Directional light scanning laser ophthalmoscope.

Abstract

The cone photoreceptor mosaic of the living human eye has in a limited number of cases been imaged without the use of wavefront-correction techniques. To accomplish this, the directionality of the photoreceptors, as manifested by their waveguiding properties, may be used to advantage. In the present paper we provide a model of our recently proposed directional light scanning laser ophthalmoscope [Opt. Lett. 29, 968 (2004)] together with a detailed numerical analysis of the device. The outcome is compared with experimental results.

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Directional light scanning laser ophthalmoscope
Brian Vohnsen, Ignacio Iglesias, and Pablo Artal
Laboratorio de Óptica, Universidad de Murcia, Campus de Espinardo (Edificio C), 30071 Murcia, Spain
Received March 4, 2005; revised manuscript received May 10, 2005; accepted May 16, 2005
The cone photoreceptor mosaic of the living human eye has in a limited number of cases been imaged without
the use of wavefront-correction techniques. To accomplish this, the directionality of the photoreceptors, as
manifested by their waveguiding properties, may be used to advantage. In the present paper we provide a
model of our recently proposed directional light scanning laser ophthalmoscope [Opt. Lett. 29, 968 (2004)] to-
gether with a detailed numerical analysis of the device. The outcome is compared with experimental results.
© 2005 Optical Society of America
OCIS codes: 170.4470, 170.5810, 330.5310.
1. INTRODUCTION
The optical performance of the normal human eye dete-
riorates at large pupil diameters owing to the presence of
aberrations. Aberrations also limit the resolution that can
be attained with ocular imaging devices. Thus, to get be-
yond this limitation the aberrations need to be compen-
sated for. The introduction of adaptive optics in studies of
the eye1–4has allowed for correction of even higher-order
aberrations in essentially real time and thereby has led to
the acquisition of high-resolution retinal images. Never-
theless, these results are somewhat contradicted by re-
ported cone photoreceptor mosaic images obtained in the
livingeye withouttheaid
methods.5–7
The Stiles–Crawford effect refers to the reduced visual
sensitivity to light that is incident off the pupil center and
therefore obliquely incident on the retina.8,9A similar
phenomenon occurs for light reflected off the retina10–13
where it is typically known as the optical Stiles–Crawford
effect. Based on this observation, we recently introduced a
confocal scanning laser ophthalmoscope (c-SLO) designed
to make use of the directionality of reflected light in high-
resolution retinal imaging.7This technique relies on an
accurate alignment of the incident beam (chosen suffi-
ciently narrow to reduce the influence of aberrations) at
the pupil point where its visibility is maximized, i.e., at
the peak of the Stiles–Crawford effect. In this way the
coupling of light at the retina to the underlying photore-
ceptors is maximized (allowing for the largest signal).10,14
At the confocal detection a sufficiently small pinhole is
chosen to highlight the contribution of directional backre-
flected lightproduced by
photoreceptors.7The photoreceptors permit waveguiding
with negligible absorption if bleached or if near-IR illumi-
nation is used, and a major fraction of the returning light
can therefore be directional.11,15
Generally, this light has suffered less from aberrations
than broadly scattered light since it exits the eye mostly
through a fraction of the entire pupil area.11A valid alter-
native would be a reduced exit pupil at the eye although
this would presumably require additional transverse
alignment to be properly centered at the peak of the (op-
ofwavefront-correction
thewaveguidingof the
tical) Stiles–Crawford effect (which is often displaced
from the apparent pupil center).8,12,13The use of a small
confocal pinhole has the additional advantage of high-
lighting the contribution of scattering sources (both
guided and nonguided light) located in the plane of the
retina conjugate to the pinhole while discriminating
against scattered light from elsewhere that could deterio-
rate image quality.
In this paper we make a numerical analysis of the im-
aging capabilities of the technique in order to gain further
insight and, in particular, to examine under what circum-
stances the c-SLO may be used to directly access param-
eters of the photoreceptor mosaic even in the absence of
wavefront correction. The model will be used on light that
originates in photoreceptor
bleached or nonabsorbing cones), but it should be stressed
that the same approach can easily be generalized to
handle imaging of arbitrary scattering sources (not only
photoreceptor waveguides) by a simple modification of
their pupil field. The paper is organized as follows. In Sec-
tion 2 a model of the directional light c-SLO is described.
