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Color measurement plays an increasing role in quality control of products. Especially the checking of color differences between reference materials and later produced samples is important for the customer acceptance. The easiest way is to observe the samples by the human eye in special cabins, but there arises the problem of objectivity and reproducibility. So color measuring instruments are used, which have to imitate the process of human color perception.
"Let us consider the ´classic island experiment´, in which a random collection of pebbles of all colors are classified by a lonely castaway. Thinking of color in terms of the common names red, blue, green, etc., her first step is to separate those, which have color from those, which have not. In other words, she separates the CROMATIC pebbles from the ACHROMATIC ones. The achromatic pebbles she now arranges from black through gray to white: i.e. she arranges them in order of LIGHTNESS. Turning her attention to the chromatic pebbles, she first separates them into piles of red, yellow, green, etc.: i.e. according to their HUE. Each of these piles she then sorts by lightness in the same way as for the achromatic pebbles. However, she notices that there are still pebbles, which appear different despite being of the same hue and lightness. After some thought, she realizes that this kind of difference relates to how much the colors differ from gray - in crude terms, how much color they contain. This third variable is called CHROMA or SATURATION. Any color can be uniquely specified by the three properties of HUE, LIGHTNESS and SATURATION." (From: Multi-channel detector applications. Andor Technology Ltd. Workshop Belfast October 26-29,1992. p.5). In technical words: Color is a 3 dimensional quantity. The human eye can distinguish between more than 1 million chromaticity values. Each impression of color for a human being arises from the superposition of the illumination, the reflectivity/ transmittance of the object and the detectivity of the human eye (it contains three kinds of detectors (uvulas) with red, green and blue sensitivity). Therefore, a color-measuring instrument has to "know" the spectral characteristics of the illumination and of the eye. The latter characteristics are different from person to person, so a standard detectivity was defined by the CIE (Commission International de Eclarage) in 1931 as an average of over 1000 testing persons and is called the normal observer (a new standard is currently under development).
It consists of the three standardized uvula sensitivities as shown in fig. 1. They are called values of standard colorimetric observer or color matching functions  .
Figure 1: Functions for the 2° and 10° standard colorimetric observer (available in tables with 5 nm step width, see e.g. DIN 5033/2 or CIE 15.2
It can be seen from the diagram, that the eye sensitivity above 700 nm can be neglected. This is the reason that some color measuring instruments use only the range up to 700 nm. Color perception is a subjective human observation; this makes the measurement of color very difficult. Influences besides the differing spectral sensitivity of individual persons are the age, the psychological feeling and the surrounding conditions, respectively.
The uvulas are distributed across the cornea with different density, resulting in a changed perception of colors with regard to the illuminated area. The above curves of fig. 1 show two data sets for a narrow viewing angle (2°) and a wider one (10°). The detectivity changes slightly for higher angles, so the characteristics for two observers were defined.
Color measuring instruments can be splitted up into two categories - filter-based and spectrometer-based devices. Filter devices use three special filters, whose transmission characteristics are matched to the three functions of the standard colorimetric observer as precisely as possible. Spectral measuring devices use a spectrometer and therefore have much more detectors with their sensitivity distributed across the VIS spectrum. The standard observer characteristics are used as calculation values, therefore they are more accurate. GetSpec.com offers a device of this type with its getSpec COLOR. The object is illuminated by an internal light source and the signal remitted from the surface under test is measured by a spectrometer.
There exist three different kinds to receive a color impression for the human eye: the color, observed in reflexion, e.g. of a car body (A), the color, observed in transmission, e.g. the colored windows of a church (B) and the color of a light source, e.g. of a light emitting diode (C). Spectral measuring instruments for A are commonly called spectro colorimeters, for B spectro photometers, devices for C spectro radiometers (see fig. 2).
Figure 2: Kinds of color impression (the physical terms are A - reflexion spectroscopy, B - transmission spectroscopy and C - emission spectroscopy
Fig. 3 shows a light source illuminating an object, which is observed by the human eye. The illumination spectrum is remitted by the object and therefore weighted with its spectral reflexion behavior. The eye receives this signal and processes it with its own three sensitivity curves. The result is the color impression of the object, expressed by the tristimulus values X, Y and Z.
Figure 3: Object with illuminant and observer
The physical quantity color is a three dimensional value. The following scheme shows the principal calculation process:
Figure 4: Procedure of colorimetric calculation (see DIN 5033/2 and /3) *k is used for the normalization of the tristimulus values like that Y equals 100 for the pure matt white body
The tristimulus values of X, Y and Z do not offer information about lightness, hue and saturation (see the beginning of this chapter). Therefore, they are transformed into other color systems. Since the perceived color only depends on the relative amplitudes of X, Y and Z, the chromaticity coordinates x and y are defined as in fig. 4. Additionally z = Z/(X+Y+Z). Because of :
only x and y are mentioned. These two values do not give information about the intensity; therefore it will be extended by Y. The triple xyY is often used to characterize a color impression.
The x,y diagram has the shape of a sole, the pure wavelengths (spectrum locus) and the so-called purpur line form its boundaries.
