Vision Research 48 (2008) 2578–2585

Contents lists available at ScienceDirect

Vision Research

journal homepage: www.elsevier .com/locate /v isres

Spatial distribution of macular birefringence associated with the Henle fibers q

Ann E. Elsner a,*, Anke Weber b, Michael C. Cheney c, Dean A. VanNasdale a

a School of Optometry, Indiana University, 800 East Atwater, Bloomington, IN 47405, USAb Department of Ophthalmology, University Hospital, Pauwelsstr. 30, 52074 Aachen, Germanyc Gene Network Sciences, Inc. 10 Canal Park, Cambridge, MA 02141, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 18 October 2007Received in revised form 20 April 2008

Keywords:ConeHenle fiber layerPolarization imagingRetinaFovea

0042-6989/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.visres.2008.04.031

q Supported by EY007624 to A.E.E.* Corresponding author. Fax: +1 812 855 7045.

E-mail address: aeelsner@indiana.edu (A.E. Elsner)

The spatial distribution of macular birefringence was modeled to examine the contribution from thefoveal Henle fiber layer, particularly cone axons. The model was tested in 20 normal subjects, age 17–55 yr. Phase retardance due to Henle fibers was modeled for rings increasing in radius around the fovea,using a sinewave of two periods (2f). The 2f sinewave amplitude increased linearly with eccentricity foreach individual, (p < 0.004) in 19 of 20 subjects. A good fit to linearity implies regular cone distributionand radial symmetry, and the uniformly excellent fits indicate no effect of age in our sample. The peak ofthe 2f sinewave amplitude varied across subjects from 1.06 to 2.46 deg. An increasingly eccentric peakwith increasing age would indicate a relative decrease of cone axons in the central fovea, but the locationof the peak was not associated with age for our sample, which did not include elderly subjects.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

In assessing changes to the retina with aging or disease, the fo-veal cone photoreceptors are considered crucial. Visual acuity is atypical means of assessing foveal cone photoreceptors, as tightlypacked and functioning cones are required for good visual acuity.However, this clinically accepted standard can miss pathology. Fur-ther, poor visual acuity may result from problems in any part of thevisual pathway, ranging from optical aberrations and clarity of theocular media to the visual information processing and recognitionof characters by the brain.

To provide more specific information about cones than obtainedfrom either visual acuity or light sensitivity techniques, Pokornyand Smith (1976) demonstrated that foveal cones contain morephotopigment per unit retinal surface area than the more eccentriccones. The underlying concept is that photopigment optical densitydepends on pathlength of light through the photopigment. As longas concentration of photopigment per unit volume, as well asextinction spectra of the photopigments, do not vary within the fo-veal region, the health of the outer segments is directly reflected bymeasures corresponding to optical density of photopigment (Burns& Elsner, 1985). This seminal finding led to our current under-standing that cone photopigment changes in aging are minimaloutside the central fovea, but the central fovea for healthy eyesof older subjects has less photopigment optical density than foryounger subjects (Eisner, Fleming, Klein, & Mauldin, 1987a; Elsner,

ll rights reserved.

.

Berk, Burns, & Rosenberg, 1988; Swanson & Fish, 1996) and disease(Burns, Elsner, & Lobes, 1988; Eisner, Stoumbos, Klein, & Fleming,1991; Elsner, Burns, & Lobes, 1987c; Elsner, Burns, Lobes, & Doft,1987b; Elsner, Burns, & Weiter, 2002; Smith, Pokorny, & Diddie,1978; Smith, Pokorny, & Diddie, 1988).

Cone photoreceptor outer segment health is also assessed withreflectometry, a complementary technique that measures the opti-cal density of cone photopigment (Keunen, van Norren, & van Meel,1987; Kilbride, Read, Fishman, & Fishman, 1983; Smith, Pokorny, &van Norren, 1983). Imaging reflectometry measurements agreewith the color matching techniques, demonstrating overall de-creases in foveal cone photopigment with age consistent withchanges in the distribution of the cone photopigment (Elsner,Burns, Beausencourt, & Weiter, 1998; Elsner, Burns, & Webb,1993; Marcos, Tornow, Elsner, & Navarro, 1997). In young subjects,there is a sharp peak of cone photopigment optical density in thecentral fovea. In middle-aged subjects, there is a peak of conephotopigment in the central fovea, but this is less sharp than inyounger subjects. In older subjects with normal retinas, the conephotopigment is displaced away from the foveal center in a man-ner that is better described as an annular distribution than a peak(Elsner et al., 1998). Macular pigment can also have an annular dis-tribution (Elsner et al., 1998), with the annular distribution dis-placed outward radially as expected from the lateraldisplacement of cone axons. An annular distribution of macularpigment is consistent with several hypotheses (Berendschot &van Norren, 2006; Elsner et al., 1998), but when photopigmentand macular pigment distribution changes are found in the samesubjects with independent image datasets, a parsimonious expla-nation is needed. One explanation is that cone photoreceptors

A.E. Elsner et al. / Vision Research 48 (2008) 2578–2585 2579

migrate eccentrically and their axons, which contain macular pig-ment, are displaced laterally and are also located more eccentri-cally (Elsner et al., 1998).