Section 3 contains a numerical analysis in which the im-
portance of various physical parameters (pinhole size,
photoreceptor diameter, etc.) is studied in order to eluci-
date their influence on high-resolution retinal images,
and the outcome is compared with experimental results.
In Section 4 we present our conclusions.
waveguiding (asfrom
2. MODEL OF THE DIRECTIONAL LIGHT
SCANNING LASER OPHTHALMOSCOPE
In this section the model constructed to analyze our re-
cently proposed directional light c-SLO is discussed.7The
description includes only directional light produced by
cone photoreceptor waveguiding; consequently scattering
from all other retinal structures has been omitted. This
assumption is justified by the often large contribution of
directionallight compared
light11,15and by the selectivity of the confocal pinhole.7
On the basis of a simulation of the optical Stiles–
Crawford effect, and in agreement with the findings of
others,16we have recently found that the light reflected
withbroadly scattered
2606J. Opt. Soc. Am. A/Vol. 22, No. 12/December 2005 Vohnsen et al.
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from each cone photoreceptor may be dominated by the
fundamental waveguide mode of each inner segment.14
This mode can be well approximated by a Gaussian func-
tion of the type exp?−r2/wm
tance from the photoreceptor axis and wmis the half-
width of the mode (which is related to the diameter of the
inner segment). Thus, in the following we assume that
each illuminated photoreceptor radiates a Gaussian beam
of light directed toward the center of the pupil17as shown
schematically in Fig. 1. It may be noted that the intensity
distribution produced at the pupil for a single photorecep-
tor is Gaussian, too, in agreement with the commonly
used model for the (optical) Stiles–Crawford effect when a
directionality parameter is sought.14A shift away from
the pupil center can easily be incorporated by translating
the Gaussian distribution in the pupil plane.
For simplicity, the incident beam scanning of the c-SLO
is omitted at first. Instead, an image is considered to be
formed by scanning with the confocal pinhole across a
steady image plane (where all contributing photorecep-
tors are brought to a focus) while recording the transmit-
ted light power versus position. Leaving out the incident
beam scanning simplifies the analysis of the imaging pro-
cess and corresponds to the realistic case of a poorly fo-
cused beam that simultaneously illuminates several pho-
toreceptors. Nevertheless, it should be kept in mind that
the dual scanning of an actual confocal system can lead to
improved image resolution and contrast.18
Wavefront aberrations too will have a detrimental ef-
fect on the quality of recorded images but may be reduced
byeithercustomizedphase
optics.1,2,4,20The wavefront aberrations ?WAof the real
eye and system, as measured with a Hartmann–Shack
sensor in a plane conjugate to the eye pupil,21can be in-
cluded in the model by introducing them on each Gauss-
ian beam. It may be assumed that each beam suffers
identical aberrations (apart from the tilt that separates
them) when scanning only a small retinal area. A similar
2?, where r is the radial dis-
plates19
oradaptive
situation arises in experiments with wavefront correction
where an average is used during the rapid image
acquisition.1,2,4,20
Thus, the field in the plane of the confocal pinhole from
N simultaneously illuminated photoreceptors can be ex-
pressed via the Fourier transform of the (scaled) pupil
field as
F?A exp?i?WA?x,y? −
F??pupil? =?
j=1
N
x2+ y2
wp
2 ??? ??r − rj?,
?1?
where ? denotes a convolution. In this expression wpis
the spot size at the pupil of the reflected Gaussian beam
which at wavelength ? is related to the photoreceptor
mode through wp=?feye/?neyewm[i.e., the standard rela-
tion between pupil field width and focal spot size (here the
waveguide mode) for a Gaussian beam in a homogenous
medium]. Here feye=22.2 mm and neye=1.33 in the re-
duced eye model. In Eq. (1) the unaberrated image of the
jth photoreceptor is centered at rjin the pinhole plane,
and the Fourier transform is carried out at frequencies
that take into account the system magnification as well as
the focal length of the lens nearest the pinhole. Although
it has been written explicitly for Gaussian beams, the
equation may also be used to simulate imaging of retinal
structures other than photoreceptor waveguides by sim-
ply replacing the Gaussian amplitude weighting with a
different pupil field (a uniform pupil would be represen-
tative, e.g., of a pointlike scattering object located in the
retinal plane, and out-of-focus features can be considered
through their phase variation at the pupil). Thus, with
only small modifications the model would be suitable to
analyze imaging of retinal structures other than photore-
ceptor waveguides.
