基于TCS230颜色传感器的色彩识别器的设计-外文翻译.doc

完整版)基于TCS230颜色传感器的色彩识别器的设计 外文翻译
Sensing color with the TAOS TCS230
The TAOS TCS230 is a small, highly integrated color sensing device packaged in a clear plastic 8—pin 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 6-step 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 shortwave-sensitive 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 ρ,γ, 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 con—sider 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 (λ）, y （λ), and z (λ), 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—by-wavelength 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 tristim-ulus values characterize color. They are linear-light quantities, propor—tional 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 (cd·m-2）。 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 illuminants are graphed here. Illuminant A， shown in orange， is representative of tungsten light sources; it is deficient in shortwave power， and may cause errors in sensing blue colors. The blue line graphs the SPD of a Nichia white LED. There is a peak in the blue portion of the spectrum: Uncorrected， the sensor would report excessive blue values. The other four lines represent CIE standard illuminants C, D50， D55, and D65。
In many applications， tristimulus signals （including luminance) scale with the illumination， and are otherwise uninteresting in themselves。 What is more interesting is the ratios among them, which characterize color disregarding luminance. The CIE has standardized the projective transformation of Equation 1， in the margin， to transform ［X, Y, Z] values into a pair of [x, y] chromaticity coordinates that represent color disregarding luminance. These coordinates are suitable for plotting in two dimensions on a chromaticity diagram。

Eq 1 Chromaticity coordinates
Illumination
A nonemissive object must be illuminated in order to be visible. The SPD reflected from an illuminated object is the wavelength-by-wave—length product of the illuminant’s SPD and the spectral reflectance of the object. Before light reaches the eye, the interaction among light sources and materials takes place in the spectral domain, not in the domain of trichromaticity。 To accurately model these interactions requires spectral computations。 When applying the TCS230, attention must be paid to the spectral content of the illumination and to poten-tial interaction between the illumination and the samples to be sensed。 Generally， the less spiky the spectra, the better。 Figure 8 graphs several illuminants.
Your application may involve sensing color, in which case the preceding description applies。 However， some applications of the TCS230 involve not so much estimating color as seen by the eye but rather sensing physical parameters associated with optical power in the visible range。 In such applications， to approximate the visual response may not be the best approach： It may be more effective to take a more direct approach to estimating the parameters of the underlying physical process.
The Color Checker
Equipped with knowledge of how spectra are related to colors, the plotting of chromaticity coordinates, and the dependence of colors upon illumination， we can return to the ColorChecker。 GretagMac—beth doesn’t publish or guarantee the spectral composition of the patches of the ColorChecker。 However， nominal CIE [X， Y, Z］ values are published。 The patches in the bottom row of the ColorChecker contain neutral colors； the numeric notations in the legends of Figure 5 reflect one tenth of the lightness （L＊） values of those patches。
The spectra graphed on pages 2 and 3 represent the physical wave-length-by-wavelength reflectance of the patches。 These spectral reflec-tances have been measured by color measurement instrument called a spectrophotometer。 If you had access to a light source having perfectly even distribution of power across the visible spectrum, then the reflectance curves graphed here could simply be scaled to repre-sent the reflectance in your application. Practical light sources do not have perfectly even spectral distributions, so compensation is neces—sary： You must compute the wavelength—by—wavelength product of the illuminant’s SPD with the spectral reflectance of the chart.
We will first calculate the CIE ［X, Y， Z］ values from the chart。 (These values should agree with the figures provided by Gretag.) Then we will calculate the [R, G， B］ values that will be detected by a TCS230.
To calculate CIE [X， Y， Z］， we take the 31×3 matrix representing the color matching functions （CMFs） of the CIE Standard Observer, and perform a matrix product with 31 spectral response values as corrected for illumination. This produces the [X， Y， Z] tristimulus values. When chromaticity coordinates [x, y] are computed from ［X, Y, Z] through the projective transform in Equation 1, then plotted， the chromaticity diagram in Figure 9 results. The horseshoe-shaped figure, closed at the bottom, contains all colors： Every non-negative spectral distribution produces an [x， y] pair that plots within this region. The lightly—shaded triangle shows the region containing all colors that can be produced by an additive RGB system using sRGB (Rec. 709) primary colors。 This region typifies video and desktop computing (sRGB）. The points plotted in Figure 9 are the colors of the ColorChecker. White and gray values are clustered near the center of the chart.

