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13.3. Eye spectral and intensity response, contrast sensitivitySpectral response of human eye There are two basic types of retinal photo-receptors: cones, responding to bright-light conditions, and rods, responding to low-intensity light. Depending on their spectral sensitivity, the former belong to either L (long-wavelengths sensitive), M (mid-wavelengths sensitive) or S (short-wavelengths sensitive) cones. By combining their separate inputs, the brain creates colors. The cones are concentrated in the center of retina (fovea), where they are as small as ~2μ in diameter. That puts the angular size of smallest individual foveal cones at ~1/3 arc minute. Cones become larger - up to about four times - toward outer areas of the retina. Therefore, eye spectral response is directly related, and influenced by illuminance levels (light intensity) to which it is exposed. Illuminance level determines the level of activity of cones and rods, and with it main characteristics of human vision (FIG. 129).
Sensitivity of cones and rods varies with the wavelength, within so called visible spectrum, extending from ~370nm to ~730nm (FIG. 130).
FIGURE 130: Spectral response of the eye. Peak cone sensitivity is over 200 times lower than peak rod sensitivity. Relative sensitivities of S, L and M cones are shown within photopic mode; by combining their inputs, the brain creates colors. Top right: Exposed to low-light conditions in full photopic mode, cone sensitivity increases 30-100 times within ~10 minutes, reaching its maximum sensitivity level. Then, at the point of cone-rode break, rods become dominant, gaining in sensitivity some 200-1000 times over the peak cone sensitivity within the next ~20 minutes (individual sensitivity varies within the shown approximate range: by a factor of ~3 and ~10 for the cones and rods, respectively). In the process, peak sensitivity shifts from ~555nm (photopic) to ~507nm (scotopic). Also, the response range shifts from ~400-730nm to ~370-650nm, respectively. Dark-to-light adaptation of the eye requires considerably less time: only about 7 minutes. a Maximum sensitivity level, after ~10 min in darkness; maximum brigt-light cone sensitivity is 30-100 times lower. Outer area of the retina is nearly exclusively populated by the rods. They become predominant at less then 1mm away from the retinal center, and peak at about 15° from the it. Similarly to the cones, their size varies from the smallest - about 2.5 microns - in the area of highest concentration, to roughly double that size far out. Rods are more numerous than cones in roughly 100:1 ratio in the retinal area out of the <2mm of central fovea (FIG. 131). In the entire retina, rods outnumber the cones approx. 20:1 (120 millions vs. 6 millions). Despite similar average size, the rods have much poorer resolution than cones. This is mainly a consequence of so called "convergence": neural output from several rods converge into a single neural brain connection, as opposed to the cones, which have individual neural outputs. Neural convergence of the rods improves sensitivity, sacrificing the resolution.
Eye response to signal intensity (brightness) is logarithmic for the most part (Weber's law). This means that the perceived signal strength is nearly in proportion to the logarithm of its actual strength (that is, illuminance). The response changes for very high level stimuli, due to saturation, and for very low level stimuli, due to the increased role of neural noise (dark light). At very low brightness levels, rod response follows the square root law (de Vries-Rose Law), changing approximately in proportion to the inverse of the square root of mean retinal illuminance. Eye brightness response, among other factors, also depends on the detail size, length of exposure and background.
Size of retinal image determines how
many photo-sensitive retinal cells are stimulated. Telescopic images of
extended objects, even with lower surface brightness than that of the
object itself, have hundreds of times greater area than the naked eye
image, thus stimulating as
many more retinal cells. This results in significantly greater total
energy received by the brain, resulting in a significantly increased
perceived brightness. Anyone who has seen the Moon in a telescope can attest to it. Eye contrast sensitivity MTF analysis of the image formed by a telescope objective is not a "finished product". To some degree, it will be changed by eyepiece aberrations and, when finally projected onto the retina, it is a subject to the effect of physiological processes. As a result, perceived contrast and resolution limit will depend not only on those inherent to the image, but also on its brightness level and angular size on the retina. The specifics of it are described with the aid of eye Contrast Sensitivity Function (CSF) a plot interpolated into empirical data, as shown on FIG. 132.
FIGURE
132: Minimum contrast needed by the eye to resolve MTF-like
high-contrast pattern, varies with its illumination level and
angular size on the retina. Both, spatial frequency (cycles/degree)
and contrast level are given in logarithmic form, to "magnify" the
effect at the level of a fraction of the percent in the contrast scale,
as well as the effect in the range of large details. Detail size on
the retina is given in cycles/degree; 60 cycles
per degree is the conventional limiting eye resolution of 1 arc
minute. Contrast sensitivity, as a function of detail size and
retinal illuminance, is defined by the minimum contrast level at which
the image remains resolved. For instance, 10 cycles/degree (6 arc
minutes) image size requires 0.5% minimum contrast in photopic (bright-light) conditions, ~1% in average mesopic conditions, and ~8% in
average scotopic (low light) conditions. Contrast sensitivity peaks
for ~8' detail size in photopic conditions,
shifting toward larger details in mesopic and
scotopic conditions. At the same time, maximum contrast sensitivity
diminishes from nearly 0.5% (photopic) to ~1% (scotopic). Limiting resolution, at 100% contrast level (along
the horizontal
scale), also diminishes noticeably with the decrease in
illumination being, as expected, the highest in bright-light
conditions, and lowest in low-light conditions. Range of peak contrast sensitivity change
with the change in illumination level for any given detail size is smallest
in the photopic mode, roughly 0.2%, and largest in the scotopic
mode, roughly 15%. The significance of the CSF for
astronomical observing is in helping to determine optimum
magnification level for details and objects of different luminosity
levels. Like other eye properties, contrast sensitivity can vary widely
individually. It is not determined by the quality of the eyesight; an
individual with poor eyesight can have better than average contrast
sensitivity, and the other way around.
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FIGURE 131: Distribution of
photoreceptors on the retina of the human eye. The total field of view, approximately 140° is constructed through the principal
point (P) of the eye. The cones (yellow line), sensitive to
bright light, have highest concentration in the small central area (foveola) of
~1/3 mm (1°) in diameter, shifted nearly 12° from the optical center. The three types of cones, L (most
sensitive to longer visual wavelengths), M (mid wavelengths) and
S (short wavelengths), provide input from which the brain creates
sensation of colors. The S cones are by far the least numerous; also,
they are least sensitive, with their main function
being supplying the brain with needed input to create color blue. Since
the S cones are entirely absent from the central ~0.1mm of fovea, this spot
is blue blind (it has so called tritanopic vision, in which blue
wavelengths are seen as green). The rods (violet line), active in low light
conditions, are absent from the central ~1/3 mm of fovea (foveola), but their concentration quickly
rises toward the edges of macula, and farther out, to reach a maximum
some 18° off the foveal center. While rods, similarly to cones, also differ in size
depending on their position on the retina (generally being larger in the
outer areas), they only have a single pigment, rhodopsin.
It is
ultra-sensitive to light but, being a single pigment available in
low-light conditions, doesn't allow to the brain to create sensation of color. As the
surrounding light intensifies, rhodopsin level diminishes, until
rods gradually deactivate and cones, also gradually, take over. And vice
versa, as the light intensity decreases toward low-light conditions,
it falls bellow the threshold of the cones, while the rods get
activated, and become dominant visual receptors. 