Spectral reflectance of the human ocular fundus
Frangois C. Delori and Kent P. Pflibsen
Reflectance spectra from discrete sites in the human ocular fundus were measured with an experimental
reflectometer in the visible and near-infrared parts of the spectrum. The principal study population
consisted of ten subjects 22 to 38 years of age withba wide range of degree of fundus melanin pigmentation.
Reflectance spectra were obtained from the nasal fundus, the fovea, and an area 2.5°from the fovea. Spectra
were also recorded from several older subjects and from one aphakic patient with a coloboma. The
reflectance spectra were found to be influenced by the degree of individual and local melanin pigmentation of
the fundus, the amount of blood in the choroid, the transmission properties of the ocular media, and the
discrete reflections in the stratified fundus layers. Mathematical models of the optical properties of the
stratified layers are proposed and are fitted to the experimental fundus reflectance spectra. The models
account for the absorption by blood, melanin, macular pigment, and ocular media, and incorporate tissue
scattering and discrete reflectors corresponding to anatomical layers.
I.
Introduction
The interaction between light and intraocular tissues plays an important role in the application and
interpretation of optical methods for diagnosing and
treating ocular disease. Fundus photography, ophthalmoscopy, fluorescein angiography, psychophysical
testing, photocoagulation, and several noninvasive optical diagnostic methods are dependent on and, to
various degrees, affected by the absorption or scattering characteristics of tissues in the stratified layers of
the fundus. As these methods become more refined, it
is important to gain a better understanding of light
interaction with the fundus layers.
Fundus reflectometry has been used to investigate
the optical properties of the fundus,1-10 to study the
dynamics of visual pigments,1 1- 13 to obtain quantitative and qualitative information on the choroidal1 4 -17
and retinal1 8 circulation, to optimize photocoagulation,19 and to measure the amount of ocular melanin2 0
and macular pigment.2 1 22 Differences in spectral reflectance from various fundus sites are the basis of
color observation of the fundus and have been exploited in monochromatic photography.2 3 24 Although
these studies have provided useful results on specific
The authors are with Eye Research Institute of Retina Foundation, Biomedical Physics Unit, 20 Staniford Street, Boston, Massachusetts 02114.
Received 5 July 1988.
0003-6935/89/061061-17$02.00/0.
© 1989 Optical Society of America.
entities, they have not yielded detailed information on
spectral characteristics of fundus reflectance and on
the influence of melanin pigmentation. This may be
due to the limited spectral range and resolution used in
most previous studies and to the smallness of populations studied. Furthermore, the interrelated effects of
absorption by pigments and reflection or scattering by
tissues have not been systematically analyzed.
This paper presents measurements of fundus reflectance from 450 to 800 nm from discrete fundus areas in
normal subjects with a wide range of fundus melanin
pigmentation. The influence of the degree of fundus
melanin pigmentation and age on the reflectance spectra is examined in detail.
A first level of analysis
considers the effect of the individual ocular absorbers
and reflectors on fundus reflectance characteristics.
A second level combines information on the individual
absorption and scattering components into optical
(mathematical) models of the fundus layers and fits
these models to the experimental reflectance data. A
model proposed by van Norren and Tiemeijer1 0 was
evaluated and a new model, incorporating added complexity, was proposed and assessed.
II.
Experimental Methods
A.
Fundus Reflectometer
and Data Analysis
The experimental fundus reflectometer used in this
study is based on a modified Carl Zeiss fundus camera
(Fig. 1). Illumination for observation and focusing is
provided by lamp TL (maximum retinal irradiance: 7
mW cm- 2 , 5-min maximal permissible exposure
time2 5' 26). Polychromatic illumination for reflectance
measurements is provided by 3-ms flashes of the xenon
15 March 1989 / Vol. 28, No. 6 / APPLIEDOPTICS
1061
dent as far as light safety calculations are concerned.2 5
The resulting spectrum Sf,xwas recorded by means of a
monochromator
digital printer.
A reference spectrum
S
was ob-
tained after each fundus measurement by measuring
the light reflected from a barium sulfate surface (diffuse reflector, 96
±
3% reflectance, 400-1200 nm), lo-
cated 155 mm from the entrance pupil of the camera
(adjusted to be in the subject's pupil plane). If the
focal length of the eye is assumed to be 22 mm, the
equivalent reflectance of this reference is 0.96(22/155)2
= 1.9%. The reference spectrum was recorded with
the same flash power setting as used for fundus measurements and with the same illumination and sampling apertures. Light intensities for successive
flashes were constant within 5%.
The spectral reflectance R, of the fundus was calculated for each wavelength Xby
R = 0.019
Fig. 1. Diagram of the experimental
fundus reflectometer.
See
text for explanation of symbols. Unmarked components are standard optical parts of the fundus camera.
arc lamp FL (maximum retinal irradiance: 70 mJ cm-2 , 36%of the maximum permissible exposure2 5' 26).
An aperture FA, located in the illumination beam in a
plane conjugate to the retina, limits the illumination to
a circular fundus area of -5° in angular diameter (visual angle). The light reflected by the fundus is imaged
by the camera optics in the plane of a diaphragm MA.
The latter is initially open (6°), allowing the observer
to focus and to align the camera, via mirror SM, on the
fundus area of interest. The diaphragm is then closed
to define the sampling area of 1-4° in diameter. The
diameter of the sampling area is noted for each measurement from a graduated scale visible through the
eyepiece. Rotation of SM activates the xenon flash,
and the light sampled by MA is imaged by lens R on a
fiber optic LF. The input face of this fiber is located in
a plane conjugate to the entrance pupil of the optical
system, and its output face, which is slit-shaped, serves
as the entrance slit to a grating monochromator. The
intensity distribution in the dispersed spectrum is
measured simultaneously at all wavelengths by a Vidicon camera used in conjunction with a multichannel
analyzer (Princeton Applied Research). This system
allows integration and storage of reflected light intensities on 512 wavelength channels. The spectral range
of the reflectometer system is 400-912 nm (700-1212
nm after monochromator adjustment). The effective
spectral resolution of the system is 7.5 nm.
Two or
three spectra from one fundus site were generally accumulated in the instrument's memory to improve the
signal-to-noise ratio. These repeated measurements
were recorded with at least 5-s intervals to allow for
alignment and can therefore be considered indepen1062
APPLIEDOPTICS / Vol. 28, No. 6 / 15 March 1989
n,
S, )
(1)
where n and nr are the number of flashes used to
record the fundus and reference spectra, respectively.
Each reflectance spectrum was plotted as log reflectance vs wavelength. For each spectrum, reflectances
at twenty selected wavelengths (listed in Table I) were
tabulated for statistical analysis and curve fitting using RSE software (BBN Research System).
The calculated fundus reflectances represent total
fundus reflectance (integrated over all angular directions) only if the eye had perfectly transparent media,
a focal length of 22 mm, and a perfectly diffuse reflecting fundus. Although corrections could be made to
account for media transmission2 7 and for focal length
differences, it is not possible to measure the angular
distribution of the reflected light and therefore determine which fraction of the reflected light is collected
by the entrance pupil of the reflectometer. Because of
Table 1. Average Fundus Reflectance for Ten Subjects at Three Different
Sites
Equivalent reflectance in %
Wavelength
(coefficient of variation in %)
(nm)
Nasal fundus
Perifovea
Fovea
445
455
480
505
522
540
548
560
565
569
575
586
595
610
640
675
705
728
750
805
1.01 (18)
1.14 (14)
1.44 (13)
1.82 (23)
1.94 (24)
1.88 (18)
2.04 (20)
2.25 (26)
2.27 (26)
2.24 (23)
2.20 (21)
2.72 (33)
4.17 (44)
6.36 (47)
8.46 (46)
10.21 (43)
11.28 (40)
11.82 (38)
11.94 (36)
12.52 (30)
0.68 (32)
0.73 (31)
0.89 (31)
1.20 (26)
1.41 (23)
1.44 (22)
1.53 (23)
1.61 (22)
1.61 (22)
1.61 (22)
1.62 (22)
1.88 (23)
2.62 (34)
3.99 (49)
5.79 (55)
7.70 (53)
8.93 (49)
9.71 (46)
10.42 (43)
11.27 (36)
0.23 (29)
0.25 (30)
0.33 (30)
0.58 (26)
0.94 (18)
1.11 (14)
1.18 (13)
1.24 (14)
1.26 (15)
1.28 (15)
1.29 (16)
1.48 (18)
2.11 (30)
3.30 (49)
4.97 (54)
6.68 (52)
7.83 (50)
8.63 (46)
9.30 (44)
10.37 (38)
these limitations, we refer to our measurements as
"equivalent
reflectances."
M=
E
2
(2)
- RmodX),
WX(RObsX
n1
1i0
where n is the number of wavelengths (n = 19), and Wx
B.
Subjects and Measurement Sites
Our principal study population was composed of ten
normal subjects ranging in age from 22 to 38 years and
with no ocular abnormalities. Two subjects were
Black and eight were Caucasian. Among the latter,
two subjects had brown irises, three hazel or green
irises, and three blue irises. The pupil of one eye of
each subject was dilated to a diameter of at least 6 mm
with 1% benzeneacetamide (Tropicamide). The subject's head was stabilized on the chin rest of the cam-
is a weight assigned to each wavelength measurement.
We used WA = Robs,X-1 as a compromise between equally weighting absolute errors at different wavelengths
(Wx = 1) and equally weighting relative errors (WA =
Robs,- 2 ).30
For each completed fit, we calculated the standard
error associated with each parameter, the F/ratio, the
statistical significance, and a relative error (RE in %)
defined as
RE = 100 [(1/n)
era. Reflectance spectra were also recorded from sev-
eral older subjects (age 60-65 years) and from one
aphakic patient (age 74 years) with a coloboma in one
eye.
