Alignment conditions of the human eye for few-photon vision experiments

TL;DR

The paper addresses how to align the human eye for few-photon vision experiments by combining Gullstrand's exact eye model with retinal rod-density data in a 3D ray-tracing framework. It explores the input orientation and source misalignment to determine the best way to hit the HDR region located above the fovea and to quantify angular and translational tolerances. The key findings are that directing light at the nodal point with theta0 = [0, 13.1] degrees towards a target 3.80 mm above the fovea, with a 0.5 mm radius, requires angular precision of about 0.85 degrees given translational precision of 1 mm in x/y and 5 mm in z; the results are robust to plausible OA-VA misalignment and suggest practical experimental guidelines. The work provides a quantitative framework for aligning stimuli in few-photon experiments and informs how head stabilization and fixation affect measurement feasibility.

Abstract

In experiments probing human vision at the few-photon level, precise alignment of the eye is necessary such that stimuli reach the highest-density rod region of the retina. However, in literature there seems to be no consensus on the optimal eye alignment for such experiments. Typically, experiments are performed by presenting stimuli nasally or temporally, but the angle under which the few-photon pulses are presented varies between 7 deg and 23 deg. Here we combine a $3$-dimensional eye model with retinal rod density measurements from literature in a ray tracing simulation to study the optimal eye alignment conditions and necessary alignment precision. We find that stimuli, directed at the eye's nodal point, may be best presented under an inferior angle of 13.1 deg with respect to the visual axis. Defining a target area on the retina with a radius of 0.5 mm around the optimum location, we find the horizontal and vertical angular precision should be better than 0.85 deg given a horizontal and vertical translational precision of 1 mm and a depth translational precision of 5 mm.

Figures (5)

• Figure 1: The human eye and simulation model. (a) Schematic overview (sagittal [side] view) of the human eye according to Gullstrand's exact eye model with relevant parts indicated (see text). (b) Beam transmission ($\vec{\theta}_0=[5,-2]^{\circ}$, $\Delta r_{\text{m}}=\vec{0}$, $\theta_{1/2}=0.5^{\circ}$) through the $3$-dimensional Gullstrand model. The spherical surfaces represent the various refractive elements in the human eye and the central ray as well as the spot of the beam are shown, highlighting the ray-surface interaction points. At each intersection, Snell's law is applied to obtain the new ray direction. (c) The beam spot on the retina in perimetric view, along with the approximate hDR ring and HDR region, and the target area (see text). Due to the $5.94mm$-scale (black dotted circle), positions are directly comparable with the data from Curcioetal1990.
• Figure 2: Determination of the optimal input angle $\theta_{0,y}$ ($\theta_{0,x}=0$, $\Delta\vec{r}_0=\vec{0}$). The inset shows the retinal impact position of rays in perimetric view, while varying $\theta_{0,y}$ from $0^{\circ}$ to $20^{\circ}$, featuring hits and misses. Calculating the great-circle distance between the fovea and the ray's retinal impact location, we find the optimum angle equals $13.1^{\circ}$ and the target area is hit for angles in between $11.4^{\circ}$ and $14.8^{\circ}$, as indicated by the dashed lines.
• Figure 3: Necessary angular precision for $\Delta\vec{r}_0=\vec{0}$. (a) Hits and misses varying $\theta_{0,x}$ from $-2^{\circ}$ to $2^{\circ}$ and $\theta_{0,y}$ from $11^{\circ}$ to $15^{\circ}$ in perimetric view. (b) and (c) show the great-circle distance between the retinal impact location and the target as a function of $\theta_{0,x}$ ($\theta_{0,y}$ constant, b) and $\theta_{0,y}$ ($\theta_{0,x}$ constant, c). The target area is indicated using a dashed line. (d) Parameter space plot of $\vec{\theta}_0$. Rays with $\vec{\theta}_0$ originating from the shaded region hit the target area.
• Figure 4: Necessary translational precision for $\vec{\theta}_0=[0,13.1]^{\circ}$. (a) and (b) show the great-circle distance between the retinal impact location of the ray and the target for several values of $\Delta z_0$ as a function of $\Delta x_{0}$ ($\Delta y_0=0$, a) and $\Delta y_{0}$ ($\Delta x_0=0$, b). The target area is indicated by the dashed line. (c) depicts the parameter space plot of $\Delta\vec{r}_0$. If the precision in $\Delta z_0=10mm$, rays originating from the region shaded darkgray hit the target area. If one would consider equal precision in $\Delta x_0$ and $\Delta y_0$, the region within the small square remains yielding a precision of $1.0mm$ for both $\Delta x_0$ and $\Delta y_0$. In case the precision in $\Delta z_0=5mm$, the lightgray region represents the allowed parameter space and the large square yields the equal $\Delta x_0$, $\Delta y_0$ precision to be $1.8mm$.
• Figure 5: Full $(\vec{\theta}_0,\Delta\vec{r}_0)$-parameter space precision. Assuming the precision in $x$- and $y$-direction is $1mm$, and the precision in $z$-direction equals $5mm$, the allowed parameter space of $\vec{\theta}_0$ is represented by the shaded area. Requiring the precision of $\theta_{0,x}$ and $\theta_{0,y}$ to be equal and centred around 0, the remaining allowed $\vec{\theta}_0$ parameter space is indicated using a square. This leads to a necessary angular precision of $0.85^{\circ}$ in both $\theta_{0,x}$ and $\theta_{0,y}$.