The directional component of the retinal reflection, i.e., the optical Stiles-Crawford effect (SCE), is well established to result from the waveguiding property of photoreceptors. Considerable uncertainty, however, remains as to which retinal reflections are waveguided and thus contribute. To this end we have developed a retina camera based on spectral-domain optical coherence tomography (SD-OCT) that axially resolves (~5 µm) these reflections and permits a direct investigation of the SCE origin at near infrared wavelengths. Reflections from the photoreceptor inner/outer segments junction (IS/OS) and near the posterior tip of the outer segments (PTOS) were found highly sensitive to beam entry position in the pupil with a considerable decrease in brightness occurring with an increase in aperture eccentricity. Reflections from the retinal pigment epithelium (RPE) were largely insensitive. The average directionality (ρoct value) at 2 degree eccentricity across the four subjects for the IS/OS, PTOS, and RPE were 0.120, 0.270, and 0.016 mm-2, respectively. The directionality for the IS/OS approached typical psychophysical SCE measurements, while that for the PTOS approached conventional optical SCE measurements. Precise measurement of the optical SCE was found to require significant A-scan averaging.
© 2008 Optical Society of America
It has been long established that the human visual system has reduced sensitivity to light rays that enter near the edge of the eye’s pupil compared to those entering near the center. This effect, referred to as the psychophysical Stiles-Crawford effect (SCE), was discovered by Stiles and Crawford, and results from the waveguiding property of photoreceptors[1-3]. The same effect also manifests itself in the retinal reflection that exits the eye, which is commonly referred to as the optical SCE. Light that returns from the fundus in ophthalmoscopy reflects from many layers within the retina, choroid and sclera. The optical SCE is created by those reflections that are directed back towards the center of the pupil by the photoreceptors, producing more light at the pupil center than at the pupil edge.
Normal directionality of the SCE requires normal morphology of the photoreceptors and extracellular space, making the SCE of clinical interest. The SCE has been used in preliminary studies to indicate the stage and degree of various retinal abnormalities. These include diabetic retinopathy , macular edema , age-related macular changes , pigment epitheliopathy , retinal detachments [8, 9], and others [7, 10-14]. An added benefit of the SCE as a biomarker is its stability with age [15, 16].
The psychophysical and optical SCEs have been extensively studied – the latter using a variety of objective reflectometers. Gorrand and Delori  flood illuminated the fovea and detected the resulting reflection through small, displaced entrance and exit pupils that were mechanically scanned in tandem across the pupil plane of the eye. De Lint, et al.  used a similar approach on the fovea albeit with a scanning laser ophthalmoscope (SLO). Burns, et al.  improved on these designs by capturing the entire SCE in a single snapshot, realized by illuminating the fovea through a small entrance pupil and then imaging the entire pupil plane with a sensitive areal CCD array. Zagers, et al.  measured the optical SCE across the entire visible spectrum using an imaging spectrograph.
These reflectometers have largely established our current understanding of the optical SCE, yet while successful considerable uncertainty remains as to the portion of the fundus reflections that is waveguided. Two leading views are that the waveguided light originates from (1) reflections across the entire axial length of the outer segment due to refractive index variations induced by the stack of photopigment carrying discs  and (2) reflections from the posterior tips of the photoreceptor outer segments (PTOS) and possibly from melanin granules of the RPE [21-23]. A third view has been suggested recently in that light reflecting from layers further behind the photoreceptors is also waveguided, especially at longer wavelengths . It is not clear what factors account for the major discrepancies between these reports. Nevertheless, an overarching concern with all these studies is that the waveguided reflections are inferred from reflectometric measurements in which axial resolution is no better than the full thickness of the retina (~300 µm), let alone comparable to the distances between tissue reflections that the techniques aim to distinguish.
To address this concern, we propose a paradigm shift in SCE instrumentation by taking advantage of the major advances that have occurred in OCT. Specifically, we evaluate the efficacy of a reflectometer based on SD-OCT [25, 26] whose axial resolution (~5 µm) and sensitivity (~94 dB with a ~27 dB dynamic range across the retina) greatly surpass those of current SCE methods. The instrument is used to measure the directionality of several prominent layers of the retina to determine which contribute to the optical SCE. Early accounts of this work were presented at the 2006 and 2007 ARVO meetings [27, 28].
