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▪ CONTENTS ◄ 12.7. Combined eye aberrations, diffraction 12.8. Eye spectral and intensity response, contrast sensitivitySpectral responseThere 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 the 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. 166).
Sensitivity
of cones and rods varies with the wavelength, within so called
visible
spectrum, extending from ~370nm to ~730nm. Energy level
corresponding to the wavelength of light wave - inversely proportional
to the wavelength, and in proportion to the frequency (photon of light
has the energy E=hν,
h being the Plank's constant, and
ν
the frequency, a number of waves per unit of time) - stimulates
eye photoreceptors, which send received stimulus to the brain. Specific
combinations of stimuli from the three different cone receptor types produce an input from which the
brain creates perception of color.
In general, eye sensitivity to light increases exponentially with the decrease in light intensity, with the wavelength of peak sensitivity shifting from ~550nm in day-light conditions, to ~510nm in darkness. As illuminance decreases, cone function transforms toward more effective light collection (elevated pigments level, suppression of lateral inhibition, and convergence of individual outputs) at a price of lower acuity. Bellow certain illumination level, cone function enters dormancy, but cones are still ready to respond to a sufficiently intense light. On the other hand, decreasing illumination level stimulates accumulation of rhodopsin (pigment) in rods, which was washed out at higher illumination levels. It activates rods, enabling the eye to respond to light stimuli of much lower intensity. As mentioned, this gradual shift in eye sensitivity mode goes through three main stages: (1) photopic, in bright light conditions, (2) mesopic, in low light conditions, and (3) scotopic in near total darkness (FIG. 167).
Mesopic eye function is considerably more complex than either photopic or scotopic, due to the simultaneous input of cones and rods, both only partly activated. As a result, there is no agreement (within U.S. or internationally) about its exact modeling. It is most commonly presented as a simple sum of the cones and rods functions, as Vmes=xVpho+(1-x)Vsco, respectively, with x varying with illumination level from 0 at the low, to 1 at the high of the mesopic range. As illumination continues to decrease bellow photopic level, this theoretical curve (FIG. 154 top right) gradually shifts from the photopic to scotopic curve, maintaining a single peak, and similar overall shape. However, more recent empirical evidence suggests that the actual mesopic sensitivity follows more complex patterns, with a well developed mesopic curve having two main peaks, one converging toward peak rods sensitivity, the other toward yellow range of the spectrum (FIG. 154 bottom right). Such outcome is logically plausible, since both types of photoreceptors are active, widening eye sensitivity curve. The shift of the cone peak from green to yellow is caused by their relative sensitivity under reduced illumination increasing more in the red and blue than in green/yellow (FIG. 154 bottom left; keep in mind that the plots to the right show relative sensitivities - cone sensitivity is generally much higher than rods sensitivity). Simply summing up adjusted photopic and scotopic function also neglects the fact that cone sensitivity in mesopic light conditions also increases relative to that in full photopic mode. Similarly to rods, but to a smaller extent, this increase in sensitivity comes at a price of lowered acuity. Both mesopic plots in FIG. 154 (right) approximate foveal retinal sensitivity as combined sensitivity of cones and rods. However, actual sensitivity varies from predominantly cone sensitivity in the inner fovea (particularly foveola), to predominantly rods sensitivity toward the outskirts of fovea and further off. In other words, within approximately inner half of the fovea mesopic sensitivity is approximated with the right mesopic wing on the bottom plot, which is higher toward both, red and blue wavelength, than cone sensitivity in the photopic mode. Toward outer portions of foveola, and beyond, where rods become dominant, relative sensitivity increases for medium to short (green-to-violet) wavelengths, and decreases for longer (red) wavelengths, nearly vanishing for the deep red; mesopic sensitivity for this portion of the retina is approximated mainly by the left mesopic wing on the bottom right plot on FIG. 154. Obviously, sensitivity properties of the retina vary greatly with its particular area. Its small off-center portion, foveola, is nearly exclusively covered by a dense cone structure; cones remain dominant up to about half the radius of fovea, an area surrounding foveola, 4-5 times larger in diameter. Outer half of the fovea has a mixed cones/rods structure. Rods begin to dominate at the outskirts of foveola, nearly exclusively populating the outer area of the retina. 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. 168). In the entire retina, rods outnumber the cones approx. 20:1 (120 millions vs. 6 millions). Despite similar average size, 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.
The above comparison of the common size of Jupiter on the retina with the size of its respective cones- and rods-dominated areas suggests that centering an object that requires high resolution in the field of view significantly improves its definition. On the other hand, averted vision will be more helpful with objects where detection is more important than resolution - as long as they radiate mainly in the green-to-violet portion of the visible spectrum. The highest rods acuity is at about 4° from foveola, near to half-radius of the macula. So, for detection of very faint objects, it should work best with the eye directed some 4° off the field center (about 1/5 and 1/10 of the field radius in 40° AFOV and 80° AFOV eyepiece, respectively), with the object centered in the field. Eye intensity response 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). For point-like sources, the logarithm base is 1000.2, upon which was built the familiar concept of stellar magnitude. 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, producing significantly higher
perceived brightness. Anyone who has seen the Moon in a telescope can attest to it. Eye contrast sensitivityMTF 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. 169.
FIGURE
169: 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 (in 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 limit to 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 0.6-0.7% minimum contrast in photopic (bright-light) conditions,1-2% in average mesopic conditions, and
10-15% in
average scotopic (low light) conditions. Contrast sensitivity peaks
for ~9' detail size in photopic conditions,
shifting toward larger details in mesopic and
scotopic conditions. At the same time, maximum contrast sensitivity
diminishes from nearly 0.6% (photopic) to nearly 2% (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. 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.
◄
12.7. Combined eye aberrations,
diffraction |
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FIGURE 168: 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 area (foveola)
of ~1/3 mm (1°) in diameter, shifted nearly 12° from the optical center.
The three cone types, L (most
sensitive to longer visual wavelengths), M (mid wavelengths) and
S (short wavelengths), have different color pigments, providing 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 the 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 in the green/blue wavelength range 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 below the threshold of the cones, while the rods get
activated, and become dominant visual receptors. For illustration, size
of Jupiter's disc on retina, when magnified 200 times, is shown next to
the areas dominated by the cones (smaller than Jupiter's disc), mixed,
and rods dominated.