their dispersion constant12
was assumed to be the same as
for water. A Fourier analysis of this spectrum as a function of was
then performed and is shown in Figure 2E . (Subtraction of
p() in step 5 improves the Fourier transform by reducing
artifacts due to steps at the ends of the spectrum). Interference
between reflections from two surfaces gives rise to a peak in the
Fourier transform whose frequency corresponds to the thickness,
t, of a layer (or more precisely, the depth of the second
surface behind the air surface). This is shown by rewriting Equation 1
for normal incidence, that is,
 |
) is given by
 |
) with the function
 | (4) |
 | (5) |
) is given by Equation 3 (but with new
constants A through F). A, B, C, D, E, F,
G, T, H, and J are adjusted to provide a least squares
fit. p'() is found to be similar but not identical with
p(). The cos(2
T + H) term
gives the "spectral oscillations," whereas the decay term,
exp(-J), is empiric, providing a better fit to the
spectrum.17
The function, s(), is shown as
the thick gray curve in Figure 2C . T is a new estimate of
thickness, which generally has better repeatability than estimates from
Fourier analysis. Values of thickness, T, corresponding to
different peaks, can be obtained by limiting the Fourier analysis in
step 6 to different thickness ranges; for example, for a range 20 to
100 µm in Figure 2E , the peak near 55 µm would be studied. Step 8:
The fractional deviation of reflectance from p', that is,
[r() - p'()]/p'() is
calculated and a second Fourier analysis is performed resulting in
Figure 2F
. Typically this Fourier transform is found to have somewhat
smaller artifacts than the original transform (Fig. 2E)
. Step 9: The
fractional deviation of reflectance from the overall fit, q,
that is, [r() -
q()]/q() is calculated and is shown in
Figure 2D
. Another Fourier analysis is then performed, resulting in
Figure 2G
. This eliminates or reduces the peak in the Fourier transform
near T, so that nearby weaker peaks may be studied better.
In summary, the least squares fit of step 7 gives the best estimate of
thickness, the Fourier transform of step 8 indicates the presence of
interference from surfaces at different depths behind the air surface,
whereas the transform of step 9 allows study of interference peaks near
a major peak.
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Procedure
Experiments were approved by our institutional review board and
the tenets of the Declaration of Helsinki were followed. Informed
consent was obtained from each subject.
A main experiment and several control experiments were performed. For the main experiment, low-resolution spectra were obtained using the slow "array-mode" of spectral readout. After the eye was aligned, the subject was asked to blink, and the reflection spectrum was recorded 2 seconds after the blink, with a 1-second exposure. Six normal subjects (3 men, 3 women; age range, 23 to 45 years; mean age, 32 years) and two subjects with dry eye symptoms (fluorescein break up time <10 seconds) took part in this experiment. Six spectra were obtained from the right eye of each subject. Average temperature and humidity were 26°C and 72%, respectively. Summary plots are given for only the normal subjects, but individual results from the dry eye subjects are included to illustrate certain findings.
The following control experiments were performed. (1) The time course of thickness changes was measured in six subjects. Low-resolution spectra were obtained using the fast "binning" spectral read out. In some experiments, the recording time was 20 seconds, and the subject was asked to blink approximately 1 second after the start of the recording; spectra were obtained every 27.5 ms. Two of the authors, who had exceptionally long break up times, kept their eyes open for 6 minutes without blinking while the time course of thickness change was measured (sampled every 0.525 seconds). (2) The main experiment was repeated in three subjects interspersed with trials during which the luminance of the measuring light had been reduced by a factor of 10. (3) The main experiment was repeated in three subjects, with the measurement area at the cornea reduced to 33 x 35 µm by using a narrow horizontal slit for S1. (4) High-resolution spectra were obtained in six subjects using binning mode.
Statistical analysis was performed with Minitab 12 for Windows (State College, PA). P < 0.05 was considered to be statistically significant.