2.1 Description of spectral-domain OCT apparatus
Figure 1 shows a schematic of the laboratory SD-OCT instrument that was used to measure reflectivity as a function of (1) depth in the retina and (2) beam location in the subject’s pupil. The instrument represents a modified version of that described in detail by Zhang, et al. . In short, the instrument employs a fiber-based beamsplitter that optically connects four channels: (1) illumination channel for generating short-temporal coherence light by way of a broadband 10 mW superluminescent diode (SLD) (λ=842 nm, Δλ=50 nm); (2) sample channel for scanning a focused beam across the retina, and collecting reflected and backscattered light from the retina; (3) reference channel for matching the optical path of the sample channel; and (4) detection channel for recording the superimposed sample and reference light after being dispersed by a transmission grating.
The instrument in Zhang, et al. was designed with an adaptive optics (AO) sub-system for correction of ocular and instrument aberrations across a 6.6 mm pupil at the eye. For the experiment in this paper, a small diaphragm was inserted in the sample channel at a plane conjugate to the pupil of the eye. The diaphragm was centered on the optical axis of the instrument and reduced the beam diameter to 2 mm, a size small enough that the effects of ocular aberrations are greatly reduced and diffraction likely limits image quality [30, 31]. As such AO was used to provide static compensation of only instrument aberrations, which were the same for all subjects imaged. The 2 mm pupil size is consistent with that used in conventional double-pass measurements of the optical SCE, i.e., 1 to 2 mm [16, 17]. Because the instrument was designed for a 6.6 mm pupil, insertion of the 2 mm diaphragm reduced the power incident on the eye to just 71 µW, a level that complied with the American National Standards Institute (ANSI) . The low power level is undesirable for most retinal imaging applications as it yields unacceptably low signal to noise (S/N). However, we were able to substantially increase the S/N by using long exposure durations (200 µs/A-scan) and averaging many A-scans. The final S/N was more than sufficient for quantifying reflections from all major retinal layers and evaluating their contributions to the optical SCE. Furthermore, averaging of A-scans proved necessary (regardless of the power level) to reduce speckle noise, which is intrinsic to the interferometric nature of OCT.
The OCT instrument included a fixation channel that consisted of a 90:10 pellicle beamsplitter and a visual target positioned at the subject’s far point of accommodation. The target was back illuminated with uniform red light and contained high contrast cross hairs regularly spaced on a rectilinear grid at one degree intervals. The fixation channel also included a pellicle beamsplitter that redirected half of the light to a video camera that was used for aligning the subject’s pupil to the instrument. The camera was pre-focused on the exit pupil of the SD-OCT instrument. The pupil camera imaged the 842 nm light in retro-illumination and was sensitive enough to detect backscatter from the cornea and iris, and thus permitted real-time monitoring of the beam location in the subject’s pupil. Beam location was measured relative to the center of the subject’s pupil using a calibrated bull’s eye pattern that was fixed to the pupil camera monitor. The pattern consisted of a transparency with printed concentric black rings calibrated at 1 mm intervals and was centered on the optical axis of the OCT instrument.
The full width at half height (FWHH) axial resolution of the OCT instrument was measured at 6.6 µm (air) on an intensity scale using a model eye. The 6.6 µm corresponds to 4.8 µm in retinal tissue assuming a refractive index of 1.38 . Lateral resolution at the focal plane was nominally 8.6 µm, the diffraction-limited spot size for a 2 mm pupil as defined by 1.22 λ f/d. λ is the mean wavelength of light (842 nm), f is the nominal focal length of the eye (16.7 mm), and d is the pupil diameter. A-scans were acquired at 1 µm intervals, which is much finer than the diffraction-limited spot size. Depth of focus was more than 500 µm when defined as two times the Rayleigh range.
2.2 Human subjects
The four subjects (3 male, 1 female) who participated in the experiment were free of ocular disease and had normal corrected vision. The refractive errors of the subjects were -4.5, -2.5, -2.75, and -3.75 diopter sphere and 0, 0, 1.25, and 0 diopter cylinder, respectively. The subjects were cyclopleged and their pupils dilated using a drop of Tropicamide 1% and another of Phenylephrine Hydrochloride 2.5% that were administered prior to measurements. A dental impression and forehead rest attached to a sturdy xyz bite-bar translation stage stabilized the subject’s head and provided accurate pupil positioning. The subject’s line of sight was initially centered along the optical axis of the OCT instrument with the aid of the fixation target, bite-bar stage, and pupil camera. Trial lenses were inserted into the spectacle plane to correct the subject’s refractive errors of sphere and cylinder. The distance between the subject’s pupil and trial lens plane was about 10 mm. This minified the pupil as viewed through the trial lens to 0.97±0.0075 of its original size (average ± standard deviation across the four subjects). This slight minification did not warrant compensation in the experiment.