The studies with cone photopigment clearly demonstrate thepotential for functional loss, given the low or even negligibleamount of photopigment in the foveal center. Quantifying conephotopigment provides a measure of outer segment health, anddocuments the necessary relation of outer segment to inner seg-ment in the capture of light and generation of a neural signal. How-ever, these measures do not show whether a cone potentially canbe rescued, but at the time of examination is unable to producefunctional outer segments with photopigment.

A potential measure of whether foveal cones, even compromisedones, exist is obtained from quantifying the cone axons in the Henlefiber layer. In the central macula, the cone axons and Mueller cellsprocesses are displaced away from the foveal center. Thus, in thecentral macula the Henle fiber layer is oriented primarily perpendic-ular with respect to incoming light, since axons run radially outwardto connect with bipolar cells. The birefringence of the fovea has beenmodeled as the interaction of polarized light with the Henle fiberlayer by Brink and van Blokland (1988). The tightly packed axonsand Mueller cells are modeled as producing form birefringencewhen struck in a mainly perpendicular direction by incoming light.That is, the Henle fiber layer acts as a crystal, and retards the lightin one orientation of polarization more than in another.

There is no measurable phase retardation expected in the verycentral portion of the fovea, since even most cone cell bodies aredisplaced eccentrically. With increasing eccentricity, the numbersof axons that are displaced and therefore run laterally increases,since the cumulative numbers of cones increases. This gives riseto a potential increase in phase retardation. With further increas-ing eccentricity, outside the foveal pit, the layers in the inner retinaare not displaced. The cone axons are oriented less radially andincreasingly more perpendicularly with respect to the surface ofthe retina, reducing the expected form birefringence due to theHenle fiber layer. The inner retinal layers thicken with increasingeccentricity, and the thickness of the retinal nerve fiber layer in-creases sufficiently that it leads to quantifiable form birefringence(Weinreb et al., 1990). The relation of the total birefringence fromthe two major sources in the retina, Henle fiber and retinal nervefiber, has not been quantified to date. The expected birefringencefrom the two difference layers in the retina, the Henle fiber layerand the retinal nerve fiber layer, differs in pattern and amount,depending on the retinal location (Fig. 1). Near the fovea center,the thin but radially symmetric Henle fiber layer should dominatethe measured birefringence, but with increasing eccentricity, thecontribution from the Henle fiber layer becomes minimal and theasymmetric retinal nerve fiber layer dominates.

Fig. 1. Macular birefringence schematic. Light passes through a fixed region of the cocontributions from both the Henle fiber layer and the retinal nerve fiber layer, with thedominant.

The interaction of polarized light with macular birefringenceleads to the macular cross, also known as the macular bow tie,which is a windmill shaped pattern centered about the fovea thatshows differing strength as a function of retinal position of thelight return from the retina. The strength of the difference acrossthe retina and the orientations of the bright parts of the cross de-pend on the orientation and degree of polarization of the lightstriking the retina, which is a function of both the instrumentationand the individual corneal properties. Polarization changes acrossthe retina may be illustrated with a single image under the rightconditions (Elsner, Weber, Cheney, VanNasdale, & Miura, 2007),but quantification generally requires a series of differing polariza-tion conditions. The macular cross is radially symmetric in the cen-tral macula (Fig. 2), since collinear cone axons running from thefoveal center outward produce the same form birefringence, for in-stance whether they run superiorly or inferiorly. The presence andlocation of the macular cross have been used to demonstrate theexistence of cone photoreceptors, even in the presence of severeexudative Age-related Macular Degeneration (Elsner et al., 2007;Weber, Elsner, Miura, Kompa, & Cheney, 2006) or an infant eyewith refractive error (Nassif, Piskun, & Hunter, 2006).

The changes in the configuration of cone axons with increasingeccentricity, that is less horizontally displaced from the inner seg-ments and an overall cell body distribution with idodensity con-tours that are elliptical rather than circular, have called intoquestion the measurement of cone axon length and radial distribu-tion. The more eccentric axons are not completely included in asingle serial section on histology (Drasdo, Millican, Katholi, & Cur-cio, 2007). Nevertheless, the small amount of data at the central fo-vea does not indicate that there is the high degree of ellipticity thathas been reported for more eccentric locations. Radial symmetry ofthe birefringence is expected in the healthy eye, and that is what isobserved with the macular cross. The cone axons running tempo-rally from the fovea are expected to mirror those running nasally,and similarly for superior and inferior axons, leading to an interac-tion with a fixed input polarization with a period of twice aroundthe fovea. This implies that the radially symmetric retardance nearthe foveal center may serve as a model for the Henle fiber layer,without a significant contribution from retinal nerve fiber layer.This model and its implications are examined.

