35–2 Color depends on intensity
One of the most striking phenomena of vision is the dark adaptation of
the eye. If we go into the dark from a brightly lighted room, we
cannot see very well for a while, but gradually things become more and
more apparent, and eventually we can see something where we could see
nothing before. If the intensity of the light is very low, the things
that we see have no color. It is known that this dark-adapted
vision is almost entirely due to the rods, while the vision in bright
light is due to the cones. As a result, there are a number of
phenomena that we can easily appreciate because of this transfer of
function from the cones and rods together, to just the rods.
There are many situations in which, if the light intensity were
stronger, we could see color, and we would find these things quite
beautiful. One example is that through a telescope we nearly always see
“black and white” images of faint nebulae, but W. C.
Miller of the Mt. Wilson and
Palomar Observatories had the patience to make color pictures of
some of these objects. Nobody has ever really seen these colors with the
eye, but they are not artificial colors, it is merely that the light
intensity is not strong enough for the cones in our eye to see them.
Among the more spectacular such objects are the ring nebula and the Crab
nebula. The former shows a beautiful blue inner part, with a bright red
outer halo, and the latter shows a general bluish haze permeated by
bright red-orange filaments.
In the bright light, apparently, the rods are at very low sensitivity
but, in the dark, as time goes on they pick up their ability to see
light. The variations in light intensity for which one can adapt is
over a million to one. Nature does not do all this with just one kind
of cell, but she passes her job from bright-light-seeing cells, the
color-seeing cells, the cones, to low-intensity, dark-adapted cells,
the rods. Among the interesting consequences of this shift is, first,
that there is no color, and second, that there is a difference in the
relative brightness of differently colored objects. It turns out that
the rods see better toward the blue than the cones do, and the cones
can see, for example, deep red light, while the rods find that
absolutely impossible to see. So red light is black so far as the rods
are concerned. Thus two pieces of colored paper, say blue and red, in
which the red might be even brighter than the blue in good light,
will, in the dark, appear completely reversed. It is a very striking
effect. If we are in the dark and can find a magazine or something
that has colors and, before we know for sure what the colors are, we
judge the lighter and darker areas, and if we then carry the magazine
into the light, we may see this very remarkable shift between which
was the brightest color and which was not. The phenomenon is called
the Purkinje effect.
In Fig.
35–3, the dashed curve represents the
sensitivity of the eye in the dark, i.e., using the rods, while the
solid curve represents it in the light. We see that the peak
sensitivity of the rods is in the green region and that of the cones
is more in the yellow region. If there is a red-colored page (red is
about
650 m
μ) we can see it if it is brightly lighted, but in
the dark it is almost invisible.
Another effect of the fact that rods take over in the dark, and that
there are no rods in the fovea, is that when we look
straight at something in the dark, our vision is not quite as acute as
when we look to one side. A faint star or nebula can sometimes be seen
better by looking a little to one side than directly at it, because we
do not have sensitive rods in the middle of the fovea.
Another interesting effect of the fact that the number of cones
decreases as we go farther to the side of the field of view is that
even in a bright light color disappears as the object goes far to one
side. The way to test that is to look in some particular fixed
direction, let a friend walk in from one side with colored cards, and
try to decide what color they are before they are right in front of
you. One finds that he can see that the cards are there long before he
can determine the color. When doing this, it is advisable to come in
from the side opposite the blind spot, because it is otherwise rather
confusing to almost see the color, then not see anything, then to see
the color again.
Another interesting phenomenon is that the periphery of the retina is
very sensitive to motion. Although we cannot see very well from the
corner of our eye, if a little bug moves and we do not expect anything
to be moving over there, we are immediately sensitive to it. We are
all “wired up” to look for something jiggling to the side of the
field.
35–3 Measuring the color sensation
Now we go to the cone vision, to the brighter vision, and we come to
the question which is most characteristic of cone vision, and that is
color. As we know, white light can be split by a prism into a whole
spectrum of wavelengths which appear to us to have different colors;
that is what colors are, of course: appearances. Any source of light
can be analyzed by a grating or a prism, and one can determine the
spectral distribution, i.e., the “amount” of each wavelength. A
certain light may have a lot of blue, considerable red, very little
yellow, and so on. That is all very precise in the sense of physics,
but the question is, what color will it appear to be? It is
evident that the different colors depend somehow upon the spectral
distribution of the light, but the problem is to find what
characteristics of the spectral distribution produce the various
sensations. For example, what do we have to do to get a green color?
We all know that we can simply take a piece of the spectrum which is
green. But is that the only way to get green, or orange, or any
other color?
Is there more than one spectral distribution which produces the same
apparent visual effect? The answer is, definitely yes. There is
a very limited number of visual effects, in fact just a
three-dimensional manifold of them, as we shall shortly see, but there
is an infinite number of different curves that we can draw for the
light that comes from different sources. Now the question we have to
discuss is, under what conditions do different distributions of light
appear as exactly the same color to the eye?
