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13.8. Eye intensity response  

13.9. Eye 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 the 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. 248).

 
FIGURE 148
: 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 retinal illumination from 1mm
2 pupil area exposed to 1cd/m2 (candelas/m2) luminance, hence illumination in trolands is a product of luminance in cd/m2 and pupil area in mm2 (inset at right is the relation between pupil area and luminance level, from Hecht, 1924). 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 the weighted sum of photons absorbed by L- and M-cones, while for scotopic (rod) illuminance is proportional to the number of photons absorbed by rods (based on Hood and Finkeistein, 1984).

Note that there is no general agreement on the illuminance level that effectively inactivates cones or rods. Estimates of the mesopic range vary by tenfold, or more, on both, low (0.001 vs. 0.01 cd/m2) and high end (0.6 vs. 10 cd/m2 or even higher). Two recent models are fairly close in their estimate of the low end (~0.01 cd/m2, or somewhat lower, depending on the type of light), but not at the high end: one puts it at about 0.6cd/m2 (X-model, Rea et al. 2004, based on results of He et al. 1997/8), and the other at 10 cd/m2 (Mesopic Optimisation of Visual Efficiency, or MOVE model of the European research consortium, Eloholma and Halonen 2006). Several others, mainly compromising models also have been proposed.

It is helpful to clarify some basic terminology related to this subject, since it can be confusing. While the physical light intensity is measured with radiometric units, its human perception is subjected to eye's selective reaction to it, which is measured in photometric units. The basic radiometric unit is watt (W), and photometric candela (cd), with the latter defined as the luminous intensity produced by a monochromatic light source emitting radiant (photon) flux of 1/683 watt at 555nm into the solid angle of 1 steradian (sr). The original definition of one candela (which was called candle, or candlepower) was the light intensity emitted by a plumber's candle made to specified standards.

Closely related to candela is the luminous flux unit, lumen (lm), defined as a flux (i.e. photon density) corresponding to 1cd of luminous intensity (thus, 1cd=1lm/sr, and a point radiating freely at 1cd luminous intensity produces a 4π lm luminous flux). And the illuminance unit lux is defined as 1lux=1lm/m2.

 Following table summarizes these units and related terms.
 
PHOTOMETRIC UNITS RADIOMETRIC UNITS
QUALITY UNIT QUALITY UNIT
Luminous flux lumen (lm) Radiant flux watt (W)
Luminous intensity candela (1cd=1lm/sr) Radiant intensity W/sr
Luminance cd/m2, or
millilambert (1mL=10/π cd/m2)
Radiance W/(sr m2)
Illuminance general lux (lm/m2) Irradiance W/m2
retinal troland (cd/m2 per mm2 of pupil area)

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 - 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

 Photon of light has the energy E=hν, h being the Plank's constant, h=6.6256x10-34 J (Joul), with 1J=6.2418x1018 eV (electron-volts), and ν the frequency, the number of waves per unit of time usually expressed in Hertz, as the number of complete oscillations per second (so ν=c/λ Hz, c being the speed of light per second and λ the wavelength, in the same unit).

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 total 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 (or mesotopic), in low light conditions, and (3) scotopic in near total darkness  (FIG. 249).



FIGURE 249
: Top right: 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. Bottom left: 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 takes considerably less: only  about 7 minutes.
aMaximum sensitivity level, after ~10 min in darkness; maximum bright-light cone sensitivity is 30-100 times lower.

RELATIVE SPECTRAL SENSITIVITY OF THE EYE
λ (nm) Photopic Scotopic λ (nm) Photopic Scotopic λ (nm) Photopic Scotopic λ (nm) Photopic Scotopic
380 0.000039 0.000589 480 0.139020 0.793000 580 0.870000 0.121200 680 0.017000 0.000072
390 0.000120 0.002209 490 0.208020 0.904000 590 0.757000 0.065500 690 0.008210 0.000035
400 0.000396 0.009290 500 0.323000 0.982000 600 0.631000 0.033150 700 0.004102 0.000018
410 0.001210 0.034840 510 0.503000 0.997000 610 0.503000 0.015930 710 0.002091 0.000009
420 0.004000 0.096600 520 0.710000 0.935000 620 0.381000 0.007370 720 0.001047 0.000005
430 0.011600 0.199800 530 0.862000 0.811000 630 0.265000 0.003335 730 0.000520 0.000003
440 0.023000 0.328100 540 0.954000 0.655000 640 0.175000 0.001497 740 0.000249 0.000001
450 0.038000 0.455000 550 0.994950 0.481000 650 0.107000 0.000677 750 0.000120 0.000001
460 0.060000 0.567000 560 0.995000 0.328800 660 0.061000 0.000313 760 0.000060 0.000000
470 0.090980 0.676000 570 0.952000 0.207600 670 0.032000 0.000148 770 0.000030 0.000000

It should be noted that these sensitivity figures assume the same level of light intensity. As already mentioned, photon energy is inversely proportional to the wavelength, but what ultimately determines magnitude of response over the visible spectrum - assuming no selective absorption in the imaging system - is the spectral intensity distribution of the emission. For the sunlight, it peaks at about 500nm wavelength, with about 10% decrease at the violet end and about 20% decrease at the red end of the visible spectrum. Stellar peak emissions can be shifted significantly to either side and, to a smaller extent, planetary emissions (for instance, typical reflectance from Mars' reddish iron oxide areas is about 2.5 times higher at the red end of the visible spectrum than in the green).

