TOWARDS A USER ORIENTED DESCRIPTION OF COLOUR RENDITION OF LIGHT SOURCES 2.METHODS

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1 TOWARDS A USER ORIENTED DESCRIPTION OF COLOUR RENDITION OF LIGHT SOURCES J.T.C. van Kemenade, P.J.M.van der Burgt authors' affiliations: Philips Lighting BV, Eindhoven, The Netherlands ABSTRACT Colour shifts, due to artificial light sources, depend on the hue, chroma and to a lesser extent the lightness of an object colour. By defining a 'chroma reduced' colour shift the 'reduced' colour shifts only depend on the hue of the colours. The 'reduced' colour shifts are a smooth function of hue which can be used to predict the colour shift of any other colour, once its hue and chroma are known. RESUME La deviation chromatique des couleurs, causée par les sources lumineuses artificielles, dépend du teinte, de la chroma et, dans une moindre mesure, de la clarté de la couleur d un objet. Si nous définissons une reduction chroma" de cette deviation chromatique de la couleur, cette deviation réduite, ne dépendra plus que du teinte de la couleur. Les "deviations réduites étant peu dépendantes du teinte, celui-ci peut être utilisé pour prévoir les deviations chromatiques de n importe quelles autres couleurs, si l on connaît son teinte et sa chroma. ZUSAMMENFASSUNG Farbverschiebungen aufgrund von künstlichen Lichtquel-len hängen von Buntton, Chroma und - in minderem Masse - von der Helligkeit der Objektfarbe ab. Durch die Definition einer "Chroma reduzierten" Farbverschie-bung hängen diese Farbabweichungen lediglich vom Buntton ab. Die "reduzierten Farbverschiebungen" bil-den eine glatte Funktion des Bunttones. Diese Funktion kann zur Vorhersage der Farbverschiebungen jeder Farbe verwendet werden, sobald Buntton und Chroma gegeben sind. 1. INTRODUCTION In the perception of most scenes colours play an important role. Artificial lighting will influence the appearance of object colours. The colour rendition properties of a light source are expressed by the General Colour Rendering Index (Ra) which is derived from the colour points of eight object colours which are calculated for a light source and a reference source. For each object colour these two colour points define a colour difference vector in a three-dimensional colour space, having not only a magnitude but also a direction. The general colour rendering index gives only the average magnitude of these eight vectors. However in lighting design often choices between light sources must be made which require not only the average magnitude but also the For the CRV we used the CIELAB colour space. This individual size and direction of the vector. Colours can be described in terms of hue, chroma and lightness and therefore the calculated colour shifts can be regarded as vectors composed of these three colour attributes and we will denote them by the term Colour Rendition Vector (CRV). In this paper an overview will be given of a new method of supplying CRV information for large sets of object colours. Furthermore the composing elements of the CRV will be discussed in detail. 2.METHODS In principle we will elaborate the colour rendition properties of light sources by using the following procedure. The CRV for a light source will be calculated in a perceptually uniform colour space with respect to a Planckian or reconstituted daylight radiator. To account for the difference in chromaticity between light source and reference illuminant a von Kries transformation is used, according to CIE publication To obtain extensive information a large set of object colours uniformly distributed over the entire perceptually uniform colour space is needed. Furthermore such a set must be representative for commonly occurring object colours. Opstelten defined a set of 215 colours. For this set he showed that the average magnitude of the CRV correlates well with other colour sets including the CIE reference sets (8 or 14). In our approach to study the parameters influencing the CRV we used additional sets of object colours from various origins like: man made textiles and paints (including the MacBeth colour chart and the NCS-colours) and natural colours such as fruits, flowers, meat etc. Especially for the man made colours the colour sets were quite large consisting of over 1500 colours. In our method the CRV is defined as the vector originating at the chromaticity of the object colour under the reference source and ending at the chromaticity of the object colour under the test source with a chromatic adaption correction for the colour difference between test and reference light source being applied. (see Fig.1.) Fig.1 Colour rendition vector in CIELAB. colour space is perceptually uniform and is generally