Reflectance measurements were recorded for the ten
young subjects from the nasal fundus, the perifovea,
and the fovea. These sites were selected because they
present substantial differences in anatomy and in pigment content. Spectra were also recorded from the
optic disk, and those results will be reported in another
communication.2 8 In this study, the illumination area
was always 5 in angular diameter. For the nasal
fundus, the measurement was made (nf = 1-2) at about
1 disk diameter from the disk edge, in an area devoid of
large retinal vessels, with a sampling area of 3-4 in
diameter (fixation: subject looking at a fixation target
with fellow eye). The sampling aperture used nasally
was larger than that used for the other sites to minimize the variability associated with nonuniformities in
the nasal fundus. For the perifovea, a measurement
consisted of the average of four measurements
(nf = 4)
obtained at 2.50 from the fovea in the horizontal and
vertical directions, with a sampling area of 1.2-1.6 in
diameter (fixation: subject looking at top, bottom,
left, and right side of the illuminated area with measurement eye). For the fovea, the measurement (nf =
2-3) was made centered on the fovea, with the same
sampling area as for the perifovea (fixation: subject
looking at center of illuminated area using a crosshair
with open intersection).
C.
Curve-Fitting Procedure
Two mathematical models representing the optical
properties of the fundus layers are analyzed in this
study (see Sec. V). In each case, the reflectance predicted by the model (RmodX) was represented
by a
complex function of unknown parameters. The observed fundus reflectances (Robs,0) at nineteen wavelengths (listed in Table I, except for 445 nm) were
fitted to the Rmod,X function using the curve-fitting
procedure CURFIT described by Bevington.2 9 This
very efficient algorithm makes a least-squares fit to a
function, which may be nonlinear in its parameters,
using a combination of a gradient search with an analytical solution developed from linearizing the function. The unknown parameters were found by minimizing a figure of merit M defined as
.
E (R0 bSX- RmodX)2/Robs X
(3)
To characterize the goodness of the regressions for all
spectra at each of the three sites, we used two criteria.
First, we calculated a pooled relative error (PRE in %)
given by
E
I
~~~~~~~~~~~~~~1
F
PRE = 100 [(/ns)
(R.,.,, - Rmod,) /Robs,X
(4)
where s is the number of spectra at one site (s = 10).
Second, we computed the average F/ratios (AFR) of
the regression for all spectra at one site.
Ill.
Fundus Reflectance Spectra
A.
Experimental Results
Reflectance spectra from the nasal fundus (N), the
perifovea (P), and the fovea (F) for the ten young
subjects are shown in Figs. 2(a) and (b). Table I gives,
for the twenty selected wavelengths, the average reflectances and coefficients of variation for the three
sites. Figure 3 (top) shows spectra recorded at different sites between the arcuate bundle and the macula in
one subject to illustrate changes in reflectance spectra
with fundus location. Figure 3 (bottom) shows the
reflectance spectra recorded at a choroidal nevus and
in the area surrounding that nevus to demonstrate the
effect of a marked variation in choroidal melanin pigmentation.
Fundus reflectance at all sites was always lowest at
the shortest wavelength measured (445 nm) and highest at long wavelengths (>640 nm). Measurements on
two subjects for wavelengths >800 nm (results not
shown) revealed a pronounced reflectance minimum
centered at 790 nm, a maximum around 1070 nm, and
no reflectance above 1200 nm. These characteristics
correspond with the absorption spectrum of water in
the ocular media. Similarly, the slight irregularities
observed in the spectra around 760 nm (Figs. 2 and 3)
may correspond with a weak absorption band of water
centered at that wavelength. As the degree of melanin
pigmentation increases, the wavelength of maximal
reflectance lengthens and the reflectance decreases.
This reduction is more pronounced in red than in green
light: the ratio of the reflectance of the lightest fundus
(subject 1, Fig. 2) and that of the darkest fundus (subject 10) is -6 at 675 nm, but only -1.7 at 575 nm.
Similarly, the coefficients of variation associated with
15 March 1989 / Vol. 28, No. 6 / APPLIEDOPTICS
1063
100.
........................................
(a)
80
1
2
3
4
5
a)
C)
F
N
a'
NN
N
P
F
N
P
F
20
P
F
P
N
a)
N
LL
a:
/
1.0
-a
P~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
NI
P
N
P
N
N~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
a)
F
F
03
0.
2
450
F
550
650
750
450
550
650
750
450
1
.
550
650
750
450
S50
650
750
450
550
650
750
Wavelength (nm)
100
l(b).
6
7
8
9
10
a)
N
F
p
N
P
._
U)
N
a,
F
N
~~~~~~P
P
F
C
UCL
1.0
N
N
N
P
P
N
N
,P
P
~~~~~~~~~~~~P
I
a,
F
0U
F
0.1
450
550
50
750)
450)
550
i50
750
450
F
550
650
750
450
F
550
r650
750
450
550
650
750
Wavelength (nm)
Fig. 2. Reflectance spectra from the nasal fundus (N), the perifovea (P), and the fovea (F) in ten subjects (1-10) with different degrees of ocular melanin pigmentation. Subjects 1-8 were Caucasians with blue irises (1,2,3), green or hazel irises (4,5,6), brown irises (7,8), and subjects 9
and 10were Black. The illumination area was 50 in diameter in all cases, and the sampling area was -4° for the nasal data and 1.6° for the
macular data.
the mean reflectance (Table I) are substantially larger
for red light (45-55%) than for blue and green light
(13-26%). An extreme example of the lower dependence of green light reflectance on the choroidal melanin concentration is that of the nevus (Fig. 3, N and S):
the green light reflectances are about equal for the
nevus (N) and the surrounding area (S), but the red
light reflectances are different.
All spectra reveal to various degrees the absorption
characteristics
of oxyhemoglobin
(Fig. 4).
Distinct
reflection minima or inflections in the spectra at 540
and 575 nm correspond to the absorption maxima of
oxyhemoglobin at those wavelengths, and the pronounced increase in the reflectance for wavelengths
longer than 575 nm corresponds to the dramatic decrease in hemoglobin absorption in that spectral range.
With increased ocular pigmentation there is a marked
reduction of the prominence of the hemoglobin absorption bands at 540 and 575 nm. The reflectance
maximum at 560 nm, seen clearly in the lightly pigmented fundus, and the increase in reflectance above
1064
APPLIEDOPTICS / Vol. 28, No. 6 / 15 March 1989
575 nm become gradually less pronounced as the de-
gree of pigmentation increases. The flattening of the
blood spectra observed with increased degree of individual melanin pigmentation is also seen with changes
in local pigmentation between the nasal (Fig. 2, N) and
macular (P and F) sites, and between a site above the
arcuate bundle (Fig. 3, spectrum 1) and the macula
(spectrum 5). The hemoglobin absorption bands of
the macular spectra show distinct flattening, even in
the lightly pigmented eyes where the reflectance maximum at 560 nm is barely resolved. The sudden increase in reflectance for wavelengths longer than 575
nm is less marked than nasally, but is nevertheless
always detected even in the darkest fundi investigated
(subjects 9 and 10).
Two-way analysis of variance (three sites, ten subjects) performed separately for each wavelength of
Table I showed that fundus reflectance was significantly (p < 0.05) affected by choice of site for all
wavelengths, and by subject for wavelengths longer
than 575 nm. This confirms that variation in degree of
I
(0=
10 0
2
4
5
.0
c
10
-
0)
5U)Z
a)
C
a)
°I
0()
0)
0
S
N
C:
a)
0
I
C
Ca
0
0
Hb
1.0-
0
0
C.)D
C
L
Cr
c~
x
aw
S
N
0.
I
400
500
600
700
8600
Wavelength(nm)
Fig. 3. Top, reflectance spectra from subject 2 for an area superior
to the arcuate bundle (spectrum 1), for an area centered on the fovea
(spectrum 5), and for three equally spaced areas between the previous sites (spectra 2-4). Bottom, reflectance spectra from subject 4
in an area centered on a choroidal nevus (N) and from an area
adjacent to the nevus (S). These spectra were offset by a factor of 10
toward lower reflectances to avoid overlap with the other spectra.
The reflectance in the 530-580-nm range was slightly higher for N
(nm)
Wavelength
Fig. 4. Absorption characteristics of the ocular pigments. HbO 2 ,
9
oxygenated hemoglobin, data from van Assendelft3 ; right scale,
extinction coefficients of hemoglobin with an oxygen saturation of
15 mg/100 mliter). Data were
95% (hemoglobin concentration:
ME, melaaveraged over the 7-nm bandwidth of the reflectometer.
4
3
nin, data from Gabel et al.3 and Menon et al.3 (solid line) and from
Geeraets et al.3 5 (interrupted line), representing extremes in the rate
of spectral dependence; relative scale. MP, macular pigment, data
from Snodderly et al. 44 ; left scale, approximate optical density in
humans.
optical density for the standard observer.
than for S. Examination of fundus photographs showed slight
alteration in the RPE in the area of the nevus. Both sets of spectra
were obtained with an illumination aperture of 50 and a sampling
area of -4°.
Pairpigmentation is mainly manifested in red light.
wise comparisons via the Scheffe method3 l indicated
further that, with a confidence of 95%,the reflectance
of the nasal fundus was significantly higher than that
of the perifovea (455 < X < 725) and that the reflectance of the perifovea was significantly higher than
that of the fovea (455 < X< 575). The latter difference
is most marked for X < 520 nm (Fig. 2) and is caused by
the absorption by the macular pigment in the fovea.