2. Methods

2.1. Polarization imaging

We acquired digital scanning laser polarimetry images in 20 normal subjects, 10males and 10 females, ages 17–55 yr (mean age = 30.8 ± 9.2). These subjects all had20/20 visual acuity and no abnormal fundus findings in the computed images at thetime of test. In addition, we report the results for one subject from our Indiana

rnea, which acts like a crystal to retard light. The total macular birefringence hasdouble arrow indicating the spatial extent that the Henle fiber layer contribution is

Fig. 2. (Top) Normal macular birefringence image, a phase retardance map, showing the change in modulation of the gray scale with input polarization angle. Light areasindicate a large amount of modulation across the input angles, and dark areas indicate a small amount, due to the interaction of corneal birefringence at a fixed orientationwith birefringent layers in the retina that vary in orientation with location. (Bottom) Diagram of decomposition of the intensity of the macular birefringence. The fit to asinwave of two periods around the fovea (sin 2f) is compared with the fit to a sinewave of only one period (sin f). The 2f data are consistent with the interaction of a radiallysymmetric structure interacting with constant corneal birefringence. The f data represent other major sources of macular birefringence that might be radially asymmetric,such as the ganglion cell axons.

2580 A.E. Elsner et al. / Vision Research 48 (2008) 2578–2585

database that illustrates one example of our criteria for normal. All procedures con-formed to the Declaration of Helsinki, and the study was approved by the Institu-tional Review Board of either the Schepens Eye Research Institute or of IndianaUniversity, as appropriate.

Scanning laser polarimetry and image analysis were performed as previouslydescribed, using a confocal Scanning Laser Polarimeter with illumination at780 nm and 15 � 15 deg on the retina (GDx, Zeiss Meditec, San Diego, CA)(Burns, Elsner, Mellem-Kairala, & Simmons, 2003; Elsner et al., 2007; Mellem-Kairala, Elsner, Weber, Simmons, & Burns, 2005; Miura, Elsner, Cheney, Usui, &Iwasaki, 2007; Miura et al., 2005; Weber, Cheney, Smithwick, & Elsner, 2004;Weber et al., 2006). This instrument features a 2.5 mm fixed entrance/exit pupiland a fixed corneal compensator and a roughly telecentric design. Therefore, cor-neal birefringence is effectively constant for each subject over each pixel and im-age, with a fixed offset that can be calibrated. A series of 20 input polarizationsis scanned across the retina in less than 1 s, with the light returning from theretina split by a polarizing beam splitter into two confocal detection pathways,a cross and a parallel detector.

The resulting 40 images were used to compute a series of images that vary inpolarization content using Matlab (Mathworks, Natick, MA). The modulation inthe crossed detector is computed, pixel by pixel, using a Fast Fourier Transformto smooth the data (Fig. 2, top). The result is the macular cross (Fig. 2, bottom,Fig. 3, bottom left). From this, the amplitude of the modulation is plotted, pixelby pixel, to show the phase retardance map. The phase retardance varies with radialposition and retinal eccentricity.

The amount of light that is unmodulated by the changing input polarizationis computed as the minimum grayscale of the minimum of the modulation func-tion (Fig. 3, top left). The average of both detectors is similar to a typical confocalimage (Fig. 3, top right). The maximum of the phase retardation, when plotted ingrayscale, is radially symmetric near the fovea (Fig. 3, bottom left). The inputpolarization that produced the maximum phase retardance was mapped usinga pseudo-color scale, the Cardinal Directions Space (Elsner et al., 2007). Thisspace maps input polarizations that are out of phase along a continuum in addi-tive color space, e.g. from red through achromatic to green, and allows phasewrapping. Increasing amplitude of the modulation is plotted as a more saturatedcolor; therefore, desaturated colors indicate weak retardance with respect to sur-rounding retina. The input polarization that produces the maximum of the phaseretardation, i.e. seen for the crossed detector, emphasizes that the birefringenceis not constant in phase at greater eccentricities (Fig. 3, bottom right), and thusshows more contribution from less regularly oriented structures with increasingeccentricity.

