The tuning properties of the ensemble of cone photoreceptors is due to the tuning properties of individual cones convolved with the disarray in pointing direction between the cones. We used direct imaging with the Rochester adaptive optics ophthalmoscope to directly image these properties in individual cones in living human eyes. We found that cone disarray is very small, accounting for less than 1% of the breadth of the tuning function of an ensemble of cones. The implication is that the optical fiber properties of an ensemble of cones mimic the tuning properties of a single cone.

^{6}td-s) before each pair of images. The 10 best images at each location were selected, aligned with subpixel accuracy, and added together.

*A*is the peak reflectance,

*x*

_{o}and

*y*

_{o}define the location of peak reflectance in the entrance pupil plane (or the pointing direction), and

*σ*is the spread of the angular tuning. We also calculated the 95% confidence intervals for each of the fitted parameters on each cone. This was important because in order to conclude confidently that there is disarray in a mosaic, the pointing direction of one cone must exceed the 95% range of the other. We chose not to include in our fit a constant term, which is often used to account for a nondirectional component in the reflection. The reason for omitting the constant term was because our 550-nm measurement wavelength was expected to give rise to only a small diffuse component in the reflection. The diffuse component was further reduced because we measured intensity from the centers of the cones, and not the spaces between them, where the nondirectional light would be expected to pass. Finally, our sampling geometry precluded fitting a constant nondirectional term with any degree of confidence.

*A*is the amplitude,

*x*

_{o}and

*y*

_{o}defines the average pointing direction of the ensemble of cones, and

*σ*

_{disarray}and

*σ*

_{tuning}are the spreads for the disarray and tuning, respectively. This vector addition has the property so that when one term is much smaller than the other, it contributes negligibly to the overall tuning function. In our work, we found this to be the case; the measured disarray was about 5% of the tuning spread. We also determined that the blurring could cause a change in apparent disarray by a factor of 2 at most. Therefore, our estimation of the tuning function of the individual cones would have been essentially the same with or without optical blur, and so, for the simulation, its value was set to the initial estimated value. We added real estimates of the optical blur and noise to each of the images. (The noise was measured directly from the cones in the actual data set.) Then we computed the disarray of the simulated mosaic and compared it to the disarray that was input into the simulation. The process was repeated and we varied the initial disarray until the final disarray matched what was measured in the experiment. The estimated disarray was the initial disarray that produced the closest postsimulation match to our measured result.

Average angular tuning | Average angular tuning after deconvolution with illumination aperture | Average pointing direction in pupil plane (mm) | Average photoreceptor disarray σ | |||||
---|---|---|---|---|---|---|---|---|

Subject | ρ | σ | ρ | σ | X peak | Y peak | Measured | Estimated |

J.P. | 0.096 | 1.50 +/− 0.07 | 0.109 | 1.41 | 1.41 | 0.194 | 0.093 | 0.18 |

G.Y. | 0.079 | 1.66 +/− 0.05 | 0.091 | 1.54 | 0.11 | 0.19 | 0.078 | 0.16 |

The angular tuning properties are expressed as both rho, *ρ*, and sigma, *σ*. The relationship between *ρ* and *σ* is: *ρ* = 0.434/2*σ*^{2}. All values are the mean (+/− 1 standard deviation) of 275 cones for J.P. and 200 cones for G.Y. The correction for the size of the finite aperture of the illumination beam narrowed the cone tuning function slightly and the disarray nearly doubled after correction for optical blur and noise.

*ρ*are very close to those that have been collected in a similar manner (i.e., multiple-entry techniques described by Marcos & Burns, 1999). Incidentally, these

*ρ*-values for angular tuning are about twice those of the Stiles-Crawford effect measured psychophysically (Applegate & Lakshminarayanan, 1993), but as yet there is no explanation for this difference. The current measurements are somewhat broader than those objective measurements (Burns, Wu, Delori, & Elsner, 1995; Gorrand & Delori, 1995; van Blokland, 1986) that are not immune to further narrowing due to coherent interaction of scattered light from the photoreceptor mosaic (Marcos & Burns, 1999).