B.
Comparison with Other Studies
Reflectances of the human fundus are affected by
variations in the degree of fundus pigmentation and by
variations related to the fundus site measured. Hence
it is difficult to accurately compare our results with
those obtained in other studies,1,6"0,2 0 ,21 often on a
single site in only a few subjects.
Comparison is fur-
ther complicated by differences in reflectometry
methods, particularly with regard to reflectance references, spectral resolution, area of sampling, and illumination field. Best agreement between different studies appears to occur for the green spectral range,
especially with regard to foveal measurements. However, most studies, with the exception of that of Hunold and Malessa, 2 0 do not reveal the spectral detail
seen here, particularly with regard to the hemoglobin
absorption bands. This results from the larger num-
7
OM, ocular media, data of van Norren and Vos2 ; left scale,
ber of wavelengths recorded by Hunold's and our technique which allow better resolution of the hemoglobin
spectral bands. Variability of results among studies is
largest for red light measurements. This may be due
to the inherent large variability of red light reflectance
associated with variation in degree of melanin pigmentation (Table I). Results for wavelengths shorter than
500 nm are also more variable than those in green light.
Our data correspond well with those of Brindley and
Willmer, 2 ' Charman, 8 and van Norren and Tiemeijer,10 but the other studies 6 20 report larger reflectances. This appears to be related to a larger contribu-
tion from backscattering in the ocular media
associated with the larger illumination areas used in
the latter studies. Indeed, for constant retinal irradiance, light density in the lens and hence the amount of
backscattered light, increases with the area of illumination.
IV.
Optical Constituents of the Fundus
Interpretation of the reflectance spectra requires a
working knowledge of the absorption properties of the
various pigments and of the reflection and scattering
properties of the different anatomical layers of the
fundus. Analysis of the spectra is aided by distinct
spectral signatures of some pigments (oxyhemoglobin,
macular pigment), but complicated when the absorption and/or scattering properties vary monotonically
throughout the spectrum (melanin, ocular media, and
tissue scattering). We discuss the optical properties
15 March 1989 / Vol. 28, No. 6 / APPLIEDOPTICS
1065
of various constituents of the fundus layers and relate
those with observed reflectance characteristics.
0.37 t 0.20 D.U. The RPE density showed no racial
dependence. 3 6 One can estimate, from the highest
RPE density measured (0.8 D.U.),3 3 that the extinction
A.
coefficient of melanin
Ocular Pigments
Fundus reflectance characteristics are strongly influenced by the absorption of light by blood throughout the fundus, by melanin pigment in the choroid and
retinal pigmented epithelium (RPE), by macular pigment in the fovea, and by the ocular media. Absorption by visual pigments does not affect the present
reflectance data since more than 99.5% of the photopigments are bleached by the observation light (6.8
32
log troland units).
To facilitate initial interpretation of our results, we
use the Lambert-Beers law to derive information on
different pigments. We assume that all the light incident on the fundus is transmitted by all pigments,
reflected by a posteriorly located reflector with reflectance Rb,x\, retransmitted by the pigments, and detected by the reflectometer.
tance RA is given by
logRx = logRb 6
In that case, fundus reflec-
-
Kp - dp
2
Kpa Dp,x
(5)
p
where Kpx is the absolute extinction
coefficient for
each pigment (p), dp is the single-pass path length,
K' are the relative extinction coefficients normalized
at X, and DpAn is the single-pass optical density at a
normalizing wavelength X. The highly simplified
fundus reflectance model, described by Eq. (5), will be
referred to as model I.
The degree of melanin pigmentation of the fundus
appears to be the most important variable affecting
magnitude and shape of the reflectance spectra. The
absorption spectrum of melanin is generally found to
decrease monotonically with increasing wavelength
throughout the visible spectrum. Measurement by
Gabel et al. 3 3 on RPE melanin and by Menon et al. 3 4 on
iris melanin showed a -4.6 spectral dependence of the
absorption coefficient around 550 nm (ME, solid
curve, Fig. 4). Other studies showed flatter spectra,
with the absorption spectra recorded by Geeraets et
al. 35 (ME, interrupted line, Fig. 4) demonstrating the
weakest dependence (X-2.2). In vitro studies by Weiter et al.3 6 of melanin pigmentation have shown that,
for a population of Caucasian and Black subjects, the
optical density (500 nm) of choroidal melanin at the
posterior pole varies between 0.2 and 4 D.U. (Density
Units),3 7 with a marked racial dependence. Fundus
reflectance, assuming double passage of light through
the choroid, does not reveal this large density range,
indicating substantial flattening of the melanin absorption spectrum. The optical density (500 nm) of
the RPE at the posterior pole was found by Weiter et
36
3
1066
(Caucasian), and brown (Black) irises, respectively.
The Spearman's p were 0.94 (p < 0.0001), 0.75 (p <
0.02), and 0.82 (p < 0.004) for the nasal fundus, perifovea, and fovea, respectively. The correlations between iris color and the amount of melanin in the
defined) always showed negative p. However, these
correlations were statistically significant only in the
595-750-nm range for each site and in the 480-505-nm
range for the nasal fundus (low absorption by blood).
2. Blood (Hemoglobin)
Absorption of light by blood occurs primarily in the
highly vascularized choroid. The contribution of reti-
nal capillaries is small as they occupy a volume of 0. 15
gt liter
cm- 2 of fundus3 8 or an equivalent blood layer
-1.5,gm thick.
Melanin
to be 0.27
ranked as 1, 2, 3, and 4 for blue, green or hazel, brown
choroid are expected since choroid and iris are part of
= logRb,\ - 2
al.
is at least 800 cm- 1 (as-
the same anatomical layer (the uvea). Rank correlations between iris color and fundus reflectances at
wavelengths other than 675 nm (where the P index is
p
1.
Kme,500
suming -10-um thick RPE cells).
To characterize fundus melanin pigmentation, we
used, as did Hunold and Malessa,2 0 a melanin pigmentation index defined as P index = -ogR 6 7 5 . Absorption by choroidal blood is very low at 675 nm and ocular
media transmission is highest (Fig. 4). Under the
assumption of Eq. (5), the P index is linearly related to
the amount of melanin. The P indices of the nasal
fundus, perifovea, and fovea correlate significantly
with each other (all p < 0.001). The P indices for the
three sites also correlate significantly with iris color,
0.08 D.U.,
7
and by Gabel et
al.33
to be
APPLIEDOPTICS / Vol. 28, No. 6 / 15 March 1989
The average oxygen saturation of cho-
roidal blood is high, because the arteriovenous oxygen
saturation difference in the highly perfused choroid is
small. As a result, the absorption spectrum of choroidal blood is essentially related to that of oxyhemoglobin (Fig.4).39 The blood volume in the human choroid
is not known with accuracy. Comparison of the ultrasonographically determined choroidal thickness in
vivo, 350-450 m,40 41 with the thickness in enucleated
eyes, 200-250,gm, 4 2 allows one to estimate that 30-60%
of the choroid is occupied by blood, in the assumption
that vascular collapse is the primary reason for the
difference in thicknesses.
41
Interpretation of the blood signature on the reflectance spectra is facilitated by considering a particular
property of the oxyhemoglobin absorption spectrum,
which is that light absorption by oxyhemoglobin is
approximately equal at 455, 540, and 575 nm (Fig. 4).
The extinction coefficients Kb at these wavelengths,
when averaged over the spectral bandwidth of the
reflectometer, are within 5% of each other, and this
equality is maintained at other oxygen saturations.
Figure 5 shows how this property is used to associate
with any fundus reflectance spectrum, a hypothetical
spectrum R, for which the extinction coefficient Kb of
blood would be a constant.
The slope of the logRA
expected amount of blood in the choroid. This is
especially true if one considers the sole contribution of
the choriocapillaris, which forms a quasicontinuous
vascular sheet, -10 ,m thick.4 3 If reflection from the
fundus involved reflection from the choroid only, one
would expect the reflectance spectra to at least show
the spectral signature of the choriocapillaris. This
may be the case for lightly pigmented fundi using the
610-nm estimate of dhb, but not for darker fundi and
CO
IDI
LL
for all values of the 560-nm estimate.
540
455
t575
560
610
Wavelength(nm)
Fig. 5.
Schematic reflectance spectrum from the fundus with the
The RXspectrum drawn through the
hypothetical spectrum R.
455-, 540-, and 575-nm points of the real spectrum (logRx) always
shows a slight negative curvature. The logR* spectrum represents
fundus reflectance if blood were replaced by a spectrally neutral
absorber with extinction coefficientKb (= Khb,455 = Khb,540 = Khb,575,
see Fig. 4). This spectrum is influenced by melanin absorption,
ocular media transmission, etc., but not by spectral changes in blood
absorption. Because of the low curvature of logR, one can assume
that logR< varies linearly with X beween 540 and 610 nm, and logRx
can then be calculated by intra- or extrapolation along a line through
the 540- and 575-nm points. The differences, at 560 and 610 nm,
between the logRx and the logR; spectra are used in Eq. (6) to
estimate the amount of blood responsible for the hemoglobin spec-
tral signature on the fundus spectra.
spectrum at -550 nm was not significantly different
for the three sites and was on average 0.17 J 0.06 log
reflectance units per 100 nm (all sites, n = 30).
