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IX CONGRESO NACIONAL DEL COLOR. ALICANTE 2010 HOW THE SPECTRAL STRUCTURE OF THE LIGHT SOURCE DETERMINES COLOUR RENDERING Sérgio Miguel Cardoso Nascimento, Paulo Eduardo Reis Felgueiras, João Manuel Maciel Linhares Department of Physics, Campus de Gualtar, University of Minho, 4710-057, Braga, Portugal smcn@fisica.uminho.pt Abstract: Light sources with almost arbitrary spectral distributions, like LED and DLP based sources, are today available to the general public but their colour rendering properties are still not well characterized. In this work we studied, computationally, the chromatic effects of a large set of illuminants with almost arbitrary spectral structure. The illuminants were metamers of a Planckian radiator with colour temperature of 6500 K and metamers of non-Planckian radiators with chromaticity coordinates uniformly distributed over the same isotemperature line. The metamers were generated by the Schmitt’s elements approach and were parameterized by the spectral distance to the equi-energy illuminant E. The colour rendering properties of each illuminant were quantified by the CIE colour rendering index (CRI), by a chromatic diversity index (CDI) and by the number of discernible colours estimated for a set of indoor scenes digitized by hyperspectral imaging. It was found that CRI decreases as the spectral structure of the illuminant increase and that larger values of CDI could only be obtained with illuminants with a small number of non-zero spectral bands, that is, with highly structured spectra. In conclusion, highly structured illuminants produce larger chromatic diversity than more uniform spectrum and may therefore be best for applications where maximization of chromatic diversity is important. Keywords: colour rendering, indoor lighting, LED lighting, metamers, discernible colours INTRODUCTION Light sources with almost arbitrary spectral composition are now available to the general public. These include mainly the classes of LED and DLP based sources. However, although some research work has been carried out to characterize the colour rendering properties of these sources in specific conditions[1] a more general approach is necessary for a general characterization. The goal of this work was to address the issue of the relationships between spectral structure of the illumination and colour rendering properties by studying, computationally, the chromatic effects of a large set of illuminants with almost arbitrary spectral structure. The chromatic effects of each illuminant were quantitatively assessed by the CIE colour rendering index (CRI) [2] which measures how much the colours produced by a light source are similar to the colours produced by a daylight or a Planckian radiator. Because the colour rending of light sources also relates with the chromatic diversity they produce in addition to the CRI we used here a chromatic diversity index (CDI) related to a method based on the volume of the object-colour solid recently proposed [3] and to the Gamut Area Index (GAI) [4], which measures of the extension of the colour gamut generated. Finally, we also accessed colour rendering by the number of discernible colours estimated for a set of indoor scenes digitized by hyperspectral imaging. The illuminants were metamers of a Planckian radiator with colour temperature of 6500 K and metamers of non-Planckian radiators with chromaticity coordinates uniformly distributed over the same isotemperature line. 34
IX CONGRESO NACIONAL DEL COLOR. ALICANTE 2010 MATERIALS AND METHODS Metamers of a Planckian radiator with colour temperature of 6500 K and metamers of non- Planckian radiators with chromaticity coordinates uniformly distributed over the same isotemperature line were generated by the Schmitt’s simple elements approach [5]. A metamer set of real positive functions F can be described by a convex hyperpolyhedron volume in an Mdimensional space, where M is the number of spectral bands considered. The apexes of that hyperpolyhedron Sj are functions that have at most 3 non-zero coordinates, that is, no more than 3 spectral bands. Any element fi of the set can be written as a positive barycentric combination of simple elements, i.e., for any fi ∈ F there is at least one set of N positive numbers αj such that: ∑ fi = α jS j (Eq. 1) Considering δi the absolute spectral differences between fi and the equi-energy illuminant E, a total of 10000 metamers were generated for each colour by choosing the weights αj. The spectral difference δi is defined here in relation to E rather than to D65 because in this way provides a measure of how structure the spectra are. All metamers were generated for the spectral range 400 nm - 720 nm, with 5 nm spectral resolution. Thus, the number of bands was 65. Note that because E is a uniform spectrum, δi is a measure of how much spectrally structured fi is. For each metamer the general colour rendering index CRI was computed accordingly to CIE. To quantify the colour gamut generated by each metamer, the CIELAB colour volume occupied by the set of 1269 samples from the Munsell book of Colour [6] was computed. The spectral reflectances were used as tabulated by the University of Joensuu Colour Group [7]. The set was assumed rendered by each metamer and the coordinates of each Munsell sample were computed in CIELAB colour space. The volume was then computed using a three-dimensional convex hull routine. Note that this method gives the volume inside the envelope defined by the Munsell surfaces in the periphery of the set. This quantity is strongly correlated with the chromatic diversity or number of discernible colours produced in natural scenes and can be used as a Chromatic Diversity Index (CDI)[8]. Figure 1 shows pictures of the scenes analysed. The three pictures represented on the right column are from publicly available hyperspectral image data [9] and the other 12 scenes were digitalized in our laboratory. Brainard’s data were acquired from 400 to 700 nm in 10 nm steps using narrowband interference filters and a monochromatic CCD camera with a spatial resolution of 2000×2000 pixels and 12-bit output . Our images were acquired over the range 400-720 nm at 10 nm intervals using a fast-tunable liquid-crystal filter and a low-noise Peltier-cooled digital camera with a spatial resolution of 1344×1024 pixels and 12-bit output. The spectral reflectance of each pixel of the scene was estimated from a grey reference surface present near the scene at the time of digitalization. The radiance spectrum reflected by each pixel of each scene was estimated by multiplying each spectrum of a set of 60 illuminants by the spectral reflectance estimated for that pixel. Illuminants spectra were considered from 400 nm to 720 nm for our data and from 400 nm to 700 nm for Brainard’s data. Both spectral reflectance data were interpolated to 5 nm steps. The number of discernible colours was estimated for each scene and metamer by segmenting the CIELAB colour volume into unitary cubes and by counting the number of non-empty unitary cubes. The methodology gives an approximate but reasonable estimate. 35
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