To better model the birefringence contributions in normal eyes, we testedonly subjects younger than those typically diagnosed with Age-related maculardegeneration, and excluded subjects with diabetes or glaucomatous optic neu-ropathy. As seen in Fig. 4, glaucomatous optic neuropathy leads to degenera-tion of the retinal nerve fiber layer around the optic nerve head. Thedegeneration extends towards the macula, and the contribution of the retinalnerve fiber layer to macular birefringence seems to be unusually low in thisindividual (Fig. 5). Further, there are changes to the retinal pigment epitheliumthat are nasal to the optic nerve head, which are inconsistent with healthyphotoreceptors (Fig. 5, top right). Although cone axons at this peripheral loca-tion run vertically, and would not contribute to total macular birefringence,our goal is to model normal Henle fiber layers and retinal ganglion cell axoncontributions.

2.2. Birefringence model

To study the component of birefringence due to the Henle fiber layer, whichproduces the macular cross, and minimize unwanted contributions from other bire-fringent structures in the macula, we fit the following function from the data ineach subject’s birefringence image:

AmplitudeðeccentricityÞ ¼ a sin f þ b sin 2f þ C;

where the total phase retardance is comprised of the sum of two sinewaves, one atthe fundamental frequency (f) that has one period around the fovea and the other at(2f) to allow for the interaction of the birefringence of the cornea and the Henle fiberlayer. The sin (f) component allows for asymmetry around the fovea, for example dueto structures such as the Raphe of the retinal nerve fiber layer. For each concentricring around the fovea, the phase of each sinewave was iteratively and independentlyvaried to find the best fit, as was the amplitude of each sinewave, given by a and b.

The phase of the 2f sinusoidal component, in fact, did not vary with eccentricityin the central ±1 deg. This is illustrated graphically in the macular cross in Fig. 2,since the bright or dark portions expand outward along the same radii over that dis-tance. Thus, phase was not analyzed further, nor were the higher harmonics such as4f. The constant C allows for variations in amplitude, such as for reflections due tothe shape of the foveal crest, and for our subjects did not vary systematically witheccentricity. Linear regression of the amplitude of the 2f component as a function ofeccentricity was performed for each subject. The fit to linearity was assessed by an rto z transform. The peak of the 2f component as a function of retinal eccentricitywas estimated for each subject.

Fig. 3. Macular polarization image data for a normal subject. Four of the image types computed from the raw data of the scanning laser polarimetry are shown. (Top left)Depolarized light image, computed as the minimum grayscale over all 20 input polarization angles, and is dominated by scattered light from deeper structures. (Top right)Confocal image, which is the average of both crossed and parallel detectors. (Bottom left) Birefringence image, which is the modulation of the crossed detector.

Fig. 4. Optic nerve head data for polarization imaging for subject with glaucomatous optic neuropathy changes. Image types as in Fig. 3. The large amount of peripapillaryatrophy and lack of strong birefringence along the vessel arcades indicate a damaged and thinned nerve fiber layer. This implies abnormally low peripheral macularbirefringence, excluding the subject from analysis.

A.E. Elsner et al. / Vision Research 48 (2008) 2578–2585 2581

The present analysis is similar to that of Brink and van Blokland (1988),except that they used a 1.5 deg diameter sampling region at various funduslocations and averaged over the sample. We did not use the Mueller matrixapproach to remove the corneal birefringence in this study. Thus, to avoidaveraging over peaks and troughs that would both be included in a 1.5 degwide birefringence sample near the fovea (Fig. 2), we used rings of increasingdiameter, centered around the fovea, that were 3 pixels wide. The foveal reflex

prevents measurements at the foveal center. Close to the fovea, the rings hadtoo few data points to compute the model parameters. There were no datapoints within 0.25 deg within of the fovea. To further study the effects ofeccentricity on the 2f sinusoidal component, we compared 3 pixel wide ringsof eccentricities of 1.4 and 3.2 deg. These were selected to be similar to theeccentricity of the circular sampling regions used by Brink and van Blokland(1988).

Fig. 5. Macular polarization image data for the subject with glaucomatous optic neuropathy in Fig. 4. Image types as in Fig. 4. The damage to the nerve fiber layer is seen alsoin unusually low macular birefringence outside the central macula, excluding the subject from analysis.

2582 A.E. Elsner et al. / Vision Research 48 (2008) 2578–2585

3. Results

The amplitude of the sine wave fit to the 2f component of bire-fringence increased with increasing eccentricity (Figs. 6–8). Thelinear portion of the data was particularly striking for eccentricitiesless than 1.25 deg (Fig. 7). There was an excellent linear fit of theamplitude sin 2f as a function of eccentricity for the individual data

Fig. 6. The amplitudes of the 2f and the 2 sinusoidal components of the macularbirefringence for 2 typical subjects, plotted as a function of retinal eccentricity, forsuccessively larger rings centered about the fovea. The 2f component increaseslinearly with increasing eccentricity, in the foveal region.

of 19 of 20 subjects in this portion of the data, with intercepts near0 (p < 0.004). This is consistent with excellent radial symmetry ofthe Henle fibers in the foveal region. For Subject 20, age 27 yr, therewas a general increase of the 2f component with increasing eccen-tricity, but the fit was poorer (Fig. 8), particularly in the central fo-vea where there were few data points in the ring used for the fit(p < 0.09). This subject, who was neither the oldest nor youngest,had similar data on repeated measurement. This assumption ofcorneal birefringence that is well-modeled as a crystal might havebeen violated for this subject, who despite 20/20 visual acuity hadlong term problems with refractive error that could not be resolvedwith traditional sphere or cylinder corrections. However, the fitnear 1 deg is linear for Subject 20. Therefore, by considering onlydata in the region of 1 deg eccentricity, the amplitude of the 2fcomponent was well-fit by a linear function of eccentricity for eachof the 20 subjects tested.