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 mesopic range. As illumination continues to decrease bellow photopic level, this theoretical curve (FIG. 249 top right) gradually shifts from the photopic to scotopic curve, maintaining a single peak, and similar overall shape.

However, more recent empirical evidence (Mesopic vision, optimized illumination, Varady et al. 2008, ten young subjects) suggests that the actual mesopic sensitivity follows more complex patterns, with the mesopic sensitivity curve having two main peaks, one converging toward peak rods sensitivity, the other toward yellow range of the spectrum (FIG. 249 bottom right, based on detecting 2 disc on darkened background). 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. 249 bottom left; keep in mind that the plots to the right show normalized sensitivities - rods sensitivity is generally much higher). Simply summing up the adjusted photopic and scotopic function also neglects the fact that the cone sensitivity in mesopic light conditions also increases relative to that in full photopic mode. Similarly to the rod function, but to a smaller extent, this increase in sensitivity comes at a price of lowered acuity.

Both mesopic plots in FIG. 249 (right) approximate foveal retinal sensitivity as combined sensitivity of cones and rods (note that the third plot, for 10 off center, is outside of fovea). 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. 249.

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 fovea, nearly exclusively populating the outer area of the retina. They become predominant at less than 1mm off the center of fovea, and reach the highest concentration at about 15 (5mm) from the center. 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. 250). 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.

FIGURE 250: 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.

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.

Mesopic vision

During the typical nighttime observing, eye is most likely to be in the mesopic mode. That warrants its more detailed coverage.

Determining characteristics of the eye function during typical observing session is not a simple mater, even very approximately. Eye response varies with the surrounding luminance level, with the telescopic view (brightness, size, shape of the object observed, background characteristics), time at and off of the eyepiece, and other factors. In general, dark-to-light adaptation is much faster than light-to-dark, although the latter very much depends on the intensity of pre-adapting illuminance. A large, bright object like Moon will quickly shift the observing eye into photopic mode, but the other eye will have mixed signals from the light-exposed eye and its own dark environment, while also being a source of conflicting feedback for the other eye.

In the upper range of mesopic mode cones function is still dominant. Sensitivity of the cones and rods soon equalizes with the further drop in luminance level, after which the rods become increasingly dominant for most of the mesopic range (FIG. 251, based mainly on data from Fundamentals of spatial vision, J. A. Ferwerda). Along with it, both acuity (FIG. 218) and color response deteriorate, with the latter vanishing as the eye enters scotopic mode. Since the upper mesopic luminance is well over a hundred times closer to the indoor lighting level than that of a starry moonless night, we can assume that the surrounding-induced spectral response mode is mesopic, varying between cone and rode dominated sub-mode with the object of observation.



FIGURE 251
: Mesopic range of eye spectral sensitivity in the continuum from photopic to scotopic mode. Plotted pairs of cone and rode spectral sensitivity are for the illumination levels marked with the vertical dotted lines. The two plots descending from left to right mark the peak cone and rode sensitivity as a function of luminance level. The pairs of plots of sensitivity over the spectral range are effectively rotated by 90
clockwise to show the spectrum scale; Actual locations of the peaks on these paired plots - as projected toward you - are as indicated by arrows. Sensitivity of both cones and rods increases with the decrease in luminance, but the cones reach their upper sensitivity limit sooner, which leaves them blind at low luminance levels, when eye can only see through the rods. The sensitivity of either type of photoreceptor changes over the spectrum with the luminance level: for the cones, it is higher on both, blue/violet and red side in photopic (solid) than scotopic luminance levels (dashed) than. It is reverse for the rods, which are more sensitive in the blue/violet and red in the scotopic than in photopic mode. With either cones or rods the increase in sensitivity toward their mode of dominance is significantly greater in the blue/violet (dashed plots showing the sensitivity outside of the mode of dominance is very approximate).

As plots above indicate, peak sensitivity for either cones or rods is nearly constant, about 555nm for the former, and 510nm for the latter. Every whole number increment indicates 10-fold difference in sensitivity. Thus sensitivity toward the ends of visual spectrum for either receptor type is a small fraction of their peak sensitivity. At the upper mesopic limit, cone function is still dominant, hence acuity and color response are nearly as good as in photopic mode. At the lower mesopic limit, however, rod function is fully dominant, acuity is poor and color response nearly non-existent.

Cone function remains dominant in the red throughout the mesopic range, and for wavelengths of about 650nm and longer in the scotopic range as well. On the other hand, rod function is dominant in the blue/violet throughout mesopic range, and more so in the scotopic. Even in the lower photopic mode, up to about indoor light luminance level, it is partly dominant partly equal, or near the level of the cone sensitivity.
 

13.8. Eye intensity response   

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