Section 35–5 The mechanism of color vision

(Young-Helmholtz theory / Dichromatic color blindness / Spectral sensitivity curves)

 

In this section, Feynman discusses Young-Helmholtz theory of color vision, dichromatic color blindness, and spectral sensitivity curves of a normal trichromat’s receptors. In a sense, the title of the section “the mechanism of color vision” may imply the interaction of light, photoreceptor cells in the retina, three types of cone cells, and complex processing in the eye-brain system. However, the trichromatic theory and the opponent-process theory (instead of Young-Helmholtz theory) help explain how the eye-brain system perceives and interprets a wide spectrum of colors and color blindness. Alternatively, the section could be titled as “Three types of cone visual pigments” that are closely related to dichromatic color blindness and spectral sensitivity curves.

 

1. Young-Helmholtz theory:

“The simplest theory, proposed by Young and Helmholtz, supposes that in the eye there are three different pigments which receive the light and that these have different absorption spectra, so that one pigment absorbs strongly, say, in the red, another absorbs strongly in the blue, another absorbs in the green (Feynman et al., 1963, p. 35–7).”

 

Historically, Young and Helmholtz did not propose that the three different cone-pigments are primarily sensitive to red, green, and blue. In 1802, Young initially thought the eye required receptors that were sensitive to three principal colors (red, yellow, and blue). In “Chromatics” (an entry in Encyclopaedia Britannica), Young (1817) proposed that the three primary colors are red, green, and violet. Building on Young’s theory, Helmholtz classified the cone photoreceptors as short (violet), middle (green), and long (red). In Handbuch der Physiologischen Optik, Helmholtz (1866) writes, “In the eye there are three types of nerve fibers. Stimulation of the first one excites the sensation of red, stimulation of the second the sensation of green, stimulation of the third the sensation of violet (Valberg, 2007, p. 278).”

 

“Now if we adjust the brightness or the intensity of one color against the other, there comes an intensity where the flicker at 16 cycles disappears… It is possible to match two colors for “equal brightness” by this flicker technique. The results are almost, but not exactly, the same as those obtained by measuring the threshold sensitivity of the eye for seeing weak light by the cones. Most workers use the flicker system as a definition of the brightness curve (Feynman et al., 1963, p. 35–8).”

 

We may use the term, flicker fusion, which refers to the phenomenon where the eye perceives a continuous image (or still image) when presented with a rapid succession of discrete images (or flickering image), typically above a certain frequency threshold. Feynman suggests that we can adjust the brightness of one color against the other such that the flicker disappears at 16 Hz, but the eye may perceive visual flicker artifacts at rates over 500 Hz when the image includes high frequency spatial edges (Davis, Hsieh, & Lee, 2015).  However, some opin that the frame rate of computer displays should be 72 Hz to avoid flicker completely (Barten, 1999). (Standard-definition television may operate at 25 or 30 frames per second, or sometimes at 50 or 60 half-frames per second.) In short, flicker fusion could be related to the Talbot-Plateau law, which describes the conditions under which the perceived brightness of a flickering image will appear to be equal to the brightness of a still image.

 

2. Dichromatic color blindness:

“By measuring all these types we can determine the three curves! It turns out that there are three types of dichromatic color blindness; there are two common types and a third very rare type, and from these three it has been possible to deduce the pigment absorption spectra (Feynman et al., 1963, p. 35–8).”

 

Feynman explains that there are three types of dichromatic color blindness. However, color blindness can be categorized as monochromatism, dichromatism, and anomalous trichromatism. Firstly, monochromatism (total color blindness) refers to the condition characterized by the total inability to perceive color. Secondly, dichromacy includes protanopia, deuteranopia, and tritanopia, where one type of cone is non-functional, leading to difficulties in perceiving or distinguishing certain colors. Lastly, anomalous trichromatism refers to conditions where there is an abnormality in two types of cones, often leading to a variation in color perception but not complete color blindness. In addition, there are variations within the sub-categories, such as protanomaly, deuteranomaly, or tritanomaly, which refer to a reduced sensitivity of the cone cells instead of a complete absence (see figure below).