In the present situation, the best possible cone mosaic
image will show an extended bright spot (corresponding
to the mode width) at the location of each imaged photo-
receptor. This differs somewhat from the common situa-
tion in confocal microscopy where a point object is imaged
as a spot because of the finite size of the numerical aper-
ture (here the waveguide objects have a finite width). For
convenience of modeling, it has been assumed that all
contributing photoreceptors radiate with equal power and
phase as contained in the amplitude factor A. This sim-
plification can easily be undone by inclusion of a complex
field scaling factor at each rjto take into account, e.g., dif-
ferences in the phase of beams radiated by neighboring
photoreceptors.14,22It should be mentioned, though, that
if the exposed retinal area is very small, as in a c-SLO,
the simultaneously illuminated photoreceptors are highly
similar,23and differences in phase of the reradiated light
are therefore expected to be small. In contrast, for an ex-
tended retinal area, with numerous photoreceptors ex-
posed to light in unison (as in fundus photography), this
is presumably no longer the case and the phase may play
a more important role.14,22
The image I?r? obtained by scanning with the confocal
pinhole P?r? can (apart from a scaling constant) be ex-
pressed as
Fig. 1.
with directional light detection including Gaussian beam radia-
tion from each cone photoreceptor (C), confocal pinhole (P), and
detector (D). Also shown is (a) point-spread function calculated
from the (b) measured wavefront aberration of an eye shown on a
2? phase map (6.0 mm pupil at a wavelength of 0.785 ?m). The
aberration, although dominated by astigmatism, includes up to
4th-order Zernike polynomials with a total RMS value of
?0.67 ?m.
Schematic of the model used to describe c-SLO imaging
Vohnsen et al.
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I?r? = ?F??pupil??2? P?r?.
?2?
Although we have assumed that all photoreceptors return
an identical amount of light this can be expected to vary
in a real experiment. This may result in an inhomoge-
neous distribution of brightness that in the presence of
noise can make the photoreceptor density seem lower
than it actually is. This can occur if the photoreceptor re-
flectivity changes (spatially or temporally), or if the cou-
pling efficiency varies as a result of nonuniform illumina-
tion, photoreceptortilt,or
Variations should also be expected when different sized
photoreceptors are scanned. Actually, time-dependent
variations in the amount of reflected light from individual
photoreceptors have been reported on a long time scale,15
but this factor has hardly a measurable influence during
the rapid acquisition of a single c-SLO image. Reflectivity
changes, however, may influence subsequently recorded
frames (in our present experimental system the frame
rate is 15 Hz).
The incident beam scanning can be modeled by inclu-
sion of a position-dependent parameter T?u?, where u is
the displacement at the retina of the incident beam from
the photoreceptor axis, and in a first approximation by re-
placing the pinhole in Eq. (2) with T?u?P?r?. This takes
into account changes in the photoreceptor-to-light cou-
pling as the focused beam sweeps across each photorecep-
tor aperture during the raster scan [ideally, T?u? should
act on the object before the convolution with the pinhole
thereby increasing the complexity of the model]. This ap-
proximation is most valid when the beam illuminates sev-
eral receptors simultaneously. If focused tightly, to a spot
size comparable with the photoreceptor spacing, a differ-
ent modeling would be required as the light may couple to
a single photoreceptor at a time. If aberrations of the in-
cident light can be ignored, as may be the case for a nar-
row beam, a position-dependent coupling efficiency can be
estimated as14
T?u? =?
wr
thescanning in itself.
2wrwm
2+ wm
2?
2
exp?
