Workplace Illumination – Part 7: Colorimetry and Color Vision

     It is easy to underestimate the importance of color as a distinct component of human visual capability.  Color often plays a significant role in our recognition of objects and perceptions of spaces.
     The perception of color varies among individuals.  Defined systems of identification make it possible to compare colors and to describe them in a way that can be communicated effectively.  Coherent communication of color information is the key to color specifications (e.g. product design) and color matching (e.g. paint mixing).
     This installment of the series explores the production, “measurement,” communication, and human perception of color in our environment.  Concepts introduced in previous installments are also revisited and expanded in the context of color vision.

Color Vision
     The ability to see color requires sufficient luminance to activate cones in the retina.  Effective discrimination between similar colors requires higher luminance than that required to merely recognize color.  That is, color vision is unavailable in scotopic conditions and is limited in mesopic conditions.  Maximum acuity and discrimination requires photopic conditions.  Exhibit 1 provides a summary comparison of these conditions.

     As a consequence of the illumination levels in which they operate, cones exhibit much lower sensitivity to light than do rods.  The relative sensitivity of each photoreceptor type is shown in Exhibit 2.  The extreme differential sensitivity explains the importance of adaptation luminance to visual performance and the discomfort caused by rapid transitions between vastly-different illumination levels.
     As a person’s eyes are exposed to a high luminance (i.e. photopic conditions), their sensitivity declines, marking a shift from rods to cones as the predominant active photoreceptors.  This is the transition from dark-adaptation to light-adaptation.  As this transition occurs, the appearance, or perception, of colors also changes.  This phenomenon, called color adaptation, is caused by the changing rates of photopigment bleaching corresponding to the eyes’ overall sensitivity.

Spectral Distributions
     When mention is made of color, it is often assumed to refer to light entering our eyes.  However, characteristics of the source of light and its path to the eye must also be considered to develop an understanding of color vision.  Light sources, objects from which light reflects, and media through which light is transmitted each exhibit a spectral distribution that influences the light reaching our eyes.  Color is not inherent to light; it is its spectral distribution, as interpreted by the brain, that shapes our perception of color.
     The spectral power distributions (SPDs) of some light source examples are plotted in Exhibit 3.  The SPD is the source’s relative radiant power as a function of wavelength.  The appearance of a light source, when observed directly, can be predicted by studying its SPD plot.  For example, the plot for a high-pressure sodium light source, with mid-range wavelengths dominating its power distribution, explains the yellowish appearance of this type of light, often used for highway lighting.

     An object’s spectral reflectance distribution (SRD) describes its reflectance as a function of wavelength.  The SRD plots in Exhibit 4 use several common fruits as examples.  Note that all of the examples exhibit very low reflectance of short wavelengths; for this reason, none of these fruits appear to be blue or purple.
     A transmission medium may differentially influence light as it passes through, as described by its spectral transmittance distribution (STD), the medium’s transmittance as a function of wavelength.  Exhibit 5 plots the STDs of two examples of architectural glass.  Though the difference may not seem large, the lower transmittance of long-wavelength light offered by the standard-transmittance glass could have a significant aesthetic impact in some applications.
     A light source/object interaction accounts for the SPD of a light source and the SRD of an object to determine a reflected spectral distribution.  A graphical representation of this mathematical calculation is provided, in Exhibit 6, for one of the example fruits shown in Exhibit 4 illuminated by the light sources shown in Exhibit 3.  The calculation can also be expanded to include any effects of transmission media, whether between the source and object or between the object and observer, on the perceived appearance of an object by multiplying the appropriate distribution by the STD of the medium.

Color Mixing
     Two methods of color mixing – additive and subtractive – are used to create the desired appearance of objects; both are in common use.  Additive color mixing can be used when the light source is controlled; subtractive color mixing can be used as an alternative to source control or when control of the light source is impossible.
     Additive color mixing creates a desired appearance by adjusting the SPD of incident light.  A common method mixes three primary colors in proportions necessary to generate the desired output.  This is often referred to as the RGB system, which is shorthand for the three primary colors red, green, and blue; it is the basis of many electronic displays.  Exhibit 7 depicts the overlapping of primary colors to create the secondary colors yellow, magenta, and cyan.  Where all three primary colors exist in equal proportion (i.e. center of image), white light results.