Source: What Is Color Blindness? Condition and Types Explained (verywellhealth.com)

 

“Figure 35–6 shows the color mixing of a particular type of color-blind person called a deuteranope. For him, the loci of constant colors are not points, but certain lines, along each of which the color appears to him to be the same. If the theory that he is missing one of the three pieces of information is right, all these lines should intersect at a point (Feynman et al., 1963, p. 35–8).”

 

Feynman says that the loci of constant colors for a color-blind person are not points, but certain lines along each of which the color appears to him to be the same and all these lines should intersect at a point. Specifically, these lines of confusion* cannot be distinguished (or confused) by the protanope or deuteranope, are also known as pseudo-isochromatic lines. One may clarify that these apply not only to the colors on the confusion lines, but all the colors between any two closest lines, especially under certain lighting conditions. Furthermore, we may adopt the term copunctal point, which refers to the convergence point of these confusion lines outside the chromaticity diagram. This is a theoretical reference point where all the confusion lines meet or intersect.

Source: Color blindness - Wikipedia

 

In the Audio Recordings* [46 min: 00 sec] of this lecture, Feynman says: “lines of confusion” instead of “loci of constant colors.”

*The Feynman Lectures Audio Collection: https://www.feynmanlectures.caltech.edu/flptapes.html

 

“If we carefully measure on this graph, they do intersect perfectly. Obviously, therefore, this has been made by a mathematician and does not represent real data! (Feynman et al., 1963, p. 35–8).”

 

The co-punctal-point of the CIE diagram could be attributed to James Clerk Maxwell. In a letter dated Jan. 4, 1855 to G. Wilson, J. C. Maxwell writes, “If we find two combinations of colors which appear identical to a color-blind person, and mark their positions on the triangle of colors, then the straight line passing through these points will pass through all points corresponding to other colors, which, to such a person, appear identical with the first two. We may in the same way find other lines passing through the series of colors which appear alike to the color-blind. All these lines either pass through one point or are parallel, according to the standard colors which we have assumed, and the other arbitrary assumptions we may have made. Knowing this law of color-blind vision, we may predict any number of equations which will be true for eyes having this defect.” Maxwell was a Scottish physicist, but he was also known as a mathematician.

 

3. Spectral sensitivity curves:

“Yustova gets approximately the same position in this case. Using the three different kinds of color blindness, the three pigment response curves have finally been determined, and are shown in Fig. 35–8  (Feynman et al., 1963, p. 35–9).”

 

It could be confusing to some that Feynman mentions pigment response curves, but the caption of Fig. 35–8 is “The spectral sensitivity curves of a normal trichromat’s receptors.” However, the spectral sensitivity curves are essentially a representation of how the human visual system responds to light across the spectrum, and they are due to the responses of color-sensitive pigments in the cones of the retina. Interestingly, Feynman explains that the spectral sensitivity curves were obtained using an ophthalmoscope in the next section. This experiment relied on the subjective judgment of the observer to interpret the reflection of light from the retina and determine the spectral sensitivity. Thus, Feynman adds that “[e]ven today it can be said that the color pigments of the cones have never been obtained in a test tube (Feynman et al., 1963, Section 35–6).”

Spectral sensitivity curves represent the response of the eye's different types of cones to varying wavelengths of light. There are at least three aspects that make them somewhat arbitrary: (1) Individual differences: Spectral sensitivity curves are based on averages derived from studying groups of individuals with normal color vision. (2) Experimental limitations: Color matching experiments or testing with different monochromatic lights have their constraints, and the accuracy of the measurements might be influenced by the experimental setup used. (3) Environmental factors: Factors such as lighting conditions, adaptation to different light levels, and background colors can influence cone responses. In essence, the spectral sensitivity curves are not entirely arbitrary but are based on measurements obtained through the experiments.

 

Review Questions:

1. Did Young and Helmholtz propose that the three different cone-pigments are primarily sensitive to red, green, and blue (or violet)?

2. How would you explain the three types of dichromatic color blindness?

3. How would you explain the spectral sensitivity curves or pigment response curves?

 

The moral of the lesson: the three types of cone visual pigments are integral to normal color vision, and their properties help explain both dichromatic color blindness and the spectral sensitivity of the human visual system; variations in these pigments contribute to individual differences in color perception.