2 used by the industry and end users to specify and describe colours. Moreover a number of colour atlases in CIELAB units are available. For the graphical representation of the three-dimensional CRV we will use a projection of these CRV vectors onto the a* b* plane for the following reasons. In the CIELAB space hue and chroma are defined as: hue angle=arctan(b*/a*) chroma=sqrt(a* 2 +b* 2 ). So hue and chroma are functions of a* and b* only: Hue angle is the angle with the positive a*-axis measured counter clockwise. Chroma is the distance towards the L* axis, hence to the origin of this projection. In the a*-b* plane neutral greys are found at the origin. Unique colours such as red, yellow, green and red are found close to the a*- and b*- axis. Δchroma Δlightness = chroma source - chroma reference = lightness source - lightness reference For the halophosphate lamp the upper part of Fig. 3 shows the Δhues(represented by the tangent of Δhue) plotted versus the hue angle being the most pronounced colour ordering attribute. A positive Δhue indicates a hue shift due to the test source in a counter clock wise direction. As can be seen the Δhue values show a regular dependency on hue, independent of the chroma and 3. RESULTS To illustrate the method in Fig. 2 the CRV's are given for the standard cool-white halophosphate fluorescent lamp and the set of 215 colours as defined by Opstelten. From this CRV plot lighting and interior designers can read immediately how a particular colour is rendered by the light source. For the cool-white lamp the desaturation of colours in the reddish region is evident. This will help them in selecting a proper combinations of light sources and colours in their design. Fig.2 The CRV's for a standard halophosphate lamp. Looking at the origin of the CRV's, it can be seen that the test colours show a regular distribution over the colour space. The CRV plot contains all the necessary information but a more practical way to describe this pattern can be found. This is achieved by decomposing the CRV in three components, i.e. being resp.δhue, Δchroma and Δlightness and defined as: Δhue = hue source - hue reference To verify the effect of using other colour sets we applied this method to several colour sets. For a large lightness of the object colour. This curve can be used to estimate the hue shift due to the artificial light once the hue of the object colour is known. Fig.3 Δhue and ΔC* as a function of hue angle Inspection of Fig. 2 reveals that there seems to be a correlation between the chroma and the CRV magnitude. The CRV's tend to be larger for an increasing distance to the origin. Therefore we define a reduced chroma being Δchroma/chroma, further on depicted as ΔC* which is plotted as a function of hue angle in the lower part of Fig 3. We excluded very unsaturated colours (ΔC<0.1) from our considerations. This figure shows that also the ΔC* (like the Δhue) is a smooth function of the hue angle independent of the chroma of the object colour. The reduced chroma is a function of only hue. Again, once the hue of a specific object colour is known, the relative chroma shift can be read from this curve immediately. Moreover the sign of the ΔC* immediately shows whether the colour is rendered more (positive ΔC*) or less (negative ΔC*) saturated. These observations imply that the relative changes in hue and chroma only depend on hue and can be obtained from the smooth functions in Fig. 3. Inspection of the data shows that, in those cases where a significant CRV is found, the lightness component contributes in a minor way to its magnitude. Moreover, in most colour appraisals lightness is the least dominant attribute. Therefore we restrict ourselves here to a description in terms of hue and chroma shifts. set of paint colours (1240) the Δhue and ΔC* as a function of hue angle are shown in Fig.4. As can be seen