Figure 5: xy diagram
The intention of color measuring theory during the last decades was to create systems, which are better adapted to the feeling of the human eye. One of the mainly used systems is L*a*b* in which visible color differences ( DE*) in the whole 3D space are reflected with approximately the same value. The distinction of the asterisk values (e.g. Y*) to the values without asterisk (e.g. Y) is not indicated in figure 5 for simplicity. The L*a*b* system is better adapted to the subjective color feeling of the human eye than the xyY system.
As mentioned above, a main task of color measuring is color comparison. The geometrical distance of the 3 dimensional color values of reference and sample is used ( DE*) for easier handling of the measuring results.
Color Measurement of Opaque Surfaces
Colorimetry (Spectral Reflexion Measurement)
The color impression of an opaque body is a result of the scattering of the illuminating light colored pigments in the surface region and the following diffuse escaping of the scattered light. This process is called remission. The remissioned light is influenced by the illumination and the illuminated surface (see fig. 2 and 3). Regularly reflected light contains no color information of the reflecting surface.
The measuring geometry, especially the kind of illumination, has a significant influence on the measurement. Two standardized geometries are used for the color impression measurement. The main criterion for the selection of the suited geometry for an application is the kind of the sample surface. Smooth surfaces, e.g. of plastics and varnished materials demand a directed illumination by an angle of 45°, related to the measuring direction. It is preferably arranged cylindrically symmetric around the perpendicular measurement axis. This arrangement avoids the influence of gloss on the measuring result (remember: the regular reflex contains no color information). Rough surfaces, as those of textiles and brickwork, demand a diffuse illumination, obtained by a lamp arranged in an integrating sphere. Two kinds of measurement are possible in this case . gloss included and excluded. The exclusion is obtained by a special gloss trap. The detection of the remission is done directly in both cases. Schemes of both measuring geometries are shown in the following figure:
Figure 6: Both kinds of geometries for reflective measurement of body colors
Left: Directed 45° illumination and 0° measurement (illumination preferably symmetrically) (45°/ 0°)
Right: Diffuse illumination by an integrating sphere and 8° measurement (d/8°)
Light source and detector can be exchanged (Helmholtz reproducibility). This statement is exactly valid only for samples without fluorescence properties. The measuring geometry is described by the specification of the illumination, followed by the specification of the illumination, followed by the specification of the observation path (according to ASTM and CIE).
The getSpec COLOR has a fiberoptic 45°/ 0° measuring geometry. Its measuring head has to be placed in direct contact to the object under test.
The results of a color measurement are strongly influenced by the details of the used measuring geometry, e.g. by the aperture of illuminant and detector. This is the reason for different results obtained by different instruments, especially if different manufacturers design them. The main criterion of an instrument is the comparability between devices of the same type .
As outlined in the general chapter about color measurement the color impression of an object is dependent on the illumination spectrum and on the colorimetric observer. To obtain comparable measuring results the observer (see fig. 1) as well as the illumination (e.g. daylight or the light of an incandescent lamp under specified conditions, see fig. 7) are standardized. Every measuring result has to include the related measuring conditions.
It is not possible to obtain a standardized illumination spectrum in an ideal way for measuring purposes, but if the special illumination spectrum of the measuring device is known, it can be mathematically converted into such standardized characteristics.
The calculation of the color values is proceeded according to the scheme of fig. 4. The only addition is that the measured spectrum Phi (Lambda) is the product of the standard illuminating spectrum S Lambda , which shall be used as reference for the color coordinates, and the spectral reflexion coefficient (spectral density) of the sample R Lambda)
The sample spectral density is determined by the ratio of the spectrum measured with the sample to the spectrum measured with a white standard of known spectral reflectivity. Therefore, it is not necessary to illuminate with a standard illumination.
with I sample(l) the measured spectrum with the sample and Iref(l) the measured spectrum with the reference standard. It is a fundamental condition for this measurement that the instrument illuminant spectrum is kept constant during the measuring period (measurement of standard and of sample), if no referencing is used.
The instrument illumination spectrum can have an arbitrary distribution, but has to include all parts of the visible range from 380 to 760 nm or at least from 400 to 700 nm. Best results are obtained by a homogeneous distribution across the spectrum due to an equal dynamics.
Fig. 7 shows two different standardized illuminations, which are often used. Several more spectra, as daylight of other color temperatures, artifical daylight, Xe lamp light, etc. are defined (see DIN 5033/7).
Figure 7: Standardized spectra D65 (daylight with a color temperature of 6500K) and A (incandescent lamp)
Two samples with different remission (or transmission) spectra, which give the same color values with one illuminant, mainly show different color values for other illuminants. This effect is called metamery. The value characterizing this behavior, is the metamery index. It describes the color difference of the samples measured at a specified illuminant and related to the reference illuminant where the color difference is zero.
Every body color measurement instrument is delivered with at least one reference standard. This standard, a white sample, has to be traceable to measurements of a standardization institute. It is used for calibration of the instrument before a measurement series to know the instrument illuminant spectrum Iref( l ). So the measuring results are fitted to this normal and internal effects of the instrument (as degradation of the light source) are excluded.
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