Averaging is a common colorimetric tool to “even out” the measurement highs and lows that are possible within a single sample or batch. The average measurement best represents the color of the sample or batch as a whole.
Averaging can take two forms - optical and statistical
Colorimetric instruments optically “average“ all spatial detail within the field of view of the sensor to provide a color reading representing the average color within the view. It is recommended that the largest area of sample view possible be measured. The reason is that when you double (2x) the diameter of the sample view, the optical averaging is tripled (3x) based on the sample area. In addition to optical averaging for a single reading, multiple readings can be statistically averaged for a single measurement that best represents the color of the sample.
This application note further considers statistical averaging as a tool.
Types of Samples for Averaging
The ideal sample for yielding repeatable color measurements is completely opaque or transparent, flat, smooth and homogenous. However, as few samples meet this ideal, a variety of sample preparation and presentation techniques are employed to make color measurements as repeatable as possible. One technique for reporting the best result is to statistically average multiple readings from the same sample in different areas of the sample (measuring with replacement), or average multiple readings of different samples from the same lot.
To illustrate, shown in Table 1 are five (5) individual readings made on a D25LT tristimulus colorimeter from a bag of pretzel pieces in a 5 inch diameter sample cup. The range and standard deviation provide an estimate of the measurement variation on this very non-uniform sample. In Table 2, five (5) readings were averaged for each measurement, reducing the measurement variability. Between readings, the sample cup was emptied and refilled from the same bag. A single reading alone quantifies the approximate color. The average of the five readings best represents the overall color of the bag.
Examples of samples that benefit from averaging include non-homogenous translucent liquids with suspended particles, samples containing bubbles, scratches, and hazy areas, those with random color or texture distributions and directional samples such as corduroy fabric, ruled paper, and yarn. In each case, the samples should be read at least two to four times, with rotation and/or refills between each readings so that the sample is well presented to the instrument. The statistical average of the multiple readings, using the largest area of sample view possible, is reported as best quantifying the color of the sample.
Define the Measurement Method
Six parameters are important for any good color measurement method and optical and statistical averaging is a key part of that method. Changing any of the following parameters will affect the color values.
1. Color Scale - Select the color or color difference scale. If unsure, use CIE L*, a*, b* or Hunter L, a, b.
2. CIE Illuminant - Select the illuminant. If unsure, use CIE D65. The D25Lt is fixed for the CIE illuminant C representing average daylight.
3. CIE Standard Observer - Select the observer. If unsure, use the 1964 10 degree Standard Observer. The D25LT is fixed to the 1931 2 degree Standard Observer.
4. Instrument Geometry - This parameter is fixed by the choice of instrument model which can be a directional 45°/0° or diffuse d/8° sphere. Typically an instrument with a directional 45°/0° like the D25LT is used to measure the very non-uniform samples.
5. Sample Preparation - Sample preparation must be consistent with techniques that support making the sample more uniform leading to a more repeatable reading.
6. Sample Presentation - Presentation techniques use optical (largest area of sample view) and statistical (multiple readings with replacement per measurement) to ensure a repeatable and representative color measurement of the sample.
The variation between measurements can be lowered by averaging multiple readings per measurement with replacement, using the largest area of view possible with each reading. It is important to document the measurement methodology for the purpose of effectively replicating and communicating color values.
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