To estimate the amount of blood sampled by reflec-
tometry, it is possible to calculate the thickness of an
equivalent layer of blood that would be needed to
account for the observed spectral signature of blood on
the fundus spectra. Assuming that all the incident
light traverses this blood layer twice with reflection by
deeper layers, we use Eq. (5) for logRx (extinction
coefficient Khb,x) and for logR' (extinction coefficient
Khb). The reflectance of the deeper layers and the
contribution of all nonblood terms can then be eliminated, and the blood layer thickness dhb (arterial
blood) is then derived as
logR,\
dhb
-
2
-
We can con-
clude that reflectometry samples the choroid only partially, that a substantial amount of light is reflected
anterior to the choriocapillaris, and that light penetration in the choroid is less pronounced at 560 nm than at
610 nm. A reflector must be located anterior to the
choroid (Sec. IV.B.2), and light transmitted by this
reflecting layer must, in darkly pigmented fundi, be
strongly absorbed in the choroidal stroma.
3. MacularPigment (Xanthophyll)
The macular pigment is located in the inner retinal
layers and extends over an area of 0.5-2.0° in diameter,
centered on the fovea.2 4 44 The spectral signature of
this pigment, with its high absorption in blue light
(Fig.
4),44
is recognized in most subjects (Fig. 2) by the
fact that foveal reflectance Rf, is lower than the perifoveal reflectance Rp,\ for X < 520 nm.
An estimate of the macular pigment density can be
obtained by comparing the foveal reflectance to the
perifoveal one. Following Brindley and Willmer2 l and
van Norren and Tiemeijer,1 0 we assume that all the
light reflected from the fovea is reflected by the deeper
layers with double transmission through the macular
pigment. Applying Eq. (5) for the fovea (reflectance
Rfx, macular pigment density Dmp,460) and for the perifovea (reflectance Rpx,assuming no macular pigment),
after subtraction one finds
log f,\ = log
RP,A
'
R ,A
2
-D
K'
PX
(7)
mp4
where R >x and Rpx are the reflectances of the deeper
layers at the fovea and perifovea, respectively. KmpX
is the extinction coefficient of the macular pigment,
normalized at 460 nm (Fig. 4). For each subject, the
data at 445, 455, 480, 505, 522, 540, and 548 nm were
fitted to Eq. (7), assuming that the ratio Rcx/Rp,,
logR~
(KhbX - K4b)
(6)
The thickness dhb was calculated for X = 560 and 610
nm (Table II), with logR' computed as indicated in Fig.
5. The significant decrease in dhbwith P index demondecrease in the apstrates a pigmentation-dependent
Table II.
Equivalent BloodLayer Thickness Calculated with Eq. (6) at
560 and 610 nm for Three Sites inTen Subjects
Wavelength
Equivalent
blood layer
Linear correlation
thickness dhb
of dhb with the
P index
parent amount of blood sampled by reflectometry.
(nm)
Site
in /im
Equivalent blood layer thicknesses dhbare substantially higher for the estimation at 610 nm than at 560 nm,
560
Nasal fundus
3.9 ± 2.7
-0.73
Perifovea
Fovea
2.1 i 0.8
1.5 ± 0.7
-0.50
-0.08
n.s.
n.s.
6.1
-0.90
p < 0.0004
indicating that the simple model (in which all the
reflected light traverses the blood layer) cannot be
reconciled with fundus reflectance spectra.
The absolute values of the equivalent blood layer
thickness (Table II) are very small compared to the
610
Nasal fundus
14.9
Perifovea
Fovea
12.7 ± 6.0
12.6 ± 6.4
+
p <0.02
-0.92 p < 0.0002
-0.94 p < 0.0001
15 March 1989 / Vol. 28, No. 6 / APPLIEDOPTICS
1067
(which accounts for reflectance difference in the absence of macular pigment) was wavelength independent. For the ten subjects, Dmp,460was found to vary
. . . . . . . .
1001.
Sc
between 0.12 and 0.32 D.U., with a mean of 0.19 ± 0.06
D.U. (single pass). The factor log(Rf \/Rp,\) was 0.10
CO
+ 0.08,and all regressions were statistically significant
(worst case: p < 0.02). The individual Dmp,460 results
c
for absorption by the macular pigment.
a:
will be used in the optical model (Sec. V.A) to account
4. Ocular Media
Equivalent reflectances are affected by absorption
in the ocular media, which are traversed by both the
incident and reflected light. Transmission through
the media of young subjects increases rapidly from 400
to 550 nm and reaches a constant value of -80% above
45
650 nm.
ing contribution
depends on field size and can be
estimated to be 0.1 D.U. (80%transmission) for the
aperture sizes used here. 4 6
With age, there is a decrease in the transmission of
the media and an increase of the slope of the transmission spectrum. 4 5
This is seen in Fig. 6 for the spectra
recorded from the nasal fundus of two older subjects
(N60 and N64): a faster decrease in reflectance with
decreasing wavelength is observed compared to young
subjects. Indeed, the slope of logR\ spectrum (Fig. 5)
was 0.30 and 0.34 log reflectance units per 100 nm,
compared with 0.17 + 0.06 for the young subjects (Sec.
IV.A.2). The spectrum of the aphakic eye (Fig. 6,
N74) had a slope of 0.11, smaller than those of the
young subjects, indicating that the crystalline lens is
the major contributor to ocular media absorption and
scattering. Thus, ocular media have an important
influence on measured fundus spectra of older subjects; however, they are not expected to play a major
role for the young subjects in this study.
Ocular Reflectors
1. Sclera
The sclera is often considered the most important
reflector in the fundus. Smith and Stein4 7 measured
its reflectance on enucleated eyes as 50-70%at 675 nm.
Alpern et al.4 8 measured scleral reflectance in three
subjects with ocular colobomas as
30% at 675 nm.
Our measurement in an aphakic subject with a coloboma (Fig. 6, CO) also indicated an equivalent reflec-
tance of
transmission
33% at 675 nm.
With an ocular media
of 70-80%, this would correspond to a
scleral reflectance of 40-50%. The scleral reflectance
decreases slightly with increasing wavelength, as seen
for the coloboma (Fig. 6, CO) and from measurements
of the scleral reflectance at the conjunctiva (Fig. 6,
1068
10-
0
N64
cn
cC
CO
cc
cc
C.
w
I-
UJ
Van Norren and Vos27 compiled literature
data on media density in young subjects (ages 20-30),
and derived an optical density spectrum for a standard
observer (Fig. 4). They showed that these densities
correspond to subject-dependent light absorption in
the media, and that a wavelength-independent contribution must be added to the absorption term to account for light scattering in the media. This scatter-
B.
CO
N60
N74
APPLIEDOPTICS / Vol. 28, No. 6 / 15 March 1989
10. ! I !
400
!
500
1 i
600
700
I
I
800
4
Wavelength(nm)
Fig. 6. Reflectance spectra from the nasal fundus (N) in three
subjects with age as indicated.
The 74-yr old subject was aphakic;
the other two subjects were phakic. CO,reflectance spectrum from
a coloboma in the 74-yr old aphakic subject. These measurements
were obtained with an illumination aperture of 5 and a sampling
area of 40. SC, reflectance from the sclera at the conjunctiva in a
young subject (2). This measurement is relative as no absolute
reference was used in this instance. The absorption bands of blood
from the conjunctival capillaries are clearly seen; the interrupted
line is the R spectrum associated with the SC spectrum (see Sec.
IV.A.2). These spectra demonstrate that scleral reflectance decreases continuously with increasing wavelength.
SC). The latter reflectance was found to decrease by a
factor of 2.2 ± 0.6 between 500 and 800 nm (four young
subjects).
2. Reflectorsin the Retinal Layers
Reflections by the deeper retinal layers have been
shown in separate experiments to originate from layers
between the photoreceptors and Bruch's membrane,2
from layers between the photoreceptors and the choriocapillaris,17 from the RPE or sites close to the
RPE,5 7, and from the photoreceptors.3' 9 Interpretation of monochromatic fundus photographs2 3 2 4 also
supports the existence of reflections originating at the
level of the RPE.
The analysis of our spectra, using the argument involving the spectral signature of the choriocapillaris
(Sec. IV.A.2), argues for the existence of one or several
reflecting layers anterior to the choriocapillaris. For
green wavelengths, these layers reflect a substantial
amount of light resulting in a poor sampling of the
choroidal space by the incident light. The poor penetration of green light in the choroid was also strikingly
demonstrated by the spectra of the nevus (Fig. 3, S and
N), which show the inability of green light reflectance
measurements to detect the increased melanin concentration in the choroid.
The photograph of Fig. 7 clearly demonstrates the
presence of a reflecting layer, by the fact that distinct
(c)
(b)
(a)
RX
om e
.
phr
rpe\
bm -
1111 I I
IIII
E
D..
Do.,
D~mp
r ji
D.
Dmp
D
Dpc
Dine
cc
*x
D.e
-_
dhb
chs
S.
dhb
D,,
l
rM
SC -
Model III
Model II
of the fundus layers:
(a) Schematic representation
Fig. 8.
rSt
om,
ocular media; im, inner limiting membrane; phr, photoreceptors;
rpe, retinal pigmented ephithelium; bm, Bruch's membrane; cc,
choriocapillaris; chs, choroidal stroma; and sc, sclera. (b) and (c)
Diagrams for model II and model III, respectively. Parameters with
an asterisk are fixed; the others are adjusted by curve fitting in each
model. The D symbols represent single-pass densities, r, reflec-
tances, and d, blood layer thicknesses.
Fig. 7.
