## Calculation of Color Tolerances and Color Differences Using Instrumental Color Coordinates

Meaning and use
5.1 The original CIE color scale based on the tri stimulus values X, Y, Z and chroma coordinates x and y was visually uneven. Each subsequent color scale based on CIE values applies a weighting factor to provide a degree of uniformity so that the color differences in each region of the color space will be more comparable. On the other hand, the same samples evaluated in different color scale systems are unlikely to achieve the same color difference. To avoid confusion, comparisons should be made only when color differences or related tolerances between samples are obtained for the same color scale system. For all the colors of the sample, there is no single factor that can be used to accurately convert a color difference or color tolerance in one system into a difference or tolerance unit in another system.

5.2 Color difference E00 in δIs strongly recommend the use of units in the range 0.0 to 5.0δ. (6) E* blood group units. The color difference equation is applicable to and widely used in industrial and commercial applications, including but not limited to automobiles, paints, cosmetics, inks, packaging, paints, plastics, printing, safety and textiles.

5.3 Users of the color tolerance equation find that, in each system, adding the three vector color difference components to a single scalar value is useful for determining whether a sample color falls within the tolerance specified in the standard. However, in order to control color in production, it may be necessary to know not only the magnitude of the deviation from the standard, but also the direction of this deviation. Information about the direction of the small color difference can be contained by listing the components determined by the three instruments for the color difference.

5.4 Color tolerance selection based on instrument values should be carefully related to visual assessment of acceptability of hue, brightness and saturation differences obtained using practice D1729. The three tolerance equations presented here have been extensively tested against such data for textiles and plastics, and have been shown to be consistent with visual assessments, within the range of experimental uncertainty for visual judgments. This means that the equation itself misclassifies the color difference of a frequency no greater than that of a very experienced visual color matcher.

5.5 Although the color difference equation and the color tolerance equation are commonly applied to a variety of light sources, they have been derived or optimized, or both, for use in daylight lighting. Good correlation with visual judgments may not be obtained when calculations are made using other light sources. The use of tolerance equations under conditions other than daylight conditions requires visual confirmation of heterochromatic levels according to practice D4086.

Calculation of Color Tolerances and Color Differences Using Instrumental Color Coordinates

range
1.1 This practice includes the calculation of colour tolerances and small colour differences between opaque samples such as painted panels, plastic patches or textile samples, based on colour coordinates measured by instruments based on daylight illumination. If it is suspected that the specimen may be metamorphic, that is, have different spectral curves despite visually similar colours, Practice D4086 should be used to verify instrumental results. The tolerances and differences determined by these programs are expressed in terms of DIN99o color difference formulas given in CIE 1976 CIELAB chromatic space (1), 2 CMC tolerance units (2), CIE94 tolerance units (3), DIN 6176 (4) or approximately uniform visual color vision in CIEDE2000 chromatic difference units (5).

1.2 For product specifications, Buyer and Seller shall agree on the allowable color tolerance between sample and reference and the procedure for calculating the color tolerance. Each material and condition of use may require specific color tolerances, as other appearance factors (for example, sample proximity, glossiness, and texture) may affect the correlation between the size of the color difference measured and its commercial acceptability.

1.3 This standard is not intended to address all, if any, safety concerns associated with its use. It is the responsibility of users of this standard to establish appropriate safety, health and environmental practices and to determine the applicability of regulatory restrictions prior to use.

1.4 This international standard is based on the internationally recognized standardization principles established in the Decision on Principles for the Development of International Standards, Guidelines and Recommendations issued by the WTO Committee on Technical Barriers to Trade.