The most powerful psycho-physical technique in color judgment is to
use the eye as a null instrument. That is, we do not try to
define what constitutes a green sensation, or to measure in what
circumstances we get a green sensation, because it turns out that this
is extremely complicated. Instead, we study the conditions under which
two stimuli are indistinguishable. Then we do not have to
decide whether two people see the same sensation in different
circumstances, but only whether, if for one person two sensations are
the same, they are also the same for another. We do not have to decide
whether, when one sees something green, what it feels like inside is
the same as what it feels like inside someone else when he sees
something green; we do not know anything about that.
To illustrate the possibilities, we may use a series of four projector
lamps which have filters on them, and whose brightnesses are
continuously adjustable over a wide range: one has a red filter and
makes a spot of red light on the screen, the next one has a green
filter and makes a green spot, the third one has a blue filter, and
the fourth one is a white circle with a black spot in the middle of
it. Now if we turn on some red light, and next to it put some green,
we see that in the area of overlap it produces a sensation which is
not what we call reddish green, but a new color, yellow in this
particular case. By changing the proportions of the red and the green,
we can go through various shades of orange and so forth. If we have
set it for a certain yellow, we can also obtain that same yellow, not
by mixing these two colors but by mixing some other ones, perhaps a
yellow filter with white light, or something like that, to get the
same sensation. In other words, it is possible to make various colors
in more than one way by mixing the lights from various filters.
What we have just discovered may be expressed analytically as
follows. A particular yellow, for example, can be represented by a
certain symbol Y, which is the “sum” of certain amounts of
red-filtered light (R) and green-filtered light (G). By using two
numbers, say r and g, to describe how bright the R and G are,
we can write a formula for this yellow:
The question is, can we make all the different colors by adding
together two or three lights of different, fixed colors? Let us see
what can be done in that connection. We certainly cannot get all the
different colors by mixing only red and green, because, for instance,
blue never appears in such a mixture. However, by putting in some blue
the central region, where all three spots overlap, may be made to
appear to be a fairly nice white. By mixing the various colors and
looking at this central region, we find that we can get a considerable
range of colors in that region by changing the proportions, and so it
is not impossible that all the colors can be made by mixing
these three colored lights. We shall discuss to what extent this is
true; it is in fact essentially correct, and we shall shortly see how
to define the proposition better.
In order to illustrate our point, we move the spots on the screen so
that they all fall on top of each other, and then we try to match a
particular color which appears in the annular ring made by the fourth
lamp. What we once thought was “white” coming from the fourth lamp
now appears yellowish. We may try to match that by adjusting the red
and green and blue as best we can by a kind of trial and error, and we
find that we can approach rather closely this particular shade of
“cream” color. So it is not hard to believe that we can make all
colors. We shall try to make yellow in a moment, but before we do
that, there is one color that might be very hard to make. People who
give lectures on color make all the “bright” colors, but they never
make brown, and it is hard to recall ever having seen brown
light. As a matter of fact, this color is never used for any stage
effect, one never sees a spotlight with brown light; so we think it
might be impossible to make brown. In order to find out whether it is
possible to make brown, we point out that brown light is merely
something that we are not used to seeing without its background. As a
matter of fact, we can make it by mixing some red and yellow. To prove
that we are looking at brown light, we merely increase the brightness
of the annular background against which we see the very same light,
and we see that that is, in fact, what we call brown! Brown is always
a dark color next to a lighter background. We can easily change the
character of the brown. For example, if we take some green out we get
a reddish brown, apparently a chocolaty reddish brown, and if we put
more green into it, in proportion, we get that horrible color which
all the uniforms of the Army are made of, but the light from that
color is not so horrible by itself; it is of yellowish green, but seen
against a light background.
Now we put a yellow filter in front of the fourth light and try to
match that. (The intensity must of course be within the range of the
various lamps; we cannot match something which is too bright, because
we do not have enough power in the lamp.) But we can match the
yellow; we use a green and red mixture, and put in a touch of blue to
make it even more perfect. Perhaps we are ready to believe that, under
good conditions, we can make a perfect match of any given color.