The subjective peak of the 2f component of birefringence differsacross subjects (Fig. 9), ranging from about 1.06–2.46 deg from the

Fig. 7. The amplitudes of the 2f and the f sinusoidal components of the macularbirefringence for Subject 1, plotted only for the linear portion in the central 1.25 degeccentricity. Amplitude sin 2f = 1.823 + 9.229 *eccentricity in deg; R2 = .974. Ampli-tude sin f = 1.916 + .93 *eccentricity in deg; R2 = .187. The dotted lines indicate the95% Confidence Limits for slope.

Fig. 8. The amplitude of the 2f and the f sinusoidal components of the macularbirefringence for subject 20, plotted as a function of retinal eccentricity. This wasthe only subject without an excellent linear fit for the 2f sinusoindal componentnear fovea, but demonstrates the strong influence on macular birefringence of the fsinusoindal component outside the fovea.

A.E. Elsner et al. / Vision Research 48 (2008) 2578–2585 2583

foveal center, mean = 1.63 ± .404 deg (489 l). The peak was gener-ally a broad maximum (Fig. 6). Beyond the peak of the 2f compo-nent, there was a decrease with increasing eccentricity, and forsome subjects at greater eccentricities, the 2f component can beof lower amplitude than the f component. However, at 1.25 degeccentricity the 2f component was still at least twice as large asthe f component for 17 of 20 subjects. For all 20 subjects, the 2fcomponent dominated the total macular birefringence wheneccentricities of about 1 deg were examined.

For computations in a large group of subjects, there is thepotential of significant intrusion of other components into the totalbirefringence, such as those due to retinal nerve fiber layer. Whenthe data for only the 2f component of birefringence were scaled tobe 1 at 3.22 deg, the mean retardance for the 1.4 deg data was 1.53times larger than the 3.22 deg data, which was statistically signif-icant (p < 0.0039).

An increase with increasing age of the peak of the 2f amplitudewould indicate a decrease in the distribution of cone axons. Asdemonstrated in Fig. 9, there was no strong relation of the peakof the 2f sinusoidal component with age (R2 = 0.018), thereby notsupporting a linear model of change throughout the lifespan. Theonly subject without an excellent linear fit of the 2f sinusoidalcomponent to retinal eccentricity only nearer to 1 deg, was amongthe younger subjects. The subjects in this study overlapped the ageof subjects in previous studies who had peaked distributions ofcone photopigment and macular pigment, whether the peaks weresteep or gradual. All subjects in the present study were all at least10 years younger than those found to have an annular distributionof cone photopigment and macular pigment. Thus, there was good

Fig. 9. The eccentricity of the maximum amplitude of the 2f sinusoindal compo-nent, indicating where the peak birefringence associated with the Henle fiber layeroccurred for each subject, plotted as a function of age. Regression of the retinaleccentricity for the peak of 2f on age, with 95% Confidence Limits shown as dottedlines. There was no clear trend with age for our sample of normal subjects.Peak = 24.713 + .1 *age; R2 = .018.

agreement between the present study and the previous studies ofphotopigment and macular pigment.

4. Discussion

Macular birefringence was shown to have at least two compo-nents, with a strong sinusoidal component at 2f in the central mac-ula. This component is consistent with phase retardance due to theHenle fiber layer. The 2f component increases linearly until about1 deg eccentricity. At greater eccentricities, the amplitude of the2f component decreases for all subjects, but is still readily measur-able even in the presence of the contribution from the retinal nervefiber layer.

The peak of the linear portion of the 2f component variedsomewhat across subjects, but not with age in the narrow agerange studied. All subjects had an excellent linear fit for the 2fsinusoidal data near 1 deg eccentricity, regardless of age. Thepresent subjects were younger than those found to have anannular distribution of cone photopigment and macular pigment(Elsner et al., 1998). This indicates that the alteration in the conemaps, with maxima at increasing eccentricities, has not yet oc-curred. Thus, there is no support in these data for the outwardmigration of cones, or relatively greater death of central cones,in this age group. Older age groups with healthy retinas areanticipated to also have strong macular birefringence at 1 deg,since the diameter of the annuli for macular pigment was great-er than that for photopigment. This previous finding implies thatthe cone axons tend to travel laterally, as in younger subjects,but with the longer axons still displaced eccentrically. The recentdata on Henle fibers do not include comparison data for olderand younger subjects in the central fovea (Drasdo et al., 2007).However, if the changes with eccentricity are due to the thick-ness of the Henle fiber layer, which indicates the number of coneaxons, then the excellent fits and lack of change with age in thecentral ±1 deg indicate radial symmetry and similar distributionsof the cone axons for our subjects.

