Adaptive optics scanning light ophthalmoscopy (AOSLO) enables direct observation of the human photoreceptor mosaic with single-cell resolution (1–3). Of particular interest are the cone photoreceptors at the fovea – a highly specialized region of the retina that supports our high-acuity vision (4, 5). Relative to the parafoveal cone mosaic, foveal cone density is higher and the cones are contiguously packed (due in part to the absence of rod photoreceptors) (6). Given the vital importance of foveal cone photoreceptors for our vision, and the involvement of the fovea in many pathologies, there is significant interest in advancing quantitative biomarkers to assess the foveal cone mosaic. Numerous metrics exist for describing geometric properties of the cone mosaic, though cone density and cone spacing are used most often (7–10). Despite convergence on these metrics to characterize the foveal cone mosaic, there remain differences in the methods used to derive them – limiting the ability to compare results from different studies and ultimately limiting progress toward the development of robust clinical biomarkers.

A frequent inconsistency between studies relates to the size and shape of the sampling window used to derive metrics of the cone mosaic. The steep cone density gradient in the central fovea requires special consideration of how large of an area to use when deriving a local estimate of cone density (6). Larger sampling windows will result in lower values of peak density due to inclusion of lower density neighboring regions, while smaller sampling windows result in more noisy density maps that can make derivation of the global peak cone density (PCD) location challenging. Despite this, fixed-area sampling windows have been used in many studies (6, 8, 9, 11–20). This issue is partially overcome by using sampling windows that include a fixed number of cones, regardless of the retinal location. While this approach has been used by some investigators (10, 21–24), there is inconsistency in the number of cones sampled. Here we examined the relationship between the number of cones included in the sampling window and cone mosaic metrics (location and value of PCD, location of the cone density centroid (CDC), and density at the CDC). We also report the effect of variable sampling windows on the overall cone density topography for individual participants.

Across all window sizes, average PCD values were larger than those extracted at the CDC location (p=0.0012, paired t test; Figure 4A ). On average, PCD and CDC both decreased with increasing sampling window size, though the effect was larger for PCD (r=-0.8099, p=0.0045) than CDC (r=-0.7596, p=0.0108). As the density values at the CDC with the smallest window sizes behaved in an inconsistent fashion, we also examined the relationship between density and window size using only window sizes of 20 cones and larger ( Figure 4B ). We again see a strong relationship between PCD and window size (r=-0.9192, p=0.0034) and also for CDC density values (r=-0.8595, p=0.0132). As summarized in Supplementary Table 2 , our density values are comparable to previous estimates in individuals with normal vision (10, 13, 21, 23, 24, 33–36). For example, with a window size of 100 cones, the average PCD from all 44 participants was 185,501 cones/mm² (range=128,007-244,921 cones/mm²) and the average density at the CDC was 174,696 cones/mm² (range=121,169-242,614 cones/mm²). At a window size of 150 cones, the average PCD from all 44 participants was 182,184 cones/mm² (range=126,323-239,362 cones/mm²) and the average density at the CDC was 174,295 cones/mm² (range=121,891-235,663 cones/mm²). The intra-participant differences in density estimates at the PCD and CDC locations decreased significantly as window size increased (p<0.0001, ANOVA, Figure 4C ). This was driven largely by the increased PCD values obtained with smaller sampling windows (Tukey’s multiple comparisons test, see Supplementary Table 3 ). The same trends were observed when reporting density in angular units (cones/deg²), see Supplementary Figure 2 . Across, the 44 participants, as the number of cones in the sampling window increase, we observed a proportional increase in window area (y=9.21x + 1.7146, R² = 1; where x is the window size in number of cones and y is the average bound area window size across all participants). For example, the average area for the 200-cone sampling window was 1,841.14µm² while the average area for a 5-cone sampling window was 45.98µm² (see Supplementary Table 4 ).

In addition to density values, we observed variation in PCD and CDC location as a function of window size. Across all 440 ROIs (44 participants with 10 window sizes each), there were no instances where the reported PCD value occurred at more than one point. The average PCD confidence ellipse area across all participants was 844.10µm², which was significantly greater than the average CDC confidence ellipse area (47.56µm², p<0.0001, Wilcoxon matched-pairs signed-rank test). PCD 95% confidence ellipse areas were greater than CDC 95% confidence ellipse areas for all participants with one exception (JC_11830). Across the 44 participants, PCD 95% confidence ellipse area ranged from 105.28 to 8,389.90µm², while CDC 95% confidence ellipse area ranged from 2.50 to 481.73µm². Example 95% confidence ellipses are shown for four participants in Figure 5 . There was variation between participants in the relationship between the magnitude of the offset between PCD and CDC location and sampling window size. On average, the 44 participants demonstrate relative stability in PCD-CDC location offset as sampling window size increases ( Figure 6A ). However, when assessed individually, some participants showed convergence of the PCD and CDC location with increasing sampling window, some showed divergence, while others showed inconsistent trends ( Figure 6B ). This heterogeneity in how window size impacts PCD-CDC offset is likely due to the underlying global topography of each cone mosaic.

Consistent with prior studies of cone topography (6, 22, 35), we observed a decline in average cone density as a function of eccentricity in both the horizontal and vertical meridians ( Figure 3 ). Additionally, we observed greater within-participant standard deviation near the CDC location compared to locations toward the edge of the foveal ROI – indicating that the variability induced by using different sampling windows affects density more in areas of rapidly changing density (foveal center) compared to areas where density is more uniform (edge of the foveal ROI used here).

