Color measurement

Colorimetry is always a spectral measurement

Along the spectrum of electromagnetic waves, the human eye can resolve visible light energy in the wavelength range from approx. 380 nm to 780 nm. In addition to the perception of lightness and dark (luminosity), the detectors in the eye are capable of resolving three-color stimuli: blue, green, and red. Numerical color stimuli is determined by values arranged according to visible wavelengths according to standardized procedures. These values simulate what would be generated in a defined "standard human eye" under standardized conditions. The color impression is formed in the human sensory system by linking these three stimuli with the optical characteristics of the samples surface. The objective of measuring colors (colorimetry) is to describe the color effect ("chromaticity") of samples independent of the subjective color impression of the individual observer by means of objective numbers.

Formation of Color

Formation of the Color Impression

The color impression an observer gets from a sample depends on three interrelated factors.

1. Light source

Different light sources (e.g. daylight, incandescent lamp) have different spectral power distributions ( Color and intensity) and thus generate a different illumination of the sample.

2. Sample

The composition of the sample is crucial for determining the fractions of absorption, transmission, and reflection of the incident light from the light source. Accordingly, the spectral composition of the reflected and/or transmitted light that ultimately reaches the eye of the observer is changed by the sample.

3. Observer

Due to the difference in the sensitivity of the three light-sensitive receptors in the retina, even normal-sighted individual observers have slightly varying color perception. In order to determine an objective measure of the spectral change due to the sample (i.e. the "color effect" of the sample), the influence of both illumination and individual observer needs to be determined.

For this purpose, standard illuminants and two defined "standard observers" have been defined on an international level. Accordingly, all calculated color values should be reference these factors based on their standardized derivation. For this reason, objective color numbers always need to be accompanied by specification of the standard illuminant and standard observer for which the color values are to be calculated. This is usually done by means of a corresponding setting in the software of the device.
Tristimulus value
Tristimulus Values XYZ

The eye possesses three types of color receptors (cones) on the retina. These differ in their spectral sensitivities. Whereas One type of cone is particularly sensitive to red-orange (X), the second and third types are more sensitive for green (Y) and blue (Z), respectively.

This was used as the basis for definition of a standardized "normal human eye" with defined spectral sensitivities (standard spectral value functions) for three receptors for a defined observation angle. This definition was established in 1931 for the CIE 2° standard observer and in 1964 for the now most commonly used 10° standard observer. This generally accepted definition of color stimuli provides the foundation for most other color coordinate systems. By means of appropriate transformations, the tristimulus values can be converted into other derived color coordinates (e.g. CIE Lab, Hunter Lab, CIE LCh), which define color and color differences that can be understood by humans better than with XYZ coordinates.
Under standardized illumination

A larger, non-glossy, uniformly colored surface stimulates in a neutral environment

Observed under a spatial angle of 2°

In 3 receptors with standardized spectral sensitivity

Tristimulus Values XYZ
Observer

Standard Observer

To allow the nature of human perception to be integrated into a measuring result in a controlled manner, it was necessary to define a standard for human vision. This standardized vision was then defined in the so-called CIE standard observers.
Firstly, the standard observer is based on the premise that the observer perceives colors without any interference. Moreover, CIE took into account that humans perceive colors most exactly in the eye if the colors impinge in the region of the fovea (fovea centralis).

Since this region, for a standard observation distance from a color sample, deviates from the optical axis of the eye by approx. 2°, the angle under which the standard observer sees was defined to be exactly these 2°. Accordingly, the so-called CIE 1931 2° standard observer was defined as early as in 1931.

However, the eye sees objects that are more distant under a different viewing angle. Therefore, another standard viewing angle was defined in 1964, the CIE 1964 10° standard observer, in order to consider these circumstances as well.
Illuminant
Standard Illuminant

Since the color of objects looks different for different light sources, the type of light source always needs to be defined. For unambiguous definition of the illumination conditions during the determination of colors, the spectral composition of the light source must be known.
In absolute spectral measurements, the real light source must physically emulate one of the defined standard illuminants. In the more common relative spectral measurements (versus a white standard), one of the standard light sources must be included in the color calculation as a defined spectral power distribution curve. The color coordinates thus calculated then identify the color stimuli that would be generated by the sample at the selected illumination setting.

