Page 40 - Computational Retinal Image Analysis

30 CHAPTER 3 The physics, instruments and modalities of retinal imaging

can also be obtained however from simplified models based on the Beer-Lambert law for
light propagation in absorbing media [11, 32] or the more accurate and complex modi-
fied Beer-Lambert law [22] for light propagation in scattering and absorbing media. The
Beer-Lambert law states that the intensity of light transmitted through a medium of thick-
ness l, extinction coefficient ε and concentration c is given by
I = Ie −ε cl (2)
t
o
where I o is the incident light intensity. For wavelengths between about 600 nm and
800 nm, ε is much higher for deoxyhemoglobin than for oxyhemoglobin (see Fig. 8)
and so oxygenated blood is more transparent than deoxygenated blood. The retina is
relatively transparent so light absorption by the highly oxygenated blood in the cho-
roid dominates the main spectral characteristics of the retina and explains the very
high reflectivity of the retina in red and infrared light.
For light transmission through the blood vessels, the Beer-Lambert law provides
a reasonable approximation to both the absolute absorption and also for calcula-
tion of the spatial intensity profile across the width of the vessel [23, 24]. For the
venules, which contain blood with oxygen saturations of 50–70% [25], and with a
maximum diameter of about 130 μm the product εcl is such that attenuation is typi-
cally sufficient to yield good contrast. For the deoxygenated blood in arteries, ε is
several times smaller and l also tends to be a little smaller (maximum caliber is about
100 μm). Consequently the product εcl is sufficiently small for arteries that arteries
have very low contrast, often almost transparent, in this wavelength regime. Between
the wavelengths of 500 nm and 600 nm the product εcl is relatively close to unity so
that contrast is moderately high and varies sufficiently strongly that it can be used as
to provide accurate measurement of blood oxygenation [23–27].
A lower value of extinction coefficient, ε, leads to a higher optical transmis-
sion in both the axial direction (as described above) and also for scattering in the
transverse direction to yield a more extended so-called tissue point-spread function,
which extends in three dimensions. At red and near infrared wavelengths this tis-
sue point-spread function is quite large (several mm) and leads to a smoothing of a
retinal image compared to in the green and blue where the tissue point-spread func-
tion is more compact (10 s of microns). A consequence of this is the smoothing of
the retinal images in Fig. 5 at the redder wavelengths. An additional consequence is
that, as shown in Fig. 4, blood vessels tend to be back illuminated by light that has
diffused through the choroid so that the most accurate value for l to be used within
the Beer-Lambert law corresponds to a single pass transmission through the blood
vessel, although there is a also contribution from light that has been transmitted twice
through the vessel [20, 32]. The ratio of single pass light to double-pass light can be
derived by calibration [33], fitting of multi-spectral data [26, 27] or Monte-Carlo
modeling [20, 21].
When a confocal SLO is employed, the dominant light path corresponds almost
exclusively to a double-pass through the vasculature increasing the contrast as can be
seen in Fig. 6. A so-called indirect SLO is also possible, which images only single-
pass, multiply-scattered light can be useful for enhancing the contrast of opaque