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Results |
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Figure 3 shows the Fourier transform of a spectrum for a subject who shows particularly large peaks in the range above 20 µm. (This subject had dry eye symptoms, but this probably does not limit the generality of the findings because the position of the major peaks are very close to those in Fig. 2 .) In this subject, the largest peak, of contrast 0.59%, is at a depth of 3.4 µm; the next largest, of contrast 0.14% is at 56.6 µm; and the third largest, of contrast 0.039% is at a depth of 72.9 µm. These three peaks will be called the "3-µm peak," the "55-µm peak," and the "70-µm peak," corresponding to the approximate location of the peaks. A possible interpretation of these Fourier transforms is that the 3-µm peak corresponds to the reflection from the front of the epithelium, the 55-µm peak corresponds to the reflection from the back of the epithelium, and the 70-µm peak is from the back of Bowman’s layer. Corresponding thicknesses of the tear film, epithelium, and Bowman’s layer are indicated in Figure 3 . If this interpretation is correct, the thickness of epithelium and Bowman’s layer should be corrected for their respective refractive indices21 (this is considered further in the Discussion).
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Figure 4C shows the largest peaks in the range 5 to 20 µm, including the values of 10 to 12 µm of Danjo et al.16 The average contrast was 0.040%, that is, only approximately 4% of the contrast of the 3-µm peaks in Figure 4A . No significant difference between subjects was found by the Kruskal-Wallis test. Figure 4D shows the largest peaks in the range 20 to 50 µm, including the values of Prydal et al.6 The average contrast was 0.017%, that is, only approximately 2% of the contrast of the 3-µm peaks in Figure 4A . No significant difference between subjects was found by the Kruskal-Wallis test.
Figure 4E shows the largest peaks in the range 60 to 80 µm, which should presumably include the 70-µm peaks of Figures 2 and 3 . The Kruskal-Wallis test did not show a significant difference between subjects. However, the eye represented by solid squares, which gave the six shallowest depths in Figure 4B (55-µm peaks), also gave the four shallowest depths in Figure 4E (70-µm peaks). This is expected if the 55- and 70-µm peaks correspond to reflection from the front and back of Bowman’s layer, respectively, so that an eye with a thin epithelium and hence a shallow 55-µm peak (thickness of tear film + epithelium) would tend to have a shallow 70-µm peak (thickness of tear film + epithelium + Bowman’s layer). A test of this proposal is shown in Figure 5A , where the depth of the largest peak in the range 60 to 80 µm (Fig. 4E) is plotted against the depth of the 55-µm peaks (Fig. 4B) . The small symbols are the data from the main experiment. A significant positive correlation, P < 0.001, between the two values is found by the Spearman rank-order test. No correlation would be expected if the 70-µm peaks were an artifact of the equipment or quantum noise or a combination of both. The regression line fitted through all the data points is shown and has a slope of 1.23, which is not significantly different from 1; this is consistent with the interpretation that the difference between the 70- and the 55-µm peaks is the thickness of Bowman’s layer, which is similar in all the subjects. Figure 5B is a plot of the depth difference between the 70- and the 55-µm peaks as a function of the depth of the 55-µm peak. Two data points, an open and a solid square, lie above the main distribution of data points and perhaps represent reflection from keratocytes. Omitting these two data points, the average difference between the 70- and 55-µm peaks, which is interpreted as the thickness of Bowman’s layer, is 15.0 ± 1.3 µm (SD between subjects). The large symbols in Figure 5 are median values from two repeat sets of spectra for each of three subjects. The correlation between the 55- and 70-µm peaks in Figure 5A is consistent with that of the main experiment.
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Control Experiments
If the 3-µm layer is associated with the tear film, rather than
being an artifact of the equipment, it should be systematically altered
by blinking. Figure 6
confirms this prediction. Figure 6A shows the depth of the 3-µm layer
recorded every 27.5 ms over a 20-second time period, using the rapid
binning mode of the spectrograph detector. The subject was asked to
blink approximately 1 second after the start of the recording and then
to keep her eyes open for the remaining 19 seconds. During the blink,
the lid scatters the measuring beam diffusely, so less light is
reflected back to the spectrograph than from the eye; thus, the timing
of the blink is given by the drop in reflectance seen in Figure 6B
. The
blink causes the depth of the layer to jump from approximately 2.4 to
3.9 µm; it then decays rapidly in approximately 1 second to
approximately 2.7 µm, followed by a slow decay to approximately 2.3
µm over the remaining 18 seconds. Thus, the 3-µm layer is
associated with the subject’s eye and is not an artifact of the
equipment.
