Abstract
The spatial distribution of macular birefringence was modeled to examine the contribution from the foveal 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 for each individual, (p < 0.004) in 19 of 20 subjects. A good fit to linearity implies regular cone distribution and radial symmetry, and the uniformly excellent fits indicate no effect of age in our sample. The peak of the 2f sinewave amplitude varied across subjects from 1.06 to 2.46 deg. An increasingly eccentric peak with increasing age would indicate a relative decrease of cone axons in the central fovea, but the location of the peak was not associated with age for our sample, which did not include elderly subjects.
1. Introduction
In assessing changes to the retina with aging or disease, the foveal cone photoreceptors are considered crucial. Visual acuity is a typical means of assessing foveal cone photoreceptors, as tightly packed and functioning cones are required for good visual acuity. However, this clinically accepted standard can miss pathology. Further, poor visual acuity may result from problems in any part of the visual pathway, ranging from optical aberrations and clarity of the ocular media to the visual information processing and recognition of characters by the brain.
To provide more specific information about cones than obtained from either visual acuity or light sensitivity techniques, Pokorny and Smith (1976) demonstrated that foveal cones contain more photopigment per unit retinal surface area than the more eccentric cones. The underlying concept is that photopigment optical density depends on pathlength of light through the photopigment. As long as concentration of photopigment per unit volume, as well as extinction spectra of the photopigments, do not vary within the foveal region, the health of the outer segments is directly reflected by measures corresponding to optical density of photopigment. This seminal finding led to our current understanding that cone photopigment changes in aging are minimal outside the central fovea, but the central fovea for healthy eyes of older subjects has less photopigment optical density than for younger subjects (Eisner, Fleming, Klein, and Mauldin, 1987; Elsner, Berk, Burns, and Rosenberg, 1988; Swanson and Fish, 1996) and disease (Burns, Elsner, and Lobes, 1988; Eisner, Stoumbos, Klein, and Fleming, 1991; Elsner, Burns, Lobes, and Doft, 1987; Elsner, Burns, and Lobes, 1987; Elsner, Burns, and Weiter, 2002; Smith, Pokorny, and Diddie, 1978, 1988).
Cone photoreceptor outer segment health is also assessed with reflectometry, a complementary technique that measures the optical density of cone photopigment (Keunan, vanNorren, and vanMeel, 1987; Kilbride, Read, Fishman GA, and Fishman, 1983; Smith, Pokorny, and vanNorren, 1983). Imaging reflectometry measurements agree with the color matching techniques, demonstrating overall decreases in foveal cone photopigment with age consistent with changes in the distribution of the cone photopigment (Elsner, Burns, Beausencourt, and Weiter, 1998; Elsner, Burns, and Webb, 1993; Marcos, Tornow, Elsner, and Navarro, 1997). In young subjects, there is a sharp peak of cone photopigment optical density in the central fovea. In middle-aged subjects, there is a peak of cone photopigment in the central fovea, but this is less sharp than in younger subjects. In older subjects with normal retinas, the cone photopigment is displaced away from the foveal center in a manner that is better described as an annular distribution than a peak (Elsner et al., 1998). Macular pigment can also have an annular distribution (Elsner et al., 1998), with the annular distribution displaced outward radially as expected from the lateral displacement of cone axons. An annular distribution of macular pigment is consistent with several hypotheses (Berendschot and vanNorren, 2006; Elsner et al., 1998), but when photopigment and macular pigment distribution changes are found in the same subjects with independent image datasets, a parsimonious explanation is needed. One explanation is that cone photoreceptors migrate eccentrically and their axons, which contain macular pigment, are displaced laterally and are also located more eccentrically (Elsner et al., 1998.)
The studies with cone photopigment clearly demonstrate the potential for functional loss, given the low or even negligible amount of photopigment in the foveal center. Quantifying cone photopigment provides a measure of outer segment health, and documents the necessary relation of outer segment to inner segment in the capture of light and generation of a neural signal. However, these measures do not show whether a cone potentially can be rescued, but at the time of examination is unable to produce functional outer segments with photopigment.
A potential measure of whether foveal cones, even compromised ones, exist is obtained from quantifying the cone axons in the Henle fiber layer. In the central macula, the cone axons and Mueller cells processes are displaced away from the foveal center. Thus, in the central macula the Henle fiber layer is oriented primarily perpendicular with respect to incoming light, since axons run radially outward to connect with bipolar cells. The birefringence of the fovea has been modeled as the interaction of polarized light with the Henle fiber layer by Brink and Blokland (1988). The tightly packed axons and Mueller cells are modeled as producing form birefringence when struck in a mainly perpendicular direction by incoming light. That is, the Henle fiber layer acts as a crystal, and retards the light in one orientation of polarization more than in another.