2.3 Data acquisition and processing
The subject’s retina was illuminated and imaged (double pass) through the same 2 mm circular aperture. The common aperture was systematically positioned at 13 locations in the subject’s pupil by translating the subject’s head and monitoring the pupil camera. Translation of the head did not cause eye rotation as light from the fixation target was collimated at the subject’s pupil and overfilled it. Narrow B-scans were acquired of a vertical strip of the retina 2 degrees nasal to the fovea for each of 13 pupil positions (spaced at 1 mm) along the vertical and horizontal meridians as illustrated in Fig. 1 (bottom). A retinal eccentricity of 2 degrees was chosen to facilitate comparison to optical and psychophysical SCE measurements in the literature [17, 33]. B-scans were reconstructed following the protocol described in Zhang, et al.  with careful attention to compensating dispersion by employing both hardware (water vial in reference channel) and software  techniques. For one subject, dispersion compensation was systematically optimized in software for each of the 13 entrance pupil positions. Because the effect on dispersion was negligible, compensation was not adjusted for pupil position for any of the subjects.
Speckle is a granular noise fundamental to the interferometric nature of OCT and can introduce errors in the reflectivity measurements of the retina. To reduce this noise as well as artifacts caused by structural inhomogeneities residing in individual retinal layers, many A-scans of the same local patch of retina were axially registered and averaged. Specifically, 100 B-scans were acquired at each of the 13 entry positions with each B-scan composed of 512 A-scans that subtended approximately 1.7 degrees. From the 100 B-scans, 10 were selected that exhibited minimal motion artifacts and high S/N, and that captured the retina at about the same axial location along the B-scan. The latter assured that the sensitivity drop of the OCT detector with depth was approximately the same for the 10 B-scans. This was further refined in software by calibrating out the actual sensitivity drop of the OCT detector (see Fig. 3 of Zhang, et al. ) in conjunction with axial registration of A-scans using a cross correlation method. From each of the 10 B-scans, 51 corresponding A-scans (0.17 degree) were selected, and these 510 A-scans were axially registered, averaged and used in the analysis. Next we assessed the effectiveness of our averaging protocol to reduce speckle noise and structural inhomogeneities within retinal layers as a function of A-scans averaged. To do this, the contrast of the fluctuations, which is defined as the standard deviation over mean , was determined for four targeted depths located within and in front of the retina: vitreous, ganglion cell layer (GCL), PTOS, and RPE. These were selected as they vary significantly in reflectance and structural information, are more or less distributed across the retina, and two were examined as potential sources of the optical SCE.
As a first step at determining the axial origin of the optical SCE, the reflection peaks that occur at the IS/OS, PTOS, and RPE were examined as a function of pupil position. These three layers were selected as they generate some of the brightest reflections in the retina and represent light that has traversed at least a portion of the photoreceptor layer, the layer universally considered pivotal in generating the optical SCE [3, 15]. Our labeling of these three layers is consistent with that widely reported in the OCT literature, including studies of histologic correlation of OCT images [35-37]. For each subject in our experiment, the axial position of the three layers was determined from all of the averaged A-scans (i.e., from the 13 sub-aperture positions). This approach provided reasonable confidence in the depth location of the layers, even in those individual averaged A-scans in which some of the layers were not prominent. Because measurement of the IS/OS, PTOS, and RPE reflections is made through the ocular media, the measurements are biased by absorption, scatter, and birefringence in the cornea, crystalline lens, and nerve fiber layer that may vary with pupil position [38-40]. There is also possible variation due to transverse chromatic aberration intrinsic to the eye . To avoid these effects as well as possible fluctuations in instrument performance, each A-scan was normalized to the same inner retinal reflection (i.e., the collective reflectance from the GCL, inner and outer plexiform layers, and inner nuclear layer). This normalization strategy rests on the assumption that the inner retina is an isotropic scatterer for the illumination and imaging angles considered in this experiment. Our measurements should be insensitive to birefringence of Henle’s fiber layer as all layers examined (IS/OS, PTOS and RPE) lie below this layer, and therefore should be affected in the same manner by the birefringence. Reflections from the inner limiting membrane and underlying nerve fiber layer were explicitly excluded to avoid specular reflections, which are highly directional and angular dependent.