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Evidence for the effects of reflex tears on the 3-µm layer is presented in Figure 7 , which shows the variation of the depth of this layer for one subject when he held his eye open for 6 minutes without blinking. It is seen that the layer thinned steadily for about the first minute from approximately 3 µm down to 2 µm but then increased to a peak of nearly 5 µm before decaying back to approximately 2 µm. He afterward reported that his eye felt some irritation during the early part of the measurement, but the irritation then disappeared. Both the measurements and the subject’s report can be explained by reflex tears, stimulated by the early irritation, and drifting down the cornea to cause thickening after the first minute. This presumably caused the relief of irritation. For another subject, the depth increased to a maximum of approximately 9 µm, which is the highest value that we have observed. In conclusion, our studies indicate that reflex tears do not contribute to the 3-µm layer, measured in the conditions of the main experiment. Reflex tears may thicken this layer up to approximately 9 µm.
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Discussion |
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These findings bear a striking resemblance to the observations of Li et al.,22 who studied reflectance as a function of depth in the human cornea using confocal microscopy through focusing (CMTF). They also found four consistent peaks with the shallowest and deepest peaks, A and D, having considerably higher reflectance than the inner two, B and C. Using video pictures obtained from the confocal microscopy, they identified the four peaks in reflectance as follows: A, superficial epithelium; B, basal epithelial nerve plexus, corresponding to the basement membrane of the epithelium; C, anterior layer of keratocyte nuclei, behind Bowman’s layer; and D, endothelium. They therefore interpreted distances between these peaks as the thickness of different layers as follows; AB, epithelial thickness (mean, 50.6 ± 3.9 µm; SD between subjects); BC, thickness of Bowman’s layer (16.6 ± 1.1 µm); AD, corneal thickness (532 ± 19 µm). For our 33 x 350 µm measurement area and using published values for the refractive indices of epithelium (1.401), Bowman’s layer (1.380), and stroma (1.376),21 our findings are similar: epithelial thickness, 49.7 ± 2.2 µm (SD between subjects); Bowman’s layer, 14.6 ± 1.4 µm; and cornea (after subtracting 3 µm for assumed tear film thickness), 508 ± 19 µm. Thus, our findings are consistent with those from CMTF, not only in the relative contrast or reflectances from the four peaks, but also in the separation between the peaks; our interpretation of the origin of the four peaks agrees with that of Li et al.22
If the high-contrast interference peak at a depth near 510 µm comes from the back of the cornea, this would support the proposal that the other high-contrast peak near 3 µm comes from the front of the cornea. But does the 510 µm peak really come from the back of the endothelium, or could it derive from one of the surfaces of Descemet’s membrane? The fact that the deepest reflectance peak in CMTF corresponds to an image of endothelial cells,22 similar to images seen in scanning electron micrographs, is consistent with an origin at the back of the endothelium. However, it is possible that this pattern of polygonal cells could correspond to the front of the endothelium. Various observations make this alternative unlikely. First, when inflammatory cells in the aqueous humor settle on the endothelial surface, black spots are seen in the confocal microscopic image of the endothelium,23 as would be expected if this image is from the back of the endothelium.
Additional evidence comes from the histograms of secondary peaks in Figure 10 . As noted previously, there are many secondary peaks shallower than the primary peak, but few are deeper; this is to be expected if the primary peak corresponds to the back of the cornea. The endothelium is approximately 5 µm thick,24 and Descemet’s membrane is approximately 9 µm thick at the mean subject age of 36 years.25 The maximum in the histogram of Figure 10B is at 13.4 µm, which is close to the combined thickness of endothelium and Descemet’s membrane of approximately 14 µm. This is consistent with the proposal that the primary peak comes from the back of the endothelium. whereas the maximum in Figure 10B corresponds to the front of Descemet’s membrane. In Figure 10 , it is seen that there are three secondary peaks at approximately 5 µm shallower than the primary peak; these are consistent with reflections from the front of the endothelium if the primary peak corresponds to the back of the endothelium. Given that the reflectance of a surface depends on the difference in refractive index across that surface,12 the finding that there are only three peaks near this depth could be explained if the refractive index of endothelial cells was close to that of Descemet’s membrane. It may be noted that the refractive index of parts of monkey photoreceptors26 varies from approximately 1.36 to 1.41, so that a value of refractive index of endothelium near that of the corneal stroma (1.376) is not unreasonable.