There is no measurable phase retardation expected in the very central portion of the fovea, since even most cone cell bodies are displaced eccentrically. With increasing eccentricity, the numbers of axons that are displaced and therefore run laterally increases, since the cumulative numbers of cones increases. This gives rise to a potential increase in phase retardation. With further increasing eccentricity, outside the foveal pit, the layers in the inner retina are not displaced. The cone axons are oriented less radially and increasingly more perpendicularly with respect to the surface of the retina, reducing the expected form birefringence due to the Henle fiber layer. The inner retinal layers thicken with increasing eccentricity, and the thickness of the retinal nerve fiber layer increases sufficiently that it leads to quantifiable form birefringence (Weinreb, Dreher, Coleman, Quigley, Shaw, and Reiter, 1990). The relation of the total birefringence from the two major sources in the retina, Henle fiber and retinal nerve fiber, has not been quantified to date. The expected birefringence from the two difference layers in the retina, the Henle fiber layer and 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 dominate the measured birefringence, but with increasing eccentricity, the contribution from the Henle fiber layer becomes minimal and the asymmetric retinal nerve fiber layer dominates.
Fig. 1.
Macular birefringence schematic. Light passes thorugh a fixed region of the cornea, which acts like a crystal to retard light. The total macular birefringence has contributions from both the Henle fiber layer and the retinal nerve fiber layer, with the double arrow indicating the spatial extent that the Henle fiber layer contribution is dominant.
The interaction of polarized light with macular birefringence leads to the macular cross, also known as the macular bow tie, which is a windmill shaped pattern centered about the fovea that shows differing strength as a function of retinal position of the light return from the retina. The strength of the difference across the retina and the orientations of the bright parts of the cross depend on the orientation and degree of polarization of the light striking the retina, which is a function of both the instrumentation and the individual corneal properties. Polarization changes across the retina may be illustrated with a single image under the right conditions (Elsner, Weber, Cheney, VanNasdale, and Miura, 2007), but quantification generally requires a series of differing polarization conditions. The macular cross is radially symmetric in the central macula (Fig. 2), since collinear cone axons running from the foveal center outward produce the same form birefringence, for instance whether they run superiorly or inferiorly. The presence and location of the macular cross have been used to demonstrate the existence of cone photoreceptors, even in the presence of severe exudative Age-related Macular Degeneration (Elsner, Weber, Cheney et al., 2007; Weber, Elsner, Miura, Kompa, Cheney, 2006) or an infant eye with refractive error (Nassif, Piskun, Hunter, 2006).
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 areas indicate 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 orientation with 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 a sinwave 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 radially symmetric 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.
The changes in the configuration of cone axons with increasing eccentricity, that is less horizontally displaced from the inner segments and an overall cell body distribution with idodensity contours that are elliptical rather than circular, have called into question the measurement of cone axon length and radial distribution. The more eccentric axons are not completely included in a single serial section on histology (Drasdo Millican, Katholi, and Curcio, 2007). Nevertheless, the small amount of data at the central fovea does not indicate that there is the high degree of ellipticity that has been reported for more eccentric locations. Radial symmetry of the birefringence is expected in the healthy eye, and that is what is observed with the macular cross. The cone axons running temporally from the fovea are expected to mirror those running nasally, and similarly for superior and inferior axons, leading to an interaction with a fixed input polarization with a period of twice around the fovea. This implies that the radially symmetric retardance near the 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, 10 males and 10 females, ages 17–55 yr (mean age = 30.8 ± 9.2). These subjects all had 20/20 visual acuity and no abnormal fundus findings in the computed images at the time of test. In addition, we report the results for one subject from our Indiana database that illustrates one example of our criteria for normal. All procedures conformed to the Declaration of Helsinki, and the study was approved by the Institutional Review Board of either the Schepens Eye Research Institute or of Indiana University, as appropriate.