Fundus photograph obtained using oblique illumination of
the fundus. An illuminating fiber optics was applied on the conjunctiva. The angle of incidence of light at the posterior pole of the
eye was estimated to be 30°, and the projected direction is indicated
by an arrow. The distance between the vessel and its shadow is 149
± 10 ,tm (average of sixteen sites). The shadow is formed on a
surface located -140/tan (300) or 240 Am posterior to the vessels.
shadows of the retinal vessels can be observed when
the fundus is obliquely illuminated. The shadows are
formed on a surface capable of localized reflection and
located -240 gm posterior to the retinal vessels and
thus at the level of the RPE or the anterior choroid. A
located near
similar demonstration of a reflecting layer
the RPE was given by Mori et al.4 9 by projecting
through the pupil a very fine slit of light obliquely on
the fundus. Detection of the reflections at a different
angle demonstrates two discrete reflections:
one orig-
inates at the limiting membrane and the other from a
to the limiting membrane (at
layer 280 gm posterior
50
2.50 from the fovea).
Specular reflections from the inner limiting membrane are easily detected by ophthalmoscopy (especially in darkly pigmented fundi), and several studies
have suggested that the limiting membrane is the principal origin of retinal reflections.4 5 7 The intensity of
this reflection depends critically on curvature and orientation of the retinal surface, on direction of the
incident light, and on position of the entrance pupil of
the detecting system.9
V.
Optical Models of the Fundus
Each fundus layer has different absorption and scattering properties [Fig.8(a)]. If the anterior layers can
be considered anatomically well organized and hence
optically relatively homogeneous (with the exception
of large retinal vessels which could be avoided during
reflectometry), this is not the case for the deeper lay-
ers. The choroid is composed of blood vessels, melanocytes, and other scattering bodies distributed in a
nonhomogeneous fashion. Explicit modeling of each
constituent of the fundus strata is an intractable problem. Instead, we propose models based on simplifying
assumptions and will evaluate how well they describe
the experimental results. By gradually increasing the
complexity of the models and by including optical
properties from the literature, we have attempted to
explain the interrelationship between reflectance
spectra and the optical properties of the fundus layers.
The simplest reflectance model for the fundus layers
is one where all the incident light is transmitted
by the
retinal and choroidal layers, reflected by the sclera,
and retransmitted by the- choroid and retina [Eq. (5),
model I]. However, as discussed in Sec. IV.B.2, reflec-
tions originating from the retinal layers contribute
substantially to the overall fundus reflectance, especially at short wavelengths and for darkly pigmented
fundi. A model for fundus reflectance, incorporating
such a retinal reflecting layer, was proposed by van
Norren and Tiemeijero and tested on experimental
reflectance data of four subjects. We evaluate this
model (model II) as a description of our experimental
reflectance spectra.
A.
Fundus Reflectance Model 11
1. Descriptionand Parametersof ModelII
Model II [Fig.8(b)] consists of two spectrally neutral
reflectors, the sclera (reflectance rsC)and an anterior
reflector (located anterior to the RPE but posterior to
the macular pigment in the fovea, reflectance rpe),
which sandwich all the blood and melanin of the fundus. A blood layer (thickness dhb) simulates choroidal
blood, and a melanin layer (density Dme,500)simulates
melanin in the RPE and choroid. The model also
accounts for absorption by the macular pigment
15 March 1989 / Vol. 28, No. 6 / APPLIEDOPTICS
1069
the five remaining parameters were calculated by fitting Eq. (8) to the experimental data using the curve-
r
fitting procedure of Sec. II.C.
2. Results of Regressions for Model II
Figure 9 presents the regression results of model II
for three individual spectra, and Table III gives the
average model parameters at the three sites. The fits
were always highly significant (p < 0.0001) and generally tighter for moderate pigmentation. The nasal fits
were on average better than the macular ones (PRE,
Table III). The fine detail of the hemoglobin absorption bands in the 500-600-nm range was generally not
0.2
a)
Dmne
- 1.26(0.05)
C)
,
.'
c
ID
a)
'
11
,
,
"
.dhb
,, ,/
- 33 (17)
Dom - 0.76 (0.06)
,.
,
,
well fitted (Ni, Fig. 9).
-
p,,e----- 2.3(0.. L
Examination of the correlation coefficients indicates
that the model parameters show pronounced
1517
E
trends, statistically significant in many cases, to be
negatively correlated with the amount of melanin.
Since these relationships do not correspond with our
expectations, based on the anatomical evidence, we
must conclude that model II is less than optimal at
describing the optical properties of the fundus layers.
In particular, the inverse correlation between the
amount of blood and melanin, which strongly affected
~~~~~~~~~~~~Dom
~~~~~~~~~~~rpe
model I (Table II), is reduced but still present in model
~~~~~~~~~~~rsc
-8.9 (1.1)
:
~~~~~~~~~~~RE
II despite the introduction of rpe.
~~~~~~~~~~~~F-ratio
Because of these interrelationships, it is difficult to
comment on the results obtained for the various parsc - 17.7 (0.6)
a),
RE-4.4
DC
g
/F-ratio
C
.
LlW.1i/-
Dme
l
I ,,,,,,,.~~~..........,,:,,,,,,
i am
Zf
f
/
D.
- 21
f
(0.2)
j 4(9
- 044 (0.07)-,
1.3
:"'
X
X
h..........
43)......... dh
a
(0. 1)
.
-4.1
/
2100
Table Ill.
,
ADO
500
600~~~Bo
700
BOO
Parameter
900
Dme,
500
Wavelength
Unit
D.U.
(Melanin)
(nm)
Fig. 9. Model II results: experimental reflectance data ()and
fitted regression (solid lines) for three spectra; N, nasal fundus of
dhb
rp, and RE. The interrupted lines are spectra reconstructed from
(a) reflectance contri-
bution of the anterior reflector seen through the ocular media (and
macular pigment) and (b) reflectance of the choroid in the absence of
the anterior reflector.
(Dmp,460)
and the ocular media (Dwn,420).The absorption spectra for the four pigments are given in Fig. 4, in
absolute terms for blood (Khbx)and in normalized
terms for other pigments (KA). Application of the
Lambert-Beer law gives the reflectance R correspond-
,lm
(Hemoglobin)
subject 1; P7, perifovea of 7; and F10, fovea of 10. The regression
results (S.E. in parentheses) are given for each spectrum. The units
are D.U. for D,, D, and D p; m for db; and percent reflectance for
the model results in the following conditions:
Resultsof Regressionsfor Model Iia
Dom,420
(Ocular media)
D.U.
10
2(KmADm,420
+Kmp,ADmp4a)
[rp + (1 -re)rsc
X 10 2(KmeDme,50
+ Khsdhb)]
(8)
six unknown parameters. The macular pigment densities were assumed zero for the nasal and perifoveal
data, and the values for Dmp,460, obtained in Sec.
IV.A.3, were used for the foveal data.
1070
The values of
APPLIEDOPTICS / Vol. 28, No. 6 / 15 March 1989
Fovea
0.64 (57)
[0.00-1.24]
1.09 (51)
[0.45-2.171
1.16 (50)
[0.51-2.20]
93 (61)
[21-204]
r = -0.63
p = 0.05
111 (58)
[30-216]
r = -0.58
n.s.
99 (58)
[32-1863
r = -0.74
p < 0.02
0.51 (37)
[0.15-0.87]
r = -0.66
0.65 (17)
[0.48-0.82]
r = -0.12
0.66 (21)
[0.43-0.93]
r = -0.33
p <0.04
n.s.
n.s.
1.7 (15)
[1-3-2.1]
r = -0.59
n.s.
%
2.7 (33)
[1.6-4.9]
r = -0.80
p < 0.006
2.1 (21)
[1.5-2.9]
r = -0.59
n.s.
rsc
(Sclera)
%
14 (35)
[6-22]
16 (31)
[8-25]
PRE
AFR
a
where Dom,420,Dme,500 Dmp,460,dhb, rc, and rpe are the
Perifovea
rpe
(RPE reflector)
ing to Fig. 8(b):
Rmod., =
Nasal
fundus
%
-
15 (33)
[8.9-24.5]
r =-0.37
r = -0.75
r = -0.73
n.s.
p < 0.02
p < 0.02
3.52
4254
4.03
3706
4.58
4188
See text for explanation of symbols.
For each group of data,
bold numbers indicate the mean of ten subjects; parentheses indicate coefficient of variation; square brackets indicate range; r represents the linear correlation coefficient of the parameter with Dme,500;
and p represents the statistical significance of this correlation (p =
0.05 attained with
Irl = 0.63,
through each pigment.
n = 10). The densities are single pass
rameters. Although the mean dhb results are reasonable (90-110 gim, -25% of the volume of a 400-um
choroid), the dhb obtained for high pigmentation (-20
corresponds
,gm) are clearly too low. The mean Dom,420
well with the standard observer data of van Norren and
Vos.2 7
The scleral reflectance r
for all spectra (6-
25%) are low compared to the expected values (4060%), as discussed in Sec. IV.B.1. Comparison of our
results with those obtained by van Norren and Tiemeijero are complicated by the strong dependences on
degree of melanin pigmentation. Their four Caucasian subjects appeared to have been fairly darkly pig-
mented compared with our subjects, as judged from
the shape of the published spectra and from the reflectance data at 675 nm. With this in mind and within
the limitations of the comparison, our values correspond well with those obtained in van Norren's study.
3. Limitations of Model II
The anterior reflector rpeis efficient at flattening the
hemoglobin absorption bands in the 500-575-nm
range but has little effect at longer wavelengths because of its low relative magnitude.
Thus, the ob-
served reflectance changes in the 575-650-nm spectral
range are principally fitted by dhb (similar to the model
I, 610-nm estimate of Sec. IV.A.2). Large changes in
Robsx for light pigmented fundi are therefore matched
by large dhb whereas the more attenuated changes for
dark fundi are fitted by lower dhb, resulting in the
observed correlation between dhb and Dne500 (Table
III). An attenuation of the hemoglobin spectrum at
high melanin pigmentation would reduce this interde-
B.