The 3-µm Peak
The effects of a blink on the thickness of the 3-µm layer, shown
in Figure 6
, show that this layer is not an artifact of the equipment.
An interpretation of this recording is that the rapid decay after the
blink corresponds to the redistribution of tear film associated with
upward motion of the lipid layer,3
27
whereas the slow
decay corresponds to evaporation from the tear film.28
The
results of Figure 7
also help to demonstrate that the 3-µm layer is
not an artifact.
What is the 3-µm layer? Spectral oscillations are generated by interference between the strong reflection from the air surface and a reflection from some deeper surface. The 3-µm layer is too thick to be the lipid layer,9 15 but it could be the aqueous layer (plus the thin lipid layer), or it could be the complete thickness of the tear film. High contrast fringes can occur if the reflection from the deeper surface is relatively strong. By Fresnel’s equation,12 this will occur if there is a large change in refractive index across the surface; an additional condition for a strong reflection is that the step change in refractive index should be sharp compared with the wavelength of light. The refractive index step between the tear film20 and the epithelium21 is relatively large (approximately 0.064) and sharp, and so this interface would be expected to give a relatively strong reflection. However, at the aqueous/mucus interface, reflectance should be weak because of the small difference in refractive index between aqueous and mucus. This is because the concentration of mucin in mucus is relatively low (approximately 0.5–1%29 ), and thus the refractive index difference between mucus and aqueous tears should be small (approximately 0.0018 for a mucin concentration of 1%,30 that is, only approximately 3% of the step at the tear/cornea interface). Additionally, it may be noted that mucin molecules can be as long as 3 µm,31 so that the boundary between aqueous and mucus layers may be blurred over a distance comparable to the wavelength of light, again reducing the reflectance of this boundary. The conclusion is that interference from the aqueous/mucus interface should be weak compared with interference from the tear/corneal interface. If the 3-µm peak corresponds to the aqueous/mucus interface, then this should be much smaller than a peak at a greater depth, corresponding to the tear/corneal interface. This is inconsistent with our results; Figure 4 shows that the 3-µm peak is much larger than any other peak in the range up to 50 µm. It also seems improbable that any of the peaks seen in the 5- to 50-µm range in Figures 4C and 4D could come from the tear/cornea interface, because they are much smaller than the peaks from the cornea/aqueous humor interface in Figure 9 . Finally, it may be noted that the mucus layer may extend, without discontinuity, from the corneal surface to the lipid layer32 ; in this case the 3-µm layer obviously could not be the aqueous layer. In summary, the finding that the 3-µm peaks in Figure 4 are the much larger than others up to 50 µm depth, is consistent with the proposal that the they come from the tear/corneal interface, implying that the thickness of the human tear film is approximately 3 µm. The fact that the 3-µm peaks are comparable in size to the primary peaks in Figure 9 , which come from the cornea/aqueous humor interface, is also consistent with their coming from the tear/cornea interface.
We have not found a peak at a depth of less than 3 µm, which might correspond to the aqueous/mucus boundary (see Fig. 2G ). As noted above, the refractive indices of mucus and aqueous layers would differ by only approximately 0.13%. Correspondingly, regardless of whether the tear film is mainly aqueous, is mainly mucus, has about equal thicknesses of both, or has a gradient of mucin concentration, the estimate of tear film thickness would be affected by only about this small percentage (cf. Eq. 1 , which shows that calculated thickness, t, is inversely proportional to assumed refractive index, n).
Our analysis indicates similarities between interference effects from the anterior and posterior regions of the cornea. In Figure 3 , it is proposed that the front surface of the cornea gives rise to a strong interference peak, whereas the internal boundaries between epithelium, Bowman’s layer, and stroma give weaker peaks. A symmetrical explanation is proposed for interference peaks from the posterior layers shown in Figures 9 and 10 . The strong, primary peak is interpreted as interference from the back surface of the cornea, whereas weaker, secondary peaks may occur at the internal boundaries between endothelium, Descemet’s membrane, and stroma. Thus, for both the anterior and posterior regions of the cornea, the external surface may give stronger interference than the internal boundaries.