In 1931, CIE defined the first standards of typical light sources, including standard illuminants A and C. This was expanded in 1964 to include the now most commonly used standard illuminants for daylight at various color temperatures, D55, D65, D75, etc.

Standard illuminant A = standardized incandescent light (2,856 K)

Standard illuminant C = average daylight, no UV fraction (6,750 K)

Standard illuminant C = average daylight, including UV fraction (6,500 K)
Standard illuminants D65 and D75 are used very commonly. They correspond to the spectral composition of average daylight (color temperature 6,500 K) or of a sunny day with blue sky (7,500 K) and take into consideration the corresponding UV fraction of this light.

Nowadays, standard illuminant D65 in combination with CIE 1964 10° standard observer is used most commonly. This is often used as the default setting for color calculations from spectral data in the corresponding software.

The underlying standard observer needs to be specified as well in color calculations from a spectral measurement; usually this is a software setting.
Geometry

Standard Geometries

The measuring geometry plays a crucial role in the measurement and assessment of color samples. Due to structural and surface features of the samples, the incident radiation reflected or transmitted in various directions shows spectral differences. The angle of incidence and the aperture angle of the illuminating beam of rays as well as the direction and aperture angle of the radiation detected by the detector have an impact on the colorimetric result.

CIE recommends four measuring geometries for colorimetry, including the 0°/45° and 45°/0° geometries.

0°/45° Measuring geometry:
Illumination of the sample under 0°, measurement under 45°

45°/0° Measuring geometry:
Illumination of the sample under 45°, measurement under 0°

In the 45/0 geometry, the mirror-reflecting component is eliminated deliberately to avoid falsification of the measuring result by gloss. Surfaces showing a preferred structural direction may yield different results depending on the relative position with respect to the incident light. In these cases a geometry with diffuse illumination or observation must be chosen.

CIE recommends four measuring geometries for colorimetry, including the 0°/d and d/0° geometries.

In this context, d stands for observation of the light that is diffusely scattered by the sample by means of the wall of an integrating sphere or diffuse illumination of the sample by means of an integrating sphere

0°/d Measuring geometry:
Illumination of the sample under 0°, measurement on the sphere

d/0° Measuring geometry:
Diffuse illumination of the sample, measurement under 0°

According to CIE definition, the axis of the beam of rays must be tilted by no more than 10° with respect to the surface normal upon perpendicular illumination or observation of the sample.

This is made possible by the d/8° measuring geometry, which offers particular advantages in the measurement of glossy or structured samples. Observation of the diffusely illuminated sample under an angle of 8° allows the influence of the mirror-reflected component of glossy samples to be eliminated by inserting a beam trap in the integrating sphere.

d/8° Measuring geometry:
Diffuse illumination of the sample, measurement under 8°
Color space

CIE Lab Color Space

The most commonly used system in practical application, aside from the CIE color triangle, is the nearly perception-true L*, a*, b* system that was developed by Judd and Hunter and standardized in 1976. In this system, the L* value indicates the position on the light-dark axis, the a* value indicates the position on the red/green axis, and the b* value indicates the position on the blue/yellow axis). The L*, a*, b* coordinates are correlated directly to the standard color values, X, Y, and Z.

CIE Color Triangle

The three tristimulus values, XYZ, form a color coordinate system. In order to represent individual colors in a descriptive manner, the standardized red and green color fractions x and y are projected into a planar coordinate system (often called "shoe sole" for its shape).

This xy representation is independent of the brightness of the coloring and produces all object colors that can be produced. Moreover, it allows the wavelengths of the colors triggering a monochromatic color stimulus to be determined. The so-called line of purples, which represents the violet hues between red and blue, is situated in the lower region.

However, one deficit of the xy chromaticity values is that color distances in this coordinate system do not correspond to differences in color as they are perceived physiologically.

More Color Spaces

The coordinate systems and the algorithms for determination of color differences are the subject of steady ongoing development, to reflect correctly perceived color differences by means of color coordinates that can be measured. Current formulas for the determination of color differences (e.g. Delta E cmc, Delta E 2000) take the latest insights into the physiology of color vision into account.

The most commonly used color coordinates in practical application continue to be those of the 1976 CIE Lab System. However, some definitions in certain ISO and ASTM standards occasionally necessitate the use of different color systems in the calculation of certain parameters.