Fundus Reflectance Model II
We modified model II to include a light scattering
contribution in the choroid. Light scattering in a pigmented tissue limits the depth of penetration of light
and causes light to be reflected back toward the detector from various depths within the tissue. The resulting reduced path lengths through the pigments decrease net absorption and weaken the influence of the
absorption bands. We also introduced several fixed
parameters corresponding to specific anatomic layers
and values chosen consistent with the literature. Furthermore, we reduced the number of adjustable model
parameters and chose these to best represent the anatomical quantities expected to vary among individuals.
We fixed the density of the ocular media and the
reflectance of the sclera, because these parameters are
not expected to vary greatly among young healthy
subjects. To offset the resulting constraint, we introduced a single parameter under the form of an unknown density (D,) and located this source of light loss
in the layer for which we have the largest uncertainties,
i.e., the choroid. From analysis of D. behavior, we
hoped to learn more about the imperfection of the
model, without the confounding influence of several
interdependent parameters.
1. Descriptionand Parametersof Model III
Model III [Fig. 8(c)] consists of a scleral reflector, an
absorbing-scattering layer simulating the choroidal
stroma, a blood layer simulating the choriocapillaris
(thickness d,,), a melanin layer simulating the RPE
and a spectrally neutral anterior re(density Drpe,500),
pendence of dhb and Dme,50
flector (reflectance rpe). The model also accounts for
The fit in the 640-805-nm range is essentially de- absorption by the macular pigment (density Dmp,460)
and r,, since the other pigments and rpe and the ocular media, but neglects the contribution of
fined by Dme,500
have little effect in that range. The slope of logRmod,x the retinal capillaries (Sec. IV.A.2). The reflection at
is thus that of (logr, - 2K'mexDme5OO).When Dme,500 the limiting membrane was not implicitly included in
decreases and becomes steeper. This
increases, Rmod,X
the model and can be thought as being part of rpe for
increase in slope is apparently too pronounced for the
the nasal fundus and perifovea. In Sec. V.B.5, we
slope of Robs,x,forcing r,, to decrease and Dmeto adopt a
lower value. This interaction is the origin of the nega-
tive correlation between rc and Dme(Table III) and
would be diminished if the effect of melanin spectrum
was weakened.
The low values of r,, obtained in this
and the van Norren and Tiemeijer study1 0 result partially from the fact that transmission of the ocular
media in the 640-805-nm range was assumed to be
100% (Fig. 4). In fact, media transmission at those
wavelengths is -80% (Sec. IV.A.4), and accounting for
this in Eq. (8) causes an increase in the fitted r,, value.
In conclusion, the effect of absorption by hemoglo-
bin and melanin is too pronounced in model II. Introduction of light scattering within the choroidal space
would result in an attenuation of the influence of these
pigments. The anterior reflector coarsely flattens the
hemoglobin bands in the middle of the spectrum but is
unable to influence the reflectances at long wavelengths. Finally, although the use of six parameters
(including Dmp,
460) generally provided tight regressions, too many parameters could contribute to the
interparameter correlations observed in this model.
investigate separately the influence of rilm on the mac-
ular pigment density in the fovea. For light losses in
the ocular media, we maintain the absorption component of model II (density DO,,420)but introduce a wavelength-independent scattering term (density Dms),as
discussed in Sec. V.A.3. Application of the Lambert-
Beer law gives the reflectance RAcorresponding to Fig.
8(c):
R-.d A=
10
mpxDmp,460+Dms)
2(K.,D.., 420+K
[rpe+ (1 - re)rch
X 10
2(KmeDrpeO5O+KhbXdc)]
(9)
The absorption spectra for the pigments are those
given in Fig. 4, in absolute terms for blood (Khb) and
in normalized terms for other pigments (K'm 'K'mp,
and Kme,) The reflectance r~h is that of all the layers
posterior to the choriocapillaris, or the choroidal stroma backed by the sclera (reflectance r
The cho-
roidal stroma is simulated by a homogeneous scattering layer in which hemoglobin and melanin are
uniformly distributed. Mathematical solutions describing light reflectance by such layers were derived
15 March 1989 / Vol. 28, No. 6 / APPLIEDOPTICS
1071
by Kubelka and Munk,51 and have offered a simple
means for quantitative treatment of absorption and
scattering in biologicaltissues.52 5 3 The reflectance rch
for the choroidal stroma backed by the sclera (reflectance r,,x) is given by the Kubelka-Munk equations51 :
(1 - r')(a - b coth bSth)(10)
rh-a + b coth bStch - rS,,'(10
with b = (a2 - 1)1/2 and
(D.e, 500K'me,X+ Khb, dhb + D,) log1 Oe
a1+
e,
hbIhb(1
1)
Stch
where tch is the thickness of the choroid, and S is the
bulk scattering coefficient (in cm-') of the homogeneous absorber-scatterer layer. For clarity, the notations used in model II have been maintained. The
blood layer thickness dhb represents the amount of
blood (fractional volume = dhb/t~h), and Dme,500 represents the amount of melanin in the choroid (fractional
volume not known with accuracy). The wavelengthindependent parameter D. can be considered as a neu-
tral absorber in the choroid or any other source of light
loss from that space.
Several parameters were kept permanently constant. The choroidal thickness th was 400 gim,the
thickness of the choriocapillaris d
was 10 gtm (Sec.
IV.A.2),and the ocular media scattering term Dm, was
0.1 D.U. (Sec. IV.A.4).
The scleral reflectance
(in
percent) was described by r,,x = 50 exp[-0.00261(X 675)], simulating the observed spectral dependence of
the scleral reflectance (Sec. IV.B.1) and being 50% at
675 nm. Three other parameters were always equal
for all sites in all subjects but were varied to optimize
the quality of the fits at all sites. These parameters
were the ocular media absorption density Dom,420,
the
scattering coefficient S, and the RPE density Drpe,500
The latter was initially equal at all sites but was then
adjusted to match each site separately. Attempts to
fit
Drpe,500
together with Dine,500were not successful, as
the two melanin signatures are too competitive in the
curve-fitting procedure.
The five remaining parameters Dme,500,dhb, D, rpe,
and Dp, 460 were computed by fitting Eqs. (9)-(11) to
the measured reflectance spectra, using the curve-fitting procedure of Sec. II.C. In model II, we used a
macular pigment density Dmp,460
determined from foveal and perifoveal reflectances (Sec. IV.A.3). In
model III,
Dp,
460
was included in the curve fitting
allowing an independent determination of the macular
pigment density at all sites.
2. Selection of Parameters S, Dom,42o,
and Drpe,500
Starting with Drpe,50o= 0.4 D.U., the approximate
mean at the posterior pole from the study of Gabel et
al., 3 3 we first adjusted combinations ofDom,420
and S to
optimize the regressions by monitoring the average
F/ratios (AFR) and the quality of the individual fits.
With increasing S, we observed an improvement in the
regressions, an increase in fitted values of dhb, Dme,500,
and D, a flattening of the absorption bands of choroidal hemoglobin, and a decrease in rpe. The latter two
1072
APPLIEDOPTICS / Vol. 28, No. 6 / 15 March 1989
changes allowed for a tighter fit in the 500-600-nm
spectral range (especially in lightly pigmented fundi).
A broad optimum in AFRs was found for the combination S = 6 cm- 1 and
Dom,420
0.5 D.U.
A scattering coefficient S 6 cm-' means that the
reflectance of the choroidal layer in the absence of a
sclera and choroidal pigments is -20%, indicating that
a substantial amount of light is now reflected from
within the model choroid. Furthermore, the fitted
value for dhb is 200 gim on average or -50% of the
choroidal volume. Since the scattering coefficient of
whole blood is -15 cm- 1 ,5 4 a half-filled choroid would
have a scattering coefficient of -7.5 cm-', which is in
reasonable agreement with our value of 6 cm-'. Our
selected value Dom,420= 0.5 D.U. is smaller than the
mean value of 0.6 D.U. for the standard observer data
of van Norren and Vos.2 7 This difference might be
justified in accounting for a contribution of stray light,
which would effectively lower the media density.
Since RPE densities vary for different areas of the
fundus,3 3 36
, we next investigated the effect of changing
Drpe,soo. The five model parameters were fitted to the
reflectance data of the three sites for Drpe,500 values
between 0.1 and 0.8 D.U. (Fig. 10). With increasing
Drpe,500we observed a decrease in the amount of choroi-
dal melanin Dre,500(the melanin signature on the spectra must remain the same), a decrease in dhb, an increase in rpe and in D, and no substantial
change for
Dmp,460.The changes in the average F/ratios (AFR)
indicate that the regressions are on average optimal for
Drpe,500= 0.2-0.4 D.U. at the nasal fundus, for Drpe50 =
0.3-0.6 D.U. at the perifovea, and for Drpe,500
= 0.5-0.7
D.U. at the fovea. Similar conclusions could be drawn
from the changes in the PREs for the three sites.
In vitro measurements by Weiter et al.3 6 indicated
that the RPE density in the macular area (our foveal
and perifoveal sites) is on average 1.6 times higher
than at the posterior pole, and that the RPE density
nasal to the disk (our nasal site) is on average equal or
slightly smaller than at the posterior pole. A similar
distribution of RPE melanin was found by Gabel et
33
al., who reported a mean value of 0.4 D.U. at the
posterior pole (Sec. IV.A.1). We therefore selected a
density Drpesoo = 0.35 D.U. for all nasal fundi. The
density for the macular sites should then be -0.56 D.U.
