12. THE HUMAN EYE

12.1. Physical properties of the eye, transmittance and acuity

The entire purpose of a telescope is to gather light from distant objects and to enlarge the incoming light angles, so that these objects appear brighter, larger and more detailed to the eye. Both, properties of the telescope and the eye determine properties the final image created by the brain.

Being an optical element itself, the eye is, just as the telescope objective, subjected to the effects of diffraction of light and wavefront aberrations. Both, physical and optical properties of the eye vary individually, often significantly; those presented here are based on experimental averages (FIG. 148).

FIGURE 148: Top view of the human right eye cross-section. The light entering the eye first passes through the cornea, ~0.5mm thick negative meniscus of ~7.8/6.5mm radii, and n~1.38 refractive index. Between cornea and the eye lens is aqueous humour, watery fluid with n~1.33. The iris is a muscle that forms circular opening - the pupil P, eye aperture - varying from ~2mm to ~8mm in diameter. The eye lens is bi-convex, made of thousands of roughly concentric layers with refractive indici varying from ~1.38 to ~1.41. Change in the lens' shape accomplished by the action of ciliary muscle enables eye accommodation, maintaining focus on the retina for varying object distances. When focused at infinity, the lens is ~3.6mm thick, with front and back radii ~10mm and ~6mm, respectively, and focal length ƒ~22mm. The eye focuses through the vitreous humour, watery fluid with n~1.33, onto the retina, made of the layers of cells and photo-receptors connected to the brain via optic nerve. A small spot on the retina - fovea centralis - is about 4.5° (1.3mm) in diameter, nearly 12° off the optical center. Its central ~1/3, called foveola, is the most acute vision area of the eye in day-light conditions (as opposed to wider ring-shaped area around fovea, highly sensitive to low-intensity light).

Retinal arc extends ~32mm through the central meridian. Outer retinal area of relatively low sensitivity to daylight surrounds the yellowish oval spot of ~4mm (nearly 15°) in diameter, centered at ~3.4mm (nearly 12°) from the optical axis of the eye, called macula, which converges toward fovea, the highest daylight sensitivity area. From the outskirts of macula outwards, roughly 20° wide, extends the ring-shaped area of the highest sensitivity to low-intensity light.

Eye light transmittance is relatively high in the 500nm-700nm range (and beyond, into infrared), but falling off quickly toward the blue/violet end of the spectrum (FIG. 149).

FIGURE 149: Range of eye spectral transmittance, based on several small-scale studies. The results indicate wide individual differences, although it could also result from small sample sizes (four to nine individuals in four separate studies) and/or differences in procedures. It is unclear whether eye transmittance - specifically its preference for mid- and longer wavelengths within the visual spectrum - has been factored out from the eye spectral response (sensitivity) curve. If not, it would superficially lower actual sensitivity of the eye in the blue/violet relative to that in the green and red for both, cones and rods. Since the relative change in transmittance over the range of wavelengths doesn't seem to vary significantly with the transmission level, it shouldn't affect individual perception of chromatism. Variations in eye transmittance would mainly affect perceived brightness, with the difference between high and low transmission level being close to one magnitude, roughly evenly across the visible spectrum (possible exception is that some individuals may have the ability to sense wavelengths well bellow 400nm, and some not).

Eye photoreceptors cells, cones and rods, form layers on the retina. We need them to sense light, just as we need nerve endings in the skin to sense touch. They range in size from ~2μ to over 10μ, in general becoming larger toward the outer area of the retina. Dominant retinal photoreceptors at small pupil sizes (and bright-light conditions) are the cones, while at large pupil sizes (in low-light conditions) the dominant photoreceptors are the rods. The two differ significantly in, among other properties, their respective resolution limits. Eye resolution level is termed acuity. It varies over the retina, depending on the receptor type and size. It is also a function of the illumination level (FIG. 150).

FIGURE 150: Left, average resolution of cones and rods over the retina, in lines per arc minute. To the right, resolution in lines per arc minutes as a function of illumination level, for the photopic (bright-light), scotopic (low-light) and mesopic (transitional) eye modes. Maximum rods resolution is somewhat over 5 arc minutes, a fraction of the maximum resolution of the cones. Resolution of rods is inferior due to the input from several rods merging before they reach the eye nerve. Cones, on the other side, send individual inputs to the eye nerve; with the Airy disc for a typical 2mm photopic eye pupil diameter being ~1.6 arc minutes, diffraction resolution (defined as the FWHM of the PSF, or 0.4 of the Airy disc diameter) is in the 0.6'-0.7' range (in laboratory conditions; not to be confused with the limit in field conditions, which is ~1 arc minute).

The area of highest cone acuity coincides with the area of their highest density and smallest individual size - foveola. Area of the highest rode acuity is just outside the macula, in the ring roughly centered at the fovea, some 10° to 15° in radius.

Highest acuity level doesn't coincide with the highest image quality, in terms of contrast level. For the naked eye, retinal images are of the highest quality at a pupil diameter of ~2mm (which means in bright-light conditions with the cones dominant), when the combined effect of aberrations and diffraction is at its lowest. In regard to point-image resolution, it is better at ~4mm pupil size (in dim light conditions), with the cones still sufficiently active, diffraction disc is half the size of the disc at 2mm pupil, and the aberration level of ~0.15 wave RMS still doesn't significantly affect the size of central diffraction disc, thus neither resolution of near-equal intensity point sources. However, for most other detail forms, resolution is inferior to that at 2mm pupil size.

For the telescopic eye, there is no point sources, since it images (through the eyepiece) the Airy disc formed by the objective. Hence, given aberration level of the objective, it is the level of eye aberrations that determines image quality which, in general, favors smaller eyepiece exit pupil (this, in turn, favors smaller apertures, with smaller exit pupil for given nominal magnification). However, this effect is, after a certain level, outweighed by the negative effects of higher magnifications.

◄ 11.2. Eyepiece aberrations II ▐ 12.2. Eye aberrations ►

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