Scanning laser polarimetry and image analysis were performed as previously described, using a confocal Scanning Laser Polarimeter with illumination at 780 nm and 15 × 15 deg on the retina (GDx, Zeiss Meditec, San Diego, CA) (Burns, Elsner, Mellem-Kairala, & Simmons, 2003; Elsner, Weber, Cheney, VanNasdale, & Miura, 2007; Mellem-Kairala, Elsner, Weber A, Simmons, and Burns, 2005; Miura, Elsner, Cheney, Usui, Iwasaki, and 2007; Miura, Elsner, Weber, Cheney, Osako, Usui, Iwasaki, 2005; Weber, Cheney, Smithwick, Elsner, 2004; Weber et al., 2006). This instrument features a 2.5 mm fixed entrance/exit pupil and a fixed corneal compensator and a roughly telecentric design. Therefore, corneal birefringence is effectively constant for each subject over each pixel and image, with a fixed offset that can be calibrated. A series of 20 input polarizations is scanned across the retina in less than 1 second, with the light returning from the retina 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 in polarization content using Matlab (Mathworks, Natick, MA). The modulation in the crossed detector is computed, pixel by pixel, using a Fast Fourier Transform to 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, pixel by pixel, to show the phase retardance map. The phase retardance varies with radial position and retinal eccentricity.
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.
The amount of light that is unmodulated by the changing input polarization is computed as the minimum grayscale of the minimum of the modulation function (Fig. 3, top left). The average of both detectors is similar to a typical confocal image (Fig. 3, top right). The maximum of the phase retardation, when plotted in grayscale, is radially symmetric near the fovea (Fig. 3, bottom left). The input polarization that produced the maximum phase retardance was mapped using a pseudo-color scale, the Cardinal Directions Space (Elsner, Weber, Cheney et al., 2007). This space maps input polarizations that are out of phase along a continuum in additive color space, e.g. from red through achromatic to green, and allows phase wrapping. Increasing amplitude of the modulation is plotted as a more saturated color; therefore, desaturated colors indicate weak retardance with respect to surrounding retina. The input polarization that produces the maximum of the phase retardation, i.e. seen for the crossed detector, emphasizes that the birefringence is not constant in phase at greater eccentricities (Fig. 3, bottom right), and thus shows more contribution from less regularly oriented structures with increasing eccentricity.
To better model the birefringence contributions in normal eyes, we tested only subjects younger than those typically diagnosed with Age-related macular degeneration, and excluded subjects with diabetes or glaucomatous optic neuropathy. As seen in Fig. 4, glaucomatous optic neuropathy leads to degeneration of the retinal nerve fiber layer around the optic nerve head. The degeneration extends towards the macula, and the contribution of the retinal nerve fiber layer to macular birefringence seems to be unusually low in this individual (Fig. 5). Further, there are changes to the retinal pigment epithelium that are nasal to the optic nerve head, which are inconsistent with healthy photoreceptors (Fig. 5, top right). Although cone axons at this peripheral location run vertically, and would not contribute to total macular birefringence, our goal is to model normal Henle fiber layers and retinal ganglion cell axon contributions.
Fig. 4.
Optic nerve head data for polarization imaging for subject with glaucomatous optic neuropathy changes. Image types as in Fig. 4. The large amount of peripapillary atrophy and lack of strong birefringence along the vessel arcades indicate a damaged and thinned nerve fiber layer. This implies abnormally low peripheral macular birefringence, excluding the subject from analysis.
Fig. 5.
Macular polarization image data for the subject with glaucomatous optic neuropathy in Fig. 5. Image types as in Fig. 4. The damage to the nerve fiber layer is seen also in unusually low macular birefringence outside the central macula, excluding the subject from analysis.
2.2 Birefringence Model
To study the component of birefringence due to the Henle fiber layer, which produces the macular cross, and minimize unwanted contributions from other birefringent structures in the macula, we fit the following function from the data in each subject’s birefringence image:
where the total phase retardance is comprised of the sum of two sinewaves, one at the 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 fiber layer. The sin (f) component allows for asymmetry around the fovea, for example due to structures such as the Raphe of the retinal nerve fiber layer. For each concentric ring around the fovea, the phase of each sinewave was iteratively and independently varied 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 eccentricity in 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 distance. Thus, phase was not analyzed further, nor were the higher harmonics such as 4f. The constant C allows for variations in amplitude, such as for reflections due to the shape of the foveal crest, and for our subjects did not vary systematically with eccentricity. Linear regression of the amplitude of the 2f component as a function of eccentricity was performed for each subject. The fit to linearity was assessed by an r to z transform. The peak of the 2f component as a function of retinal eccentricity was estimated for each subject.
