Lesson 1  Lesson 2  Lesson 3  Lesson 4  Lesson 5  Lesson 6  Lesson 7  Lesson 8  Lesson 9  Lesson 10

Applied Mathematics |Прикладная математика

LESSON 7

Read the text: COMPARISON OF COLOR TOLERANCE FORMULAE

Color is the result of the combination of a light source, an object that it illuminates, and a visual system to perceive the color which is usually the eye and the brain of a human being working together. Color is commonly described by the attributes of lightness, chroma, and hue. Lightness is how the color is classified according to a series of grays ranging from black to white. Chroma describes the degree of saturation of color; i.e. the difference between the color and a gray of that same lightness. Hue is what we humans call the 'color' of an object: red, yellow, blue, etc. Any color can be uniquely described by these three attributes in a color order system known as CIELCH space. CIELCH space was defined by the International Commission on Illumination, or CIE, to standardize color descriptions using lightness, L, chroma, C, and hue, H. The CIELCH color order system is a three-dimensional space which has a shape similar to a football. The cylindrical coordinates L* (lightness), C* (chroma), and h* (hue) most closely describe how we perceive color.

Given any two objects' colors described in L*C*h* coordinates, one can apply a color difference formula to determine if the two objects can be said to be the same color. (Usually one object is considered to be the standard, or be the color to be matched, and the other object is a sample submitted for color approval.) One color difference formula is *E-CMC which is based on the concept of color acceptability ellipsoids in CIELCH space. Given a standard color and a sample color, the sample is acceptably close to the standard if it lies on or within an ellipsoid centered at the standard. The ellipsoid is oriented along the lightness, chroma, and hue axes of the standard. The lengths of the semi-axes of the ellipsoid are the lightness, chroma, and metric hue tolerances associated with the standard. (The tolerances are pre-determined for any standard by the CMC formula.) The value of *E-CMC for a sample point is the Euclidean distance from the standard to the sample where the differences have been scaled by the respective tolerances. There exist instruments known as spectrophotometers which can accurately describe an object's color in L*C*h* coordinates. Textile and apparel manufacturers use spectrophotometers and the *E-CMC formula to determine color acceptability of fabrics for their end use.

The Defense Personnel Support Center (DPSC) in Philadelphia currently uses instrumental color evaluation to determine the acceptability of fabrics relative to a given standard color. (Those fabrics are used to make U.S. Military uniforms, fatigues, etc.) The procedures which were developed and are now used by DPSC incorporate a proprietary color difference formula known as *A. Since *E-CMC is widely used and accepted in industry, DPSC has interest in converting from the *A formula to *E-CMC. Our work here at Clemson Apparel Research has consisted of comparing the two color difference formulae structurally and statistically and converting existing *A color acceptability tolerances to *E-CMC color tolerances.

 

1. Match the left part with the right:     

 

1) Lightness is how the color is classified according to a series of

a)between the color and a gray of that same lightness.

2)Chroma describes the degree of saturation of color; i.e. the difference

b) any standard by the CMC formula.

 

3) The tolerances are pre-determined for

c) DPSC incorporate a proprietary color difference formula known as *A.”

4) The procedures which were developed and are now used by

d)grays ranging from black to white.

 

2. Complete the sentences with the suggested words: differences, spectrophotometers, color, sample, tolerances

       The value of *E-CMC for a___________ point is the Euclidean distance from the standard to the sample where the _____________ have been scaled by the respective___________. There exist instruments known as _____________________which can accurately describe an object's ______in L*C*h* coordinates.