For a complete model of total macular birefringence, the contri-bution of each individual’s cornea must be removed (Weinreb,Bowd, & Zangwill, 2003). As the 2f sinusoidal component resultedin excellent fits to the model, then the birefringence remainingafter this component is removed may be used to model the corneaand the retinal nerve fiber layer. At 1 deg, the young to middle-aged subjects tested in the study had a strong signal for the 2f com-ponent. Thus, for quantitative models, the data at 1 deg provide theopportunity for excellent signal to noise ratio in the fitting of thethree components, and the fixed corneal birefringence can be re-moved to provide the signal from the retinal components alone.

As the signal for the 2f sinusoidal at 1 deg is strong for the agerange tested, and likely to be strong also for healthy older retinas,this component provides a potential standard against which dis-eased eyes can be compared for phase retardance. There are signif-icant birefringence changes with exudative Age-related maculardegeneration (Elsner et al., 2007), and the present data providethe first step in a model to discriminate normal from diseased eyes.The phase information may also be useful in a complete model ofmacular birefringence.

Light that does not retain its polarization characteristics uponinteraction with disease tissues or several layers or normal tissuesbecomes randomly polarized. The amount of light returning that isunmodulated with input polarization quantifies the scattered lightreturning from altered structures and deeper layers. Scattered lighthas been used to visualize features not otherwise seen (Burns et al.,2003; Elsner et al., 2007; Mellem-Kairala et al., 2005; Elsner, Burns,Weiter, & Delori, 1996). A quantitative measure of scattered lightmay potentially quantify early disease changes, and computations

2584 A.E. Elsner et al. / Vision Research 48 (2008) 2578–2585

made using data at about 1 deg eccentricity will ensure a good sig-nal of the modulated component, so that the remaining weak sig-nal of the scattered light is measured under favorable conditions.

Our data are based on reflectometry measures, and light maynot fully pass through the retina at every point and thereforeunderestimate the phase retardation. Even though we found a lin-ear fit, linearity per se is not a necessary consequence of the radialincrease in form birefringence due to cone axons. A gradual de-crease in the 2f component is consistent with the change from rel-atively horizontal to vertical of the cone axons, that is a changefrom perpendicular to the illumination to parallel to the illumina-tion. A sharp decrease in the 2f component would be more consis-tent with a defect in the photoreceptor distribution.

The elegant methods that magnify the structures of the humanretina in a noninvasive manner typically do not provide quantita-tive measures of the Henle fiber layer. Photoreceptor imaging al-lows counting of photoreceptors, but not in the foveal region formost subjects (Burns, Tumbar, Elsner, Ferguson, & Hammer,2007; Li & Roorda, 2007; Pircher, Baumann, Gotzinger, & Hitzen-berger, 2006a; Roorda & Williams, 2002; Wade & Fitzke, 1998;Xue, Choi, Doble, & Werner, 2007). This procedure often requireswide dilation, and depends upon relatively clear media.

Even with the newest methods of Optical Coherence Tomogra-phy, the Henle fiber layer is often not visualized well enough toquantify cone axons in the foveal region, and in some case the in-ner segment and outer segment are combined into a single layerfor purposes of labeling (Iftimia et al. (2006), Nassif et al., 2004, Pir-cher et al., 2006b, Srinivasan et al., 2007). When OCT is combinedwith polarization, the Henle fiber layer is better visualized thanwith reflected light OCT alone. However, the signal to noise ratiois still not high enough to provide a smooth curve in the en facesections, with radial banding that are not seen in our images (Pir-cher et al., 2004).

In summary, we present a first step in modeling macular birefrin-gence that can isolate the signal from foveal cone photoreceptorsfrom the remaining elements with retinal birefringence. We identi-fied a location, 1 deg eccentric, that should provide a good signal tonoise ratio for quantification of birefringence and scattered light.For modeling birefringence, by adding a second step that removesthe contribution of the corneal birefringence, the absolute value ofmacular birefringence could be obtained. This provides a noninva-sive and inexpensive quantification of foveal cones.

Acknowledgments

The project described was supported by Grant No.R01EY007624 from the National Eye Institute. The content is solelythe responsibility of the authors and does not necessarily representthe official views of the National Eye Institute or the National Insti-tutes of Health.

