The document discusses additive mixing of colored lights and some key properties: 1) We can match a wide range of colors using mixtures of primaries like red, green, and blue lights. 2) Grassman's law from 1853 states that stimuli of the same color will produce identical effects in mixtures regardless of spectral composition. 3) Modern colorimetry is based on experimental properties of additive mixtures of colored lights established over a century ago. Subsequent experiments have refined the conditions where simple laws hold.

1. Properties of
ADDITIVE MIXING
As indicated earlier, coloured lights are easy to
define
and hence seem to be suitable for
use as primaries in a system of colour
specification.
The properties of additive mixtures
of coloured light have been studied for many
years [1–5], and those that are particularly
relevant to their use in systems of colour
specification are considered here.
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2. We can match a wide range of colours using a mixture
of, say, red, green and blue primaries.
Suppose our primaries are single wavelengths
and we use them to match
white light
consisting of a mixture of all the wavelengths in the visible
region
using an arrangement such as that shown in Figure 3.
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3. WHITE LIGHT
Although the mixture is physically
quite different from the white light,
by carefully adjusting the amounts of the primaries we
can match the white light:
that is, we can produce with the mixture a white that looks
identical to the white light.
If we change the colour or lightness of the surround,
Our white colours change in appearance.
Over a wide range of conditions, however, the
match holds:
if the colours change, they both do so by the same amount.
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4. Grassman’s law
This was recognised by Grassman, who stated in 1853:
‘Stimuli of the same colour
(that is, same hue, same brightness, and same saturation)
produce identical effects in mixtures
Regardless of their spectral composition’.
Hence we can deal with colours without considering
their spectral composition, at least in many applications.
Grassman’s law also implies that
if colour A matches colour B
and colour C matches colour D,
then colour A additively mixed with C matches colour B mixed with D.
This is vital when we consider that normal colours are additive
mixtures of all the wavelengths in the visible spectrum.
We need to consider the effect of the additive mixture of all the wavelengths.
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5. Modern Colorimetry Based on EXPERIMENT
It cannot be stressed too strongly that modern
colorimetry is based on
the properties of additive mixtures of coloured lights,
and that these properties have been determined
by experiment.
The main properties were established well over a century
ago.
Subsequent work has confirmed that the simple
properties described above are indeed valid,
 but has defined much more closely
the range of experimental conditions
Under which the simple laws hold.
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6. COLOR VISION THEORY
Theories of colour vision must attempt to explain
such laws, and also their exceptions.
The fact that colours can be produced using only
three primaries implies that
there are three types of receptor among the cone cells of the eye,
and that variations in the magnitude of the responses
from the three types produce the range of colour sensations
that we call colour vision.
This theory was originally put forward by Young and elaborated by
Helmholtz.
Modern theories suggest that the visual mechanism is complicated,
particularly with respect to the ways
in which the receptors are linked to the brain.
Modern colorimetry and the CIE system are based on
the experimental facts, not on any particular theory of colour vision.
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7. Mixture of Primaries
Suppose we represent our red, green and
blue primary light sources by
[R], [G] and [B].
If we use these to match a colour using a
mixture of the primaries, we can represent the amounts
of our primaries by
R, G and B respectively. We can then write Eqn 3.1:
which is equivalent to saying that C units
of the colour [C] can be matched
by R units
of the red primary [R]
additively mixed with
G units of
the green primary [G] together
with B units of
the primary [B].
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8. Mixture of Primaries
It is important to distinguish carefully between the primaries
themselves,
such as [R], and the amounts of the primaries used in
a match, such as R.
The amounts used of each primary, R, G and B, are known as
the tristimulus values of the colour [C].
These values depend on the colour [C].
If the values are known, they give an indication of the colour. Thus if R
and B are high and G is low,
the colour can be matched using a lot of the red and blue primaries
and only a little of the green primary:
thus the colour is some sort of purple.
The exact colour obviously depends on the exact nature of
our primaries [R], [G] and [B],
and if these are very pure
the colour is likely to be a saturated purple.
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9. MIXING PRIMARIES
In most respects, equations such as Eqn 3.1 can be treated as ordinary algebraic
equations. Thus if we write Eqn 3.2:
 then an additive mixture of C1 units of [C1] with C2 units of [C2]
can be matched by
R1 + R2 units of the red primary [R],
 additively mixed with G1 + G2 units of the green primary [G],
together with B1 + B2 units of the blue primary [B] (Eqn 3.4):
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