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12.3. Eye spectral and intensity response, contrast sensitivity

Spectral response

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. 153).

FIGURE 153: The main three modes of eye function under different illuminance levels, photopic (bright light), scotopic (low light conditions) and mesopic (intermediary), result from the specific response of its two types of photoreceptor cells, cones and rods. Their activity is specific to retinal illuminance level, which is determined by the brightness level of the object observed, as well as brightness of the background and surroundings. Unit of retinal illuminance is Troland, defined as the retinal illumination level produced with a pupil area of 1mm2 exposed to 1Cd/m2 (Candelas/m2) luminance. Due to different modes of operation, size and distribution, cones and rods have different level of retinal illuminance for a given input: photopic (cone) retinal illuminance is proportional to a weighted sum of the photons absorbed by L- and M-cones, while for the scotopic (rod) illuminance is proportional to the number of photons absorbed by rods.

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.

VISIBLE SPECTRUM OF LIGHT

Vacuum wavelength (nm)

Frequency (1012Hz)

Brain color response

730-622

410-482

RED

622-597

482-503

ORANGE

597-577

503-520

YELLOW

577-492

520-610

GREEN

492-455

610-659

BLUE

455-370

659-810

VIOLET

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 (FIG. 154).

FIGURE 154: 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 (the darker it is, the faster transition from cones-to-rods function; in near-complete darkness, the cones shut down almost instantly). At the point of cones-rods break, rods become dominant, gaining in sensitivity some 200-1000 times over 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). The response range shifts from ~400-730nm to ~370-650nm, respectively. Dark-to-light eye adaptation lasts considerably less: only about 7 minutes.
aMaximum 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. 155). 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.

FIGURE 155: 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.

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). 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 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. 156.

FIGURE 156: 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. The range of peak contrast sensitivity, defined as high-to-low differential at the sensitivity peak, also changes with the change in illumination level. It is smallest in photopic mode, roughly 0.2%, nearly doubled in mesopic mode, and largest in 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.

◄ 12.2. Eye aberrations

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