 

References:

1. Barten, P. G. (1999). Contrast sensitivity of the human eye and its effects on image quality. Bellingham: SPIE press.

2. Davis, J., Hsieh, Y. H., & Lee, H. C. (2015). Humans perceive flicker artifacts at 500 Hz. Scientific reports, 5(1), 7861.

3. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

4. Maxwell, J. C. (1855). On the theory of colours in relation to colour-blindness, Letter of Jan. 4, 1855 to G. Wilson. Researches on Colour-Blindness. Edinburgh: Sutherland-Knox.

5. Valberg, A. (2007). Light vision color. Hoboken, NJ: John Wiley & Sons.

6. Young, T. (1817). Chromatics. Supplement to the Encyclopaedia Britannica, 3, 141-63.

Section 35–4 The chromaticity diagram

 (Dotted Triangle / Horseshoe shaped area / Spectral sensitivity curves)

In this section, Feynman discusses the dotted triangle and horseshoe shaped area of a chromaticity diagram as well as spectral sensitivity curves. Alternatively, the section could be titled “The CIE chromaticity diagram (1931 version)” because it was based on CIE 1931 color space in which CIE stands for Commission Internationale de l’Eclairage. The chromaticity diagram is a representation of human color perception developed from the experimental results conducted by John Guild and David Wright. In addition, the CIE defined the standard observer in 1931 using a 2° field of view, which represents an average human’s chromatic response. In 1964, the CIE proposed some improvements, e.g., they defined an additional standard observer using a 10° field of view.

 

1. Dotted Triangle:

“If any one color is represented by Eq. (35.4), we can plot it as a vector in space by plotting along three axes the amounts a, b, and c, and then a certain color is a point. If another color is a′, b′, c′, that color is located somewhere else. The sum of the two, as we know, is the color which comes from adding these as vectors… If we use a blue and a green and a red, as primaries, we see that all the colors that we can make with positive coefficients are inside the dotted triangle, which contains almost all of the colors that we can ever see… (Feynman et al., 1963, p. 35–6).”

 

The dotted triangle (or triangular region) contains the colors that can be produced by mixing three primary colors. Each primary color is typically located at a corner of the triangle. The color equation can be represented by C = aR + bG + cB, in which C is the color to be matched, R, G, B are the chosen primary colors, whereas the chromaticity coordinates a, b, c are the amount of each primary color. One may adjust the brightness of the color C by multiplying the coordinates a, b, c by a constant in which a + b + c = 1. Feynman explains that we can plot any color as a vector in the context of the chromaticity diagram, however, the chromaticity coordinates do not form a vector space in the formal sense. The vector space is a mathematical structure that satisfies certain properties, such as closure under addition and scalar multiplication, among others.

 

Maxwell developed a chart in the form of an equilateral triangle, which represents the relationships between different colors and it approaches pure white at the center. The Maxwell’s color triangle is an idealized model that helps visualize how different colors can be combined in varying proportions to form a wide range of hues (colors dependent on the dominant wavelength). Essentially, any point within the triangle identifies a specific color, and it illustrates the additive color mixing process. The interior of the triangle displays the secondary and tertiary colors that result from combining different proportions of the primary colors, e.g., red and green form yellow, green and blue form cyan, whereas blue and red form magenta (see below). However, this triangle has limitations in representing the full complexity of human color perception, individual variations in color vision, and the intricacies of color mixing in different contexts.

Source: Maxwell's Triangle (appstate.edu)

 

2. Horseshoe shaped area:

“… because all the colors that we can ever see are enclosed in the oddly shaped area bounded by the curve. Where did this area come from? Once somebody made a very careful match of all the colors that we can see against three special ones (Feynman et al., 1963, p. 35–7).”

 

The chromaticity diagram is a plane diagram formed by plotting one of the chromaticity coordinates against another that shows a range of colors. Some colorists prefer the term gamut, which means the range of colors that can be formed by mixing different ratios of primary colors.  The color gamut depicted in a chromaticity diagram, appears in the shape of a horseshoe (instead of saying oddly shaped area). In other words, the chromaticity coordinates of the pure colors in the visible spectral range form a concave curve shaped like the “sole of a shoe.” The horseshoe shaped area is a representation of the limits of human vision and the range of colors that can be perceived by the average human eye. Colors lying outside the horseshoe boundary are imaginary and cannot be produced by any combination of the three primary colors within the visible spectrum.