     Subtractive color mixing employs filters to selectively remove wavelengths from incident light, a technique employed extensively in photography.  For this method, depicted in Exhibit 8, the primary and secondary colors are the reverse of RGB additive color mixing.  That is, cyan, magenta, and yellow filters create areas of blue, red, and green where they overlap.  Where all three filters overlap, all wavelengths of light are removed, resulting in a black appearance.
     Paints, dyes, and inks also employ subtractive color mixing to achieve desired appearances.  In this case, pigments are used to selectively absorb unwanted wavelengths and reflect the remainder.  The fruit examples above demonstrate natural occurrences of selective reflection; the development of pigments allows us to produce similar effects at will.
     An important concept related to color mixing is that of metamerism.  Metamers are lights of differing SPDs that present the same color.  A certain color appearance can be achieved with multiple combinations of constituent colors.  In practice, this means that two light sources that appear identical when viewed directly can result in significantly different visual perceptions after transmission through a medium or reflection from an object.

Characterization of Color
The Munsell System
     Though a light’s appearance can be quantified by its spectral distribution, this is not a convenient method for many applications and practitioners.  Instead, colors are often described by a color order(ing) system, a prevalent one being the Munsell system.  The Munsell system defines color on three dimensions, pictorially represented in Exhibit 9:  hue, value, and chroma.
     Generic references to “color” describe the hue of observed light.  The hue scale, represented by the azimuth of the Munsell system model, consists of 100 gradations.  Major gradations are defined by five principal hues (purple, blue, green, yellow, red), abbreviated to the first letter of each (P, B, G, Y, R).  A set of five intermediate hues is also defined (purple-blue, blue-green, green-yellow, yellow-red, red-purple), also abbreviated by initials (PB, BG, GY, YR, RP).  [A note on convention:  an azimuthal scale is defined as increasing in a clockwise direction, as depicted in Exhibit 9.  However, the sequence of hues cited above progresses in counterclockwise fashion.  This was done to mimic the common presentation of the visible spectrum that progresses from violet on the left to red on the right (see Part 2, Exhibit 1).]

     The central spine in the Munsell system model represents the value scale.  This dimension consists of gradations ranging from black (0) to white (10).  “Colors” on this axis are achromatic (i.e. no hue) and are referenced as “Neutral X,” where “X” is the value number.
     Some sources, and other color order systems, refer to the value dimension as lightness or brightness.  Brightness is the term typically applied to self-luminous objects, while lightness typically refers to reflective surfaces.
     The radial dimension of the Munsell system model is the chroma scale.  It ranges from 0, for neutral (i.e. on the value axis), to 20, for highly-saturated colors, on the periphery.  This characteristic is often called saturation or strength; each of these terms references a color’s deviation from neutral, or grayscale.
     The Munsell system identifies each color by an alphanumeric code of the format hue/value/chroma.  For example, 10R/5/20 refers to highly-saturated, “pure” red – as red as red gets!  A corresponding point on the value axis – that is, absent hue and chroma, a “middle gray” – is called Neutral 5 or N5.  Possession by each of a Munsell Color Atlas allows disparate individuals to discuss a color sample as if they were looking at the same object.  Although individuals’ perception of a specified color differ, use of a Munsell color chip approximates that which would be experienced were the conversants collocated.
     Books containing a Munsell Color Atlas are available for physical comparisons of samples.  Pictorial models, such as that in Exhibit 9, remain useful conceptual representations.  The system can also be represented by the Munsell solid; it is often depicted as shown in Exhibit 10.  Munsell, in his seminal work, describes a color sphere, but the scales, as described, define a cylinder.  A cylinder also facilitates visualization of the entire range of colors, as the segments of a sphere become exceedingly small near the poles.