(1.6 times 0.35). Weiter et al.36 further showed that
the distribution of choroidal melanin shows a broad
maximum in the macular area. We can thus assume
that the amount of choroidal melanin is the same for
the perifovea and for the fovea (sites are 2.50 apart).
Examination of Fig. 10 indicates that the model
achieves this if Drpesooin the fovea is -0.1 D.U. larger
than in the perifovea. We therefore selected a RPE
density Drpe,500= 0.50 D.U. for the perifovea and 0.60
D.U. for the fovea. The three selected values for
Drpes50o
fall in the respective ranges of Drpe,500for which
the regressions were optimal (Fig. 10). This does not
necessarily prove that our choices are correct, but it is
advantageous for achieving the best possible fits.
Examination of the correlation coefficients indicates that the model III parameters, compared with
model II, show reduced correlations with the amount
0.8
0.6
0.4
0.2
0.0
. . . . . . . . . . . .
.
.
.
7000
6000
N -fN
of melanin Dme 500 Although some trends, such as a
5000
tendency for rpeto decrease with increasing Dme,5oo,are
4000
3000
2000
P
/
F
z
F
1000
.4
.3
_e
-2
P
5-
8
*1
N
43.
N
P
2.
F
-
- 400
1*
- 300
- o
-200
F
N
E100 1
0
0.2
_D
0.1
5
the choroidal volume. The average quantity of choroidal melanin in the two Black subjects was 3-4 times
xi
F
~
F -c~-~
P
~
0.3a
F
'_ne
P
.~~~~~~
-0.1
N
~~~~.
0.0
the reduction in the coefficient of variation associated
with dhb (Tables III and IV). The large coefficient of
variation associated with Dme5oo demonstrates the enhanced sensitivity of model III at detecting changes in
the amount of melanin.
The amount of choroidal melanin Dne,500 calculated
from the model (Table IV) varies between 0.01 and 7.9
D.U. Although this range is larger than that measured
36
by in vitro measurements on enucleated eyes, it is not
for
estimate
lower
the
unreasonable. Indeed, using
Sec.
cm-',
(800
melanin
of
coefficient
extinction
the
IV.A.1), the highest density of 7.9 D.U. represents at
most a melanin layer of 99 ,um or no more than 25% of
Ne
0.0
clearly detected, only 1 out of 12 correlations is statistically significant (DX with Dne,500for the fovea) compared with 6 out of 12 in model II. The absence of
marked correlation between dhb and Dme,500is clearly
an improvement over model II, especially considering
0.2
0.4
Drpe,50
.
0.6
.
.
.
.
-
,
8
S
CL
Table IV. Results of Regressions for Model Ilila
0.0
Unit
Nasal
fundus
Perifovea
Fovea
Drpe,500
D.U.
0.35 (fixed)
0.50 (fixed)
0.60 (fixed)
Dme,500
(Melanin)
D.U.
0.96 (109)
[0.01-3.4]
1.92 (122)
[0.22-6.4]
2.13 (139)
[0.19-7.9]
gm
146 (42)
[65-2861
182 (48)
[61-321]
168 (50)
[60-304]
Parameter
I
0.8
(.U.)
Fig. 10. Mean results for the average F/ratios (AFR) and for the
five fitted parameters of model III, for different values of the RPE
density Drpe,500. The symbolsN, P, and F (for nasal fundus, perifovea, and fovea, respectively) are located adjacent to the scale corresponding with each parameter. The filled squares indicate a significant (p < 0.05) correlation between Dme,50oand the parameter; open
squares indicate no significant correlation.
dhb
(Hemoglobin)
rpe
(RPE reflector)
%
3. Results of Regressions for Model III
Figure 11 presents the regression results of model III
for three spectra (same spectra as in Fig. 9), and Table
IV gives the average model parameters for the three
sites. The regressions of model III are always highly
significant (p < 0.0001) and in general improved compared with those of model II (PRE and AFR, Tables III
and IV).
The relative errors RE [Eq. (3)] were de-
creased by at least 10% for twenty-two out of thirty
spectra (three sites). The improvement was most
marked for the light and medium pigmented fundi,
and a decrease in fit quality was observed in some dark
fundi (Figs. 9 and 11, F10). The effect of scattering in
the choroid can be seen from the much attenuated
hemoglobin bands in the spectrum of choroidal reflec-
tance (Figs. 9 and 11, curves b). The reflectance rpe
seen through the ocular media (curves a) is relatively
lower than in model II, allowing for a tighter fit for X <
600 nm.
D.U.
D,
(Choroidal loss)
Dmp,460
(Macular
r=0.11
r=0.23
n.s.
n.s.
n.s.
3.7 (19)
[2.8-5.21
2.9 (24)
[2.2-4.2]
2.3 (16)
[1.7-2.81
r = -0.62
r = -0.42
r =-0.35
n.s.
n.s.
n.s.
0.17 (58)
[0.05-0.36]
0.09 (63)
[0.00-0.15]
0.10 (79)
[0.00-0.22]
r =0.59
r =-0.27
r =-0.66
n.s.
n.s.
p < 0.04
D.U. -0.016 (208) 0.024 (117)
[-0.08-0.0441 [-0.02-0.081
pigment)
%
PRE
AFR
r=0.12
-
r = -0.43
r = -0.02
n.s.
n.s.
2.74
6882
3.47
5245
a See text for explanation of symbols.
0.21 (26)
[0.12-0.31]
r = 0.52
.
n.s.
4.65
6593
For each group of data,
bold number indicate the mean often subjects; parentheses indicate
coefficient of variation; square brackets indicate range; r represents
and p
the linear correlation coefficient of the parameter with Dme,500;
represents the statistical significance of this correlation (p = 0.05
attained
with Irl = 0.63, n = 10).
The densities are single pass
through each pigment.
15 March 1989 / Vol. 28, No. 6 / APPLIEDOPTICS
1073
roidal volume (thickness:
dhb (42-49%) appears
N1
.
b
Dme -0.00(0.01)
dhb - 68 (4)
rpe - 5.0. (0.0)
D - 0.13 (0.01)
Dmp - 0.04 (0.00)
RE -4.7
F-ratio - 1124
,.0
400 gim). The variability in
large, especially for the macular
sites. For the different subjects, the amount of blood
dhb in the adjacent fovea and perifovea correlated with
each other (r > 0.95, p < 0.0001), but no significant
correlation was found between either of the macular
sites and the nasal fundus (r = 0.44 for both combinations).
The amount of macular pigment Dp,460 derived
from the model (Table IV) is 0.21
0
P7
0. 1:
Dme -1.5(0.1)
dhb - 61 (10)
rpe - 3.0 (03)
Dx - 0.07 (0.02)
Omp - 0.04 (0.03)
RE - 4.4
F-ratio - 1522
a)
U
C
a)
U)
crease results from the fact that a slight amount of
macular pigment was detected at the perifovea. The
Dmp,460 values found in this study are lower than the
(n = 2 subjects) and by van Norren and Tiemeijer (n
= 4), but higher than the 0.15 D.U. found by Alexander
et al.22 (n = 5). However, the macular pigment densities measured by reflectometry are in general much
lower than those determined by psychophysical meth-
20
,j
F10
LU
f
...........
*..-b
Dme - 7.6 (0.0)
..............
dhb
-
126(35)
,.
Dx -0.00 (0.02)
Dmp - 0.31 (0.00)
RE - 6.9
F-ratio -782
I.
402D
5OD
60
Wvplpnnth
60
70
00
nm
Fig. 11. Model III results: experimental reflectance data (+) and
fitted regression (solid lines) for three spectra: N1, nasal fundus of
subject 1; P7, perifovea of 7; and F10, fovea of 10, The regression
results (S.E. in parentheses) are given for each spectrum. The units
are D.U. for De, D,, and Dmp;gm for dhb;and percent reflectance for
rpe and RE. The interrupted lines are spectra reconstructed from
the model results in the following conditions: (a) reflectance contri-
bution of the anterior reflector seen through the ocular media (and
macular pigment) and (b) reflectance of the choroid in the absence of
the anterior reflector.
higher than that in the darkest Caucasians. The lower
melanin density in the nasal fundus corresponds with
our ophthalmoscopic experience: choroidal vessels
are often seen nasally in fundi that do not reveal any
choroidal detail in the macular area, The amount of
melanin De, 500 of the three sites correlated highly with
each other (r > 0.93, p < 0.0001 for all three combinations). As expected, De,,500 also correlates significant-
ly with the P index (Sec. IV.A.1) at each site (all r >
0.92, p < 0.0002).
The amount of blood in the choroidal stroma dhb
derived from model III (Table IV) ranges between 60
and 320 gim. Including the 10-,umcontribution of the
choriocapillaris, this corresponds to 18-83%of the cho1074
al and perifoveal reflectances (Sec. IV.A.3). This in-
average of 0.25 D.U. found by Brindley and Willmer 2 l
C
LL
C
0.05 D.U. on
average for the fovea (single pass), slightly higher than
the...0.19 D.U. determined from the comparison of fove-
APPLIEDOPTICS / Vol. 28, No. 6 / 15 March 1989
ods: Bone and Sparrock 5 5 found a mean density of
0.54 D.U. (460 nm) for a population of forty-nine subjects. Two factors could account for the differences
between the reflectometric and psychophysical estimates. First, the size of the sampling field in reflectometry, 1.0-2.5° in the different studies, may be too
large to resolve the narrow maximum in pigment density in the fovea.4 4 Second, the contribution of stray
light and reflections at the limiting membrane (foveal
reflex) would inevitably reduce the density measured
by reflectometry. To investigate the influence of such
reflection on the macular pigment density, we introduced a neutral reflectance rilm at the limiting membrane [Fig. 8(c)] and used our curve-fitting procedure
to determine which value of rilm would cause the mean
to increase to -0.5 D.U. For a reflectance rilm
Dmp,460
= 0.8%, we found that the mean pigment density
Dmp,460
became 0.51
0.22 D.U.
Thus, small reflec-
tions at the limiting membrane or small amounts of
stray light have a pronounced effect on the measured
pigment densities in blue light (low fundus reflectance).