The normalized reflectance of the IS/OS, PTOS, and RPE was determined for the 13 entry positions and four subjects. The intensity measurements were fit to a five parameter model consisting of a Gaussian function and constant bias:.
The general form of Eq. (1) is well established for representing the optical SCE [16, 17, 19, 22]. B represents a uniform illumination of the pupil generated by non-directional scatter in the retina. I, ρoct, and xo and yo define the optical SCE and represent the peak intensity, directionality, and displacement of the peak position from the geometric pupil center, respectively. Because the retina is illuminated and imaged through the same aperture (double pass), the OCT measurements are affected twice by the optical SCE, making ρoct the directionality in double pass. This is consistent with the usual reporting of ρ in the literature for double pass measurements using similar entrance and exit aperture configurations that are scanned across the eye’s pupil [16, 17]. For clarity, ρ values are specified in units of mm-2.
3.1 Directionality of the retinal layers measured with SD-OCT
Figure 2 shows a representative final A-scan generated by averaging 510 A-scans. The A-scan has a dynamic range (defined as the ratio of maximum reflectance to noise floor) of 27 dB and reveals distinguishable reflections from all major layers of the retina. The 27 dB is lower than that typically reported in the literature for (unaveraged) OCT retinal images. While this might suggest our images are inferior, the difference in dynamic range is largely attributable to bright speckle in the (unaveraged) OCT images that inflate the dynamic range and which are greatly reduced when images are averaged. To illustrate the influence of beam location in the pupil, Fig. 3 shows averaged, normalized A-scans for entry locations along the vertical meridian of the same eye. The semilog ordinate used in the figure compresses the reflectivity, however, the strong dependence of the IS/OS and PTOS reflections on beam entry position is still readily apparent, even at the near-infrared wavelength of 842 nm. Figure 4 shows the normalized (to the inner retina) reflectance distribution of the three selected retinal layers as a function of pupil position and subject. The five parameter model, Eq.(1), was fit to these distributions and yielded ρ oct values (average of vertical and horizontal measurements) as given in the first five columns of Table 1.
3.2 Noise reduction by A-scan averaging
Photon noise, speckle noise, and structural inhomogeneities within individual retinal layers introduce errors in the reflectance measurements and subsequently the fitting of Eq.(1). Variations in reflectance due to these sources can be expressed as a coefficient of variation (or equivalently contrast of the fluctuations), equal to the standard deviation of reflectance at a given depth in the retina over the mean reflectance at the same depth.. Averaging A-scans can reduce this source of error, and we sought to quantify the effectiveness of averaging, in particular for the case of 510 A-scans that was used to measure the optical SCE. For each of four specific retinal layers, the coefficient of variation was plotted against the number of A-scans averaged (Fig. 5, asterisks) with the maximum number being 510. Lateral spacing of A-scans was 1 µm at the retina. Theoretical predictions of these curves required some preliminary analysis. For uncorrelated A-scans such as those in the vitreous, the theoretical curve should follow 1/√N. Since, however, A-scans in the GCL, PTOS, and RPE are correlated due to speckle and structures in those layers, the effective (uncorrelated) number of A-scans, Neffective, will be smaller than the true number, N. Specifically for a given number of A-scans N, values for Neffective were computed by dividing N by a correlation width. The correlation width for each layer was computed by determining the number of A-scans that lay between the peak and first zero crossing of the layer’s autocorrelation . These widths were found to be 1.0, 5.0, 6.0, and 5.2 µm, respectively, for the vitreous, GCL, PTOS, and RPE, yielding maximum Neffective values of 510, 102, 85, and 98. The solid curves in Fig. 5 are theoretical predictions using . The correlation width for the vitreous was the narrowest (1 µm), since it was limited by photon noise, which is uncorrelated between
A-scans (as opposed to speckle or structure). The correlation widths for the other three layers are roughly consistent with the nominal size of speckle (8.6 µm) for the pupil size and wavelength used here.