References

Berendschot, T. T., & van Norren, D. (2006). Macular pigment shows ringlikestructures. Investigative Ophthalmology and Vision Science, 47, 709–714.

Brink, H. B., & van Blokland, G. J. (1988). Birefringence of the human foveal areaassessed in vivo with Mueller-matrix ellipsometry. Journal of the Optical Societyof America A, 5, 49–57.

Burns, S. A., & Elsner, A. E. (1985). Color matching at high illuminances: The color-match-area effect and photopigment bleaching. Journal of the Optical Society ofAmerica A, 2, 698–704.

Burns, S. A., Elsner, A. E., & Lobes, L. A. Jr., (1988). Photopigment bleaching in centralserous retinopathy. Applied Optics, 27, 1045–1049.

Burns, S. A., Elsner, A. E., Mellem-Kairala, M. B., & Simmons, R. B. (2003). Improvedcontrast of subretinal structures using polarization analysis. InvestigativeOphthalmology and Vision Science, 44, 4061–4068.

Burns, S. A., Tumbar, R., Elsner, A., Ferguson, R. D., & Hammer, D. X. (2007). Largefield of view, modular, stabilized, adaptive-optics-based scanning laserophthalmoscope. Journal of the Optical Society of America A, 24, 1313–1326.

Drasdo, N., Millican, C. L., Katholi, C. R., & Curcio, C. A. (2007). The length of Henlefibers in the human retina and a model of ganglion receptive field density in thevisual field. Vision Research, 47, 2901–2911.

Eisner, A., Fleming, S. A., Klein, M. L., & Mauldin, W. M. (1987a). Sensitivities in oldereyes with good acuity: Cross-sectional norms. Investigative Ophthalmology andVision Science, 28, 1824–1831.

Eisner, A., Stoumbos, V. D., Klein, M. L., & Fleming, S. A. (1991). Relations betweenfundus appearance and function. Eyes whose fellow eye has exudative age-related macular degeneration. Investigative Ophthalmology and Vision Science,32, 8–20.

Elsner, A. E., Berk, L., Burns, S. A., & Rosenberg, P. R. (1988). Aging and human conephotopigments. Journal of the Optical Society of America A, 5, 2106–2112.

Elsner, A. E., Burns, S. A., Weiter, J. J., & Delori, F. C. (1996). Infrared imaging of sub-retinal structures in the human ocular fundus. Vision Research, 36, 191–205.

Elsner, A. E., Burns, S. A., Beausencourt, E., & Weiter, J. J. (1998). Foveal conephotopigment distribution: Small alterations associated with macular pigmentdistribution. Investigative Ophthalmology and Vision Science, 39, 2394–2404.

Elsner, A. E., Burns, S. A., Lobes, L. A., Jr., & Doft, B. H. (1987b). Cone photopigmentbleaching abnormalities in diabetes. Investigative Ophthalmology and VisionScience, 28, 718–724.

Elsner, A. E., Burns, S. A., & Lobes, L. A. Jr., (1987c). Foveal cone pigment opticaldensity in retinitis pigmentosa. Applied Optics, 26, 1378–1384.

Elsner, A. E., Burns, S. A., & Weiter, J. J. (2002). Cone photopigment in older subjects:Decreased optical density in early age-related macular degeneration. Journal ofthe Optical Society of America A, 19, 215–222.

Elsner, A. E., Burns, S. A., & Webb, R. H. (1993). Mapping cone photopigment densityin humans. Journal of the Optical Society of America A, 10, 52–58.

Elsner, A. E., Weber, A., Cheney, M. C., VanNasdale, D. A., & Miura, M. (2007).Imaging polarimetry in patients with neovascular age related maculardegeneration. Journal of the Optical Society of America A, 24, 1468–1480.

Iftimia, N. V., Hammer, D. X., Bigelow, C. E., Ustun, T., de Boer, J. F., & Ferguson, R. D.(2006). Hybrid retinal imager using line-scanning laser ophthalmoscopy andspectral domain optical coherence tomography. Optics Express, 14,12909–12914.

Keunen, J. E. E., van Norren, D., & van Meel, G. J. (1987). Density of foveal conepigments at older age. Investigative Ophthalmology and Vision Science, 28,985–991.

Kilbride, P. E., Read, J. S., Fishman, G. A., & Fishman, M. (1983). Determination ofhuman cone pigment density difference spectra in spatially resolved regions ofthe fovea. Vision Research, 23, 1341–1350.

Li, K. Y., & Roorda, A. (2007). Automated identification of cones in adaptive opticsfundus images. Journal of the Optical Society of America A, 24, 1358–1363.

Marcos, S., Tornow, R.-P., Elsner, A. E., & Navarro, R. (1997). Foveal cone spacing andcone photopigment density difference: Objective measurements in the samesubjects. Vision Research, 37, 1909–1915.

