## Abstract

We present measurements of water absorption in human cornea *in vitro* with a differential absorption optical coherence tomography (DAOCT) technique. This technique uses two OCT images recorded simultaneously with two different light sources, one centered within (1488nm) and one centered outside (1312nm) of a water absorption band. We investigated the cornea under different conditions: First, a series of OCT images were recorded at different hydration states of the cornea, starting from a normally hydrated cornea to an almost completely dehydrated cornea. To investigate the influence of scattering on our measurements, the dehydrated cornea was re-hydrated with Deuterium oxide, which shows similar optical properties like water, but negligible absorption in the used wavelength region, and a similar series of OCT images was recorded. For a quantitative analysis, we averaged the OCT signals over adjacent A-Scans and performed a linear regression analysis of the logarithmic OCT signals versus imaging depth in the cornea for each wavelength. The difference of the slopes corresponds to the difference in the absorption coefficient, if the difference in the scattering coefficient is negligible. With the known difference in the absorption cross section it is possible to calculate the mean water concentration of the cornea.

©2003 Optical Society of America

## 1. Introduction

Optical coherence tomography (OCT) has developed to a powerful technique to obtain cross sectional images of ocular tissues [1–3]. Recent reviews of the technique can be found in references [4–6] Standard OCT images are based on the intensity of backscattered or back-reflected optical radiation. Several techniques have so far been introduced to gather additional information [7–9]. One promising technique regarding the measurement of water concentration in tissue is the differential absorption OCT-technique. This technique uses two different light sources with center wavelengths within and outside a water absorption band. To separate the effect of scattering from absorption, the scattering coefficients of the two wavelengths should be rather similar. There are many possibilities in choosing the center wavelengths. Water has absorption bands at, e.g., 1440nm, 1930nm and 2520nm [10]. For the choice of the wavelength one has to take into account that for longer wavelengths the absorption increases, but scattering decreases, with the advantage of improving the penetration depth in scattering tissue. The optimum wavelength region (in terms of penetration depth) therefore is where the total attenuation (scattering plus absorption) is a minimum. Schmitt *et al.* [11] were probably the first to introduce this technique to the field of OCT with the wavelength pair 1300nm and 1460nm. An alternative approach was published by Sathyam et al. [12] who used the slope of the interferometric signal to calculate water absorption. However these concepts were applied to non-biological samples only. Up to now no applications to imaging of absorption within scattering samples were reported.

Of great interest seems to be the knowledge of the spatial distribution of water concentration in human cornea [13], which could potentially contribute to future diagnostics and therapeutics in ophthalmology. In this paper we are presenting the first application of the differential absorption OCT-technique on biological tissue, and especially the first application on human cornea. We recorded a series of water absorption images, each taken at a different hydration state of the cornea. A second series was obtained, by re-hydrating the dehydrated cornea with deuterium oxide, which shows similar optical properties like water, but negligible absorption in the used wavelength range, thus enabling to differentiate between absorption and scattering effects.

## 2. Theory

If light propagates through a medium the light is attenuated due to scattering and absorption. The light intensity I after propagation through a thickness d of the medium can be described by Beer’s law

where I_{0} denotes the incident intensity, λ the wavelength, µ_{a} the absorption coefficient and µ_{s} the scattering coefficient.

The OCT signal, after rectifying and low-pass filtering, is proportional to the square root of the light intensities I_{s} and I_{r} returning from the sample and the reference arm, respectively:

K denotes a constant factor, which is given by the system specifications (e.g. detector responsitivity). I_{s}(z) depends on the reflectivity of the sample at a depth z within the sample, the signal intensity caused by coherent superposition of the electromagnetic fields from different scatteres within the coherence volume (speckle), and the position of the focal spot within the sample. If we take the logarithm of Eq. (2) and use Eq. (1) we obtain

where we have taken into account the double pass configuration of OCT, i.e. we have set the medium thickness d=2z. The differential absorption technique uses the OCT signals of two light sources at different center wavelengths, which minimizes the influence of the focal position and µ_{s}. By subtracting the logarithmic signals obtained from the two light sources we obtain

with Δµ_{a} and Δµ_{s} denoting the difference in the absorption and the scattering coefficient, respectively.