For the ganglion cell layer, photon noise dominates for averages up to N~50 A-scans (see figure) due to the weak reflection from this relatively transparent layer. For larger averaging, S/N becomes sufficient for speckle to dominate. Because the theoretical curve plotted in Fig. 5 for the ganglion cell layer assumes speckle (5.0 µm) rather than photon noise (1 µm) dominates, the theory underestimates reduction for small averaging. For larger averaging the two are in close agreement. The remaining two retinal layers are sufficiently bright that speckle noise dominates. Theory and experiment are in good agreement across the entire range except for the averaging of A-scans below 5 or 6. In this range 1/ is not applicable since Neffective<1.
Of most relevance to the SCE experiment here, the contrast (standard deviation/mean) for the experimental data after averaging 510 A-scans is 0.09 (vitreous), 0.14 (ganglion cell layer), 0.20 (PTOS), and 0.10 (RPE). Averaging was most effective for the vitreous and RPE, which as detailed above suggests that the spatial correlation of intensity fluctuations in these layers is smaller than that at the ganglion cell and posterior tip layers. The average contrast for the four layers is 0.13, which corresponds to a contrast reduction of 7.5 times compared to a single A-scan. Figure 6 illustrates how this contrast, which depends on the number of A-scans averaged, impacts the fit of Eq. (1), in this case the PTOS layer of subject S2. The error bars in the figure represent a first order approximation in that speckle at the PTOS layer is assumed fully developed and the dominate noise source in the SD-OCT A-scans. As shown in the figure, an estimate of the reflectance from single A-scans is limited by variability (error bars in the figure) equal to the mean reflectance (a consequence of fully developed speckle) and clearly will lead to substantive fitting errors. On the other hand, the averaging of 510 A-scans produces error bars that are appreciably smaller than the SCE signal that is to be fit. For 510 A-scans, the speckle error is sufficiently small that its magnitude is likely comparable to that of other errors in the experiment (e.g., eye motion error) given that the fitted curve does not pass through all of the bars. In general, Figure 6 indicates that substantive averaging is critical for precise measurement of the optical SCE with OCT.
4.1 Directionality of the retinal layers measured with SD-OCT
The primary results of this paper are given in Fig. 4 and Table 1. The figure shows the reflectance profile of three of the brightest retinal layers as measured with SD-OCT. Curves in the figure represent the fit of the five parameter model (Eq. 1). As evident from the width of the curves and the corresponding ρoct values listed in Table 1, the reflections from the IS/OS and PTOS are highly sensitive to the aperture position in the pupil. In contrast, the reflection from the RPE was largely insensitive. Across the four subjects, the average ρoct values for the IS/OS, PTOS, and RPE reflections were 0.12, 0.27, and 0.016, respectively.
These results suggest that the waveguided property of photoreceptors acts on two principle retinal reflections: reflections from the IS/OS and the PTOS. Interestingly, this result is not fully consistent with any of the three leading optical models of the retina described in Section 1 (Introduction), at least for wavelengths in the near infrared. The first model bases the origin of the optical SCE on reflections over the entire axial length of the outer segment due to refractive index modulations induced by the discs . Our findings indicate that only the reflections at or near the two ends of the outer segment contribute meaningfully. We did not determine ρ values inside the outer segment (which would be of interest to do) as these reflections were at least an order of magnitude dimmer than those from the IS/OS and PTOS in the averaged A-scans, making their contribution to the optical SCE likely inconsequential. The second model bases the optical SCE on reflections from the posterior tips of the outer segment and possibly from melanin granules in the RPE [21-23]. While we found the PTOS reflection to be strongly waveguided, the IS/OS was equally strong and almost no waveguiding was observed for the RPE. The third model holds that light reflected from layers further behind the photoreceptors is also waveguided, especially at longer wavelengths . Our findings showed no evidence of this in the RPE even though we imaged at 842 nm. We did not measure the choroid contribution as it appears two orders of magnitude dimmer than the brightest reflections in the retina. The detected choroid signal may be artificially reduced because of blood flow and multiple scattering at the deeper layers (which reduce the interferometric signal in the SD-OCT measurement). Nevertheless regardless of the choroid brightness, it is hard to imagine an anatomical mechanism in the photoreceptors that selectively waveguides choroid reflections that must double pass through the RPE, but not reflections from within the RPE itself. If our results hold (which will require further confirmation, in particular at shorter wavelengths), modifications to these leading optical models of the retina will be necessary to assimilate our SD-OCT findings.
