Optical radiation in the visible range, primarily white light with correlated colour temperature ranging from 3000 to 6500 K, can be emitted by electroluminescence diodes available in different technologies. For this reasons LED modules, integrated LED lamps and LED luminaries differ with respect to the quantity and quality of emitted radiation. Reliable measurements and comparisons are possible nowadays since there are many publications and standards on colorimetric and photometric measurements.

**Published by Jerzy Pietrzykowski and Miko Przybyła**,

Presently, the most important colorimetric characteristics of light sources and luminaries with white light include:

- Chromaticity of emitted source,
- Correlated Colour Temperature,
*D*parameter,_{uv}- Color rendering indices,
- Angular colour uniformity.

**How is white LED light generated?**

One of the methods uses one of the basic colorimetry laws, i.e. colour mixing by the additive method. In this method waves emitted by individual sources are mixed. In this way, when the three basic colours, i.e. blue, green and red are added, the white light is generated. This is how the white light is generated in RGB systems.

*Fig. 1. The principle of additive colour mixing of RGB diode radiation [1]*

Another method is the hybrid method, where a layer of yellow phosphor is put on a blue diode. In this way the light emitted by the diode, with wavelength of 460 – 470 nm, passes through the phosphor layer and part of the radiation triggers the photoluminescent reaction, as a result of which the phosphor begins to illuminate with a light in a longer range of waves. This is the most popular and the most effective way to get the white light from electroluminescent diodes. A very simple and reliable structure is used and the luminous efficiency of diodes is very high [2].

*Fig. 2. A white diode – sketched by the authors on the basis of [2]*

**Colorimetric systems and chromaticity diagrams **

Each colorimetric system has precisely defined reference colour stimuli and colour-matching functions (tristimulus values of monochromatic stimuli with a uniform energy stream). The basic colorimetric systems used in colorimetry of light sources and colour objects include:

- standard colorimetric system
*X*,*Y*,*Z*CIE 1931 normal, with reference colour stimuli [*X*], [*Y*], [Z] and colour-matching functions [11]. - standard colorimetric system
*X*_{10},*Y*_{10},*Z*_{10}CIE 1964 additional normal with reference color stimuli [*X*_{10}], [*Y*_{10}], [*Z*_{10}] and colour-matching functions

Colorimetric system*X*_{10},*Y*_{10},*Z*_{10}is used in some applications connected with object colorimetry and is not used in the colorimetry of light sources.

Chromaticity coordinates *x, y*, defined as a ratio of each of the three tristimulus values *X, Y, Z* to their sum, are much more convenient to define chromaticity of light sources:

*x* = *X* / (*X + Y + Z*) (3)

*y* = *Y* / (*X + Y + Z*) (4)

*z* = *Z* / (*X + Y + Z*) (5)

where *x + y + z = *1

The value of chromaticity coordinates *x*, *y* can be represented on a plane [5,6]. The representation produces a chromaticity diagram, where points defined by chromaticity coordinates represent chromaticity of colour stimuli (Fig. 3).

*Fig. 3. The CIE 1931 (x, y) chromaticity diagram with MacAdam ellipses, magnified 10x*

Chromaticity chart *x, y* is not uniform, i.e. the distance between the points on chromaticity chart *x, y* is not the equivalent of the impression of chromaticity difference, which was confirmed by MacAdam [7, 8]. In 1960 the International Commission on Illumination (CIE) introduced a uniform chromaticity diagram *u, v* CIE 1960. Its coordinates *u, v* are calculated from trichromatic components *X*, *Y*, *Z* or chromaticity coordinates *x*, *y*. Chromaticity diagram *u*, *v* CIE 1960 is shown in Fig. 4. This diagram, with much improved uniformity, has a very important feature, namely Iso-CCT lines cross the blackbody locus at the right angle.

**Fig. 4. The CIE 1960 (u, v) chromaticity diagram with MacAdam ellipses magnified 10x**

Presently, the CIE 1976 (*u’* *v’*) uniform chromaticity diagram introduced by ISO and CIE standards [3] is the best transformation. Its coordinates *u’* *v’* are calculated using the formula:

*u’ = *4*X */ (*X + *15*Y + *3*Z*)* = *4*x */ (*–*2*x + *12*y + *3) (9)

*v’ = *9*Y */ (*X + *15*Y + *3*Z*)* = *9*y */ (*–*2*x + *12*y + *3) (10)

The CIE 1976 (*u’* *v’*) chromaticity diagram is shown in Fig. 5.

*Fig. 5. The CIE 1976 (u’, v’) chromaticity diagram with MacAdam ellipses magnified 10x*

**Correlated ****colour**** temperature – CCT**

The definition of correlated colour temperature is based on the comparison of the radiation chromaticity of a blackbody and the chromaticity of the test source. The present definition of correlated color temperature is given in CIE 15 [11] and the International Lighting Dictionary [4]: **The correlated ****colour**** temperature is the temperature of a Planckian radiator having the chromaticity nearest the chromaticity associated with the given spectral distribution (based on normal colorimetric observer CIE 1931) on a diagram where the 2/3 coordinates of the Planckian locus and the test stimulus are depicted.**

Calculation methods of correlated color temperature are given e.g. in Polish standard PN-91/E-04042/03 [13] and in Ohno [9] and McCamy [10]. The concept of CCT should not be used if the chromaticity of the test source differs more than D*C* =[(*u**¢** _{t}* –

*u*

_{p}^{¢})

^{2}+4/9(

*v*

_{t}^{¢}–

*v*

_{p}*)*

^{¢}^{2}]

^{1/2 }= 5×10

^{-2}from the Planckian radiator. The approximation-polynomial calculation method of correlated color temperature and D

_{uv}, explained in Ohno Y. [9], is particularly interesting, since it requires that fairly simple computer computations are made.