Color Matching Functions
     A color matching function (CMF) defines a color by the proportions of its constituents.  For the RGB system, color matching functions have been derived empirically.  Exhibit 11 provides plots of RGB CMFs and an example of their use.  A dashed line is drawn vertically at 480 nm; the intersection of this line with each CMF is projected to the vertical axis.  Light with the proportional contributions of the primary colors represented by the projections to the vertical axis simulates monochromatic light of 480 nm wavelength.

     To eliminate negative values, RGB CMFs are transformed into XYZ color matching functions that reliably identify metamers, though the “primary colors” used are fictitious.  Two sets of CMFs have been developed by the CIE (Commission International de l’Éclaraige or International Commission on Illumination), the globally-recognized authority on lighting, color, and related topics.  One is the 2° CMFs (1931), recommended for fields of view subtending 1 - 4°.  The other is the 10° CMFs (1964), recommended for angular subtense greater than 4°.  These sets of CMF are known as standard observers; plots are shown in Exhibit 12.
     The transformed CMFs are identified as x_bar(λ), y_bar(λ), and z_bar(λ) to represent the average visual response of observers.  Tristimulus values X, Y, and Z are analogous to RGB values; both represent the contribution of each primary color required to reproduce a light’s color.  Tristimulus values are found by calculating the products of the stimulus spectrum and each CMF; the areas under the resulting distribution curves are the tristimulus values.

Chromaticity Diagrams
     Though other chromaticity diagrams have been developed, the one of primary interest is the CIE 1931 2° Chromaticity Diagram shown in Exhibit 13.  Chromaticity coordinates are found by calculating the ratio of each tristimulus value to the sum of the tristimulus values:  x = X/(X + Y + Z); y = Y/(X + Y + Z); z = Z/(X + Y + Z).

     The chromaticity diagram is plotted in two dimensions – x and y.  The third is unnecessary; because x + y + z = 1, z can easily be determined from the x-y coordinates.  The colors shown in the diagram are “directional” only; hue and saturation are represented, but the perception of color is also influenced by lightness (the z dimension), which is not accounted for in the diagram.
     The curved boundary of the chromaticity diagram is the spectrum locus, along which the most-saturated colors lie.  The straight line enclosing the diagram is the purple boundary, so named because hues comprised of combinations of red and blue lie along it.
     The chromaticity diagram is also a useful backdrop for other information.  In Exhibit 14, regions are outlined within which stimuli are typically identified as the noted color.  MacAdam ellipses are shown in Exhibit 15; each ellipse represents chromaticities surrounding the coordinates of a given stimulus that are undifferentiable from it.  The variation in size and orientation of the ellipses is noteworthy.

Correlated Color Temperature
     The simplicity of single-number metrics make them popular, despite the loss of precision they often engender.  Sources of white light can be classified by their color temperature, the absolute temperature of an ideal radiator emitting light with the same chromaticity as the source.  These sources lie on the blackbody, or Planckian, locus, the arc shown in the interior of the chromaticity diagram in Exhibit 13.
     All sources of “white light” do not lie directly on the Planckian locus, however.  For those that do not, a correlated color temperature (CCT) is assigned.  The CCT of a light source is the absolute temperature of an ideal radiator emitting light with chromaticity nearest that of the source.  The lines crossing the Planckian locus in Exhibit 13, each corresponding to an absolute temperature, are isothermal lines, or isotherms.  A light source with chromaticity coordinates that lie on or near an isotherm are said to have a CCT equal to the isotherm’s absolute temperature.
     Full definition of a light source requires a second value, though it is rarely cited; CCT alone is deemed sufficient for most applications.  The second value is the distance from the source’s chromaticity coordinates to the nearest point on the Planckian locus.  This distance is called Duv; positive values are assigned to chromaticities lying above the Planckian locus and negative values are assigned to those lying below it.  To be considered “white light,” a source’s Duv value must be in the range of ± 0.006.
     In lieu of citing a CCT, a light source may be assigned a more-generic descriptor of its temperature-correlated appearance.  Unfortunately, these descriptors are counterintuitive, as they invert the CCT scale.  That is, higher CCT light sources provide “cooler” light.  Lights with CCT up to 3300 K are considered “warm;” these typically have a yellowish tinge.  From 3300 – 4000 K CCT, light sources are “intermediate” and from 4000 – 5300 K CCT they are “intermediate-cool.”  “Cold” light sources have CCTs above 5300 K; a blue tinge becomes evident in light with higher CCT.