It is interesting to note that our findings are consistent with preliminary reports with conventional (i.e., imaging through a single entry point in the pupil of the eye) AO SD-OCT [29, 43] and time-domain OCT . Specifically, these studies report limited correlation between structure in the cone photoreceptor layer and underlying tissue layers, indirectly suggesting that reflections from behind the photoreceptors might not be predominately waveguided. Since these studies were limited to imaging through a single entry point, they could not measure the directionality of the layers.
As seen in Fig. 4, the peak of the optical SCE for two of the subjects (S1 and S4) is displaced by about 1 mm from the geometric center of the pupil. It will be of interest to confirm the magnitude and direction of this shift in these same eyes using one of the established conventional reflectometers. Related to this, it is puzzling that the peak of the optical SCE for the IS/OS and PTOS reflections in some subjects are laterally displaced relative to each other. While this displacement is small (<½mm), it is unlikely an artifact due to eye motion or operator error in alignment of the subject’s pupil to the camera. SD-OCT acquires all pixels of an A-scan in parallel, i.e., across the same exposure duration, and as such eye motion or misalignment of the eye would affect the IS/OS and PTOS reflections of the same A-scan in the exact same manner. More likely, it could be caused by a fitting error generated by the coarse sampling of the pupil (only 13 entry positions were measured) in conjunction with noise in the measurements. This can be tested by sampling the pupil more finely. If on the other hand the effect is real (which we can only speculate at this time), it may indicate some sort of misalignment within the photoreceptors thereby causing the two waveguided reflections to be slightly skewed.
The retinal reflectances plotted in Fig. 4 are normalized to the collective inner retinal reflection (i.e., GCL, IPL, OPL, and INL) to avoid biases by absorption, scatter, and birefringence in the cornea, crystalline lens, inner limiting membrane, and nerve fiber layer as well as possible fluctuations in instrument performance. The accuracy of this normalization rests on the assumption that the inner retinal reflection produces a uniform veil across the entire sampling area of the eye’s pupil. The random arrangement of cells in these layers coupled with their cellular composition suggests this might be a reasonable approximation, especially given the relatively low numerical aperture of the eye, but we have not demonstrated this. In spite of this weakness, our normalization approach for SD-OCT is a significant improvement over that of conventional reflectometer methods. These implicitly require a similar assumption about the retinal reflection plus additional ones for the inner limiting membrane, nerve fiber layer, crystalline lens, and cornea.
Figure 4 reveals possible trends in the reflectance pattern between and within eyes. For example in three of the four subjects, the brightness of the IS/OS and PTOS reflections (in the same eye) are roughly equal. In the remaining subject, the PTOS is brighter by a factor of two. As another example, the RPE reflection is consistently dimmer than that of the IS/OS and PTOS in all of the eyes (see also center plot in Fig. 3), but the extent of which varies considerably from 2.5 (S3) to 15 (S1) times.
The averaged A-scans shown in Figs. 2 and 3 indicate that some of the layers of interest are not always clearly distinguishable. In particular, the PTOS and RPE reflections sometimes appear merged suggesting a possible residual influence of the reflectance of one on the other and potentially a source of error for the optical SCE measurements. While this remains a point for future investigation, we believe this potential error is small based on two lines of reasoning. First, and perhaps the strongest, is that the measured directionality of the PTOS is almost 17 times larger than that of the RPE (see Fig. 4) with average ρoct values of 0.270 and 0.016 (Table 1), respectively. If there was noticeable overlap of these reflections, similar directionality values should be expected, not the large difference that was observed. Note that the PTOS directionality is larger than even that of the IS/OS (ρoct=0.120). Secondly, the axial resolution of our SD-OCT instrument (4.8 µm in tissue) is significantly less than the extent of the RPE apical processes that ensheathe the posterior tips of the cones. The processes typically extend 10 to 20 µm from the RPE cells, a separation that is dependent on retinal eccentricity [45, 46]. Given that the resolution is more than sufficient to resolve this separation, there might be other possible explanations for the apparent merging of the PTOS and RPE reflections. One possibility is that inevitable variability in the PTOS-RPE separation across cones, even those in the same local patch, may cause sufficient smearing to merge the PTOS and RPE reflections in an average A-scan, but not cause sufficient residual overlap at the PTOS and RPE centers (which were chosen for our measurements).
