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3.1 The eye and image formation⧉

Look from a distant building to a book in your hand. The eye changes focus while directing its highest-resolution region toward the words. Its optics obey the same refraction laws as a camera, but its sampling and processing differ substantially (Part 2, Fundamentals).

Light entering the eye passes through the cornea and the lens, the eye's two refracting elements, the same Snell's-law optics as a camera lens (the cornea does most of the bending; the lens fine-tunes focus by changing shape, accommodation). The pupil, the iris's adjustable opening, is the eye's aperture. The image lands on the retina, a thin sheet of neural tissue lining the back of the eyeball (Figure 3.1.1).

fig-eye-cross-section
Figure 3.1.1. Cross-section of the human eye. Light is refracted by the cornea and the lens, passes through the adjustable pupil (the aperture), and forms an inverted image on the retina at the back. The fovea is the small central pit of highest acuity; the optic nerve leaves at the blind spot.

Rods and cones supply most of the signals used for image-forming vision. Rods support vision at low light levels; because they share one spectral sensitivity, rods alone cannot distinguish wavelength from intensity. Cones support daylight color vision through three receptor classes. At intermediate levels, rods and cones both contribute. Their distribution is nonuniform: cones are densest near the center of gaze, while the central foveola lacks rods (Figure 3.1.2). Looking slightly away from a faint star can therefore make it easier to detect.

Foveal cones are only a few micrometers across, with spacing near $2.5\,\mu\text{m}$ in a dense central mosaic; sizes and spacing vary across observers and retinal position. Away from the fovea the cones grow to several micrometers and thin out, while rods, about $1$ to $2\,\mu\text{m}$ across, fill the spaces between them; in Curcio and colleagues' measurements, cone density peaks near 200,000 per square millimeter at the foveal center and rod density near 150,000 per square millimeter about twenty degrees out Curcio et al. 1990. Dense sampling supports fine detail, but does not alone determine acuity. Optical blur, neural pooling, contrast, and illumination also matter. A camera photosite and a cone of similar size need not have similar sensitivity or angular resolution.

fig-cone-rod-distribution
Figure 3.1.2. *Density of rods and cones across the retina. Cones peak sharply at the fovea (the center of gaze); rods dominate the periphery and vanish at the fovea. Where the optic nerve leaves the retina, there are no photoreceptors. This produces a blind spot roughly fifteen degrees toward the temporal side of the visual field in each eye. The other eye normally supplies information from that direction. With one eye covered, a small target can still disappear into its surroundings because perception fills in the missing region (Figure 3.1.4). Filling-in depends on the stimulus; it is not a detailed measurement of the hidden object.
fig-xkcd-1080
Figure 3.1.3. xkcd #1080 "Visual Field," Randall Munroe, xkcd.com/1080 (CC BY-NC 2.5).

The gap at the optic disc is worth more than a label, because it is the first and cleanest evidence that what you see is constructed. Each eye has a patch of its visual field about five degrees across, some fifteen degrees to the ear side of where you are looking, that delivers nothing at all, and you have never once noticed a hole there. Two things hide it. The other eye covers that part of the field, so closing one is enough to remove the first explanation. What remains is the second and the interesting one: the missing region is filled in with whatever surrounds it, so a line broken exactly there is seen as continuous and a textured field closes over the gap. Nothing in the retina reports the fill; it is manufactured, and it is indistinguishable from the real thing (Figure 3.1.4).

fig-blind-spot
Figure 3.1.4. The blind spot, and the filling in (interactive). Cover one eye, fixate the cross, and move toward or away from the screen until the target on the other side of it disappears (with the right eye open, the target sits to the right of the cross, since the blind spot lies on the temporal side of fixation); the figure converts the on-screen separation into degrees once you tell it your viewing distance and your screen's pixels per centimeter, since the eye works in angle and the page cannot know either number. Try the three targets. A disc on a plain field vanishes, which is the hole. A break in a line vanishes and the line is seen running straight through, which is the fill. A hole in a texture closes over with the texture, which is filling-in of texture. The vanishing point sits near fifteen degrees; if it does not, adjust the separation rather than your seat.

S cones are sparse and absent from a small region at the very center of the fovea. Short-wavelength detail also suffers from the eye's chromatic aberration. Fine luminance detail is carried mainly by combined L- and M-cone signals, while purely chromatic variations have lower spatial resolution. This does not make a green channel identical to luminance, or imply that blue detail is universally sharp through filling-in. The relative importance of luminance detail helps motivate the extra green samples in the Bayer pattern (Chapter 4.6, Sensing color: multiplexing strategies).

The retina processes signals before sending them along the optic nerve. Photoreceptors connect through intermediate neurons to ganglion cells. Many ganglion cells compare a central region with its surround, making them sensitive to local contrast; others have different spatial, temporal, or chromatic selectivity. Signals then reach several brain regions, including the lateral geniculate nucleus and visual cortex. A camera-to-retina analogy is useful for the optics, but retinal output is already a collection of processed signals.

Focus errors provide another connection to camera optics. In a simplified eye, myopia places the image of a distant point in front of the retina; hyperopia places it behind the retina when accommodation is relaxed. Astigmatism gives different focusing power along different orientations. Presbyopia reduces the range over which accommodation can adjust focus with age. These are different optical problems, not one generic blur.

Lens power is expressed in diopters:

$$P=\frac{1}{f},$$

where $f$ is the signed focal length in meters. A converging lens with focal length $0.5$ m has power $+2$ diopters; a diverging lens of $-0.5$ m has power $-2$ diopters. This describes the lens, not a complete eye prescription: cylinder power and orientation also matter for astigmatism.

An autorefractor estimates refractive error from light returned by the eye; subjective comparison with trial lenses refines the result. A Shack–Hartmann sensor measures the slopes of the outgoing wavefront using a lenslet array, allowing more detailed aberration estimates. The shared imaging idea is to infer optical properties from the recorded light. Part 22, Compound lenses, and aberration correction develops wavefront measurement.