As can be seen in Fig. 6, the extensions of Iso-CCT lines on the *u, v* CIE 1960 diagram are nearly convergent in one point with the *u*_{0} = 0.292; *v*_{0} = 0.240 coordinates. If the line is extended from point *u*_{0}, *v*_{0} to point *u, v* (chromaticity of the test source) we can see that the angle between axis *u* and the line can be treated as a parameter which identifies the Iso-CCT line and then we can assume that the correlated colour temperature is the polynomial function of that angle.

Fig. 6. Calculation of Correlated C**olour**** Temperature T_{cp} and parameter D_{uv } by the approximation-polynomial method**

The approximation-polynomial method has been incorporated into the updated ANSI standard [12]. When this method is used, the *T*_{cp} calculation error within the range of (2000 – 15000) K is smaller than 2 K.

** **

*D _{uv }*

**Parameter**

As stated above, correlated colour temperature can be calculated only when source chromaticity is within the chromaticity area. It is more and more often recommended to use D_{uv} to calculate the distance of the test source chromaticity from Planckian curve. D_{uv} defined in ANSI C78.377 [12] is as follows: **D _{uv} – the closest distance from the Planckian locus on u’_{p}, 2/3v’_{p} diagram, with + sign for above and – sign for below the Planckian locus. **The schematic position of D

_{uv}and the lines of constant D

_{uv}values on u

*, v*CIE 1960 diagram are shown in Fig. 7.

Fig. 7. D_{uv} on *u,v* CIE 1960 chromaticity diagram

**Color rendering indices**

The spectral composition of radiation, characterized by the relative spectral distribution of the source radiation power, has an impact on the color appearance of illuminated objects. It is necessary to characterize changes in the chromaticity of objects if daylight is replaced with artificial light. The size of the chromaticity change characterizes colour rendering properties of light sources.

Color rendering properties are defined using the color rendering indices described in CIE 13 [14]. In this method a set of color reference samples from Munsell atlas, numbered 1 thru 14, is used. The color of samples illuminated with the test source and reference source is calculated, followed by the calculation of the color difference *D**E*. A special colour rendering index *R _{i}* (

*R*-rendering individual) is calculated for each standard sample. Using

_{i}*R*calculated for the first eight samples, a general color rendering index

_{i}*R*is calculated as an arithmetic mean of the value of eight particular color rendering indices (

_{a}*R*– rendering averaged).

_{a}**Angular color uniformity**

In view of the structure of light diodes, LED lamps and luminaries, which have different color depending on the angle, the new European standard [15], apart from the colorimetric characteristics described above, also contains the definition and calculation method of angular color uniformity. Angular color uniformity is defined as the largest deviation of chromaticity of a LED source emitting in different directions from its mean chromaticity . Chromaticity coordinates are measured using a goniocolorimeter or a goniospectroradiometer in the angle vertical range of 10° or less (recommended 2.5°) and the angle horizontal range of 90° or less (recommended 22.5°).

**Conclusion**

Application of LED diodes as white light sources resulted in many changes in the illumination industry and everyday life. Colorimetric functional characteristics of LED lamps emitting white light and other sources of white light require development and application of standardized tests and measurement methods. A considerable part of standardization documents, both international and European, developed in the recent years and presently, creates large challenges for the laboratories which perform tests of new light sources and luminaries.

** **

Literature

[1] Wikipedia http://fr.wikipedia.org/wiki/Utilisateur:Quark67.

[2] Wandachowicz K. *Wykład nr 5 – LED* Politechnika Poznańska Studia niestacjonarne.

[3] ISO/CIE 11664-5:2015 Colorimetry. Part 5: CIE 1967 *L*u*v** colour space and *u’,v’ *uniform chromaticity scale diagram.

[4] CIE S 017/E:2011 ILV: International Lighting Vocabulary.

[5] Pietrzykowski J.: Kolorymetryczne charakterystyki funkcjonalne lamp LED o świetle białym. XXIV Krajowa Konferencja Oświetleniowa Technika świetlna ‘2015, 173-191 (2015).

[6] Pietrzykowski J.: Elipsy MacAdama i ich zastosowanie do ustalenia tolerancji i zmian chromatyczności światła emitowanego przez lampy. Oświetlenie LED nr 3, 16-17 (2015).

[7] MacAdam D.L.: Visual sensitivities to colour differences in daylight. J. Opt. Soc. Am., vol. 32 (1942).

[8] MacAdam D.L.: Specifications of small chromaticity differences. J. Opt. Soc. Am., vol. 33, 18-26 (1943).

[9] Ohno Y.: Calculation of CCT and *D _{uv}* and practical conversion formulae. CORM 2011 Conference, Gaithersburg, May 3-5, 2011, 1-28 (2011).

[10] McCamy C.S.: Correlated color temperature as an explicit function of chromaticity coordinates. Color Res. Appl. vol. 17, nr 2, 142-144 (1992).

[11] Publ. CIE 15:2004 Colorimetry.

[12] ANSI C78.377-2011 Specification for the chromaticity of solid state lighting products.

[13] PN-91/E-04042/03 Pomiary promieniowania optycznego. Pomiary kolorymetryczne. Metody wyznaczania charakterystyk widmowych i kolorymetrycznych źródeł światła.

[14] Publ. CIE 13.3.3-1995 Method of measuring and specifying colour rendering properties of light sources.

[15] EN 13032-4:2015 Light and lighting. Measurement and presentation of photometric data of lamps and luminaires Part 4: LED lamps, modules and luminaires.