Finally, it is useful to compute the contribution of
light reflected by the choroid and sclera [rch,Eq. (9)] to
the total reflectance. This contribution was calculated using the model parameters obtained for each spectrum and correlated with the amount of choroidal melanin De,500. For the nasal fundus, rh contributes 615%of the total reflectance at 540 nm (r = -0.56, n.s.),
and 50-80%at 675 nm (r =-0.91, p <0.0002). For the
macular sites, rch is 2-8% of the total reflectance at 540
nm (r = 0.51, n.s.), and 40-90%at 675 nm (r = 0.96,p <
0.0001). Thus, light reflected by the choroid in blue
and green light contributes only a small fraction of the
total reflectance, especially in darkly pigmented fundi.
It is also interesting to note that removal of the sclera
(rS = 0) from the model reduces the total reflectance
by only 1-4% in the darkest fundi at 675 nm and by 40-
55% in the lightest fundi. This corresponds well to
16
Thus, choexperimental measurements in rabbits.
roidal scattering in the model (S) causes a substantial
amount of light to be reflected from within the stroma,
and the contribution of the scleral reflectance is very
small in darkly pigmented eyes.
4. Limitations of Model III
Model III is limited by its oversimplification of a
complex biological tissue. As in any model, assump-
tions must be made to reduce the number of parameters to be fitted by the model. In particular, our
simulation of the choroidal stroma by a homogeneous
absorbing-scattering
layer is naive when one considers
that choroidal vessels and melanocytes are irregularly
distributed
in the stroma.
Choroidal vessels may be
more numerous in the inner stromal layers, toward the
choriocapillaris, 4 2 whereas melanin pigment is more
densely concentrated in the outer layers (suprachoroid).16 ,42 The irregular distribution of vessels within
the sampling area results in a light reflection from the
stroma that is the summation of many components
associated with different path lengths through blood
and melanin. Although mathematical treatments for
light propagation through media with heterogeneous
distribution
of path lengths have been proposed,
56
their application to the choroid is at present limited by
lack of precise information on the content and distribution of both vessels and melanocytes. Instead we
have used the simple phenomenological model of Kubelka-Munk.51 This theory assumes that tissue inhomogeneities are small compared to layer thickness
and that the incident radiation is diffuse. Although
these conditions are not rigorously met, the theory
nevertheless offers a means for simple quantitative
treatment of light propagation in the choroidal stroma.
The introduction of a single unspecified source of
light loss in the choroid, in the form of D, is a weakness
of model III. However, analysis of D, behavior allows
one to draw some conclusions about the model's short-
comings. The parameter Dxranges in absolute magnitude between 0 and 0.36 D.U. (Table IV), and is on
average larger for the nasal fundus than for the macular sites. The parameter DXtends to increase with
Dme,,500
nasally, decreases with Dne,5oo at the fovea, and
did not correlate significantly with any of the other
three fitted parameters. The effect of the light loss,
Dx, is best analyzed, not in absolute terms, but in
relation to the contributions of the other absorbers and
elements of the model. For the fitted parameter of
each spectrum, we calculated the ratio Px of the predicted reflectance with D, = 0 and the predicted reflectance with the actual fitted values of D,. The results
indicated that DX has a very low influence in blue and
green light (PX< 1.02 at all sites and all spectra), which
means that DX is always negligible compared to the
absorption by blood and melanin for X < 580 nm.
However, in red light, the relative contribution of DX
increases rapidly to reach a maximum in the 640-805nm range. The average Px at 675 nm was 1.42 + 0.24,
1.24 ± 0.20, and 1.31 + 0.27 for the nasal fundus,
At each of the
perifovea, and fovea, respectively.
three sites the ratio Px showed a strong tendency, significant at some wavelengths in the 590-805-nm range,
to decrease with increasing melanin Dme 500(r = -0.64,
-0.60, and -0.61 for the three sites, p - 0.05). This
means that the light loss characterized by D, is relatively highest at low pigmentation. A possible explanation for this finding is that light incident in the
sampling area diffuses out of the sampling volume by
multiple scattering in the choroidal stroma. Such
light loss, which is not accounted for in the KubelkaMunk theory, would be more marked in lightly pig-
mented fundi. This effect is easily demonstrated by
the halo observed around a focally illuminated area on
a light fundus. The larger loss observed for the nasal
fundus might, in addition to a lower pigmentation, be
explained by the fact that a larger sampling area was
used at that site (large perimeter, large loss).
Another nonconflicting explanation for D. might be
related to the shape of the effective absorption spectrum of melanin in the stroma. We have seen in model
II (Sec. V.A.3) that a lowering of the fitted scleral
reflectance rSc effectively decreased the slope of
the absorption spectrum. An increase in D. has the
same effect, since the slope is then determined by
(Dne, 50oK'me,x + D.) instead of by Dne,500K'mex [Eq.
(11)]. At the highest choroidal melanin concentra-
tion, no more than 25% of the choroidal volume is
occupied by melanin (Sec. V.B.3). Thus, a consider-
able amount of light can propagate through the choroid without absorption by melanin, resulting in reflected light contributions that have no choroidal
melanin signature. Together with contributions that
were absorbed by choroidal melanin, the resulting reflected light would contain a flattened melanin signature.5 7 Thus we expect flattening of the choroidal
melanin spectrum, and D, may represent an attempt
to correct for the heterogeneity of the choroidal melanin distribution.
A final restriction of model III is the use of constant
parameters to describe biological entities. In particuwas assumed constant at
lar, the RPE density Drpe,500
each site. The individual variability in RPE density
was therefore ignored and some of the variability de-
tected in Dne,500results in fact from individual variations in RPE melanin. The inability to differentiate
between RPE and choroidal melanin is a severe limitation of reflectometry. This is of particular importance
in photocoagulation dosimetry19 since the RPE is the
major source of heat (largest absorption per unit volume) in fundus photocoagulation. Furthermore, ocular media density Dom,420 was assumed constant for all
young subjects in this study. Determination of the
individual ocular media density by a psychophysical
method 2 7 would clearly improve the modeling, especially if older subjects are to be investigated.
VI.
Summary and Conclusions
The magnitude and shape of the reflectance spectra
from the human ocular fundus are critically affected
by the amount of melanin in the choroidal stroma. In
red light and at low degree of pigmentation, most of the
15 March 1989 / Vol. 28, No. 6 / APPLIEDOPTICS
1075
light originates from the highly vascularized choroid,
causing the spectra to reveal pronounced absorption
bands of blood.
As the degree of pigmentation
in-
creases, the spectral signature of melanin gradually
dominates that of blood, and the contribution of the
deeper layer decreases. In green and blue light, the
contribution of the choroidal reflections is small compared with that of reflections originating in the retina.
This results in a weakening of the spectral signature of
blood and in difficulties in quantifying the amount of
blood in green light. In red light, quantification of the
amount of blood is also complicated by the confound-
ing influence of the spectral signature of melanin.
The decrease in the apparent amount of blood with
increasing degree of fundus pigmentation is a major
problem in interpreting the reflectance spectra. We
have shown, using an argument involving the spectral
signature of the choriocapillaris, that one or several
retinal layers must be the origin of substantial reflec-
tions. The exact anatomical layer (or layers) responsible for those reflections has not been identified, with
the exception of the inner limiting membrane. The
retinal reflections are partially responsible for the flattening of the spectral signature of blood with increasing fundus pigmentation. The reflectance spectra
also demonstrate the influence of absorption by the
macular pigment in blue light and the effect of agerelated changes on absorption by the ocular media.
To gain an understanding of the interrelated contribution of the absorption spectra of blood and melanin
to the fundus reflectance spectra, one must attempt to
model the various constituents of the fundus layers.
We first assessed the fundus reflectance model proposed by van Norren and Tiemeijer,10 model II, and
found that it adequately fitted the experimental spectra. However, model II suffers from the fact that some
model parameters correlate significantly with each
other, in ways not consistent with our expectations,
based on anatomical evidence. We modified model II
by including a light scattering component in the choroid and by introducing several constant parameters
corresponding to specific anatomical layers. This
model, model III, which has one fewer adjustable parameter than model II, uses a uniform absorbing-scattering layer as an oversimplified representation of the
choroidal stroma. Curve fitting of this model to the
experimental reflectance spectra produced better regressions to the data and demonstrated an enhanced
sensitivity at detecting differences in the amount of
choroidal melanin. The interdependence of the different model parameters was markedly reduced, particularly with regard to the relationship between the
amount of blood and melanin. The inclusion in the
model of an unspecified source of light loss has helped
in interpreting the shortcomings of the model and may
point the way for improved quantitative modeling of
the fundus layers.
The authors acknowledge K. A. Fitch for expert
technical assistance throughout this project. Special
thanks are due to 0. Pomerantzeff, R. Webb, and A.
Garsd for numerous discussions and suggestions.
1076
APPLIEDOPTICS / Vol. 28, No. 6 / 15 March 1989
This work was supported in part by grant EY02094
from the National Eye Institute, National Institutes of
Health, Bethesda, MD, and by generous support from
the Walters Family Foundation, Manhasset, NY.
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