The present analysis is similar to that of Brink and Blokland (1988), except that they used a 1.5 deg diameter sampling region at various fundus locations and averaged over the sample. We did not use the Mueller matrix approach to remove the corneal birefringence in this study. Thus, to avoid averaging over peaks and troughs that would both be included in a 1.5 deg wide birefringence sample near the fovea (Fig. 2), we used rings of increasing diameter, centered around the fovea, that were 3 pixels wide. The foveal reflex prevents measurements at the foveal center. Close to the fovea, the rings had too few data points to compute the model parameters. There were no data points within 0.25 deg within of the fovea. To further study the effects of eccentricity on the 2f sinusoidal component, we compared 3 pixel wide rings of eccentricities of 1.4 deg and 3.2 deg. These were selected to be similar to the eccentricity of the circular sampling regions used by Brink and Blokland (1988).
3. Results
The amplitude of the sine wave fit to the 2f component of birefringence increased with increasing eccentricity (Fig. 6–Fig. 8). The linear portion of the data was particularly striking for eccentricities less than 1.25 deg (Fig. 7). There was an excellent linear fit of the amplitude sin 2f as a function of eccentricity for the individual data of 19 of 20 subjects in this portion of the data, with intercepts near 0 (p< 0.004). This is consistent with excellent radial symmetry of the Henle fibers in the foveal region. For Subject 20, age 27 yr, there was a general increase of the 2f component with increasing eccentricity, but the fit was poorer (Fig. 8), particularly in the central fovea 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 of corneal birefringence that is well-modeled as a crystal might have been violated for this subject, who despite 20/20 visual acuity had long term problems with refractive error that could not be resolved with traditional sphere or cylinder corrections. However, the fit near 1 deg is linear for Subject 20. Therefore, by considering only data in the region of 1 deg eccentricity, the amplitude of the 2f component was well-fit by a linear function of eccentricity for each of the 20 subjects tested.
Fig. 6.
The amplitudes of the 2f and the 2 sinusoidal components of the macular birefringence for 2 typical subjects, plotted as a function of retinal eccentricity, for successively larger rings centered about the fovea. The 2f component increases linearly with increasing eccentricity, in the foveal region.
Fig. 8.
The amplitude of the 2f and the f sinusoidal components of the macular birefringence for subject 20, plotted as a function of retinal eccentricity. This was the only subject without an excellent linear fit for the 2f sinusoindal component near fovea, but demonstrates the strong influence on macular birefringence of the f sinusoindal component outside the fovea.
Fig. 7.
The amplitudes of the 2f and the f sinusoidal components of the macular birefringence for Subject 1, plotted only for the linear portion in the central 1.25 deg eccentricity. Amplitude sin 2f = 1.823 + 9.229 * eccentricity in deg; R^2 = .974. Amplitude sin f = 1.916 + .93 * eccentricity in deg; R^2 = .187. The dotted lines indicate the 95% Confidence Limits for slope.
The subjective peak of the 2f component of birefringence differs across subjects (Fig. 9), ranging from about 1.06 to 2.46 deg from the foveal center, mean = 1.63 ± .404 deg (489 microns). The peak was generally a broad maximum (Fig. 6). Beyond the peak of the 2f component, there was a decrease with increasing eccentricity, and for some subjects at greater eccentricities, the 2f component can be of lower amplitude than the f component. However, at 1.25 deg eccentricity the 2f component was still at least twice as large as the f component for 17 of 20 subjects. For all 20 subjects, the 2f component dominated the total macular birefringence when eccentricities of about 1 deg were examined.
Fig. 9.
The eccentricity of the maximum amplitude of the 2f sinusoindal component, indicating where the peak birefringence associated with the Henle fiber layer occurred for each subject, plotted as a function of age. Regression of the retinal eccentricity for the peak of 2f on age, with 95% Confidence Limits shown as dotted lines. There was no clear trend with age for our sample of normal subjects. Peak = 24.713 + .1 * age; R^2 = .018.
For computations in a large group of subjects, there is the potential of significant intrusion of other components into the total birefringence, such as those due to retinal nerve fiber layer. When the data for only the 2f component of birefringence were scaled to be 1 at 3.22 deg, the mean retardance for the 1.4 deg data was 1.53 times larger than the 3.22 deg data, which was statistically significant (p < 0.0039).