Consistent with previous studies of the parafoveal cone mosaic (16, 37–39), our results highlight the importance of defining the sampling window used in deriving maps of foveal cone density. Importantly, we find that the value and location of PCD (versus CDC) is more significantly affected by using a variable sampling window size. This is demonstrated by the steeper decline in PCD as window size increases as compared to density at the CDC ( Figure 4A ). Additionally, the smaller average CDC 95% confidence ellipse area compared to PCD 95% confidence ellipse area demonstrates greater stability in CDC location compared to PCD location as sampling window size changes. These findings are expected based on how we define PCD versus density at the CDC. PCD is the interpolated point of absolute highest density in a given montage whereas density at the CDC describes a relative maximum based on a pooled region of highly dense locations. Thus, when the sampling window is small, we can resolve several high-density regions in the foveal mosaic, visible as small “islands” of 80% isodensity contour ( Figures 2A–D ). To derive the CDC, we generate a best fit ellipse of the 80% isodensity contour and define the center of that ellipse as the CDC location. This method identifies a point whose density is an average of a region of high cone density. Therefore, despite changes in sampling window size, the CDC location of an individual ROI remains more stable than the PCD location. As well, previous studies have demonstrated superior intersession repeatability for CDC location compared to PCD location (32) as well as superior intergrader reproducibility in CDC location relative to PCD location (23). Taken together, the emerging picture is that CDC represents a more robust metric to describe the “center” of the foveal cone mosaic.

As reported by Wang et al. (2019), use of smaller sampling windows may produce unreliable estimates of PCD and PCD location (34), though it is important to note they used a fixed dimension sampling window, which may contain variable numbers of cones across participants. Additionally, their sampling window of 10 arcmin contains over 200 cones, which would be larger than the largest sampling window used in our study. Our data support the notion that smaller window sizes impact PCD and we show that this also applies to the CDC (albeit to a lesser degree). When excluding the smallest sampling window sizes, we observe a strong relationship between sampling window size and both PCD and density at CDC (Figure 4B). This observation may allow comparison of density estimates between studies that used different sampling windows to construct their respective cone density maps. However, while this approach may work on average, there is variation between individual cone mosaics in how density estimates and locations vary as a function of sampling window size ( Figure 6B ). This is likely due to more global features of cone topography, including individual variation in kurtosis of the cone density versus eccentricity function. Further work is needed to understand if and how best to combine data across studies employing different methodology, as large and robust normative databases are needed to advance the use of AOSLO imaging.

Limitations of our study include reliance on a single observer’s cone markings – errors or biases in their coordinates may exist (23). As such, generalization of these trends should be applied carefully to other datasets where coordinates were derived from different observers. Additional factors related to sampling the cone mosaic could be considered in future studies – such as inclusion of “edge” cells within the window, shape of the window (square, arcuate, circular), and interpolation methods. Additionally, our sample of 44 participants was almost 2:1 female (27F, 17M) and almost exclusively white (approximately 70% of participants self-reported race as white). As it is unknown whether cone mosaic topography varies with race and ethnicity, our analysis should be repeated in a more heterogenous population.

Ultimately, the “cost” of variation in any metric (including those assessed here: PCD/CDC value and PCD/CDC location) depends on the subsequent application. For this reason, we do not identify one sampling window as the ideal size when extracting density metrics. Correlation of cone density with measures of function (e.g., acuity or sensitivity) may wish to utilize sampling windows with sizes comparable to some feature of the visual system (such as fixational stability) (34). Moreover, correlation with measures of function would be best made using cone density at the retinal location used for the specific task (40–42), which may not occur at the PCD or the CDC (32, 43, 44). Thus, in these scenarios, the PCD or CDC location may not be overly relevant. Likewise, correlation of mosaic metrics to other structural features in other imaging modalities would require co-registration of images to ensure alignment of the cone mosaic measures with these other retinal features (45, 46). One application that depends on having a reliable “anchor” within the cone mosaic is selecting parafoveal and perifoveal regions of interest from a larger montage for subsequent analysis. Whether PCD or CDC, this anchor serves as the (0,0) reference point from which retinal eccentricity of a given region of interest is computed (47). Though we observe an offset in PCD and CDC location at all window sizes, if choosing PCD or CDC as an anchor point this offset would remain a fixed value at all retinal eccentricities. However, as cone (and rod) density changes with eccentricity (6, 35), this fixed offset in the location assigned to a given region of interest could result in variably misleading conclusions about the health of the underlying mosaic. Our findings support the use of CDC as a more reliable anchor for such applications, even where resolution of the most densely packed cones is possible and PCD measures are desired for different purposes.

The raw data (foveal montages, cone coordinate files, density matrices) supporting the conclusions of this article will be made available upon request to the corresponding author (jcarroll@mcw.edu), without undue reservation.

The studies involving human participants were reviewed and approved by the Medical College of Wisconsin IRB. The studies were conducted in accordance with local legislation and institutional requirements. The participants (or when appropriate, their parent’s or guardian’s) provided their written informed consent to participate in this study.

EW: Conceptualization, Formal analysis, Visualization, Writing – original draft, Writing – review & editing. JG: Software, Writing – review & editing. RFC: Funding acquisition, Software, Writing – review & editing. JC: Conceptualization, Formal analysis, Funding acquisition, Supervision, Visualization, Writing – review & editing.