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where R is the sample spectrum, E is the source light spectrum, and x, y, z are the standard observer curves.

Many of the more expensive colorimeters available today record a spectrum from the sample as the initial signal and calculate CIE values from it. This approach allows considerable flexibility because the signal can be programmed to produce data for any illuminant, several types of sample presentation, a number of mathematical color systems, special color scales, and many types of color difference calculations. Interestingly, the early spectrophotometers designed for color measurement 70 years ago all used this approach, but the calculations for CIE values were tedious. Mechanical integrators helped, but they were expensive. This led to the development of the much simpler tristimulus colorimeters about fifty years ago. Today with the development of electronic calculation, the cost of calculation is simply not a significant consideration, and spectrophotometers are coming back into fashion.

Interestingly, a tristimulus colorimeter can also be used as a chemical absorptimeter for analytical purposes (9,10).

Data Presentation

Spectrophotometers usually present data in XYZ units but there are other conventional ways. Chromaticity coordinates (xyz) calculated by the following equations are often used to plot a chromaticity diagram (Fig. 4). The convention Yxy is also used, where Y represents CIE Y expressed as a percent of X + Y + Z:

Figure 4. CIE chromaticity diagram showing dominant wavelength and purity.
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