An increase with increasing age of the peak of the 2f amplitude would indicate a decrease in the distribution of cone axons. As demonstrated in Fig. 9, there was no strong relation of the peak of the 2f sinusoidal component with age (R2 = 0.018), thereby not supporting a linear model of change throughout the lifespan. The only subject without an excellent linear fit of the 2f sinusoidal component to retinal eccentricity only nearer to 1 deg, was among the younger subjects. The subjects in this study overlapped the age of subjects in previous studies who had peaked distributions of cone photopigment and macular pigment, whether the peaks were steep or gradual. All subjects in the present study were all at least 10 years younger than those found to have an annular distribution of cone photopigment and macular pigment. Thus, there was good agreement between the present study and the previous studies of photopigment and macular pigment.
4. Discussion
Macular birefringence was shown to have at least two components, with a strong sinusoidal component at 2f in the central macula. This component is consistent with phase retardance due to the Henle fiber layer. The 2f component increases linearly until about 1 deg eccentricity. At greater eccentricities, the amplitude of the 2f component decreases for all subjects, but is still readily measurable even in the presence of the contribution from the retinal nerve fiber layer.
The peak of the linear portion of the 2f component varied somewhat across subjects, but not with age in the narrow age range studied. All subjects had an excellent linear fit for the 2f sinusoidal data near 1 deg eccentricity, regardless of age. The present subjects were younger than those found to have an annular distribution of cone photopigment and macular pigment (Elsner at al., 1998). This indicates that the alteration in the cone maps, with maxima at increasing eccentricities, has not yet occurred. Thus, there is no support in these data for the outward migration of cones, or relatively greater death of central cones, in this age group. Older age groups with healthy retinas are anticipated to also have strong macular birefringence at 1 deg, since the diameter of the annuli for macular pigment was greater than that for photopigment. This previous finding implies that the cone axons tend to travel laterally, as in younger subjects, but with the longer axons still displaced eccentrically. The recent data on Henle fibers do not include comparison data for older and younger subjects in the central fovea (Drasdo et al., 2007). However, if the changes with eccentricity are due to the thickness of the Henle fiber layer, which indicates the number of cone axons, then the excellent fits and lack of change with age in the central ± 1 deg indicate radial symmetry and similar distributions of the cone axons for our subjects.
For a complete model of total macular birefringence, the contribution of each individual’s cornea must be removed (Weinreb, Bowd, and Zangwill, 2003). As the 2f sinusoidal component resulted in excellent fits to the model, then the birefringence remaining after this component is removed may be used to model the cornea and 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 component. Thus, for quantitative models, the data at 1 deg provide the opportunity for excellent signal to noise ratio in the fitting of the three components, and the fixed corneal birefringence can be removed to provide the signal from the retinal components alone.
As the signal for the 2f sinusoidal at 1 deg is strong for the age range tested, and likely to be strong also for healthy older retinas, this component provides a potential standard against which diseased eyes can be compared for phase retardance. There are significant birefringence changes with exudative Age-related macular degeneration (Elsner, et al, 2007), and the present data provide the first step in a model to discriminate normal from diseased eyes. The phase information may also be useful in a complete model of macular birefringence.
Light that does not retain its polarization characteristics upon interaction with disease tissues or several layers or normal tissues becomes randomly polarized. The amount of light returning that is unmodulated with input polarization quantifies the scattered light returning from altered structures and deeper layers. This has been used to visualize features not otherwise seen (Burns et al., 2003; Elsner et al, 2007; Mellem-Kairalla, 2005). A quantitative measure of scattered light may potentially quantify early disease changes, and computations made using data at about 1 deg eccentricity will ensure a good signal of the modulated component, so that the remaining weak signal of the scattered light is measured under favorable conditions.
Our data are based on reflectometry measures, and light may not fully pass through the retina at every point and therefore underestimate the phase retardation. Even though we found a linear fit, linearity per se is not a necessary consequence of the radial increase in form birefringence due to cone axons. A gradual decrease in the 2f component is consistent with the change from relatively horizontal to vertical of the cone axons, that is a change from perpendicular to the illumination to parallel to the illumination. A sharp decrease in the 2f component would be more consistent with a defect in the photoreceptor distribution.
The elegant methods that magnify the structures of the human retina in a noninvasive manner typically do not provide quantitative measures of the Henle fiber layer. Photoreceptor imaging allows counting of photoreceptors, but not in the foveal region for most subjects (Burns, Tumbar, Elsner, Ferguson, and Hammer, 2007; Li and Roorda, 2007; Pircher, Baumann, Gotzinger, and Hitzenberger, 2006; Roorda and Williams,2002; Wade and Fitzke, 1998; Xue, Choi, Doble, and Werner, 2007). This procedure often requires wide dilation, and depends upon relatively clear media.