3 the results are similar to the Opstelten set of 215 colours. Also, for other sets of colours we have found similar results. The benefit of using a very large set is of course that a better distinction between average and limited set of colours. Comparing the CRV diagrams of the SDW and the MHW lamp the main differences in the colour changes are in the region of hue angles between 0 0 and 90 0, the reddish to yellow colours. Looking at the ΔC* values (Fig.6) in that region, it shows that for the MHW these values are negative, showing that these colours are rendered less saturated. For the SDW the ΔC* values are positive meaning a more saturated rendering of these colours. Moreover for the SDW the hue shifts towards the red whereas the MHW shows opposite shifts towards the yellow. This extreme object colours is possible by statistical analysis. Fig.4 Δhue and ΔC* as a function of hue angle So far we have established some general rules that related the CRV to the hue and chroma of object colours. These indicate clearly that the magnitude of the reduced components of the CRV is a smooth function of hue. For a specific hue the non-reduced CRV components are linear dependent on the chroma of the object colour. quite different behaviour cannot be extracted from the general colour rendering index Ra. Yet, in application 4. CRV INFORMATION OF LIGHT SOURCES From all the sets of available colours we selected a representative set of 1240 colours. With this selection we will illustrate the advantages of the CRV- method for the description of the colour rendering properties of light sources. In shop lighting and accent lighting 2 types of Compact High Intensity Discharge lamps are frequently used. These lamps are respectively: - a high pressure sodium lamp SDW -a metal halide lamp in quartz MHW For the SDW the general rendering index Ra is between 80 and 85 and the colour temperature 2500K. The MHW has an Ra of about 77 to 80 and a colour temperature of 3000K. With respect to the Ra the colour rendering of all the lamps is about the same. As the CRV's will show there are nevertheless remarkable differences between the lamps. In Fig.5 the CRV's are given for both the lamps. For reasons of clarity the CRV's are not given for all 1240 colours but for a such as shop lighting these effects are very important. Fig.5 The CRV diagrams of SDW and MHW 5. DISCUSSION

4 to add to the average CRI one or more values representing characteristics of the smooth function such as the The analysis by means of the CRV shows that, compared to the Colour rendering Index (CRI) additional information can be obtained about changes in colours. The CRI results in a 'loss' in colour information, because only an average of the magnitudes of the CRV's is considered. Furthermore the CRI depends on the minimum, maximum and the corresponding hue angles. Fig. 7 ΔE* as a function of hue For the CRI the number and type of object colours to be used in the calculation are frequently discussed. Fig. 7 clearly depicts the minimal requirements on the colour sets to be used. At the selection of a set of colours sufficient hues must be present. Initially one should incorporate in the colour set sufficient values of chroma at every hue value. After checking if all the selected sets show a regular pattern of ΔE* versus hue, a reduction of the set by taking out some chroma values can be considered. 6. CONCLUSIONS selection of the. Fig.6. Δhue and ΔC* of SDW (a) and MHW (b) object colours. In CRI calculations the resulting CRI decreases when more saturated colours are consideredfor example Ra14 is always lower than Ra8. Nevertheless the concept of the CRI is widely used and accepted in the world of lighting. From our analysis some recommendations to improve the CRI can be derived. The CRI deals with the magnitude of the CRV. We defined a reduced magnitude, denoted by ΔE*,by dividing the magnitude by chroma. In Fig.7 the ΔE* is plotted as a function of hue angle. Considering our previous results on ΔC* and Δhue it is not surprising that again a smooth function of ΔE* versus hue can be seen. This smooth function clearly shows the dependance of the CRI on the selected object colours. To describe the smooth function properly, for CRI calculations at least a set of object colours with sufficiently spread hue angles must be used. In the final stage of a CRI calculation an averaging of the magnitudes of the CRV takes place. Looking at the smooth function of ΔE* versus hue it is clear that with averaging information will be lost. The function cannot be represented by just the average. For practical reasons however it might be needed to reduce the function into some quality figures. In such cases it can be considered Colour shifts due to artificial lighting depend on the hue, chroma and to a lesser extent on the lightness of the object colours. Therefore the colour shifts can be presented as a vector in the a*-b* plane. This CRV plot can be used to read directly which colours are rendered different and to which extent. By decomposing the vector into its Δhue and Δchroma components and by reducing these components over chroma smooth functions of the reduced shifts in chroma and hue are obtained. These functions depend only on the hue and therefore allow a precise prediction of the colour shift in both hue and chroma once the hue and chroma of an object colour are known. In comparison with to the Colour Rendering Index the CRV method supplies additional information with respect to the magnitude and direction of the colour shift. The 'reduction' of the magnitude of the colour shifts and the subsequent smooth function of the reduced magnitude with hue clearly shows the dependance of the Colour Rendering Index on the selection of colours. If the smooth function of 'reduced' magnitude has to be characterised into a quality figure, i.e. a general colour rendering index, it is necessary to select a set of object colours comprising a sufficient distribution over the hue range. J.T.C. van Kemenade et. al. Philips Lighting P.O. Box JM Eindhoven The Netherlands

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