Mellem-Kairala, M. B., Elsner, A. E., Weber, A., Simmons, R. B., & Burns, S. A. (2005).Improved contrast of peripapillary hyperpigmentation using polarizationanalysis. Investigative Ophthalmology and Vision Science, 46, 1099–1106.

Miura, M., Elsner, A. E., Weber, A., Cheney, M. C., Osako, M., Usui, M., et al. (2005).Imaging polarimetry in central serous chorioretinopathy. American Journal ofOphthalmology, 140, 1014–1019.

Miura, M., Elsner, A. E., Cheney, M. C., Usui, M., & Iwasaki, T. (2007). Imagingpolarimetry and retinal blood vessel quantification at the epiretinal membrane.Journal of the Optical Society of America A, 24, 1431–1437.

Nassif, N., Cense, B., Park, B., Pierce, M., Yun, S., Bouma, B., et al. (2004). In vivo high-resolution video-rate spectral-domain optical coherence tomography of thehuman retina and optic nerve. Optics Express, 12, 367–376.

Nassif, D. S., Piskun, N. V., & Hunter, D. G. (2006). The Pediatric Vision Screener III:Detection of strabismus in children. Archives of Ophthalmology, 124, 509–513.

Pircher, M., Baumann, B., Gotzinger, E., & Hitzenberger, C. K. (2006a). Retinal conemosaic imaged with transverse scanning optical coherence tomography. OpticsLetters, 15, 1821–1823.

Pircher, M., Götzinger, E., Leitgeb, R., Sattmann, H., Findl, O., & Hitzenberger, C.(2004). Imaging of polarization properties of human retina in vivo with phaseresolved transversal PS-OCT. Optics Express, 12, 5940–5951.

Pircher, M., Gotzinger, E., Findl, O., Michels, S., Geitzenauer, W., Leydolt, C., et al.(2006b). Human macula investigated in vivo with polarization-sensitive opticalcoherence tomography. Investigative Ophthalmology and Vision Science, 47,5487–5494.

Pokorny, J., & Smith, V. C. (1976). Effect of field size on red–green color mixtureequations. Journal of the Optical Society of America, 66, 705–708.

Roorda, A., & Williams, D. R. (2002). Optical fiber properties of individual humancones. Journal of Vision, 2, 404–412.

Smith, V. C., Pokorny, J., & Diddie, K. R. (1978). Color matching and Stiles-Crawfordeffect in central serous choroidopathy. Modern Problems in Ophthalmology, 19,284–295.

Smith, V. C., Pokorny, J., & Diddie, K. R. (1988). Color matching and the Stiles-Crawford effect in observers with early age-related macular changes. Journal ofthe Optical Society of America A, 5, 2113–2121.

Smith, V. C., Pokorny, J., & van Norren, D. (1983). Densitometric measurement ofhuman cone photopigment kinetics. Vision Research, 23, 517–524.

Srinivasan, V. J., Huber, R., Gorczynska, I., Fujimoto, J. G., Jiang, J. Y., Reisen, R., et al.(2007). High-speed, high-resolution optical coherence tomography retinalimaging with a frequency-swept laser at 850 nm. Optics Letters, 32, 361–363.

Swanson, W. H., & Fish, G. E. (1996). Age-related changes in the color-match-areaeffect. Vision Research, 36, 2079–2085.

A.E. Elsner et al. / Vision Research 48 (2008) 2578–2585 2585

Wade, A., & Fitzke, F. (1998). A fast, robust pattern recognition system for low lightlevel image registration and its application to retinal imaging. Optics Express, 3,190–197.

Weber, A., Cheney, M. C., Smithwick, Q. Y. J., & Elsner, A. E. (2004).Polarimetric imaging and blood vessel quantification. Optics Express, 12,5178–5190.

Weber, A., Elsner, A. E., Miura, M., Kompa, S., & Cheney, M. C. (2006). Relationshipbetween foveal birefringence and visual acuity in neovascular age-relatedmacular degeneration. Eye, 21, 353–361.

Weinreb, R. N., Bowd, C., & Zangwill, L. M. (2003). Glaucoma detection usingscanning laser polarimetry with variable corneal polarization compensation.Archives of Ophthalmology, 12, 218–224.

Weinreb, R. N., Dreher, A. W., Coleman, A., Quigley, H., Shaw, B., & Reiter, K. (1990).Histopathologic validation of fourier-ellipsometry measurements of retinalnerve-fiber layer thickness. Archives of Ophthalmology, 108, 557–560.

Xue, B., Choi, S. S., Doble, N., & Werner, J. S. (2007). Photoreceptor counting andmontaging of en-face retinal images from an adaptive optics fundus camera.Journal of the Optical Society of America A, 24, 1364–1372.