Even with the newest methods of Optical Coherence Tomography, the Henle fiber layer is often not visualized well enough to quantify cone axons in the foveal region, and in some case the inner segment and outer segment are combined into a single layer for purposes of labeling (Iftimia, Hammer, Bigelow, Ustun, de Boer, and Ferguson, (2006) ; Nassif, Cense, Park, Pierce, Yun, Bouma, Tearney, Chen, and de Boer, 2004; Pircher, Gotzinger, Findl, Michels, Geitzenauer, Leydolt, Schmidt-Erfurth, Hitzenberger, 2006; Srinivasan, Huber, Gorczynska, Fujimoto, Jiang, Reisen, and Cable, 2007). When OCT is combined with polarization, the Henle fiber layer is better visualized than with reflected light OCT alone. However, the signal to noise ratio is still not high enough to provide a smooth curve in the en face sections, with radial banding that are not seen in our images (Pircher, Götzinger, Leitgeb, Sattmann, Findl, and Hitzenberger, 2004).
In summary, we present a first step in modeling macular birefringence that can isolate the signal from foveal cone photoreceptors from the remaining elements with retinal birefringence. We identified a location, 1 deg eccentric, that should provide a good signal to noise ratio for quantification of birefringence and scattered light. For modeling birefringence, by adding a second step that removes the contribution of the corneal birefringence, the absolute value of macular birefringence could be obtained. This provides a noninvasive and inexpensive quantification of foveal cones.
Acknowledgments
The project described was supported by Grant Number R01EY007624 from the National Eye Institute. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Eye Institute or the National Institutes of Health.
Footnotes
Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
References
- Berendschot TT, van Norren D. Macular pigment shows ringlike structures. Investigative Ophthalmology and Vision Science. 2006;47:709–714. doi: 10.1167/iovs.05-0663. [DOI] [PubMed] [Google Scholar]
- Brink HB, van Blokland GJ. Birefringence of the human foveal area assessed in vivo with Mueller-matrix ellipsometry. Journal of the Optical Society of America A. 1988;5:49–57. doi: 10.1364/josaa.5.000049. [DOI] [PubMed] [Google Scholar]
- Burns SA, Elsner AE. Color matching at high illuminances: the color-match-area effect and photopigment bleaching. Journal of the Optical Society of America A. 1985;2:698–704. doi: 10.1364/josaa.2.000698. [DOI] [PubMed] [Google Scholar]
- Burns SA, Elsner AE, Lobes LA., Jr Photopigment Bleaching in Central Serous Retinopathy. Applied Optics. 1988;27:1045–1049. doi: 10.1364/AO.27.001045. [DOI] [PubMed] [Google Scholar]
- Burns SA, Elsner AE, Mellem-Kairala MB, Simmons RB. Improved contrast of subretinal structures using polarization analysis. Investigative Ophthalmology and Vision Science. 2003;44:4061–4068. doi: 10.1167/iovs.03-0124. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Burns SA, Tumbar R, Elsner A, Ferguson RD, Hammer DX. Large Field of View, Modular, Stabilized, Adaptive-Optics-Based Scanning Laser Ophthalmoscope. Journal of the Optical Society of America A. 2007;24:1313–1326. doi: 10.1364/josaa.24.001313. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Drasdo N, Millican CL, Katholi CR, Curcio CA. The length of Henle fibers in the human retina and a model of ganglion receptive field density in the visual field. Vision Research. 2007;47:2901–2911. doi: 10.1016/j.visres.2007.01.007. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Eisner A, Fleming SA, Klein ML, Mauldin WM. Sensitivities in older eyes with good acuity: cross-sectional norms. Investigative Ophthalmology and Vision Science. 1987;28:1824–1831. [PubMed] [Google Scholar]
- Eisner A, Stoumbos VD, Klein ML, Fleming SA. Relations between fundus appearance and function. Eyes whose fellow eye has exudative age-related macular degeneration. Investigative Ophthalmology and Vision Science. 1991;32:8–20. [PubMed] [Google Scholar]