− 2u2
wr
2+ wm
2?,
?3?
where wris the focused spot size at the retina of an inci-
dent Gaussian beam. Equation (3) results from a calcula-
tion of the overlap integral between the incident ampli-
tude field and the fundamental mode of the photoreceptor
waveguide. Inclusion of this position-dependent param-
eter can be expected to reduce the blur of each cone in
simulated images, although a better estimate should also
include the aberrations of the incident beam. It should be
mentioned that the retinal object may be extracted from
the resulting image by inverting Eq. (2) and removing the
influence of measured aberrations. However, because of
the low-pass filtering of images by the finite-sized confo-
cal pinhole, noise in the recorded data, and the uncer-
tainty in measurements of ?WA, this is not easily accom-
plished.
In summary, to resolve the photoreceptor mosaic re-
quires obviously either a pinhole smaller than the spacing
of the imaged receptors, or alternatively that only a single
photoreceptor is exposed to light at a time as by a tightly
focused (aberration-corrected) incident beam.4The influ-
ence of T?u? on the recorded image quality may, together
with a faster acquisition, plausibly explain why the ap-
parently best high-resolution cone mosaic images to date
have been obtained with flood illumination systems,1,2
since in this case T?u? may be considered approximately
constant. In a scanning system, its influence may change
the amount of coupled light (and thereby also the signal)
each time a given photoreceptor is scanned. In the follow-
ing, we examine numerically the possibilities of cone mo-
saic imaging with a tiny pinhole in the c-SLO tailored to
directional-light detection.
3. NUMERICAL RESULTS AND
COMPARISON WITH EXPERIMENTS
The actual c-SLO has been calibrated by scanning a
copper-on-glass mesh of 63.5 ?m period through an ach-
romatic lens (25 mm focal length). A conversion factor of
280 ?m/degree has been used for the eye, and based on
this calibration all of the following images cover 140
?140 ?m at the retina (with 256?256 pixels). Experi-
mentally obtained results for different pinhole sizes are
shown in Fig. 2. To reduce the influence of aberrations on
the incident beam its diameter has been restricted to
2.0 mm at the eye pupil. For the near-IR wavelength ?
=0.785 ?m used in the experiments, this corresponds at
best to an ?8 ?m bright spot on the retina. With a suffi-
ciently small pinhole the presence of the photoreceptor
mosaic becomes apparent in the recorded images as re-
ported previously.7To simulate the situation, cone photo-
receptors have been distributed in a hexagonal arrange-
ment with added random jitter (each one bounded in a
hexagonal area to avoid overlapping cones) thereby re-
Fig. 2.
frames) obtained with a 0.785 ?m wavelength laser diode in the
right eye at ?2° nasal with different-sized pinholes: (a) 200, (b)
100, (c) 50, (d) 30 ?m. In (d) a small signal-to-noise ratio hinders
high image quality. Ocular motion prevents repeated recording of
exactly the same retinal location and images are therefore some-
what shifted with respect to each other.
Experimental images (correlation of 6–8 consecutive
2608J. Opt. Soc. Am. A/Vol. 22, No. 12/December 2005 Vohnsen et al.

Page 4

sembling the in vitro photoreceptor distributions studied
by Curcio et al.23
Figures 3 and 4 show simulated distributions of cones
(Gaussian beamintensity
=10,000/mm2and 20,000/mm2, respectively (correspond-
ing to typical cone spacings, lc=1.075/?1/2, of ?10.75 ?m
and ?7.60 ?m), and simulated c-SLO images for different
confocal pinholes. The wavefront aberration used in the
calculation is the experimentally recorded one shown in
Fig. 1. To match the situation at the periphery of the
fovea we have chosen wm=1.50 ?m for the quasi-
Gaussian mode (corresponding to an inner segment diam-
eter of approximately 3.6 ?m14). This mode results in a
spot size of wp=2.78 mm at the pupil for the near-IR
wavelength used. A smaller width at the pupil can be ob-
tained with a larger wm(i.e., for wider cones) or for a
shorter wavelength of illumination.
