Sensing color with the TAOS TCS230The TAOS TCS230 is a small， highly integrated color sensing device packaged in a clear plastic 8pin SOIC。 It reports, as analog frequency, the amount of shortwave （blue）， mediumwave （green）， longwave （red), and wideband （white） optical power incident onto the device。 It can be used in a variety of color sensing applications。 Details of the device can be found in its datasheet. This white paper details the concepts and calculations involved in color sensing using the TCS230。 We will use the ColorChecker chart as an optical stimulus to work through a numerical example of color sensing。 The chart, depicted in Figure 1， is manufactured and distributed by GretagMacbeth。 The chart measures approximately 13 inches by 9 inches （330 mm by 230 mm）； it contains 24 colored patches arranged in a 6 by 4 array。 Figures 2 through 5 overleaf show the spectral reflectance of the patches in each of the four rows of the chart that is， the fraction of incident light that is reflected （with respect to an ideal diffuse reflector)， as a function of wavelength from 350 nm to 750 nm.Figure 1 The ColorChecker contains 18 colored patches and a 6step gray series。Figure 2 ColorChecker spectra， top row。Figure 3 ColorChecker spectra, second row.Figure 4 ColorChecker spectra， third row.Figure 5 ColorChecker spectra, bottom row （neutral series)Figure 6 Cone sensitivities of cone photoreceptors are shown. The shortwavesensitive photoreceptors are much less sensitive than the other two types。 The responses of the mediumwave and longwave photoreceptors have a great deal of overlap。 Vision is not sensitive to the precise wavelength of the stimulus: What atters is optical power integrated under each response curve.Introduction to color vision Photoreceptor cells called cones in the retina are responsible for human color vision。 There are three types of cone cells, sensitive to longwave， mediumwave, and shortwave radiation within the electro-magnetic spectrum between about 400 nm and 700 nm。 Because the cone sensitivities are very roughly in the parts of the spectrum that appear red， green, and blue, color scientists denote the cell types as ， and , the Greek letters for r, g， and b. (To denote the sensors R， G, and B would wrongly suggest a closer correspondence。） Estimates of the spectral response of the cone types are graphed in Figure 6 above。Light in the physical world can be characterized by spectral power distributions （SPDs）. Colored objects can be characterized by spectral reflectance curves, such as those of the ColorChecker。 However, vision is insensitive to the exact wavelength of a stimulus: According to the modern theory of color science， all that matters is the integral of optical power underneath each response curve。 That there are exactly three types of cone cells leads to the property of trichromaticity： Three components are necessary and sufficient to characterize color. Some people might use the phrase “color as sensed by the eye，” but I consider that qualifier to be redundant at best, and misleading at worst： Color is defined by vision， so there is no need to use the qualifying phrase “as sensed by the eye，” or to use the adjective visible when referring to color.Overview of CIE Colorimetry The spectral responses of the cone cells that I graphed in Figure 6 were unavailable to researchers in the 1920s。 Researchers at the time used psychophysical experiments, such as the famous color matching experiment， to tease out the data. The CIE is the international body responsible for color standards。 In1931， that organization adopted the color matching functions denoted x （）， y （), and z (）, graphed in Figure 7.Figure 7 CIE 1931， 2 color-matching functions。 A camera with 3 sensors must have these spectral response curves， or linear combinations of them， in order to capture all colors。 However, practical considerations make this difficult. These analysis functions are not comparable to spectral power distributions！Weighting a physical SPD under each of these three curves （that is, forming the wavelength-bywavelength product）, and summing the results， forms a triple of three numbers， denoted X, Y， and Z. In continuous mathematics， three integrals need to be computed； in discrete math， a matrix product is sufficient. The X, Y， and Z tristimulus values characterize color. They are linearlight quantities， proportional to optical power， that incorporate the wavelength sensitivity of human vision。 The Y value is luminance， which is ordinarily expressed in units of candela per meter squared (cdm2)。 If you are measuring reflectance， the reflected tristimulus values depend upon the spectral characteristics of the illuminant, and their amplitudes scale with the power of the illumination。 Relative luminance is the ratio of reflected luminance to the luminance of the illumination； it is also known as the luminance factor。Figure 8 SPDs of various