- Elsner AE, Berk L, Burns SA, Rosenberg PR. Aging and human cone photopigments. Journal of the Optical Society of America A. 1988;5:2106–2112. doi: 10.1364/josaa.5.002106. [DOI] [PubMed] [Google Scholar]
- Elsner AE, Burns SA, Weiter JJ, Delori FC. Infrared imaging of sub-retinal structures in the human ocular fundus. Vision Research. 1996;36:191–205. doi: 10.1016/0042-6989(95)00100-e. [DOI] [PubMed] [Google Scholar]
- Elsner AE, Burns SA, Beausencourt E, Weiter JJ. Foveal cone photopigment distribution: small alterations associated with macular pigment distribution. Investigative Ophthalmology and Vision Science. 1998;39:2394–2404. [PubMed] [Google Scholar]
- Elsner AE, Burns SA, Lobes LA, Jr, Doft BH. Cone photopigment bleaching abnormalities in diabetes. Investigative Ophthalmology and Vision Science. 1987;28:718–724. [PubMed] [Google Scholar]
- Elsner AE, Burns SA, Lobes LA., Jr Foveal cone pigment optical density in retinitis pigmentosa. Applied Optics. 1987;26:1378–1384. doi: 10.1364/AO.26.001378. [DOI] [PubMed] [Google Scholar]
- Elsner AE, Burns SA, Weiter JJ. Cone photopigment in older subjects: decreased optical density in early age-related macular degeneration. Journal of the Optical Society of America A. 2002;19:215–222. doi: 10.1364/josaa.19.000215. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Elsner AE, Burns SA, Webb RH. Mapping cone photopigment density in humans. Journal of the Optical Society of America A. 1993;10:52–58. doi: 10.1364/josaa.10.000052. [DOI] [PubMed] [Google Scholar]
- Elsner AE, Weber A, Cheney MC, VanNasdale DA, Miura M. Imaging Polarimetry in Patients with Neovascular Age Related Macular Degeneration. Journal of the Optical Society of America A. 2007;24:1468–1480. doi: 10.1364/josaa.24.001468. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Iftimia NV, Hammer DX, Bigelow CE, Ustun T, de Boer JF, Ferguson RD. Hybrid retinal imager using line-scanning laser ophthalmoscopy and spectral domain optical coherence tomography. Optics Express. 2006;14:12909–12914. doi: 10.1364/oe.14.012909. [DOI] [PubMed] [Google Scholar]
- Keunen JEE, van Norren D, van Meel GJ. Density of foveal cone pigments at older age. Investigative Ophthalmology and Vision Science. 1987;28:985–991. [PubMed] [Google Scholar]
- Kilbride PE, Read JS, Fishman GA, Fishman M. Determination of human cone pigment density difference spectra in spatially resolved regions of the fovea. Vision Research. 1983;23:1341–1350. doi: 10.1016/0042-6989(83)90145-1. [DOI] [PubMed] [Google Scholar]
- Marcos S, Tornow R-P, Elsner AE, Navarro R. Foveal cone spacing and cone photopigment density difference: objective measurements in the same subjects. Vision Research. 1997;37:1909–1915. doi: 10.1016/s0042-6989(96)00295-7. [DOI] [PubMed] [Google Scholar]
- Mellem-Kairala MB, Elsner AE, Weber A, Simmons RB, Burns SA. Improved contrast of peripapillary hyperpigmentation using polarization analysis. Investigative Ophthalmology and Vision Science. 2005;46:1099–1106. doi: 10.1167/iovs.04-0574. [DOI] [PubMed] [Google Scholar]
- Li KY, Roorda A. Automated Identification of Cones in Adaptive Optics Fundus Images. ” Journal of the Optical Society of America A. 2007;24:1358–1363. doi: 10.1364/josaa.24.001358. [DOI] [PubMed] [Google Scholar]
- Miura M, Elsner AE, Weber A, Cheney MC, Osako M, Usui M, Iwasaki T. Imaging polarimetry in central serous chorioretinopathy. American Journal of Ophthalmology. 2005;140:1014–1019. doi: 10.1016/j.ajo.2005.06.033. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Miura M, Elsner AE, Cheney MC, Usui M, Iwasaki T. Imaging Polarimetry and Retinal Blood Vessel Quantification at the Epiretinal Membrane. Journal of the Optical Society of America A. 2007;24:1431–1437. doi: 10.1364/josaa.24.001431. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Nassif N, Cense B, Park B, Pierce M, Yun S, Bouma B, Tearney G, Chen T, de Boer J. In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve. Optics Express. 2004;12:367–376. doi: 10.1364/opex.12.000367. [DOI] [PubMed] [Google Scholar]