Now let us discuss the laws of color mixture. In the first place, we
found that different spectral distributions can produce the same
color; next, we saw that “any” color can be made by adding together
three special colors, red, blue, and green. The most interesting
feature of color mixing is this: if we have a certain light, which we
may call X, and if it appears indistinguishable from Y, to the eye
(it may be a different spectral distribution, but it appears
indistinguishable), we call these colors “equal,” in the sense that
the eye sees them as equal, and we write
Here is one of the great laws of color: if two spectral distributions
are indistinguishable, and we add to each one a certain light,
say Z (if we write X+Z, this means that we shine both lights on
the same patch), and then we take Y and add the same amount of the
same other light, Z, the new mixtures are also
indistinguishable:
We have just matched our yellow; if we now shine pink light on the
whole thing, it will still match. So adding any other light to the
matched lights leaves a match. In other words, we can summarize all
these color phenomena by saying that once we have a match between two
colored lights, seen next to each other in the same circumstances,
then this match will remain, and one light can be substituted for the
other light in any other color mixing situation. In fact, it turns
out, and it is very important and interesting, that this matching of
the color of lights is not dependent upon the characteristics of the
eye at the moment of observation: we know that if we look for a long
time at a bright red surface, or a bright red light, and then look at
a white paper, it looks greenish, and other colors are also distorted
by our having looked so long at the bright red. If we now have a match
between, say, two yellows, and we look at them and make them match,
then we look at a bright red surface for a long time, and then turn
back to the yellow, it may not look yellow any more; I do not know
what color it will look, but it will not look yellow. Nevertheless
the yellows will still look matched, and so, as the eye adapts
to various levels of intensity, the color match still works, with the
obvious exception of when we go into the region where the intensity of
the light gets so low that we have shifted from
cones to
rods; then the color
match is no longer a color match, because we are using a different
system.
The second principle of color mixing of lights is this: any
color at all can be made from three different colors, in our case,
red, green, and blue lights. By suitably mixing the three together we
can make anything at all, as we demonstrated with our two
examples. Further, these laws are very interesting mathematically. For
those who are interested in the mathematics of the thing, it turns out
as follows. Suppose that we take our three colors, which were red,
green, and blue, but label them A, B, and C, and call them our
primary colors. Then any color could be made by certain amounts
of these three: say an amount a of color A, an amount b of
color B, and an amount c of color C makes X:
Now suppose another color Y is made from the same three colors:
Then it turns out that the mixture of the two lights (it is one of the
consequences of the laws that we have already mentioned) is obtained
by taking the sum of the components of X and Y:
It is just like the mathematics of the addition of vectors, where
(a,b,c) are the components of one vector, and (a′,b′,c′) are those
of another vector, and the new light Z is then the “sum” of the
vectors. This subject has always appealed to physicists and
mathematicians. In fact, Schrödinger wrote a wonderful
paper on color vision in which he developed this theory of vector
analysis as applied to the mixing of colors.
Now a question is, what are the correct primary colors to use? There
is no such thing as “the” correct primary colors for the mixing of
lights. There may be, for practical purposes, three paints that are
more useful than others for getting a greater variety of mixed
pigments, but we are not discussing that matter now. Any three
differently colored lights whatsoever can always
be mixed in the correct proportion to produce any color
whatsoever. Can we demonstrate this fantastic fact? Instead of using
red, green, and blue, let us use red, blue, and yellow in our
projector. Can we use red, blue, and yellow to make, say, green?
By mixing these three colors in various proportions, we get quite an
array of different colors, ranging over quite a spectrum. But as a
matter of fact, after a lot of trial and error, we find that nothing
ever looks like green. The question is,
can we make green? The
answer is yes. How?
By projecting some red onto the green, then
we can make a match with a certain mixture of yellow and blue! So we
have matched them, except that we had to cheat by putting the red on
the other side. But since we have some mathematical sophistication, we
can appreciate that what we really showed was not that
X could
always be made, say, of red, blue, and yellow, but by putting the red
on the other side we found that red plus
X could be made out of blue
and yellow. Putting it on the other side of the equation, we can
interpret that as a
negative amount, so if we will allow that
the coefficients in equations like (
35.4) can be both
positive and negative, and if we interpret negative amounts to mean
that we have to
add those to the
other side, then any
color can be matched by any three, and there is no such thing as
“the” fundamental primaries.
We may ask whether there are three colors that come only with positive
amounts for all mixings. The answer is no. Every set of three
primaries requires negative amounts for some colors, and therefore
there is no unique way to define a primary. In elementary books they
are said to be red, green, and blue, but that is merely because with
these a wider range of colors is available without minus signs
for some of the combinations.
35–6 Physiochemistry of color vision
Now, what about checking these curves against actual pigments in the
eye? The pigments that can be obtained from a retina consist mainly of
a pigment called
visual purple. The most remarkable
features of
this are, first, that it is in the eye of almost every vertebrate
animal, and second, that its response curve fits beautifully with the
sensitivity of the eye, as seen in Fig.
35–9, in which
are plotted on the same scale the absorption of visual purple and the
sensitivity of the dark-adapted eye. This pigment is evidently the
pigment that we see with in the dark: visual purple is the
pigment for
the rods, and it has nothing
to do with color vision. This fact was
discovered in 1877. Even today it can be said that the color pigments
of the cones have never been obtained in a test tube. In 1958 it could
be said that the color pigments had never been seen at all. But since
that time, two of them have been detected by
Rushton by a very simple and beautiful technique.
