**4.2.3 Colorimetry (Ohta & Robertson, 2005)**

The ability of humans to distinguish radiation of different colours is due to the three types of cone cells that are present in the retina (Ohta & Robertson, 2005). Based upon measurements of the human visual response, the CIE has standardized a system of colorimetry (CIE 015:2004) that enables color to be specified precisely for any arbitrary color stimulus. This *XYZ* color specification system is based upon the calculation of three colorimetric CIE tristimulus values *X*, *Y* and *Z* of a radiation source or colour stimulus *S*( ) as given in equation (29).

$$\begin{aligned} X &= K\_m \int \mathbf{S}(\lambda) \overline{\mathbf{z}}(\lambda) d\lambda \\ Y &= K\_m \int \mathbf{S}(\lambda) \overline{\mathbf{y}}(\lambda) d\lambda \\ Z &= K\_m \int \mathbf{S}(\lambda) \overline{\mathbf{z}}(\lambda) d\lambda \end{aligned} \tag{29}$$

The spectral shapes of the three CIE color matching functions *x*( ) , *y*( ) and *z*( ) are shown in Figure 10. A virtual observer having these color matching functions is called the CIE 1931 Standard Colorimetric Observer or the CIE 2° Colorimetric Observer, where the 2° indicates that the color matching functions are based upon those measured for a visual 2° field of view. Similar values are available for a 10° field of view, called the CIE 1964 Standard Colorimetric Observer or the CIE 10° Colorimetric Observer.

Fig. 10. CIE color matching functions

#### **4.2.4 Correlated Colour Temperature (CCT)**

Many of the radiation sources used as standards for radiometric and photometric measurements are incandescent lamps whose relative spectral output closely resembles that of a Planckian radiator or blackbody. Since the spectral radiation from a Planckian radiator can be described with the single temperature variable, it is often convenient to describe the colour of an incandescent source using only one variable similar to the absolute temperature used to describe the radiation from a Planckian radiator. For example, the electrical operating variables (current, voltage) of incandescent lamps used for many photometric standards and measurements are set such that the correlated colour temperature of the radiation from the lamp is approximately 2856 K. This provides a spectral distribution that is reasonably reproducible for use in many photometric and colorimetric applications. The CIE Standard Illuminant A is a specified relative spectral distribution equal to that of a blackbody at a temperature of approximately 2856 K (CIE S 014-2, 2006)

The definition of correlated colour temperature (CCT) is standardized by the CIE (CIE S017, 2011) such that it may be calculated from the measured spectral radiation. The complete colour specification of a radiation source or color stimulus *S*( ) is three colorimetric tristimulus values as given in Section 4.2.3 above. In addition, the CIE defined the *y*( ) colour matching function to be equal to the photometric V() spectral weighting function, so that the *Y* tristimulus value holds all the information about the source brightness. This enabled the definition (Equation 30) of two normalized quantities *x* and *y*, called chromaticity coordinates, that contain the colour information about the source.

$$\begin{aligned} \mathbf{x} &= \mathbf{X} \{ (\mathbf{X} + \mathbf{Y} + \mathbf{Z}) \\ \mathbf{y} &= \mathbf{Y} \{ (\mathbf{X} + \mathbf{Y} + \mathbf{Z}) \end{aligned} \tag{30}$$

Many of the radiation sources used as standards for radiometric and photometric measurements are incandescent lamps whose relative spectral output closely resembles that of a Planckian radiator or blackbody. Since the spectral radiation from a Planckian radiator can be described with the single temperature variable, it is often convenient to describe the colour of an incandescent source using only one variable similar to the absolute temperature used to describe the radiation from a Planckian radiator. For example, the electrical operating variables (current, voltage) of incandescent lamps used for many photometric standards and measurements are set such that the correlated colour temperature of the radiation from the lamp is approximately 2856 K. This provides a spectral distribution that is reasonably reproducible for use in many photometric and colorimetric applications. The CIE Standard Illuminant A is a specified relative spectral distribution equal to that of a blackbody at a temperature of approximately 2856 K (CIE S

The definition of correlated colour temperature (CCT) is standardized by the CIE (CIE S017, 2011) such that it may be calculated from the measured spectral radiation. The complete

tristimulus values as given in Section 4.2.3 above. In addition, the CIE defined the *y*( )

colour matching function to be equal to the photometric V() spectral weighting function, so that the *Y* tristimulus value holds all the information about the source brightness. This enabled the definition (Equation 30) of two normalized quantities *x* and *y*, called

> ( ) ( ) *x XX Y Z y YX Y Z*

(30)

is three colorimetric

colour specification of a radiation source or color stimulus *S*( )

chromaticity coordinates, that contain the colour information about the source.

Fig. 10. CIE color matching functions

014-2, 2006)

**4.2.4 Correlated Colour Temperature (CCT)** 

This enables the representation of colours in two-dimensional plots. Note that for determination of the chromaticity coordinates, it is only necessary to know the relative spectral distribution for *S*( ) . The chromaticity coordinates are shown in Figure 11 for several colour stimuli. The bounding curve for color stimuli is given by the spectrum locus, which is composed of the chromaticity coordinates of all the pure monochromatic wavelengths of radiation, and the purple boundary, which is the line joining the ends of the spectrum locus. The chromaticity coordinates of blackbody radiators form a smooth curve within the spectrum locus. This smooth curve gives us the basis for our single variable color temperature definitions. If the source has a relative spectral distribution equal to a Planckian radiator, its chromaticity coordinates will fall upon this curve and the source is said to have a color temperature *Tc* equal to that of the corresponding blackbody radiator with the same chromaticity coordinates. The radiation from most practical sources will have a chromaticity that does not equal that of a blackbody. In this case their correlated colour temperature *Tcp* is defined as the temperature of the blackbody whose chromaticity is nearest to that of the radiation. There are several methods of determining *Tcp* from the relative spectral distribution of the stimulus *S*( ) (Ohta & Robertson, 2005, Gardner, 2000).

Fig. 11. CIE xy chromaticity diagram of the XYZ color specification system. The points indicated along the Spectrum Locus are monochromatic wavelengths in units of nanometres. The points indicated along the Blackbody Locus are temperatures of Planckian radiators in units of Kelvin.