Figure 9 Coordinates of ColorChecker patches are graphed on the CIE [x, y］ chromaticity diagram. The horseshoe encloses all colors； the triangle encloses the colors that can be represented in video （Rec. 709) and in desktop computing (sRGB）.
The TCS230
Figure 10 shows the responses of the four channels of the TCS230. The black curve shows the response of the unfiltered sensor elements。 The red, green, and blue curves show the responses of the longwave-sensitive， mediumwave-sensitive, and shortwave—sensitive elements respectively。
As I mentioned on page 5, the CIE model of color vision involves inte-grating an SPD under the X（λ)， Y（λ), and Z（λ) color matching func-tions (graphed in Figure 7), producing X， Y， and Z values. To use the TCS230 to estimate color we perform an analogous calculation, but using the TCS230 sensitivity functions instead of the CIE CMFs: We integrate the SPD under the TCS230's sensitivity curves， and produce R， G, and B values. The device R, G， and B values will depend upon several factors: the spectral content of the illuminant, the spectral reflectance of the sample, the spectral attenuation of any intervening optical components (such as the lens)， and finally, the spectral response functions of the TCS230. The various spectral phenomena are modelled by computing wavelength-by—wavelength products.

Figure 10 TCS230 spectral sensitivities are graphed here。 The red, green， and blue channels are graphed in the corresponding colors; the gray line reflects the sensitivity of the clear (unfiltered） channel。 Because these responses are different from the CIE standard observer, the values reported by the TCS230 are not colorimetric。 However, suitable signal processing yields color information that is sufficiently accurate for many industrial applications.
Owing to the fact that the TCS230 is sensitive to infrared light (having wavelengths above 700 nm）， and the fact that most light sources produce power in the infrared region， typical applications include an IR cut filter in front of the TCS230。 Figure 11 overleaf shows the response of a typical IR cut filter。
To form a more accurate estimate of color requires processing the raw TCS230 R， G， and B values through a linear 3×3 matrix whose coeffi—cients are optimized with respect to the spectrum of the illuminant， the spectral response of intervening optical components, and the response curves of the TCS230. The data processing operation can be represented in matrix form as follows：
x=M•t Eq 2
The symbol t represents a three—element vector containing the device values captured from a color patch。 M represents the 3×3 color correction matrix that we will apply to these values through matrix multiplication， denoted by the • symbol。 The symbol x represents the resulting vector of estimated [X， Y, Z］ values。
We can use matrix notation to symbolize processing a set of three color patches at once, by arranging the three sets of device values into successive columns of a 3×3 matrix T. Successive rows of T contain red， green, and blue data respectively. Upon matrix multiplication by M, the columns of the resulting matrix X contain XYZ values of the successive samples; the rows of X contain X， Y， and Z values respec—tively。 One equation expresses the mapping of three patches at once:
X=M•T Eq 3
Given a matrix T whose columns contain three sets of device samples, and a matrix X containing the corresponding set of three ideal XYZ triples， there is a unique matrix M that maps from T to X。 It is found by computing the matrix inverse of T, then computing the matrix product (by premultiplication) with X:
M=X • Eq 4
The resulting 3×3 color correction matrix M exactly maps the each of the chosen three sets of device values to the corresponding set of tris-timulus values。 It is not necessary to invert matrices at the time of sensing！ The matrix M can be computed in advance, based upon the samples that are expected to be presented to the sensor in the intended application. To process three device values upon sensing a sample, all that is necessary is computation of the matrix product of Equation 3。
A color correction matrix that produces good results across more than three samples can be computed through a numerical optimization procedure. When this is done, no particular sample is likely to map exactly to its ideal tristimulus set, but a linear matrix can be constructed that minimizes the error across a range of samples (where the error is measured in a least—squares sense）。 The color correction operation is still accomplished exactly as in Equation 2.

基于TAOS公司的TCS230的颜色感应
TAOS公司的TCS230是一个小的、高度集成、8引脚、SOIC封装的色彩传感装置.它以模拟频率的方式输出短波(蓝色）、中波（绿色）、长波（红色）、宽带（白）光功率的事件数量.它可用于各种色彩感应应用领域。该设备的详细资料中可以找到它的数据表.本白皮书详细介绍了色彩感应的概念和使用TCS230参与计算.
我们将使用一个光学刺激方案的ColorChecker图表工作,通过检测的色彩数值例子。下图，在图1所示，是由GretagMacbeth生产和分配.图表长约13英寸,9英寸(330毫米×230毫米)，它包含了64阵列安排24色斑.到5背面图2显示了在图表的每一行四个补丁的光谱反射-即入射光被反射的那部分（相对于一个理想的漫反射)作为波长从350功能，纳米到750纳米。

图1 ColorChecker色补丁包含18个和6步灰色系列

图2 ColorChecker谱,第一行

图3 ColorChecker谱,第二排

图4 ColorChecker光谱，第三行

图5 ColorChecker谱，底排（中性系列）

图6锥锥光感受器敏感性所示。短波敏感的感光细胞远远低于其他两种类型的敏感。中波和长波的感光细胞的反应有很大的重叠。视觉是不敏感，准确的刺激波长:什么是光功率下