4.2 Comparison of directionality with conventional reflectrometric and psychophysical values in the literature.
In Table 1, our measurements of directionality (ρoct) are compared to that in the literature, obtained with conventional reflectometer and psychophysical techniques. The analysis, however, is not straightforward. This is because several different definitions of ρ exist that stem from fundamental differences in how the reflectometers illuminate the retina and detect the backscatter (e.g., configuration of entrance and exit pupils). ρ also varies with the imaging wavelength and retinal eccentricity. As an additional complexity, there is increasing evidence that ρ is a function (a weighted sum) of two independent retinal components: waveguiding by cone photoreceptors (ρwg) and scatter by the optically rough retina (ρscatter) such as related to the topography of the cone mosaic [22, 33, 47, 48]. The former, ρwg, is wavelength independent, while the latter, ρscatter, scales as 1/λ 2, where λ is the wavelength of the light. Meaningful comparison of our ρoct measurements to that in the literature must therefore account for these differences. As examples, comparisons are made with measurements by Marcos and Burns  and Gorrand and Delori , which were chosen as they measured at 2 degree eccentricity, the same as used here. In order to compare the different directionality measurements, ρMarcos and ρGorrand in the two published studies were converted to an equivalent ρoct as described below and defined as ρMarcos equiv and ρGorrand equiv (see Table 1).
ρMarcos and ρoct differ primarily in definition and wavelength used (543 nm versus 842 nm). ρoct is defined for double pass through a common entrance and exit aperture that is scanned across the pupil of the eye. Mathematically, ρoct equals 2ρwg+ρscatter(λ) with a ρwg generated in the illumination of the retina and the remaining ρwg+ρscatter(λ) generated in reflectance. Here we provisionally assume a ρscatter(λ) dependence on the grounds that ρoct was determined from 510 A-scans of a patch of retina, though this will require confirmation. In contrast to ρoct, ρMarcos is defined as only the reflectance component, i.e., ρwg+ρscatter(λ). To convert ρMarcos to an equivalent ρoct (i.e., ρMarcos equiv) requires determining ρwg and ρscatter, and then substituting into ρoct=2ρwg+ρscatter(λ). In Marcos and Burns , ρscatter(λ=543nm)=0.089 at 2 degree eccentricity, obtained by taking the difference between directionality from single (0.189) and multiple (0.1) entry measurements. Single and multiple entry measurements are defined in the citation. ρscatter(λ=842nm) is obtained by applying the relationship, 1/λ2 [47, 48] and yields (543nm/842nm)2*0.089=0.037. In other words, the directional component due to scatter reduces by more than ½ at the longer wavelength of 842 nm. The corresponding ρwg is equal to the directionality of the multiple-entry measurement (which is independent of wavelength) and is 0.1 (at 2 deg eccentricity) in the citation. Thus ρMarcos equiv=2(0.1)+0.037=0.237, which is repeated in Table 1.
ρGorrand and ρoct were measured using similar entrance and exit aperture configurations, and therefore are governed by the same expression, i.e., 2ρwg+ρscatter(λ). However, different wavelengths were used (543 nm and 842 nm). Conversion of ρGorrand to ρGorrand equiv requires accounting for the difference in scattering due to wavelength, i.e., ρGorrand equiv=ρGorrand-ρscatter(λ=543 nm)+ρscatter(λ=842 nm). Using the reported value of ρGorrand in Gorrand and Delori  in conjunction with ρscatter in Marcos and Burns , ρGorrand equiv=0.279-0.089+0.037=0.227, which is repeated in Table 1.