From the results obtained it is apparent that a suffi-
ciently small pinhole (comparable to the photoreceptor
spacing when imaged onto the retina) can reveal the un-
derlying photoreceptor mosaic as suggested by Eq. (2) and
images)for densities
?
as verified also by the spectral images. The larger pinhole
smears out any detailed structure with only some con-
trast produced by the variation in the number of simulta-
neously scanned cones (as contained within the area of
the pinhole) and by interference among the contributing
light beams. In reality, the simulated case of the large
pinhole is perchance somewhat exaggerated since the in-
cident beam hardly couples equally well to all contribut-
ing photoreceptors, thereby violating the assumption of
equal radiation from all (see Fig. 6 below). As the pinhole
is reduced the image resembles more closely the structure
of the original object, but the relationship is not a simple
one because of the overlap of light from neighboring cones
and the loss in resolution due to the finite pinhole size.
Thus, only in some cases can bright spots be unambigu-
ously identified with the presence of a corresponding pho-
toreceptor. Moreover, the greater the photoreceptor den-
sity the harder it becomes to identify contributions from
individual receptors.
To examine the image-deteriorating effect of aberra-
tions more closely, the process has been simulated with
different scalings of ?WAproducing the results shown in
Fig. 5. It can be seen that even with all aberrations cor-
rected, the image differs from the object because of the
blurring by the pinhole [cf. Fig. 5(d) and Fig. 3(a)]. The
resulting resolution loss prevents the distinction of closely
spaced photoreceptors although an increased brightness
Fig. 3.
10,000/mm2and corresponding c-SLO images for pinholes of (b)
100, (c) 50, (d) 30 ?m. The imaged retina is 6-times magnified in
the plane of the pinhole. Corresponding two-dimensional ampli-
tude spectra of (a) and (d) are shown in (e) and (f), respectively,
(to enhance contrast of the hexagonal frequency pattern the cen-
tral part of each spectrum has been suppressed). The wavefront
aberration used in the simulation is the experimentally obtained
one shown in Fig. 1(b).
Simulated (a) retinal section for a cone density of
Fig. 4.
20,000/mm2; otherwise, details are the same as in Fig. 3.
Simulated (a) retinal section for a cone density of
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Page 5

(when in phase) indicates the presence of more than one.
If the phase of each Gaussian beam is allowed to vary ar-
bitrarily, which may be the case if many photoreceptors
contribute at a time with a poorly focused incident
beam,14the image appearance does not change signifi-
cantly apart from some redistribution of brightness (for
simplicity not shown here).
We have also examined the consequences of including
the incident beam scanning in the model by taking a
2.0 mm wide (untruncated) incident beam at the eye pupil
(corresponding to wr?4.2 ?m), and letting it act as a
Gaussian weighting of the pinhole in accordance with Eq.
(3). The results obtained (Fig. 6) show a sharpening of de-
tails, but perhaps most apparent when compared to Fig. 3
is the absence of circular structures (pinhole images)
when larger pinholes are used. Thus, the situation comes
closer to the experimentally realized one, although proper
inclusion of the incident beam aberrations in T?u? is ex-
pected to produce an even greater resemblance.
Finally, the influence of the chosen illumination wave-
length has been considered. Near-IR has some clear ad-
vantages over the visible in the context of imaging apart
Fig. 5.
10,000/mm2and a 30 ?m pinhole for different amounts of the
wavefront aberration ?WAshown in Fig. 1(b): (a) ?WAsame as in
Fig. 3(d), (b) ?WA/2, (c) ?WA/4, (d) no aberrations (corresponding
to a completely corrected wavefront).
Simulated c-SLO images for a cone density of
Fig. 6.
scanning. For simplicity the spectral images are not shown.
Same as Fig. 3 but with the inclusion of incident beam
Fig. 7.
30 ?m pinhole for objects (a) 10,000/mm2with wm=1.50 ?m, (e)
5000/mm2with wm=2.00 ?m, respectively. Images of the objects
are shown at wavelengths of (b), (f) 0.785 ?m; (c), (g) 0.543 ?m,
all with the aberration map shown in Fig. 3(b); (d), (h) 0.543 ?m
without aberrations. Note that (a) and (b) are identical to Fig.
3(a) and Fig. 3(d), respectively, but have been reproduced here for
ease of comparison.
Simulated c-SLO images (b), (c), (d) and (f), (g), (h) with
2610 J. Opt. Soc. Am. A/Vol. 22, No. 12/December 2005Vohnsen et al.