 

Historically, scientists assumed that three primary colors could be mixed to form all colors, but it was not achievable due to the impurity (or imperfection) of the paints. Furthermore, the original CIE chromaticity diagram is an imperfect system because it is unable to generate the full range of visible (perceptually possible) colors. However, it is possible to “mix” imaginary primary colors and quantify all colors, i.e., these non-real primary colors are defined as lying outside the range of visible colors (see below). Specifically, CIE 1931 XYZ color space (based on imaginary primary colors) was developed from experimental data performed by Wright and Guild in the 1920’s and it serves as a reference for other color spaces. In essence, it is impossible to create all visible colors using real primary colors (e.g., red, green, and blue), however, all visible colors can be mixed using imaginary primary colors that are perceptually impossible.

 

Source: handprint: colormaking attributes

3. Spectral sensitivity curves:

“An example of such experimental results for mixing three lights together is given in Fig. 35–5. This figure shows the amount of each of three different particular primaries, red, green and blue, which is required to make each of the spectral colors. Red is at the left end of the spectrum, yellow is next, and so on, all the way to blue. Notice that at some points minus signs are necessary. It is from such data that it is possible to locate the position of all of the colors on a chart, where the x- and the y-coordinates are related to the amounts of the different primaries that are used (Feynman et al., 1963, p. 35–7).”

 

Fig. 35–5 is described in The Feynman Lectures as “The color coefficients of pure spectral colors in terms of a certain set of standard primary.” Perhaps Feynman could use the term Color Matching Functions (CMFs) or “original Wright and Guild RGB functions,” which are a set of mathematical functions that describe how the human eye perceives different wavelengths of light. In short, the CMFs are the amounts of red, green, and blue light needed to match the standardized intensity of light of a certain wavelength. On the other hand, there are spectral sensitivity curves of three idealized light detectors yielding the CIE tristimulus values X, Y and Z (see below). Feynman explains that at some points minus signs are necessary for RGB CMFs in Fig. 35–5, but this is not necessary for XYZ CMFs that have positive values for all wavelengths, which is an advantage.

Source: CIE 1931 color space - Wikipedia

“That is the way that the curved boundary line has been found. It is the locus of the pure spectral colors. Now any other color can be made by adding spectral lines, of course, and so we find that anything that can be produced by connecting one part of this curve to another is a color that is available in nature (Feynman et al., 1963, p. 35–7).”

 

The curved boundary line in the chromaticity diagram (see below) shows three aspects of color perception: (1) Limits of vision: It delineates the limits of color vision that can be perceived by the human eye under normal lighting conditions. (2) Hue and saturation: It defines the perceivable hues and maximum saturation, while those nearer to the center are less saturated. Saturation refers to “the attribute of color perception that expresses the degree of departure from the gray of the same lightness (Hunter & Harold, 1987, p. 407).” (3) Spectral (monochromatic) locus: It represents the path of pure spectral colors at various wavelengths (as shown below in nanometers) along the visible spectrum. In summary, the Color Matching Functions (CMFs) and curved boundary line are closely linked, as the CMFs guide our understanding of how the three primary colors should be mixed to replicate the perception of colors found along the boundary curve, representing the pure spectral colors visible to human vision.

 

Source: (Rhyne, 2012)

 

Review Questions:

1. Do you agree with Feynman that any color within the dotted triangle can be plotted as a vector in space?

2. How would you explain the oddly shaped area in the chromaticity diagram?

3. How would you explain the curved boundary line in the chromaticity diagram?

 

The moral of the lesson: the horseshoe-shaped area in the chromaticity diagram contains the entire range of colors visible to the human eye, encompassing both pure spectral colors and all the colors that result from combinations of the three primary colors.

 

References:

1. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

2. Hunter, R. S., & Harold, R. W. (1987). The measurement of appearance. New York: John Wiley & Sons.

3. Rhyne, T. M. (2012). Applying color theory to digital media and visualization. Boca Raton: CRC Press.