Abstract
In Chap. 13, we saw that one can characterize a light source in terms of its spectral intensity. We now turn to the question as to the relationship between the objective characteristics of a light and the subjective perception of the light. We have already identified three attributes of one’s visual perception – hue, saturation, and brightness. The first two are the attributes that, together, are referred to as the color. Thus, our goal is to establish the relationship between the spectral intensity and these three attributes. We will first summarize this relationship as it was determined through years of testing many individuals. Then we will discuss how this relationship can be understood in terms of the biophysical behavior of the visual apparatus, the rods of the retina.
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Notes
- 1.
In addition to the elementary book,Light and Color by Overheim and Wagner (op, cit. in Chap. 13), the reader is referred to the advanced texts: T. N. Cornsweet’s Visual Perception (Academic Press, N.Y., 1970) and Y. Le Grand’s Light, Color, and Vision (Dover, N.Y., 1957).
- 2.
It should be recognized that any particular individual is limited in their ability to discriminate one color from another. There are Just Noticeable Differences in Color in analogy with Just Noticeable Differences in Frequency. Therefore, a particular individual can discriminate among only a finite number of distinct colors.
- 3.
We will discuss the modern developments in the field of color. The history of the science of color vision started with Isaac Newton, who in the 1600s proposed that there are seven primaries that can be mixed in appropriate proportions to produce any color sensation. The basis of the proposal was Newton’s studies of the decomposition of white light by a prism into its rainbow of colors. He identified the color of an object as an attribute of the response of the eye to various wavelengths of light that are reflected off the object as opposed to the idea that the color “resides” in the object itself. The proposal that there are three primaries is due to Thomas Young (1807). Many other scientists helped develop the basic principles of color mixing – in particular, James C. Maxwell, who provided a theoretical basis for electromagnetic waves, as discussed in Chap. 5. In 1860, Maxwell produced the first, albeit crude, set of color-matching functions, which will be discussed in detail in this chapter. For an excellent history of studies of color vision, see Deane Judd in the publication: NATIONAL BUREAU OF STANDARDS: VOL. 55, p. 1313, (1966).
- 4.
Frank Preucil, Color Hue and Ink Transfer Their Relation to Perfect Reproduction, TAGA Proceedings, p 102–110 (1953).
- 5.
It should be clear from our study of color in Chap. 13 that physicists are far from inclined to get involved with the age old philosophical question as to whether a color resides in a colored object. Or, whether the color of an object is merely perceived.
- 6.
Wright, William David (1928). “A re-determination of the trichromatic coefficients of the spectral colours”. Transactions of the Optical Society 30: 141–164. Guild, John (1931). “The colorimetric properties of the spectrum”. Philosophical Transactions of the Royal Society of London (Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, Vol. 230) A230: 149–187.
- 7.
In the late 1800s, the mathematician Georg Cantor pioneered the study of levels of infinity and introduced a clearly defined method of comparing these levels. The lowest order of infinity is the number of integers, given the symbol ℵ 0. The next order of infinities is the set of real numbers, given the symbol \(\mathcal{C}\). It can be shown that \(\mathcal{C} = 1{0}^{{\aleph }_{0}}\). As surprising as it may seem, Cantor was able to show using his method of comparing infinities that \(\mathcal{C}\) is also the number of points in a finite area. This infinity is the infinite number of chromaticities. The number of spectral intensities is the number of ways you can draw a continuous graph along a finite axis. This number is an even higher infinity than \(\mathcal{C}\) and can be shown to be equal to \({\aleph }_{0}^{\mathcal{C}}\). See the Wikipedia article (1-8-2011): http://en.wikipedia.org/wiki/Georg_Cantor.
- 8.
Here is a wonderful website that enables you to play around with pairs of spectral intensities, each independently and see their respective color patches. You can then produce metamers galore.http://www.cs.brown.edu/exploratories/freeSoftware/repository/edu/brown/cs/exploratories/ applets/spectrum/metamers_guide.html.
- 9.
If a given spectral intensity is increased uniformly for all wavelengths by the same factor, it has been found from studies of human subjects that the color coordinates do not change. This observation amounts to saying that color is independent of brightness or, analogously, that pitch is independent of loudness.
- 10.
There is an arbitrariness as to the choice of white. Some standard sources say sunlight at noon will do. Most commonly, equal energy white is chosen, corresponding to I(λ) = constant.
- 11.
The values in this table were obtained by interpolation, using Table 14.2.
- 12.
See Stiles, Walter Stanley & Birch, Jennifer M. (1958), N.P.L. colour matching investigation: final report. Optica Acta 6: 1–26. See also the website: http://cvrl.ioo.ucl.ac.uk/database/text/cmfs/sbrgb2.htm.
- 13.