The trouble is, presumably, that since the eye is so weakly sensitive
to bright light compared with light of low intensity, it needs a lot
of visual purple to see with, but not much of the color
pigments for seeing colors. Rushton’s idea
is to
leave the pigment in the eye, and measure it anyway. What
he does is this. There is an instrument called an ophthalmoscope for
sending light into the eye through the lens and then focusing the light
that comes back out. With it one can measure how much is reflected. So
one measures the reflection coefficient of light which has gone
twice through the pigment (reflected by a back layer in the
eyeball, and coming out through the pigment of the cone again). Nature
is not always so beautifully designed. The cones are interestingly
designed so that the light that comes into the cone bounces around and
works its way down into the little sensitive points at the apex. The
light goes right down into the sensitive point, bounces at the bottom
and comes back out again, having traversed a considerable amount of the
color-vision pigment; also, by looking at the fovea, where
there are no rods, one is not confused by visual purple. But the color
of the retina has been seen a long time ago: it is a sort of orangey
pink; then there are all the blood vessels, and the color of the
material at the back, and so on. How do we know when we are looking at
the pigment?
Answer: First we take a color-blind person, who has
fewer pigments and for whom it is therefore easier to make the analysis.
Second, the various pigments, like visual purple, have an intensity
change when they are bleached by light; when we shine light on them they
change their concentration. So, while looking at the absorption spectrum
of the eye, Rushton put
another beam in the whole eye, which changes the concentration of
the pigment, and he measured the
change in the spectrum, and the
difference, of course, has nothing to do with the amount of blood or the
color of the reflecting layers, and so on, but only the pigment, and in
this manner Rushton obtained
a curve for the pigment of the protanope eye, which is given in
Fig.
35–10.
The second curve in Fig.
35–10 is a curve obtained with a
normal eye. This was obtained by taking a normal eye and, having already
determined what one pigment was, bleaching the other one in the red
where the first one is insensitive. Red light has no effect on the
protanope eye, but does in the normal eye, and thus one can obtain the
curve for the missing pigment. The shape of one curve fits beautifully
with Yustova’s green curve,
but the red curve is a little bit displaced. So perhaps we are getting
on the right track. Or perhaps not—the latest work with deuteranopes
does not show any definite pigment missing.
Color is not a question of the physics of the light itself. Color is a
sensation, and the sensation for different colors is different
in different circumstances. For instance, if we have a pink light,
made by superimposing crossing beams of white light and red light (all
we can make with white and red is pink, obviously), we may show that
white light may appear blue. If we place an object in the beams, it
casts two shadows—one illuminated by the white light alone and the
other by the red. For most people the “white” shadow of an object
looks blue, but if we keep expanding this shadow until it covers the
entire screen, we see that it suddenly appears white, not blue! We can
get other effects of the same nature by mixing red, yellow, and white
light. Red, yellow, and white light can produce only orangey yellows,
and so on. So if we mix such lights roughly equally, we get only
orange light. Nevertheless, by casting different kinds of shadows in
the light, with various overlaps of colors, one gets quite a series of
beautiful colors which are not in the light themselves (that is only
orange), but in our sensations. We clearly see many
different colors that are quite unlike the “physical” ones in the
beam. It is very important to appreciate that a retina is already
“thinking” about the light; it is comparing what it sees in one
region with what it sees in another, although not consciously. What we
know of how it does that is the subject of the next chapter.
BIBLIOGRAPHY
Committee on Colorimetry, Optical Society of
America, The Science of Color, Thomas Y. Crowell Company,
New York, 1953.
HECHT, S., S. SHLAER, and
M. H. PIRENNE, “Energy, Quanta, and Vision,”
Journal of General Physiology, 1942, 25, 819-840.
MORGAN, CLIFFORD, and
ELIOT STELLAR, Physiological Psychology, 2nd ed., McGraw-Hill Book Company, Inc., 1950.
NUBERG, N. D. and E. N. YUSTOVA, “Researches on Dichromatic Vision and the Spectral
Sensitivity of the Receptors of Trichromats,” presented at Symposium
No. 8, Visual Problems of Colour, Vol. II, National
Physical Laboratory, Teddington, England, September 1957. Published by
Her Majesty’s Stationery Office, London, 1958.
RUSHTON, W. A., “The Cone Pigments
of the Human Fovea in Colour Blind and Normal,” presented at
Symposium No. 8, Visual Problems of Colour, Vol. I,
National Physical Laboratory, Teddington, England, September
1957. Published by Her Majesty’s Stationery Office, London, 1958.
WOODWORTH, ROBERT S.,
Experimental Psychology, Henry Holt and Company, New York,
1938. Revised edition, 1954, by Robert S. Woodworth and H.
Schlosberg.