The Color Gamut
     While other color-characterization methods compare a light source’s properties to those of a reference light source, the color gamut approach uses a set of test colors.  The chromaticity coordinates of eight standard test colors are plotted on a chromaticity diagram; the area enclosed by connecting the eight points is called the color gamut of the light source.  The size and shape of a color gamut represent the extent to which color discrimination is possible under the light source.  For example, the color gamut of the high-pressure sodium light source, shown among other examples in Exhibit 16, is localized in the yellow region.  This provides similar insight into the nature of this type of light source to that of its SPD, discussed previously.

Color Rendering
     Color rendering is the term used to describe the effect a light source has on the chromaticity of observed colors when compared to the same object viewed under a reference light source.  A color rendering index (CRI) is used to quantify a light source’s effect.  Higher CRIs indicate that colors appear “truer to the originals;” a CRI of 100, the value assigned to the reference light source, indicates that no color distortion occurs.  A CRI > 80 is considered “good” for most applications.
     Computation of the CIE color rendering index involves comparing the color gamut of the subject light source to that of the reference light source.  CIE defines fourteen test colors, summarized in Exhibit 17.  The first eight colors, used to compute CRI, are pastels covering the full range of hues.  The remaining six are special test colors, including samples representing skin tones and foliage.

     A graphical representation of the method of computation of CRI is shown in Exhibit 18, where a high-pressure sodium light source is, once again, the example.  The magnitude of the chromaticity shift of each test color is called a CIE special CRI.  The CIE general CRI, the value cited on light source packaging, for example, is the average of the CIE special CRIs of the eight pastel test colors.  Large chromaticity shifts result in a CRI of 16 for the example light source in Exhibit 18; its CCT is 1975 K.  Though several deficiencies have been identified in the CIE test color method, the CIE CRI continues to be the index of choice and is commonly found in lighting catalogs.


     Interested readers can find much more information on additional chromaticity diagrams, color order systems, and related topics in the references cited below and other sources.  The scope of this installment, like others in the series, must be limited to avoid overwhelming readers with excessive detail that may not be immediately applicable.  However, the information presented here provides sufficient background to facilitate understanding of forthcoming discussions of other visual phenomena and lighting system design.

     For additional guidance or assistance with Safety, Health, and Environmental (SHE) issues, or other Operations challenges, feel free to leave a comment, contact JayWink Solutions, or schedule an appointment.

     For a directory of “Workplace Illumination” volumes on “The Third Degree,” see Part 1:  An Introduction to Lighting (21Aug2024).

References
[Link] A Color Notation.  A. H. Munsell.  Geo. H. Ellis Co.; 1905.
[Link] Lighting for Health and Safety.  N.A. Smith.  Butterworth-Heinemann; 2000
[Link] The IESNA Lighting Handbook, 9ed.  Mark S. Rea (ed).  Illuminating Engineering Society of North America; 2000.
[Link] The IESNA Lighting Handbook, 10ed.  David L. DiLaura, Kevin W. Houser, Richard G. Mistrick, Gary R. Steffy (eds).  Illuminating Engineering Society of North America; 2011.
[Link] Handbook of Human Factors and Ergonomics, 4ed.  Gavriel Salvendy (ed).  John Wiley and Sons; 2012.
[Link] Human Factors in Lighting, 3ed.  Peter R. Boyce.  CRC Press; 2014.

Jody W. Phelps, MSc, PMP®, MBA
Principal Consultant
JayWink Solutions, LLC
[email protected]