With the assumption of a constant incident and reference intensity, equal reflectivity of the sample and equal focal parameter for both wavelengths, Eq. (4) can be reduced to

Still present in this equation is the influence of speckle. Equation (5) is a linear function in z and the slope k is given by:

If we choose the center wavelengths of the two light sources in a way that the difference in the absorption coefficient is much larger than the difference in the scattering coefficient, the influence of scattering can be neglected, and k is a direct measure of the differential absorption coefficient. If we know the differential absorption cross section Δσ_{a} of the pure substance (measured by conventional spectroscopy) we are able to calculate the concentration c of the absorbing substance via

## 3. Experimental methods

The experimental setup, shown in Fig. 1, is based on a Michelson interferometer. Two different short coherence light sources can be used simultaneously. They are coupled by a wavelength division multiplexer (WDM) at the interferometer entrance and separated by a WDM at the interferometer exit, enabling independent, unbalanced recording of the corresponding interferometric signals. For exact position and velocity control an auxiliary Michelson interferometer illuminated by a He-Ne-laser is used, which shares the reference arm with the main interferometer. After correction of non linearities in motor scanning speed with the use of the signal from the He-Ne-Laser we applied a digital filter with bandwidths of 2.6kHz (1312nm) and 3.8kHz (1488nm) on the interferometric signals. Dynamic focusing ensures an improved signal to noise ratio and provides depth independent constant transversal resolution [14]. The chromatic aberration of the lens causes a slight constant offset in the focal point depths and hence in the amplitude of the interferometric signal. This has no influence on the slope of the signal. For this work we used two fiber pigtailed SLDs with center wavelengths at 1312nm (FWHM bandwidth Δλ=36nm) and at 1488nm (FWHM bandwidth Δλ=57nm), respectively. The corresponding roundtrip coherence lengths are 21 µm and 17 µm and remain unchanged after propagating through the optical setup. The coherence signals of the interferometric signals of the two wavelengths are recorded independently by two separate detectors. The emission powers of the SLD’s were 3.2mW for the 1312nm light source and 1.9mW for the 1488nm light source, respectively. On the sample we measured a power of 440µW (1312nm) and 240µW (1488nm). The system sensitivity was measured as 96dB for the 1312nm and 92dB for the 1488nm light source.

Human donor corneas from an eye bank were used in the experiments. Only hepatitis B positive corneas, which could not be used for transplantation, were taken. They were stored in a nutrient solution and removed from this solution immediately before the OCT imaging. For qualitative measurements it is sufficient to calculate the difference between the logarithmic intensity images recorded at the different wavelengths. For this experiment we recorded 1200 A-scans with a lateral step size of 7,5µm (transversal resolution ~8µm) at a scan rate of 8 scans per second. To reduce speckle noise we performed a floating average of the OCT image over an area of approximately 50µm×50µm before calculating the differential attenuation image. The results of these qualitative measurements and the corresponding intensity images recorded at each wavelength are shown in Fig. 2. The intensity images (Figs. 2(a) and 2(b)) are displayed on a logarithmic gray scale. In the differential intensity image (Fig. 2(c)) the attenuation is displayed in false colors, with attenuation increasing from blue to red. Only values above a threshold are displayed. This threshold was set by 1.5 times of the averaged noise level of each intensity image. Only intensity values which are above the noise level for both wavelengths were used for calculation, intensity levels below this threshold appear gray. Notable is the increase in the differential intensity in the central part of the cornea. Adjacent to this part on both sides are areas, where, due to the weak signals obtained at 1488nm, no reliable attenuation could be determined (cf. Fig. 2(b)).

To investigate the contribution of the difference in the scattering coefficient between the two wavelengths to the differential attenuation, we dehydrated the cornea and rehydrated it with Deuterium oxide. D_{2}O has similar optical properties as water but it shows almost no absorption in the 1488nm wavelength range. The intensity images at the two wavelengths and the corresponding differential intensity image of the D_{2}O rehydrated cornea are shown in Fig. 3. Figure 3(c) shows that there is no change in the differential intensity with penetration depth, which indicates, that the difference in the scattering coefficients at the two wavelengths is almost zero and that Fig. 2(c) is only determined by the difference in the absorption coefficients.

To investigate different hydration states, we made the following experiment: We recorded a set of tomograms, starting with a fully hydrated cornea (immediately after removal from the nutrient solution) we recorded a tomogram every 4 min. with a total of 20 tomograms (80 min.). During this experiment the water in the cornea evaporates, which results in a decrease of the cornea’s hydration as well as the cornea’s thickness. To reduce the measuring time only 400 A-scans per tomogram were recorded in this experiment, covering the central part of the cornea. After recording this set of tomograms we immersed the cornea into Deuterium oxide, until it gained its original thickness (and hydration state), and recorded another set of tomograms with similar timing. Image areas below a certain intensity threshold are displayed in black. The two tomogram series were combined to differential intensity image series and mounted to two movies showing the dehydration of the cornea with time. The upper part of Fig. 4 shows the dehydration of the cornea containing H_{2}O, the lower part that of the cornea containing D_{2}O. The movie clearly shows that the attenuation (red color indicates high attenuation; blue color indicates low attenuation) in the posterior part of the cornea containing normal water decreases with time (upper image) as expected from a reduced water content and a reduced thickness of the cornea, while the cornea containing the non-absorbing heavy water shows constant low attenuation independent of hydration state. The line at the top of the upper image is an artifact, probably from multiple reflections.