In conclusion, we interpret the 3-µm peak as coming from the front of
the cornea, implying that the normal tear film thickness is
approximately 3 µm; reflex tears can increase this thickness (Fig. 7)
. A thickness of 3 µm is comparable to that of the prelens tear
film.13
17
This thickness is considerably less than
previous interferometric estimates using angle-dependent6
and wavelength-dependent16
fringes. It is probable that
the 3-µm layer was too thin to be detected in those experiments;
Prydal et al.6
note that 6 µm was the minimum thickness
measurable by their method, whereas Danjo et al.16
used a
limited spectral range, which would make it difficult to detect
relatively thin films. Regarding their reported thickness values, it is
possible that thin films in the equipment (e.g., cement layers in
doublet lenses) may have caused artifacts in both sets of measurements.
(In our method, the effect of such artifacts was reduced by dividing
the recorded spectrum by that from the reference lens [Eq. 2
] and by
the terms v() and h() in Eqs. 3
and 4
).
Additionally, in Danjo’s experiment,16
the spectrum was
scanned over a 2-second period, which could cause artifacts due to eye
movements and thinning of the tears during the spectral scan; we used a
shorter (1 second) exposure and collected responses for all wavelengths
simultaneously. In Prydal’s experiment,6
spatial noise
from the laser source may have caused problems in detecting and
analyzing fringes. An advantage of our method is its low noise level,
so that fringes of below 0.1% contrast can be readily detected and
analyzed (e.g., Fig. 3
). It seems difficult to find an alternative
explanation for Prydal’s data, which showed thinning of his 40-µm
layer after application of acetylcysteine; however, the reported
results in humans are for only one subject, and an attempt to reproduce
them was not convincing (D. Maurice, personal communication,
1999).
Regarding invasive methods, Mishima7 reported measurements by two methods that gave an average thickness of 7 µm. One concern with these measurements is that they were performed in the rabbit, whose tear film may differ considerably from the human; for example, the interblink interval in the rabbit can be more than 300 seconds, compared with only approximately 7 seconds in the human.33 An additional reservation about Mishima’s first method, immersion of fine glass filaments in the tear film, is that the filament may indent the epithelium. Evidence for this is, first, that a transient indentation in the tear film can be seen after removal of the filament; second, that the filament is quite uncomfortable in the unanesthetized eye; and third, that when fluorescein is instilled after the experiment, a persistent, very fine, fluorescent line is seen in the epithelium (D. Maurice, personal communication, 2000). A reservation about Mishima’s second experiment, fluorometry, is that the eye was proptosed and the tear film was washed away with saline containing fluorescein; it is not obvious that this saline film will have the same thickness as the normal tear film. A fluorometric estimate in the human of 4 µm5 is closer to ours; however, the authors were interested in the effect of instilled agents and only, in passing, extrapolated their data to estimate tear film thickness, so this result may not be considered to be definitive. By applying an absorbent paper disc to the cornea,8 human tear film thickness was estimated to be approximately 8 µm, which could be an overestimate if reflex tears were generated and/or if fluid was drawn from the tear film surrounding the disc or epithelium. Finally, theoretical predictions of fluid mechanics have been used to predict tear film thickness, yielding a mean value of 10.4 µm34 ; although the theory of the calculations is well established,2 there are uncertainties in assumptions of the model (e.g., in the values of viscosity, surface tension, and upper eye lid velocity and in the assumption that the upper tear meniscus is not depleted during its upward motion) that could be the basis of the discrepancy between that estimate and ours.
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Acknowledgements |
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Footnotes |
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Submitted for publication February 28, 2000; revised May 16, 2000; accepted May 24, 2000.
Commercial relationships policy: N.
Corresponding author: P. Ewen King-Smith, College of Optometry, The Ohio State University, 338 W. 10th Avenue, Columbus, OH 43210. king-smith.1{at}osu.edu
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