- Nassif DS, Piskun NV, Hunter DG. The Pediatric Vision Screener III: detection of strabismus in children. Archives of Ophthalmology. 2006;124:509–513. doi: 10.1001/archopht.124.4.509. [DOI] [PubMed] [Google Scholar]
- Pircher M, Baumann B, Gotzinger E, Hitzenberger CK. Retinal cone mosaic imaged with transverse scanning optical coherence tomography. Optics Letters. 2006;15:1821–1823. doi: 10.1364/ol.31.001821. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Pircher M, Götzinger E, Leitgeb R, Sattmann H, Findl O, Hitzenberger C. Imaging of polarization properties of human retina in vivo with phase resolved transversal PS-OCT. Optics Express. 2004;12:5940–5951. doi: 10.1364/opex.12.005940. [DOI] [PubMed] [Google Scholar]
- Pircher M, Gotzinger E, Findl O, Michels S, Geitzenauer W, Leydolt C, Schmidt-Erfurth U, Hitzenberger CK. Human macula investigated in vivo with polarization-sensitive optical coherence tomography. Investigative Ophthalmology and Vision Science. 2006;47:5487–5494. doi: 10.1167/iovs.05-1589. [DOI] [PubMed] [Google Scholar]
- Pokorny J, Smith VC. Effect of field size on red--green color mixture equations. Journal of the Optical Society of America. 1976;66:705–708. doi: 10.1364/josa.66.000705. [DOI] [PubMed] [Google Scholar]
- Roorda A, Williams DR. Optical fiber properties of individual human cones. Journal of Vision. 2002;2:404–412. doi: 10.1167/2.5.4. [DOI] [PubMed] [Google Scholar]
- Smith VC, Pokorny J, Diddie KR. Color matching and Stiles-Crawford effect in central serous choroidopathy. Modern Problems in Ophthalmology. 1978;19:284–295. [PubMed] [Google Scholar]
- Smith VC, Pokorny J, Diddie KR. Color matching and the Stiles-Crawford effect in observers with early age-related macular changes. Journal of the Optical Society of America A. 1988;5:2113–2121. doi: 10.1364/josaa.5.002113. [DOI] [PubMed] [Google Scholar]
- Smith VC, Pokorny J, van Norren D. Densitometric measurement of human cone photopigment kinetics. Vision Research. 1983;23:517–524. doi: 10.1016/0042-6989(83)90126-8. [DOI] [PubMed] [Google Scholar]
- Srinivasan VJ, Huber R, Gorczynska I, Fujimoto JG, Jiang JY, Reisen R, Cable AE. High-speed, high-resolution optical coherence tomography retinal imaging with a frequency-swept laser at 850 nm. Optics. Letters. 2007;32:361–363. doi: 10.1364/ol.32.000361. [DOI] [PubMed] [Google Scholar]
- Swanson WH, Fish GE. Age-related changes in the color-match-area effect. Vision Research. 1996;36:2079–2085. doi: 10.1016/0042-6989(95)00280-4. [DOI] [PubMed] [Google Scholar]
- Wade A, Fitzke F. A fast, robust pattern recognition asystem for low light level image registration and its application to retinal imaging. Optics Express. 1998;3:190–197. doi: 10.1364/oe.3.000190. [DOI] [PubMed] [Google Scholar]
- Weber A, Cheney MC, Smithwick QYJ, Elsner AE. Polarimetric imaging and blood vessel quantification. Optics Express. 2004;12:5178–5190. doi: 10.1364/opex.12.005178. [DOI] [PubMed] [Google Scholar]
- Weber A, Elsner AE, Miura M, Kompa S, Cheney MC. Relationship between foveal birefringence and visual acuity in neovascular age-related macular degeneration. Eye. 2006;21:353–361. doi: 10.1038/sj.eye.6702203. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Weinreb RN, Bowd C, Zangwill LM. Glaucoma detection using scanning laser polarimetry with variable corneal polarization compensation. Archives of Ophthalmology. 2003;12:218–224. doi: 10.1001/archopht.121.2.218. [DOI] [PubMed] [Google Scholar]
- Weinreb RN, Dreher AW, Coleman A, Quigley H, Shaw B, Reiter K. Histopathologic Validation of Fourier-Ellipsometry Measurements of Retinal Nerve-Fiber Layer Thickness. Archives of Ophthalmology. 1990;108:557–560. doi: 10.1001/archopht.1990.01070060105058. [DOI] [PubMed] [Google Scholar]
- Xue B, Choi SS, Doble N, Werner JS. Photoreceptor counting and montaging of en-face retinal images from an adaptive optics fundus camera. Journal of the Optical Society of America A. 2007;24:1364–1372. doi: 10.1364/josaa.24.001364. [DOI] [PMC free article] [PubMed] [Google Scholar]