For a quantitative analysis the influence of speckle noise was reduced by averaging over all A-scans of each tomogram in Fig. 4. Figure 5 shows the averaged logarithmic intensities of the first tomograms (corresponding to the fully hydrated) of each set of the movies. The slopes of the logarithmic intensities recorded with the two light sources are significantly different in the case of the cornea containing water, whereas in the case of the cornea containing Deuterium oxide, the slopes are rather similar. We performed a linear regression analysis (Eq. (4)) of the difference of the logarithmic OCT signal amplitudes versus sampling depth in the cornea. To eliminate the influence of surface reflections, the areas near the surfaces were omitted in the calculation.

The linear regression therefore was calculated along an optical distance of approximately 600 µm for the first 12 images of a series. The last 8 images of a series were not included in the quantitative analysis, because the thickness of the cornea did not allow a linear regression with sufficient accuracy. The water concentration in the cornea was calculated via Eq. (5) and Eq. (7) (assuming a mean refractive index of 1.38 and a difference in the scattering coefficient of zero) and a difference in the absorption cross-section between the two wavelengths of 2/mm [10].

The water concentration of a cornea can be calculated in a different way with the use of an empirical formula, if the geometrical thickness of the cornea is known [15]. In our investigations we used this result as a reference for the differential absorption measurement. Figure 6 shows a comparison of water concentration obtained by differential absorption OCT with values obtained from the geometrical thickness of the cornea. Remaining speckle noise causes the deviations of the measured data points from the reference values and will be discussed in the next chapter.

## 4. Discussion

Speckles are the main source of error in the differential absorption OCT technique. Since the speckle fields recorded at two different wavelengths with emission spectra, which do not overlap, are completely uncorrelated, the speckle-induced intensity errors are added for the calculation of the differential absorption. Speckle can be characterized by the speckle contrast K:

with *σ* denoting the standard deviation and *A̅* denoting the mean value of the signal intensity [16]. Speckle in OCT are Rayleigh distributed and therefore the speckle contrast is 0.52 [17]. This contrast constitutes noise and can be reduced by averaging over adjacent A-scans, which is most effective, if the A-scans are statistically uncorrelated. This is the case if the lateral spacing between the A-scans is larger than the size of a speckle. The reduction in the speckle contrast is then ~N^{1/2} if N denotes the number of averaged A-scans.

Our method is based on a linear regression of the difference in the logarithmic signals. The error S_{k} of the slope is given by

with S_{y} denoting the error of the y values, N the number of statistically uncorrelated sampling points in depth and x_{i} the sampling point positions. S_{y} can be calculated from the speckle statistics in OCT [17] and the use of standard error propagation. N is given by

with x_{tot} the total depth over which the linear regression is performed, and l_{c} denoting the round trip coherence length. The error of the water concentration can then be calculated by

and Eq. (7). To investigate the error of our method and to compare it with the calculated values from Eq. (11), we recorded 100 adjacent tomograms consisting of 100 A-scans each (lateral spacing of 40µm) of a normally hydrated cornea with a lateral distance between the tomograms of approximately 60µm and calculated the water concentration of each tomogram. The result is given in Fig. 7. The calculated mean hydration of 86% with a standard deviation of 8% is in excellent agreement with the hydration calculated from the geometrical thickness of the cornea (85%). From Eq. (11) we calculated an error of the water concentration of 6%. The small difference between the theoretically expected error and the experimentally obtained error may result from a non-homogenous water concentration of the cornea.

We have shown, to the best of our knowledge for the first time, that the DAOCT technique can be used to measure the water concentration of a human cornea. We investigated the influence of scattering and made an error analysis based on the speckle statistics of OCT signals. The accuracy of the method can be increased in two ways: Averaging over more adjacent statistically uncorrelated A-scans and increasing the depth range over which the linear regression is performed. Since the maximum depth range is given by the cornea’s thickness, the accuracy can only be improved by a larger number of A-Scans.

## Acknowledgments

The authors wish to thank H. Sattmann and L. Schachinger for technical assistance and R. Amon, General Hospital of Vienna, for providing the donor corneas. Financial assistance from the Austrian Fonds zur Förderung der wissenschaftlichen Forschung (grant P14103-MED) is acknowledged.

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