Recall from Chap. 10 that the loudness in phons is not directly related to the perceived loudness; the latter is measured by the sone level, which we learned is proportional to I′ 0. 3 where I’ is a scaled intensity that takes into account the equal loudness curves. Similarly, the perceived brightness for a given wavelength is not proportional to the intensity. The actual perceived brightness with respect to intensity is expressed by the lightness L ∗ wherein approximately, L ∗ ∝ Y β, where β is an exponent. Some sources claim that β = 0. 3. (See (1-12-2011): http://en.wikipedia.org/wiki/Lightness_(color)). However, others point out that the value varies depending upon whether the eye has adapted to the level of light intensity and that it can vary from about 0.4 for the dark adapted eye to about 0.5 for the light adapted eye.
- 14.
The subject of gamma and its related gamma correction is very complex. As a result, it is extremely difficult to find resources that are reliable. Articles abound with contradictory information. For what I consider a very reliable reference I highly recommend Charles Poynton, Video and HDTV, [Morgan Kaufmann Publishers and Elsevier Science, San Francisco, 2003].
- 15.
Tests of some monitors have revealed that their three RGB values do not have the same value of gamma. In this case, the chromaticity will change.
- 16.
The table was produced by using transformation matrices between the CIE table of color-matching functions and the RGB coordinates for the sRGB primaries.
- 17.
For example, in the website (1-12-2011): http://www.gizmag.com/sharp-4-primary-color-tvs-enables-trillion-colors/13823/we read: “By adding yellow to the colors red, green and blue, the televisions are capable of rendering nearly all the colors a human eye can discern.”
- 18.
Adding a fourth color with 8-bits will increase this number by a factor of 256, so that we would have over four billion different combinations! In a recent (May, 2010) website of the SHARP Corporation, it was claimed that their monitor would produce trillions of colors. It is incomprehensible to understand how they can arrive at such a number. See SHARP website: http://www.sharpusa.com/AboutSharp/NewsAndEvents/PressReleases/2010/January/2010_01_06_Booth_Overview.aspx.
- 19.
Note that the ellipses are largest in the green region, indicating that the eye does not discriminate changes in chromaticity as well. On the other hand, the ellipses are much smaller towards the blue region. We can see this variation in discrimination in the CIE chromaticity diagram of Fig. 14.13.
- 20.
See D. B. Judd and G. Wyszecki (1975), Color in Business, Science and Industry, Wiley Series in Pure and Applied Optics (3rd ed.). New York: Wiley-Interscience. p. 388.
- 21.
J. M. Linhares, et al., J Optical Society of America, volume 25, p. 2918 (2008).
- 22.
This number is just under 20 times the number of distinguishable pitches of pure tones, which has been found to be about 1,400. See Wikipedia (1-7-2011): http://en.wikipedia.org/wiki/Pitch_(music).
- 23.
In Appendix I, I show how this set of primaries is close to producing the largest possible gamut of colors.
- 24.
I am grateful to Raymond Soneira for communication on this subject. You are invited to see his extremely informative website (1-27-2011): http://www.displaymate.com/eval.html.
- 25.
For more details, see http://en.wikipedia.org/wiki/Retina and http://webvision.med.utah.edu/sretina.html.
- 26.
See the article by Jeremy Nathans, who first identified the genes: Scientific American, volume 260, pp. 42–49 (1989).
- 27.
The figure is based on Bowmaker J.K. and Dartnall H.J.A., “Visual pigments of rods and cones in a human retina.” J. Physiol. 298: pp501–511 (1980).
- 28.
If we plot the absorption spectrum as a function of the frequency, we would obtain a peak for the L-cone that has a width in frequency that is about 34% of the frequency at the peak.
- 29.
See a full discussion of this subject in the section “Complex Scenarios of Absorption and Emission” in Chap. 6.
- 30.
In mathematics, we say that r is a monotonically increasing function of n R, and so on.
- 31.
Omitted is the absorption of the macula, which contains the fovea. See the Wikipedia site (1-26-2011): http://en.wikipedia.org/wiki/Macular_degeneration, wherein it is pointed out that while “the macula comprises only 2.1% of the area of the retina …almost half of the visual cortex (in the brain) is devoted to processing macular information.”
- 32.
See the following website for a wonderful resource on color blindness (1-12-2011):http://en.wikipedia.org/wiki/Color_blindness It includes a fascinating set of figures that displays how the rainbow of colors appears for various types of color blindness. It also discusses anomalous dichromacy, wherein there are three cones, but one of them is defective. See also the website (1-12-2011): http://en.wikipedia.org/wiki/Evolution_of_color_vision_in_primates for material on the evolution of color vision in primates through mutation. Most interesting is the article’s claim that a remote ancestor of the primates was a tetranope, in having four different types of cones.
- 33.
See the websites http://www.neitzvision.com/content/home.html and http://www.handprint.com/HP/WCL/color1.html#dichromat for details.
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Gunther, L. (2012). Theory of Color Vision. In: The Physics of Music and Color. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0557-3_14
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