Table 1 shows that ρMarcos equiv and ρDelori equiv compare favorably to ρoct measured at the PTOS (0.27), while noticeably larger than that at the IS/OS and RPE, 0.12 and 0.016, respectively. A comparison to the psychophysical SCE, ρpsycho, (~0.05 [22, 33]) can also be made by extracting ρwg from the ρoct measurement (=2ρwg+ρscatter(λ)). The rationale for comparing ρwg is that the psychophysical SCE is expected to depend on the waveguide properties of the photoreceptors in single pass and with no dependence on retinal scatter. Assuming for our SD-OCT measurements that ρscatter(λ=842 nm) equals 0.037 as extrapolated from Marcos and Burns , ρwg becomes 0.042 and 0.117 for the IS/OS and PTOS, respectively. Thus in contrast to the conventional optical SCE measurements, ρMarcos equiv and ρGorrand equiv, ρpsycho compares favorably to the waveguide directionality of the IS/OS reflection (0.042) and noticeably less so for that of the PTOS (0.117). These findings need additional confirmation, but at this point suggest a strong link between the IS/OS reflection and the psychophysical SCE, and the PTOS reflection with the conventional optical SCE. In order for the former (ρoct of the IS/OS=ρpsycho) to occur, light incident on the cones must be captured before the IS/OS interface (e.g., waveguiding of light in the inner segment) and the ensuing reflection at the IS/OS interface must be specular so as to preserve the mode structure of the captured light. In order for the latter (ρoct of the PTOS= conventional optical SCE) to occur, higher-order modes of the captured light must be lost in the outer segment (e.g., due to the narrowing of the outer segment compared to that of the inner) or are lost on reflection at the PTOS, which would occur if the reflection was only partially specular.
4.3 Noise reduction by A-scan averaging
As shown in Fig. 5, averaging of A-scans reduces contrast of the noise and enables more precise estimates of the IS/OS, PTOS, and RPE reflections. Principle noise sources include speckle and photon noise, and structural inhomogeneities within individual retinal layers. In this paper, we chose to average 510 A-scans (spaced at 1 µm) that reduced the contrast of the total noise by 5 to 11 times (depending on the retina layer) compared to a single A-scan. While our choice of 510 was based primarily on practical reasons associated with the amount of effort required to process the A-scans, additional automation of this step could readily increase the number significantly. This would lead to further noise reduction and improved reliability of the reflectance measurements, albeit at a diminishing benefit that follows the inverse of the square root. Specifically, we confirmed that averaging follows , where Neffective is the number of uncorrelated A-scans. In this study, the width of an effective A-scan varied from 1 µm (photon noise limited) to 5-6 µm (speckle noise limited) depending on which noise source dominated the layer. Sampling the retina finer than the speckle size (as we did here) improves signal-to-noise for those layers limited by photon noise (vitreous), but yielded negligible benefit for those limited by speckle noise (IS/OS, PTOS, and RPE as well as the ganglion layer for N>50). In general, averaging is critical for precise measurement of the optical SCE with OCT.
OCT represents a new approach to study the optical SCE and to directly investigate its origin in the thick retina. The axial resolution (~5 µm) and sensitivity to weak reflections (~94 dB with a ~27 dB dynamic range across the retina) of our SD-OCT greatly surpass those of established SCE methods. As an additional benefit, OCT is unaffected by the bright specular reflections from the cornea and inner limiting membrane, both of which can be orders of magnitude brighter than the underlying retina. A potential weakness is that significant A-scan averaging is necessary for precise measurement of the optical SCE. A reflectometer based on SD-OCT measured the directionality of several prominent layers of the retina (IS/OS, PTOS, and RPE). Using near infrared (842 nm), the optical SCE was readily apparent at two of the layers examined. Reflections from the IS/OS were found sensitive to beam entry position in the pupil with the directional strength consistent with psychophysical SCE measurements. Reflections from the PTOS were more sensitive with the directional strength roughly a factor of two larger and consistent with conventional optical SCE measurements. In contrast, the RPE was largely insensitive to beam entry position. In general, the primary contributors to the optical SCE at near infrared wavelengths appear to be localized reflections at the photoreceptor IS/OS and PTOS interfaces. Our implementation of this new technique to measure the optical SCE was only partially automated and therefore required significant time to acquire, select, and process the retinal A-scans. However, the entire procedure could be readily automated making it potentially attractive for clinical applications.
The authors thank Stephen Burns and Brian Vohnsen for discussions about the Stiles-Crawford effect. The authors also thank the staff of Daniel Jackson and William Monette for machining and electronic support. Financial support was provided by the National Eye Institute grants 1R01 EY018339 and 5R01 EY014743. This work was also supported in part by the National Science Foundation Science and Technology Center for Adaptive Optics, managed by the University of California at Santa Cruz under cooperative agreement No. AST-9876783.
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